references.bib

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@article{jop_constitutive_2006,
	abstract = {Equations describing how granular materials move under shear are still a matter of debate. Jop et al. now propose a new model for dense granular flows in three dimensions, inspired by the behaviour of visco-plastic fluids such as toothpaste. The results could serve as a basic tool for modelling complex flows in geophysical or industrial applications.},
	author = {Jop, Pierre and Forterre, Yo{\"e}l and Pouliquen, Olivier},
	copyright = {2006 Nature Publishing Group},
	date-added = {2023-03-30 23:22:05 -0700},
	date-modified = {2023-03-30 23:22:05 -0700},
	doi = {10.1038/nature04801},
	file = {Full Text PDF:/home/eyoo/Zotero/storage/AWZ7ASKL/Jop et al. - 2006 - A constitutive law for dense granular flows.pdf:application/pdf;Snapshot:/home/eyoo/Zotero/storage/4DPZSERY/nature04801.html:text/html},
	issn = {1476-4687},
	journal = {Nature},
	keywords = {Humanities and Social Sciences, multidisciplinary, Science},
	language = {en},
	month = jun,
	note = {Number: 7094 Publisher: Nature Publishing Group},
	number = {7094},
	pages = {727--730},
	title = {A constitutive law for dense granular flows},
	url = {https://www.nature.com/articles/nature04801},
	urldate = {2022-06-14},
	volume = {441},
	year = {2006},
	bdsk-url-1 = {https://www.nature.com/articles/nature04801},
	bdsk-url-2 = {https://doi.org/10.1038/nature04801}}

@article{chauchat_three-dimensional_2014,
	abstract = {This paper presents a three-dimensional implementation of the so-called $\mu(I)$ rheology to accurately and efficiently compute steady-state dense granular flows. The tricky pressure dependent visco-plastic behaviour within an incompressible flow solver has been overcome using a regularisation technique along with a complete derivation of the incremental formulation associated with the Newton-Raphson algorithm. The computational accuracy and efficiency of the proposed numerical model have been assessed on two representative problems that have an analytical solution. Then, two application examples dealing with actual lab experiments have also been considered: the first one concerns a granular flow on a heap and the second one deals with the granular flow around a cylinder. In both configurations the obtained computational results are in good agreement with available experimental data.},
	author = {Chauchat, Julien and M{\'e}dale, Marc},
	date-added = {2023-03-30 23:22:05 -0700},
	date-modified = {2023-03-30 23:22:05 -0700},
	doi = {10.1016/j.jcp.2013.09.004},
	file = {ScienceDirect Snapshot:/home/eyoo/Zotero/storage/VXEGN2LK/S0021999113006098.html:text/html;Submitted Version:/home/eyoo/Zotero/storage/P3YM4JYG/Chauchat and M{\'e}dale - 2014 - A three-dimensional numerical model for dense gran.pdf:application/pdf},
	issn = {0021-9991},
	journal = {Journal of Computational Physics},
	keywords = {Dense granular flows, Finite element method, Regularisation techniques, Visco-plastic flows},
	language = {en},
	month = jan,
	pages = {696--712},
	title = {A three-dimensional numerical model for dense granular flows based on the $\mu(I)$ rheology},
	url = {https://www.sciencedirect.com/science/article/pii/S0021999113006098},
	urldate = {2022-06-10},
	volume = {256},
	year = {2014},
	bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0021999113006098},
	bdsk-url-2 = {https://doi.org/10.1016/j.jcp.2013.09.004}}

@article{thakral_compression-induced_2019,
	abstract = {Our goals were to evaluate the effects of (i) hydrostatic pressure alone and (ii) its combined effect with shear stress during compaction, on the polymorphic transformation (form C → A) of a model drug, chlorpropamide. The powder was either subjected to hydrostatic pressure in a pressure vessel or compressed in a tablet press, at pressures ranging from 25 to 150 MPa. The overall extent of phase transformation was determined by powder X-ray diffractometry, whereas 2D-X-ray diffractometry enabled quantification of the spatial distribution of phase composition in tablets. Irrespective of the pressure, the extent of transformation following compaction was higher than that because of hydrostatic pressure alone, the difference attributed to the contribution of shear stress experienced during compaction. At a compression pressure of 25 MPa, there was a pronounced gradient in the extent of phase transformation when monitored from radial tablet surface to core. This gradient decreased with increase in compression pressure. Four approaches were attempted to minimize the effect of compression-induced phase transformation: (a) site-specific lubrication, (b) use of a viscoelastic excipient, (c) ceramic-lined die, and (d) use of cavity tablet. The ceramic-lined die coupled with site-specific lubrication was most effective in minimizing the extent of compression-induced phase transformation.},
	author = {Thakral, Naveen K. and Thakral, Seema and Stephenson, Gregory A. and Sedlock, Robert and Suryanarayanan, Raj},
	date-added = {2023-03-30 23:22:05 -0700},
	date-modified = {2023-03-30 23:22:05 -0700},
	doi = {10.1016/j.xphs.2018.09.015},
	file = {Full Text:/home/eyoo/Zotero/storage/LWR849QS/Thakral et al. - 2019 - Compression-Induced Polymorphic Transformation in .pdf:application/pdf;ScienceDirect Snapshot:/home/eyoo/Zotero/storage/KZYEJAA9/S0022354918305422.html:text/html},
	issn = {0022-3549},
	journal = {Journal of Pharmaceutical Sciences},
	keywords = {hydrostatic pressure, phase transformation, shear stress, tablet, viscoelastic excipients},
	language = {en},
	month = jan,
	number = {1},
	pages = {476--484},
	shorttitle = {Compression-{Induced} {Polymorphic} {Transformation} in {Tablets}},
	title = {Compression-{Induced} {Polymorphic} {Transformation} in {Tablets}: {Role} of {Shear} {Stress} and {Development} of {Mitigation} {Strategies}},
	url = {https://www.sciencedirect.com/science/article/pii/S0022354918305422},
	urldate = {2022-06-21},
	volume = {108},
	year = {2019},
	bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0022354918305422},
	bdsk-url-2 = {https://doi.org/10.1016/j.xphs.2018.09.015}}

@book{simo_computational_2000,
	abstract = {This book goes back a long way. There is a tradition of research and teaching in inelasticity at Stanford that goes back at least to Wilhelm Flugge ̈ and Erastus Lee. I joined the faculty in 1980, and shortly thereafter the Chairman of the Applied Mechanics Division, George Herrmann, asked me to present a course in plasticity. I decided to develop a new two-quarter sequence entitled ``Theoretical and C- putational Plasticity'' which combined the basic theory I had learned as a graduate student at the University of California at Berkeley from David Bogy, James Kelly, Jacob Lubliner, and Paul Naghdi with new computational techniques from the ?nite-element literature and my personal research. I taught the course a couple of times and developed a set of notes that I passed on to Juan Simo when he joined thefacultyin1985. IwasChairmanatthattimeandIaskedJuantofurtherdevelop the course into a full year covering inelasticity from a more comprehensive p- spective. Juan embarked on this path creating what was to become his signature course. He eventually renamed it ``Computational and Theoretical Inelasticity'' and it covered much of the material that was the basis of his research in material modeling and simulation for which he achieved international recognition. At the outset we decided to write a book that would cover the material in the course.},
	author = {Simo, J. C. and Hughes, T. J. R.},
	date-added = {2023-03-30 23:22:05 -0700},
	date-modified = {2023-03-30 23:22:05 -0700},
	isbn = {978-0-387-97520-7},
	keywords = {Computers / Programming / Algorithms, Mathematics / General, Mathematics / Numerical Analysis, Science / Physics / Mathematical \& Computational},
	language = {en},
	month = aug,
	publisher = {Springer New York},
	title = {Computational {Inelasticity}},
	url = {https://link.springer.com/book/10.1007/b98904},
	year = {2000},
	bdsk-url-1 = {https://link.springer.com/book/10.1007/b98904}}

@article{artoni_effective_2014,
	abstract = {Wall slip is an important phenomenon for the flow of granular materials in chutes and channels. The appearance of a slip velocity at the wall critically affects wall stresses and flow profiles, and particularly the total flowrate. In this work we show, through numerical simulations and experiments, that the global slip phenomenon at a wall has peculiar features which deviate significantly from simple sliding behavior. At first we present experimental data for the vertical chute flow which highlight that wall slip depends on many operating and system variables such as flow rate, material properties, wall properties. Secondly, we resume a large campaign of numerical data performed in 2D with polygonal particles, and try to analyse the effect of material properties, contact parameters, operating variables, different flow configurations, on the slip phenomenon. The numerical campaign allowed to identify the main parameters affecting the wall slip behavior of a numerical model of granular flow, providing the ingredients for the creation of a framework for the description of wall slip.},
	author = {Artoni, Riccardo and Santomaso, Andrea},
	date-added = {2023-03-30 23:22:05 -0700},
	date-modified = {2023-03-30 23:22:05 -0700},
	doi = {10.1007/s10035-013-0431-y},
	file = {Full Text PDF:/home/eyoo/Zotero/storage/H25X7A3A/Artoni and Santomaso - 2014 - Effective wall slip in chutes and channels experi.pdf:application/pdf},
	issn = {1434-7636},
	journal = {Granular Matter},
	keywords = {Dense granular flows, Discrete numerical simulations, Experiments, Scaling laws, Wall slip},
	language = {en},
	month = jun,
	number = {3},
	pages = {377--382},
	shorttitle = {Effective wall slip in chutes and channels},
	title = {Effective wall slip in chutes and channels: experiments and discrete element simulations},
	url = {https://doi.org/10.1007/s10035-013-0431-y},
	urldate = {2022-07-05},
	volume = {16},
	year = {2014},
	bdsk-url-1 = {https://doi.org/10.1007/s10035-013-0431-y}}

