3,435 research outputs found
Directing Brownian motion on a periodic surface
We consider an overdamped Brownian particle, exposed to a two-dimensional,
square lattice potential and a rectangular ac-drive. Depending on the driving
amplitude, the linear response to a weak dc-force along a lattice symmetry axis
consist in a mobility in basically any direction. In particular, motion exactly
opposite to the applied dc-force may arise. Upon changing the angle of the
dc-force relatively to the square lattice, the particle motion remains
predominantly opposite to the dc-force. The basic physical mechanism consists
in a spontaneous symmetry breaking of the unbiased deterministic particle
dynamics.Comment: 4 Pages, 4 figures, accepted for Phys. Rev. Let
BIOMECHANICAL ANALYSIS OF THE DEADLIFT DURING THE 1999 SPECIAL OLYMPICS WORLD GAMES
Sumo and conventional deadlifts and high and low skilled lifters were compared during the 1999 Special Olympics World Games. Two video cameras collected 60 Hz data from 40 subjects, and parameters were quantified at barbell liftoff (LO) and barbell knee passing (KP). The sumo group had a more vertical trunk and horizontal thigh at LO, a less vertical shank at KP, and greater forefoot abduction. The sumo group generated ankle dorsiflexor, knee extensor, and hip extensor moments, while the conventional group produced ankle plantar flexor, knee flexor & extensor, and hip extensor moments. High skilled lifters had a 40% greater barbell load, greater knee flexion at LO and greater knee extension at KP, 15% less vertical bar distance, smaller plantar flexor and hip extensor moment arms at LO and KP, and greater knee extensor moment arms at LO
Shuffle relations for regularised integrals of symbols
We prove shuffle relations which relate a product of regularised integrals of
classical symbols to regularised nested (Chen) iterated integrals, which hold
if all the symbols involved have non-vanishing residue. This is true in
particular for non-integer order symbols. In general the shuffle relations hold
up to finite parts of corrective terms arising from renormalisation on tensor
products of classical symbols, a procedure adapted from renormalisation
procedures on Feynman diagrams familiar to physicists. We relate the shuffle
relations for regularised integrals of symbols with shuffle relations for
multizeta functions adapting the above constructions to the case of symbols on
the unit circle.Comment: 40 pages,latex. Changes concern sections 4 and 5 : an error in
section 4 has been corrected, and the link between section 5 and the previous
ones has been precise
Spontaneous symmetry breaking: exact results for a biased random walk model of an exclusion process
It has been recently suggested that a totally asymmetric exclusion process
with two species on an open chain could exhibit spontaneous symmetry breaking
in some range of the parameters defining its dynamics. The symmetry breaking is
manifested by the existence of a phase in which the densities of the two
species are not equal. In order to provide a more rigorous basis to these
observations we consider the limit of the process when the rate at which
particles leave the system goes to zero. In this limit the process reduces to a
biased random walk in the positive quarter plane, with specific boundary
conditions. The stationary probability measure of the position of the walker in
the plane is shown to be concentrated around two symmetrically located points,
one on each axis, corresponding to the fact that the system is typically in one
of the two states of broken symmetry in the exclusion process. We compute the
average time for the walker to traverse the quarter plane from one axis to the
other, which corresponds to the average time separating two flips between
states of broken symmetry in the exclusion process. This time is shown to
diverge exponentially with the size of the chain.Comment: 42 page
Exact solutions for a mean-field Abelian sandpile
We introduce a model for a sandpile, with N sites, critical height N and each
site connected to every other site. It is thus a mean-field model in the
spin-glass sense. We find an exact solution for the steady state probability
distribution of avalanche sizes, and discuss its asymptotics for large N.Comment: 10 pages, LaTe
Algebraic Aspects of Abelian Sandpile Models
The abelian sandpile models feature a finite abelian group G generated by the
operators corresponding to particle addition at various sites. We study the
canonical decomposition of G as a product of cyclic groups G = Z_{d_1} X
Z_{d_2} X Z_{d_3}...X Z_{d_g}, where g is the least number of generators of G,
and d_i is a multiple of d_{i+1}. The structure of G is determined in terms of
toppling matrix. We construct scalar functions, linear in height variables of
the pile, that are invariant toppling at any site. These invariants provide
convenient coordinates to label the recurrent configurations of the sandpile.
