Related papers: Equations of state for simple liquids from the Gau…
Droplets form a cornerstone of the spatiotemporal organization of biomolecules in cells. These droplets are controlled using physical processes like chemical reactions and imposed gradients, which are costly to simulate using traditional…
We analyze the Gaussian approximation as a method to obtain the first and second moments of a stochastic process described by a master equation. We justify the use of this approximation with ideas coming from van Kampen's expansion approach…
This work proposes a methodology to develop new numerical integration algorithms for ordinary differential equations based on state quantization, generalizing the notions of Linearly Implicit Quantized State Systems (LIQSS) methods. Using…
A new closed virial equation of state of hard-sphere fluids is proposed which reproduces the calculated or estimated values of the first sixteen virial coefficients at the same time as giving very good accuracy when compared with computer…
Quantum state smoothing is a technique for assigning a valid quantum state to a partially observed dynamical system, using measurement records both prior and posterior to an estimation time. We show that the technique is greatly simplified…
A numerical method using implicit surface representations is proposed to solve the linearized Poisson-Boltzmann equations that arise in mathematical models for the electrostatics of molecules in solvent. The proposed method used an implicit…
Suspensions with fiber-like particles in the low Reynolds number regime are modeled by two different approaches that both use a Lagrangian representation of individual particles. The first method is the well-established formulation based on…
We present two independent approaches for computing the thermodynamics for classical particles interacting via the Moser--Calogero potential. Combining the results we propose the form of equation of state or, what is equivalent, the…
In many situations, one can approximate the behavior of a quantum system, i.e. a wave function subject to a partial differential equation, by effective classical equations which are ordinary differential equations. A general method and…
We discuss a new version of a method for obtaining exact solutions of nonlinear partial differential equations. We call this method the Simple Equations Method (SEsM). The method is based on representation of the searched solution as…
The gauging of equations method, introduced in the preceding paper, is applied to the four-dimensional integral equations describing the strong interactions of three identical relativistic particles. In this way we obtain gauge invariant…
A new computational method is presented to resolve hydrodynamic interactions acting on solid particles immersed in incompressible host fluids. In this method, boundaries between solid particles and host fluids are replaced with a continuous…
We present a direct numerical simulation method for investigating the dynamics of dispersed particles in a compressible solvent fluid. The validity of the simulation is examined by calculating the velocity relaxation of an impulsively…
This paper is devoted to filtering, smoothing, and prediction of polynomial processes that are partially observed. These problems are known to allow for an explicit solution in the simpler case of linear Gaussian state space models. The key…
We introduce the ideal Gaussian glass-forming system as a model to describe the thermodynamics and dynamics of supercooled liquids on a local scale in terms of the properties of the potential energy landscape (PEL). The first ingredient is…
We discuss the viability of ensemble simulations of fluid flows on quantum computers. The basic idea is to formulate a functional Liouville equation for the probability distribution of the flow field configuration and recognize that, due to…
We derive a hierarchy of equations which allow a general $n$-body distribution function to be measured by test-particle insertion of between $1$ and $n$ particles, and successfully apply it to measure the pair and three-body distribution…
This paper proposes a novel particle scheme that provides convergent approximations of a weak solution of the Navier-Stokes equations for the 1-D flow of a viscous compressible fluid. Moreover, it is shown that all differential inequalities…
A statistical method for calculating equilibrium solutions of the shallow water equations, a model of essentially 2-d fluid flow with a free surface, is described. The model contains a competing acoustic turbulent {\it direct} energy…
A new theory on gas-liquid phase transition is given. The new idea is that the total intermolecular potential energy for a classical system in equilibrium is relative with the average distance of molecules. A new space homogeneity…