@article{forterre_flows_2008,
	abstract = {We review flows of dense cohesionless granular materials, with a special focus on the question of constitutive equations. We first discuss the existence of a dense flow regime characterized by enduring contacts. We then emphasize that dimensional analysis strongly constrains the relation between stresses and shear rates, and show that results from experiments and simulations in different configurations support a description in terms of a frictional visco-plastic constitutive law. We then discuss the successes and limitations of this empirical rheology in light of recent alternative theoretical approaches. Finally, we briefly present depth-averaged methods developed for free surface granular flows.},
	author = {Forterre, Yo{\"e}l and Pouliquen, Olivier},
	date-added = {2023-03-30 23:22:05 -0700},
	date-modified = {2023-03-30 23:22:05 -0700},
	doi = {10.1146/annurev.fluid.40.111406.102142},
	file = {Forterre and Pouliquen - 2008 - Flows of Dense Granular Media.pdf:/home/eyoo/Zotero/storage/PLZBE9SZ/Forterre and Pouliquen - 2008 - Flows of Dense Granular Media.pdf:application/pdf},
	issn = {0066-4189, 1545-4479},
	journal = {Annual Review of Fluid Mechanics},
	language = {en},
	month = jan,
	number = {1},
	pages = {1--24},
	title = {Flows of {Dense} {Granular} {Media}},
	url = {https://www.annualreviews.org/doi/10.1146/annurev.fluid.40.111406.102142},
	urldate = {2022-06-08},
	volume = {40},
	year = {2008},
	bdsk-url-1 = {https://www.annualreviews.org/doi/10.1146/annurev.fluid.40.111406.102142},
	bdsk-url-2 = {https://doi.org/10.1146/annurev.fluid.40.111406.102142}}

@article{sverdrup_highly_2018,
	abstract = {We present the extension of an efficient and highly parallelisable framework for incompressible fluid flow simulations to viscoplastic fluids. The system is governed by incompressible conservation of mass, the Cauchy momentum equation, and a generalised Newtonian constitutive law. In order to simulate a wide range of viscoplastic fluids, we employ the Herschel-Bulkley model for yield-stress fluids with nonlinear stress-strain dependency above the yield limit. We utilise Papanastasiou regularisation in our algorithm to deal with the singularity in apparent viscosity. The resulting system of partial differential equations is solved using the IAMR (Incompressible Adaptive Mesh Refinement) code, which uses second-order Godunov methodology for the advective terms and semi-implicit diffusion in the context of an approximate projection method to solve adaptively refined meshes. By augmenting the IAMR code with the ability to simulate regularised Herschel-Bulkley fluids, we obtain efficient numerical software for time-dependent viscoplastic flow in three dimensions, which can be used to investigate systems not considered previously due to computational expense. We validate results from simulations using this new capability against previously published data for Bingham plastics and power-law fluids in the two-dimensional lid-driven cavity. In doing so, we expand the range of Bingham and Reynolds numbers which have been considered in the benchmark tests. Moreover, extensions to time-dependent flow of Herschel-Bulkley fluids and three spatial dimensions offer new insights into the flow of viscoplastic fluids in this test case, and we provide missing benchmark results for these extensions.},
	author = {Sverdrup, Knut and Nikiforakis, Nikolaos and Almgren, Ann},
	date-added = {2023-03-30 23:22:05 -0700},
	date-modified = {2023-03-30 23:22:05 -0700},
	doi = {10.1063/1.5049202},
	file = {Submitted Version:/home/eyoo/Zotero/storage/B58GTA4F/Sverdrup et al. - 2018 - Highly parallelisable simulations of time-dependen.pdf:application/pdf},
	issn = {1070-6631},
	journal = {Physics of Fluids},
	month = sep,
	note = {Publisher: American Institute of Physics},
	number = {9},
	pages = {093102},
	title = {Highly parallelisable simulations of time-dependent viscoplastic fluid flow with structured adaptive mesh refinement},
	url = {https://aip.scitation.org/doi/10.1063/1.5049202},
	urldate = {2022-06-03},
	volume = {30},
	year = {2018},
	bdsk-url-1 = {https://aip.scitation.org/doi/10.1063/1.5049202},
	bdsk-url-2 = {https://doi.org/10.1063/1.5049202}}

@article{kim_power-law_2020,
	abstract = {Based on discrete element method simulations, we propose a new form of the constitutive equation for granular flows independent of packing fraction. Rescaling the stress ratio $\mu$ by a power of dimensionless temperature Θ makes the data from a wide set of flow geometries collapse to a master curve depending only on the inertial number I. The basic power-law structure appears robust to varying particle properties (e.g., surface friction) in both 2D and 3D systems. We show how this rheology fits and extends frameworks such as kinetic theory and the nonlocal granular fluidity model.},
	author = {Kim, Seongmin and Kamrin, Ken},
	date-added = {2023-03-30 23:22:05 -0700},
	date-modified = {2023-03-30 23:22:05 -0700},
	doi = {10.1103/PhysRevLett.125.088002},
	file = {APS Snapshot:/home/eyoo/Zotero/storage/K3C5CC6X/PhysRevLett.125.html:text/html;Full Text PDF:/home/eyoo/Zotero/storage/NHBZNQJG/Kim and Kamrin - 2020 - Power-Law Scaling in Granular Rheology across Flow.pdf:application/pdf},
	journal = {Physical Review Letters},
	month = aug,
	note = {Publisher: American Physical Society},
	number = {8},
	pages = {088002},
	title = {Power-{Law} {Scaling} in {Granular} {Rheology} across {Flow} {Geometries}},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.125.088002},
	urldate = {2022-07-05},
	volume = {125},
	year = {2020},
	bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.125.088002},
	bdsk-url-2 = {https://doi.org/10.1103/PhysRevLett.125.088002}}

@article{mcelwaine_surface_2012,
	abstract = {Laboratory experiments have shown that the steady flow of granular material down a rough inclined plane has a surface that is not parallel to the plane, but has a curvature across the slope with the height increasing toward the middle of the flow. We study this observation by postulating a new granular rheology, similar to that of a second order fluid. This model is applied to the experiments using a shallow water approximation, given that the depth of the flow is much smaller than the width. The model predicts that a second normal stress difference allows cross-slope height variations to develop in regions with considerable cross-slope velocity shear, consistent with the experiments. The model also predicts the development of lateral eddies, which are yet to be observed.},
	author = {McElwaine, Jim N. and Takagi, Daisuke and Huppert, Herbert E.},
	date-added = {2023-03-30 23:22:05 -0700},
	date-modified = {2023-03-30 23:22:05 -0700},
	doi = {10.1007/s10035-012-0339-y},
	file = {Full Text PDF:/home/eyoo/Zotero/storage/6M6BZGRF/McElwaine et al. - 2012 - Surface curvature of steady granular flows.pdf:application/pdf},
	issn = {1434-7636},
	journal = {Granular Matter},
	keywords = {Lev{\'e}e formation, Normal stress difference, Shallow granular flow},
	language = {en},
	month = apr,
	number = {2},
	pages = {229--234},
	title = {Surface curvature of steady granular flows},
	url = {https://doi.org/10.1007/s10035-012-0339-y},
	urldate = {2022-07-05},
	volume = {14},
	year = {2012},
	bdsk-url-1 = {https://doi.org/10.1007/s10035-012-0339-y}}

@article{srivastava_viscometric_2021,
	abstract = {, This study examines the flow of dense granular materials under external shear stress and pressure using discrete element method simulations. In this method, the material is allowed to strain along all periodic directions and adapt its solid volume fraction in response to an imbalance between the internal state of stress and the external applied stress. By systematically varying the external shear stress and pressure, the steady rheological response is simulated for: (1) rate-independent quasi-static flow; and (2) rate-dependent inertial flow. The simulated flow is viscometric with non-negligible first and second normal stress differences. While both normal stress differences are negative in inertial flows, the first normal stress difference switches from negative to slightly positive, and second normal stress difference tends to zero in quasi-static flows. The first normal stress difference emerges from a lack of coaxiality between a second-rank contact fabric tensor and strain rate tensor in the flow plane, while the second normal stress difference is linked to an excess of contacts in the shear plane compared with the vorticity direction. A general rheological model of second order (in terms of strain rate tensor) is proposed to describe the two types of flow, and the model is calibrated for various values of interparticle friction from simulations on nearly monodisperse spheres. The model incorporates normal stress differences in both regimes of flow and provides a complete viscometric description of steady dense granular flows.},
	author = {Srivastava, Ishan and Silbert, Leonardo E. and Grest, Gary S. and Lechman, Jeremy B.},
	date-added = {2023-03-30 23:22:05 -0700},
	date-modified = {2023-03-30 23:22:05 -0700},
	doi = {10.1017/jfm.2020.811},
	file = {Full Text PDF:/home/eyoo/Zotero/storage/3EWKQ3W3/Srivastava et al. - 2021 - Viscometric flow of dense granular materials under.pdf:application/pdf;Snapshot:/home/eyoo/Zotero/storage/CGD9GGCU/416296B44B0F3C9CDAD6FE8BDD0B93AB.html:text/html},
	issn = {0022-1120, 1469-7645},
	journal = {Journal of Fluid Mechanics},
	keywords = {granular media, rheology},
	language = {en},
	month = jan,
	note = {Publisher: Cambridge University Press},
	title = {Viscometric flow of dense granular materials under controlled pressure and shear stress},
	url = {https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/viscometric-flow-of-dense-granular-materials-under-controlled-pressure-and-shear-stress/416296B44B0F3C9CDAD6FE8BDD0B93AB},
	urldate = {2022-06-01},
	volume = {907},
	year = {2021},
	bdsk-url-1 = {https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/viscometric-flow-of-dense-granular-materials-under-controlled-pressure-and-shear-stress/416296B44B0F3C9CDAD6FE8BDD0B93AB},
	bdsk-url-2 = {https://doi.org/10.1017/jfm.2020.811}}

