470 research outputs found
Propagation of a laser beam in a plasma
This paper shows that for a nonabsorbing medium with a prescribed index of refraction, the effects of beam stability, line focusing, and beam distortion can be predicted from simple ray optics. When the paraxial approximation is used, diffraction effects are examined for Gaussian, Lorentzian, and square beams. Most importantly, it is shown that for a Gaussian beam, diffraction effects can be included simply by adding imaginary solutions to the paraxial ray equations. Also presented are several procedures to extend the paraxial approximation so that the solution will have a domain of validity of greater extent
The time-history of a satellite around an oblate planet
Time history of satellite around oblate plane
The Higher Orders of the Theory of Strong Perturbations in Quantum Mechanics and the Secularity Problem
We solve the higher order equations of the theory of the strong perturbations
in quantum mechanics given in M. Frasca, Phys. Rev. A 45, 43 (1992), by
assuming that, at the leading order, the wave function goes adiabatically. This
is accomplished by deriving the unitary operator of adiabatic evolution for the
leading order. In this way it is possible to show that at least one of the
causes of the problem of phase-mixing, whose effect is the polynomial increase
in time of the perturbation terms normally called secularities, arises from the
shifts of the perturbation energy levels due to the unperturbed part of the
hamiltonian. An example is given for a two-level system that, anyway, shows a
secularity at second order also in the standard theory of small perturbations.
The theory is applied to the quantum analog of a classical problem that can
become chaotic, a particle under the effect of two waves of different
amplitudes, frequencies and wave numbers.Comment: 13 pages, Late
Transient resonances in the inspirals of point particles into black holes
We show that transient resonances occur in the two body problem in general
relativity, in the highly relativistic, extreme mass-ratio regime for spinning
black holes. These resonances occur when the ratio of polar and radial orbital
frequencies, which is slowly evolving under the influence of gravitational
radiation reaction, passes through a low order rational number. At such points,
the adiabatic approximation to the orbital evolution breaks down, and there is
a brief but order unity correction to the inspiral rate. Corrections to the
gravitational wave signal's phase due to resonance effects scale as the square
root of the inverse of mass of the small body, and thus become large in the
extreme-mass-ratio limit, dominating over all other post-adiabatic effects. The
resonances make orbits more sensitive to changes in initial data (though not
quite chaotic), and are genuine non-perturbative effects that are not seen at
any order in a standard post-Newtonian expansion. Our results apply to an
important potential source of gravitational waves, the gradual inspiral of
white dwarfs, neutron stars, or black holes into much more massive black holes.
It is hoped to exploit observations of these sources to map the spacetime
geometry of black holes. However, such mapping will require accurate models of
binary dynamics, which is a computational challenge whose difficulty is
significantly increased by resonance effects. We estimate that the resonance
phase shifts will be of order a few tens of cycles for mass ratios , by numerically evolving fully relativistic orbital dynamics
supplemented with an approximate, post-Newtonian self-force.Comment: 4 pages, 1 figure, minor correction
Enzyme kinetics for a two-step enzymic reaction with comparable initial enzyme-substrate ratios
We extend the validity of the quasi-steady state assumption for a model double intermediate enzyme-substrate reaction to include the case where the ratio of initial enzyme to substrate concentration is not necessarily small. Simple analytical solutions are obtained when the reaction rates and the initial substrate concentration satisfy a certain condition. These analytical solutions compare favourably with numerical solutions of the full system of differential equations describing the reaction. Experimental methods are suggested which might permit the application of the quasi-steady state assumption to reactions where it may not have been obviously applicable before
Noise Effects on Synchronized Globally Coupled Oscillators
The synchronized phase of globally coupled nonlinear oscillators subject to
noise fluctuations is studied by means of a new analytical approach able to
tackle general couplings, nonlinearities, and noise temporal correlations. Our
results show that the interplay between coupling and noise modifies the
effective frequency of the system in a non trivial way. Whereas for linear
couplings the effect of noise is always to increase the effective frequency,
for nonlinear couplings the noise influence is shown to be positive or negative
