Sound pulses in a conducting medium

1959 ◽  
Vol 55 (4) ◽  
pp. 341-367 ◽  
Author(s):  
F. G. Friedlander
Keyword(s):  
Acoustic Waves ◽  
Equations Of Motion ◽  
Displacement Current ◽  
Hydrodynamic Waves ◽  
Sound Waves ◽  
First Order ◽  
The Subject ◽  
Sound Pulses ◽  
Considerable Complexity ◽  
Small Disturbances

1. Introduction. The subject of this paper is the propagation of small disturbances in a compressible fluid which is also a conductor of electricity, in the presence of a magnetic field. The characteristic feature of the problem is that it combines sound waves and magneto-hydrodynamic waves. The theory is based on linearized equations which generalize the equations of motion of the theory of sound. The disturbances with which it deals might therefore be called magneto-acoustic waves. Energy dissipation by viscosity, heat conduction and Joule heat is neglected, and so is the displacement current. Even so, a hyperbolic system of seven partial differential equations of the first order is obtained, whose solution requires analysis of considerable complexity.

Small disturbances in a conducting fluid in the presence of a current-carrying conductor

1964 ◽  
Vol 60 (2) ◽  
pp. 325-339
Author(s):  
A. M. J. Davis
Keyword(s):  
Uniform Magnetic Field ◽  
Equations Of Motion ◽  
Conducting Fluid ◽  
Alfven Wave ◽  
Displacement Current ◽  
Wave Fronts ◽  
Acoustic Disturbance ◽  
Linear Partial Differential Equations ◽  
A Current ◽  
Small Disturbances

1. Introduction. The problem considered here derives its motivation from a paper by Friedlander (8) on the propagation of small disturbances in a compressible, conducting fluid in the presence of a uniform magnetic field (see also Courant and Hilbert (3), VI, §3a). In this the displacement current and energy dissipation by viscosity, heat conduction and Joule heat are neglected and a system of linear partial differential equations is obtained, which generalizes the equations of motion of the theory of sound. Their solution is in general the superposition of an arbitrary incompressible Alfven wave and a magneto-acoustic disturbance. This latter was considered by constructing a Green's function by means of suitable combinations of plane wave solutions and it was found that there are fast and slow wave fronts diverging from a point disturbance. The latter are conoidal in shape and have a singularity at their vertices which propagate along the field line in either direction from the source.

An exact solution to the equation of propagation of magneto-acoustic waves

1975 ◽  
Vol 343 (1634) ◽  
pp. 421-425
Keyword(s):  
Magnetic Field ◽  
Exact Solution ◽  
Acoustic Waves ◽  
Equations Of Motion ◽  
Nonlinear Partial Differential Equation ◽  
Finite Amplitude ◽  
Uniform Density ◽  
Sound Waves ◽  
Horizontal Magnetic Field ◽  
Specific Heats

By assuming a uniform horizontal magnetic field and using Lagrangian coordinates the equations of motion, continuity, and magnetic induction are combined to give the exact nonlinear partial differential equation of propagation of vertically travelling magneto-acoustic waves in an atmosphere of uniform density. By means of an intermediary integral, an exact solution is then derived for the cases of a polytropic gas with the ratio of the principal specific heats equal to 5/3 and 2. The solutions are compared with the classical solution of Riemann which describes pure, finite amplitude sound waves propagating in a uniform atmosphere. The degeneration of a magneto-acoustic wave into a shock is illustrated, and the effect of increasing the permanent magnetic field is found to decrease the time for the creation of the discontinuity.

Kinetic theory

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Distribution Function ◽  
Kinetic Theory ◽  
Liouville Equation ◽  
Vlasov Equation ◽  
Particle Distribution ◽  
Equations Of Motion ◽  
Poisson Brackets ◽  
Hamiltonian Form ◽  
First Order ◽  
Number Of Particles

This chapter covers the equations governing the evolution of particle distribution and relates the macroscopic thermodynamical quantities to the distribution function. The motion of N particles is governed by 6N equations of motion of first order in time, written in either Hamiltonian form or in terms of Poisson brackets. Thus, as this chapter shows, as the number of particles grows it becomes necessary to resort to a statistical description. The chapter first introduces the Liouville equation, which states the conservation of the probability density, before turning to the Boltzmann–Vlasov equation. Finally, it discusses the Jeans equations, which are the equations obtained by taking various averages over velocities.

