We have developed a scaled parametric equation of state to describe and predict thermodynamic properties of supercooled water. The equation of state, built on the growing evidence that the critical point of supercooled liquid-liquid water separation exists, is universal in terms of theoretical scaling fields and is shown to belong to the Ising-model class of universality. The theoretical scalin...

We derive a stochastic nonlinear equation to describe the evolution and scaling properties of surfaces eroded by ion bombardment. The coefficients appearing in the equation can be calculated explicitly in terms of the physical parameters characterizing the sputtering process. We find that transitions may take place between various scaling behaviors when experimental parameters such as the angle...

The Kolmogorov scaling law of turbulences has been considered the most important theoretical breakthrough in the last century. It is an essential approach to analyze turbulence data present in meteorological, physical, chemical, biological and mechanical phenomena. One of its very fundamental assumptions is that turbulence is a stochastic Gaussian process in small scales. However, experiment da...

Differential equations for scaling relation of prepotential in N = 2 supersym-metric SU(2) Yang-Mills theory coupled with massive matter hypermultiplet are proposed and are explicitly demonstrated in one flavour (N f = 1) theory. By applying Whitham dynamics, the first order derivative of the prepotential over the T 0 variable corresponding to the mass of the hypermultiplet, which has a line in...

We introduce a new method for the analysis of singularities in the unstable problem ∆u = −χ{u>0}, which arises in solid combustion as well as in the composite membrane problem. Our study is confined to points of “supercharacteristic” growth of the solution, i.e. points at which the solution grows faster than the characteristic/invariant scaling of the equation would suggest. At such points the ...

The nondeterministic Kuramoto-Sivashinsky ~KS! equation is solved numerically in 211 dimensions. The simulations reveal the presence of early and late scaling regimes. The initial-time values for the growth exponent b, the roughness exponent a, and the dynamic exponent z are found to be 0.22–0.25, 0.75–0.80, and 3.0–4.0, respectively. For long times, the scaling exponents are notably less than ...

an analytical equation of state is applied to calculate the thermodynamic properties for argon. theequation of state is that of song and mason. it is based on a statistical-mechanical perturbation theory ofhard convex bodies and can be written as fifth-order polynomial in the density. there exist three temperaturedependentparameters: the second virial coefficient, an effective molecular volume,...

We present a phenomenological one-parameter scaling equation of state that accurately represents osmotic pressures of neutral flexible polymers in good solvents from the dilute through the semidilute regime. The equation comprises a sum of scaled van't Hoff and des Cloizeaux terms including a fitted parameter alpha, the "crossover index", which encapsulates all chemical specificity and determin...