depending on the problem parameters. Possible experimental verification of the
results is discussed.Comment: 6 Pages, 4 EPS figures included (RevTeX and epsfig needed). Submitted
to Phys. Re
Second-order gravitational self-force
Using a rigorous method of matched asymptotic expansions, I derive the
equation of motion of a small, compact body in an external vacuum spacetime
through second order in the body's mass (neglecting effects of internal
structure). The motion is found to be geodesic in a certain locally defined
regular geometry satisfying Einstein's equation at second order. I outline a
method of numerically obtaining both the metric of that regular geometry and
the complete second-order metric perturbation produced by the body.Comment: 5 pages, added clarifications in response to referee comments,
accepted for publication in PR
Nonlinear dynamics in one dimension: On a criterion for coarsening and its temporal law
We develop a general criterion about coarsening for a class of nonlinear
evolution equations describing one dimensional pattern-forming systems. This
criterion allows one to discriminate between the situation where a coarsening
process takes place and the one where the wavelength is fixed in the course of
time. An intermediate scenario may occur, namely `interrupted coarsening'. The
power of the criterion lies in the fact that the statement about the occurrence
of coarsening, or selection of a length scale, can be made by only inspecting
the behavior of the branch of steady state periodic solutions. The criterion
states that coarsening occurs if lambda'(A)>0 while a length scale selection
prevails if lambda'(A)<0, where is the wavelength of the pattern and A
is the amplitude of the profile. This criterion is established thanks to the
analysis of the phase diffusion equation of the pattern. We connect the phase
diffusion coefficient D(lambda) (which carries a kinetic information) to
lambda'(A), which refers to a pure steady state property. The relationship
between kinetics and the behavior of the branch of steady state solutions is
established fully analytically for several classes of equations. Another
important and new result which emerges here is that the exploitation of the
phase diffusion coefficient enables us to determine in a rather straightforward
manner the dynamical coarsening exponent. Our calculation, based on the idea
that |D(lambda)|=lambda^2/t, is exemplified on several nonlinear equations,
showing that the exact exponent is captured. Some speculations about the
extension of the present results to higher dimension are outlined.Comment: 16 pages. Only a few minor changes. Accepted for publication in
Physical Review
Nonlinear dynamics of coupled transverse-rotational waves in granular chains
The nonlinear dynamics of coupled waves in one-dimensional granular chains with and without a substrate
is theoretically studied accounting for quadratic nonlinearity. The multiple time scale method is used to derive
the nonlinear dispersion relations for infinite granular chains and to obtain the wave solutions for semiinfinite
systems. It is shown that the sum-frequency and difference-frequency components of the coupled
transverse-rotational waves are generated due to their nonlinear interactions with the longitudinal wave.
Nonlinear resonances are not present in the chain with no substrate where these frequency components have
low amplitudes and exhibit beating oscillations. In the chain positioned on a substrate two types of nonlinear
resonances are predicted. At resonance, the fundamental frequency wave amplitudes decrease and the
generated frequency component amplitudes increase along the chain, accompanied by the oscillations due to
the wave numbers asynchronism. The results confirm the possibility of a highly efficient energy transfer
between the waves of different frequencies, which could find applications in the design of acoustic devices
for energy transfer and energy rectification
Theory for a dissipative droplet soliton excited by a spin torque nanocontact
A novel type of solitary wave is predicted to form in spin torque oscillators
when the free layer has a sufficiently large perpendicular anisotropy. In this
structure, which is a dissipative version of the conservative droplet soliton
originally studied in 1977 by Ivanov and Kosevich, spin torque counteracts the
damping that would otherwise destroy the mode. Asymptotic methods are used to
derive conditions on perpendicular anisotropy strength and applied current
under which a dissipative droplet can be nucleated and sustained. Numerical
methods are used to confirm the stability of the droplet against various
perturbations that are likely in experiments, including tilting of the applied
field, non-zero spin torque asymmetry, and non-trivial Oersted fields. Under
certain conditions, the droplet experiences a drift instability in which it
propagates away from the nanocontact and is then destroyed by damping.Comment: 15 pages, 12 figure
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