34 research outputs found
Frame Indifferent Formulation of Maxwell's Elastic Fluid and the Rational Continuum Mechanics of the Electromagnetic Field
We show that the linearized equations of the incompressible elastic medium
admit a `Maxwell form' in which the shear component of the stress vector plays
the role of the electric field, and the vorticity plays the role of the
magnetic field. Conversely, the set of dynamic Maxwell equations are strict
mathematical corollaries from the governing equations of the incompressible
elastic medium. This suggests that the nature of `electromagnetic field' may
actually be related to an elastic continuous medium. The analogy is complete if
the medium is assumed to behave as fluid in shear motions, while it may still
behave as elastic solid under compressional motions. Then the governing
equations of the elastic fluid are re-derived in the Eulerian frame by
replacing the partial time derivatives by the properly invariant (frame
indifferent) time rates. The `Maxwell from' of the frame indifferent
formulation gives the frame indifferent system that is to replace the Maxwell
system. This new system comprises terms already present in the classical
Maxwell equations, alongside terms that are the progenitors of the
Biot--Savart, Oersted--Ampere's, and Lorentz--force laws. Thus a frame
indifferent (truly covariant) formulation of electromagnetism is achieved from
a single postulate that the electromagnetic field is a kind of elastic (partly
liquid partly solid) continuum.Comment: accepte
Physical dynamics of quasi-particles in nonlinear wave equations
By treating the centers of solitons as point particles and studying their
discrete dynamics, we demonstrate a new approach to the quantization of the
soliton solutions of the sine-Gordon equation, one of the first model nonlinear
field equations. In particular, we show that a linear superposition of the
non-interacting shapes of two solitons offers a qualitative (and to a good
approximation quantitative) description of the true two-soliton solution,
provided that the trajectories of the centers of the superimposed solitons are
considered unknown. Via variational calculus, we establish that the dynamics of
the quasi-particles obey a pseudo-Newtonian law, which includes cross-mass
terms. The successful identification of the governing equations of the
(discrete) quasi-particles from the (continuous) field equation shows that the
proposed approach provides a basis for the passage from the continuous to a
discrete description of the field.Comment: 10 pages, 3 figures (6 images); v2: revised and improved the
presentation, updated the references, fixed typos; v3: corrected a few minor
mistakes and typos, version accepted for publication in Phys. Lett.
Asymmetric Mach-Zehnder fiber interferometer test of the anisotropy of the speed of light
Two optical fiber Mach-Zehnder interferometers were constructed in an
environment with a temperature stabilization of better than 1 mK per day. One
interferometer with a length of 2 m optical fiber in each arm with the main
direction of the arms parallel to each other. A path (length 175 mm) filled
with atmospheric air is inserted in one arm. Another interferometer with a
length of 2 m optical fiber in each parallel arm acts as a control. In each arm
1 m of fiber was wound around a ring made of piezo material enabling the
control of the length of the arms by means of a voltage. The influence of
rotation of the interferometers at the Earth surface on the observed phase
differences was determined. For one interferometer (with the air path) it was
found that the phase difference depends on the azimuth of the interferometer.
For the other one no relevant dependence on the azimuth has been measured.Comment: 6 pages, 6 figure
Stable two-dimensional solitary pulses in linearly coupled dissipative Kadomtsev-Petviashvili equations
A two-dimensional (2D) generalization of the stabilized Kuramoto -
Sivashinsky (KS) system is presented. It is based on the Kadomtsev-Petviashvili
(KP) equation including dissipation of the generic (Newell -- Whitehead --
Segel, NWS) type and gain. The system directly applies to the description of
gravity-capillary waves on the surface of a liquid layer flowing down an
inclined plane, with a surfactant diffusing along the layer's surface.
Actually, the model is quite general, offering a simple way to stabilize
nonlinear waves in media combining the weakly-2D dispersion of the KP type with
gain and NWS dissipation. Parallel to this, another model is introduced, whose
dissipative terms are isotropic, rather than of the NWS type. Both models
include an additional linear equation of the advection-diffusion type, linearly
coupled to the main KP-NWS equation. The extra equation provides for stability
of the zero background in the system, opening a way to the existence of stable
localized pulses. The consideration is focused on the case when the dispersive
part of the system of the KP-I type, admitting the existence of 2D localized
pulses. Treating the dissipation and gain as small perturbations and making use
of the balance equation for the field momentum, we find that the equilibrium
between the gain and losses may select two 2D solitons, from their continuous
family existing in the conservative counterpart of the model (the latter family
is found in an exact analytical form). The selected soliton with the larger
amplitude is expected to be stable. Direct simulations completely corroborate
the analytical predictions.Comment: a latex text file and 16 eps files with figures; Physical Review E,
in pres
Implicit time splitting for fourth-order parabolic equations
A coordinate-splitting economic difference scheme is proposed for generalized parabolic equations (GPE) containing fourth-order diffusion operators and the algorithm for its implementation is developed. The performance of the scheme is demonstrated for different cases, e.g. for treating bifurcation phenomena. The technique is applied to the numerical solution of Swift-Hohenberg equation describing the Rayleigh-Bénard convection and results are obtained for very large system sizes and for very long times on small computational platform.SCOPUS: ar.jinfo:eu-repo/semantics/publishe