@article{bonn_yield_2017,
	abstract = {A comprehensive review is presented of the physical behavior of yield stress materials in soft condensed matter, which encompasses a broad range of materials from colloidal assemblies and gels to emulsions and non-Brownian suspensions. All these disordered materials display a nonlinear flow behavior in response to external mechanical forces due to the existence of a finite force threshold for flow to occur: the yield stress. Both the physical origin and rheological consequences associated with this nonlinear behavior are discussed and an overview is given of experimental techniques available to measure the yield stress. Recent progress is discussed concerning a microscopic theoretical description of the flow dynamics of yield stress materials, emphasizing, in particular, the role played by relaxation time scales, the interplay between shear flow and aging behavior, the existence of inhomogeneous shear flows and shear bands, wall slip, and nonlocal effects in confined geometries.},
	author = {Bonn, Daniel and Denn, Morton M. and Berthier, Ludovic and Divoux, Thibaut and Manneville, S{\'e}bastien},
	date-added = {2023-03-30 23:22:05 -0700},
	date-modified = {2023-03-30 23:22:05 -0700},
	doi = {10.1103/RevModPhys.89.035005},
	file = {APS Snapshot:/home/eyoo/Zotero/storage/EKEDTV43/RevModPhys.89.html:text/html;Full Text PDF:/home/eyoo/Zotero/storage/NRHPZNDT/Bonn et al. - 2017 - Yield stress materials in soft condensed matter.pdf:application/pdf},
	journal = {Reviews of Modern Physics},
	month = aug,
	note = {Publisher: American Physical Society},
	number = {3},
	pages = {035005},
	title = {Yield stress materials in soft condensed matter},
	url = {https://link.aps.org/doi/10.1103/RevModPhys.89.035005},
	urldate = {2022-06-03},
	volume = {89},
	year = {2017},
	bdsk-url-1 = {https://link.aps.org/doi/10.1103/RevModPhys.89.035005},
	bdsk-url-2 = {https://doi.org/10.1103/RevModPhys.89.035005}}

@article{gurel_studies_1955,
	abstract = {Series of experiments on the sedimentation of a variety of isometrically-shaped bodies are described and it is shown that the resistance to motion R, of a body moving with velocity v, in an infinite extent of fluid in the region of streamline flow is given by R = vηK√(surface area of body), where η is the viscosity of the fluid and K a shape factor of the particle which varies from 3√π for spheres to 3√2.92 for tetrahedra. By using a value of 3√3 for K the equation may be applied to isometric and other compact shapes, where the axial ratio does not exceed about 1.4 to 1, with an error not greater than $\pm$2\%. A more accurate, but less easily applied, empirical relationship for the settling rate of compact bodies is also given and an equation which satisfies the interference effects of the walls of a sedimentation vessel upon a falling body is developed experimentally.},
	author = {Gurel, S. and Ward, S. G. and Whitmore, R. L.},
	doi = {10.1088/0508-3443/6/3/304},
	issn = {0508-3443},
	journal = {British Journal of Applied Physics},
	language = {en},
	month = mar,
	note = {Publisher: IOP Publishing},
	number = {3},
	pages = {83--87},
	shorttitle = {Studies of the viscosity and sedimentation of suspensions},
	title = {Studies of the viscosity and sedimentation of suspensions: {Part} 3. - {The} sedimentation of isometric and compact particles},
	url = {https://doi.org/10.1088/0508-3443/6/3/304},
	urldate = {2021-01-13},
	volume = {6},
	year = {1955},
	bdsk-url-1 = {https://doi.org/10.1088/0508-3443/6/3/304}}

@article{johnson_drag_1987,
	abstract = {Inhaled particles have been implicated in many forms of respiratory disease. Mathematical lung deposition models have been developed for spheres and fibers, but not for non-spherical, noncylindrical particles because theory and experimental data have been unavailable. To satisfy this need, non-spherical, orthotropic particles settling in air were modeled under dynamically similar conditions using aluminum prisms settling in viscous oil. Twenty-five rectangular prisms, each with a different length: width: thickness ratio, were settled in each of their three primary orientations and the resulting drag forces determined. Linear regression using predictors related to prism geometry and orientation resulted in an empirical drag force equation. Equation drag predictions are in excellent agreement with published data for rectangular prisms and other orthotropic objects including cylinders, ellipsoids, and double-conicals. The equation was validated by settling a quasi-monodisperse aerosol of tungstic acid platelets in a St{\"o}ber spiral centrifuge, and comparing predicted with observed aerodynamic behavior. Using these results, lung deposition models for flakes and other non-spherical particles are now possible.},
	author = {Johnson, David L. and Leith, David and Reist, Parker C.},
	doi = {10.1016/0021-8502(87)90013-9},
	file = {ScienceDirect Full Text PDF:/Users/eunji/Zotero/storage/ZJQQU7CW/Johnson et al. - 1987 - Drag on non-spherical, orthotropic aerosol particl.pdf:application/pdf;ScienceDirect Snapshot:/Users/eunji/Zotero/storage/IUQMJZFH/0021850287900139.html:text/html},
	issn = {0021-8502},
	journal = {Journal of Aerosol Science},
	language = {en},
	month = feb,
	number = {1},
	pages = {87--97},
	title = {Drag on non-spherical, orthotropic aerosol particles},
	url = {http://www.sciencedirect.com/science/article/pii/0021850287900139},
	urldate = {2021-01-13},
	volume = {18},
	year = {1987},
	bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/0021850287900139},
	bdsk-url-2 = {https://doi.org/10.1016/0021-8502(87)90013-9}}

@article{mcnown_effects_1950,
	abstract = {Extensive theoretical and experimental studies have been conducted at the Iowa Institute of Hydraulic Research in an investigation of the effect of shape on the settling velocity of particles. A number of representative axisymmetric shapes were used in the experiments, the Reynolds numbers of the particle motion ranging from 10−4 to 10+1. Stability of orientation was also investigated. Analytical results were obtained for the motion of ellipsoids within the Stokes range by solving Oberbeck's integral equation. The ratio of the principal-axis lengths was found to be by far the most significant of the various shape factors which have been proposed. In fact, the settling velocities of particles over a wide range of shape can be estimated within ten per cent from the theoretical results for ellipsoids.},
	author = {McNown, John S. and Malaika, Jamil},
	copyright = {{\copyright}1950. American Geophysical Union. All Rights Reserved.},
	doi = {https://doi.org/10.1029/TR031i001p00074},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/IM2V4N44/McNown and Malaika - 1950 - Effects of particle shape on settling velocity at .pdf:application/pdf;Snapshot:/Users/eunji/Zotero/storage/YH35QSSC/TR031i001p00074.html:text/html},
	issn = {2324-9250},
	journal = {Eos, Transactions American Geophysical Union},
	language = {en},
	note = {\_eprint: https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/TR031i001p00074},
	number = {1},
	pages = {74--82},
	title = {Effects of particle shape on settling velocity at low {Reynolds} numbers},
	url = {https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/TR031i001p00074},
	urldate = {2021-01-13},
	volume = {31},
	year = {1950},
	bdsk-url-1 = {https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/TR031i001p00074},
	bdsk-url-2 = {https://doi.org/10.1029/TR031i001p00074}}

@article{omand_sinking_2020,
	abstract = {The sinking of organic particles produced in the upper sunlit layers of the ocean forms an important limb of the oceanic biological pump, which impacts the sequestration of carbon and resupply of nutrients in the mesopelagic ocean. Particles raining out from the upper ocean undergo remineralization by bacteria colonized on their surface and interior, leading to an attenuation in the sinking flux of organic matter with depth. Here, we formulate a mechanistic model for the depth-dependent, sinking, particulate mass flux constituted by a range of sinking, remineralizing particles. Like previous studies, we find that the model does not achieve the characteristic `Martin curve' flux profile with a single type of particle, but instead requires a distribution of particle sizes and/or properties. We consider various functional forms of remineralization appropriate for solid/compact particles, and aggregates with an anoxic or oxic interior. We explore the sensitivity of the shape of the flux vs. depth profile to the choice of remineralization function, relative particle density, particle size distribution, and water column density stratification, and find that neither a power-law nor exponential function provides a definitively superior fit to the modeled profiles. The profiles are also sensitive to the time history of the particle source. Varying surface particle size distribution (via the slope of the particle number spectrum) over 3 days to represent a transient phytoplankton bloom results in transient subsurface maxima or pulses in the sinking mass flux. This work contributes to a growing body of mechanistic export flux models that offer scope to incorporate underlying dynamical and biological processes into global carbon cycle models.},
	author = {Omand, Melissa M. and Govindarajan, Rama and He, Jing and Mahadevan, Amala},
	copyright = {2020 The Author(s)},
	doi = {10.1038/s41598-020-60424-5},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/EWVXJP25/Omand et al. - 2020 - Sinking flux of particulate organic matter in the .pdf:application/pdf;Snapshot:/Users/eunji/Zotero/storage/WP8TBVUA/s41598-020-60424-5.html:text/html},
	issn = {2045-2322},
	journal = {Scientific Reports},
	language = {en},
	month = mar,
	note = {Number: 1 Publisher: Nature Publishing Group},
	number = {1},
	pages = {5582},
	shorttitle = {Sinking flux of particulate organic matter in the oceans},
	title = {Sinking flux of particulate organic matter in the oceans: {Sensitivity} to particle characteristics},
	url = {https://www.nature.com/articles/s41598-020-60424-5},
	urldate = {2021-01-13},
	volume = {10},
	year = {2020},
	bdsk-url-1 = {https://www.nature.com/articles/s41598-020-60424-5},
	bdsk-url-2 = {https://doi.org/10.1038/s41598-020-60424-5}}

