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AuthorGoriely, Alain (19)Byrne, Helen M. (18)Erban, Radek (17)Goriely, A. (17)Vella, Dominic (14)View MoreJournalPhysical Review E (18)Bulletin of Mathematical Biology (15)SIAM Journal on Applied Mathematics (14)Journal of Fluid Mechanics (12)Journal of Theoretical Biology (12)View MoreKAUST Grant Number

KUK-C1-013-04 (327)

PublisherSpringer Nature (61)Elsevier BV (50)Society for Industrial & Applied Mathematics (SIAM) (37)American Physical Society (APS) (27)AIP Publishing (19)View MoreSubjectAsymptotic analysis (10)Preconditioning (7)lubrication theory (6)capillary flows (5)Elasticity (5)View MoreTypeArticle (319)Book Chapter (5)Conference Paper (3)Year (Issue Date)2017 (3)2016 (2)2015 (21)2014 (53)2013 (84)View MoreItem AvailabilityMetadata Only (314)Open Access (13)

Now showing items 31-40 of 327

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Excluded-volume effects in the diffusion of hard spheres

Bruna, Maria; Chapman, S. Jonathan (Physical Review E, American Physical Society (APS), 2012-01-03) [Article]

Excluded-volume effects can play an important role in determining transport properties in diffusion of particles. Here, the diffusion of finite-sized hard-core interacting particles in two or three dimensions is considered systematically using the method of matched asymptotic expansions. The result is a nonlinear diffusion equation for the one-particle distribution function, with excluded-volume effects enhancing the overall collective diffusion rate. An expression for the effective (collective) diffusion coefficient is obtained. Stochastic simulations of the full particle system are shown to compare well with the solution of this equation for two examples. © 2012 American Physical Society.

Front Propagation in Stochastic Neural Fields

Bressloff, Paul C.; Webber, Matthew A. (SIAM Journal on Applied Dynamical Systems, Society for Industrial & Applied Mathematics (SIAM), 2012-01) [Article]

We analyze the effects of extrinsic multiplicative noise on front propagation in a scalar neural field with excitatory connections. Using a separation of time scales, we represent the fluctuating front in terms of a diffusive-like displacement (wandering) of the front from its uniformly translating position at long time scales, and fluctuations in the front profile around its instantaneous position at short time scales. One major result of our analysis is a comparison between freely propagating fronts and fronts locked to an externally moving stimulus. We show that the latter are much more robust to noise, since the stochastic wandering of the mean front profile is described by an Ornstein-Uhlenbeck process rather than a Wiener process, so that the variance in front position saturates in the long time limit rather than increasing linearly with time. Finally, we consider a stochastic neural field that supports a pulled front in the deterministic limit, and show that the wandering of such a front is now subdiffusive. © 2012 Society for Industrial and Applied Mathematics.

Frost Heave in Colloidal Soils

Peppin, Stephen; Majumdar, Apala; Style, Robert; Sander, Graham (SIAM Journal on Applied Mathematics, Society for Industrial & Applied Mathematics (SIAM), 2011-01) [Article]

We develop a mathematical model of frost heave in colloidal soils. The theory accountsfor heave and consolidation while not requiring a frozen fringe assumption. Two solidificationregimes occur: a compaction regime in which the soil consolidates to accommodate the ice lenses, and a heave regime during which liquid is sucked into the consolidated soil from an external reservoir, and the added volume causes the soil to heave. The ice fraction is found to vary inversely with thefreezing velocity V , while the rate of heave is independent of V , consistent with field and laboratoryobservations. © 2011 Society for Industrial and Applied Mathematics.

A volume-preserving sharpening approach for the propagation of sharp phase boundaries in multiphase lattice Boltzmann simulations

Reis, T.; Dellar, P.J. (Computers & Fluids, Elsevier BV, 2011-07) [Article]

Lattice Boltzmann models that recover a macroscopic description of multiphase flow of immiscible liquids typically represent the boundaries between phases using a scalar function, the phase field, that varies smoothly over several grid points. Attempts to tune the model parameters to minimise the widths of these interfaces typically lead to the interfaces becoming fixed to the underlying grid instead of advecting with the fluid velocity. This phenomenon, known as lattice pinning, is strikingly similar to that associated with the numerical simulation of conservation laws coupled to stiff algebraic source terms. We present a lattice Boltzmann formulation of the model problem proposed by LeVeque and Yee (1990) [3] to study the latter phenomenon in the context of computational combustion, and offer a volume-conserving extension in multiple space dimensions. Inspired by the random projection method of Bao and Jin (2000) [1] we further generalise this formulation by introducing a uniformly distributed quasi-random variable into the term responsible for the sharpening of phase boundaries. This method is mass conserving, gives correct average propagation speeds over many timesteps, and is shown to significantly delay the onset of pinning as the interface width is reduced. © 2010 Elsevier Ltd.

