We propose a scaling equation describing transport properties (diffusion and viscosity) in the solutions of colloidal particles. We apply the equation to 23 different systems including colloids and proteins differing in size (range of diameters: 4 nm to 1 μm), and volume fractions (10(-3)-0.56). In solutions under study colloids/proteins interact via steric, hydrodynamic, van der Waals and/or e...

The noisy Burgers equation describing for example the growth of an interface subject to noise is one of the simplest model governing an intrinsically nonequilibrium problem. In one dimension this equation is analyzed by means of the MartinSiggia-Rose technique. In a canonical formulation the morphology and scaling behavior are accessed by a principle of least action in the weak noise limit. The...

The intermolecular structure of semidilute polymer solutions is studied theoretically. The low-density limit of a generalized Ornstein-Zernicke integral equation approach to polymeric liquids is considered. Scaling laws for the dilute-to-semidilute crossover of the random-phase approximation (RPA)-like structure are derived for the intermolecular structure factor on large distances when intermo...

A method for predicting liquid densities of binary mixtures from heat of vaporization and liquid densityat boiling point temperature (ΔHvap and n b ρ ) as scaling constants, is presented. B2(T) follows a promisingcorresponding-states principle. Calculation of α(T) and b(T), the two other temperature-dependentconstants of the equation of state, are made possible by scaling. As a result ΔHvap and...

Some dosimeters require a relationship between detector signal and delivered dose. The relationship (characteristic curve or calibration equation) usually depends on the environment under which the dosimeters are manufactured or stored. To compensate for the difference in radiation response among different batches of dosimeters, the measured dose can be scaled by normalizing the measured dose t...

An analytical equation of state by Song and Mason is developed to calculate the PVT properties ofmercury. The equation of state is based on the statistical-mechanical perturbation theory of hard convexbodies and can be written as a fifth-order polynomial in the density. There exists three temperaturedependentparameters in the equation of state; the second virial coefficient, an effective molecu...

We propose a unified moving boundary problem for surface growth by electrochemical and chemical vapor deposition, which is derived from constitutive equations into which stochastic forces are incorporated. We compute the coefficients in the interface equation of motion as functions of phenomenological parameters. The equation features the Kardar-Parisi-Zhang (KPZ) nonlinearity and instabilities...

We study the small dispersion limit for the Korteweg-de Vries (KdV) equation ut + 6uux + ǫ uxxx = 0 in a critical scaling regime where x approaches the trailing edge of the region where the KdV solution shows oscillatory behavior. Using the Riemann-Hilbert approach, we obtain an asymptotic expansion for the KdV solution in a double scaling limit, which shows that the oscillations degenerate to ...

We consider a harmonic chain perturbed by an energy conserving noise depending on a parameter γ . When γ is of order one, the energy diffuses according to the standard heat equation after a space-time diffusive scaling. On the other hand, when γ = 0, the energy superdiffuses according to a 3/4 fractional heat equation after a subdiffusive space-time scaling. In this paper, we study the existenc...

The traditional Richards' equation implies that the wetting front in unsaturated soil follows Boltzmann scaling, with travel distance growing as the square root of time. This study proposes a fractal Richards' equation (FRE), replacing the integer-order time derivative of water content by a fractal derivative, using a power law ruler in time. FRE solutions exhibit anomalous non-Boltzmann scalin...