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Spherical Diffusion Model with Semi-Permeable Boundary: A Transfer Function Approach [article]

Maximilian Schäfer, Wayan Wicke, Werner Haselmayr, Rudolf Rabenstein, Robert Schober
2019 arXiv   pre-print
In this paper, we develop a realistic model for particle diffusion in a bounded sphere and particle transport through a semi-permeable boundary.  ...  The proposed solution of the bounded spherical diffusion problem is formulated in terms of a state-space description and the semi-permeable boundary is accounted for by a feedback loop.  ...  The diffusion problem in a bounded sphere with semi-permeable boundary was recently considered in [11] using a Green's function approach.  ... 
arXiv:1910.14319v2 fatcat:thydtsb7evfxpczbq72p52t5ei

Simulation of Osmotic Swelling by the Stochastic Immersed Boundary Method

Chen-Hung Wu, Thomas G. Fai, Paul J. Atzberger, Charles S. Peskin
2015 SIAM Journal on Scientific Computing  
We introduce Stochastic Immersed Boundary Methods (SIBM) that can capture osmotically driven fluid transport through semi-permeable elastic membranes subject to thermal fluctuations.  ...  We also develop numerical methods to handle within SIBM an elastic shell model for a Neo-Hookean material.  ...  PJA was also supported by the NSF CAREER DMS -0956210, which also supported a visit of CHW to UC Santa Barbara that was important for this work.  ... 
doi:10.1137/14098404x fatcat:j4m5sqiqing7bkiptx7xuhp5ae

Immersed boundary method for multiphase transport phenomena

Wei Xiao, Hancong Zhang, Kun Luo, Chaoli Mao, Jianren Fan
2020 Reviews in chemical engineering  
Discussions on the implementation of various boundary conditions at the interphase surface with momentum, heat, and mass transfer for different IB methods are then presented, together with a summary.  ...  AbstractMultiphase flows with momentum, heat, and mass transfer exist widely in a variety of industrial applications.  ...  et al. (2009) with a simulation of mass diffusion across a fixed permeable interface.  ... 
doi:10.1515/revce-2019-0076 fatcat:cb2dpet4fvharl2y2nmzzbpmz4

Hygro-thermo-mechanical analysis of spalling in concrete walls at high temperatures as a moving boundary problem

Michal Beneš, Radek Štefan
2015 International Journal of Heat and Mass Transfer  
A simplified mechanical approach to account for effects of thermal stresses and pore pressure build-up on spalling is incorporated into the model.  ...  A mathematical model allowing coupled hygro-thermo-mechanical analysis of spalling in concrete walls at high temperatures by means of the moving boundary problem is presented.  ...  For the model represented by a system of partial differential equations and appropriate boundary and initial conditions, the finite element discretization in space and the semi-implicit discretization  ... 
doi:10.1016/j.ijheatmasstransfer.2015.01.050 fatcat:s3wu33sc4rhcnpjrdltjpx4zcm

A spherical shell numerical dynamo benchmark with pseudo-vacuum magnetic boundary conditions

A. Jackson, A. Sheyko, P. Marti, A. Tilgner, D. Cébron, S. Vantieghem, R. Simitev, F. Busse, X. Zhan, G. Schubert, S. Takehiro, Y. Sasaki (+4 others)
2013 Geophysical Journal International  
magnetic field generation and heat transfer in the setting of a spherical shell, namely a sphere containing an inner core.  ...  This latter condition should be compared with the more frequently used insulating boundary condition.  ...  This benchmark exercise was set in the geometry of a spherical shell, with convection driven by a temperature difference between an inner core and the outer boundary of the spherical shell.  ... 
doi:10.1093/gji/ggt425 fatcat:puqr743gcjcaxb766k4lodmfuu

Exact and numerical solutions to a Stefan problem with two moving boundaries

Steven I. Barry, James Caunce
2008 Applied Mathematical Modelling  
The swelling of grease, grain and polymers can be modelled by a nonlinear diffusion equation with two moving boundaries, commonly called a Stefan problem.  ...  We present here numerical and exact analytical solutions for both linear and nonlinear diffusivities for a variety of parameter ranges.  ...  Discussions with Dr. Geoff Mercer provided many useful insights and improvements on this work.  ... 
doi:10.1016/j.apm.2006.11.004 fatcat:5cysshxsdrfcvp5rhlo7tcv7ti

Modeling Non-Darcy Natural Convection Flow of a Micropolar Dusty Fluid with Convective Boundary Condition

F. M. Hady, A. Mahdy, R. A. Mohamed, Omima A. Abo Zaid
2020 Zenodo  
In addition, a convective boundary condition is scrutinized into the micropolar dusty fluid model.  ...  A numerical approach of the effectiveness of numerous parameters on magnetohydrodynamic (MHD) natural convection heat and mass transfer problem of a dusty micropolar fluid in a non-Darcy porous regime  ...  of boundary viscous diffusion and Inertia.  ... 
doi:10.5281/zenodo.3669257 fatcat:gakgua7ivfhyfijuqyfdn3fzla

A bibliography on moving-free boundary problems for the heat-diffusion equation. The stefan and related problems

