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1.
We study the asymptotic behavior of an inertial tracer particle in a random force field. We show that there exists a probability
measure, under which the process describing the velocity and environment seen from the vantage point of the moving particle
is stationary and ergodic. This measure is equivalent to the underlying probability for the Eulerian flow. As a consequence
of the above we obtain the law of large numbers for the trajectory of the tracer. Moreover, we prove also some decorrelation
properties of the velocity of the particle, which lead to the existence of a non-degenerate asymptotic covariance tensor.
The research of both authors was supported by the Polish Committee for Scientific Research (KBN) grant No. 2PO3A03123. 相似文献
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Lubomira Balková Jean-Pierre Gazeau Edita Pelantová 《Letters in Mathematical Physics》2008,84(2-3):179-198
Beta-integers (“β-integers”) are those numbers which are the counterparts of integers when real numbers are expressed in an irrational base β > 1. In quasicrystalline studies, β-integers supersede the “crystallographic” ordinary integers. When the number β is a Parry number, the corresponding β-integers realize only a finite number of distances between consecutive elements and are in this sense the most comparable to ordinary integers. In this paper, we point out the similarity of β-integers and ordinary integers in the asymptotic sense, in particular for a subclass of Parry numbers – Pisot numbers for which their Parry and minimal polynomial coincide. 相似文献
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Saulo R. M. Barros Pablo A. Ferrari Nancy L. Garcia Servet Martínez 《Journal of statistical physics》2002,106(3-4):521-546
We study the nearest neighbors one dimensional uniform q-model of force fluctuations in bead packs,(1) a stochastic model to simulate the stress of granular media in two dimensional silos. The vertical coordinate plays the role of time, and the horizontal coordinate the role of space. The process is a discrete time Markov process with state space {1,...,N}. At each layer (time), the weight supported by each grain is a random variable of mean one (its own weight) plus the sum of random fractions of the weights supported by the nearest neighboring grains at the previous layer. The fraction of the weight given to the right neighbor of the successive layer is a uniform random variable in [0, 1] independent of everything. The remaining weight is given to the left neighbor. In the boundaries, a uniform fraction of the weight leans on the wall of the silo. This corresponds to absorbing boundary conditions. For this model we show that there exists a unique invariant measure. The mean weight at site i under the invariant measure is i(N+1–i); we prove that its variance is
(i(N+1–i))2+O(N
3) and the covariances between grains ij are of order O(N
3). Moreover, as N, the law under the invariant measure of the weights divided by N
2 around site (integer part of) rN, r(0, 1), converges to a product of gamma distributions with parameters 2 and 2(r(1–r))–1 (sum of two exponentials of mean r(1–r)/2). Liu et al.
(2) proved that for a silo with infinitely many weightless grains, any product of gamma distributions with parameters 2 and 2/ with [0, ) are invariant. Our result shows that as the silo grows, the model selects exactly one of these Gamma's at each macroscopic place. 相似文献
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We study the inflated phase of two dimensional lattice polygons with fixed perimeter N and variable area, associating a weight exp [pA−Jb] to a polygon with area A and b bends. For convex and column-convex polygons, we calculate the average area for positive values of the pressure. For large
pressures, the area has the asymptotic behaviour
, where
, and ρ<1. The constant K(J) is found to be the same for both types of polygons. We argue that self-avoiding polygons should exhibit the same asymptotic
behavior. For self-avoiding polygons, our predictions are in good agreement with exact enumeration data for J=0 and Monte Carlo simulations for J≠0. We also study polygons where self-intersections are allowed, verifying numerically that the asymptotic behavior described
above continues to hold. 相似文献
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A new proof of the diffusion approximation for ordinary differential equations is given. It is based on an asymptotic expansion of the solution of the corresponding Liouville partial differential equations. In contrast to previous results obtained for the suspension under Holderian mappings of subshift of finite type or Fourier analysis techniques, our proof relies only on symbolic dynamics. 相似文献
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We obtain the asymptotic behavior of the Takhtajan-Zograf metric on the Teichmüller space of punctured Riemann surfaces.
