When the scattered photon is lower in energy, or frequency, it is said to be Stokes shifted. The shift in frequency of the Stokes is related to the characteristic of the medium. This is illustrated in Fig. 2. Calling this material characteristic frequency , the Stokes frequency is then . The Raman Stokes scattering results in an excitation from the ground state of the medium to an excited state...

We present a novel theory that determines the sensitivity of linear stability to changes in the density or velocity of a base flow. The sensitivity is based on global direct and adjoint eigenmodes of the linearized Boussinesq equation, and is inspired by constantdensity sensitivity analysis. The theory can be applied broadly to incompressible flows with small density variations, but it specific...

In this study, Lane–Emden complex differential equations have been randomized by selecting random variables for the coefficients, initial conditions, and force functions of equations. addition, finding solutions obtained equations, probability characteristics are examined. The version transformation method (DTM) is used to obtain an analytical solution close equation. Approximate expected value...

geometrical profile (roughness) of joint surfaces influences the behaviour of rock joints under shear loading. with regard to the dilation, there are two models of direct shear test that may simulate the original loading condition existing in the location from where the specimens have been sampled. the first model in which the normal load is constant (cnl) and the discontinuity is free to dilat...

in this paper a first step in classifying the fuzzy normalsubgroups of a finite group is made. explicit formulas for thenumber of distinct fuzzy normal subgroups are obtained in theparticular cases of symmetric groups and dihedral groups.

Generating multivariate random vectors is a crucial part of the input analysis involved in discrete-event stochastic simulation modeling of multivariate systems. The NORmal-To-Anything (NORTA) algorithm, in which generating the correlation matrices of normal random vectors is the most important task, is one of the most efficient methods in this area. In this algorithm, we need to solve the so-c...

ARTICLE OUTLINE Definition of the Subject and Importance Introduction Granular Matter and its Statistical Mechanics Nonequilibrium statistical mechanics Liouville equation Stationary homogeneous state Macroscopic Balance Equations ”Normal” States and Hydrodynamics Navier-Stokes Approximation Constitutive equations Green-Kubo expressions Hydrodynamic equations Discussion and Outlook Bibliography...

A spirometric reference equation consists of a mathematical model with constants and coefficients optimized to fit a specific data set from healthy individuals. Commonly applied models are selected on statistical rather than physiological considerations. A predetermined model with constants and coefficients optimized to various populations would enable interpretable and interesting comparisons ...

BACKGROUND Published predicted values for total lung capacity and residual volume are often based on a small number of subjects and derive from different populations from predicted spirometric values. Equations from the only two large studies gave smaller predicted values for total lung capacity than the smaller studies. A large number of subjects have been studied from a population which has a...