共查询到20条相似文献,搜索用时 15 毫秒
1.
We study the threshold in systems which exhibit a symmetry breaking instability, described by a PDE that is of first order in time like the Ginzburg-Landau or Swift-Hohenberg equation, with the control parameter fluctuating in space and time. From the zero-dimensional case it is known that due to the long tails of the probability distributions all the moments of the linearized equation have different thresholds and none of them coincides with the threshold of the full nonlinear equation, which in fact has no noise-induced shift. We show that in the spatially extended case and with noise of finite correlation length there is a noise-induced threshold shift. At linear order in the fluctuation strength ε the threshold coincides with that of the first (and second) moment of the linearized equation. At order ε2 differences in the thresholds arise. We introduce a method to obtain the threshold of the full system up to order ε2 from the stability exponents of the first and second moment of the linearized equations. A preliminary account of this work has been given elsewhere [A. Becker and L. Kramer, Phys. Rev. Lett. 73 (1994) 955]. 相似文献
2.
P. Mandel 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2000,8(3):431-442
The global integro-differential rate equations describing a multimode laser are analyzed. Expressions for the relaxation oscillation
frequencies and their damping rates in the single-mode and two-mode regimes are obtained without specifying either the cavity
geometry or the longitudinal pump profile. On the same level of generality, we prove the existence of universal relations
relating the peaks of the power spectra in the two-mode regime. For a Fabry-Perot with arbitrary longitudinal pump profile,
series expansions of all the physical functions are derived in powers of the pump moments. These moments are averages of the
pump profile over cavity modes at linear combinations of the lasing frequencies and their harmonics. These results apply to
end-pumped and/or partially filled lasers. For a single mode Fabry-Perot laser, we prove that the contribution to the steady
state intensity from the lasing mode varies from 75% close to the lasing threshold to zero at high intensity. The remainder
comes from the harmonics of the lasing mode. Analyzing the steady state single mode intensity equation in terms of the pump
gratings, we prove that close to the lasing threshold only the space average of the pump and its grating oscillating at twice
the lasing wave number do not vanish. This provides a hint towards the justification of the usual modal rate equations which
retain only these two functions in the dynamical evolution of a laser. For a Fabry-Perot with constant pump profile, an exact
expression for the upper boundary of the stable single mode regime is derived. In that two-mode regime, we prove that there
is a critical value of the pump at which the ratio of the two relaxation oscillation frequencies is 2, leading to an internal
resonance. 相似文献
3.
4.
Frequency degenerate and non-degenerate nonlinear
regimes for semi-linear photorefractive oscillator
M. Grapinet P. Mathey H. R. Jauslin B. Sturman D. Rytz S. Odoulov 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2007,41(2):363-369
We present a theoretical analysis, analytical and numerical, of
the oscillation regimes for the semi-linear photorefractive
oscillator beyond the instability threshold. This analysis
includes the limiting cases of dominating transmission and
reflection gratings as well as the cases of spontaneous violation
of the frequency degeneracy between the oscillation and pump
waves. 相似文献
5.
M. Hoyuelos G.-L. Oppo P. Colet M. San Miguel 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2003,22(3):441-451
We analyze the quantum fluctuations of the degenerate optical parametric oscillator close to an instability for the formation
of a square pattern. While strong correlations between the fluctuations of the signal modes emitted at the critical wave number
and with opposite wave vector are present both below and above threshold, no features signaling the square character of the
pattern forming above threshold have been identified below threshold in the spatio-temporal second-order coherence. We also
explore in which regimes a reduced few mode model gives meaningful results.
Received 17 September 2002 / Received in final form 11 November 2002 Published online 26 February 2003 相似文献
6.
