3,726 research outputs found
Explicit computation of the electrostatic energy for an elliptical charged disc.
International audienceThis letter describes a method for obtaining an explicit expression for the electrostatic energy of a charged elliptical infinitely thin disc. The charge distribution is assumed to be polynomial. Such explicit values for this energy are fundamental for assessing the accuracy of boundary element codes. The main tools used are an extension of Copson's method and a diagonalization, given by Leppington and Levine, of the single-layer potential operator associated with the electrostatic potential created by a distribution of charges on the elliptical disc
Electromagnetic Force and the Maxwell Stress Tensor in Condensed Systems
While the electromagnetic force is microscopically simply the Lorentz force,
its macroscopic form is more complicated, and given by expressions such as the
Maxwell stress tensor and the Kelvin force. Their derivation is fairly opaque,
at times even confusing, and their range of validity all but a well kept
secret. These circumstances unnecessarily reduce the usefulness and
trustworthiness of some key quantities in macroscopic electrodynamics.
This article presents a thorough yet pedagogical derivation of the Maxwell
stress tensor and electromagnetic force in condensed media. It starts from
universally accepted inputs: conservation laws, thermodynamics and the Maxwell
equations. Simplifications are considered for various limits, especially the
equilibrium, with a range of validity assigned to each expression. Some
widespread misconceptions are scrutinized, and hidden ambiguities in popular
notations revealed.
A number of phenomena typical of strongly polarizable systems, especially
ferrofluid, are then considered. In addition to enhancing the appreciation of
these systems, it helps to solidify the grasp of the introduced concepts and
derived formulas, and it demonstrates the ease with which the Maxwell stress
tensor can be handled, inviting theorists and experimentalists alike to embrace
this useful quantity.Comment: 27 pages, 7 fi
Effective conditions for the reflection of an acoustic wave by low-porosity perforated plates
International audienceThis paper describes an investigation of the acoustic properties of a low-porosity perforated plate in a compressible ideal inviscid fluid in the absence of mean flow. The study shows in particular how the reflection and transmission coefficients of an acoustic plane wave produced by such a device can be expressed in terms of the Rayleigh conductivity of an isolated perforation by extending the approach introduced for the case of thick plates by Leppington and Levine, \textit{Reflexion and transmission at a plane screen with periodically arranged circular or elliptical apertures}, J. Fluid Mech., 1973, p.109-127. Lower and upper bounds for the Rayleigh conductivity of a perforation in a thick plate are usually derived from intuitive approximations and by reasoning based on physical observation. The paper addresses a mathematical justification of these approaches, yielding accurate bounds for various geometries, untilted or tilted, with a conical shape or an elliptical section. Accurate estimates of the Rayleigh conductivity for a single perforation have a direct impact on the precision of models used for predicting the acoustic behavior of a perforated plate mainly on the basis of its reflection and transmission coefficients. It is shown in this paper how asymptotic expansions can be used to derive first and second-order accurate, albeit approximate expressions of these coefficients, as well as of the effective compliance of the perforated plate
Index to NASA Tech Briefs, 1975
This index contains abstracts and four indexes--subject, personal author, originating Center, and Tech Brief number--for 1975 Tech Briefs
Determination of impact parameter for CEE with Digi-input neural networks
Impact parameter is an important quantity which characterizes the centrality
in nucleus-nucleus collision geometry. The determination of impact parameter in
real experiments takes use of the hits on detector system or the reconstructed
tracks of the secondary particles. As a task of feature recognition, methods
such as sharp cut-off, Bayesian methods and Neural Networks (NN) has been
studied and applied. However, in the situation of the Cooler-storage-ring
External-target Experiment (CEE), the low beam energy brings a lapse of
dependency between impact parameter and charged particle multiplicity, which
decreases the validity of the explicit determination methods. This work
proposes a regressor constructed with Graph Attention neural network, which
takes the hit-level data as input. This model has shown a mean absolute error
of 0.496 fm for the IQMD collision data of the UU system at 0.5 AMeV. The
performance of such a model is compared with reference models, showing its
capacity in handling the original but potentially interrelated digi
information.Comment: 13 pages, 9 figure
Darwin-Lagrangian Analysis for the Interaction of a Point Charge and a Magnet: Considerations Related to the Controversy Regarding the Aharonov-Bohm and Aharonov-Casher Phase Shifts
The classical electromagnetic interaction of a point charge and a magnet is
discussed by first calculating the interaction of point charge with a simple
model magnetic moment and then suggesting a multiparticle limit. The Darwin
Lagrangian is used to analyze the electromagnetic behavior of the model
magnetic moment (composed of two oppositely charged particles of different mass
in an initially circular orbit) interacting with a passing point charge. The
changing mangetic moment is found to put a force back on a passing charge; this
force is of order 1/c^2 and depends upon the magnitude of the magnetic moment.
It is suggested that in the limit of a multiparticle magnetic toroid, the
electric fields of the passing charge are screened out of the body of the
magnet while the magnetic fields penetrate into the magnet. This is consistent
with our understanding of the penetration of electromagnetic velocity fields
into ohmic conductors. Conservation laws are discussed. The work corresponds to
a classical electromagnetic analysis of the interaction which is basic to
understanding the controversy over the Aharonov-Bohm and Aharonov-Casher phase
shifts and represents a refutation of the suggestions of Aharonov, Pearle, and
Vaidman.Comment: 33 page
Elastic Instability Triggered Pattern Formation
Recent experiments have exploited elastic instabilities in membranes to
create complex patterns. However, the rational design of such structures poses
many challenges, as they are products of nonlinear elastic behavior. We pose a
simple model for determining the orientational order of such patterns using
only linear elasticity theory which correctly predicts the outcomes of several
experiments. Each element of the pattern is modeled by a "dislocation dipole"
located at a point on a lattice, which then interacts elastically with all
other dipoles in the system. We explicitly consider a membrane with a square
lattice of circular holes under uniform compression and examine the changes in
morphology as it is allowed to relax in a specified direction.Comment: 15 pages, 7 figures, the full catastroph
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