Analysis of Linear Nonconservative Vibrations

1995 ◽  
Vol 62 (3) ◽  
pp. 685-691 ◽  
Author(s):  
F. Ma ◽  
T. K. Caughey
Keyword(s):  
Modal Analysis ◽  
Equations Of Motion ◽  
Substantial Reduction ◽  
Computational Effort ◽  
Equivalence Transformations ◽  
State Space Approach ◽  
Nonconservative System ◽  
First Order ◽  
Physical Insight ◽  
Space Approach

The coefficients of a linear nonconservative system are arbitrary matrices lacking the usual properties of symmetry and definiteness. Classical modal analysis is extended in this paper so as to apply to systems with nonsymmetric coefficients. The extension utilizes equivalence transformations and does not require conversion of the equations of motion to first-order forms. Compared with the state-space approach, the generalized modal analysis can offer substantial reduction in computational effort and ample physical insight.

scholarly journals Actions, topological terms and boundaries in first-order gravity: A review

2016 ◽  
Vol 25 (04) ◽  
pp. 1630011 ◽  
Author(s):  
Alejandro Corichi ◽  
Irais Rubalcava-García ◽  
Tatjana Vukašinac
Keyword(s):  
Boundary Conditions ◽  
Symplectic Structure ◽  
Equations Of Motion ◽  
Hamiltonian Formalism ◽  
Action Principle ◽  
Internal Boundary ◽  
Four Dimensions ◽  
First Order ◽  
Conserved Charges ◽  
Boundary Terms

In this review, we consider first-order gravity in four dimensions. In particular, we focus our attention in formulations where the fundamental variables are a tetrad [Formula: see text] and a [Formula: see text] connection [Formula: see text]. We study the most general action principle compatible with diffeomorphism invariance. This implies, in particular, considering besides the standard Einstein–Hilbert–Palatini term, other terms that either do not change the equations of motion, or are topological in nature. Having a well defined action principle sometimes involves the need for additional boundary terms, whose detailed form may depend on the particular boundary conditions at hand. In this work, we consider spacetimes that include a boundary at infinity, satisfying asymptotically flat boundary conditions and/or an internal boundary satisfying isolated horizons boundary conditions. We focus on the covariant Hamiltonian formalism where the phase space [Formula: see text] is given by solutions to the equations of motion. For each of the possible terms contributing to the action, we consider the well-posedness of the action, its finiteness, the contribution to the symplectic structure, and the Hamiltonian and Noether charges. For the chosen boundary conditions, standard boundary terms warrant a well posed theory. Furthermore, the boundary and topological terms do not contribute to the symplectic structure, nor the Hamiltonian conserved charges. The Noether conserved charges, on the other hand, do depend on such additional terms. The aim of this manuscript is to present a comprehensive and self-contained treatment of the subject, so the style is somewhat pedagogical. Furthermore, along the way, we point out and clarify some issues that have not been clearly understood in the literature.

Consistent section-averaged equations of quasi-one-dimensional laminar flow

2010 ◽  
Vol 656 ◽  
pp. 337-341 ◽  
Author(s):  
PAOLO LUCHINI ◽  
FRANÇOIS CHARRU
Keyword(s):  
Equations Of Motion ◽  
Stability Result ◽  
Momentum Equation ◽  
Dissipation Function ◽  
Dimensional Solution ◽  
First Order ◽  
Averaged Equations ◽  
Classical Stability ◽  
Momentum Integral ◽  
Free Falling

Section-averaged equations of motion, widely adopted for slowly varying flows in pipes, channels and thin films, are usually derived from the momentum integral on a heuristic basis, although this formulation is affected by known inconsistencies. We show that starting from the energy rather than the momentum equation makes it become consistent to first order in the slowness parameter, giving the same results that have been provided until today only by a much more laborious two-dimensional solution. The kinetic-energy equation correctly provides the pressure gradient because with a suitable normalization the first-order correction to the dissipation function is identically zero. The momentum equation then correctly provides the wall shear stress. As an example, the classical stability result for a free falling liquid film is recovered straightforwardly.

Photoacoustic Nanotracers for Subsurface Applications: Opportunities and Challenges

2021 ◽  
Author(s):  
Jesus Manuel Felix Servin ◽  
Hala A. Al-Sadeg ◽  
Amr Abdel-Fattah
Keyword(s):  
Acoustic Waves ◽  
Oil And Gas ◽  
Continuous Wave ◽  
Tracer Tests ◽  
Oil And Gas Industry ◽  
Oil Reservoirs ◽  
Medical Community ◽  
Sound Waves ◽  
Time Data ◽  
Gas Industry

