Related papers: On parameterized nonlocal-fractional transmission …
We discuss computational and qualitative aspects of the fractional Plateau and the prescribed fractional mean curvature problems on bounded domains subject to exterior data being a subgraph. We recast these problems in terms of energy…
We consider a diffusion process with coefficients that are periodic outside of an "interface region" of finite thickness. The question investigated in this article is the limiting long time/large scale behavior of such a process under…
Nonlocal gradient operators are basic elements of nonlocal vector calculus that play important roles in nonlocal modeling and analysis. In this work, we extend earlier analysis on nonlocal gradient operators. In particular, we study a…
In this research, we investigate in-depth the nonlinear energy transmission phenomenon in a metastable modular metastructure and develop efficient tools for the design of such systems. Previous studies on a one-dimensional (1D)…
We derive novel algorithms for optimization problems constrained by partial differential equations describing multiscale particle dynamics, including non-local integral terms representing interactions between particles. In particular, we…
Parametric correlations are studied in several classes of covariant density functional theories (CDFTs) using a statistical analysis in a large parameter hyperspace. In the present manuscript, we investigate such correlations for two…
Numerical resolution of exterior Helmholtz problems requires some approach to domain truncation. As an alternative to approximate nonreflecting boundary conditions and invocation of the Dirichlet-to-Neumann map, we introduce a new, nonlocal…
In this paper the study of a non-local Cahn-Hilliard-type singularly perturbed family of functionals is undertaken, generalizing known results by Alberti & Bellettini. The kernels considered include those leading to Gagliardo seminorms for…
The in silico simulations are widely used in contemporary systems biology including the analysis of nerve pulse propagation. As known from numerous experiments, the propagation of an action potential is accompanied by mechanical and thermal…
We explore an autonomous system analysis of dark energy models with interactions between dark energy and cold dark matter in a general systematic approach to cosmological fluids. We investigate two types of models such as local and…
We introduce a class of partial differential equations on metric graphs associated with mixed evolution: on some edges we consider diffusion processes, on other ones transport phenomena. This yields a system of equations with possibly…
The fiber bundle model is essentially an array of elements that break when sufficient load is applied on them. With a local loading mechanism, this can serve as a model for a one-dimensional interface separating the broken and unbroken…
We present the most general parametrisation of models of dark energy in the form of a scalar field which is explicitly coupled to dark matter. We follow and extend the Parameterized Post-Friedmannian approach, previously applied to modified…
We analyze the energetics of domains and interfaces in the presence of quenched random fields, particularly at the lower critical dimension of the random field Ising model. The relevance of this study to experiments is also discussed.
A class of parameter dependent Chen--Fliess series is introduced where the series coefficients are taken from a noncommutative ring of multivariable differential operators. Such series are shown in the linear case to represent formal…
In the present paper new insights into the study of the Non-central Dirichlet distribution are provided. This latter is the analogue of the Dirichlet distribution obtained by replacing the Chi-Squared random variables involved in its…
A classical pseudodifferential operator $P$ on $R^n$ satisfies the $\mu$-transmission condition relative to a smooth open subset $\Omega $, when the symbol terms have a certain twisted parity on the normal to $\partial\Omega $. As shown…
We introduce the geometric structure underlying the port-Hamiltonian models for distributed parameter systems exhibiting moving material domains.
We analyze a nonlocal coupled system arising as the Euler--Lagrange equations of an energy functional involving regional fractional Laplacians of orders $s_1$ and $s_2$ ($ 0 < s_1,s_2 < 1$), each acting on a separate disjoint domain and…
We present control-oriented models for transient dynamics of isothermal one-dimensional gas flow through multiple pipes in series and intersecting pipe geometries. These composite models subsume algebraic constraints that would otherwise…