@article{power_second_1987,
	abstract = {The problem of determining the slow viscous flow of an unbounded fluid past a single solid particle is formulated exactly as a system of linear Fredholm integral equations of the second kind for a distribution of Stresslets over the particle surface plus a pair of singularities (Stokeslet and Rotlet) located in the interior of the particle, singularities which give rise to a force and torque with magnitude depending linearly upon the unknown density of the surface Stresslets. It is shown that this integral equation possesses a unique continuous solution when the particle boundary is a Lyapunov surface and the velocity data on the boundary surface is continuous.},
	author = {Power, Henry and Miranda, Guillermo},
	doi = {10.1137/0147047},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/4KY3ABLM/Power and Miranda - 1987 - Second Kind Integral Equation Formulation of Stoke.pdf:application/pdf;Snapshot:/Users/eunji/Zotero/storage/MISDR7AM/0147047.html:text/html},
	issn = {0036-1399},
	journal = {SIAM Journal on Applied Mathematics},
	month = aug,
	note = {Publisher: Society for Industrial and Applied Mathematics},
	number = {4},
	pages = {689--698},
	title = {Second {Kind} {Integral} {Equation} {Formulation} of {Stokes}' {Flows} {Past} a {Particle} of {Arbitrary} {Shape}},
	url = {https://epubs.siam.org/doi/abs/10.1137/0147047},
	urldate = {2021-01-13},
	volume = {47},
	year = {1987},
	bdsk-url-1 = {https://epubs.siam.org/doi/abs/10.1137/0147047},
	bdsk-url-2 = {https://doi.org/10.1137/0147047}}

@book{pozrikidis_boundary_1992,
	abstract = {This book presents a coherent introduction to boundary integral, boundary element and singularity methods for steady and unsteady flow at zero Reynolds number. The focus of the discussion is not only on the theoretical foundation, but also on the practical application and computer implementation. The text is supplemented with a number of examples and unsolved problems, many drawn from the field of particulate creeping flows. The material is selected so that the book may serve both as a reference monograph and as a textbook in a graduate course on fluid mechanics or computational fluid mechanics.},
	address = {Cambridge},
	author = {Pozrikidis, C.},
	doi = {10.1017/CBO9780511624124},
	file = {Snapshot:/Users/eunji/Zotero/storage/LJ42HHMP/219AA1CE5DE05AE67096EA59692E25B3.html:text/html},
	isbn = {978-0-521-40502-7},
	publisher = {Cambridge University Press},
	series = {Cambridge {Texts} in {Applied} {Mathematics}},
	title = {Boundary {Integral} and {Singularity} {Methods} for {Linearized} {Viscous} {Flow}},
	url = {https://www.cambridge.org/core/books/boundary-integral-and-singularity-methods-for-linearized-viscous-flow/219AA1CE5DE05AE67096EA59692E25B3},
	urldate = {2021-01-13},
	year = {1992},
	bdsk-url-1 = {https://www.cambridge.org/core/books/boundary-integral-and-singularity-methods-for-linearized-viscous-flow/219AA1CE5DE05AE67096EA59692E25B3},
	bdsk-url-2 = {https://doi.org/10.1017/CBO9780511624124}}

@book{trefethen_spectral_2000,
	abstract = {The aim of this book is to teach you the essentials of spectral collocation methods with the aid of 40 short MATLAB{\textregistered} programs, or ``M-files.''* The programs are available online at http://www.comlab.ox.ac.uk/oucl/work/nick.trefethen, and you will run them and modify them to solve all kinds of ordinary and partial differential equations (ODEs and PDEs) connected with problems in fluid mechanics, quantum mechanics, vibrations, linear and nonlinear waves, complex analysis, and other fields. Concerning prerequisites, it is assumed that the words just written have meaning for you, that you have some knowledge of numerical methods, and that you already know MATLAB. If you like computing and numerical mathematics, you will enjoy working through this book, whether alone or in the classroom---and if you learn a few new tricks of MATLAB along the way, that's OK too!},
	author = {Trefethen, Lloyd N.},
	doi = {10.1137/1.9780898719598},
	file = {Snapshot:/Users/eunji/Zotero/storage/KQIBY52P/1.html:text/html},
	isbn = {978-0-89871-465-4},
	month = jan,
	publisher = {Society for Industrial and Applied Mathematics},
	series = {Software, {Environments} and {Tools}},
	title = {Spectral {Methods} in {MATLAB}},
	url = {https://locus.siam.org/doi/book/10.1137/1.9780898719598},
	urldate = {2021-01-14},
	year = {2000},
	bdsk-url-1 = {https://locus.siam.org/doi/book/10.1137/1.9780898719598},
	bdsk-url-2 = {https://doi.org/10.1137/1.9780898719598}}

@article{yoo_hydrodynamic_2020,
	abstract = {We study numerically the fluid forces acting on aggregates formed by a collation of cubic particles as a model of marine aggregates in the ocean. The flow around the aggregates and the resulting stresses on the surface of the aggregates are computed in the limit of zero Reynolds number using a boundary integral method, resulting in an accurate evaluation of the flow around fractal objects. We compare a single- and double-layer integral method to compute the velocity, and we determine that the single-layer approach is more suitable to capturing the flow around aggregates. We then characterize the drag of translation flows, the torque of rotational flows, and the straining force of extensional flows acting on aggregates as a function of their size and mode of formation. We determine that the force and torque are best characterized using the gyration radius of the aggregates, and the straining force is better characterized by the maximal radius.},
	author = {Yoo, Eunji and Khatri, Shilpa and Blanchette, Fran{\c c}ois},
	doi = {10.1103/PhysRevFluids.5.044305},
	file = {APS Snapshot:/Users/eunji/Zotero/storage/E4MDYHP6/PhysRevFluids.5.html:text/html},
	journal = {Physical Review Fluids},
	month = apr,
	note = {Publisher: American Physical Society},
	number = {4},
	pages = {044305},
	title = {Hydrodynamic forces on randomly formed marine aggregates},
	url = {https://link.aps.org/doi/10.1103/PhysRevFluids.5.044305},
	urldate = {2021-01-16},
	volume = {5},
	year = {2020},
	bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevFluids.5.044305},
	bdsk-url-2 = {https://doi.org/10.1103/PhysRevFluids.5.044305}}

@book{greengard_rapid_1988,
	abstract = {"The Rapid Evaluation of Potential Fields in Particle Systems" presents a group of algorithms for the computation of the potential and force fields in large-scale systems of particles that are likely to revolutionize a whole class of computer applications in science and engineering.In many areas of scientific computing, from studying the evolution of galaxies, to simulating the behavior of plasmas and fluids, to modeling chemical systems, a numerical scheme is used to follow the trajectories of a collection of particles moving in accordance with Newton's second law of motion in a field generated by the whole ensemble. Extending the earlier work of Rokhlin, Greengard has developed general, numerically stable methods for evaluating all pairwise interactions in linear time, a great improvement over the quadratic time required by the naive approach, and significantly better than any other proposed alternative.The "Rokhlin-Greengard" algorithm promises to make previously prohibitive simulations feasible, with speedups of three to four orders of magnitude in a system of a million particles. Moreover, the algorithm is well-suited for vector and parallel machines, and should make full use of their capabilities. The author presents his work with great clarity, and demonstrates the superiority of his methods both by mathematical analysis and by the results of numerical experiments."1987 ACM Distinguished Dissertation"},
	author = {Greengard, Leslie},
	isbn = {978-0-262-07110-9},
	language = {en},
	note = {Google-Books-ID: pXjke29Ptc8C},
	publisher = {MIT Press},
	title = {The {Rapid} {Evaluation} of {Potential} {Fields} in {Particle} {Systems}},
	year = {1988}}

@article{cheng_fast_1999,
	abstract = {We present an adaptive fast multipole method for the Laplace equation in three dimensions. It uses both new compression techniques and diagonal forms for translation operators to achieve high accuracy at a reasonable cost.},
	author = {Cheng, H. and Greengard, L. and Rokhlin, V.},
	doi = {10.1006/jcph.1999.6355},
	file = {ScienceDirect Snapshot:/Users/eunji/Zotero/storage/5TK9D765/S0021999199963556.html:text/html;ScienceDirect Full Text PDF:/Users/eunji/Zotero/storage/E4QMW5BF/Cheng et al. - 1999 - A Fast Adaptive Multipole Algorithm in Three Dimen.pdf:application/pdf},
	issn = {0021-9991},
	journal = {Journal of Computational Physics},
	keywords = {adaptive algorithms, fast multipole method, Laplace equation, translation operators},
	language = {en},
	month = nov,
	number = {2},
	pages = {468--498},
	title = {A {Fast} {Adaptive} {Multipole} {Algorithm} in {Three} {Dimensions}},
	url = {http://www.sciencedirect.com/science/article/pii/S0021999199963556},
	urldate = {2021-01-27},
	volume = {155},
	year = {1999},
	bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/S0021999199963556},
	bdsk-url-2 = {https://doi.org/10.1006/jcph.1999.6355}}

@article{tornberg_fast_2008,
	abstract = {Many problems in Stokes flow (and linear elasticity) require the evaluation of vector fields defined in terms of sums involving large numbers of fundamental solutions. In the fluid mechanics setting, these are typically the Stokeslet (the kernel of the single layer potential) or the Stresslet (the kernel of the double layer potential). In this paper, we present a simple and efficient method for the rapid evaluation of such fields, using a decomposition into a small number of Coulombic N-body problems, following an approach similar to that of Fu and Rodin [Y. Fu, G.J. Rodin, Fast solution methods for three-dimensional Stokesian many-particle problems, Commun. Numer. Meth. En. 16 (2000) 145--149]. While any fast summation algorithm for Coulombic interactions can be employed, we present numerical results from a scheme based on the most modern version of the fast multipole method [H. Cheng, L. Greengard, V. Rokhlin, A fast adaptive multipole algorithm in three dimensions, J. Comput. Phys. 155 (1999) 468--498]. This approach should be of value in both the solution of boundary integral equations and multiparticle dynamics.},
	author = {Tornberg, Anna-Karin and Greengard, Leslie},
	doi = {10.1016/j.jcp.2007.06.029},
	file = {ScienceDirect Snapshot:/Users/eunji/Zotero/storage/YECWG2GY/S0021999107002744.html:text/html;ScienceDirect Full Text PDF:/Users/eunji/Zotero/storage/ZDVXJXMS/Tornberg and Greengard - 2008 - A fast multipole method for the three-dimensional .pdf:application/pdf},
	issn = {0021-9991},
	journal = {Journal of Computational Physics},
	language = {en},
	month = jan,
	number = {3},
	pages = {1613--1619},
	title = {A fast multipole method for the three-dimensional {Stokes} equations},
	url = {http://www.sciencedirect.com/science/article/pii/S0021999107002744},
	urldate = {2021-01-27},
	volume = {227},
	year = {2008},
	bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/S0021999107002744},
	bdsk-url-2 = {https://doi.org/10.1016/j.jcp.2007.06.029}}

