Related papers: Improved first order mean spherical approximation …
An approximation within Wertheim's second order perturbation theory is proposed which allows for the development of a general solution for pure component fluids with an arbitrary number and functionality of association sites. The solution…
Algorithms based on normalizing flows are emerging as promising machine learning approaches to sampling complicated probability distributions in a way that can be made asymptotically exact. In the context of lattice field theory,…
We develop a maximum relative entropy formalism to generate optimal approximations to probability distributions. The central results consist in (a) justifying the use of relative entropy as the uniquely natural criterion to select a…
We solve the Einstein constraint equations for a first-order causal viscous relativistic hydrodynamic theory in the case of a conformal fluid. For such a theory, a direct application of the conformal method does not lead to a decoupling of…
A simple practical approach to describe transverse (shear) waves in strongly-coupled Yukawa fluids is presented. Theoretical dispersion curves, based on hydrodynamic consideration, are shown to compare favorably with existing numerical…
Structural and thermodynamic properties of multicomponent hard-sphere fluids at odd dimensions have recently been derived in the framework of the rational function approximation (RFA) [Rohrmann and Santos, Phys. Rev. E \textbf{83}, 011201…
We propose a deep learning approach to the obstacle problem inspired by the first-order system least-squares (FOSLS) framework. This method reformulates the problem as a convex minimization task; by simultaneously approximating the…
This thesis explores the evolution of liquid-state theories based on the Ornstein-Zernike (OZ) equation, summarizing the foundational methods developed by Baxter, Lebowitz, Wertheim, and others. A unifying feature of these approaches is…
We devise a simplified parameter estimator for a second order stochastic differential equation by a first order system based on the Smoluchowski-Kramers approximation. We establish the consistency of the estimator by using…
We introduce a simple and efficient numerical method to compute mean curvature flow with obstacles. The method augments the Merrimam-Bence-Osher scheme with a pointwise update that enforces the constraint and therefore retains the…
The first well founded perturbation theory for classical solid systems is presented. Theoretical approaches to thermodynamic and structural properties of the hard-sphere solid provide us with the reference system. The traditional…
This paper concerns quasi-stochastic approximation (QSA) to solve root finding problems commonly found in applications to optimization and reinforcement learning. The general constant gain algorithm may be expressed as the…
The swimming of a deformable uniform sphere is studied in second order perturbation theory in the amplitude of the stroke. The effect of the first order reaction force on the first order center of mass velocity is calculated in linear…
The Self-Consistent Ornstein-Zernike Approximation (SCOZA) is an accurate liquid state theory. So far it has been tied to interactions composed of hard core repulsion and long-range attraction, whereas real molecules have soft core…
The Ornstein-Zernike equation is solved for the hard-sphere and square-well fluids using a diverse selection of closure relations; the attraction range of the square-well is chosen to be $\lambda=1.5.$ In particular, for both fluids we…
We calculate the shear relaxation times in four important simple monatomic model fluids: Lennard-Jones, Yukawa, soft-sphere and hard-sphere fluids. It is observed that in properly reduced units, the shear relaxation times exhibit…
Itinerant ferromagnetism in dilute Fermi gases is predicted to emerge at values of the gas parameter where second-order perturbation theory is not accurate enough to properly describe the system. We have revisited perturbation theory for…
Solving Fredholm equations of the first kind is crucial in many areas of the applied sciences. In this work we adopt a probabilistic and variational point of view by considering a minimization problem in the space of probability measures…
A mean-field approach (MFA) is proposed for the analysis of orientational order in a two-dimensional system of stochastic self-propelled particles interacting by local velocity alignment mechanism. The treatment is applied to the cases of…
We study several aspects of the recently introduced fixed-phase spin-orbit diffusion Monte Carlo (FPSODMC) method, in particular, its relation to the fixed-node method and its potential use as a general approach for electronic structure…