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1.
We consider a spinning charge coupled to the Maxwell field. Through the appropriate symmetry in the initial conditions the charge remains at rest. We establish that any time-dependent finite energy solution converges to a sum of a soliton wave and an outgoing free wave. The convergence holds in global energy norm. Under a small constant external magnetic field the soliton manifold is stable in local energy seminorms and the evolution of the angular velocity is guided by an effective finite-dimensional dynamics. The proof uses a non-autonomous integral inequality method. 相似文献
2.
We consider the scalar field φ
t
with a reversible stochastic dynamics which is defined by the standard Dirichlet form relative to the Gibbs measure with
formal energy . The potential V is even and strictly convex. We prove that under a suitable large scale limit the φ
t
-field becomes deterministic such that locally its normal velocity is proportional to its mean curvature, except for some
anisotropy effects. As an essential input we prove that for every tilt there is a unique shift invariant, ergodic Gibbs measure
for the -field.
Received: 1 February 1996 / Accepted: 2 July 1996 相似文献
3.
We determine the stationary two-point correlation function of the one-dimensional KPZ equation through the scaling limit of a solvable microscopic model, the polynuclear growth model. The equivalence to a directed polymer problem with specific boundary conditions allows one to express the corresponding scaling function in terms of the solution to a Riemann–Hilbert problem related to the Painlevé II equation. We solve these equations numerically with very high precision and compare our, up to numerical rounding exact, result with the prediction of Colaiori and Moore(1) obtained from the mode coupling approximation. 相似文献
4.
Preparation and mechanical properties of layers made of recombinant spider silk proteins and silk from silk worm 总被引:1,自引:0,他引:1
F. Junghans M. Morawietz U. Conrad T. Scheibel A. Heilmann U. Spohn 《Applied Physics A: Materials Science & Processing》2006,82(2):253-260
Layers of recombinant spider silks and native silks from silk worms were prepared by spin-coating and casting of various solutions.
FT-IR spectra were recorded to investigate the influence of the different mechanical stress occurring during the preparation
of the silk layers. The solubility of the recombinant spider silk proteins SO1-ELP, C16, AQ24NR3, and of the silk fibroin
from Bombyx mori were investigated in hexafluorisopropanol, ionic liquids and concentrated salt solutions. The morphology and thickness of
the layers were determined by Atomic Force Microscopy (AFM) or with a profilometer. The mechanical behaviour was investigated
by acoustic impedance analysis by using a quartz crystal microbalance (QCMB) as well as by microindentation.
The density of silk layers (d<300 nm) was determined based on AFM and QCMB measurements. At silk layers thicker than 300 nm
significant changes of the half-band-half width can be correlated with increasing energy dissipation. Microhardness measurements
demonstrate that recombinant spider silk and sericine-free Bombyx mori silk layers achieve higher elastic penetration modules EEP and Martens hardness values HM than those of polyethylenterephthalate (PET) and polyetherimide (PEI) foils. 相似文献
5.
6.
We investigate the stationary nonequilibrium (heat transporting) states of the Lorentz gas. This is a gas of classical point particles moving in a region gL containing also fixed (hard sphere) scatterers of radiusR. The stationary state considered is obtained by imposing stochastic boundary conditions at the top and bottom of , i.e., a particle hitting one of these walls comes off with a velocity distribution corresponding to temperaturesT
1 andT
2 respectively,T
1 <T
2. Letting be the average density of the randomly distributed scatterers we show that in the Boltzmann-Grad limit,,R 0 with the mean free path fixed, the stationary distribution of the Lorentz gas converges in theL
1-norm to the stationary distribution of the corresponding linear Boltzmann equation with the same boundary conditions. In particular, the steady state heat flow in the Lorentz gas converges to that of the linear Boltzmann equation, which is known to behave as (T
2-T
1)/L for largeL, whereL is the distance from the bottom to the top wall: i.e., Fourier's law of heat conduction is valid in the limit. The heat flow converges even in probability. Generalizations of our result for scatterers with a smooth potential as well as the related diffusion problem are discussed.Research supported in part by NSF Grant no. Phy 77-22302.On leave of absence from the Fachbereich Physik der Universität, München. Work supported by a DFG fellowship. 相似文献
7.
Herbert Spohn 《Journal of statistical physics》1977,17(6):385-412
A single (nonrelativistic, spinless) electron subject to a constant external electric field interacts with impurities located on an infinitely extended lattice by a potential of random strength. The random strength is given by a field of Gaussian random variables. We show the existence of the averaged dynamics and prove that in the weak coupling limit, 0, 2
t= fixed, one obtains the usual transport equation for the velocity distribution.Work supported by a Max Kade Foundation fellowship.On leave of absence of the Fachbereich Physik der Universität München. 相似文献
8.
9.
10.
We establish that the static height fluctuations of a particular growth model, the PNG droplet, converges upon proper rescaling to a limit process, which we call the Airy process A(y). The Airy process is stationary, it has continuous sample paths, its single time (fixed y) distribution is the Tracy–Widom distribution of the largest eigenvalue of a GUE random matrix, and the Airy process has a slow decay of correlations as y
–2. Roughly the Airy process describes the last line of Dyson's Brownian motion model for random matrices. Our construction uses a multi-layer version of the PNG model, which can be analyzed through fermionic techniques. Specializing our result to a fixed value of y, one reobtains the celebrated result of Baik, Deift, and Johansson on the length of the longest increasing subsequence of a random permutation. 相似文献