AN ANALYTICAL SOLUTION FOR THE SELF- AND MUTUAL RADIATION RESISTANCES OF A RECTANGULAR PLATE

2001 ◽  
Vol 245 (1) ◽  
pp. 1-16 ◽  
Author(s):  
W.L. LI
Keyword(s):  
Analytical Solution ◽  
Rectangular Plate ◽  
The Self

scholarly journals On the structure of the self-sustaining cycle in separating and reattaching flows

2018 ◽  
Vol 857 ◽  
pp. 907-936 ◽  
Author(s):  
A. Cimarelli ◽  
A. Leonforte ◽  
D. Angeli
Keyword(s):  
Shear Layer ◽  
Rectangular Plate ◽  
Large Scale ◽  
Reverse Flow ◽  
Leading Edge ◽  
Streamwise Velocity ◽  
The Self ◽  
Small Scale ◽  
Spectral Evolution ◽  
Mean Velocity

The separating and reattaching flows and the wake of a finite rectangular plate are studied by means of direct numerical simulation data. The large amount of information provided by the numerical approach is exploited here to address the multi-scale features of the flow and to assess the self-sustaining mechanisms that form the basis of the main unsteadinesses of the flows. We first analyse the statistically dominant flow structures by means of three-dimensional spatial correlation functions. The developed flow is found to be statistically dominated by quasi-streamwise vortices and streamwise velocity streaks as a result of flow motions induced by hairpin-like structures. On the other hand, the reverse flow within the separated region is found to be characterized by spanwise vortices. We then study the spectral properties of the flow. Given the strongly inhomogeneous nature of the flow, the spectral analysis has been conducted along two selected streamtraces of the mean velocity field. This approach allows us to study the spectral evolution of the flow along its paths. Two well-separated characteristic scales are identified in the near-wall reverse flow and in the leading-edge shear layer. The first is recognized to represent trains of small-scale structures triggering the leading-edge shear layer, whereas the second is found to be related to a very large-scale phenomenon that embraces the entire flow field. A picture of the self-sustaining mechanisms of the flow is then derived. It is shown that very-large-scale fluctuations of the pressure field alternate between promoting and suppressing the reverse flow within the separation region. Driven by these large-scale dynamics, packages of small-scale motions trigger the leading-edge shear layers, which in turn created them, alternating in the top and bottom sides of the rectangular plate with a relatively long period of inversion, thus closing the self-sustaining cycle.

scholarly journals Breve argumentación didáctica de la mecánica cuántica de muchos cuerpos

Respuestas ◽  
2017 ◽  
Vol 22 (1) ◽  
pp. 29
Author(s):  
Cristian Andrés Aguirre-Téllez ◽  
José Barba-Ortega
Keyword(s):  
Quantum Mechanics ◽  
Analytical Solution ◽  
Schrödinger Equation ◽  
Analytical Method ◽  
Schrodinger Equation ◽  
Quantum Systems ◽  
The Self ◽  
Self Consistent ◽  
El Sistema ◽  
Self Consistent Field

El problema general en mecánica cuántica está basado en la solución de una ecuación en valores propios de un operador dado (en una representación adecuada), generalmente  dicho operador es el Hamiltoniano que da cuenta de la interacción energética (salvo que dependa del tiempo) del sistema en cuestión. La solución de la ecuación de Schrödinger permite escribir el comportamiento dinámico del sistema sometido a ciertas restricciones. Sin embargo, la solución analítica de esta ecuación es viable solo en sistemas simples, cuando el sistema se describe desde la interacción de muchas partículas (problema electrónico-base de la construcción de sistemas cuánticos complejos aplicable a la descripción de moléculas, sólidos y sistemas cuánticos interactuantes en general.) la solución de la ecuación de Schrödinger del sistema no se puede realizar vía método analítico; con lo cual existe una forma más global de enfrentar dicho problema, el método auto consistente; mediante el cual se puede solucionar sistemas complejos de muchos cuerpos. Es así que en el presente paper presentamos una comparación entre el sistema auto consistente y algunas variantes que existen, con el método analítico en sistemas demuchos cuerpos y como opera dicho método, esto aplicado a un problema de dos cuerpos con interacción Coulombiana, ya que este problema presenta solución analítica y ha sido extensamente estudiado; esto con la finalidad de que los estudiantes interesados en la materia comprendan como se abordan problemas vía métodos auto consistentes y como opera este método, ya que en la literatura pocas veces se presenta el algoritmo de solución mediante este método.Palabras clave: Mecánica Cuántica, Método Auto-Consistente, problema de dos cuerpos.AbstractThe general problem in quantum mechanics is based on the solution of an equation in eigenvalues of a given operator (in a suitable representation), generally said operator is the Hamiltonian that accounts for the energy interaction (unless it depends on the time) of the system in question. The solution of the Schrodinger equation allows writing the dynamic behavior of the system subject to certain restrictions. however, the analytical solution of this equation is feasible only in simple systems, when the system is described from the interaction of many particles (electronic problem- basis of the construction of complex quantum systems applicable to the description of molecules, solids and interacting quantum systems in general.), the solution of the Schrödinger equation of the system can´t be performed via analytical method; with which there is a more global way of facing this problem, the self-consistent method; through which complex systems of many bodies can be solved. thus, in the present paper we present a comparison between the self-consistent system and some variants that exist, with the analytical method in systems of many bodies and how this method operates, this applied to a problem of two bodies with Coulombian interaction, since this problem presents an analytical solution and has been extensively studied; this in order that students interested in the subject understand how problems are addressed through self-consistent methods and how this method operates, since in the literature rarely the solution algorithm is presented by this method.Keywords: Quantum mechanics, Self Consistent Field, Two body problem.

