The Lagrangian Function and Separation of Variables for Elastic Vibrations in Axially Symmetric Layered media

2013 ◽  
pp. 183-192 ◽  
Author(s):  
A. N. Kuznetsov
Keyword(s):  
Separation Of Variables ◽  
Layered Media ◽  
Lagrangian Function ◽  
Axially Symmetric ◽  
Elastic Vibrations

Capabilities and features of the “HIFU beam” nonlinear modeling tool for axially symmetric acoustic fields generated by focused therapeutic transducers in layered media

2021 ◽  
Vol 150 (4) ◽  
pp. A165-A165
Author(s):  
Petr V. Yuldashev ◽  
Maria M. Karzova ◽  
Wayne Kreider ◽  
Pavel Rosnitskiy ◽  
Oleg A. Sapozhnikov ◽  
...  
Keyword(s):  
Nonlinear Modeling ◽  
Layered Media ◽  
Acoustic Fields ◽  
Axially Symmetric ◽  
Modeling Tool

SEPARATING STATIONARY AXIALLY-SYMMETRIC ASYMPTOTICALLY FLAT METRICS

1989 ◽  
Vol 04 (12) ◽  
pp. 2953-2958 ◽  
Author(s):  
Z. YA. TURAKULOV
Keyword(s):  
Gordon Equation ◽  
Separation Of Variables ◽  
Vacuum Solution ◽  
Complete Separation ◽  
Kerr Metric ◽  
Axially Symmetric ◽  
Spherical System ◽  
Asymptotically Flat ◽  
Klein Gordon ◽  
Klein Gordon Equation

Stationary axially-symmetric asymptotically flat metrics allowing the complete separation of variables in the Klein-Gordon equation are considered. It is shown that if such metrics coincide at infinity with the metric of spherical system of coordinates, the variables for them in the Einstein equation are completely separable and the only vacuum solution is the Kerr metric.

Propagation of axially symmetric elastic vibrations along a waveguide in an elastic medium

1975 ◽  
Vol 10 (1) ◽  
pp. 90-94 ◽  
Author(s):  
S. L. Davydov ◽  
G. G. Zaretskii-Feoktistov ◽  
V. V. Sudakov
Keyword(s):  
Elastic Medium ◽  
Axially Symmetric ◽  
Elastic Vibrations

A Method for Computing the Analytical Solution of the Steady-State Heat Equation in Multilayered Media

2014 ◽  
Vol 136 (9) ◽  
Author(s):  
Ivor Dülk ◽  
Tamás Kovácsházy
Keyword(s):  
Steady State ◽  
Analytical Solution ◽  
Separation Of Variables ◽  
Layered Media ◽  
Steady State Solution ◽  
Multilayered Media ◽  
Number Of Layers ◽  
Layer Medium ◽  
Steady State Heat ◽  
Weighting Coefficients

The computation of the analytical solution of the steady temperature distribution in multilayered media can become numerically unstable if there are different longitudinal (i.e., the directions parallel to the layers) boundary conditions for each layer. In this study, we develop a method to resolve these computational difficulties by approximating the temperatures at the junctions step-by-step and solving for the thermal field separately in only the single layers. First, we solve a two-layer medium problem and then show that multilayered media can be represented as a hierarchy of two-layered media; thus, the developed method is generalized to an arbitrary number of layers. To improve the computational efficiency and speed, we use varying weighting coefficients during the iterations, and we present a method to decompose the multilayered media into two-layered media. The developed method involves the steady-state solution of the diffusion equation, which is illustrated for 2D slabs using separation of variables (SOV). A numerical example of four layers is also included, and the results are compared to a numerical solution.

Solar Internal Rotation and Dynamo Waves: A Two-Dimensional Asymptotic Solution in the Convection Zone

2000 ◽  
Vol 179 ◽  
pp. 379-380
Author(s):  
Gaetano Belvedere ◽  
Kirill Kuzanyan ◽  
Dmitry Sokoloff
Keyword(s):  
Magnetic Field ◽  
Asymptotic Solution ◽  
Internal Rotation ◽  
Convection Zone ◽  
General Idea ◽  
Dynamo Model ◽  
Axially Symmetric ◽  
Dynamo Action ◽  
Regeneration Rate ◽  
Dynamo Waves

Extended abstractHere we outline how asymptotic models may contribute to the investigation of mean field dynamos applied to the solar convective zone. We calculate here a spatial 2-D structure of the mean magnetic field, adopting real profiles of the solar internal rotation (the Ω-effect) and an extended prescription of the turbulent α-effect. In our model assumptions we do not prescribe any meridional flow that might seriously affect the resulting generated magnetic fields. We do not assume apriori any region or layer as a preferred site for the dynamo action (such as the overshoot zone), but the location of the α- and Ω-effects results in the propagation of dynamo waves deep in the convection zone. We consider an axially symmetric magnetic field dynamo model in a differentially rotating spherical shell. The main assumption, when using asymptotic WKB methods, is that the absolute value of the dynamo number (regeneration rate) |D| is large, i.e., the spatial scale of the solution is small. Following the general idea of an asymptotic solution for dynamo waves (e.g., Kuzanyan & Sokoloff 1995), we search for a solution in the form of a power series with respect to the small parameter |D|–1/3(short wavelength scale). This solution is of the order of magnitude of exp(i|D|1/3S), where S is a scalar function of position.

Center of Mass Theorem and the Separation of Variables for Two-Body System on a Three-Dimensional Sphere

2020 ◽  
Vol 23 (3) ◽  
pp. 306-311
Author(s):  
Yu. Kurochkin ◽  
Dz. Shoukavy ◽  
I. Boyarina
Keyword(s):  
Constant Curvature ◽  
Jacobi Equation ◽  
Separation Of Variables ◽  
Center Of Mass ◽  
Three Dimensional ◽  
Relative Distance ◽  
Dimensional Sphere ◽  
Body System ◽  
Spaces Of Constant Curvature ◽  
Hamilton Jacobi Equation

The immobility of the center of mass in spaces of constant curvature is postulated based on its definition obtained in [1]. The system of two particles which interact through a potential depending only on the distance between particles on a three-dimensional sphere is considered. The Hamilton-Jacobi equation is formulated and its solutions and trajectory equations are found. It was established that the reduced mass of the system depends on the relative distance.

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