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This paper introduces a modeling framework that is suitable to resolve singularities of impact phenomena encountered in applications. The method involves an exact transformation that turns the continuum, often partial differential equation…
In this article we propose and numerically implement a mathematical model for the simulation of three-dimensional semiconductor devices characterized by an heterogeneous material structure. The model consists of a system of nonlinearly…
This paper concerns with the heat equation in the half-space $\mathbb{R}_{+}^{n}$ with nonlinearity and singular potential on the boundary $\partial\mathbb{R}_{+}^{n}$. We develop a well-posedness theory (without using Kato and Hardy…
In this paper an asymptotic homogenization method for the analysis of composite materials with periodic microstructure in presence of thermodiffusion is described. Appropriate down-scaling relations correlating the microscopic fields to the…
A novel finite element method (FEM) is developed to study mechanical response of axons embedded in extra cellular matrix (ECM) when subjected to harmonic uniaxial stretch under purely non-affine kinematic boundary conditions. The proposed…
This work studies the approximation of plane problems concerning transversely isotropic elasticity, using a low-order Virtual Element Method (VEM), with a focus on near-incompressibility and near-inextensibility. Additionally, both…
Exploring the bulk-boundary correspondences and the boundary-induced phenomena in the strongly-correlated quantum systems belongs to the most fundamental topics of condensed matter physics. In this work, we study the bulk-boundary…
Electric, thermal and thermoelectric transport in correlated electron systems probe different aspects of the many-body dynamics, and thus provide complementary information. These are well studied in the low- and high-temperature limits,…
We consider variational problems that model the bending behavior of curves that are constrained to belong to given hypersurfaces. Finite element discretizations of corresponding functionals are justified rigorously via Gamma-convergence.…
Elliptic partial differential equations arise in many fields of science and engineering such as steady state distribution of heat, fluid dynamics, structural/mechanical engineering, aerospace engineering and seismology etc. In three…
A spectral formulation of the plane-strain boundary integral equations for an interface between dissimilar elastic solids is presented. The boundary integral equations can be written in two equivalent forms: (a) The tractions can be written…
The magnetic and entanglement thermal (equilibrium) properties in spin-1/2 Ising-Heisenberg model on a triangulated Kagome lattice are analyzed by means of variational mean-field like treatment based on Gibbs-Bogoliubov inequality. Because…
An efficient procedure using a novel semi-analytical forward solver for identifying heterogeneous and anisotropic elastic parameters from only one full-field measurement is proposed and explored. We formulate the inverse problem as an…
The hidden Bose-Einstein singularities of correlated electron systems, whose possible existence has been pointed out in a previous paper based on quantum field theory of ordered phases [T. Kita, J. Phys. Soc. Jpn. {\bf 93}, 124704 (2024)],…
A finite element based computational scheme is developed and employed to assess a duality based variational approach to the solution of the linear heat and transport PDE in one space dimension and time, and the nonlinear system of ODEs of…
We extend to incremental thermoelectroelasticity with biasing fields certain classical theorems, that have been stated and proved in linear thermopiezoelectricity referred to a natural configuration. A uniqueness theorem for the solutions…
On the basis of the balance equations for energy-momentum, spin, particle and entropy density, an approach is considered which represents a comparatively general framework for special- and general-relativistic continuum thermodynamics. In…
In this paper, we investigate a transmission eigenvalue problem that couples the principles of acoustics and elasticity. This problem naturally arises when studying fluid-solid interactions and constructing bubbly-elastic structures to…
This work presents a comparative review and classification between some well-known thermodynamically consistent models of hydrogel behavior in a large deformation setting, specifically focusing on solvent absorption/desorption and its…
Alternative approach for description of the non-equilibrium phenomena arising in solids at a severe external loading is analyzed. The approach is based on the new form of kinetic equations in terms of the internal and modified free energy.…