146,975 research outputs found
Weighted Surface Algebras
A finite-dimensional algebra over an algebraically closed field is
called periodic if it is periodic under the action of the syzygy operator in
the category of bimodules. The periodic algebras are self-injective and
occur naturally in the study of tame blocks of group algebras, actions of
finite groups on spheres, hypersurface singularities of finite Cohen-Macaulay
type, and Jacobian algebras of quivers with potentials. Recently, the tame
periodic algebras of polynomial growth have been classified and it is natural
to attempt to classify all tame periodic algebras. We introduce the weighted
surface algebras of triangulated surfaces with arbitrarily oriented triangles
and describe their basic properties. In particular, we prove that all these
algebras, except the singular tetrahedral algebras, are symmetric tame periodic
algebras of period . Moreover, we describe the socle deformations of the
weighted surface algebras and prove that all these algebras are symmetric tame
periodic algebras of period . The main results of the paper form an
important step towards a classification of all periodic symmetric tame algebras
of non-polynomial growth, and lead to a complete description of all algebras of
generalized quaternion type. Further, the orbit closures of the weighted
surface algebras (and their socle deformations) in the affine varieties of
associative -algebra structures contain wide classes of tame symmetric
algebras related to algebras of dihedral and semidihedral types, which occur in
the study of blocks of group algebras with dihedral and semidihedral defect
groups
The production of Tsallis entropy in the limit of weak chaos and a new indicator of chaoticity
We study the connection between the appearance of a `metastable' behavior of
weakly chaotic orbits, characterized by a constant rate of increase of the
Tsallis q-entropy (Tsallis 1988), and the solutions of the variational
equations of motion for the same orbits. We demonstrate that the variational
equations yield transient solutions, lasting for long time intervals, during
which the length of deviation vectors of nearby orbits grows in time almost as
a power-law. The associated power exponent can be simply related to the
entropic exponent for which the q-entropy exhibits a constant rate of increase.
This analysis leads to the definition of a new sensitive indicator
distinguishing regular from weakly chaotic orbits, that we call `Average Power
Law Exponent' (APLE). We compare the APLE with other established indicators of
the literature. In particular, we give examples of application of the APLE in
a) a thin separatrix layer of the standard map, b) the stickiness region around
an island of stability in the same map, and c) the web of resonances of a 4D
symplectic map. In all these cases we identify weakly chaotic orbits exhibiting
the `metastable' behavior associated with the Tsallis q-entropy.Comment: 19 pages, 12 figures, accepted for publication by Physica
Algebras of generalized dihedral type
We provide a complete classification of all algebras of generalised dihedral
type, which are natural generalizations of algebras which occurred in the study
of blocks with dihedral defect groups. This gives a description by quivers and
relations coming from surface triangulations.Comment: arXiv admin note: text overlap with arXiv:1703.0234
Phase space geometry and slow dynamics
We describe a non-Arrhenius mechanism for slowing down of dynamics that is
inherent to the high dimensionality of the phase space. We show that such a
mechanism is at work both in a family of mean-field spin-glass models without
any domain structure and in the case of ferromagnetic domain growth. The
marginality of spin-glass dynamics, as well as the existence of a `quasi
equilibrium regime' can be understood within this scenario. We discuss the
question of ergodicity in an out-of equilibrium situation.Comment: 23 pages, ReVTeX3.0, 6 uuencoded postscript figures appende
Comparison of Different Parallel Implementations of the 2+1-Dimensional KPZ Model and the 3-Dimensional KMC Model
We show that efficient simulations of the Kardar-Parisi-Zhang interface
growth in 2 + 1 dimensions and of the 3-dimensional Kinetic Monte Carlo of
thermally activated diffusion can be realized both on GPUs and modern CPUs. In
this article we present results of different implementations on GPUs using CUDA
and OpenCL and also on CPUs using OpenCL and MPI. We investigate the runtime
and scaling behavior on different architectures to find optimal solutions for
solving current simulation problems in the field of statistical physics and
materials science.Comment: 14 pages, 8 figures, to be published in a forthcoming EPJST special
issue on "Computer simulations on GPU
Bubble statistics and coarsening dynamics for quasi-two dimensional foams with increasing liquid content
We report on the statistics of bubble size, topology, and shape and on their
role in the coarsening dynamics for foams consisting of bubbles compressed
between two parallel plates. The design of the sample cell permits control of
the liquid content, through a constant pressure condition set by the height of
the foam above a liquid reservoir. We find that in the scaling state, all
bubble distributions are independent not only of time but also of liquid
content. For coarsening, the average rate decreases with liquid content due to
the blocking of gas diffusion by Plateau borders inflated with liquid. By
observing the growth rate of individual bubbles, we find that von Neumann's law
becomes progressively violated with increasing wetness and with decreasing
bubble size. We successfully model this behavior by explicitly incorporating
the border blocking effect into the von Neumann argument. Two dimensionless
bubble shape parameters naturally arise, one of which is primarily responsible
for the violation of von Neumann's law for foams that are not perfectly dry
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