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Scalar-tensor theories are one of the most natural and well-constrained alternative theories of gravity, while still allowing for significant deviations from general relativity. We present the equations of motion of nonspinning compact…
We describe a method to perform functional operations on probability distributions of random variables. The method uses reproducing kernel Hilbert space representations of probability distributions, and it is applicable to all operations…
This paper presents a method for the accurate and efficient computations on scalar, vector and tensor fields in three-dimensional spherical polar coordinates. The methods uses spin-weighted spherical harmonics in the angular directions and…
Scale-space energy density function, $E(\mathbf{x}, \mathbf{r})$, is defined as the derivative of the two-point velocity correlation. The function E describes the turbulent kinetic energy density of scale r at a location x and can be…
A collisional model of a confined quasi-two-dimensional granular mixture is considered to analyze homogeneous steady states. The model includes an effective mechanism to transfer the kinetic energy injected by vibration in the vertical…
We propose a variational framework for nonequilibrium thermodynamics built around the effective number of accessible state, a multiplicative count that ranges from for a uniform distribution to one under complete localization, and whose…
This work concerns the numerical approximation with a finite volume method of inviscid, nonequilibrium, high-temperature flows in multiple space dimensions. It is devoted to the analysis of the numerical scheme for the approximation of the…
Identification of nonlinear dynamical systems is crucial across various fields, facilitating tasks such as control, prediction, optimization, and fault detection. Many applications require methods capable of handling complex systems while…
We calculate ground-state energies and densities of a helium atom confined in an impenetrable spherical box within density functional theory. These calculations are performed by variationally solving Kohn-Sham equation with the ground-state…
This work presents a novel formulation and numerical strategy for the simulation of geometrically nonlinear structures. First, a non-canonical Hamiltonian (Poisson) formulation is introduced by including the dynamics of the stress tensor.…
In this paper, we investigate the dynamics of radial solutions at threshold energy for a 3-component Schr\"{o}dinger system with cubic nonlinearity in four dimensions. The main difference from the cases previously addressed in the…
We study the construction of analytical non-radially solutions for the 1-dimensional compressible adiabatic Euler equations in this article. We could design the perturbational method to construct a new class of analytical solutions. In…
In this work, we propose a method for calculating the free energy of anisotropic quantum spin systems. We use the Hubbard-Stratonovich transformation to express the partition function of a generic bilinear super-exchange Hamiltonian in…
We present a quantum solver for partial differential equations based on a flexible matrix product operator representation. Utilizing mid-circuit measurements and a state-dependent norm correction, this scheme overcomes the restriction of…
In this paper, we consider nonlinear PDEs in a port-Hamiltonian setting based on an underlying jet-bundle structure. We restrict ourselves to systems with 1-dimensional spatial domain and 2nd-order Hamiltonian including certain dissipation…
We calculated the total energy of a semiconductor quantum dot which is defined by the trench gate method. In our calculation we used a recently developed energy functional called ``orbital-free energy functional". We compared the total…
Nonlinear behavior of electro-osmosis in dilute non-adsorbing polymer solutions with low salinity is investigated with Brownian dynamics simulations and a kinetic theory. In the Brownian simulations, the hydrodynamic interaction between the…
We study nonlinear hyperbolic conservation laws with non-convex flux in one space dimension and, for a broad class of numerical methods based on summation by parts operators, we compute numerically the kinetic functions associated with each…
This work proposes a novel numerical scheme for solving the high-dimensional Hamilton-Jacobi-Bellman equation with a functional hierarchical tensor ansatz. We consider the setting of stochastic control, whereby one applies control to a…
Nonlinearities in piezoelectric systems can arise from internal factors such as nonlinear constitutive laws or external factors like realizations of boundary conditions. It can be difficult or even impossible to derive detailed models from…