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1.
In this paper the Lorentz transformations (LT) and the standard transformations (ST) of the usual Maxwell equations (ME) with
the three-dimensional (3D) vectors of the electric and magnetic fields, E and B, respectively, are examined using both the geometric algebra and tensor formalisms. Different 4D algebraic objects are used
to represent the usual observer dependent and the new observer independent electric and magnetic fields. It is found that
the ST of the ME differ from their LT and consequently that the ME with the 3D E and B are not covariant upon the LT but upon the ST. The obtained results do not depend on the character of the 4D algebraic objects
used to represent the electric and magnetic fields. The Lorentz invariant field equations are presented with 1-vectors E and B, bivectors EHv and BHv and the abstract tensors, the 4-vectors Ea and Ba. All these quantities are defined without reference frames, i.e., as absolute quantities. When some basis has been introduced,
they are represented as coordinate-based geometric quantities comprising both components and a basis. It is explicitly shown
that this geometric approach agrees with experiments, e.g., the Faraday disk, in all relatively moving inertial frames of
reference, which is not the case with the usual approach with the 3D bf E and B and their ST. 相似文献
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Kai Koike 《Journal of statistical physics》2018,172(3):795-823
Linear motion of a rigid body in a special kind of Lorentz gas is mathematically analyzed. The rigid body moves against gas drag according to Newton’s equation. The gas model is a special Lorentz gas consisting of gas molecules and background obstacles, which was introduced in Tsuji and Aoki (J Stat Phys 146:620–645, 2012). The specular boundary condition is imposed on the resulting kinetic equation. This study complements the numerical study by Tsuji and Aoki cited above—although the setting in this paper is slightly different from theirs, qualitatively the same asymptotic behavior is proved: The velocity V(t) of the rigid body decays exponentially if the obstacles undergo thermal motion; if the obstacles are motionless, then the velocity V(t) decays algebraically with a rate \(t^{-\,5}\) independent of the spatial dimension. This demonstrates the idea that interaction of the molecules with the background obstacles destroys the memory effect due to recollision. 相似文献
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The Lorentz transformations are used within the model of a noninertial reference frame without infinitely high accelerations arising at instantaneous jumps of an accelerated observer between different inertial reference frames. It is demonstrated that the twin paradox can be explained within this model with the help of the Lorentz transformations. Based on the model of a noninertial reference frame, the acceleration a
measured in the noninertial reference frame is related to the acceleration a measured in an inertial reference frame. 相似文献
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Journal of Experimental and Theoretical Physics - The structural transformations in a nematic liquid crystal (NLC) layer with a hybrid orientation (planar director orientation is created on one... 相似文献
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A linearized system of equations of hydrodynamics with time-dependent spatially localized right-hand side placed both on the free surface (and on the bottom of the basin) and also in the layer of the liquid is considered in a layer of variable depth with a given basic plane-parallel flow. A method of constructing asymptotic solutions of this problem is suggested; it consists of two stages: (1) a reduction of the three-dimensional problem to a two-dimensional inhomogeneous pseudodifferential equation on the nonperturbed free surface of the liquid, (2) a representation of the localized right-hand side in the form of a Maslov canonical operator on a special Lagrangian manifold and the subsequent application of a generalization to evolution problems of an approach, which was recently suggested in the paper [A. Yu. Anikin, S. Yu. Dobrokhotov, V. E. Nazaikinskii, and M. Rouleux, Dokl. Ross. Akad. Nauk 475 (6), 624–628 (2017); Engl. transl.: Dokl. Math. 96 (1), 406–410 (2017)], to solving stationary problems with localized right-hand sides and its combination with “nonstandard” characteristics. A method of calculation (generalizing long-standing results of Dobrokhotov and Zhevandrov) of an analog of the Kelvin wedge and the wave fields inside the wedge and in its neighborhood is suggested, which uses the consideration that this method is the projection to the extended configuration space of a Lagrangian manifold formed by the trajectories of the Hamiltonian vector field issuing from the intersection of the set of zeros of the extended Hamiltonian of the problem with conormal bundle to the graph of the vector function defining the trajectory of motion of an equivalent source on the surface of the liquid. 相似文献
7.
O. V. Rudenko 《Acoustical Physics》2018,64(4):422-431
The phenomenon of “wave resonance” which occurs at excitation of traveling waves in dissipative media possessing modular, quadratic and quadratically-cubic nonlinearities is studied. The mathematical model of this phenomenon is the inhomogeneous (or “forced”) equation of Burgers type. Such nonlinearities are of interest because the corresponding equations admit exact linearization and describe real physical objects. The presence of “accompanying sources” (traveling with the wave) on the right-hand side of the inhomogeneous equations ensures the inflow of energy into the wave, which thereafter spreads throughout the wave profile, flows to emerging shock fronts, and then dissipates due to linear and nonlinear losses. As an introduction, the phenomenon of wave resonance in ideal and dissipative media is described and physical examples are given. Exact expressions for nonlinear steady-state wave profiles are derived. Non-stationary processes of wave generation, spatial “beating” of amplitudes with different relationship between the speed of motion of the sources and the natural wave velocity in the medium are studied. Resonance curves are constructed that contain a nonlinear shift of the absolute maxima to the “supersonic” region. The features of the resonance in each of the three types of nonlinearity are discussed. 相似文献
8.
