scholarly journals Swarms in Periodically Time Dependent Electric Fields

1995 ◽  
Vol 48 (3) ◽  
pp. 365 ◽  
Author(s):  
Kailash Kumar
Keyword(s):  
Integral Equation ◽  
Exact Solution ◽  
Electric Fields ◽  
Transport Theory ◽  
Time Development ◽  
Time Dependent ◽  
Bgk Model ◽  
Physical Description ◽  
Dependent Field ◽  
The Ideal

The transport theory of swarms in a time dependent electric field is formulated in terms of the Boltzmann equation expressed as an integral equation in time. It allows for a convenient physical description of the time development of the swarm for the case of a periodically time dependent field. The exact solution of the ideal charge transfer or BGK model, obtained earlier by Robson and Makabe, is expressed in a closed form.

scholarly journals An exact solution of linearized flow of an emitting, absorbing and scattering grey gas

1971 ◽  
Vol 45 (4) ◽  
pp. 673-699 ◽  
Author(s):  
Ping Cheng ◽  
A. Leonard
Keyword(s):  
Integral Equation ◽  
Exact Solution ◽  
Transport Theory ◽  
Neutron Transport ◽  
Separation Of Variables ◽  
Closed Form Solution ◽  
Strong Shock ◽  
Form Solution ◽  
Isotropic Scattering ◽  
Differential Approximation

The governing equations for the problem of linearized flow through a normal shock wave in an emitting, absorbing, and scattering grey gas are reduced to two linear coupled integro-differential equations. By separation of variables, these equations are further reduced to an integral equation similar to that which arises in neutron-transport theory. It is shown that this integral equation admits both regular (associated with discrete eigenfunctions) and singular (associated with continuum eigenfunctions) solutions to form a complete set. The exact closed-form solution is obtained by superposition of these eigen-functions. If the gas downstream of a strong shock is absorption–emission dominated, the discrete mode of the solution disappears downstream. The effects of isotropic scattering are discussed. Quantitative comparison between the numerical results based on the exact solution and on the differential approximation are presented.

scholarly journals Exact Solution for the Time-Dependent Temperature Field in Dry Grinding: Application to Segmental Wheels

2011 ◽  
Vol 2011 ◽  
pp. 1-28 ◽  
Author(s):  
J. L. González-Santander ◽  
J. M. Valdés Placeres ◽  
J. M. Isidro
Keyword(s):  
Integral Equation ◽  
Exact Solution ◽  
Temperature Field ◽  
Analytical Solution ◽  
Time Evolution ◽  
Time Dependent ◽  
Temperature Fields ◽  
Grinding Wheel ◽  
Workpiece Surface ◽  
Dry Grinding

We present a closed analytical solution for the time evolution of the temperature field in dry grinding for any time-dependent friction profile between the grinding wheel and the workpiece. We base our solution in the framework of the Samara-Valencia model Skuratov et al., 2007, solving the integral equation posed for the case of dry grinding. We apply our solution to segmental wheels that produce an intermittent friction over the workpiece surface. For the same grinding parameters, we plot the temperature fields of up- and downgrinding, showing that they are quite different from each other.

Correlations of substituent effects on proton and fluorine chemical shifts with inverse ionization potentials

1967 ◽  
Vol 45 (24) ◽  
pp. 3143-3151 ◽  
Author(s):  
T. Schaefer ◽  
F. Hruska ◽  
H. M. Hutton
Keyword(s):  
Electric Fields ◽  
Chemical Shifts ◽  
Substituent Effects ◽  
Group Iv ◽  
The Other ◽  
Ionization Potentials ◽  
Time Dependent ◽  
Practical Application ◽  
Methyl Proton ◽  
Proton Chemical Shifts

The fluorine and proton chemical shifts in some geminally disubstituted vinylidene fluorides and ethylenes are discussed. For these compounds, at least, there are difficulties with an interpretation based on intramolecular time-dependent electric fields. On the other hand, the shifts correlate with the inverse ionization potentials of the substituents, indicating a paramagnetic effect arising from the second term in Ramsey's expression. It is suggested that the effect operates via the bonds and not across space. Methyl proton shifts in a series of substituted methyl compounds of group IV, V, and VI elements show similar correlations. A practical application of the correlation to spectral analysis problems is given.

Schrödinger dynamics and optimal transport of measures

2021 ◽  
pp. 2150016
Author(s):  
Lorenzo Zanelli
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Transport Theory ◽  
Optimal Transport ◽  
Time Dependent ◽  
Probability Measures ◽  
Flat Torus ◽  
Optimal Transport Theory

In this paper, we recover a class of displacement interpolations of probability measures, in the sense of the Optimal Transport theory, by means of semiclassical measures associated with solutions of Schrödinger equation defined on the flat torus. Moreover, we prove the completing viewpoint by proving that a family of displacement interpolations can always be viewed as a path of time-dependent semiclassical measures.

An Accelerated Retarded Potential Method for Time Dependent Acoustic Wave Scattering

1995 ◽  
Author(s):  
Toufic S. Abboud ◽  
Joseph M. Gharib ◽  
Jean Claude Nédélec ◽  
Toni G. Sayah
Keyword(s):  
Finite Element Method ◽  
Integral Equation ◽  
Wave Scattering ◽  
Numerical Approximation ◽  
Mesh Size ◽  
Integral Equation Method ◽  
Potential Method ◽  
Boundary Integral ◽  
Time Dependent ◽  
Acoustic Wave Scattering

Abstract We are interested in the numerical approximation of the problem of the scattering of a transient acoustic plane wave by a bounded obstacle in IR2 or IR3, using the boundary integral equation method. In the frequency domain it has been recently developed a boundary finite element method where the mesh size is like O(λ1/3) instead of O(λ) (λ is the wavelength) and where the obstacle is convex. This paper presents the implementation of the idea on the retarted potential representation.

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