Related papers: Basis-Independent Spectral Methods for Non-linear …
A geometry-independent effective model for the contact self-energies is proposed to calculate the quantum conductance of patterned graphene devices using Green's functions. A Corbino disk, being the simplest device where the contacts can…
In this paper the authors study a non-linear elliptic-parabolic system, which is motivated by mathematical models for lithium-ion batteries. One state satisfies a parabolic reaction diffusion equation and the other one an elliptic equation.…
We present a framework to calculate the anisotropic and non-linear photoconductivity for two band systems with application to graphene. In contrast to the usual perturbative (second order in the optical field strength) techniques, we…
We show how spectral submanifold theory can be used to construct reduced-order models for harmonically excited mechanical systems with internal resonances. Efficient calculations of periodic and quasi-periodic responses with the…
We study thermodynamical formalism of a discrete nonautonomous dynamical system determined by a sequence of continuous self-maps of a compact metric space. Using the methods of Convex Analysis we get variational principles for pressure…
In this article, we consider the problem of testing whether two latent position random graphs are correlated. We propose a test statistic based on the kernel method and introduce the estimation procedure based on the spectral decomposition…
Accurate modeling of electronic properties of nanostructures is a challenging theoretical problem. Methods making use of continuous media approximation, such as k.p, sometimes struggle to reproduce results obtained with more accurate…
A density-matrix formalism within the length gauge is developed to calculate the nonlinear response of both doped and undoped biased bilayer graphene (BBLG) at terahertz frequencies. Employing a tight-binding model, we derive an effective…
The development of inverse design, where computational optimization techniques are used to design devices based on certain specifications, has led to the discovery of many compact, non-intuitive structures with superior performance. Among…
We present a tight-binding parametrization for penta-graphene that correctly describes its electronic band structure and linear optical response. The set of parameters is validated by comparing to ab-initio density functional theory…
We introduce a data-based approach to estimating key quantities which arise in the study of nonlinear control systems and random nonlinear dynamical systems. Our approach hinges on the observation that much of the existing linear theory may…
Starting from exact eigenstates for a symmetric ring, we derive a low-energy effective generalized Anderson Hamiltonian which contains two spin doublets with opposite momenta and a singlet for the neutral molecule. For benzene, the singlet…
We propose a novel periodicity-free unfolding method of the electronic energy spectra. Our new method solves a serious problem that calculated electronic band structure strongly depends on the choice of the simulation cell, i.e.,…
We introduce a meshless method for solving both continuous and discrete variational formulations of a volume constrained, nonlocal diffusion problem. We use the discrete solution to approximate the continuous solution. Our method is…
We apply a recently developed technique utilizing machine learning for statistical analysis of computational nitrogen K-edge spectra of aqueous triglycine. This method, the emulator-based component analysis, identifies spectrally relevant…
This thesis is devoted to ab initio calculations of ground and excited state properties of different systems within density functional theory and time dependent density functional theory. From the numerical point of view we implemented an…
Spectral methods have greatly advanced the estimation of latent variable models, generating a sequence of novel and efficient algorithms with strong theoretical guarantees. However, current spectral algorithms are largely restricted to…
This paper considers the numerical solution of Timoshenko beam network models, comprised of Timoshenko beam equations on each edge of the network, which are coupled at the nodes of the network using rigid joint conditions. Through…
Biased bilayer graphene (BBG) is an important system for studies of excitonic effects in graphene--based systems, with its easily tunable bandgap. This bandgap is governed by an external gate voltage, allowing one to tune the optical…
The synthesis of robust invariant sets for nonlinear systems has traditionally been hindered by the inherent non convexity and a strict reliance on exact analytical models. This paper presents a purely data-driven framework to compute…