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1.
In this paper, we discuss the large-time behavior of solution of a simple kinetic model of Boltzmann–Maxwell type, such that the temperature is time decreasing and/or time increasing. We show that, under the combined effects of the nonlinearity and of the time-monotonicity of the temperature, the kinetic model has non trivial quasi-stationary states with power law tails. In order to do this we consider a suitable asymptotic limit of the model yielding a Fokker-Planck equation for the distribution. The same idea is applied to investigate the large-time behavior of an elementary kinetic model of economy involving both exchanges between agents and increasing and/or decreasing of the mean wealth. In this last case, the large-time behavior of the solution shows a Pareto power law tail. Numerical results confirm the previous analysis. 相似文献
2.
T. Wada A. M. Scarfone 《The European Physical Journal B - Condensed Matter and Complex Systems》2009,70(1):65-71
The asymptotic behavior of a nonlinear diffusive equation
obtained in the framework of the κ-generalized statistical mechanics is studied.
The analysis based on the classical Lie symmetry shows that the κ-Gaussian function is not a scale invariant solution of the
generalized diffusive equation.
Notwithstanding, several numerical simulations, with different
initial conditions, show that the solutions asymptotically approach to the
κ-Gaussian function.
Simple argument based on a time-dependent transformation performed on the related
κ-generalized Fokker-Planck equation, supports this conclusion. 相似文献
3.
R. Dandoloff A. Saxena 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,29(2):265-267
For a spin-polarized electron gas on an elastic cylinder in an external axial magnetic field and an axial electric field we
find that the corresponding Euler-Lagrange equation is the double sine-Gordon (DSG) equation with an exact 2π-skyrmion solution.
The DSG skyrmion is stabilized, without Coulomb repulsion, by the curvature of the cylinder. It adopts a characteristic length
ξ which is smaller than the radius of the cylinder. For an elastic cylinder this mismatch of length scales causes a deformation
of the cylinder in the region of the skyrmion.
Received 23 October 2001 / Received in final form 8 March 2002 Published online 2 October 2002
RID="a"
ID="a"e-mail: rossen.dandoloff@ptm.u-cergy.fr 相似文献
4.
Dirk Blömker Stanislaus Maier-Paape Thomas Wanner 《Communications in Mathematical Physics》2001,223(3):553-582
This paper gives theoretical results on spinodal decomposition for the stochastic Cahn–Hilliard–Cook equation, which is a
Cahn–Hilliard equation perturbed by additive stochastic noise. We prove that most realizations of the solution which start
at a homogeneous state in the spinodal interval exhibit phase separation, leading to the formation of complex patterns of
a characteristic size.
In more detail, our results can be summarized as follows. The Cahn–Hilliard–Cook equation depends on a small positive parameter
ε which models atomic scale interaction length. We quantify the behavior of solutions as ε→ 0. Specifically, we show that
for the solution starting at a homogeneous state the probability of staying near a finite-dimensional subspace ?ε is high as long as the solution stays within distance r
ε=O(ε
R
) of the homogeneous state. The subspace ?ε is an affine space corresponding to the highly unstable directions for the linearized deterministic equation. The exponent
R depends on both the strength and the regularity of the noise.
Received: 2 May 2000 / Accepted: 8 July 2001 相似文献
5.
B.K. Nikolić V.Z. Cerovski 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,30(2):227-238
We report on the comprehensive numerical study of the fluctuation and correlation properties of wave functions in three-dimensional
mesoscopic diffusive conductors. Several large sets of nanoscale samples with finite metallic conductance, modeled by an Anderson
model with different strengths of diagonal box disorder, have been generated in order to investigate both small and large
deviations (as well as the connection between them) of the distribution function of eigenstate amplitudes from the universal
prediction of random matrix theory. We find that small, weak localization-type, deviations contain both diffusive contributions
(determined by the bulk and boundary conditions dependent terms) and ballistic ones which are generated by electron dynamics
below the length scale set by the mean free path ℓ. By relating the extracted parameters of the functional form of nonperturbative
deviations (“far tails”) to the exactly calculated transport properties of mesoscopic conductors, we compare our findings
based on the full solution of the Schr?dinger equation to different approximative analytical treatments. We find that statistics
in the far tail can be explained by the exp-log-cube asymptotics (convincingly refuting the log-normal alternative), but with
parameters whose dependence on ℓ is linear and, therefore, expected to be dominated by ballistic effects. It is demonstrated
that both small deviations and far tails depend explicitly on the sample size--the remaining puzzle then is the evolution
of the far tail parameters with the size of the conductor since short-scale physics is supposedly insensitive to the sample
boundaries.
Received 19 August 2002
Published online 19 November 2002 相似文献
6.
