3,315 research outputs found
The penetrable-sphere fluid in the high-temperature, high-density limit
We consider a fluid of -dimensional spherical particles interacting via a
pair potential which takes a finite value if the two
spheres are overlapped () and 0 otherwise. This penetrable-sphere
model has been proposed to describe the effective interaction of micelles in a
solvent. We derive the structural and thermodynamic functions in the limit
where the reduced temperature and density tend
to infinity, their ratio being kept finite. The fluid exhibits a spinodal
instability at a certain maximum scaled density where the correlation length
diverges and a crystalline phase appears, even in the one-dimensional model. By
using a simple free-volume theory for the solid phase of the model, the
fluid-solid phase transition is located.Comment: 6 pages, 2 tables, 3 figures; v2: title has changed; new figure; v3:
Correction of misprints (see
http://dx.doi.org/10.1016/j.physleta.2012.05.043
On a correlation among azimuthal velocities and the flyby anomaly sign
Data of six flybys, those of Galileo I, Galileo II, NEAR, Cassini, Rosetta
and Messenger were reported by Anderson et al \citep{Anderson}. Four of them:
Galileo I, NEAR, Rosetta and Messenger gain Newtonian energy during the flyby
transfer, while Galileo II and Cassini lose energy. This is, in both cases, a
surprising anomaly since Newtonian forces derive from a potential and they are,
therefore, conservative. We show here that the gravitational field of a
rotating planet as derived from a new model introduces a non conservative force
that gives a partial, but in our opinion satisfactory, explanation of these
anomalies and suggests a correlation between the sign of the anomaly and the
sign of the azimuthal velocity at perigee.Comment: 12 pages, 3 figure
I. Territory covered by N random walkers on deterministic fractals. The Sierpinski gasket
We address the problem of evaluating the number of distinct sites
visited up to time t by N noninteracting random walkers all initially placed on
one site of a deterministic fractal lattice. For a wide class of fractals, of
which the Sierpinski gasket is a typical example, we propose that, after the
short-time compact regime and for large N, , where is the number of sites inside a hypersphere
of radius , R is the root-mean-square displacement of a
single random walker, and u and c determine how fast (the
probability that site has been visited by a single random walker by
time t) decays for large values of r/R: . For the deterministic fractals considered in this paper, , being the random walk dimension. The corrective term
is expressed as a series in (with and ), which is given explicitly up to n=2. Numerical
simulations on the Sierpinski gasket show reasonable agreement with the
analytical expressions. The corrective term contributes substantially
to the final value of even for relatively large values of N.Comment: 10 total pages (RevTex), 7 figures include
II. Territory covered by N random walkers on stochastic fractals. The percolation aggregate
The average number of distinct sites visited up to time t by N
noninteracting random walkers all starting from the same origin in a disordered
fractal is considered. This quantity is the result of a double
average: an average over random walks on a given lattice followed by an average
over different realizations of the lattice. We show for two-dimensional
percolation clusters at criticality (and conjecture for other stochastic
fractals) that the distribution of the survival probability over these
realizations is very broad in Euclidean space but very narrow in the chemical
or topological space. This allows us to adapt the formalism developed for
Euclidean and deterministic fractal lattices to the chemical language, and an
asymptotic series for analogous to that found for the non-disordered
media is proposed here. The main term is equal to the number of sites (volume)
inside a ``hypersphere'' in the chemical space of radius
where L is the root-mean-square chemical displacement of a single random
walker, and v and c determine how fast (the probability that
a given site at chemical distance from the origin is visited by a single
random walker by time t) decays for large values of :
. The parameters appearing in the
first two asymptotic terms of are estimated by numerical simulation
for the two-dimensional percolation cluster at criticality. The corresponding
theoretical predictions are compared with simulation data, and the agreement is
found to be very good.Comment: 11 total pages (RevTex), 8 figures include
Multiparticle random walks
An overview is presented of recent work on some statistical problems on
multiparticle random walks. We consider a Euclidean, deterministic fractal or
disordered lattice and N >> 1 independent random walkers initially (t=0) placed
onto the same site of the substrate. Three classes of problems are considered:
(i) the evaluation of the average number of distinct sites visited
(territory explored) up to time t by the N random walkers, (ii) the statistical
description of the first passage time t_{j,N} to a given distance of the first
j random walkers (order statistics of exit times), and (iii) the statistical
description of the time \mathbf{t}_{j,N} elapsed until the first j random
walkers are trapped when a Euclidean lattice is randomly occupied by a
concentration c of traps (order statistics of the trapping problem). Although
these problems are very different in nature, their solutions share the same
form of a series in ln^{-n}(N) \ln^m \ln (N) (with n>=1 and 0>1.