@article{salmon_fast_1994,
	author = {Salmon, John K. and Warren, Michael S.},
	doi = {10.1177/109434209400800205},
	file = {SAGE PDF Full Text:/Users/eunji/Zotero/storage/TF7K33SJ/Salmon and Warren - 1994 - Fast Parallel Tree Codes for Gravitational and Flu.pdf:application/pdf},
	issn = {1078-3482},
	journal = {The International Journal of Supercomputer Applications and High Performance Computing},
	language = {en},
	month = jun,
	note = {Publisher: SAGE Publications},
	number = {2},
	pages = {129--142},
	title = {Fast {Parallel} {Tree} {Codes} for {Gravitational} and {Fluid} {Dynamical} {N}-{Body} {Problems}},
	url = {https://doi.org/10.1177/109434209400800205},
	urldate = {2021-01-24},
	volume = {8},
	year = {1994},
	bdsk-url-1 = {https://doi.org/10.1177/109434209400800205}}

@article{sangani_on_1996,
	author = {Sangani, Ashok S. and Mo, Guobiao},
	doi = {10.1063/1.869003},
	file = {Snapshot:/Users/eunji/Zotero/storage/WY98QSSP/1.html:text/html;Full Text PDF:/Users/eunji/Zotero/storage/6VNCKMGG/Sangani and Mo - 1996 - An O(N) algorithm for Stokes and Laplace interacti.pdf:application/pdf},
	issn = {1070-6631},
	journal = {Physics of Fluids},
	month = aug,
	note = {Publisher: American Institute of Physics},
	number = {8},
	pages = {1990--2010},
	title = {An {O}({N}) algorithm for {Stokes} and {Laplace} interactions of particles},
	url = {https://aip.scitation.org/doi/abs/10.1063/1.869003},
	urldate = {2021-01-24},
	volume = {8},
	year = {1996},
	bdsk-url-1 = {https://aip.scitation.org/doi/abs/10.1063/1.869003},
	bdsk-url-2 = {https://doi.org/10.1063/1.869003}}

@article{fu_fast_2000,
	abstract = {It is demonstrated that three-dimensional single- and double-layer Stokesian potentials can be computed using fast solution methods for the N-body electrostatics problem. This allows one to develop fast iterative solution methods for a broad class of boundary integral equations corresponding to three-dimensional Stokesian many-particle problems. Copyright {\copyright} 2000 John Wiley \& Sons, Ltd.},
	author = {Fu, Yuhong and Rodin, Gregory J.},
	copyright = {Copyright {\copyright} 2000 John Wiley \& Sons, Ltd.},
	doi = {https://doi.org/10.1002/(SICI)1099-0887(200002)16:2<145::AID-CNM323>3.0.CO;2-E},
	file = {Snapshot:/Users/eunji/Zotero/storage/MNISBWDX/(SICI)1099-0887(200002)162145AID-CNM3233.0.html:text/html;Full Text PDF:/Users/eunji/Zotero/storage/B76AIZQI/Fu and Rodin - 2000 - Fast solution method for three-dimensional Stokesi.pdf:application/pdf},
	issn = {1099-0887},
	journal = {Communications in Numerical Methods in Engineering},
	keywords = {fast multipole method, boundary integral equation, many-particle problems},
	language = {en},
	note = {\_eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/\%28SICI\%291099-0887\%28200002\%2916\%3A2\%3C145\%3A\%3AAID-CNM323\%3E3.0.CO\%3B2-E},
	number = {2},
	pages = {145--149},
	title = {Fast solution method for three-dimensional {Stokesian} many-particle problems},
	url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/%28SICI%291099-0887%28200002%2916%3A2%3C145%3A%3AAID-CNM323%3E3.0.CO%3B2-E},
	urldate = {2021-01-24},
	volume = {16},
	year = {2000},
	bdsk-url-1 = {https://onlinelibrary.wiley.com/doi/abs/10.1002/%28SICI%291099-0887%28200002%2916%3A2%3C145%3A%3AAID-CNM323%3E3.0.CO%3B2-E},
	bdsk-url-2 = {https://doi.org/10.1002/(SICI)1099-0887(200002)16:2%3C145::AID-CNM323%3E3.0.CO;2-E}}

@article{mammoli_stokes_1999,
	abstract = {The multipole technique has recently received attention in the field of boundary element analysis as a means of reducing the order of data storage and calculation time requirements from O(N2) (iterative solvers) or O(N3) (gaussian elimination) to O(N log N) or O(N), where N is the number of nodes in the discretized system. Such a reduction in the growth of the calculation time and data storage is crucial in applications where N is large, such as when modelling the macroscopic behaviour of suspensions of particles. In such cases, a minimum of 1000 particles is needed to obtain statistically meaningful results, leading to systems with N of the order of 10 000 for the smallest problems. When only boundary velocities are known, the indirect boundary element formulation for Stokes flow results in Fredholm equations of the second kind, which generally produce a well-posed set of equations when discretized, a necessary requirement for iterative solution methods. The direct boundary element formulation, on the other hand, results in Fredholm equations of the first kind, which, upon discretization, produce ill-conditioned systems of equations. The model system here is a two-dimensional wide-gap couette viscometer, where particles are suspended in the fluid between the cylinders. This is a typical system that is efficiently modelled using boundary element method simulations. The multipolar technique is applied to both direct and indirect formulations. It is found that the indirect approach is sufficiently well-conditioned to allow the use of fast multipole methods. The direct approach results in severe ill-conditioning, to a point where application of the multipole method leads to non-convergence of the solution iteration. Copyright {\copyright} 1999 John Wiley \& Sons, Ltd.},
	author = {Mammoli, A. A. and Ingber, M. S.},
	copyright = {Copyright {\copyright} 1999 John Wiley \& Sons, Ltd.},
	doi = {https://doi.org/10.1002/(SICI)1097-0207(19990310)44:7<897::AID-NME530>3.0.CO;2-S},
	file = {Snapshot:/Users/eunji/Zotero/storage/2H47SHX9/(SICI)1097-0207(19990310)447897AID-NME5303.0.html:text/html;Full Text PDF:/Users/eunji/Zotero/storage/5734LU7I/Mammoli and Ingber - 1999 - Stokes flow around cylinders in a bounded two-dime.pdf:application/pdf},
	issn = {1097-0207},
	journal = {International Journal for Numerical Methods in Engineering},
	keywords = {BEM, multiphase flow, multipole acceleration},
	language = {en},
	note = {\_eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/\%28SICI\%291097-0207\%2819990310\%2944\%3A7\%3C897\%3A\%3AAID-NME530\%3E3.0.CO\%3B2-S},
	number = {7},
	pages = {897--917},
	title = {Stokes flow around cylinders in a bounded two-dimensional domain using multipole-accelerated boundary element methods},
	url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/%28SICI%291097-0207%2819990310%2944%3A7%3C897%3A%3AAID-NME530%3E3.0.CO%3B2-S},
	urldate = {2021-01-22},
	volume = {44},
	year = {1999},
	bdsk-url-1 = {https://onlinelibrary.wiley.com/doi/abs/10.1002/%28SICI%291097-0207%2819990310%2944%3A7%3C897%3A%3AAID-NME530%3E3.0.CO%3B2-S},
	bdsk-url-2 = {https://doi.org/10.1002/(SICI)1097-0207(19990310)44:7%3C897::AID-NME530%3E3.0.CO;2-S}}

@article{yan_kernel_2020,
	abstract = {Many different simulation methods for Stokes flow problems involve a common computationally intense task---the summation of a kernel function over \$O(N{\textasciicircum}2)\$ pairs of points. One popular technique is the Kernel Independent Fast Multipole Method (KIFMM), which constructs a spatial adaptive octree and places a small number of equivalent multipole and local points around each octree box, and completes the kernel sum with \$O(N)\$ performance. However, the KIFMM cannot be used directly with nonlinear kernels, can be inefficient for complicated linear kernels, and in general is difficult to implement compared to less-efficient alternatives such as Ewald-type methods. Here we present the Kernel Aggregated Fast Multipole Method (KAFMM), which overcomes these drawbacks by allowing different kernel functions to be used for specific stages of octree traversal. In many cases a simpler linear kernel suffices during the most extensive stage of octree traversal, even for nonlinear kernel summation problems. The KAFMM thereby improves computational efficiency in general and also allows efficient evaluation of some nonlinear kernel functions such as the regularized Stokeslet. We have implemented our method as an open-source software library STKFMM with support for Laplace kernels, the Stokeslet, regularized Stokeslet, Rotne-Prager-Yamakawa (RPY) tensor, and the Stokes double-layer and traction operators. Open and periodic boundary conditions are supported for all kernels, and the no-slip wall boundary condition is supported for the Stokeslet and RPY tensor. The package is designed to be ready-to-use as well as being readily extensible to additional kernels. Massive parallelism is supported with mixed OpenMP and MPI.},
	author = {Yan, Wen and Blackwell, Robert},
	file = {arXiv.org Snapshot:/Users/eunji/Zotero/storage/NZPGLU3K/2010.html:text/html;arXiv Fulltext PDF:/Users/eunji/Zotero/storage/VT2SV8N2/Yan and Blackwell - 2020 - Kernel Aggregated Fast Multipole Method Efficient.pdf:application/pdf},
	journal = {arXiv:2010.15155 [physics]},
	keywords = {Mathematics - Numerical Analysis, Physics - Computational Physics, Physics - Fluid Dynamics},
	month = oct,
	note = {arXiv: 2010.15155},
	shorttitle = {Kernel {Aggregated} {Fast} {Multipole} {Method}},
	title = {Kernel {Aggregated} {Fast} {Multipole} {Method}: {Efficient} summation of {Laplace} and {Stokes} kernel functions},
	url = {http://arxiv.org/abs/2010.15155},
	urldate = {2021-01-21},
	year = {2020},
	bdsk-url-1 = {http://arxiv.org/abs/2010.15155}}

