3,993 research outputs found
On stochasticity in nearly-elastic systems
Nearly-elastic model systems with one or two degrees of freedom are
considered: the system is undergoing a small loss of energy in each collision
with the "wall". We show that instabilities in this purely deterministic system
lead to stochasticity of its long-time behavior. Various ways to give a
rigorous meaning to the last statement are considered. All of them, if
applicable, lead to the same stochasticity which is described explicitly. So
that the stochasticity of the long-time behavior is an intrinsic property of
the deterministic systems.Comment: 35 pages, 12 figures, already online at Stochastics and Dynamic
Tube Models for Rubber-Elastic Systems
In the first part of the paper we show that the constraining potentials
introduced to mimic entanglement effects in Edwards' tube model and Flory's
constrained junction model are diagonal in the generalized Rouse modes of the
corresponding phantom network. As a consequence, both models can formally be
solved exactly for arbitrary connectivity using the recently introduced
constrained mode model. In the second part, we solve a double tube model for
the confinement of long paths in polymer networks which is partially due to
crosslinking and partially due to entanglements. Our model describes a
non-trivial crossover between the Warner-Edwards and the Heinrich-Straube tube
models. We present results for the macroscopic elastic properties as well as
for the microscopic deformations including structure factors.Comment: 15 pages, 8 figures, Macromolecules in pres
Elastic systems
Elastic systems provide tolerance to the variations in computation and communication delays. The incorporation of elasticity opens new opportunities for optimization using new correct-by-construction transformations that cannot be applied to rigid non-elastic systems. The basics of synchronous and asynchronous elastic systems will be reviewed. A set of behavior-preserving transformations will be presented: retiming, recycling, early evaluation, variable-latency units and speculative execution. The application of these transformations for performance and power optimization will be discussed. Finally, a novel framework for microarchitectural exploration will be introduced, showing that the optimal pipelining of a circuit can be automatically obtained by using the previous transformations.Peer ReviewedPostprint (published version
Anderson Localization Phenomenon in One-dimensional Elastic Systems
The phenomenon of Anderson localization of waves in elastic systems is
studied. We analyze this phenomenon in two different set of systems: disordered
linear chains of harmonic oscillators and disordered rods which oscillate with
torsional waves. The first set is analyzed numerically whereas the second one
is studied both experimentally and theoretically. In particular, we discuss the
localization properties of the waves as a function of the frequency. In doing
that we have used the inverse participation ratio, which is related to the
localization length. We find that the normal modes localize exponentially
according to Anderson theory. In the elastic systems, the localization length
decreases with frequency. This behavior is in contrast with what happens in
analogous quantum mechanical systems, for which the localization length grows
with energy. This difference is explained by means of the properties of the re
ection coefficient of a single scatterer in each case.Comment: 15 pages, 10 figure
Wannier-Stark ladders in one-dimensional elastic systems
The optical analogues of Bloch oscillations and their associated
Wannier-Stark ladders have been recently analyzed. In this paper we propose an
elastic realization of these ladders, employing for this purpose the torsional
vibrations of specially designed one-dimensional elastic systems. We have
measured, for the first time, the ladder wave amplitudes, which are not
directly accessible either in the quantum mechanical or optical cases. The wave
amplitudes are spatially localized and coincide rather well with theoretically
predicted amplitudes. The rods we analyze can be used to localize different
frequencies in different parts of the elastic systems and viceversa.Comment: 10 pages, 6 figures, accepted in Phys. Rev. Let
Thermal Effects in the dynamics of disordered elastic systems
Many seemingly different macroscopic systems (magnets, ferroelectrics, CDW,
vortices,..) can be described as generic disordered elastic systems.
Understanding their static and dynamics thus poses challenging problems both
from the point of view of fundamental physics and of practical applications.
Despite important progress many questions remain open. In particular the
temperature has drastic effects on the way these systems respond to an external
force. We address here the important question of the thermal effect close to
depinning, and whether these effects can be understood in the analogy with
standard critical phenomena, analogy so useful to understand the zero
temperature case. We show that close to the depinning force temperature leads
to a rounding of the depinning transition and compute the corresponding
exponent. In addition, using a novel algorithm it is possible to study
precisely the behavior close to depinning, and to show that the commonly
accepted analogy of the depinning with a critical phenomenon does not fully
hold, since no divergent lengthscale exists in the steady state properties of
the line below the depinning threshold.Comment: Proceedings of the International Workshop on Electronic Crystals,
Cargese(2008
Specific Heat of Quantum Elastic Systems Pinned by Disorder
We present the detailed study of the thermodynamics of vibrational modes in
disordered elastic systems such as the Bragg glass phase of lattices pinned by
quenched impurities. Our study and our results are valid within the (mean
field) replica Gaussian variational method. We obtain an expression for the
internal energy in the quantum regime as a function of the saddle point
solution, which is then expanded in powers of at low temperature .
In the calculation of the specific heat a non trivial cancellation of the
term linear in occurs, explicitly checked to second order in . The
final result is at low temperatures in dimension three and
two. The prefactor is controlled by the pinning length. This result is
discussed in connection with other analytical or numerical studies.Comment: 14 page
Pohozhaev and Morawetz Identities in Elastostatics and Elastodynamics
We construct identities of Pohozhaev type, in the context of elastostatics
and elastodynamics, by using the Noetherian approach. As an application, a
non-existence result for forced semi-linear isotropic and anisotropic elastic
systems is established
Stability criteria for completely symmetrical discrete elastic systems
Deformation of completely symmetric elastic system with stability analysis of coupled and uncoupled modes of equilibrium pat
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