7,444 research outputs found
Monoidal Hom-Hopf algebras
Hom-structures (Lie algebras, algebras, coalgebras, Hopf algebras) have been
investigated in the literature recently. We study Hom-structures from the point
of view of monoidal categories; in particular, we introduce a symmetric
monoidal category such that Hom-algebras coincide with algebras in this
monoidal category, and similar properties for coalgebras, Hopf algebras and Lie
algebras.Comment: 25 pages; extended version: compared to the version that appeared in
Comm. Algebra, the Section Preliminary Results and Remarks 5.1 and 6.1 have
been adde
Dynamics of a Rigid Rod in a Glassy Medium
We present simulations of the motion of a single rigid rod in a disordered
static 2d-array of disk-like obstacles. The rotational, , and
center-of-mass translational, , diffusion constants are calculated
for a wide range of rod length and density of obstacles . It is found
that follows the behavior predicted by kinetic theory for a hard
disk with an effective radius . A dynamic crossover is observed in
for comparable to the typical distance between neighboring
obstacles . Using arguments from kinetic theory and reptation, we
rationalize the scaling laws, dynamic exponents, and prefactors observed for
. In analogy with the enhanced translational diffusion observed in
deeply supercooled liquids, the Stokes-Einstein-Debye relation is violated for
.Comment: 8 pages, 4 figures. Major changes. To be published in Europhysics
Letter
Topological versus rheological entanglement length in primitive path analysis protocols
Primitive path analysis algorithms are now routinely employed to analyze
entanglements in computer simulations of polymeric systems, but different
analysis protocols result in different estimates of the entanglement length,
N_e. Here we argue that standard PPA measures the rheological entanglement
length, typically employed by tube models and relevant to quantitative
comparisons with experiment, while codes like Z or CReTA also determine the
topological entanglement length. For loosely entangled systems, a simple
analogy between between phantom networks and the mesh of entangled primitive
paths suggests a factor of two between the two numbers. This result is in
excellent agreement with reported values for poly-ethylene, poly-butadiene and
bead-spring polymer melts.Comment: 3 pages, no figure
Dynamics of short polymer chains in solution
We present numerical and analytical results describing the effect of
hydrodynamic interactions on the dynamics of a short polymer chain in solution.
A molecular dynamics algorithm for the polymer is coupled to a direct
simulation Monte Carlo algorithm for the solvent. We give an explicit
expression for the velocity autocorrelation function of the centre of mass of
the polymer which agrees well with numerical results if Brownian dynamics,
hydrodynamic correlations and sound wave scattering are included
Efficient simulation of non-crossing fibers and chains in a hydrodynamic solvent
An efficient simulation method is presented for Brownian fiber suspensions,
which includes both uncrossability of the fibers and hydrodynamic interactions
between the fibers mediated by a mesoscopic solvent. To conserve hydrodynamics,
collisions between the fibers are treated such that momentum and energy are
conserved locally. The choice of simulation parameters is rationalised on the
basis of dimensionless numbers expressing the relative strength of different
physical processes. The method is applied to suspensions of semiflexible fibers
with a contour length equal to the persistence length, and a mesh size to
contour length ratio ranging from 0.055 to 0.32. For such fibers the effects of
hydrodynamic interactions are observable, but relatively small. The
non-crossing constraint, on the other hand, is very important and leads to
hindered displacements of the fibers, with an effective tube diameter in
agreement with recent theoretical predictions. The simulation technique opens
the way to study the effect of viscous effects and hydrodynamic interactions in
microrheology experiments where the response of an actively driven probe bead
in a fiber suspension is measured.Comment: 12 pages, 2 tables, 5 figure
Sudden collapse of a colloidal gel
Metastable gels formed by weakly attractive colloidal particles display a
distinctive two-stage time-dependent settling behavior under their own weight.
Initially a space-spanning network is formed that for a characteristic time,
which we define as the lag time \taud, resists compaction. This solid-like
behavior persists only for a limited time. Gels whose age \tw is greater than
\taud yield and suddenly collapse. We use a combination of confocal
microscopy, rheology and time-lapse video imaging to investigate both the
process of sudden collapse and its microscopic origin in an refractive-index
matched emulsion-polymer system. We show that the height of the gel in the
early stages of collapse is well described by the surprisingly simple
expression, h(\ts) = \h0 - A \ts^{3/2}, with \h0 the initial height and
\ts = \tw-\taud the time counted from the instant where the gel first yields.
We propose that this unexpected result arises because the colloidal network
progressively builds up internal stress as a consequence of localized
rearrangement events which leads ultimately to collapse as thermal equilibrium
is re-established.Comment: 14 pages, 11 figures, final versio
Force-Extension Relation and Plateau Modulus for Wormlike Chains
We derive the linear force-extension relation for a wormlike chain of
arbitrary stiffness including entropy elasticity, bending and thermodynamic
buckling. From this we infer the plateau modulus of an isotropic
entangled solution of wormlike chains. The entanglement length is
expressed in terms of the characteristic network parameters for three different
scaling regimes in the entangled phase. The entanglement transition and the
concentration dependence of are analyzed. Finally we compare our findings
with experimental data.Comment: 5 pages, 1 eps-figure, to appear in PR
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