445 research outputs found
Interface Depinning in a Disordered Medium - Numerical Results
We propose a lattice model to study the dynamics of a driven interface in a
medium with random pinning forces. For driving forces F smaller than a
threshold force F_c the whole interface gets pinned. The depinning transition
can be characterized by a set of critical exponents: the static and dynamical
roughness exponent, the velocity exponent defined by the scaling of the
velocity of the interface with F-F_c, and a correlation length exponent. The
critical exponents are determined numerically in 1+1 and 2+1 dimensions. Our
findings are compared with recent numerical and analytical results for a
Langevin equation with quenched noise, which is expected to be in the same
universality class. Our results support a recent functional renormalization
group calculation by T.Nattermann et.al. (J.Phys.II France 2, 1483 (1992)).Comment: 12 pages, (10 figures will be mailed upon request), Plain TeX,
RUB-TP3-93-0
Experiments of Interfacial Roughening in Hele-Shaw Flows with Weak Quenched Disorder
We have studied the kinetic roughening of an oil--air interface in a forced
imbibition experiment in a horizontal Hele--Shaw cell with quenched disorder.
Different disorder configurations, characterized by their persistence length in
the direction of growth, have been explored by varying the average interface
velocity v and the gap spacing b. Through the analysis of the rms width as a
function of time, we have measured a growth exponent beta ~= 0.5 that is almost
independent of the experimental parameters. The analysis of the roughness
exponent alpha through the power spectrum have shown different behaviors at
short (alpha_1) and long (alpha_2) length scales, separated by a crossover
wavenumber q_c. The values of the measured roughness exponents depend on
experimental parameters, but at large velocities we obtain alpha_1 ~= 1.3
independently of the disorder configuration. The dependence of the crossover
wavenumber with the experimental parameters has also been investigated,
measuring q_c ~ v^{0.47} for the shortest persistence length, in agreement with
theoretical predictions.Comment: 20 pages, 22 figure
The resting human brain and motor learning.
Functionally related brain networks are engaged even in the absence of an overt behavior. The role of this resting state activity, evident as low-frequency fluctuations of BOLD (see [1] for review, [2-4]) or electrical [5, 6] signals, is unclear. Two major proposals are that resting state activity supports introspective thought or supports responses to future events [7]. An alternative perspective is that the resting brain actively and selectively processes previous experiences [8]. Here we show that motor learning can modulate subsequent activity within resting networks. BOLD signal was recorded during rest periods before and after an 11 min visuomotor training session. Motor learning but not motor performance modulated a fronto-parietal resting state network (RSN). Along with the fronto-parietal network, a cerebellar network not previously reported as an RSN was also specifically altered by learning. Both of these networks are engaged during learning of similar visuomotor tasks [9-22]. Thus, we provide the first description of the modulation of specific RSNs by prior learning--but not by prior performance--revealing a novel connection between the neuroplastic mechanisms of learning and resting state activity. Our approach may provide a powerful tool for exploration of the systems involved in memory consolidation
Effect of Long-Range Interactions in the Conserved Kardar-Parisi-Zhang Equation
The conserved Kardar-Parisi-Zhang equation in the presence of long-range
nonlinear interactions is studied by the dynamic renormalization group method.
The long-range effect produces new fixed points with continuously varying
exponents and gives distinct phase transitions, depending on both the
long-range interaction strength and the substrate dimension . The long-range
interaction makes the surface width less rough than that of the short-range
interaction. In particular, the surface becomes a smooth one with a negative
roughness exponent at the physical dimension d=2.Comment: 4 pages(LaTex), 1 figure(Postscript
Stochastic Growth Equations and Reparametrization Invariance
It is shown that, by imposing reparametrization invariance, one may derive a
variety of stochastic equations describing the dynamics of surface growth and
identify the physical processes responsible for the various terms. This
approach provides a particularly transparent way to obtain continuum growth
equations for interfaces. It is straightforward to derive equations which
describe the coarse grained evolution of discrete lattice models and analyze
their small gradient expansion. In this way, the authors identify the basic
mechanisms which lead to the most commonly used growth equations. The
advantages of this formulation of growth processes is that it allows one to go
beyond the frequently used no-overhang approximation. The reparametrization
invariant form also displays explicitly the conservation laws for the specific
process and all the symmetries with respect to space-time transformations which
are usually lost in the small gradient expansion. Finally, it is observed, that
the knowledge of the full equation of motion, beyond the lowest order gradient
expansion, might be relevant in problems where the usual perturbative
renormalization methods fail.Comment: 42 pages, Revtex, no figures. To appear in Rev. of Mod. Phy
The Tribology of Sliding Elastic Media
The tribology of a sliding elastic continuum in contact with a disordered
substrate is investigated analytically and numerically via a bead-spring model.
