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The Direct Simulation Monte Carlo (DSMC) method was widely used to simulate low density gas flows with large Knudsen numbers. However, DSMC encounters limitations in the regime of lower Knudsen numbers (Kn<0.1). In such cases, approaches…
We present a dynamic van der Waals theory. It is useful to study phase separation when the temperature varies in space. We show that if heat flow is applied to liquid suspending a gas droplet at zero gravity, a convective flow occurs such…
Convex relaxations of the power flow equations and, in particular, the Semi-Definite Programming (SDP), Second-Order Cone (SOC), and Convex DistFlow (CDF) relaxations, have attracted significant interest in recent years. Thus far, studies…
Direct numerical simulations (DNS) of microscale fluid-structure interactions (mFSI) in multicomponent multiphase flows pose many challenges, including the thermodynamic consistency of multiphysics couplings, tracking of moving interfaces,…
In this paper we consider the problem of analyzing the effect a change in the load vector can have on the optimal power generation in a DC power flow model. The methodology is based upon the recently introduced concept of the…
The dielectric function is one of the most important quantities that describes the electrical and optical properties of solids. Accurate modeling of the frequency-dependent dielectric function has great significance in the study of the…
The theoretical description of sparse matter attracts much interest, in particular for those ground-state properties that can be described by density functional theory (DFT). One proposed approach, the van der Waals density functional…
Using classical density functional theory (DFT) in a modified mean-field approximation we investigate the fluid phase behavior of quasi-two dimensional dipolar fluids confined to a plane. The particles carry three-dimensional dipole moments…
Optimal Power Flow (OPF) is a fundamental problem in power systems. It is computationally challenging and a recent line of research has proposed the use of Deep Neural Networks (DNNs) to find OPF approximations at vastly reduced runtimes…
The non-local van der Waals density functional (vdW-DF) of Dion et al. [Phys. Rev. Lett. 92, 246401 (2004)] is a very promising scheme for the efficient treatment of dispersion bonded systems. We show here that the accuracy of vdW-DF can be…
Neural operators have gained recognition as potent tools for learning solutions of a family of partial differential equations. The state-of-the-art neural operators excel at approximating the functional relationship between input functions…
Optimal power flow (OPF) is an important tool for Independent System Operators (ISOs) to deal with the power generation management. With the increasing penetration of renewable energy into power grids, challenges arise in tackling the OPF…
Compressible interfacial multiphase flows (CIMF) are essential to different applications, such as liquid fuel injection in supersonic propulsion systems. Since high-level details in CIMF are often difficult to measure in experiments,…
We propose a methodology to infer collision operators from phase space data of plasma dynamics. Our approach combines a differentiable kinetic simulator, whose core component in this work is a differentiable Fokker-Planck solver, with a…
A density functional theory (DFT) that accounts for van der Waals (vdW) interactions in condensed matter, materials physics, chemistry, and biology is reviewed. The insights that led to the construction of the Rutgers-Chalmers van der Waals…
We discuss an active phase field crystal (PFC) model that describes a mixture of active and passive particles. First, a microscopic derivation from dynamical density functional theory (DDFT) is presented that includes a systematic treatment…
DFT is a valuable tool for calculating adsorption energies toward designing materials for hydrogen storage. However, dispersion forces being absent from the theory, it remains unclear how the consideration of van der Waals (vdW)…
The rapidly advancing field of Fluid Mechanics has recently employed Deep Learning to solve various problems within that field. In that same spirit we try to perform Direct Numerical Simulation(DNS) which is one of the tasks in…
In conventional spectral/finite element methods, the triangulation/quadrilateralization of the domain produces many interior edges which require additional DOF. What if we could directly use the original hull without going to…
Classical density functional theory (cDFT) provides a systematic approach to predict the structure and thermodynamic properties of chemical systems through the single-molecule density profiles. Whereas the statistical-mechanical framework…