Nonparaxial scalar Airy light-sheets and their higher-order spatial derivatives

2017 ◽  
Vol 110 (9) ◽  
pp. 091104 ◽  
Author(s):  
F. G. Mitri
Keyword(s):  
Higher Order ◽  
Spatial Derivatives

Localization of damage with speckle shearography and higher order spatial derivatives

2014 ◽  
Vol 49 (1-2) ◽  
pp. 24-38 ◽  
Author(s):  
H. Lopes ◽  
F. Ferreira ◽  
J.V. Araújo dos Santos ◽  
P. Moreno-García
Keyword(s):  
Higher Order ◽  
Spatial Derivatives

scholarly journals MODEL OF THE STRUCTURED CONTINUUM, AND THE RELATION BETWEEN SPECIFIC SURFACE AREA, POROSITY AND PERMEABILITY

2013 ◽  
Vol 31 (4) ◽  
pp. 559 ◽  
Author(s):  
Boris Sibiryakov ◽  
Lourenildo W.B. Leite ◽  
Wildney W.S. Vieira
Keyword(s):  
Porous Media ◽  
Degrees Of Freedom ◽  
Infinite Order ◽  
Energy Content ◽  
Equation Of Motion ◽  
Higher Order ◽  
Structured Media ◽  
Porosity And Permeability ◽  
Spatial Derivatives ◽  
The Continuum

ABSTRACT. Contrary to the Cauchy and Poisson classical seismic theory of the continuum, the new theory for structured (also called porous, fractured, or blocked) media must contain several degrees of freedom. This fact is evident because elementary blocks (grains) may transfer the motion by contact interaction, by rotation, and by group of particles. Therefore, the energy content is not only contained within the first spatial derivatives (strains), but the potential energy content is within the second (curvatures) and other higher order spatial derivatives. Thus, the equation of motion of porous media should contain higher order spatial derivatives, andmay even contain infinite order spatial derivatives.Keywords: seismic structured media, porous media, fractured media. RESUMO. Contrariamente aos problemas clássicos da teoria sísmica do contínuo de Cauchy e Poisson, a nova teoria para meios estruturados (também denominados de porosos, fraturados e blocados) deve conter vários graus de liberdade. Este fato é evidente porque blocos elementares (grãos) podem transferir movimento por interação de contato, por rotação, e por grupo de partículas. Desta forma, o conteúdo de energia não está apenas contido nas primeiras derivadas espaciais (deformações), como também o conteúdo de energia potencial está presente na segunda (curvaturas), e em derivadas espaciais de maior ordem. Sendo assim, a equação de movimento para meios porosos deveria conter derivadas espaciais de ordem mais altas, e até mesmo uma ordem infinita de derivadas espaciais.Palavras-chave: meios sísmicos estruturados, meios porosos, meios fraturados.

Electrochemical digital simulations with an exponentially expanding grid: General expressions for higher order approximations to spatial derivatives

2009 ◽  
Vol 54 (3) ◽  
pp. 1042-1055 ◽  
Author(s):  
Francisco Martínez-Ortiz ◽  
Noemí Zoroa ◽  
Ángela Molina ◽  
Carmen Serna ◽  
Eduardo Laborda
Keyword(s):  
Higher Order ◽  
Spatial Derivatives ◽  
Digital Simulations

Radiation from charged particles in weakly inhomogeneous magnetic fields

1971 ◽  
Vol 6 (1) ◽  
pp. 33-51 ◽  
Author(s):  
David M. Cook
Keyword(s):  
Electromagnetic Field ◽  
Angular Distribution ◽  
Azimuthal Angle ◽  
Charged Particles ◽  
Polar Axis ◽  
Higher Order ◽  
Spectral Lines ◽  
Larmor Radius ◽  
Spatial Derivatives ◽  
Derivatives Of

The spectral distribution of radiation emitted by a charged particle moving nonrelativistically in a prescribed electromagnetic field, consisting of a strong uniform magnetic induction on which is superimposed a weak inhomogeneity, is determined. The calculation is confined to trajectories characterized by small Larmor radii, and to the azimuthal average of the full angular distribution of the radiation, the azimuthal angle being measured in a co-ordinate system for which the uniform component of the field defines the polar axis. If the particle gyrates for a time long compared to the gyro-period, the spectrum separates into several independent lines. Quantitative expressions for the distribution of energy within each line are presented, and then evaluated for selected inhomogeneities. Qualitatively, it is found that inhomogeneities (i) may distort the distribution of energy within the spectral line at the gyro-frequency by broadening, displacing, destroying the symmetry of, and/or splitting that line, and (ii) may also generate spectral lines at aipproximate harmonics of the gyro-frequency. These harmonics are second order in the inhomogeneity, are of successively higher order in the Larmor radius, involve successively higher-order spatial derivatives of the inhomogeneities, may occur at frequencies whose ratios are not precisely ratios of integers, and may be split into two or more closely spaced components.

Sign in / Sign up

Export Citation Format

Share Document