1,130 research outputs found
Stochastic Generation of Particle Structures with Controlled Degree of Heterogeneity
The recently developed void expansion method (VEM) allows for an efficient
generation of porous packings of spherical particles over a wide range of
volume fractions. The method is based on a random placement of the structural
particles under addition of much smaller "void-particles" whose radii are
repeatedly increased during the void expansion. Thereby, they rearrange the
structural particles until formation of a dense particle packing and introduce
local heterogeneities in the structure. In this paper, microstructures with
volume fractions between 0.4 and 0.6 produced by VEM are analyzed with respect
to their degree of heterogeneity (DOH). In particular, the influence of the
void- to structural particle number ratio, which constitutes a principal
VEM-parameter, on the DOH is studied. The DOH is quantified using the pore size
distribution, the Voronoi volume distribution and the density-fluctuation
method in conjunction with fit functions or integral measures. This analysis
has revealed that for volume fractions between 0.4 and 0.55 the void-particle
number allows for a quasi-continuous adjustment of the DOH. Additionally, the
DOH-range of VEM-generated microstructures with a volume fraction of 0.4 is
compared to the range covered by microstructures generated using previous
Brownian dynamics simulations, which represent the structure of coagulated
colloidal suspensions. Both sets of microstructures cover similarly broad and
overlapping DOH-ranges, which allows concluding that VEM is an efficient method
to stochastically reproduce colloidal microstructures with varying DOH.Comment: 10 pages, 7 figure
Microstructures and Mechanical Properties of Dense Particle Gels: Microstructural Characterization
The macroscopic mechanical properties of densely packed coagulated colloidal
particle gels strongly depend on the local arrangement of the powder particles
on length scales of a few particle diameters. Heterogeneous microstructures
exhibit up to one order of magnitude higher elastic properties and yield
strengths than their homogeneous counterparts. The microstructures of these
gels are analyzed by the straight path method quantifying quasi-linear particle
arrangements of particles. They show similar characteristics than force chains
bearing the mechanical load in granular material. Applying this concept to gels
revealed that heterogeneous colloidal microstructures show a significantly
higher straight paths density and exhibit longer straight paths than their
homogeneous counterparts.Comment: 7 pages, 9 figure
C-Terminal truncation of NR2A subunits impairs synaptic but not extrasynaptic localization of NMDA receptors
NMDA receptors interact via the extended intracellular C-terminal domain of the NR2 subunits with constituents of the postsynaptic density for purposes of retention, clustering, and functional regulation at central excitatory synapses. To examine the role of the C-terminal domain of NR2A in the synaptic localization and function of NR2A-containing NMDA receptors in hippocampal Schaffer collateral–CA1 pyramidal cell synapses, we analyzed mice which express NR2A only in its C-terminally truncated form. In CA1 cell somata, the levels, activation, and deactivation kinetics of extrasynaptic NMDA receptor channels were comparable in wild-type and mutant NR2A^(ΔC/ΔC) mice. At CA1 cell synapses, however, the truncated receptors were less concentrated than their full-length counterparts, as indicated by immunodetection in cultured neurons, synaptosomes, and postsynaptic densities. In the mutant, the NMDA component of evoked EPSCs was reduced in a developmentally progressing manner and was even more reduced in miniature EPSCs (mEPSCs) elicited by spontaneous glutamate release. Moreover, pharmacologically isolated NMDA currents evoked by synaptic stimulation had longer latencies and displayed slower rise and decay times, even in the presence of an NR2B-specific antagonist. These data strongly suggest that the C-terminal domain of NR2A subunits is important for the precise synaptic arrangement of NMDA receptors
The Influence of the Degree of Heterogeneity on the Elastic Properties of Random Sphere Packings
The macroscopic mechanical properties of colloidal particle gels strongly
depend on the local arrangement of the powder particles. Experiments have shown
that more heterogeneous microstructures exhibit up to one order of magnitude
higher elastic properties than their more homogeneous counterparts at equal
volume fraction. In this paper, packings of spherical particles are used as
model structures to computationally investigate the elastic properties of
coagulated particle gels as a function of their degree of heterogeneity. The
discrete element model comprises a linear elastic contact law, particle bonding
and damping. The simulation parameters were calibrated using a homogeneous and
a heterogeneous microstructure originating from earlier Brownian dynamics
simulations. A systematic study of the elastic properties as a function of the
degree of heterogeneity was performed using two sets of microstructures
obtained from Brownian dynamics simulation and from the void expansion method.
