456 research outputs found
Coincidence isometries of a shifted square lattice
We consider the coincidence problem for the square lattice that is translated
by an arbitrary vector. General results are obtained about the set of
coincidence isometries and the coincidence site lattices of a shifted square
lattice by identifying the square lattice with the ring of Gaussian integers.
To illustrate them, we calculate the set of coincidence isometries, as well as
generating functions for the number of coincidence site lattices and
coincidence isometries, for specific examples.Comment: 10 pages, 1 figure; paper presented at Aperiodic 2009 (Liverpool
The Johnson-Segalman model with a diffusion term in Couette flow
We study the Johnson-Segalman (JS) model as a paradigm for some complex
fluids which are observed to phase separate, or ``shear-band'' in flow. We
analyze the behavior of this model in cylindrical Couette flow and demonstrate
the history dependence inherent in the local JS model. We add a simple gradient
term to the stress dynamics and demonstrate how this term breaks the degeneracy
of the local model and prescribes a much smaller (discrete, rather than
continuous) set of banded steady state solutions. We investigate some of the
effects of the curvature of Couette flow on the observable steady state
behavior and kinetics, and discuss some of the implications for metastability.Comment: 14 pp, to be published in Journal of Rheolog
Absence of Phase Transition for Antiferromagnetic Potts Models via the Dobrushin Uniqueness Theorem
We prove that the -state Potts antiferromagnet on a lattice of maximum
coordination number exhibits exponential decay of correlations uniformly at
all temperatures (including zero temperature) whenever . We also prove
slightly better bounds for several two-dimensional lattices: square lattice
(exponential decay for ), triangular lattice (), hexagonal
lattice (), and Kagom\'e lattice (). The proofs are based on
the Dobrushin uniqueness theorem.Comment: 32 pages including 3 figures. Self-unpacking file containing the tex
file, the needed macros (epsf.sty, indent.sty, subeqnarray.sty, and
eqsection.sty) and the 3 ps file
Trajectory and Foothold Optimization using Low-Dimensional Models for Rough Terrain Locomotion
We present a trajectory optimization framework for legged locomotion on rough terrain. We jointly optimize the center of mass motion and the foothold locations, while considering terrain conditions. We use a terrain costmap to quantify the desirability of a foothold location. We increase the gait's adaptability to the terrain by optimizing the step phase duration and modulating the trunk attitude, resulting in motions with guaranteed stability. We show that the combination of parametric models, stochastic-based exploration and receding horizon planning allows us to handle the many local minima associated with different terrain conditions and walking patterns. This combination delivers robust motion plans without the need for warm-starting. Moreover, we use soft-constraints to allow for increased flexibility when searching in the cost landscape of our problem. We showcase the performance of our trajectory optimization framework on multiple terrain conditions and validate our method in realistic simulation scenarios and experimental trials on a hydraulic, torque controlled quadruped robot
Rheological Chaos in a Scalar Shear-Thickening Model
We study a simple scalar constitutive equation for a shear-thickening
material at zero Reynolds number, in which the shear stress \sigma is driven at
a constant shear rate \dot\gamma and relaxes by two parallel decay processes: a
nonlinear decay at a nonmonotonic rate R(\sigma_1) and a linear decay at rate
\lambda\sigma_2. Here \sigma_{1,2}(t) =
\tau_{1,2}^{-1}\int_0^t\sigma(t')\exp[-(t-t')/\tau_{1,2}] {\rm d}t' are two
retarded stresses. For suitable parameters, the steady state flow curve is
monotonic but unstable; this arises when \tau_2>\tau_1 and
0>R'(\sigma)>-\lambda so that monotonicity is restored only through the
strongly retarded term (which might model a slow evolution of material
structure under stress). Within the unstable region we find a period-doubling
sequence leading to chaos. Instability, but not chaos, persists even for the
case \tau_1\to 0. A similar generic mechanism might also arise in shear
thinning systems and in some banded flows.Comment: Reference added; typos corrected. To appear in PRE Rap. Com
PRIVATE SAVINGS IN TRANSITION ECONOMIES: ARE THERE TERMS OF TRADE SHOCKS?
The paper examines the impact of terms of trade shocks on private savings in the transition economies after accounting for the effect of other determinants. Economic agents in the transition economies are subject to tight credit constraints which are more pronounced during bad state of nature. Thus, adverse shocks to commodity prices in the world market can force them to reduce savings by a larger amount than they would otherwise have. Empirical analysis using a dynamic panel model and data from twenty one transition economies confirm that most of the determinants of savings identified in the literature also apply to the transition economies. Favorable movements in both the permanent and transitory components of the terms of trade have a significant positive impact on private savings with transitory movements having a larger impact than the permanent component. This reflects the lack of access to foreign borrowing that many of the transition economies have faced during the last decade. Although the impact of terms of trade shocks are found to be asymmetric, the magnitude of the impact appears to be small. The results are robust for alternative estimators, determinants, and country groupings.http://deepblue.lib.umich.edu/bitstream/2027.42/39958/3/wp572.pd
Oscillations of a solid sphere falling through a wormlike micellar fluid
We present an experimental study of the motion of a solid sphere falling
through a wormlike micellar fluid. While smaller or lighter spheres quickly
reach a terminal velocity, larger or heavier spheres are found to oscillate in
the direction of their falling motion. The onset of this instability correlates
with a critical value of the velocity gradient scale
s. We relate this condition to the known complex rheology of wormlike
micellar fluids, and suggest that the unsteady motion of the sphere is caused
by the formation and breaking of flow-induced structures.Comment: 4 pages, 4 figure
Shear-banding in a lyotropic lamellar phase, Part 1: Time-averaged velocity profiles
Using velocity profile measurements based on dynamic light scattering and
coupled to structural and rheological measurements in a Couette cell, we
present evidences for a shear-banding scenario in the shear flow of the onion
texture of a lyotropic lamellar phase. Time-averaged measurements clearly show
the presence of structural shear-banding in the vicinity of a shear-induced
transition, associated to the nucleation and growth of a highly sheared band in
the flow. Our experiments also reveal the presence of slip at the walls of the
Couette cell. Using a simple mechanical approach, we demonstrate that our data
confirms the classical assumption of the shear-banding picture, in which the
interface between bands lies at a given stress . We also outline
the presence of large temporal fluctuations of the flow field, which are the
subject of the second part of this paper [Salmon {\it et al.}, submitted to
Phys. Rev. E]
Mechanisms explaining transitions between tonic and phasic firing in neuronal populations as predicted by a low dimensional firing rate model
Several firing patterns experimentally observed in neural populations have
been successfully correlated to animal behavior. Population bursting, hereby
regarded as a period of high firing rate followed by a period of quiescence, is
typically observed in groups of neurons during behavior. Biophysical
membrane-potential models of single cell bursting involve at least three
equations. Extending such models to study the collective behavior of neural
populations involves thousands of equations and can be very expensive
computationally. For this reason, low dimensional population models that
capture biophysical aspects of networks are needed.
\noindent The present paper uses a firing-rate model to study mechanisms that
trigger and stop transitions between tonic and phasic population firing. These
mechanisms are captured through a two-dimensional system, which can potentially
be extended to include interactions between different areas of the nervous
system with a small number of equations. The typical behavior of midbrain
dopaminergic neurons in the rodent is used as an example to illustrate and
interpret our results.
\noindent The model presented here can be used as a building block to study
interactions between networks of neurons. This theoretical approach may help
contextualize and understand the factors involved in regulating burst firing in
populations and how it may modulate distinct aspects of behavior.Comment: 25 pages (including references and appendices); 12 figures uploaded
as separate file
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