H. A. Batarfi S. S. Hassan R. Saunders R. K. Bullough 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2000,8(3):417-429
Linear stability analysis and (numerical) investigation of the periodic and chaotic self-pulsing behaviour are presented for
the Maxwell-Bloch equations of a bistable model in contact with a squeezed vacuum field. Effect of the squeeze phase parameter
on the period doubling bifurcation that preceeds chaos is examined for the adiabatic and non-adiabatic regimes. 相似文献
7.
P. Mathey M. Grapinet H. R. Jauslin B. Sturman D. Rytz S. Odoulov 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2006,39(3):445-451
A general analysis of the threshold behavior for the
photorefractive semi-linear oscillator is performed within the
linear approximation on the basis of the classical wave-coupling
model. This analysis shows that the well known particular results
on the frequency degenerate oscillation are valid only within a
restricted range of the external parameters. The theory specifies
the conditions for onset and properties of the frequency
non-degenerate oscillations, including the necessary values of the
coupling strength, pump intensity ratio, the increments of the
instability, and the frequency splits. Important generalizations
of the basic model are considered. 相似文献
8.
9.
We study theoretically the dynamical reorientation phenomena when a long-pitch cholesteric liquid-crystal film with homeotropic alignment is illuminated by a circularly polarized lightwave. In the present case, the natural cholesteric pitch is of the order of (or larger than) the film thickness. The helical cholesteric structure is thus frustrated by the boundary conditions without illumination. However, above a light intensity threshold reorientation occurs and the bifurcation scenario depends strongly on the natural cholesteric pitch. Recalling that a long-pitch cholesteric is achieved in practice by adding a small amount of chiral agents in a nematic liquid crystal, the observed dynamics can be viewed as the result of the competition between intrinsic and extrinsic unidimensional helical patterns. The intrinsic part consists of the helical deformations induced by the chirality of the dopant, whereas the extrinsic part is related to the chirality induced by the optical field through the non-uniform angular momentum transfer of light to a nematic. The all-optical analog in the case of a pure nematic (without chiral dopant), is also discussed. 相似文献
10.
M. Baptista S. M.A. Gama V. A. Zheligovsky 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,60(3):337-351
An eigenvalue equation, for linear instability modes involving large
scales in a convective hydromagnetic system, is derived in the framework
of multiscale analysis. We consider a horizontal layer with electrically
conducting boundaries, kept at fixed temperatures and with free surface
boundary conditions for the velocity field; periodicity in horizontal
directions is assumed. The steady states must be stable to short (fast)
scale perturbations and possess symmetry about the vertical axis,
allowing instabilities involving large (slow) scales to develop. We
expand the modes and their growth rates in power series in the scale
separation parameter and obtain a hierarchy of equations, which are
solved numerically. Second order solvability condition yields a closed
equation for the leading terms of the asymptotic expansions and respective
growth rate, whose origin is in the (combined) eddy diffusivity phenomenon.
For about 10% of randomly generated steady convective hydromagnetic
regimes, negative eddy diffusivity is found. 相似文献
11.
12.
13.
F. Pétrélis S. Aumaître 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,51(3):357-362
We study two dynamical systems submitted to white and Gaussian random noise acting multiplicatively. The first system is an
imperfect pitchfork bifurcation with a noisy departure from onset. The second system is a pitchfork bifurcation in which the
noise acts multiplicatively on the non-linear term of lowest order. In both cases noise suppresses some solutions that exist
in the deterministic regime. Besides, for the first system, the imperfectness of the bifurcation reduces the regime of on-off
intermittency. For the second system, the unstable mode can achieve a jump of finite amplitude at instability but without
hysteresis. We finally identify a generic property that is verified by the stationary probability density function of the
dynamical variable when a control parameter is varied. 相似文献
14.
Yong Yuan Shan Shu Chang & Ning Qin 《advances in applied mathematics and mechanics.》2009,1(5):615-638
The conventional finite difference (FD) schemes are based on the low
order polynomial approximation in a local region. This paper shows
that when the polynomial approximation is replaced by the
multiquadric (MQ) function approximation in the same region, a new
FD method, which is termed as MQ-FD method in this work, can be
developed. The paper gives analytical formulas of the MQ-FD method
and carries out a performance study for its derivative approximation
and solution of Poisson equation and the incompressible
Navier-Stokes equations. In addition, the effect of the shape
parameter $c$ in MQ on the formulas of the MQ-FD method is analyzed.
