431 research outputs found
Kinetic theory for strong uniform shear flow of granular media at high density
We discuss the uniform shear flow of a fluidized granular bed composed of
monodisperse Hertzian spheres. Considering high densities around the glass
transition density of inelastic Hertzian spheres, we report kinetic theory
expressions for the Newtonian viscosity as well as the Bagnold coefficient. We
discuss the dependence of the transport coefficients on density and coefficient
of restitution.Comment: Powders & Grains 201
Nearly-logarithmic decay in the colloidal hard-sphere system
Nearly-logarithmic decay is identified in the data for the mean-squared
displacement of the colloidal hard-sphere system at the liquid-glass transition
[v. Megen et. al, Phys. Rev. E 58, 6073(1998)]. The solutions of mode-coupling
theory for the microscopic equations of motion fit the experimental data well.
Based on these equations, the nearly-logarithmic decay is explained as the
equivalent of a beta-peak phenomenon, a manifestation of the critical
relaxation when the coupling between of the probe variable and the density
fluctuations is strong. In an asymptotic expansion, a Cole-Cole formula
including corrections is derived from the microscopic equations of motion,
which describes the experimental data for three decades in time.Comment: 4 pages, 3 figure
The Glass Transition in Driven Granular Fluids: A Mode-Coupling Approach
We consider the stationary state of a fluid comprised of inelastic hard
spheres or disks under the influence of a random, momentum-conserving external
force. Starting from the microscopic description of the dynamics, we derive a
nonlinear equation of motion for the coherent scattering function in two and
three space dimensions. A glass transition is observed for all coefficients of
restitution, epsilon, at a critical packing fraction, phi_c(epsilon), below
random close packing. The divergence of timescales at the glass-transition
implies a dependence on compression rate upon further increase of the density -
similar to the cooling rate dependence of a thermal glass. The critical
dynamics for coherent motion as well as tagged particle dynamics is analyzed
and shown to be non-universal with exponents depending on space dimension and
degree of dissipation.Comment: 16 pages, 9 figure
Critical Decay at Higher-Order Glass-Transition Singularities
Within the mode-coupling theory for the evolution of structural relaxation in
glass-forming systems, it is shown that the correlation functions for density
fluctuations for states at A_3- and A_4-glass-transition singularities can be
presented as an asymptotic series in increasing inverse powers of the logarithm
of the time t: , where
with p_n denoting some polynomial and x=ln (t/t_0). The results are
demonstrated for schematic models describing the system by solely one or two
correlators and also for a colloid model with a square-well-interaction
potential.Comment: 26 pages, 7 figures, Proceedings of "Structural Arrest Transitions in
Colloidal Systems with Short-Range Attractions", Messina, Italy, December
2003 (submitted
Pressure and Motion of Dry Sand -- Translation of Hagen's Paper from 1852
In a remarkable paper from 1852, Gotthilf Heinrich Ludwig Hagen measured and
explained two fundamental aspects of granular matter: The first effect is the
saturation of pressure with depth in a static granular system confined by silo
walls -- generally known as the Janssen effect. The second part of his paper
describes the dynamics observed during the flow out of the container -- today
often called the Beverloo law -- and forms the foundation of the hourglass
theory. The following is a translation of the original German paper from 1852.Comment: 4 pages, accepted for publication in Granular Matter, original
article (German) can be found under http://www.phy.duke.edu/~msperl/Janssen
Glass glass transition and new dynamical singularity points in an analytically solvable p-spin glass like model
We introduce and analytically study a generalized p-spin glass like model
that captures some of the main features of attractive glasses, recently found
by Mode Coupling investigations, such as a glass/glass transition line and
dynamical singularity points characterized by a logarithmic time dependence of
the relaxation. The model also displays features not predicted by the Mode
Coupling scenario that could further describe the attractive glasses behavior,
such as aging effects with new dynamical singularity points ruled by
logarithmic laws or the presence of a glass spinodal line
The manifold rheology of fluidized granular media
Fluidized granular media have a rich rheology: measuring shear stress
as a function of shear rate , they exhibit Newtonian
behavior for low densities and shear rates, develop a
yield stress for intermediate shear rates and densities approaching the
granular glass transition, and finally, cross over to shear-thickening Bagnold
scaling, . This wealth of flow-behaviors makes
fluidized beds a fascinating material, but also one that is challenging to
encompass into a global theory, despite its relevance for optimizing industrial
processes and predicting natural hazards. We provide careful measurements
spanning eight orders of magnitude in shear rate, and show that all these
rheological regimes can be described qualitatively and quantitatively using the
granular integration through transient formalism, a theory for glassy dynamics
under shear adapted to granular fluids
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