Universal finite-size scaling function for coarsening in the Potts model with conserved dynamics

We study kinetics of phase segregation in multicomponent mixtures via Monte Carlo simulations of the q-state Potts model, in two spatial dimensions, for 2 ≤ q ≤ 20. The associated growth of domains in finite boxes, irrespective of q and temperature, can be described by a single universal finite-size scaling function, with only the introduction of a nonuniversal metric factor in the scaling variable. Our results show that although the scaling function is independent of the type of transition, the q-dependence of the metric factor hints to a crossover at q = 5 where the type of transition in the model changes from second to first order

Measurement of Free Stream Turbulence: It’s Modeling and Computations

Present research was initiated to study effects of free stream turbulence (FST) on flow instability and transition. Instabilities of some flows have been investigated qualitatively with respect to FST- but scant attention has been paid to compute extrinsic dynamics of flows due to FST. In actual flows, omnipresent background disturbances, e.g. FST triggers transition to turbulence. The motivation for the present work is to characterize and model FST, based on it’s statistics, obtained from wind tunnel and flight test experiments. The developed model is applied to numerically study the receptivity of flow past circular cylinder to the FS

Universality in Fluid Domain Coarsening: The case of vapor-liquid transition

Domain growth during the kinetics of phase separation is studied following vapor-liquid transition in a single component Lennard-Jones fluid. Results are analyzed after appropriately mapping the continuum snapshots obtained from extensive molecular dynamics simulations to a simple cubic lattice. For near critical quench interconnected domain morphology is observed. A brief period of slow diffusive growth is followed by a linear viscous hydrodynamic growth that lasts for an extended period of time. This result is in contradiction with earlier inclusive reports of late time growth exponent 1/2 that questions the uniqueness of the non-equilibrium universality for liquid-liquid and vapor-liquid transitions.Comment: 6 pages, 5 figure

What is the Simplest Linear Ramp?

We discuss conditions under which a deterministic sequence of real numbers, interpreted as the set of eigenvalues of a Hamiltonian, can exhibit features usually associated to random matrix spectra. A key diagnostic is the spectral form factor (SFF) -- a linear ramp in the SFF is often viewed as a signature of random matrix behavior. Based on various explicit examples, we observe conditions for linear and power law ramps to arise in deterministic spectra. We note that a very simple spectrum with a linear ramp is $E_n \sim \log n$. Despite the presence of ramps, these sequences do $not$ exhibit conventional level repulsion, demonstrating that the lore about their concurrence needs refinement. However, when a small noise correction is added to the spectrum, they lead to clear level repulsion as well as the (linear) ramp. We note some remarkable features of logarithmic spectra, apart from their linear ramps: they are closely related to normal modes of black hole stretched horizons, and their partition function with argument $s=\beta+it$ is the Riemann zeta function $\zeta(s)$. An immediate consequence is that the spectral form factor is simply $\sim |\zeta(it)|^2$. Our observation that log spectra have a linear ramp, is closely related to the Lindel\"of hypothesis on the growth of the zeta function. With elementary numerics, we check that the slope of a best fit line through $|\zeta(it)|^2$ on a log-log plot is indeed $1$, to the fourth decimal. We also note that truncating the Riemann zeta function sum at a finite integer $N$ causes the would-be-eternal ramp to end on a plateau.Comment: 16 pages, many plots, v2: minor corrections, reference