The deterministic dynamics of this system exhibits a depinning transition at a
finite driving force, with complex spatial-temporal dynamics including
stick-slip events of all sizes. These behaviors can be understood completely by
mapping the system to the well-known problem of a directed-path in {\em
higher-dimensional } random media.Comment: Uuencode file: 4 pages, small changes in the previous versio
Scaling properties of driven interfaces in disordered media
We perform a systematic study of several models that have been proposed for
the purpose of understanding the motion of driven interfaces in disordered
media. We identify two distinct universality classes: (i) One of these,
referred to as directed percolation depinning (DPD), can be described by a
Langevin equation similar to the Kardar-Parisi-Zhang equation, but with
quenched disorder. (ii) The other, referred to as quenched Edwards-Wilkinson
(QEW), can be described by a Langevin equation similar to the Edwards-Wilkinson
equation but with quenched disorder. We find that for the DPD universality
class the coefficient of the nonlinear term diverges at the depinning
transition, while for the QEW universality class either or
as the depinning transition is approached. The identification
of the two universality classes allows us to better understand many of the
results previously obtained experimentally and numerically. However, we find
that some results cannot be understood in terms of the exponents obtained for
the two universality classes {\it at\/} the depinning transition. In order to
understand these remaining disagreements, we investigate the scaling properties
of models in each of the two universality classes {\it above\/} the depinning
transition. For the DPD universality class, we find for the roughness exponent
for the pinned phase, and
for the moving phase. For the growth exponent, we find for the pinned phase, and for the moving phase.
Furthermore, we find an anomalous scaling of the prefactor of the width on the
driving force. A new exponent , characterizing the
scaling of this prefactor, is shown to relate the values of the roughnessComment: Latex manuscript, Revtex 3.0, 15 pages, and 15 figures also available
via anonymous ftp from ftp://jhilad.bu.edu/pub/abms/ (128.197.42.52
Static and Dynamic Properties of Inhomogeneous Elastic Media on Disordered Substrate
The pinning of an inhomogeneous elastic medium by a disordered substrate is
studied analytically and numerically. The static and dynamic properties of a
-dimensional system are shown to be equivalent to those of the well known
problem of a -dimensional random manifold embedded in -dimensions.
The analogy is found to be very robust, applicable to a wide range of elastic
media, including those which are amorphous or nearly-periodic, with local or
nonlocal elasticity. Also demonstrated explicitly is the equivalence between
the dynamic depinning transition obtained at a constant driving force, and the
self-organized, near-critical behavior obtained by a (small) constant velocity
drive.Comment: 20 pages, RevTeX. Related (p)reprints also available at
http://matisse.ucsd.edu/~hwa/pub.htm
Applying refinement to the use of mice and rats in rheumatoid arthritis research
Rheumatoid arthritis (RA) is a painful, chronic disorder and there is currently an unmet need for effective therapies that will benefit a wide range of patients. The research and development process for therapies and treatments currently involves in vivo studies, which have the potential to cause discomfort, pain or distress. This Working Group report focuses on identifying causes of suffering within commonly used mouse and rat ‘models’ of RA, describing practical refinements to help reduce suffering and improve welfare without compromising the scientific objectives. The report also discusses other, relevant topics including identifying and minimising sources of variation within in vivo RA studies, the potential to provide pain relief including analgesia, welfare assessment, humane endpoints, reporting standards and the potential to replace animals in RA research
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