1,476 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
Rotation Prevents Finite-Time Breakdown
We consider a two-dimensional convection model augmented with the rotational
Coriolis forcing, , with a fixed
being the inverse Rossby number. We ask whether the action of dispersive
rotational forcing alone, , prevents the generic finite time breakdown
of the free nonlinear convection. The answer provided in this work is a
conditional yes. Namely, we show that the rotating Euler equations admit global
smooth solutions for a subset of generic initial configurations. With other
configurations, however, finite time breakdown of solutions may and actually
does occur. Thus, global regularity depends on whether the initial
configuration crosses an intrinsic, critical threshold, which
is quantified in terms of the initial vorticity, ,
and the initial spectral gap associated with the initial velocity
gradient, . Specifically, global regularity of the rotational Euler equation is
ensured if and only if . We also prove that the velocity field remains smooth if and
only if it is periodic. We observe yet another remarkable periodic behavior
exhibited by the {\em gradient} of the velocity field. The spectral dynamics of
the Eulerian formulation reveals that the vorticity and the eigenvalues (and
hence the divergence) of the flow evolve with their own path-dependent period.
We conclude with a kinetic formulation of the rotating Euler equation
Alien Registration- Babin, Mary E. (Millinocket, Penobscot County)
https://digitalmaine.com/alien_docs/7928/thumbnail.jp
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
On Asymptotic Completeness of Scattering in the Nonlinear Lamb System, II
We establish the asymptotic completeness in the nonlinear Lamb system for
hyperbolic stationary states. For the proof we construct a trajectory of a
reduced equation (which is a nonlinear nonautonomous ODE) converging to a
hyperbolic stationary point using the Inverse Function Theorem in a Banach
space. We give the counterexamples showing nonexistence of such trajectories
for nonhyperbolic stationary points
Linear superposition in nonlinear wave dynamics
We study nonlinear dispersive wave systems described by hyperbolic PDE's in
R^{d} and difference equations on the lattice Z^{d}. The systems involve two
small parameters: one is the ratio of the slow and the fast time scales, and
another one is the ratio of the small and the large space scales. We show that
a wide class of such systems, including nonlinear Schrodinger and Maxwell
equations, Fermi-Pasta-Ulam model and many other not completely integrable
systems, satisfy a superposition principle. The principle essentially states
that if a nonlinear evolution of a wave starts initially as a sum of generic
wavepackets (defined as almost monochromatic waves), then this wave with a high
accuracy remains a sum of separate wavepacket waves undergoing independent
nonlinear evolution. The time intervals for which the evolution is considered
are long enough to observe fully developed nonlinear phenomena for involved
wavepackets. In particular, our approach provides a simple justification for
numerically observed effect of almost non-interaction of solitons passing
through each other without any recourse to the complete integrability. Our
analysis does not rely on any ansatz or common asymptotic expansions with
respect to the two small parameters but it uses rather explicit and
constructive representation for solutions as functions of the initial data in
the form of functional analytic series.Comment: New introduction written, style changed, references added and typos
correcte
Vortical and Wave Modes in 3D Rotating Stratified Flows: Random Large Scale Forcing
Utilizing an eigenfunction decomposition, we study the growth and spectra of
energy in the vortical and wave modes of a 3D rotating stratified fluid as a
function of . Working in regimes characterized by moderate
Burger numbers, i.e. or , our results
indicate profound change in the character of vortical and wave mode
interactions with respect to . As with the reference state of
, for the wave mode energy saturates quite quickly
and the ensuing forward cascade continues to act as an efficient means of
dissipating ageostrophic energy. Further, these saturated spectra steepen as
decreases: we see a shift from to scaling for
(where and are the forcing and dissipation scales,
respectively). On the other hand, when the wave mode energy
never saturates and comes to dominate the total energy in the system. In fact,
in a sense the wave modes behave in an asymmetric manner about .
With regard to the vortical modes, for , the signatures of 3D
quasigeostrophy are clearly evident. Specifically, we see a scaling
for and, in accord with an inverse transfer of energy, the
vortical mode energy never saturates but rather increases for all . In
contrast, for and increasing, the vortical modes contain a
progressively smaller fraction of the total energy indicating that the 3D
quasigeostrophic subsystem plays an energetically smaller role in the overall
dynamics.Comment: 18 pages, 6 figs. (abbreviated abstract
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