@article{qu_fast_2017,
	abstract = {This paper firstly employs the fast multipole method (FMM) to accelerate the singular boundary method (SBM) solution of the Stokes equation. We present a fast multipole singular boundary method (FMSBM) based on the combination of the SBM and the FMM. The proposed FMSBM scheme reduces CPU operations and memory requirements by one order of magnitude, namely O(N) (where N is the number of boundary nodes). Thus, the strategy overcomes costly expenses of the SBM due to its dense interpolation matrix while keeping its major merits being free of mesh, boundary-only discretization, and high accuracy in the solution of the Stokes equation. The performance of this scheme is tested to a few benchmark problems. Numerical results demonstrate its efficiency, accuracy and applicability. {\copyright} 2017 International Association for Mathematics and Computers in Simulation (IMACS).},
	author = {Qu, Wenzhen and Chen, Wen and Fu, Zhuo-Jia and Gu, Yan},
	doi = {10.1016/j.matcom.2017.10.001},
	file = {Full Text PDF:/Users/eunji/Zotero/storage/7E5QFWBJ/Qu et al. - 2017 - Fast multipole singular boundary method for Stokes.pdf:application/pdf},
	journal = {Mathematics and Computers in Simulation},
	month = oct,
	title = {Fast multipole singular boundary method for {Stokes} flow problems},
	volume = {146},
	year = {2017},
	bdsk-url-1 = {https://doi.org/10.1016/j.matcom.2017.10.001}}

@article{henson_global_2012,
	abstract = {The ocean's biological carbon pump is a key component of the global carbon cycle. Only a small fraction of the carbon fixed by primary production is exported to the deep ocean, yet this flux sets to first order the efficiency with which carbon is sequestered out of further contact with the atmosphere on long time scales. Here we examine global patterns in particle export efficiency (PEeff), the proportion of primary production that is exported from the surface ocean, and transfer efficiency (Teff), the fraction of exported organic matter that reaches the deep ocean. Previous studies have found a positive correlation between Teff and deep ocean calcite fluxes recovered from sediment traps, implying that ballasting by calcium carbonate may play an important role in regulating Teff. An alternative explanation is that this correlation is not causative, as regions where the dominant biomineral phase is calcite tend to be subtropical systems, which are hypothesized to produce sinking aggregates highly resistant to degradation. We attempt to distinguish between these alternative hypotheses on the control of Teff by examining the relationship between Teff and biomineral phases exported from the upper ocean, rather than those collected in deep traps. Global scale estimates derived from satellite data show, in keeping with earlier studies, that PEeff is high at high latitudes and low at low latitudes, but that Teff is low at high latitudes and high at low latitudes. However, in contrast to the relationship observed for deep biomineral fluxes in previous studies, we find that Teff is strongly negatively correlated with opal export flux from the upper ocean, but uncorrelated with calcium carbonate export flux. We hypothesize that the underlying factor governing the spatial patterns observed in Teff is ecosystem function, specifically the degree of recycling occurring in the upper ocean, rather than the availability of calcium carbonate for ballasting.},
	author = {Henson, Stephanie A. and Sanders, Richard and Madsen, Esben},
	copyright = {Copyright 2012 by the American Geophysical Union},
	doi = {https://doi.org/10.1029/2011GB004099},
	file = {Snapshot:/Users/eunji/Zotero/storage/Z85DPA8C/2011GB004099.html:text/html;Full Text PDF:/Users/eunji/Zotero/storage/2LFZBVRG/Henson et al. - 2012 - Global patterns in efficiency of particulate organ.pdf:application/pdf},
	issn = {1944-9224},
	journal = {Global Biogeochemical Cycles},
	keywords = {carbon export, global, POC flux, satellite data},
	language = {en},
	note = {\_eprint: https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2011GB004099},
	number = {1},
	title = {Global patterns in efficiency of particulate organic carbon export and transfer to the deep ocean},
	url = {https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2011GB004099},
	urldate = {2021-01-20},
	volume = {26},
	year = {2012},
	bdsk-url-1 = {https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2011GB004099},
	bdsk-url-2 = {https://doi.org/10.1029/2011GB004099}}

@book{kaye_random_2008,
	abstract = {Fractal geometry is revolutionizing the descriptive mathematics of applied materials systems. Rather than presenting a mathematical treatise, Brian Kaye demonstrates the power of fractal geometry in describing materials ranging from Swiss cheese to pyrolytic graphite. Written from a practical point of view, the author assiduously avoids the use of equations while introducing the reader to numerous interesting and challenging problems in subject areas ranging from geography to fine particle science. The second edition of this successful book provides up-to-date literature coverage of the use of fractal geometry in all areas of science. From reviews of the first edition: "...no stone is left unturned in the quest for applications of fractal geometry to fine particle problems....This book should provide hours of enjoyable reading to those wishing to become acquainted with the ideas of fractal geometry as applied to practical materials problems." MRS Bulletin},
	author = {Kaye, Brian H.},
	isbn = {978-3-527-61598-8},
	keywords = {Science / Chemistry / General, Technology \& Engineering / Materials Science / General},
	language = {en},
	month = jul,
	publisher = {John Wiley \& Sons},
	title = {A {Random} {Walk} {Through} {Fractal} {Dimensions}},
	year = {2008}}

@article{witten_diffusion-limited_1981,
	abstract = {A model for random aggregates is studied by computer simulation. The model is applicable to a metal-particle aggregation process whose correlations have been measured previously. Density correlations within the model aggregates fall off with distance with a fractional power law, like those of the metal aggregates. The radius of gyration of the model aggregates has power-law behavior. The model is a limit of a model of dendritic growth.},
	author = {Witten, T. A. and Sander, L. M.},
	doi = {10.1103/PhysRevLett.47.1400},
	file = {APS Snapshot:/Users/eunji/Zotero/storage/9UYPWB69/PhysRevLett.47.html:text/html},
	journal = {Physical Review Letters},
	month = nov,
	note = {Publisher: American Physical Society},
	number = {19},
	pages = {1400--1403},
	title = {Diffusion-{Limited} {Aggregation}, a {Kinetic} {Critical} {Phenomenon}},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.47.1400},
	urldate = {2021-01-20},
	volume = {47},
	year = {1981},
	bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.47.1400},
	bdsk-url-2 = {https://doi.org/10.1103/PhysRevLett.47.1400}}

@book{olver_introduction_2014,
	abstract = {This textbook is designed for a one year course covering the fundamentals of partial differential equations, geared towards advanced undergraduates and beginning graduate students in mathematics, science, engineering, and elsewhere. The exposition carefully balances solution techniques, mathematical rigor, and significant applications, all illustrated by numerous examples. Extensive exercise sets appear at the end of almost every subsection, and include straightforward computational problems to develop and reinforce new techniques and results, details on theoretical developments and proofs, challenging projects both computational and conceptual, and supplementary material that motivates the student to delve further into the subject. No previous experience with the subject of partial differential equations or Fourier theory is assumed, the main prerequisites being undergraduate calculus, both one- and multi-variable, ordinary differential equations, and basic linear algebra. While the classical topics of separation of variables, Fourier analysis, boundary value problems, Green's functions, and special functions continue to form the core of an introductory course, the inclusion of nonlinear equations, shock wave dynamics, symmetry and similarity, the Maximum Principle, financial models, dispersion and solutions, Huygens' Principle, quantum mechanical systems, and more make this text well attuned to recent developments and trends in this active field of contemporary research. Numerical approximation schemes are an important component of any introductory course, and the text covers the two most basic approaches: finite differences and finite elements.},
	author = {Olver, Peter J.},
	doi = {10.1007/978-3-319-02099-0},
	file = {Snapshot:/Users/eunji/Zotero/storage/SD2M4WHY/9783319020983.html:text/html},
	isbn = {978-3-319-02098-3},
	language = {en},
	publisher = {Springer International Publishing},
	series = {Undergraduate {Texts} in {Mathematics}},
	title = {Introduction to {Partial} {Differential} {Equations}},
	url = {https://www.springer.com/gp/book/9783319020983},
	urldate = {2021-01-19},
	year = {2014},
	bdsk-url-1 = {https://www.springer.com/gp/book/9783319020983},
	bdsk-url-2 = {https://doi.org/10.1007/978-3-319-02099-0}}

@book{hoffman_numerical_2018,
	abstract = {Emphasizing the finite difference approach for solving differential equations, the second edition of Numerical Methods for Engineers and Scientists presents a methodology for systematically constructing individual computer programs. Providing easy access to accurate solutions to complex scientific and engineering problems, each chapter begins with objectives, a discussion of a representative application, and an outline of special features, summing up with a list of tasks students should be able to complete after reading the chapter- perfect for use as a study guide or for review. The AIAA Journal calls the book "...a good, solid instructional text on the basic tools of numerical analysis."},
	author = {Hoffman, Joe D. and Frankel, Steven},
	isbn = {978-1-4822-7060-0},
	keywords = {Mathematics / Applied, Mathematics / Number Systems},
	language = {en},
	month = oct,
	note = {Google-Books-ID: F5K3DwAAQBAJ},
	publisher = {CRC Press},
	title = {Numerical {Methods} for {Engineers} and {Scientists}},
	year = {2018}}

