596 research outputs found
Soliton attenuation and emergent hydrodynamics in fragile matter
Disordered packings of soft grains are fragile mechanical systems that loose
rigidity upon lowering the external pressure towards zero. At zero pressure, we
find that any infinitesimal strain-impulse propagates initially as a non-linear
solitary wave progressively attenuated by disorder. We demonstrate that the
particle fluctuations generated by the solitary-wave decay, can be viewed as a
granular analogue of temperature. Their presence is manifested by two emergent
macroscopic properties absent in the unperturbed granular packing: a finite
pressure that scales with the injected energy (akin to a granular temperature)
and an anomalous viscosity that arises even when the microscopic mechanisms of
energy dissipation are negligible. Consistent with the interpretation of this
state as a fluid-like thermalized state, the shear modulus remains zero.
Further, we follow in detail the attenuation of the initial solitary wave
identifying two distinct regimes : an initial exponential decay, followed by a
longer power law decay and suggest simple models to explain these two regimes.Comment: 8 pages, 3 Figure
Extrema statistics in the dynamics of a non-Gaussian random field
When the equations that govern the dynamics of a random field are nonlinear,
the field can develop with time non-Gaussian statistics even if its initial
condition is Gaussian. Here, we provide a general framework for calculating the
effect of the underlying nonlinear dynamics on the relative densities of maxima
and minima of the field. Using this simple geometrical probe, we can identify
the size of the non-Gaussian contributions in the random field, or
alternatively the magnitude of the nonlinear terms in the underlying equations
of motion. We demonstrate our approach by applying it to an initially Gaussian
field that evolves according to the deterministic KPZ equation, which models
surface growth and shock dynamics.Comment: 9 pages, 3 figure
The physics of forgetting: Landauer's erasure principle and information theory
This article discusses the concept of information and its intimate
relationship with physics. After an introduction of all the necessary quantum
mechanical and information theoretical concepts we analyze Landauer's principle
that states that the erasure of information is inevitably accompanied by the
generation of heat. We employ this principle to rederive a number of results in
classical and quantum information theory whose rigorous mathematical
derivations are difficult. This demonstrates the usefulness of Landauer's
principle and provides an introduction to the physical theory of information.Comment: 36 pages, 13 figures, Very basic introductory article for
Contemporary Physic
Crystallography on Curved Surfaces
We study static and dynamical properties that distinguish two dimensional
crystals constrained to lie on a curved substrate from their flat space
counterparts. A generic mechanism of dislocation unbinding in the presence of
varying Gaussian curvature is presented in the context of a model surface
amenable to full analytical treatment. We find that glide diffusion of isolated
dislocations is suppressed by a binding potential of purely geometrical origin.
Finally, the energetics and biased diffusion dynamics of point defects such as
vacancies and interstitials is explained in terms of their geometric potential.Comment: 12 Pages, 8 Figure
Stochastic geometry and topology of non-Gaussian fields
Gaussian random fields pervade all areas of science. However, it is often the
departures from Gaussianity that carry the crucial signature of the nonlinear
mechanisms at the heart of diverse phenomena, ranging from structure formation
in condensed matter and cosmology to biomedical imaging. The standard test of
non-Gaussianity is to measure higher order correlation functions. In the
present work, we take a different route. We show how geometric and topological
properties of Gaussian fields, such as the statistics of extrema, are modified
by the presence of a non-Gaussian perturbation. The resulting discrepancies
give an independent way to detect and quantify non-Gaussianities. In our
treatment, we consider both local and nonlocal mechanisms that generate
non-Gaussian fields, both statically and dynamically through nonlinear
diffusion.Comment: 8 pages, 4 figure
Shocks near Jamming
Non-linear sound is an extreme phenomenon typically observed in solids after
violent explosions. But granular media are different. Right when they jam,
these fragile and disordered solids exhibit a vanishing rigidity and sound
speed, so that even tiny mechanical perturbations form supersonic shocks. Here,
we perform simulations in which two-dimensional jammed granular packings are
dynamically compressed, and demonstrate that the elementary excitations are
strongly non-linear shocks, rather than ordinary phonons. We capture the full
dependence of the shock speed on pressure and impact intensity by a
surprisingly simple analytical model.Comment: Revised version. Accepted for publication in Phys. Rev. Let
- …