Abstract Tracers are practical tools to gather information about the subsurface fluid flow in hydrocarbon reservoirs. Typical interwell tracer tests involve injecting and producing tracers from multiple wells to evaluate important parameters such as connectivity, flow paths, fluid-fluid and fluid-rock interactions, and reservoir heterogeneity, among others. The upcoming of nanotechnology enables the development of novel nanoparticle-based tracers to overcome many of the challenges faced by conventional tracers. Among the advantages of nanoparticle-based tracers is the capability to functionalize their surface to yield stability and transportability through the subsurface. In addition, nanoparticles can be engineered to respond to a wide variety of stimuli, including light. The photoacoustic effect is the formation of sound waves following light absorption in a material sample. The medical community has successfully employed photoacoustic nanotracers as contrast agents for photoacoustic tomography imaging. We propose that properly engineered photoacoustic nanoparticles can be used as tracers in oil reservoirs. Our analysis begins by investigating the parameters controlling the conversion of light to acoustic waves, and strategies to optimize such parameters. Next, we analyze different kind of nanoparticles that we deem potential candidates for our subsurface operations. Then, we briefly discuss the excitation sources and make a comparison between continuous wave and pulsed sources. We finish by discussing the research gaps and challenges that must be addressed to incorporate these agents into our operations. At the time of this writing, no other study investigating the feasibility of using photoacoustic nanoparticles for tracer applications was found. Our work paves the way for a new class of passive tracers for oil reservoirs. Photoacoustic nanotracers are easy to detect and quantify and are therefore suitable for continuous in-line monitoring, contributing to the ongoing real-time data efforts in the oil and gas industry.

scholarly journals Criterios definidores y conceptuales del enfoque basado en derechos humanos: de la teoría a la práctica

2017 ◽  
pp. 43-86
Author(s):  
Alfonso CHACÓN MATA
Keyword(s):  
Human Rights ◽  
United Nations ◽  
Public Administration ◽  
Public Policies ◽  
The State ◽  
The Public ◽  
First Order ◽  
Derechos Humanos ◽  
The Subject ◽  
Human Rights Based Approach

LABURPENA: «Giza Eskubideetan Oinarritutako Ikuspegiaren» irismena azaltzeko asmoa dauka artikulu honek, zer-nolako aldagaiak eta kontzeptuak biltzen dituen ulertze aldera. Horren bilakaeraz eta indarraldiaz arituko gara, bai eta horren modalitate aplikatua nola nabarmentzen den azalduko ere. Horretarako, Nazio Batuen Erakundearen esparruan garatu diren ekarpenak eta gaiaren inguruko doktrina aditua erabiliko ditugu. Administrazio Publikoan duen indarra ezin ukatuzkoa da; izan ere, estatuak eta horri atxikitako erakundeek oso kontuan eduki behar dute politika publikoak norbanakoen eta komunitateen beharrei arreta ematen ari zaien jakiteko balio duela ikuspegi horrek, edota politika publiko horiek kontu emanez gardentasun publikoa eratzen ari diren nahiz edozelako diskriminazioa saihesten ari diren jakiteko balio duela. Azkenik, ikuspegi horrek Giza Eskubideen Gorte Interamerikarraren jurisprudentzia-aurrekari batzuetan duen indarraldia eta eragina aztertuko dira. RESUMEN: El presente artículo tiene la intención de exponer los alcances del «Enfoque Basado en Derechos Humanos», con la finalidad de entender que variables y conceptos involucra. Haremos un recuento de su evolución, vigencia y cómo se evidencia su modalidad aplicada, a través de diferentes aportes desarrollados en el marco de la Organización de Naciones Unidas, así como de la doctrina estudiosa del tema. Su vigencia en la Administración Pública es de primer orden, puesto que el Estado y sus entidades adscritas, deben tener muy en cuenta que el enfoque citado, sirve para conocer si las políticas públicas, están atendiendo necesidades de individuos y comunidades concretas; generando transparencia pública a través de rendición de cuentas, así como evitando cualquier tipo de discriminación. Finalmente, se analizará su vigencia e impacto en algunos antecedentes jurisprudenciales de la Corte Interamericana de Derechos Humanos. ABSTRACT: This article intends to expose the scope of the «Human Rights Based Approach», in order to understand what variables and concepts it involves. We will recount its evolution, validity and how its applied modality is evidenced, through different contributions developed within the framework of the United Nations, as well as the doctrine studious of the subject. Its validity in the Public Administration is of the first order, since the State and its affiliated entities must take into account that the aforementioned approach serves to know if public policies are addressing the needs of specific individuals and communities; Generating public transparency through accountability, as well as avoiding any type of discrimination. Finally, its validity and impact will be analyzed in some jurisprudential antecedents of the Inter-American Court of Human Rights.

Dynamic Analysis of Elastic Beam-Like Mechanism Systems

1989 ◽  
Vol 111 (4) ◽  
pp. 626-629
Author(s):  
W. Ying ◽  
R. L. Huston
Keyword(s):  
Dynamic Analysis ◽  
Dynamic Behavior ◽  
Cantilever Beam ◽  
Equations Of Motion ◽  
Elastic Beam ◽  
Order Perturbation ◽  
First Order ◽  
Geometric Stiffness ◽  
Stiffness Matrices ◽  
First Order Perturbation

In this paper the dynamic behavior of beam-like mechanism systems is investigated. The elastic beam is modeled by finite rigid segments connected by joint springs and dampers. The equations of motion are derived using Kane’s equations. The nonlinear terms are linearized by first order perturbation about a system balanced configuration state leading to geometric stiffness matrices. A simple numerical example of a rotating cantilever beam is presented.

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