We investigate the location of zeros and poles of a dynamical zeta function for a family of subshifts of finite type with
an interaction function depending on the parameters . The system corresponds to the well known Kac-Baker lattice spin model in statistical mechanics. Its dynamical zeta function
can be expressed in terms of the Fredholm determinants of two transfer operators and with the Ruelle operator acting in a Banach space of holomorphic functions, and an integral operator introduced originally by Kac, which acts in the space with a kernel which is symmetric and positive definite for positive β. By relating via the Segal-Bargmann transform to an operator closely related to the Kac operator we can prove equality of their spectra and hence reality, respectively positivity, for the eigenvalues of the operator for real, respectively positive, β. For a restricted range of parameters we can determine the asymptotic behavior of the eigenvalues of for large positive and negative values of β and deduce from this the existence of infinitely many non-trivial zeros and poles
of the dynamical zeta functions on the real β line at least for generic . For the special choice , we find a family of eigenfunctions and eigenvalues of leading to an infinite sequence of equally spaced ``trivial' zeros and poles of the zeta function on a line parallel to
the imaginary β-axis. Hence there seems to hold some generalized Riemann hypothesis also for this kind of dynamical zeta functions.
Received: 14 March 2002 / Accepted: 24 June 2002 Published online: 14 November 2002 相似文献
8.
We study a thin liquid film with a free surface on the underside of a cooled horizontal substrate. We show that if the fluid is initially in equilibrium with its own vapor in the gas phase below, regular surface patterns in the form of long-wave hexagons having a well-defined lateral length scale are observed. This is in sharp contrast to the case without evaporation where rupture or coarsening to larger and larger patterns is seen in the long time limit. In this way, evaporation could be used for regular structuring of the film surface. Finally, we estimate the finite wave length for the simplified case of an extended Cahn-Hilliard equation. 相似文献
9.
We have studied the roughness and the dynamics of the contact line of a viscous liquid on a disordered substrate. We have
used photolithographic techniques to obtain a controlled disorder with a correlation length ξ = 10μm. Liquids with different
viscosity were used: water and aqueous glycerol solution. We have found that the roughness W of the contact line depends neither on the viscosity nor on the velocity v of the contact line for v in the range 0.2-20μm/s. W is found to scale with the length L of the line as L
ζ with a roughness exponent ζ = 0.51±0.03. This value is similar to the one obtained with superfluid helium. In the present
experiment, we have checked that the motion of the contact line is actually overdamped, so that the phenomenological equation
first proposed by Ertas and Kardar should be relevant. However, our measurement of ζ is in disagreement with the predicted
value ζ = 0.39. We have also analyzed the avalanche-like motion of the contact line. We find that the size distribution does
not follow a power law dependence.
Received 18 April 2002 相似文献
10.
I.M. Sokolov 《The European Physical Journal B - Condensed Matter and Complex Systems》2001,22(3):369-373
We consider two-particle dispersion in a velocity field, where the relative two-point velocity scales according to v
2(r) ∝r
α and the corresponding correlation time scales as τ(r) ∝r
β, and fix α = 2/3, as typical for turbulent flows. We show that two generic types of dispersion behavior arize: For α/2 +
β < 1 the correlations in relative velocities decouple and the diffusion approximation holds. In the opposite case, α/2 +
β > 1, the relative motion is strongly correlated. The case of Kolmogorov flows corresponds to a marginal, nongeneric situation.
In this case, depending on the particular parameters of the flow, the dispersion behavior can be rather diffusive or rather
ballistic.
Received 13 March 2001 相似文献
11.
We investigate the asymptotic behavior of solutions to a kinetic equation describing the evolution of particles subject to
the sum of a fixed, confining, Hamiltonian, and a small, time-oscillating, perturbation. The equation also involves an interaction
operator which acts as a relaxation in the energy variable. This paper aims at providing a classical counterpart to the derivation
of rate equations from the atomic Bloch equations. In the present classical setting, the homogenization procedure leads to
a diffusion equation in the energy variable, rather than a rate equation, and the presence of the relaxation operator regularizes
the limit process, leading to finite diffusion coefficients. The key assumption is that the time-oscillatory perturbation
should have well-defined long time averages: our procedure includes general “ergodic” behaviors, amongst which periodic, or
quasi-periodic potentials only are a particular case. 相似文献
12.
13.
We introduce an enhanced multiscale analysis that yields subexponentially decaying probabilities for bad events. For quantum and classical waves in random media, we obtain exponential decay for the resolvent of the corresponding
random operators in boxes of side L with probability higher than 1 − e −
L
ζ, for any 0<ζ<1. The starting hypothesis for the enhanced multiscale analysis only requires the verification of polynomial
decay of the finite volume resolvent, at some sufficiently large scale, with probability bigger than 1 − (d is the dimension). Note that from the same starting hypothesis we get conclusions that are valid for any 0 < ζ < 1. This
is achieved by the repeated use of a bootstrap argument. As an application, we use a generalized eigenfunction expansion to
obtain strong dynamical localization of any order in the Hilbert–Schmidt norm, and better estimates on the behavior of the
eigenfunctions.
Received: 29 November 2000 / Accepted: 21 June 2001 相似文献
14.
