14,669 research outputs found
Teaching statistical physics by thinking about models and algorithms
We discuss several ways of illustrating fundamental concepts in statistical
and thermal physics by considering various models and algorithms. We emphasize
the importance of replacing students' incomplete mental images by models that
are physically accurate. In some cases it is sufficient to discuss the results
of an algorithm or the behavior of a model rather than having students write a
program.Comment: 21 pages, 4 figures, submitted to the American Journal of Physic
Lax Operator for the Quantised Orthosymplectic Superalgebra U_q[osp(2|n)]
Each quantum superalgebra is a quasi-triangular Hopf superalgebra, so
contains a \textit{universal -matrix} in the tensor product algebra which
satisfies the Yang-Baxter equation. Applying the vector representation ,
which acts on the vector module , to one side of a universal -matrix
gives a Lax operator. In this paper a Lax operator is constructed for the
-type quantum superalgebras . This can in turn be used to
find a solution to the Yang-Baxter equation acting on
where is an arbitrary module. The case is included
here as an example.Comment: 15 page
On implicit-factorization constraint preconditioners
Recently Dollar and Wathen [14] proposed a class of incomplete factorizations for saddle-point problems, based upon earlier work by Schilders [40]. In this paper, we generalize this class of preconditioners, and examine the spectral implications of our approach. Numerical tests indicate the efficacy of our preconditioners
On solving trust-region and other regularised subproblems in optimization
The solution of trust-region and regularisation subproblems which arise in unconstrained optimization is considered. Building on the pioneering work of Gay, Mor´e and Sorensen, methods which obtain the solution of a sequence of parametrized linear systems by factorization are used. Enhancements using high-order polynomial approximation and inverse iteration ensure that the resulting method is both globally and asymptotically at least superlinearly convergent in all cases, including in the notorious hard case. Numerical experiments validate the effectiveness of our approach. The resulting software is available as packages TRS and RQS as part of the GALAHAD optimization library, and is especially designed for large-scale problems
Optimization in Gradient Networks
Gradient networks can be used to model the dominant structure of complex
networks. Previous works have focused on random gradient networks. Here we
study gradient networks that minimize jamming on substrate networks with
scale-free and Erd\H{o}s-R\'enyi structure. We introduce structural
correlations and strongly reduce congestion occurring on the network by using a
Monte Carlo optimization scheme. This optimization alters the degree
distribution and other structural properties of the resulting gradient
networks. These results are expected to be relevant for transport and other
dynamical processes in real network systems.Comment: 5 pages, 4 figure
Punctuated Equilibrium in Software Evolution
The approach based on paradigm of self-organized criticality proposed for
experimental investigation and theoretical modelling of software evolution. The
dynamics of modifications studied for three free, open source programs Mozilla,
Free-BSD and Emacs using the data from version control systems. Scaling laws
typical for the self-organization criticality found. The model of software
evolution presenting the natural selection principle is proposed. The results
of numerical and analytical investigation of the model are presented. They are
in a good agreement with the data collected for the real-world software.Comment: 4 pages, LaTeX, 2 Postscript figure
Degenerate mixing of plasma waves on cold, magnetized single-species plasmas
In the cold-fluid dispersion relation ω = ω_p/[1+(k_⊥/k_z)^(2]1/2) for Trivelpiece-Gould waves on an infinitely long magnetized plasma cylinder, the transverse and axial wavenumbers appear only in the combination k_⊥/k_z. As a result, for any frequency ω<ω_p, there are infinitely many degenerate waves, all having the same value of k_⊥/k_z. On a cold finite-length plasma column, these degenerate waves reflect into one another at the ends; thus, each standing-wave normal mode of the bounded plasma is a mixture of many degenerate waves, not a single standing wave as is often assumed. A striking feature of the many-wave modes is that the short-wavelength waves often add constructively along resonance cones given by dz/dr = ±(ω_p^2/ω^2-1)^(1/2). Also, the presence of short wavelengths in the admixture for a predominantly long-wavelength mode enhances the viscous damping beyond what the single-wave approximation would predict. Here, numerical solutions are obtained for modes of a cylindrical plasma column with rounded ends. Exploiting the fact that the modes of a spheroidal plasma are known analytically (the Dubin modes), a perturbation analysis is used to investigate the mixing of low-order, nearly degenerate Dubin modes caused by small deformations of a plasma spheroid
Nonequilibrium phase transitions and tricriticality in a three-dimensional lattice system with random-field competing kinetics
We study a nonequilibrium Ising model that stochastically evolves under the
simultaneous operation of several spin-flip mechanisms. In other words, the
local magnetic fields change sign randomly with time due to competing kinetics.
This dynamics models a fast and random diffusion of disorder that takes place
in dilute metallic alloys when magnetic ions diffuse. We performe Monte Carlo
simulations on cubic lattices up to L=60. The system exhibits ferromagnetic and
paramagnetic steady states. Our results predict first-order transitions at low
temperatures and large disorder strengths, which correspond to the existence of
a nonequilibrium tricritical point at finite temperature. By means of standard
finite-size scaling equations, we estimate the critical exponents in the
low-field region, for which our simulations uphold continuous phase
transitions.Comment: 14 pages, 7 figures, accepted for publication in Phys. Rev.
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