12,259 research outputs found
Affine crystal structure on rigged configurations of type D_n^(1)
Extending the work arXiv:math/0508107, we introduce the affine crystal action
on rigged configurations which is isomorphic to the Kirillov-Reshetikhin
crystal B^{r,s} of type D_n^(1) for any r,s. We also introduce a representation
of B^{r,s} (r not equal to n-1,n) in terms of tableaux of rectangular shape r x
s, which we coin Kirillov-Reshetikhin tableaux (using a non-trivial analogue of
the type A column splitting procedure) to construct a bijection between
elements of a tensor product of Kirillov-Reshetikhin crystals and rigged
configurations.Comment: 26 pages, 3 figures. (v3) corrections in the proof reading. (v2) 26
pages; examples added; introduction revised; final version. (v1) 24 page
Microscopic theory for the glass transition in a system without static correlations
We study the orientational dynamics of infinitely thin hard rods of length L,
with the centers-of-mass fixed on a simple cubic lattice with lattice constant
a.We approximate the influence of the surrounding rods onto dynamics of a pair
of rods by introducing an effective rotational diffusion constant D(l),l=L/a.
We get D(l) ~ [1-v(l)], where v(l) is given through an integral of a
time-dependent torque-torque correlator of an isolated pair of rods. A glass
transition occurs at l_c, if v(l_c)=1. We present a variational and a
numerically exact evaluation of v(l).Close to l_c the diffusion constant
decreases as D(l) ~ (l_c-l)^\gamma, with \gamma=1. Our approach predicts a
glass transition in the absence of any static correlations, in contrast to
present form of mode coupling theory.Comment: 6 pages, 3 figure
Solid-solid phase transition in hard ellipsoids
We present a computer simulation study of the crystalline phases of hard
ellipsoids of revolution. A previous study [Phys. Rev. E, \textbf{75}, 020402
(2007)] showed that for aspect ratios the previously suggested
stretched-fcc phase [Mol. Phys., \textbf{55}, 1171 (1985)] is unstable with
respect to a simple monoclinic phase with two ellipsoids of different
orientations per unit cell (SM2). In order to study the stability of these
crystalline phases at different aspect ratios and as a function of density we
have calculated their free energies by thermodynamic integration. The
integration path was sampled by an expanded ensemble method in which the
weights were adjusted by the Wang-Landau algorithm.
We show that for aspect ratios the SM2 structure is more stable
than the stretched-fcc structure for all densities above solid-nematic
coexistence. Between and our calculations reveal a
solid-solid phase transition
Studies of superconductivity and structure for CaC6 to pressures above 15 GPa
The dependence of the superconducting transition temperature Tc of CaC6 has
been determined as a function of hydrostatic pressure in both helium-loaded gas
and diamond-anvil cells to 0.6 and 32 GPa, respectively. Following an initial
increase at the rate +0.39(1) K/GPa, Tc drops abruptly from 15 K to 4 K at 10
GPa. Synchrotron x-ray measurements to 15 GPa point to a structural transition
near 10 GPa from a rhombohedral to a higher symmetry phase
Percolation in suspensions of polydisperse hard rods : quasi-universality and finite-size effects
We present a study of connectivity percolation in suspensions of hard
spherocylinders by means of Monte Carlo simulation and connectedness
percolation theory. We focus attention on polydispersity in the length, the
diameter and the connectedness criterion, and invoke bimodal, Gaussian and
Weibull distributions for these. The main finding from our simulations is that
the percolation threshold shows quasi universal behaviour, i.e., to a good
approximation it depends only on certain cumulants of the full size and
connectivity distribution. Our connectedness percolation theory hinges on a
Lee-Parsons type of closure recently put forward that improves upon the
often-used second virial approximation [ArXiv e-prints, May 2015, 1505.07660].
The theory predicts exact universality. Theory and simulation agree
quantitatively for aspect ratios in excess of 20, if we include the
connectivity range in our definition of the aspect ratio of the particles. We
further discuss the mechanism of cluster growth that, remarkably, differs
between systems that are polydisperse in length and in width, and exhibits
non-universal aspects.Comment: 7 figure
Saddle index properties, singular topology, and its relation to thermodynamical singularities for a phi^4 mean field model
We investigate the potential energy surface of a phi^4 model with infinite
range interactions. All stationary points can be uniquely characterized by
three real numbers $\alpha_+, alpha_0, alpha_- with alpha_+ + alpha_0 + alpha_-
= 1, provided that the interaction strength mu is smaller than a critical
value. The saddle index n_s is equal to alpha_0 and its distribution function
has a maximum at n_s^max = 1/3. The density p(e) of stationary points with
energy per particle e, as well as the Euler characteristic chi(e), are singular
at a critical energy e_c(mu), if the external field H is zero. However, e_c(mu)
\neq upsilon_c(mu), where upsilon_c(mu) is the mean potential energy per
particle at the thermodynamic phase transition point T_c. This proves that
previous claims that the topological and thermodynamic transition points
coincide is not valid, in general. Both types of singularities disappear for H
\neq 0. The average saddle index bar{n}_s as function of e decreases
monotonically with e and vanishes at the ground state energy, only. In
contrast, the saddle index n_s as function of the average energy bar{e}(n_s) is
given by n_s(bar{e}) = 1+4bar{e} (for H=0) that vanishes at bar{e} = -1/4 >
upsilon_0, the ground state energy.Comment: 9 PR pages, 6 figure
The biHecke monoid of a finite Coxeter group
The usual combinatorial model for the 0-Hecke algebra of the symmetric group
is to consider the algebra (or monoid) generated by the bubble sort operators.
This construction generalizes to any finite Coxeter group W. The authors
previously introduced the Hecke group algebra, constructed as the algebra
generated simultaneously by the bubble sort and antisort operators, and
described its representation theory.
In this paper, we consider instead the monoid generated by these operators.
We prove that it has |W| simple and projective modules. In order to construct a
combinatorial model for the simple modules, we introduce for each w in W a
combinatorial module whose support is the interval [1,w] in right weak order.
This module yields an algebra, whose representation theory generalizes that of
the Hecke group algebra. This involves the introduction of a w-analogue of the
combinatorics of descents of W and a generalization to finite Coxeter groups of
blocks of permutation matrices.Comment: 12 pages, 1 figure, submitted to FPSAC'1
Crystallization in Glassy Suspensions of Hard Ellipsoids
We have carried out computer simulations of overcompressed suspensions of
hard monodisperse ellipsoids and observed their crystallization dynamics. The
system was compressed very rapidly in order to reach the regime of slow,
glass-like dynamics. We find that, although particle dynamics become
sub-diffusive and the intermediate scattering function clearly develops a
shoulder, crystallization proceeds via the usual scenario: nucleation and
growth for small supersaturations, spinodal decomposition for large
supersaturations.
In particular, we compared the mobility of the particles in the regions where
crystallization set in with the mobility in the rest of the system. We did not
find any signature in the dynamics of the melt that pointed towards the
imminent crystallization events
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