D.D. Nelson J.H. Shorter J.B. McManus M.S. Zahniser 《Applied physics. B, Lasers and optics》2002,75(2-3):343-350
Non-cryogenic, laser-absorption spectroscopy in the mid-infrared has wide applications for practical detection of trace gases
in the atmosphere. We report measurements of nitric oxide in air with a detection limit less than 1 nmole/mole (<1 ppbv) using
a thermoelectrically cooled quantum cascade laser operated in pulsed mode at 5.26 μm and coupled to a 210-m path length multiple-pass
absorption cell at reduced pressure (50 Torr). The sensitivity of the system is enhanced by operating under pulsing conditions
which reduce the laser line width to 0.010 cm-1 (300 MHz) HWHM, and by normalizing pulse-to-pulse intensity variations with temporal gating on a single HgCdTe detector.
The system is demonstrated by detecting nitric oxide in outside air and comparing results to a conventional tunable diode
laser spectrometer sampling from a common inlet. A detection precision of 0.12 ppb Hz-1/2 is achieved with a liquid-nitrogen-cooled detector. This detection precision corresponds to an absorbance precision of 1×10-5 Hz-1/2 or an absorbance precision per unit path length of 5×10-10 cm-1 Hz-1/2. A precision of 0.3 ppb Hz-1/2 is obtained using a thermoelectrically cooled detector, which allows continuous unattended operation over extended time periods
with a totally cryogen-free instrument.
Received: 1 May 2002 / Revised version: 6 June 2002 / Published online: 21 August 2002
RID="*"
ID="*"Corresponding author. Fax: +1-978/663-4918, E-mail: ddn@aerodyne.com 相似文献
15.
We analyze the large-time behavior of various kinetic models for the redistribution of wealth in simple market economies introduced
in the pertinent literature in recent years. As specific examples, we study models with fixed saving propensity introduced
by Chakraborti and Chakrabarti (Eur. Phys. J. B 17:167–170, 2000), as well as models involving both exchange between agents and speculative trading as considered by Cordier et al. (J. Stat.
Phys. 120:253–277, 2005) We derive a sufficient criterion under which a unique non-trivial stationary state exists, and provide criteria under which
these steady states do or do not possess a Pareto tail. In particular, we prove the absence of Pareto tails in pointwise conservative
models, like the one in (Eur. Phys. J. B 17:167–170, 2000), while models with speculative trades introduced in (J. Stat. Phys. 120:253–277, 2005) develop fat tails if the market is “risky enough”. The results are derived by a Fourier-based technique first developed
for the Maxwell-Boltzmann equation (Gabetta et al. in J. Stat. Phys. 81:901–934, 1995; Bisi et al. in J. Stat. Phys. 118(1–2):301–331, 2005; Pareschi and Toscani in J. Stat. Phys. 124(2–4):747–779, 2006) and from a recursive relation which allows to calculate arbitrary moments of the stationary state. 相似文献
16.
In this paper we investigate the large-time behavior of strong solutions to the one-dimensional fourth order degenerate parabolic
equation u
t
=−(u
u
xxx
)
x
, modeling the evolution of the interface of a spreading droplet. For nonnegative initial values u
0(x)∈H
1(ℝ), both compactly supported or of finite second moment, we prove explicit and universal algebraic decay in the L
1-norm of the strong solution u(x,t) towards the unique (among source type solutions) strong source type solution of the equation with the same mass. The method
we use is based on the study of the time decay of the entropy introduced in [13] for the porous medium equation, and uses
analogies between the thin film equation and the porous medium equation.
Received: 2 February 2001 / Accepted: 7 October 2001 相似文献
17.
We consider the Navier-Stokes equation on a two dimensional torus with a random force which is white noise in time, and excites
only a finite number of modes. The number of excited modes depends on the viscosity ν, and grows like ν
-3
when ν goes to zero. We prove that this Markov process has a unique invariant measure and is exponentially mixing in time.
Received: 14 March 2002 / Accepted: 7 May 2002 Published online: 22 August 2002 相似文献
18.
We develop an effective numerical method of studying large-time properties of reversible reaction-diffusion systems of type
A + B ↔ C with initially separated reactants. Using it we find that there are three types of asymptotic reaction zones. In particular
we show that the reaction rate can be locally negative and concentrations of species A and B can be nonmonotonic functions
of the space coordinate x, locally significantly exceeding their initial values.
Received 6 June 2002 / Received in final form 20 January 2003 Published online 7 May 2003 相似文献
19.
Sergei Kuksin Andrey Piatniski Armen Shirikyan 《Communications in Mathematical Physics》2002,230(1):81-85
We consider a class of discrete time random dynamical systems and establish the exponential convergence of its trajectories
to a unique stationary measure. The result obtained applies, in particular, to the 2D Navier–Stokes system and multidimensional
complex Ginzburg–Landau equation with random kick-force.
Received: 7 February 2002 / Accepted: 29 April 2002 Published online: 12 August 2002 相似文献
20.
We present the construction of an exponentially accurate time-dependent Born–Oppenheimer approximation for molecular quantum
mechanics.
We study molecular systems whose electron masses are held fixed and whose nuclear masses are proportional to ε−4, where ε is a small expansion parameter. By optimal truncation of an asymptotic expansion, we construct approximate solutions
to the time-dependent Schr?dinger equation that agree with exact normalized solutions up to errors whose norms are bounded
by , for some C and γ >0.
Received: 13 February 2001 / Accepted: 13 July 2001 相似文献