For an L X L square lattice, we show that g = L. In this case, we observe that
the system has nontrivial symmetries coming from the action of the cyclotomic
Galois group of the (2L+2)th roots of unity which operates on the set of
eigenvalues of the toppling matrix. These eigenvalues are algebraic integers,
whose product is the order |G|. With the help of this Galois group, we obtain
an explicit factorizaration of |G|. We also use it to define other simpler,
though under-complete, sets of toppling invariants.Comment: 39 pages, TIFR/TH/94-3
The grand canonical ABC model: a reflection asymmetric mean field Potts model
We investigate the phase diagram of a three-component system of particles on
a one-dimensional filled lattice, or equivalently of a one-dimensional
three-state Potts model, with reflection asymmetric mean field interactions.
The three types of particles are designated as , , and . The system is
described by a grand canonical ensemble with temperature and chemical
potentials , , and . We find that for
the system undergoes a phase transition from a
uniform density to a continuum of phases at a critical temperature . For other values of the chemical potentials the system
has a unique equilibrium state. As is the case for the canonical ensemble for
this model, the grand canonical ensemble is the stationary measure
satisfying detailed balance for a natural dynamics. We note that , where is the critical temperature for a similar transition in
the canonical ensemble at fixed equal densities .Comment: 24 pages, 3 figure
Analysis of conductor impedances accounting for skin effect and nonlinear permeability
It is often necessary to protect sensitive electrical equipment from pulsed electric and magnetic fields. To accomplish this electromagnetic shielding structures similar to Faraday Cages are often implemented. If the equipment is inside a facility that has been reinforced with rebar, the rebar can be used as part of a lighting protection system. Unfortunately, such shields are not perfect and allow electromagnetic fields to be created inside due to discontinuities in the structure, penetrations, and finite conductivity of the shield. In order to perform an analysis of such a structure it is important to first determine the effect of the finite impedance of the conductors used in the shield. In this paper we will discuss the impedances of different cylindrical conductors in the time domain. For a time varying pulse the currents created in the conductor will have different spectral components, which will affect the current density due to skin effects. Many construction materials use iron and different types of steels that have a nonlinear permeability. The nonlinear material can have an effect on the impedance of the conductor depending on the B-H curve. Although closed form solutions exist for the impedances of cylindrical conductors made of linear materials, computational techniques are needed for nonlinear materials. Simulations of such impedances are often technically challenging due to the need for a computational mesh to be able to resolve the skin depths for the different spectral components in the pulse. The results of such simulations in the time domain will be shown and used to determine the impedances of cylindrical conductors for lightning current pulses that have low frequency content
Measuring helical FCG voltage with an electric field antenna
A method of measuring the voltage produced by a helical explosive flux compression generator using a remote electric field antenna is described in detail. The diagnostic has been successfully implemented on several experiments. Measured data from the diagnostic compare favorably with voltages predicted using the code CAGEN, validating our predictive modeling tools. The measured data is important to understanding generator performance, and is measured with a low-risk, minimally intrusive approach
Phase diagram of the ABC model with nonconserving processes
The three species ABC model of driven particles on a ring is generalized to
include vacancies and particle-nonconserving processes. The model exhibits
phase separation at high densities. For equal average densities of the three
species, it is shown that although the dynamics is {\it local}, it obeys
detailed balance with respect to a Hamiltonian with {\it long-range
interactions}, yielding a nonadditive free energy. The phase diagrams of the
conserving and nonconserving models, corresponding to the canonical and
grand-canonical ensembles, respectively, are calculated in the thermodynamic
limit. Both models exhibit a transition from a homogeneous to a phase-separated
state, although the phase diagrams are shown to differ from each other. This
conforms with the expected inequivalence of ensembles in equilibrium systems
with long-range interactions. These results are based on a stability analysis
of the homogeneous phase and exact solution of the hydrodynamic equations of
the models. They are supported by Monte-Carlo simulations. This study may serve
as a useful starting point for analyzing the phase diagram for unequal
densities, where detailed balance is not satisfied and thus a Hamiltonian
cannot be defined.Comment: 32 page, 7 figures. The paper was presented at Statphys24, held in
Cairns, Australia, July 201
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