We study the problem of motion of a relativistic, ideal elastic solid with free surface boundary by casting the equations
in material form (“Lagrangian coordinates”). By applying a basic theorem due to Koch, we prove short-time existence and uniqueness
for solutions close to a trivial solution. This trivial, or natural, solution corresponds to a stress-free body in rigid motion. 相似文献
9.
W. Drechsler 《Fortschritte der Physik》1979,27(10):489-509
Heisenberg type equations of motion are established in a nonabelian gauge theory with minimal and nonminimal couplings and various relativistic particle equations of motion are derived from them. These equations for pointlike particles possessing a nonabelian gauge interaction (chosen for definiteness to be of SO(4,1) type) ore obtained in classical limit, ħ → 0, or in a semiclassical limit in which contributions of first order in ħ are retained. As a byproduct of the formalism, which can be applied to an arbitrary gauge group, a simple derivation of the Lorentz equation and the Bargmann-Michel-Telegdi equation from spinor electrodynamics with anomalous (i.e. nonminimal) coupling is given starting from the associated quantum mechanical Heisenberg equations of motion and specializing the gauge group to the electromagnetic U(1) group. 相似文献
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We study the motion of a compressible perfect liquid body in vacuum. This can be thought of as a model for the motion of the
ocean or a star. The free surface moves with the velocity of the liquid and the pressure vanishes on the free surface. This
leads to a free boundary problem for Euler's equations, where the regularity of the boundary enters to highest order. We prove
local existence in Sobolev spaces assuming a ``physical condition', related to the fact that the pressure of a fluid has
to be positive.
The author was supported in part by the National Science Foundation. 相似文献
15.
Hans Lindblad 《Communications in Mathematical Physics》2003,236(2):281-310
We study the motion of a compressible perfect liquid body in vacuum. This can be through of as a model for the motion of
the ocean or a star. The free surface moves with the velocity of the liquid and the pressure vanishes on the free surface.
This leads to a free boundary problem for Euler's equations, where the regularity of the boundary enters to highest order.
We prove linearized stability in Sobolev space assuming a ``physical condition', related to the fact that the pressure of
a fluid has to be positive.
Received: 23 September 2002 / Accepted: 2 December 2002
Published online: 14 April 2003
RID="⋆"
ID="⋆" The author was supported in part by the National Science Foundation.
Communicated by P. Constantin 相似文献
16.
Two hierarchies of new nonlinear differential-difference equations with one continuous variable and one discrete variable are constructed from the Darboux transformations of the Kaup–Newell hierarchy of equations. Their integrable properties such as recursion operator, zero-curvature representations, and bi-Hamiltonian structures are studied. In addition, the hierarchy of equations obtained by Wu and Geng is identified with the hierarchy of two-component modified Volterra lattice equations. 相似文献
17.
The problem of finding the mean field equations of motion in the theories with unstable vacuum is considered. The one- and two-loop quantum corrections to classical equations of motion are obtained. It is shown that these quantum corrections are real and causal. 相似文献
18.
Fritz Rohrlich 《Foundations of Physics》1998,28(7):1045-1056
It is argued that time's arrow is present in all equations of motion. But it is absent in the point particle approximations commonly made. In particular, the Lorentz-Abraham-Dirac equation is time-reversal invariant only because it approximates the charged particle by a point. But since classical electrodynamics is valid only for finite size particles, the equations of motion for particles of finite size must be considered. Those equations are indeed found to lack time-reversal invariance, thus ensuring an arrow of time. Similarly, more careful considerations of the equations of motion for gravitational interactions also show an arrow of time. The existence of arrows of time in quantum dynamics is also emphasized. 相似文献
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Doklady Physics - In the absence of external forces in the mechanical system consisting of an interacting body and a material point, the law of motion of the point is constructed, which implements... 相似文献
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Lorentz Invariance and Brownian Motion of Test Particles with Constant Classical Velocity in Electromagnetic Vacuum 下载免费PDF全文
We show that the velocity and position dispersions of a test particle with a nonzero constant classical velocity undergoing Brownian motion caused by electromagnetic vacuum fluctuations in a space with plane boundaries can be obgained from those of the static case by Lorentz transformation. We explicitly derive the Lorentz transformations relating the dispersions of the two cases and then apply them to the case of the Brownian motion of a test particle with a constant classical velocity parallel to the boundary between two conducting planes. Our results show that the influence of a nonzero initial velocity is negligible for nonrelativistic test particles. 相似文献