2,350 research outputs found
Relativistic point dynamics and Einstein formula as a property of localized solutions of a nonlinear Klein-Gordon equation
Einstein's relation E=Mc^2 between the energy E and the mass M is the
cornerstone of the relativity theory. This relation is often derived in a
context of the relativistic theory for closed systems which do not accelerate.
By contrast, Newtonian approach to the mass is based on an accelerated motion.
We study here a particular neoclassical field model of a particle governed by a
nonlinear Klein-Gordon (KG) field equation. We prove that if a solution to the
nonlinear KG equation and its energy density concentrate at a trajectory, then
this trajectory and the energy must satisfy the relativistic version of
Newton's law with the mass satisfying Einstein's relation. Therefore the
internal energy of a localized wave affects its acceleration in an external
field as the inertial mass does in Newtonian mechanics. We demonstrate that the
"concentration" assumptions hold for a wide class of rectilinear accelerating
motions
Trajectory and smooth attractors for Cahn-Hilliard equations with inertial term
The paper is devoted to a modification of the classical Cahn-Hilliard
equation proposed by some physicists. This modification is obtained by adding
the second time derivative of the order parameter multiplied by an inertial
coefficient which is usually small in comparison to the other physical
constants. The main feature of this equation is the fact that even a globally
bounded nonlinearity is "supercritical" in the case of two and three space
dimensions. Thus the standard methods used for studying semilinear hyperbolic
equations are not very effective in the present case. Nevertheless, we have
recently proven the global existence and dissipativity of strong solutions in
the 2D case (with a cubic controlled growth nonlinearity) and for the 3D case
with small inertial coefficient and arbitrary growth rate of the nonlinearity.
The present contribution studies the long-time behavior of rather weak (energy)
solutions of that equation and it is a natural complement of the results of our
previous papers. Namely, we prove here that the attractors for energy and
strong solutions coincide for both the cases mentioned above. Thus, the energy
solutions are asymptotically smooth. In addition, we show that the non-smooth
part of any energy solution decays exponentially in time and deduce that the
(smooth) exponential attractor for the strong solutions constructed previously
is simultaneously the exponential attractor for the energy solutions as well
Capturing design knowledge
A scheme is proposed to capture the design knowledge of a complex object including functional, structural, performance, and other constraints. Further, the proposed scheme is also capable of capturing the rationale behind the design of an object as a part of the overall design of the object. With this information, the design of an object can be treated as a case and stored with other designs in a case base. A person can then perform case-based reasoning by examining these designs. Methods of modifying object designs are also discussed. Finally, an overview of an approach to fault diagnosis using case-based reasoning is given
Giant Coulomb broadening and Raman lasing on ionic transitions
CW generation of anti-Stokes Raman laser on a number of blue-green argon-ion
lines (4p-4s, 4p-3d) has been demonstrated with optical pumping from metastable
levels 3d'^2G, 3d^4F. It is found, that the population transfer rate is
increased by a factor of 3-5 (and hence, the output power of such Raman laser)
owing to Coulomb diffusion in the velocity space. Measured are the excitation
and relaxation rates for the metastable level. The Bennett hole on the
metastable level has been recorded using the probe field technique. It has been
shown that the Coulomb diffusion changes shape of the contour to exponential
cusp profile while its width becomes 100 times the Lorentzian one and reaches
values close to the Doppler width. Such a giant broadening is also confirmed by
the shape of the absorption saturation curve.Comment: RevTex 18 pages, 5 figure
Flexible shielding system for radiation protection
Modular construction of low cost flexible radiation shielding panels consists of water filled steels cans, zinc bromide windows, turntable unit, master-slave manipulators, and interlocking lead bricks. Easy modifications of shielding wall thicknesses are obtained by rearranging overall geometry of portable components
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