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Fractional differential calculus is a mathematical tool that has found applications in the study of social and physical behaviors considered ``anomalous''. It is often used when traditional integer derivatives models fail to represent cases…
A new method is proposed for constructing energy density functionals, which include a nonlocal dependence on the density gradients. This method is used to construct functionals for kinetic energy, which is a nonlocal generalization of the…
We present an accurate and efficient formulation of the stress tensor for real-space Kohn-Sham Density Functional Theory (DFT) calculations. Specifically, while employing a local formulation of the electrostatics, we derive a linear-scaling…
We introduce an algorithmic framework based on tensor networks for computing fluid flows around immersed objects in curvilinear coordinates. We show that the tensor network simulations can be carried out solely using highly compressed…
Within exact electron density-functional theory, we investigate Kohn-Sham (KS) potentials, orbital energies, and non-interacting kinetic energies of the fractional ions of Li, C and F. We use quantum Monte Carlo densities as input, which…
In this paper we present a numerical scheme for nonlinear continuity equations, which is based on the gradient flow formulation of an energy functional with respect to the quadratic transportation distance. It can be applied to a large…
To simulate plasma phenomena, large-scale computational resources have been employed in developing high-precision and high-resolution plasma simulations. One of the main obstacles in plasma simulations is the requirement of computational…
The nonequilibrium Green's function formalism provides a versatile and powerful framework for numerical studies of nonequilibrium phenomena in correlated many-body systems. For calculations starting from an equilibrium initial state, a…
We have derived several relations, which allow the evaluation of the system free energy changes in the leading order in $\hbar^{2}$ along classically generated trajectories. The results are formulated in terms of purely classical…
We introduce a novel energy functional for ground-state electronic-structure calculations. Its fundamental variables are the natural spin-orbitals of the implied singlet many-body wave function and their joint occupation probabilities. The…
In this work we construct a bottom-up reconstruction technique for Loop Quantum Cosmology scalar-tensor theories, from the observational indices. Particularly, the reconstruction technique is based on fixing the functional form of the…
Stochastic dynamics in the energy representation is employed as a method to study non-equilibrium Brownian-like systems. It is shown that the equation of motion for the energy of such systems can be taken in the form of the Langevin…
Nonlinear thermoelastic systems play a crucial role in understanding thermal conductivity, stresses, elasticity, and temperature interactions. This research focuses on finding solutions to these systems in their fractional forms, which is a…
In this paper, nonlinear model reduction for power systems is performed by the balancing of empirical controllability and observability covariances that are calculated around the operating region. Unlike existing model reduction methods,…
We construct new solvable rational and trigonometric spin models with near-neighbors interactions by an extension of the Dunkl operator formalism. In the trigonometric case we obtain a finite number of energy levels in the center of mass…
In this paper, we consider the nonparametric estimation problem of the drift function of stochastic differential equations driven by $\alpha$-stable L\'{e}vy motion. First, the Kullback-Leibler divergence between the path probabilities of…
This paper proposes methods for reachability analysis of nonlinear systems in both open loop and closed loop with advanced controllers. The methods combine hybrid zonotopes, a construct called a state-update set, functional decomposition,…
The rich and diverse dynamics of particle-based systems ultimately originates from the coupling of their degrees of freedom via internal interactions. To arrive at a tractable approximation of such many-body problems, coarse-graining is…
We apply a variant of the Nose-Hoover thermostat to derive the Hamiltonian of a nonextensive system that is compatible with the canonical ensemble of the generalized thermostatistics of Tsallis. This microdynamical approach provides a…
The paper deals with numerical discretizations of separable nonlinear Hamiltonian systems with additive noise. For such problems, the expected value of the total energy, along the exact solution, drifts linearly with time. We present and…