Domingo Alberto Tarzia
2000 MAT Serie A  
cuyo objetivo es contribuir a la difusión de conocimientos y resultados matemáticos.  ...  La serie A y las Prepublicaciones podrán ser consultadas en:  ...  Tao96 TAO Y.X., "Modelling of melting in heterogeneous snow cover on permeable frozen soil", Numer.Heat Transfer, Part A, 30 (1996), pp.143-163. TSB84 THOMAS B.G. -SAMARASEKERA I.V.  ... 
doi:10.26422/mat.a.2000.2.tar fatcat:ikpa45typfghzfbj5hhb6dds5q

Ventilation of multi-entranced rodent burrows by boundary layer eddies

I. Brickner-Braun, D. Zucker-Milwerger, A. Braun, J. S. Turner, B. Pinshow, P. Berliner
2014 Journal of Experimental Biology  
Rodent burrows are often assumed to be environments wherein the air has a high concentration of CO 2 .  ...  We have characterized the means by which burrows of Sundevall's jird, which are representative of the burrows of many rodent species with more than one entrance, are ventilated.  ...  Funding This research was supported by a grant from the Israel Science Foundation [grant number 136/10] to B.P. and P.B.  ... 
doi:10.1242/jeb.114231 pmid:25472971 fatcat:yq4wzhinb5flfm4kksvsbjlycu

Boundary Element Model for Nonlinear Fractional-Order Heat Transfer in Magneto-Thermoelastic FGA Structures Involving Three Temperatures [chapter]

Mohamed Abdelsabour Fahmy
2019 Mechanics of Functionally Graded Materials and Structures [Working Title]  
So, we propose a new boundary element model for the solution of general and complex problems associated with this theory.  ...  The principal objective of this chapter is to introduce a new fractional-order theory for functionally graded anisotropic (FGA) structures.  ...  and phonon) radiation diffusion equations using a boundary element method.  ... 
doi:10.5772/intechopen.88255 fatcat:hwtzsthiq5fw7mpbadu6fvvgzy

A stochastic immersed boundary method for fluid-structure dynamics at microscopic length scales

Paul J. Atzberger, Peter R. Kramer, Charles S. Peskin
2007 Journal of Computational Physics  
In this work it is shown how the immersed boundary method of (Peskin2002) for modeling flexible structures immersed in a fluid can be extended to include thermal fluctuations.  ...  It is shown in three dimensions that the diffusion of immersed particles simulated with the method has the correct scaling in the physical parameters.  ...  When diffusing particles are confined to a chamber by a boundary which is permeable to fluid but less permeable to particles, a pressure difference develops between the inside and the outside of the chamber  ... 
doi:10.1016/ fatcat:4is7mm26bzflvngbmlh2dg4pgy

Determining the magnetic field in the core-mantle boundary zone by non-harmonic downward continuation

L. Ballani, H. Greiner-Mai, D. Stromeyer
2002 Geophysical Journal International  
We only consider the poloidal part of the magnetic field with boundary values that are conventionally given by a spherical harmonic expansion of the observed geomagnetic potential field at the Earth's  ...  for a parabolic partial differential equation (diffusion equation).  ...  The 1-D 'model' component and boundary functions φ(t) in (22) is the data function g 32 (t) (Gauss coefficient) from the spherical harmonic expansion of the geomagnetic potential V at the Earth's surface  ... 
doi:10.1046/j.1365-246x.2002.01655.x fatcat:aklhilar2na3nkuu5jyvc3mz5m

Interfaces and Free Boundaries: Analysis, Control and Simulation

Charles Elliott, Yoshikazu Giga, Michael Hinze, Vanessa Styles
2013 Oberwolfach Reports  
Mathematically this leads to optimization problems with partial differential equation constraints including free boundaries.  ...  The field of mathematical and numerical analysis of systems of nonlinear partial differential equations involving interfaces and free boundaries is a flourishing area of research.  ...  References The diffuse interface model We use the diffuse interface model of [1] with a double-obstacle free energy according to [2] .  ... 
doi:10.4171/owr/2013/15 fatcat:fkpzvxt6a5bhdpswg6tyhuxusq

A three-phase free boundary problem with melting ice and dissolving gas

2014 European journal of applied mathematics  
We develop a mathematical model for a three-phase free boundary problem in one dimension that involves the interactions between gas, water and ice.  ...  The model incorporates a Stefan condition at the water-ice interface along with Henry's law for dissolution of gas at the gas-water interface.  ...  Acknowledgements This work was supported by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada and a Research Grant from the North American Maple Syrup Council.  ... 
doi:10.1017/s0956792513000430 fatcat:adz6ykkxlvccjjqfbaiqfri4om

Thermal convection in Earth's inner core with phase change at its boundary

Renaud Deguen, Thierry Alboussière, Philippe Cardin
2013 Geophysical Journal International  
Convection takes a more classical form, with a one-cell axisymmetric mode at the onset and chaotic plume convection at large Rayleigh number. [...]  ...  Inner core translation, with solidification on one hemisphere and melting on the other, provides a promising basis for understanding the hemispherical dichotomy of the inner core, as well as the anomalous  ...  Here α l,i denotes the ith zero of the spherical Bessel function of degree l. The functions q l 1 (P) to q l 4 (P) are given in Appendix A by equations (A.24), (A.25), (A.27) and (A.28).  ... 
doi:10.1093/gji/ggt202 fatcat:qx7wkikdubh5jjwrglpvwc3kj4
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