Evidence of crossover phenomena in wind speed data

In this report, a systematic analysis of hourly wind speed data obtained from three potential wind generation sites (in North Dakota) is analyzed. The power spectra of the data exhibited a power-law decay characteristic of $1/f^{\alpha}$ processes with possible long-range correlations. Conventional analysis using Hurst exponent estimators proved to be inconclusive. Subsequent analysis using detrended fluctuation analysis (DFA) revealed a crossover in the scaling exponent ($\alpha$). At short time scales, a scaling exponent of $\alpha \sim 1.4$ indicated that the data resembled Brownian noise, whereas for larger time scales the data exhibited long range correlations ($\alpha \sim 0.7$). The scaling exponents obtained were similar across the three locations. Our findings suggest the possibility of multiple scaling exponents characteristic of multifractal signals

A Multifractal Description of Wind Speed Records

In this paper, a systematic analysis of hourly wind speed data obtained from four potential wind generation sites in North Dakota is conducted. The power spectra of the data exhibited a power law decay characteristic of $1/f^{\alpha}$ processes with possible long range correlations. The temporal scaling properties of the records were studied using multifractal detrended fluctuation analysis {\em MFDFA}. It is seen that the records at all four locations exhibit similar scaling behavior which is also reflected in the multifractal spectrum determined under the assumption of a binomial multiplicative cascade model

Spatial Structures and Giant Number Fluctuations in Models of Active Matter

The large scale fluctuations of the ordered state in active matter systems are usually characterised by studying the "giant number fluctuations" of particles in any finite volume, as compared to the expectations from the central limit theorem. However, in ordering systems, the fluctuations in density ordering are often captured through their structure functions deviating from Porod law. In this paper we study the relationship between giant number fluctuations and structure functions, for different models of active matter as well as other non-equilibrium systems. A unified picture emerges, with different models falling in four distinct classes depending on the nature of their structure functions. For one class, we show that experimentalists may find Porod law violation, by measuring subleading corrections to the number fluctuations.Comment: 5 pages, 3 figure

Effect of Landauer's blowtorch on the equilibration rate in a bistable potential

Kinetic aspect of Landauer's blowtorch effect is investigated for a model double-well potential with localized heating. Using the supersymmetric approach, we derive an approximate analytical expression for the equilibration rate as function of the strength, width and the position of the hot zone, and the barrier height. We find that the presence of the hot zone enhances the equilibration rate, which is found to be an increasing function of the strength and width of the hot zone. Our calculations also reveal an intriguing result, namely, that placing the hot zone away from the top of the potential barrier enhances the rate more than when it is placed close to it. A physically plausible explanation for this is attempted. The above analytical results are borne out by detailed numerical solution of the associated Smoluchowski equation for the inhomogeneous medium.Comment: 15 pages in LaTeX format and 6 figures in postscript E-Mail : [email protected] [email protected]

Violation of Porod law in a freely cooling granular gas in one dimension

We study a model of freely cooling inelastic granular gas in one dimension, with a restitution coefficient which approaches the elastic limit below a relative velocity scale v. While at early times (t << 1/v) the gas behaves as a completely inelastic sticky gas conforming to predictions of earlier studies, at late times (t >> 1/v) it exhibits a new fluctuation dominated phase ordering state. We find distinct scaling behavior for the (i) density distribution function, (ii) occupied and empty gap distribution functions, (iii) the density structure function and (iv) the velocity structure function, as compared to the completely inelastic sticky gas. The spatial structure functions (iii) and (iv) violate the Porod law. Within a mean-field approximation, the exponents describing the structure functions are related to those describing the spatial gap distribution functions.Comment: 4 pages, 5 figure