Increased Crowding during Escape Panic and Suitable Strategy for its Avoidance

Under panicky situation, human have tendency to rush toward a particular direction for escape. I show here that this tendency alone causes increase in crowding and which could eventually trigger jamming that is not preferable. Further, it is proposed that potential flow theory can be employed in finding suitable strategy for escape.Comment: 5 page

Model representation for self-consistent-field theory of isotropic turbulence

In this paper, Langevin model equation is proposed for Fourier modes of velocity field of isotropic turbulence whose statistical properties are identical to those governed by equations of Self-Consistent-Field (SCF) theory of turbulence [J. R. Herring, Physics of Fluids 9, 2106 (1966)].Comment: 8 pages. Submitted to Journal of Fluid Mechanics for possible publicatio

Comments on turbulence theory by Qian and by Edwards and McComb

We reexamine Liouville equation based turbulence theories proposed by Qian {[}Phys. Fluids \textbf{26}, 2098 (1983){]} and Edwards and McComb {[}J. Phys. A: Math. Gen. \textbf{2}, 157 (1969){]}, which are compatible with Kolmogorov spectrum. These theories obtained identical equation for spectral density $q(k)$ and different results for damping coefficient. Qian proposed variational approach and Edwards and McComb proposed maximal entropy principle to obtain equation for the damping coefficient. We show that assumptions used in these theories to obtain damping coefficient correspond to unphysical conditions.Comment: 7 pages. Submitted to arXiv.org on July 4, 201

Scaling of Spinodal Turbulence between Viscous and Inertial Hydrodynamic Regimes

The existence of unique scaling in a crossover regime between viscous and inertial hydrodynamic regimes is revealed for homogeneous, isotropic, incompressible, spinodal turbulence which is characterized, to begin with, by three different length scales and a velocity scale. The obtained scaling exponents are found to be in agreement and in consistency with available simulation results for a broad range of crossover regime. Also, it is observed that the spinodal turbulence in the crossover regime is in complete consistency with the universality class of self-preservation of decaying grid turbulence. We then obtain analytical forms for various scalings, valid in the crossover regime, through the analysis for self-preservation of spinodal turbulence

A new Eulerian theory of turbulence constrained by random Galilean invariance

We propose a new Eulerian turbulence theory to obtain a closed set of equations for homogeneous, isotropic turbulent velocity field correlations and propagator functions by incorporating constraints of random Galilean invariance. This incorporation generates a few different equations for propagator and the present theory suggests a way to utilize them into the closure solutions of two-time and single-time velocity correlations' equations so as to properly account for random sweeping phenomena. The present theory yields exact solutions when applied to simple model problem of random oscillator.Comment: 16 pages, submitted on July 8, 201

Development of Eulerian Theory of Turbulence within Kraichnan's Direct Interaction Approximation Framework

Within the framework of Kraichnan's Direct Interaction Approximation (DIA), we propose an Eulerian turbulence theory providing a closed set of equations for two-time and single-time velocity correlations, and second order correlations of infinitesimal response tensor $\hat{G}_{in}({\bf k};t,t')$. The proposed theory, namely variant of DIA (VDIA), is consistent with Kolmogorov's energy spectrum. The VDIA is further modified to make it compatible with random Galilean transformation rules. The closed set of equations does not contain equation for ensemble averaged response tensor $G_{in}({\bf k};t,t')=\langle\hat{G}_{in}({\bf k};t,t')\rangle$. The present theory can also be seen as a new remormalized perturbation theory having different method for renormalization.Comment: 17 pages. Submitted to arXiv.org on July 5, 2014 version 1. 18 Pages. Submitted to arXiv.org on July 17, 2014 version

Influence of Gravitation on Mass-Energy Equivalence Relation

We study influence of gravitational field on the mass-energy equivalence relation by incorporating gravitation in the physical situation considered by Einstein (Ann. Physik, 17, 1905, English translation in ref. [1]) for his first derivation of mass-energy equivalence. In doing so, we also refine Einstein's expression (Ann. Physik, 35, 1911, English translation in ref. [3]) for increase in gravitational mass of the body when it absorbs E amount of radiation energy.Comment: 4 pages. This paper is revised version of earlier paper, entitled "Hidden Conditions in Einstein's First Derivation for Mass-Energy Equivalence", which was containing errors and was not correc

Model representation for local energy transfer theory of isotropic turbulence

An almost-Markovian model equation is proposed for Fourier modes of velocity field of isotropic turbulence whose statistical properties are identical to those governed by equations of Local Energy Transfer theory of turbulence [McComb et al., J. Fluid Mech. {\bf 245}, 279 (1992)] compatible with the Kolmogorov spectrum.Comment: 7 pages. Submitted to Journal of Fluid Mechanics for possible publicatio

Size of Memory Objects

I consider model for flares proposed by P.-G de Gennes (PNAS, 101 (44), 15778-15781, 2004) and suggest a range for amplification factor (I) for inhibitory neurons for the time evolution of non-divergent generations of excitatory neurons which eventually die out. The exact numerical solution of the model for the suggested range of the factor (I) then provides minimum number of neurons describing size (M) for memory objects. The obtained size is M = 8 to 12.75 and which is larger than the size M = 2 to 4 as obtained theoretically by de Gennes.Comment: 6 page

Jets with Reversing Buoyancy

A jet of heavy fluid is injected upwards, at time $t=0$, into a lighter fluid and reaches a maximum height at time $t=t_i$ and then flows back around the upward flow. A similar flow situation occurs for a light fluid injected downward into a heavy one. In this paper an exact analytical expression for $t_i$ is derived. The expression remains valid for laminar and turbulent buoyant jets with or without swirl.Comment: 4 pages, 1 figure, paper first produced in 200