Both sets cover a broad and to a large extent overlapping range of degrees of
heterogeneity. The simulations have shown that the elastic properties as a
function of the degree of heterogeneity are independent of the structure
generation algorithm and that the relation between the shear modulus and the
degree of heterogeneity can be well described by a power law. This suggests the
presence of a critical degree of heterogeneity and, therefore, a phase
transition between a phase with finite and one with zero elastic properties.Comment: 8 pages, 6 figures; Granular Matter (published online: 11. February
2012
H\"older equicontinuity of the integrated density of states at weak disorder
H\"older continuity, , with
a constant independent of the disorder strength is proved for the
integrated density of states associated to a discrete random
operator consisting of a translation invariant hopping
matrix and i.i.d. single site potentials with an absolutely
continuous distribution, under a regularity assumption for the hopping term.Comment: 15 Pages, typos corrected, comments and ref. [1] added, theorems 3,4
combine
Generation of folk song melodies using Bayes transforms
The paper introduces the `Bayes transform', a mathematical procedure for putting data into a hierarchical representation. Applicable to any type of data, the procedure yields interesting results when applied to sequences. In this case, the representation obtained implicitly models the repetition hierarchy of the source. There are then natural applications to music. Derivation of Bayes transforms can be the means of determining the repetition hierarchy of note sequences (melodies) in an empirical and domain-general way. The paper investigates application of this approach to Folk Song, examining the results that can be obtained by treating such transforms as generative models
Generation of Porous Particle Structures using the Void Expansion Method
The newly developed "void expansion method" allows for an efficient
generation of porous packings of spherical particles over a wide range of
volume fractions using the discrete element method. Particles are randomly
placed under addition of much smaller "void-particles". Then, the void-particle
radius is increased repeatedly, thereby rearranging the structural particles
until formation of a dense particle packing.
The structural particles' mean coordination number was used to characterize
the evolving microstructures. At some void radius, a transition from an
initially low to a higher mean coordination number is found, which was used to
characterize the influence of the various simulation parameters. For structural
and void-particle stiffnesses of the same order of magnitude, the transition is
found at constant total volume fraction slightly below the random close packing
limit. For decreasing void-particle stiffness the transition is shifted towards
a smaller void-particle radius and becomes smoother.Comment: 9 pages, 8 figure
The importance of structural softening for the evolution and architecture of passive margins
Lithospheric extension can generate passive margins that bound oceans worldwide. Detailed geological and geophysical studies in present and fossil passive margins have highlighted the complexity of their architecture and their multi-stage deformation history. Previous modeling studies have shown the significant impact of coarse mechanical layering of the lithosphere (2 to 4 layer crust and mantle) on passive margin formation. We built upon these studies and design high-resolution (~100-300 m) thermo-mechanical numerical models that incorporate finer mechanical layering (kilometer scale) mimicking tectonically inherited heterogeneities. During lithospheric extension a variety of extensional structures arises naturally due to (1) structural softening caused by necking of mechanically strong layers and (2) the establishment of a network of weak layers across the deforming multi-layered lithosphere. We argue that structural softening in a multi-layered lithosphere is the main cause for the observed multi-stage evolution and architecture of magma-poor passive margins
Diffusion of wave packets in a Markov random potential
We consider the evolution of a tight binding wave packet propagating in a
time dependent potential. If the potential evolves according to a stationary
Markov process, we show that the square amplitude of the wave packet converges,
after diffusive rescaling, to a solution of a heat equation.Comment: 19 pages, acknowledgments added and typos correcte
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