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181.
182.
A recent article in Nature Physics unified key results from thermodynamics, statistics, and information theory. The unification arose from a general equation for the rate of change in the information content of a system. The general equation describes the change in the moments of an observable quantity over a probability distribution. One term in the equation describes the change in the probability distribution. The other term describes the change in the observable values for a given state. We show the equivalence of this general equation for moment dynamics with the widely known Price equation from evolutionary theory, named after George Price. We introduce the Price equation from its biological roots, review a mathematically abstract form of the equation, and discuss the potential for this equation to unify diverse mathematical theories from different disciplines. The new work in Nature Physics and many applications in biology show that this equation also provides the basis for deriving many novel theoretical results within each discipline. 相似文献
183.
G. Fey H. Frank W. Schütz H. Theissen 《Zeitschrift für Physik A Hadrons and Nuclei》1973,265(4):401-403
The nuclear rms charge radii measured by low energy electron scattering at Darmstadt are summarized. Improvements in the experimental equipment and method permitted a redetermination of the12C radius which yieldedR m (12C)=2.462 ± 0.022fm. This value has been used to recalibrate the radii measured relative to12C. 相似文献
184.
185.
Frank Aurzada 《Journal of Theoretical Probability》2007,20(4):843-858
We investigate the behaviour of the logarithmic small deviation probability of a sequence (σ
n
θ
n
) in l
p
, 0<p≤∞, where (θ
n
) are i.i.d. random variables and (σ
n
) is a decreasing sequence of positive numbers. In particular, the example σ
n
∼n
−μ
(1+log n)−ν
is studied thoroughly. Contrary to the existing results in the literature, the rate function and the small deviation constant
are expressed expli- citly in the present treatment. The restrictions on the distribution of θ
1 are kept to an absolute minimum. In particular, the usual variance assumption is removed. As an example, the results are
applied to stable and Gamma-distributed random variables. 相似文献
186.
Remco van der Hofstad Frank den Hollander Gordon Slade 《Communications in Mathematical Physics》2002,231(3):435-461
We construct the incipient infinite cluster measure (IIC) for sufficiently spread-out oriented percolation on ℤ
d
× ℤ+, for d +1 > 4+1. We consider two different constructions. For the first construction, we define ℙ
n
(E) by taking the probability of the intersection of an event E with the event that the origin is connected to (x,n) ℤ
d
× ℤ+, summing this probability over x ℤ
d
, and normalising the sum to get a probability measure. We let n → ∞ and prove existence of a limiting measure ℙ∞, the IIC. For the second construction, we condition the connected cluster of the origin in critical oriented percolation
to survive to time n, and let n → ∞. Under the assumption that the critical survival probability is asymptotic to a multiple of n
−1, we prove existence of a limiting measure ℚ∞, with ℚ∞ = ℙ∞. In addition, we study the asymptotic behaviour of the size of the level set of the cluster of the origin, and the dimension
of the cluster of the origin, under ℙ∞. Our methods involve minor extensions of the lace expansion methods used in a previous paper to relate critical oriented
percolation to super-Brownian motion, for d+1 > 4+1.
Received: 13 December 2001 / Accepted: 11 July 2002 Published online: 29 October 2002
RID="*"
ID="*" Present address: Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513,
5600 MB Eindhoven, The Netherlands. E-mail: rhofstad@win.tue.nl 相似文献
187.
In this paper we outline a new particle-mesh method for rapidly rotating shallow water flows based on a set of regularized equations of motion. The time-stepping method uses an operator splitting of the equations into an Eulerian gravity wave part and a Lagrangian advection part. An essential ingredient is the advection of absolute vorticity by means of translated radial basis functions. We show that this implies exact conservation of enstrophy. The method is tested on two model problems based on the qualitative features of the solutions obtained (i.e., dispersion or smoothness of potential vorticity contours) as well as on the increase in mean divergence level. 相似文献
188.
In this paper we study blowup of radially symmetric solutions of the nonlinear heat equation ut = Δu + |u|p?1u either on ?N or on a finite ball under the Dirichlet boundary conditions. We assume that the exponent p is supercritical in the Sobolev sense, that is, We prove that if ps < p < p*, then blowup is always of type I, where p* is a certain (explicitly given) positive number. More precisely, the rate of blowup in the L∞ norm is always the same as that for the corresponding ODE dv/dt = |v|p?1v. Because it is known that “type II” blowup (or, equivalently, “fast blowup”) can occur if p > p*, the above range of exponent p is optimal. We will also derive various fundamental estimates for blowup that hold for any p > ps and regardless of type of blowup. Among other things we classify local profiles of type I and type II blowups in the rescaled coordinates. We then establish useful estimates for the so‐called incomplete blowup, which reveal that incomplete blowup solutions belong to nice function spaces even after the blowup time. © 2004 Wiley Periodicals, Inc. 相似文献
189.
190.
Grosnick D Wright SC Bolton RD Cooper MD Frank JS Hallin AL Heusi PA Hoffman CM Hogan GE Mariam FG Matis HS Mischke RE Piilonen LE Sandberg VD Sanders GH Sennhauser U Werbeck R Williams RA Wilson SL Hofstadter R Hughes EB Ritter MW Highland VL McDonough J 《Physical review letters》1986,57(26):3241-3244