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We study the statistical mechanics of supercooled liquids when the system evolves at a temperature $T$ with a field $\epsilon$ linearly coupled to its overlap with a reference configuration of the same liquid sampled at a temperature $T_0$.…
We introduce a model of attractive penetrable spheres by adding a short range attractive square well outside a penetrable core, and we provide a detailed analysis of structural and thermodynamical properties in one dimension using the exact…
I evaluate the thermodynamic curvature $R$ for fourteen pure fluids along their liquid-vapor coexistence curves, from the critical point to the triple point, using thermodynamic input from the NIST Chemistry WebBook. In this broad overview,…
The supercritical state of matter is usually described as a continuous phase without sharp boundaries between liquid and gas regions. However, under non-equilibrium conditions, this view breaks down. Here we report an experimental…
In this article, we review the progress made on the statistical mechanics of liquids and fluids embedded in curved space. Our main focus will be on two-dimensional manifolds of constant nonzero curvature and on the influence of the latter…
Two-dimensional superconductivity has become a major frontier in condensed matter physics. It holds the key to the mechanism of high-temperature superconductors and offers an exceptional arena to stabilize emergent quantum states enabled by…
We apply a hybrid Molecular Dynamics and mesoscopic simulation technique to study the dynamics of two dimensional colloidal discs in confined geometries. We calculate the velocity autocorrelation functions, and observe the predicted…
Self similarity allows for analytic or semi-analytic solutions to many hydrodynamics problems. Most of these solutions are one dimensional. Using linear perturbation theory, expanded around such a one-dimensional solution, we find…
In the supercooled regime at elevated pressure two forms of liquid water, high-density (HDL) and low-density (LDL), have been proposed to be separated by a coexistence line ending at a critical point, but a connection to ambient conditions…
Traditionally quantum tunneling in a static SQUID is studied on the basis of a classical trajectory in imaginary time under a two-dimensional potential barrier. The trajectory connects a potential well and an outer region crossing their…
Scaled physical modeling is an important means to understand the behavior of fluids in nature. However, a common source of errors is conflicting similarity criteria. Here, we present using hypergravity to improve the scaling similarity of…
We consider the evolution of contact lines for viscous fluids in a two-dimensional open-top vessel. The domain is bounded above by a free moving boundary and otherwise by the solid wall of a vessel. The dynamics of the fluid are governed by…
We model the flow of a bi-viscous non-Newtonian fluid in a porous medium by a square lattice where the links obey a piece-wise linear constitutive equation. We find numerically that the flow regime where the network transitions from all…
A thermodynamic framework that predicts the thermal conductivity $\lambda$ of simple fluids beyond the dilute-gas limit is introduced. By generalizing the transition-rate approach of particles on a lattice to conserved quantities in…
We discuss the thermal conduction and convection of thermally relativistic fluids between two parallel walls under the gravitational force, both theoretically and numerically. In the theoretical discussion, we assume that the Lorentz…
Classical thermodynamics contains familiar geometric relations associated with cyclic processes, most notably the identification of mechanical work with the area enclosed by a trajectory in the $(P,V)$ plane. We show that the area laws for…
Chaotic motion in time of a number of macroscopic systems has been analyzed, in the framework of scale relativity, as motion in a fractal space with topological dimension 3 and geodesics with fractal dimension 2. The motion equation is then…
We present a class of thermodynamic systems with constant thermodynamic curvature which, within the context of geometric approaches of thermodynamics, can be interpreted as constant thermodynamic interaction among their components. In…
The classic 2pi-Theorem of Gromov and Thurston constructs a negatively curved metric on certain 3-manifolds obtained by Dehn filling. By Geometrization, any such manifold admits a hyperbolic metric. We outline a program using cross…
Dimension-varying linear systems are investigated. First, a dimension-free state space is proposed. A cross dimensional distance is constructed to glue vectors of different dimensions together to form a cross-dimensional topological space.…