Derivative approximation in one-dimensional space and Poisson
equation in two-dimensional space are taken as model problems to
study the accuracy of the MQ-FD method. Furthermore, a lid-driven
flow problem in a square cavity is simulated by the MQ-FD method.
The obtained results indicate that this method may solve the
engineering problem very accurately with a proper choice of the
shape parameter $c$. 相似文献
15.
S. S. Hassan H. A. Batarfi R. Saunders R. K. Bullough 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2000,8(3):403-416
A time-independent theoretical and numerical analysis of an optical bistable model of two-level atoms in a ring cavity, driven
by a coherent field and in contact with a squeezed vacuum field is presented in the two cases of absorptive and dispersive
optical bistability (OB). In the former case, a suitable choice of the phase of the squeezed vacuum field reduces the threshold
for OB to occur compared with the normal vacuum case. In the latter case, regions of OB are identified as one or two disconnected
simple closed curves depending on the cooperation parameter [0pt] : is the maximum possible value of the critical value of C at fixed values of the squeezed vacuum field parameters. Phase switching effects between different (output) states of the
system is investigated in detail. In the absorptive case, one- or two-way optical switching is possible depending on [0pt]
. We also present results which demonstrate more complicated switching behaviour in the dispersive case.
Received 12 March 1999 and Received in final form 20 August 1999 相似文献
16.
We show theoretically that thermomechanical effects in dye-doped nematic liquid crystals when illuminated by laser beams,
can become important and lead to molecular reorientation at intensities substantially lower than that needed for optical Fréedericksz
transition. We propose a 1D model that assumes homogenous intensity distribution in the plane of the layer and is capable
to describe such a thermally induced threshold lowering. We consider a particular geometry, with a linearly polarized light
incident perpendicularly on a layer of homeotropically aligned dye-doped nematics. 相似文献
17.
The pulse shape of a passively Q-switched microchip laser 总被引:2,自引:0,他引:2
T. Erneux P. Peterson A. Gavrielides 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2000,10(3):423-431
The shape of the intensity pulse of a passively Q-switched microchip laser is investigated numerically and analytically. Our
analysis is motivated by independent microchip laser experiments exhibiting nearly symmetric pulses in the case of a semiconductor
saturable absorber and asymmetric pulses in the case of a solid state saturable absorber. Asymptotic methods are used to determine
limiting behaviors of the pulse shape for both symmetric and asymmetric pulses. In the first case, we determine a sech2 solution parametrized by one parameter which can be determined by solving two coupled nonlinear algebraic equations. In the
second case, the pulse solution is decomposed into two distinct approximations exhibiting different amplitude and time scales
properties. We review earlier approximations of the repetition rate and the pulse width.
Received 2 August 1999 相似文献
18.
I. Kourakis P. K. Shukla 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,50(1-2):321-325
The evolution of the amplitude of two nonlinearly interacting
waves is considered, via a set of coupled nonlinear
Schr?dinger-type equations. The dynamical profile is determined
by the wave dispersion laws (i.e. the group velocities and the group velocity dispersion
terms) and the nonlinearity and coupling coefficients, on which no
assumption is made. A generalized dispersion relation is obtained,
relating the frequency and wave-number of a small perturbation
around a coupled monochromatic (Stokes') wave solution. Explicitly
stability criteria are obtained. The analysis reveals a number of
possibilities. Two (individually) stable systems may be
destabilized due to coupling. Unstable systems may, when coupled,
present an enhanced instability growth rate, for an extended wave
number range of values. Distinct unstable wavenumber windows may
arise simultaneously. 相似文献
19.