@book{leveque_numerical_1992,
	abstract = {These notes developed from a course on the numerical solution of conservation laws first taught at the University of Washington in the fall of 1988 and then at ETH during the following spring. The overall emphasis is on studying the mathematical tools that are essential in de- veloping, analyzing, and successfully using numerical methods for nonlinear systems of conservation laws, particularly for problems involving shock waves. A reasonable un- derstanding of the mathematical structure of these equations and their solutions is first required, and Part I of these notes deals with this theory. Part II deals more directly with numerical methods, again with the emphasis on general tools that are of broad use. I have stressed the underlying ideas used in various classes of methods rather than present- ing the most sophisticated methods in great detail. My aim was to provide a sufficient background that students could then approach the current research literature with the necessary tools and understanding. Without the wonders of TeX and LaTeX, these notes would never have been put together. The professional-looking results perhaps obscure the fact that these are indeed lecture notes. Some sections have been reworked several times by now, but others are still preliminary. I can only hope that the errors are. not too blatant. Moreover, the breadth and depth of coverage was limited by the length of these courses, and some parts are rather sketchy.},
	author = {LeVeque, Randall J.},
	doi = {10.1007/978-3-0348-8629-1},
	edition = {2},
	file = {Snapshot:/Users/eunji/Zotero/storage/PISQETJP/9783764327231.html:text/html},
	isbn = {978-3-7643-2723-1},
	language = {en},
	publisher = {Birkh{\"a}user Basel},
	series = {Lectures in {Mathematics}. {ETH} {Z{\"u}rich}},
	title = {Numerical {Methods} for {Conservation} {Laws}},
	url = {https://www.springer.com/gp/book/9783764327231},
	urldate = {2021-01-19},
	year = {1992},
	bdsk-url-1 = {https://www.springer.com/gp/book/9783764327231},
	bdsk-url-2 = {https://doi.org/10.1007/978-3-0348-8629-1}}

@article{alldredge_situ_1988,
	abstract = {The settling velocities of undisturbed macroscopic aggregates known as marine snow were measured with SCUBA in surface waters off southern California and analyzed as a function of aggregate size, mass, and density. The mean settling velocity was 74$\pm$39 m d−1 for aggregates ranging from 2.4 to 75 mm in maximum length. Sinking rates in the field varied exponentially with aggregate size and dry weight and were consistently up to four times slower than rates measured in the laboratory. The excess densities of the 80 aggregates examined were calculated from volume and dry weight and ranged over four orders of magnitude with a median of 1.4 × 10−4 g cm−3. Aggregates of marine snow sank more slowly than predicted for either solid or porous spheres of equivalent volume and density, although their velocities were within the range expected for equivalent sinking prolate ellipsoids. No relationships between settling velocity and either excess density or particle shape were found. Drag coefficients of marine snow were also higher than predicted by theory for spheres of equivalent volume and density. These deviations from theoretical expectations may be partially explained by errors in the estimation of the excess densities of aggregates. Variability in the densities of the heterogeneous primary particles comprising marine snow (fecal pellets, clay-mineral particles, phytoplankton, molts, etc.) and the potential for buoyancy regulation by individual phytoplankton cells inhabiting aggregates make determination of excess density especially problematic.},
	author = {Alldredge, Alice L. and Gotschalk, Chris},
	copyright = {{\copyright} 1988, by the Association for the Sciences of Limnology and Oceanography, Inc.},
	doi = {https://doi.org/10.4319/lo.1988.33.3.0339},
	file = {Snapshot:/Users/eunji/Zotero/storage/UFP9NCAA/lo.1988.33.3.html:text/html;Full Text PDF:/Users/eunji/Zotero/storage/M3JSGA3B/Alldredge and Gotschalk - 1988 - In situ settling behavior of marine snow1.pdf:application/pdf},
	issn = {1939-5590},
	journal = {Limnology and Oceanography},
	language = {en},
	note = {\_eprint: https://aslopubs.onlinelibrary.wiley.com/doi/pdf/10.4319/lo.1988.33.3.0339},
	number = {3},
	pages = {339--351},
	title = {In situ settling behavior of marine snow1},
	url = {https://aslopubs.onlinelibrary.wiley.com/doi/abs/10.4319/lo.1988.33.3.0339},
	urldate = {2021-01-19},
	volume = {33},
	year = {1988},
	bdsk-url-1 = {https://aslopubs.onlinelibrary.wiley.com/doi/abs/10.4319/lo.1988.33.3.0339},
	bdsk-url-2 = {https://doi.org/10.4319/lo.1988.33.3.0339}}

@article{burd_particle_2009,
	abstract = {A basic problem in marine biogeochemistry is understanding material and elemental distributions and fluxes in the oceans, and a key part of this problem is understanding the processes that affect particulate material in the ocean. Aggregation of particulate material is a primary process because it alters the transport properties of particulate material and provides a mechanism for transferring material from the dissolved into the particulate pools. Aggregation theory not only provides a framework for understanding these processes, but it also provides a means for making predictions and has been successfully used to predict maximum particle concentrations in the oceans and the fate of diatom blooms (including those from iron fertilization), the size spectra of particles in the oceans, and the size distributions of trace metals. Here we review the basic theory involved, summarize recent developments, and explore unresolved issues.},
	author = {Burd, Adrian B. and Jackson, George A.},
	doi = {10.1146/annurev.marine.010908.163904},
	file = {Snapshot:/Users/eunji/Zotero/storage/HU7464T2/annurev.marine.010908.html:text/html;Full Text PDF:/Users/eunji/Zotero/storage/A7Q4KRMV/Burd and Jackson - 2009 - Particle Aggregation.pdf:application/pdf},
	issn = {1941-1405},
	journal = {Annual Review of Marine Science},
	month = jan,
	note = {Publisher: Annual Reviews},
	number = {1},
	pages = {65--90},
	title = {Particle {Aggregation}},
	url = {https://www.annualreviews.org/doi/10.1146/annurev.marine.010908.163904},
	urldate = {2021-01-19},
	volume = {1},
	year = {2009},
	bdsk-url-1 = {https://www.annualreviews.org/doi/10.1146/annurev.marine.010908.163904},
	bdsk-url-2 = {https://doi.org/10.1146/annurev.marine.010908.163904}}

@book{liu_fast_2009,
	abstract = {The fast multipole method is one of the most important algorithms in computing developed in the 20th century. Along with the fast multipole method, the boundary element method (BEM) has also emerged as a powerful method for modeling large-scale problems. BEM models with millions of unknowns on the boundary can now be solved on desktop computers using the fast multipole BEM. This is the first book on the fast multipole BEM, which brings together the classical theories in BEM formulations and the recent development of the fast multipole method. Two- and three-dimensional potential, elastostatic, Stokes flow, and acoustic wave problems are covered, supplemented with exercise problems and computer source codes. Applications in modeling nanocomposite materials, bio-materials, fuel cells, acoustic waves, and image-based simulations are demonstrated to show the potential of the fast multipole BEM. Enables students, researchers, and engineers to learn the BEM and fast multipole method from a single source.},
	address = {Cambridge},
	author = {Liu, Yijun},
	doi = {10.1017/CBO9780511605345},
	file = {Liu - 2009 - Fast Multipole Boundary Element Method Theory and.pdf:/Users/eunji/Zotero/storage/QJQWUY9W/Liu - 2009 - Fast Multipole Boundary Element Method Theory and.pdf:application/pdf;Snapshot:/Users/eunji/Zotero/storage/RXQFYBKD/E522EB3361A4E033DCBD323F14F67ECE.html:text/html},
	isbn = {978-0-521-11659-6},
	publisher = {Cambridge University Press},
	shorttitle = {Fast {Multipole} {Boundary} {Element} {Method}},
	title = {Fast {Multipole} {Boundary} {Element} {Method}: {Theory} and {Applications} in {Engineering}},
	url = {https://www.cambridge.org/core/books/fast-multipole-boundary-element-method/E522EB3361A4E033DCBD323F14F67ECE},
	urldate = {2021-01-19},
	year = {2009},
	bdsk-url-1 = {https://www.cambridge.org/core/books/fast-multipole-boundary-element-method/E522EB3361A4E033DCBD323F14F67ECE},
	bdsk-url-2 = {https://doi.org/10.1017/CBO9780511605345}}

@article{greengard_fast_1987,
	abstract = {An algorithm is presented for the rapid evaluation of the potential and force fields in systems involving large numbers of particles whose interactions are Coulombic or gravitational in nature. For a system of N particles, an amount of work of the order O(N2) has traditionally been required to evaluate all pairwise interactions, unless some approximation or truncation method is used. The algorithm of the present paper requires an amount of work proportional to N to evaluate all interactions to within roundoff error, making it considerably more practical for large-scale problems encountered in plasma physics, fluid dynamics, molecular dynamics, and celestial mechanics.},
	author = {Greengard, L and Rokhlin, V},
	doi = {10.1016/0021-9991(87)90140-9},
	file = {ScienceDirect Snapshot:/Users/eunji/Zotero/storage/BZSPSPF3/0021999187901409.html:text/html;ScienceDirect Full Text PDF:/Users/eunji/Zotero/storage/QPJ3U3W8/Greengard and Rokhlin - 1987 - A fast algorithm for particle simulations.pdf:application/pdf},
	issn = {0021-9991},
	journal = {Journal of Computational Physics},
	language = {en},
	month = dec,
	number = {2},
	pages = {325--348},
	title = {A fast algorithm for particle simulations},
	url = {http://www.sciencedirect.com/science/article/pii/0021999187901409},
	urldate = {2021-01-19},
	volume = {73},
	year = {1987},
	bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/0021999187901409},
	bdsk-url-2 = {https://doi.org/10.1016/0021-9991(87)90140-9}}

