Related papers: Eshelby's method for unidirectional periodic compo…
We developed a micromagnetic method for modeling magnetic systems with periodic boundary conditions along an arbitrary number of dimensions. The main feature is an adaptation of the Ewald summation technique for evaluation of long-range…
The bispectral anti-isomorphism is applied to differential operators involving elements of the stabilizer ring to produce explicit formulas for all difference operators having any of the Hermite exceptional orthogonal polynomials as…
A mapping technique is used to derive in the context of constituent quark models effective Hamiltonians that involve explicit hadron degrees of freedom. The technique is based on the ideas of mapping between physical and ideal Fock spaces…
Thermal transport in condensed matter systems is traditionally formulated as a response to a background gravitational field. In this work, we seek a twisted-boundary-condition formalism for thermal transport in analogy to the $U(1)$ twisted…
This work presents a generalized boundary integral method for elliptic equations on surfaces, encompassing both boundary value and interface problems. The method is kernel-free, implying that the explicit analytical expression of the kernel…
Boundary integral equations lead to dense system matrices when discretized, yet they are data-sparse. Using the $\mathcal{H}$-matrix format, this sparsity is exploited to achieve $\mathcal{O}(N\log N)$ complexity for storage and…
A lack of regularity in the solution of the porous medium equation poses a serious challenge in its theoretical and numerical studies. A common strategy in theoretical studies is to utilize the pressure formulation of the equation where a…
The introduction of the infinite boundary terms and the pairwise interactions [J. Chem. Theory Comput., 10, 5254, (2014)] enables a physically intuitive approach for deriving electrostatic energy and pressure for both neutral and…
Surface-bound modes in metamaterials forged by drilling periodic hole arrays in perfect-conductor surfaces are investigated by means of both analytical techniques and rigorous numerical solution of Maxwell's equations. It is shown that…
This paper proposes a new method, in the frequency domain, to define absorbing boundary conditions for general two-dimensional problems. The main feature of the method is that it can obtain boundary conditions from the discretized equations…
Integration operational matrix methods based on Zernike polynomials are used to determine approximate solutions of a class of non-homogeneous partial differential equations (PDEs) of first and second order. Due to the nature of the Zernike…
This paper is part of a series developing $C^0$ finite element methods for fourth-order elliptic equations on polygonal domains. Here, we investigate how boundary conditions influence the design of effective $C^0$ schemes, specifically…
We study the entanglement Hamiltonian for free-fermion chains with a particular form of inhomogeneity. The hopping amplitudes and chemical potentials are chosen such that the single-particle eigenstates are related to discrete orthogonal…
The singularities that arise in elliptic boundary value problems are treated locally by a singular function boundary integral method. This method extracts the leading singular coefficients from a series expansion that describes the local…
We study some convergence issues for a recent approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains. The approach is based on the minimization on an integral functional which arises from…
We summarise three applications of the obstacle problem to membrane contact, elastoplastic torsion and cavitation modelling, and show how the resulting models can be solved using mixed finite elements. It is challenging to construct fixed…
For an efficient implementation of Buchberger's Algorithm, it is essential to avoid the treatment of as many unnecessary critical pairs or obstructions as possible. In the case of the commutative polynomial ring, this is achieved by the…
Ultracold quantum-gas mixtures of fermionic atoms with resonant control of interactions offer a unique test-bed to explore few- and many-body quantum states with unconventional properties. The emergence of such strongly correlated systems,…
We propose an open-boundary molecular dynamics method in which an atomistic system is in contact with an infinite particle reservoir at constant temperature, volume and chemical potential. In practice, following the Hamiltonian adaptive…
We develop a method of an asymptotically exact treatment of threshold singularities in dynamic response functions of gapless integrable models. The method utilizes the integrability to recast the original problem in terms of the low-energy…