An A Posteriori Error Analysis of Mixed Finite Element Galerkin Approximations to Second Order Linear Parabolic Problems

Memon, Sajid; Nataraj, Neela; Pani, Amiya Kumar (SIAM Journal on Numerical Analysis, Society for Industrial & Applied Mathematics (SIAM), 2012-01) [Article]

In this article, a posteriori error estimates are derived for mixed finite element Galerkin approximations to second order linear parabolic initial and boundary value problems. Using mixed elliptic reconstructions, a posteriori error estimates in L∞(L2)- and L2(L2)-norms for the solution as well as its flux are proved for the semidiscrete scheme. Finally, based on a backward Euler method, a completely discrete scheme is analyzed and a posteriori error bounds are derived, which improves upon earlier results on a posteriori estimates of mixed finite element approximations to parabolic problems. Results of numerical experiments verifying the efficiency of the estimators have also been provided. © 2012 Society for Industrial and Applied Mathematics.

An Asymptotic Theory for the Re-Equilibration of a Micellar Surfactant Solution

Griffiths, I. M.; Bain, C. D.; Breward, C. J. W.; Chapman, S. J.; Howell, P. D.; Waters, S. L. (SIAM Journal on Applied Mathematics, Society for Industrial & Applied Mathematics (SIAM), 2012-01) [Article]

Micellar surfactant solutions are characterized by a distribution of aggregates made up predominantly of premicellar aggregates (monomers, dimers, trimers, etc.) and a region of proper micelles close to the peak aggregation number, connected by an intermediate region containing a very low concentration of aggregates. Such a distribution gives rise to a distinct two-timescale reequilibration following a system dilution, known as the t1 and t2 processes, whose dynamics may be described by the Becker-Döring equations. We use a continuum version of these equations to develop a reduced asymptotic description that elucidates the behavior during each of these processes.© 2012 Society for Industrial and Applied Mathematics.

An Algorithm for the Convolution of Legendre Series

Hale, Nicholas; Townsend, Alex (SIAM Journal on Scientific Computing, Society for Industrial & Applied Mathematics (SIAM), 2014-01) [Article]

An O(N2) algorithm for the convolution of compactly supported Legendre series is described. The algorithm is derived from the convolution theorem for Legendre polynomials and the recurrence relation satisfied by spherical Bessel functions. Combining with previous work yields an O(N 2) algorithm for the convolution of Chebyshev series. Numerical results are presented to demonstrate the improved efficiency over the existing algorithm. © 2014 Society for Industrial and Applied Mathematics.

Calculus on Surfaces with General Closest Point Functions

März, Thomas; Macdonald, Colin B. (SIAM Journal on Numerical Analysis, Society for Industrial & Applied Mathematics (SIAM), 2012-01) [Article]

The closest point method for solving partial differential equations (PDEs) posed on surfaces was recently introduced by Ruuth and Merriman [J. Comput. Phys., 227 (2008), pp. 1943- 1961] and successfully applied to a variety of surface PDEs. In this paper we study the theoretical foundations of this method. The main idea is that surface differentials of a surface function can be replaced with Cartesian differentials of its closest point extension, i.e., its composition with a closest point function. We introduce a general class of these closest point functions (a subset of differentiable retractions), show that these are exactly the functions necessary to satisfy the above idea, and give a geometric characterization of this class. Finally, we construct some closest point functions and demonstrate their effectiveness numerically on surface PDEs. © 2012 Society for Industrial and Applied Mathematics.

Cardiac cell modelling: Observations from the heart of the cardiac physiome project

Fink, Martin; Niederer, Steven A.; Cherry, Elizabeth M.; Fenton, Flavio H.; Koivumäki, Jussi T.; Seemann, Gunnar; Thul, Rüdiger; Zhang, Henggui; Sachse, Frank B.; Beard, Dan; Crampin, Edmund J.; Smith, Nicolas P. (Progress in Biophysics and Molecular Biology, Elsevier BV, 2011-01) [Article]

In this manuscript we review the state of cardiac cell modelling in the context of international initiatives such as the IUPS Physiome and Virtual Physiological Human Projects, which aim to integrate computational models across scales and physics. In particular we focus on the relationship between experimental data and model parameterisation across a range of model types and cellular physiological systems. Finally, in the context of parameter identification and model reuse within the Cardiac Physiome, we suggest some future priority areas for this field. © 2010 Elsevier Ltd.

A review of mathematical models for the formation of vascular networks

Scianna, M.; Bell, C.G.; Preziosi, L. (Journal of Theoretical Biology, Elsevier BV, 2013-09) [Article]

Two major mechanisms are involved in the formation of blood vasculature: vasculogenesis and angiogenesis. The former term describes the formation of a capillary-like network from either a dispersed or a monolayered population of endothelial cells, reproducible also in vitro by specific experimental assays. The latter term describes the sprouting of new vessels from an existing capillary or post-capillary venule. Similar mechanisms are also involved in the formation of the lymphatic system through a process generally called lymphangiogenesis. A number of mathematical approaches have been used to analyze these phenomena. In this paper, we review the different types of models, with special emphasis on their ability to reproduce different biological systems and to predict measurable quantities which describe the overall processes. Finally, we highlight the advantages specific to each of the different modelling approaches. © 2013 Elsevier Ltd.

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