The first author is partially supported by JSPS Grant-in-Aid for Exploratory Research 2005-2007.
The second author is partially supported by the research grant R-146-000-106-112 from the National University of Singapore
and the Ministry of Education. 相似文献
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Changjiang Zhu 《Communications in Mathematical Physics》2010,293(1):279-299
In this paper, we study the one-dimensional Navier-Stokes equations connecting to vacuum state with a jump in density when
the viscosity depends on the density. Precisely, when the viscosity coefficient μ(ρ) is proportional to ρ
θ
with θ > 0, where ρ is the density, we give the asymptotic behavior and the decay rate of the density function ρ(x, t). Furthermore, the behavior of the density function ρ(x, t) near the interfaces separating the gas from vacuum and the expanding rate of the interfaces are also studied. The analysis
is based on some new mathematical techniques and some new useful estimates. This fills a final gap on studying Navier-Stokes
equations with the viscosity coefficient μ(ρ) dependent on the density ρ. 相似文献
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P. M. Krassovitskiy F. M. Pen’kov 《Bulletin of the Russian Academy of Sciences: Physics》2018,82(6):669-673
Many problems of numerically solving the Schrödinger equation require that we choose asymptotic distances many times greater than the characteristic size of the region of interaction. If the solution to one-dimensional equations can be immediately chosen in a form that preserves unitarity, the invariance of probability (in the form of, e.g., fulfilling an optical theorem) is a real problem for two-dimensional equations. An addition that does not exceed the discretization error and ensures a high degree of unitarity is proposed as a result of studying the properties of a discrete two-dimensional equation. 相似文献
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Internal friction of nanocrystalline nickel is investigated by mechanical spectroscopy from 360 K to 120 K. Two relaxation peaks are found when nanocrystalline nickel is bent up to 10% strain at room temperature and fast cooling. However, these two peaks disappear when the sample is annealed at room temperature in vacuum for ten days. The occurrence and disappearance of the two relaxation peaks can be explained by the interactions of partial dislocations and point defects in nanocrystalline materials. 相似文献
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Valentina Cammarota Alessandro De Gregorio Claudio Macci 《Journal of statistical physics》2014,154(6):1550-1568
The main results in this paper concern large and moderate deviations for the radial component of a $n$ -dimensional hyperbolic Brownian motion (for $n\ge 2$ ) on the Poincaré half-space. We also investigate the asymptotic behavior of the hitting probability $P_\eta (T_{\eta _1}^{(n)}<\infty )$ of a ball of radius $\eta _1$ , as the distance $\eta $ of the starting point of the hyperbolic Brownian motion goes to infinity. 相似文献
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Kalinin Yu. E. Kosilov A. T. Ovdak O. V. Kudrin A. M. Karaeva O. A. Kashirin M. A. Degtyarev D. Ya. 《Technical Physics》2019,64(4):535-539
Technical Physics - The temperature and amplitude dependences of internal friction in hybrid composites consisting of unidirectional carbon fibers and glass tissues in a T-107 molten epoxy matrix... 相似文献
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Asymptotic Behavior of Soliton Solutions with a Double Spectral Parameter for Principal Chiral Field
SONG Quan-Fu ZHOU Zi-Xiang 《理论物理通讯》2005,44(6):977-980
The soliton solutions with a double spectral parameter for the principal chiral field are derived by Darboux transformation. The asymptotic behavior of the solutions as time tends to infinity is obtained and the speeds of the peaks in the asymptotic solutions are not constants. 相似文献
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Asymptotic Behavior of Soliton Solutions with a Double Spectral Parameter for Principal Chiral Field
SONG Quan-Fu ZHOU Zi-Xiang 《理论物理通讯》2005,44(12)
The soliton solutions with a double spectral parameter for the principal chiral field are derived by Darboux transformation. The asymptotic behavior of the solutions as time tends to infinity is obtained and the speeds of the peaks in the asymptotic solutions are not constants. 相似文献