Related papers: A time-delay model for molecular gas flow into vac…
The modeling of multi-phase flow is very challenging, given the range of scales as well as the diversity of flow regimes that one encounters in this context. We revisit the discrete equation method (DEM) for two-phase flow in the absence of…
In the present paper we consider the problem of Laplace deconvolution with noisy discrete non-equally spaced observations on a finite time interval. We propose a new method for Laplace deconvolution which is based on expansions of the…
Recently, a morphological transition in the velocity distribution of a relativistic gas has been pointed out which shows hallmarks of a critical phenomenon. Here, we provide a general framework which allows for a thermodynamic approach to…
The intersection of machine learning and dynamical systems has generated considerable interest recently. Neural Ordinary Differential Equations (NODEs) represent a rich overlap between these fields. In this paper, we develop a continuous…
Accurate modeling of gas flow through porous media is critical for many technological applications, including reservoir performance prediction, carbon capture and sequestration, and fuel cells and batteries. However, such modeling remains…
We develop a backstepping-based observer design for a class of ODE - continuum-PDE cascade systems, which can be viewed as the limit, of a finite collection of ODE - $2 \times 2$ hyperbolic systems, as the number of individual PDE system…
Modeling of a dense spray regime using an Euler-Lagrange approach is challenging because of local high volume loading. A cluster of droplets, that are assumed subgrid, can lead to locally low void fractions for the fluid phase. Under these…
Within the framework of spatially covariant theories, we propose a general model for dark energy (DE) in which the cosmological background and perturbations are independently controlled by different sets of coefficients, and the equation of…
Coarse-grain Lagrangian methods, such as Dissipative Particle Dynamics ( Hoogerbrugge et al., EPL, 1992), are suitable for describing mesoscopic fluid systems that include thermal fluctuations. However, the realistic simulation of liquids…
Multicanonical ensemble simulations for the simulation of first-order phase transitions suffer from exponential slowing down. Monte Carlo autocorrelation times diverge exponentially with free energy barriers $\Delta F$, which in $L^d$ boxes…
The large time behavior of entropy solution to the compressible Euler equations for polytropic gas (the pressure $p(\rho)=\kappa\rho^{\gamma}, \gamma>1$) with time dependent damping like $-\frac{1}{(1+t)^\lambda}\rho u$ ($0<\lambda<1$) is…
This paper focuses on the derivation and simulation of mathematical models describing new plasma fraction in blood for patients undergoing simultaneous extracorporeal membrane oxygenation and therapeutic plasma exchange. Models for plasma…
Previous approaches of emergent thermalization for condensed matter based on typical wavefunctions are extended to generate an intrinsically quantum theory of gases. Gases are fundamentally quantum objects at all temperatures, by virtue of…
Discrete particle simulation, a combined approach of computational fluid dynamics and discrete methods such as DEM (Discrete Element Method), DSMC (Direct Simulation Monte Carlo), SPH (Smoothed Particle Hydrodynamics), PIC…
This work concerns the internal stabilization of underactuated linear systems of $m$ heat equations in cascade, where the control is placed internally in the first equation only and the diffusion coefficients are distinct. Combining the…
This paper develops an explicit spectral representation for solutions of a one-dimensional linear wave equation with a constant time delay. The model is considered on a bounded interval with non-homogeneous Dirichlet boundary data and a…
In this work, we establish the response of scalar systems with multiple discrete delays based on the Laplace transform. The time response function is expressed as the sum of infinite series of exponentials acting on eigenvalues inside…
An implicit scheme for steady state solutions of diatomic gas flow is presented. The method solves the Rykov model equation in the finite volume discrete velocity method (DVM) framework, in which the translational and rotational degrees of…
An important class of spatio-temporal models is constructed by leveraging the hierarchical structure of dynamical (or, state-space) models. This paper proposes a new statistical dynamical model for spatio-temporal processes motivated by…
In the present manuscript we consider the Boltzmann equation that models a polyatomic gas by introducing one additional continuous variable, referred to as microscopic internal energy. We establish existence and uniqueness theory in the…