These corrective terms contribute substantially to the statistical quantities
even for relatively large values of N.Comment: 14 pages, 13 figures, RevTex
Moduli of regularity and rates of convergence for Fej\'er monotone sequences
In this paper we introduce the concept of modulus of regularity as a tool to
analyze the speed of convergence, including the finite termination, for classes
of Fej\'er monotone sequences which appear in fixed point theory, monotone
operator theory, and convex optimization. This concept allows for a unified
approach to several notions such as weak sharp minima, error bounds, metric
subregularity, H\"older regularity, etc., as well as to obtain rates of
convergence for Picard iterates, the Mann algorithm, the proximal point
algorithm and the cyclic algorithm. As a byproduct we obtain a quantitative
version of the well-known fact that for a convex lower semi-continuous function
the set of minimizers coincides with the set of zeros of its subdifferential
and the set of fixed points of its resolvent
Geodesic rays, the "Lion-Man" game, and the fixed point property
This paper focuses on the relation among the existence of different types of
curves (such as directional ones, quasi-geodesic or geodesic rays), the
(approximate) fixed point property for nonexpansive mappings, and a discrete
lion and man game. Our main result holds in the setting of CAT(0) spaces that
are additionally Gromov hyperbolic
"Lion-Man" and the Fixed Point Property
This paper focuses on the relation between the fixed point property for
continuous mappings and a discrete lion and man game played in a strongly
convex domain. Our main result states that in locally compact geodesic spaces,
the compactness of the domain is equivalent to its fixed point property, as
well as to the success of the lion. The common link among these properties
involves the existence of different types of rays, which we also discuss.Comment: final version available in Geometriae Dedicata,
https://doi.org/10.1007/s10711-018-0403-
Quantitative asymptotic regularity results for the composition of two mappings
In this paper, we use techniques which originate from proof mining to give
rates of asymptotic regularity and metastability for a sequence associated to
the composition of two firmly nonexpansive mappings
On the derivation of a high-velocity tail from the Boltzmann-Fokker-Planck equation for shear flow
Uniform shear flow is a paradigmatic example of a nonequilibrium fluid state
exhibiting non-Newtonian behavior. It is characterized by uniform density and
temperature and a linear velocity profile , where is the
constant shear rate. In the case of a rarefied gas, all the relevant physical
information is represented by the one-particle velocity distribution function
, with ,
which satisfies the standard nonlinear integro-differential Boltzmann equation.
We have studied this state for a two-dimensional gas of Maxwell molecules with
grazing collisions in which the nonlinear Boltzmann collision operator reduces
to a Fokker-Planck operator. We have found analytically that for shear rates
larger than a certain threshold value the velocity distribution function
exhibits an algebraic high-velocity tail of the form , where and the
angular distribution function is the solution of a modified
Mathieu equation. The enforcement of the periodicity condition allows one to obtain the exponent as a
function of the shear rate. As a consequence of this power-law decay, all the
velocity moments of a degree equal to or larger than are
divergent. In the high-velocity domain the velocity distribution is highly
anisotropic, with the angular distribution sharply concentrated around a
preferred orientation angle which rotates counterclock-wise as the shear rate
increases.Comment: 15 pages, 5 figures; change in title plus other minor changes; to be
published in J. Stat. Phy
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