22,583 research outputs found

### Time-Dependent Random Walks and the Theory of Complex Adaptive Systems

Motivated by novel results in the theory of complex adaptive systems, we
analyze the dynamics of random walks in which the jumping probabilities are
{\it time-dependent}. We determine the survival probability in the presence of
an absorbing boundary. For an unbiased walk the survival probability is
maximized in the case of large temporal oscillations in the jumping
probabilities. On the other hand, a random walker who is drifted towards the
absorbing boundary performs best with a constant jumping probability. We use
the results to reveal the underlying dynamics responsible for the phenomenon of
self-segregation and clustering observed in the evolutionary minority game.Comment: 5 pages, 2 figure

### Mass Expansions of Screened Perturbation Theory

The thermodynamics of massless phi^4-theory is studied within screened
perturbation theory (SPT). In this method the perturbative expansion is
reorganized by adding and subtracting a mass term in the Lagrangian. We
analytically calculate the pressure and entropy to three-loop order and the
screening mass to two-loop order, expanding in powers of m/T. The truncated
m/T-expansion results are compared with numerical SPT results for the pressure,
entropy and screening mass which are accurate to all orders in m/T. It is shown
that the m/T-expansion converges quickly and provides an accurate description
of the thermodynamic functions for large values of the coupling constant.Comment: 22 pages, 10 figure

### Bounding the dimensions of rational cohomology groups

Let $k$ be an algebraically closed field of characteristic $p > 0$, and let
$G$ be a simple simply-connected algebraic group over $k$ that is defined and
split over the prime field $\mathbb{F}_p$. In this paper we investigate
situations where the dimension of a rational cohomology group for $G$ can be
bounded by a constant times the dimension of the coefficient module. We then
demonstrate how our results can be applied to obtain effective bounds on the
first cohomology of the symmetric group. We also show how, for finite Chevalley
groups, our methods permit significant improvements over previous estimates for
the dimensions of second cohomology groups.Comment: 13 page

### Comment on "Mean First Passage Time for Anomalous Diffusion"

We correct a previously erroneous calculation [Phys. Rev. E 62, 6065 (2000)]
of the mean first passage time of a subdiffusive process to reach either end of
a finite interval in one dimension. The mean first passage time is in fact
infinite.Comment: To appear in Phys. Rev.

### The mass content of the Sculptor dwarf spheroidal galaxy

We present a new determination of the mass content of the Sculptor dwarf
spheroidal galaxy, based on a novel approach which takes into account the two
distinct stellar populations present in this galaxy. This method helps to
partially break the well-known mass-anisotropy degeneracy present in the
modelling of pressure-supported stellar systems.Comment: 6 pages, 3 figures. To appear in the proceedings of IAU Symposium 254
"The Galaxy disk in a cosmological context", Copenhagen, June 200

### Anomalous diffusion and generalized Sparre-Andersen scaling

We are discussing long-time, scaling limit for the anomalous diffusion
composed of the subordinated L\'evy-Wiener process. The limiting anomalous
diffusion is in general non-Markov, even in the regime, where ensemble averages
of a mean-square displacement or quantiles representing the group spread of the
distribution follow the scaling characteristic for an ordinary stochastic
diffusion. To discriminate between truly memory-less process and the non-Markov
one, we are analyzing deviation of the survival probability from the (standard)
Sparre-Andersen scaling.Comment: 5 pages, 3 figure

### Screened Perturbation Theory to Three Loops

The thermal physics of a massless scalar field with a phi^4 interaction is
studied within screened perturbation theory (SPT). In this method the
perturbative expansion is reorganized by adding and subtracting a mass term in
the lagrangian. We consider several different mass prescriptions that
generalize the one-loop gap equation to two-loop order. We calculate the
pressure and entropy to three-loop order and the screening mass to two-loop
order. In contrast to the weak-coupling expansion, the SPT-improved
approximations appear to converge even for rather large values of the coupling
constant.Comment: 30 pages, 10 figure

### Solution to the 3-Loop $\Phi$-Derivable Approximation for Massless Scalar Thermodynamics

We develop a systematic method for solving the 3-loop $\Phi$-derivable
approximation to the thermodynamics of the massless $\phi^4$ field theory. The
method involves expanding sum-integrals in powers of $g^2$ and m/T, where g is
the coupling constant, m is a variational mass parameter, and T is the
temperature. The problem is reduced to one with the single variational
parameter m by solving the variational equations order-by-order in $g^2$ and
m/T. At the variational point, there are ultraviolet divergences of order $g^6$
that cannot be removed by any renormalization of the coupling constant. We
define a finite thermodynamic potential by truncating at $5^{th}$ order in g
and m/T. The associated thermodynamic functions seem to be perturbatively
stable and insensitive to variations in the renormalization scale.Comment: 57 pages, 10 figure

### Renormalization Group Summation and the Free Energy of Hot QCD

Using an approach developed in the context of zero-temperature QCD to
systematically sum higher order effects whose form is fixed by the
renormalization group equation, we sum to all orders the leading log (LL) and
next-to-leading log (NLL) contributions to the thermodynamic free energy in hot
QCD. While the result varies considerably less with changes in the
renormalization scale than does the purely perturbative result, a novel
ambiguity arises which reflects the strong scheme dependence of thermal
perturbation theory.Comment: 7 pages REVTEX4, 2 figures; v2: typos correcte

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