scholarly journals Total and Effective Stresses in Backfilled Stopes during the Fill Placement on a Pervious Base for Barricade Design

Minerals ◽  
2019 ◽  
Vol 9 (1) ◽  
pp. 38 ◽  
Author(s):  
Jian Zheng ◽  
Li Li ◽  
Yuchao Li
Keyword(s):  
Analytical Solution ◽  
Pore Water Pressure ◽  
Water Pressure ◽  
The Self ◽  
Underground Mines ◽  
Filling Rate ◽  
Effective Stresses ◽  
Arching Effect ◽  
The Stability ◽  
Backfilled Stopes

Backfill is increasingly used in underground mines worldwide. Its successful application depends on the stability of the barricades built at the base of the stopes to hold the backfill in place, which in turn depends on the knowledge of the pore water pressure (PWP) and stresses during, or shortly after, the placement of the slurried backfill. Until now, self-weight consolidation is usually considered for the estimation of the PWP. There is no solution available to evaluate the total and effective stresses during, and shortly after, the filling operation. As excess PWP can simultaneously be generated (increased) and dissipated (decreased) during the backfilling operation, effective stresses can develop when the filling rate is low and/or hydraulic conductivity of the backfill is high. The arching effect has to be considered to evaluate the effective and total stresses in the backfilled stopes. In this paper, a pseudo-analytical solution is proposed to evaluate the effective and total stresses in backfilled stopes during the backfill deposition on a permeable base, by considering the self-weight consolidation and arching effect. The proposed solution is validated by numerical results obtained by Plaxis2D. A few sample applications of the proposed solution are shown.

scholarly journals NAKED SINGULARITIES IN THREE-DIMENSIONS

2003 ◽  
Vol 12 (05) ◽  
pp. 791-799
Author(s):  
G. OLIVEIRA-NETO
Keyword(s):  
Scalar Field ◽  
Analytical Solution ◽  
Cosmic Censorship ◽  
The Self ◽  
Three Dimensions ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Naked Singularities ◽  
Asymptotically Flat ◽  
Self Similar

We study an analytical solution to the Einstein's equations in (2+1)-dimensions, representing the self-similar collapse of a circularly symmetric, minimally coupled, massless, scalar field. Depending on the value of certain parameters, this solution represents the formation of naked singularities. Since our solution is asymptotically flat, these naked singularities may be relevant for the weak cosmic censorship conjecture in (2+1)-dimensions.

scholarly journals A RECTANGULAR PLATE ON A TWO-PARAMETER ELASTIC BASE: THE ANALYTICAL SOLUTION

2017 ◽  
Vol 17 (8) ◽  
pp. 128-133
Author(s):  
A.A. Bolshakov
Keyword(s):  
Approximate Solution ◽  
Analytical Solution ◽  
Boundary Conditions ◽  
Rectangular Plate ◽  
Double Series ◽  
Elastic Base ◽  
Elastic Support ◽  
Analytical Expressions ◽  
Two Parameter

In the paper the approximate solution for a problem of a rectangular plate on a two-parameter elastic base is suggested. The double series of beam functions satisfying elastic support boundary conditions are constructed. The analytical expressions for series function coefficients are obtained.

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