Related papers: Scalable Computation of $\mathcal{H}_\infty$ Energ…
In this manuscript, we propose an efficient, practical and easy-to-implement way to approximate actions of $\varphi$-functions for matrices with $d$-dimensional Kronecker sum structure in the context of exponential integrators up to second…
The theory of string-like continuous curves and discrete chains have numerous important physical applications. Here we develop a general geometrical approach, to systematically derive Hamiltonian energy functions for these objects. In the…
Total energy electronic structure calculations, based on density functional theory or on the more empirical tight binding approach, are generally believed to scale as the cube of the number of electrons. By using the localisaton property of…
The method of many-body Green's functions is developed for arbitrary systems of electrons and nuclei starting from the full (beyond Born-Oppenheimer) Hamiltonian of Coulomb interactions and kinetic energies. The theory presented here…
We study the loop $O(n)$ model on the honeycomb lattice. By means of local non-planar deformations of the lattice, we construct a discrete stress-energy tensor. For $n\in [0,2]$, it gives a new observable satisfying a part of Cauchy-Riemann…
We present an energy scaling function to predict, in a specific range, the energy of bosonic trimers with large scattering lengths and finite range interactions, which is validated by quantum Monte Carlo calculations using microscopic…
This paper presents a novel method to synthesize stochastic control Lyapunov functions for a class of nonlinear, stochastic control systems. In this work, the classical nonlinear Hamilton-Jacobi-Bellman partial differential equation is…
Among numerical methods for partial differential equations arising from steepest descent dynamics of energy functionals (e.g., Allen-Cahn and Cahn-Hilliard equations), the convex splitting method is well-known to maintain unconditional…
Using a formulation of quantum mechanics based on orthogonal polynomials in the energy and physical parameters, we present a method that gives the class of potential functions for exactly solvable problems corresponding to a given energy…
Energy functionals of the Green's function can simultaneously provide spectral and thermodynamic properties of interacting electrons' systems. Though powerful in principle, these formulations need to deal with dynamical…
The energy density method is generalized to include spin polarization with the full formalism derived based on spin-density functional theory, which aims at decomposing the total energy into well-defined atomic energies. The method involves…
In 2016, the spectral theory on the $S$-spectrum was used to establish the $H^\infty$-functional calculus for quaternionic or Clifford operators. This calculus applies for example to sectorial or bisectorial right linear operators $T$ and…
In analysis and control of large-scale nonlinear dynamical systems, a distributed approach is often an attractive option due to its computational tractability and usually low communication requirements. Success of the distributed control…
The probability distribution (PD) of spin configurations in kinetic Ising models has been cast in the form of the canonical Boltzmann PD with a time-dependent effective Hamiltonian (EH). It has been argued that in systems with extensive…
In this work we address partial wave decompositions of thermal one-point functions in conformal field theories on $S^1 \times S^{d-1}$. With the help of Casimir differential equations we develop efficient algorithms to compute the relevant…
This letter aims to derive the exact relativistic orbital-free kinetic energy density functional for one-particle nuclear systems in one-dimensional case. The kinetic energy is expressed as a functional of both vector and scalar densities.…
We derive thermodynamically consistent models of reaction-diffusion equations coupled to a heat equation. While the total energy is conserved, the total entropy serves as a driving functional such that the full coupled system is a gradient…
A method is presented for calculating binding energies and other properties of extended interacting systems using the projected density of transitions (PDoT) which is the probability distribution for transitions of different energies…
We present a proof for the existence and uniqueness of weak solutions for a cut-off and non cut-off model of non-linear diffusion equation in finite-dimensional space RD useful for modelling flows on porous medium with saturation, turbulent…
An explicitly orbital-dependent correlation energy functional is proposed, which is to be used in combination with the orbital-dependent exchange energy functional in energy-band calculations. It bears a close resemblance to the…