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Inspired by some recent molecular dynamics (MD) simulations and experiments on suspended graphene nanoribbons, we study a simplified model where the atoms are disposed in a rectangular lattice coupled by nearest neighbor interactions which…
We use quantum kinetic theory to calculate the thermoelectric transport properties of the 2D single band Fermi-Hubbard model in the weak coupling limit. For generic filling, we find that the high-temperature limiting behaviors of the…
Harnessing the nonlinear response of a medium is essential for applications including frequency conversion and light amplification, as well as for the generation of quantum many-body correlations of light or matter. However, achieving these…
We present a comprehensive analytical study of radiative transfer using the method of moments and include the effects of non-isotropic scattering in the coherent limit. Within this unified formalism, we derive the governing equations and…
In this work we present two new closures for the spherical harmonics (PN) method in slab geometry transport problems. Our approach begins with an analysis of the squared-residual of the transport equation where we show that the standard…
This paper is devoted to deal with some mathematical and numerical aspects of the radiative integral transfer equations. First, the properties of the raidative integral operators are analyzed. Based on these results, the existence and…
A data-driven projection-based reduced-order model (ROM) for nonlinear thermal radiative transfer (TRT) problems is presented. The TRT ROM is formulated by (i) a hierarchy of low-order quasidiffusion (aka variable Eddington factor)…
Singularly perturbed dynamical systems play a crucial role in climate dynamics and plasma physics. A powerful and well-known tool to address these systems is the Fenichel normal form, which significantly simplifies fast dynamics near slow…
A direct numerical solution of the radiative transfer equation or any kinetic equation is typically expensive, since the radiative intensity depends on time, space and direction. An expansion in the direction variables yields an equivalent…
Periodically driven coherent conductors provide a universal platform for the development of quantum transport devices. Here, we lay down a comprehensive theory to describe the thermodynamics of these systems. We first focus on moderate…
This study investigates numerical methods to solve nonlinear transport problems characterized by various sorption isotherms with a focus on the Freundlich type of isotherms. We describe and compare second order accurate numerical schemes,…
In isolated nonlinear optical waveguide arrays with bounded energy spectrum, simultaneous conservation of energy and power of the optical modes enables study of coupled thermal and particle transport in the negative temperature regime.…
Deep learning algorithms provide a new paradigm to study high-dimensional dynamical behaviors, such as those in fusion plasma systems. Development of novel model reduction methods, coupled with detection of abnormal modes with plasma…
Governing equations are essential to the study of nonlinear dynamics, often enabling the prediction of previously unseen behaviors as well as the inclusion into control strategies. The discovery of governing equations from data thus has the…
While the thermodynamics for bosonic systems with weak $s$-wave interactions has been known for decades, a general and systematic extension to higher partial waves has not yet been reported. We provide closed-form expressions for the…
We propose an approach to the problem of low but finite temperature dynamical correlation functions in integrable one-dimensional models with a spectral gap. The approach is based on the analysis of the leading singularities of the operator…
Discovering the governing equations of a dynamical system from observed trajectories provides deeper insight into its structure than mere prediction of future states. We present a data-driven approach to model discovery based on…
A new approach to prove the one-dimensional Cauchy problem's weakly discontinuous solutions for hyperbolic PDEs are on the characteristics is discussed in this paper. To do so, I use wavelet singularity detection methods or WTMM [1] based…
Thermal radiative transfer (TRT) is an essential piece of physics in inertial confinement fusion, high-energy density physics, astrophysics etc. The physical models of this type of problem are defined by strongly coupled differential…
In this paper we discuss the properties of the reduced density matrix of quantum many body systems with permutational symmetry and present basic quantification of the entanglement in terms of the von Neumann (VNE), Renyi and Tsallis…