@article{rokhlin_rapid_1985,
	abstract = {An algorithm is described for rapid solution of classical boundary value problems (Dirichlet an Neumann) for the Laplace equation based on iteratively solving integral equations of potential theory. CPU time requirements for previously published algorithms of this type are proportional to n2, where n is the number of nodes in the discretization of the boundary of the region. The CPU time requirements for the algorithm of the present paper are proportional to n, making it considerably more practical for large scale problems.},
	author = {Rokhlin, V},
	doi = {10.1016/0021-9991(85)90002-6},
	file = {ScienceDirect Snapshot:/Users/eunji/Zotero/storage/8HYX7C3V/0021999185900026.html:text/html;ScienceDirect Full Text PDF:/Users/eunji/Zotero/storage/QZ24NVCV/Rokhlin - 1985 - Rapid solution of integral equations of classical .pdf:application/pdf},
	issn = {0021-9991},
	journal = {Journal of Computational Physics},
	language = {en},
	month = sep,
	number = {2},
	pages = {187--207},
	title = {Rapid solution of integral equations of classical potential theory},
	url = {http://www.sciencedirect.com/science/article/pii/0021999185900026},
	urldate = {2021-01-19},
	volume = {60},
	year = {1985},
	bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/0021999185900026},
	bdsk-url-2 = {https://doi.org/10.1016/0021-9991(85)90002-6}}

@misc{noauthor_kernel-independent_nodate,
	title = {A kernel-independent adaptive fast multipole algorithm in two and three dimensions - {ScienceDirect}},
	url = {https://www.sciencedirect.com/science/article/pii/S0021999103006090},
	urldate = {2021-01-31},
	bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0021999103006090}}

@article{ying_kernel-independent_2004,
	abstract = {We present a new fast multipole method for particle simulations. The main feature of our algorithm is that it does not require the implementation of multipole expansions of the underlying kernel, and it is based only on kernel evaluations. Instead of using analytic expansions to represent the potential generated by sources inside a box of the hierarchical FMM tree, we use a continuous distribution of an equivalent density on a surface enclosing the box. To find this equivalent density, we match its potential to the potential of the original sources at a surface, in the far field, by solving local Dirichlet-type boundary value problems. The far-field evaluations are sparsified with singular value decomposition in 2D or fast Fourier transforms in 3D. We have tested the new method on the single and double layer operators for the Laplacian, the modified Laplacian, the Stokes, the modified Stokes, the Navier, and the modified Navier operators in two and three dimensions. Our numerical results indicate that our method compares very well with the best known implementations of the analytic FMM method for both the Laplacian and modified Laplacian kernels. Its advantage is the (relative) simplicity of the implementation and its immediate extension to more general kernels.},
	author = {Ying, Lexing and Biros, George and Zorin, Denis},
	doi = {10.1016/j.jcp.2003.11.021},
	file = {ScienceDirect Full Text PDF:/Users/eunji/Zotero/storage/P3WID2WI/Ying et al. - 2004 - A kernel-independent adaptive fast multipole algor.pdf:application/pdf},
	issn = {0021-9991},
	journal = {Journal of Computational Physics},
	keywords = {-body problems, Double-layer potential, Fast multipole methods, Fast solvers, Integral equations, Particle methods, Single-layer potential},
	language = {en},
	month = may,
	number = {2},
	pages = {591--626},
	title = {A kernel-independent adaptive fast multipole algorithm in two and three dimensions},
	url = {http://www.sciencedirect.com/science/article/pii/S0021999103006090},
	urldate = {2021-01-31},
	volume = {196},
	year = {2004},
	bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/S0021999103006090},
	bdsk-url-2 = {https://doi.org/10.1016/j.jcp.2003.11.021}}

@book{kress_linear_2014,
	abstract = {This book combines theory, applications, and numerical methods, and covers each of these fields with the same weight. In order to make the book accessible to mathematicians, physicists, and engineers alike, the author has made it as self-contained as possible, requiring only a solid foundation in differential and integral calculus. The functional analysis which is necessary for an adequate treatment of the theory and the numerical solution of integral equations is developed within the book itself. Problems are included at the end of each chapter. For this third edition in order to make the introduction to the basic functional analytic tools more complete the Hahn--Banach extension theorem and the Banach open mapping theorem are now included in the text. The treatment of boundary value problems in potential theory has been extended by a more complete discussion of integral equations of the first kind in the classical Holder space setting and of both integral equations of the first and second kind in the contemporary Sobolev space setting. In the numerical solution part of the book, the author included a new collocation method for two-dimensional hypersingular boundary integral equations and a collocation method for the three-dimensional Lippmann-Schwinger equation. The final chapter of the book on inverse boundary value problems for the Laplace equation has been largely rewritten with special attention to the trilogy of decomposition, iterative and sampling methodsReviews of earlier editions:"This book is an excellent introductory text for students, scientists, and engineers who want to learn the basic theory of linear integral equations and their numerical solution."(Math. Reviews, 2000)"This is a good introductory text book on linear integral equations. It contains almost all the topics necessary for a student. The presentation of the subject matter is lucid, clear and in the proper modern framework without being too abstract." (ZbMath, 1999)},
	address = {New York},
	author = {Kress, Rainer},
	doi = {10.1007/978-1-4614-9593-2},
	edition = {3},
	file = {Snapshot:/Users/eunji/Zotero/storage/T8FNU2GB/9781461495925.html:text/html},
	isbn = {978-1-4614-9592-5},
	language = {en},
	publisher = {Springer-Verlag},
	series = {Applied {Mathematical} {Sciences}},
	title = {Linear {Integral} {Equations}},
	url = {https://www.springer.com/gp/book/9781461495925},
	urldate = {2021-03-23},
	year = {2014},
	bdsk-url-1 = {https://www.springer.com/gp/book/9781461495925},
	bdsk-url-2 = {https://doi.org/10.1007/978-1-4614-9593-2}}

@article{smithies_integral_1959,
	abstract = {//static.cambridge.org/content/id/urn\%3Acambridge.org\%3Aid\%3Aarticle\%3AS0025557200040717/resource/name/firstPage-S0025557200040717a.jpg},
	author = {Smithies, F.},
	doi = {10.2307/3610248},
	file = {Snapshot:/Users/eunji/Zotero/storage/WX7NXMF4/4790BC73CCD508CBE7A21A630536BE74.html:text/html},
	issn = {0025-5572, 2056-6328},
	journal = {The Mathematical Gazette},
	language = {en},
	month = may,
	note = {Publisher: Cambridge University Press},
	number = {344},
	pages = {156--156},
	title = {Integral equations and their applications to certain problems in mechanics, mathematical physics and technology. {By} {S}. {G}. {Mikhlin}. {Translated} from the {Russian} by {A}. {H}. {Armstrong}. {Pp}. xii, 338. 80s. 1957. ({Pergamon} {Press})},
	url = {https://www.cambridge.org/core/journals/mathematical-gazette/article/abs/integral-equations-and-their-applications-to-certain-problems-in-mechanics-mathematical-physics-and-technology-by-s-g-mikhlin-translated-from-the-russian-by-a-h-armstrong-pp-xii-338-80s-1957-pergamon-press/4790BC73CCD508CBE7A21A630536BE74},
	urldate = {2021-05-15},
	volume = {43},
	year = {1959},
	bdsk-url-1 = {https://www.cambridge.org/core/journals/mathematical-gazette/article/abs/integral-equations-and-their-applications-to-certain-problems-in-mechanics-mathematical-physics-and-technology-by-s-g-mikhlin-translated-from-the-russian-by-a-h-armstrong-pp-xii-338-80s-1957-pergamon-press/4790BC73CCD508CBE7A21A630536BE74},
	bdsk-url-2 = {https://doi.org/10.2307/3610248}}

@book{guazzelli_physical_2011,
	abstract = {Understanding the behaviour of particles suspended in a fluid has many important applications across a range of fields, including engineering and geophysics. Comprising two main parts, this book begins with the well-developed theory of particles in viscous fluids, i.e. microhydrodynamics, particularly for single- and pair-body dynamics. Part II considers many-body dynamics, covering shear flows and sedimentation, bulk flow properties and collective phenomena. An interlude between the two parts provides the basic statistical techniques needed to employ the results of the first (microscopic) in the second (macroscopic). The authors introduce theoretical, mathematical concepts through concrete examples, making the material accessible to non-mathematicians. They also include some of the many open questions in the field to encourage further study. Consequently, this is an ideal introduction for students and researchers from other disciplines who are approaching suspension dynamics for the first time.},
	address = {Cambridge},
	author = {Guazzelli, {\'E}lisabeth and Morris, Jeffrey F.},
	doi = {10.1017/CBO9780511894671},
	file = {Snapshot:/Users/eunji/Zotero/storage/SKFW3U57/B8EB2B34C3D3893D7E22884710AA7E7A.html:text/html},
	isbn = {978-0-521-19319-1},
	publisher = {Cambridge University Press},
	series = {Cambridge {Texts} in {Applied} {Mathematics}},
	title = {A {Physical} {Introduction} to {Suspension} {Dynamics}},
	url = {https://www.cambridge.org/core/books/physical-introduction-to-suspension-dynamics/B8EB2B34C3D3893D7E22884710AA7E7A},
	urldate = {2021-08-31},
	year = {2011},
	bdsk-url-1 = {https://www.cambridge.org/core/books/physical-introduction-to-suspension-dynamics/B8EB2B34C3D3893D7E22884710AA7E7A},
	bdsk-url-2 = {https://doi.org/10.1017/CBO9780511894671}}

@inproceedings{grengard_rapid_1988,
	address = {Berlin, Heidelberg},
	author = {Grengard, L. and Rokhlin, V.},
	booktitle = {Vortex {Methods}},
	doi = {10.1007/BFb0089775},
	editor = {Anderson, Christopher and Greengard, Claude},
	file = {Springer Full Text PDF:/Users/eunji/Zotero/storage/VWXFLC6P/Grengard and Rokhlin - 1988 - The rapid evaluation of potential fields in three .pdf:application/pdf},
	isbn = {978-3-540-46034-3},
	keywords = {Error Bound, Legendre Polynomial, Multipole Expansion, Potential Field, Translation Operator},
	language = {en},
	pages = {121--141},
	publisher = {Springer},
	series = {Lecture {Notes} in {Mathematics}},
	title = {The rapid evaluation of potential fields in three dimensions},
	year = {1988},
	bdsk-url-1 = {https://doi.org/10.1007/BFb0089775}}