273 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
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
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
Hamiltonian formulation of nonequilibrium quantum dynamics: geometric structure of the BBGKY hierarchy
Time-resolved measurement techniques are opening a window on nonequilibrium
quantum phenomena that is radically different from the traditional picture in
the frequency domain. The simulation and interpretation of nonequilibrium
dynamics is a conspicuous challenge for theory. This paper presents a novel
approach to quantum many-body dynamics that is based on a Hamiltonian
formulation of the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy of
equations of motion for reduced density matrices. These equations have an
underlying symplectic structure, and we write them in the form of the classical
Hamilton equations for canonically conjugate variables. Applying canonical
perturbation theory or the Krylov-Bogoliubov averaging method to the resulting
equations yields a systematic approximation scheme. The possibility of using
memory-dependent functional approximations to close the Hamilton equations at a
particular level of the hierarchy is discussed. The geometric structure of the
equations gives rise to reduced geometric phases that are observable even for
noncyclic evolutions of the many-body state. The formalism is applied to a
finite Hubbard chain which undergoes a quench in on-site interaction energy U.
Canonical perturbation theory, carried out to second order, fully captures the
nontrivial real-time dynamics of the model, including resonance phenomena and
the coupling of fast and slow variables.Comment: 17 pages, revise
On phenomenon of scattering on resonances associated with discretisation of systems with fast rotating phase
Numerical integration of ODEs by standard numerical methods reduces a
continuous time problems to discrete time problems. Discrete time problems have
intrinsic properties that are absent in continuous time problems. As a result,
numerical solution of an ODE may demonstrate dynamical phenomena that are
absent in the original ODE. We show that numerical integration of system with
one fast rotating phase lead to a situation of such kind: numerical solution
demonstrate phenomenon of scattering on resonances that is absent in the
original system.Comment: 10 pages, 5 figure
Gravitational radiation reaction and inspiral waveforms in the adiabatic limit
We describe progress evolving an important limit of binary orbits in general
relativity, that of a stellar mass compact object gradually spiraling into a
much larger, massive black hole. These systems are of great interest for
gravitational wave observations. We have developed tools to compute for the
first time the radiated fluxes of energy and angular momentum, as well as
instantaneous snapshot waveforms, for generic geodesic orbits. For special
classes of orbits, we compute the orbital evolution and waveforms for the
complete inspiral by imposing global conservation of energy and angular
momentum. For fully generic orbits, inspirals and waveforms can be obtained by
augmenting our approach with a prescription for the self force in the adiabatic
limit derived by Mino. The resulting waveforms should be sufficiently accurate
to be used in future gravitational-wave searches.Comment: Accepted for publication in Phys. Rev. Let
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