570 research outputs found
A Spin - 3/2 Ising Model on a Square Lattice
The spin - 3/2 Ising model on a square lattice is investigated. It is shown
that this model is reducible to an eight - vertex model on a surface in the
parameter space spanned by coupling constants J, K, L and M. It is shown that
this model is equivalent to an exactly solvable free fermion model along two
lines in the parameter space.Comment: LaTeX, 7 pages, 1 figure upon request; JETP Letters, in pres
Dynamics of lattice spins as a model of arrhythmia
We consider evolution of initial disturbances in spatially extended systems
with autonomous rhythmic activity, such as the heart. We consider the case when
the activity is stable with respect to very smooth (changing little across the
medium) disturbances and construct lattice models for description of
not-so-smooth disturbances, in particular, topological defects; these models
are modifications of the diffusive XY model. We find that when the activity on
each lattice site is very rigid in maintaining its form, the topological
defects - vortices or spirals - nucleate a transition to a disordered,
turbulent state.Comment: 17 pages, revtex, 3 figure
Propagation of travelling waves in sub-excitable systems driven by noise and periodic forcing
It has been reported that traveling waves propagate periodically and stably
in sub-excitable systems driven by noise [Phys. Rev. Lett. \textbf{88}, 138301
(2002)]. As a further investigation, here we observe different types of
traveling waves under different noises and periodic forces, using a simplified
Oregonator model. Depending on different noises and periodic forces, we have
observed different types of wave propagation (or their disappearance).
Moreover, the reversal phenomena are observed in this system based on the
numerical experiments in the one-dimensional space. As an explanation, we
regard it as the effect of periodic forces. Thus, we give qualitative
explanations to how reversal phenomena stably appear, which seem to arise from
the mixing function of the periodic force and the noise. And the output period
and three velocities (the normal, the positive and the negative) of the
travelling waves are defined and their relationship with the periodic forces,
along with the types of waves, are also studied in sub-excitable system under a
fixed noise intensity.Comment: Some references and information are added in the modified version.
Accepted, The European Physical Journal
Philosophy for Nsls-Ii Design With Sub-Nanometer Horizontal Emittance.
NSLS-II at Brookhaven National Laboratory is a new third-generation storage ring light source, whose construction is on the verge of being approved by DOE. When completed, NSLS-II with its ability to provide users with a wide range of spectrum, ranging from IR to ultra-high brightness hard x-ray beams will replace the existing two (20+ years old) NSLS light sources. While presenting an overview of the NSLS-II accelerator system, this paper focuses on the strategy and development of a novel <1 nm emittance light source
Classification of phase transitions and ensemble inequivalence, in systems with long range interactions
Systems with long range interactions in general are not additive, which can
lead to an inequivalence of the microcanonical and canonical ensembles. The
microcanonical ensemble may show richer behavior than the canonical one,
including negative specific heats and other non-common behaviors. We propose a
classification of microcanonical phase transitions, of their link to canonical
ones, and of the possible situations of ensemble inequivalence. We discuss
previously observed phase transitions and inequivalence in self-gravitating,
two-dimensional fluid dynamics and non-neutral plasmas. We note a number of
generic situations that have not yet been observed in such systems.Comment: 42 pages, 11 figures. Accepted in Journal of Statistical Physics.
Final versio
Exact correlation functions of Bethe lattice spin models in external fields
We develop a transfer matrix method to compute exactly the spin-spin
correlation functions of Bethe lattice spin models in the external magnetic
field h and for any temperature T. We first compute the correlation function
for the most general spin - S Ising model, which contains all possible
single-ion and nearest-neighbor pair interactions. This general spin - S Ising
model includes the spin-1/2 simple Ising model and the Blume-Emery-Griffiths
(BEG) model as special cases. From the spin-spin correlation functions, we
obtain functions of correlation length for the simple Ising model and BEG
model, which show interesting scaling and divergent behavior as T approaches
the critical temperature. Our method to compute exact spin-spin correlation
functions may be applied to other Ising-type models on Bethe and Bethe-like
lattices.Comment: 19 page
A thermodynamically self-consistent theory for the Blume-Capel model
We use a self-consistent Ornstein-Zernike approximation to study the
Blume-Capel ferromagnet on three-dimensional lattices. The correlation
functions and the thermodynamics are obtained from the solution of two coupled
partial differential equations. The theory provides a comprehensive and
accurate description of the phase diagram in all regions, including the wing
boundaries in non-zero magnetic field. In particular, the coordinates of the
tricritical point are in very good agreement with the best estimates from
simulation or series expansion. Numerical and analytical analysis strongly
suggest that the theory predicts a universal Ising-like critical behavior along
the -line and the wing critical lines, and a tricritical behavior
governed by mean-field exponents.Comment: 11 figures. to appear in Physical Review
Collective Effects in the NSLS-II Storage Ring.
A new high-brightness synchrotron light source (NSLS-II) is under design at BNL. The 3-GeV NSLS-II storage ring has a double-bend achromatic lattice with damping wigglers installed in zero-dispersion straights to reduce the emittance below 1nm. In this paper, we present an overview of the impact of collective effects upon the performance of the storage ring. Subjects discussed include instability thresholds, Touschek lifetime and intra-beam scattering
Theory of spiral wave dynamics in weakly excitable media: asymptotic reduction to a kinematic model and applications
In a weakly excitable medium, characterized by a large threshold stimulus,
the free end of an isolated broken plane wave (wave tip) can either rotate
(steadily or unsteadily) around a large excitable core, thereby producing a
spiral pattern, or retract causing the wave to vanish at boundaries. An
asymptotic analysis of spiral motion and retraction is carried out in this
weakly excitable large core regime starting from the free-boundary limit of the
reaction-diffusion models, valid when the excited region is delimited by a thin
interface. The wave description is shown to naturally split between the tip
region and a far region that are smoothly matched on an intermediate scale.
This separation allows us to rigorously derive an equation of motion for the
wave tip, with the large scale motion of the spiral wavefront slaved to the
tip. This kinematic description provides both a physical picture and exact
predictions for a wide range of wave behavior, including: (i) steady rotation
(frequency and core radius), (ii) exact treatment of the meandering instability
in the free-boundary limit with the prediction that the frequency of unstable
motion is half the primary steady frequency (iii) drift under external actions
(external field with application to axisymmetric scroll ring motion in
three-dimensions, and spatial or/and time-dependent variation of excitability),
and (iv) the dynamics of multi-armed spiral waves with the new prediction that
steadily rotating waves with two or more arms are linearly unstable. Numerical
simulations of FitzHug-Nagumo kinetics are used to test several aspects of our
results. In addition, we discuss the semi-quantitative extension of this theory
to finite cores and pinpoint mathematical subtleties related to the thin
interface limit of singly diffusive reaction-diffusion models
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