4 citations · 5 across the 6 of their papers we have counts for
7 papers
A variational model of nonlinear poroelasticity
James H. Adler, Xiaozhe Hu, Arkadz Kirshtein
We derive a thermodynamically-consistent model of fluid flow through a poroelastic medium. Starting from elastic and fluid free-energy densities, an energy-dissipation rate, and a…
Candidate Voter Dynamics
Christoph Borgers, Natasa Dragovic, Arkadz Kirshtein
We model dynamically changing candidate positions in the face of a dynamic electorate. To formulate our equations, we use a space-time-continuous Hegselmann-Krause equation, which…
A Phase-Field-Micromechanics Study on the Microstructural Evolution during Viscous Sintering
Xiaoxu Dai, Bo Qian, Arkadz Kirshtein +1
In the manufacturing process of high-performance particulate materials, viscous sintering plays a crucial role, particularly in fields such as polymer processing and additive manuf…
A general thermodynamically consistent phase-field-micromechanics model of sintering with coupled diffusion and grain motion
Qingcheng Yang, Arkadz Kirshtein
Sintering is a pivotal technology for processing ceramic and metallic powders into solid objects. A profound understanding of microstructure evolution during sintering is essential…
ODEs and Mandatory Voting
Christoph Börgers, Natasa Dragovic, Anna Haensch +2
This paper presents mathematics relevant to the question whether voting should be mandatory. Assuming a static distribution of voters' political beliefs, we model how politicians m…
A particle method for continuous Hegselmann-Krause opinion dynamics
Bruce Boghosian, Christoph Börgers, Natasa Dragovic +2
We derive a differential-integral equation akin to the Hegselmann-Krause model of opinion dynamics, and propose a particle method for solving the equation. Numerical experiments de…
Analysis of the energy dissipation laws in multi-component phase field models
Arkadz Kirshtein, James Brannick, Chun Liu
In this paper, two approaches for modeling three-component fluid flows using diffusive interface method are discussed. Thermodynamic consistency of the proposed models is preserved…