Approximations for analytical relations of the darck diffusion and recombination current

2015 ◽  
Author(s):  
Salhi Hanen ◽  
Samet Hekmet ◽  
B. Amar Mouhamed
Keyword(s):  
Recombination Current ◽  
Analytical Relations

Analytical Estimation of Recombination Current of Sharp Asymmetric p-n Junction

2019 ◽  
Vol 11 (5) ◽  
pp. 05005-1-05005-8
Author(s):  
A. B. Galat ◽  
◽  
A. L. Donchenko ◽  
Keyword(s):  
Analytical Estimation ◽  
Recombination Current

Some properties of Wigner coefficients and hyperspherical harmonics

1956 ◽  
Vol 52 (3) ◽  
pp. 424-430 ◽  
Author(s):  
A. P. Stone
Keyword(s):  
Angular Momentum ◽  
Euclidean Space ◽  
Rotation Group ◽  
Dimensional Euclidean Space ◽  
Hyperspherical Harmonics ◽  
Shift Operators ◽  
Analytical Relations

ABSTRACTGeneral shift operators for angular momentum are obtained and applied to find closed expressions for some Wigner coefficients occurring in a transformation between two equivalent representations of the four-dimensional rotation group. The transformation gives rise to analytical relations between hyperspherical harmonics in a four-dimensional Euclidean space.

scholarly journals Exact relation between singular value and eigenvalue statistics

2016 ◽  
Vol 05 (04) ◽  
pp. 1650015 ◽  
Author(s):  
Mario Kieburg ◽  
Holger Kösters
Keyword(s):  
Singular Values ◽  
Singular Value ◽  
Specific Class ◽  
Rotation Invariant ◽  
Exact Relation ◽  
Finite Matrix ◽  
Eigenvalue Statistics ◽  
Probability Densities ◽  
Analytical Relations ◽  
Matrix Spaces

We use classical results from harmonic analysis on matrix spaces to investigate the relation between the joint densities of the singular values and the eigenvalues for complex random matrices which are bi-unitarily invariant (also known as isotropic or unitary rotation invariant). We prove that each of these joint densities determines the other one. Moreover, we construct an explicit formula relating both joint densities at finite matrix dimension. This relation covers probability densities as well as signed densities. With the help of this relation we derive general analytical relations among the corresponding kernels and biorthogonal functions for a specific class of polynomial ensembles. Furthermore, we show how to generalize the relation between the singular value and eigenvalue statistics to certain situations when the ensemble is deformed by a term which breaks the bi-unitary invariance.

Numerical Modeling of Electroosmotically Driven Micro Flows

1999 ◽  
Author(s):  
Prashanta Dutta ◽  
Ali Beskok ◽  
Timothy C. Warburton
Keyword(s):  
Spectral Element ◽  
Double Layers ◽  
Channel Height ◽  
Shear Stresses ◽  
Pressure Gradients ◽  
Pressure Distributions ◽  
Micro Channels ◽  
Micro Flows ◽  
Analytical Relations ◽  
P Type

Abstract Electroosmotically driven flows in micro-channels are analyzed analytically and numerically. Semi-analytical relations for the velocity and pressure distributions in micro channels are obtained for electric double layers that are much smaller than the channel height, by using the Helmholtz Smoluchowski velocity. Analytical relations for wall shear stress and pressure distribution are obtained. Amplification of the normal and shear stresses on the walls are observed and documented. A high-order (h/p type) spectral element method is developed, and verified for numerical simulation of electroosmotic micro fluidic flows. Finally, flow through a step channel geometry is analyzed to document the interaction of the electroosmotic forces with adverse pressure gradients. Significant changes within the separation patterns are observed.

Effect of compact inclusion on the natural frequencies of vibrations of a pipe string in a well

2021 ◽  
pp. 73-77
Author(s):  
A.M. Svalov ◽  
Keyword(s):  
Asymptotic Expansion ◽  
Small Parameter ◽  
Natural Frequencies ◽  
Oscillation Period ◽  
Drill String ◽  
Analytical Relation ◽  
Longitudinal Vibrations ◽  
Bottom Hole ◽  
Tubing String ◽  
Analytical Relations

The influence of small-size inclusion of pipes in a well column on the natural frequency of its longitudinal vibrations is investigated. Using the asymptotic expansion in a small parameter, an analytical relation is obtained that describes the change in the period of the column oscillations in the form of some additional small term to the period of the homogeneous column oscillations. Numerical calculations show that the obtained analytical relations almost accurately describe the oscillation period of a column with a massive compact inclusion, while its difference from the oscillation period of a homogeneous column is within ~20%. The results obtained can be useful for preventing resonant phenomena in the drill string when drilling wells, as well as for optimal use of the longitudinal vibrations of the tubing string to influence the bottom-hole zones of producing wells.

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