12,259 research outputs found
Unbiased sampling of globular lattice proteins in three dimensions
We present a Monte Carlo method that allows efficient and unbiased sampling
of Hamiltonian walks on a cubic lattice. Such walks are self-avoiding and visit
each lattice site exactly once. They are often used as simple models of
globular proteins, upon adding suitable local interactions. Our algorithm can
easily be equipped with such interactions, but we study here mainly the
flexible homopolymer case where each conformation is generated with uniform
probability. We argue that the algorithm is ergodic and has dynamical exponent
z=0. We then use it to study polymers of size up to 64^3 = 262144 monomers.
Results are presented for the effective interaction between end points, and the
interaction with the boundaries of the system
A tree-decomposed transfer matrix for computing exact Potts model partition functions for arbitrary graphs, with applications to planar graph colourings
Combining tree decomposition and transfer matrix techniques provides a very
general algorithm for computing exact partition functions of statistical models
defined on arbitrary graphs. The algorithm is particularly efficient in the
case of planar graphs. We illustrate it by computing the Potts model partition
functions and chromatic polynomials (the number of proper vertex colourings
using Q colours) for large samples of random planar graphs with up to N=100
vertices. In the latter case, our algorithm yields a sub-exponential average
running time of ~ exp(1.516 sqrt(N)), a substantial improvement over the
exponential running time ~ exp(0.245 N) provided by the hitherto best known
algorithm. We study the statistics of chromatic roots of random planar graphs
in some detail, comparing the findings with results for finite pieces of a
regular lattice.Comment: 5 pages, 3 figures. Version 2 has been substantially expanded.
Version 3 shows that the worst-case running time is sub-exponential in the
number of vertice
Rate theory for correlated processes: Double-jumps in adatom diffusion
We study the rate of activated motion over multiple barriers, in particular
the correlated double-jump of an adatom diffusing on a missing-row
reconstructed Platinum (110) surface. We develop a Transition Path Theory,
showing that the activation energy is given by the minimum-energy trajectory
which succeeds in the double-jump. We explicitly calculate this trajectory
within an effective-medium molecular dynamics simulation. A cusp in the
acceptance region leads to a sqrt{T} prefactor for the activated rate of
double-jumps. Theory and numerical results agree
Performance evaluation of an emergency call center: tropical polynomial systems applied to timed Petri nets
We analyze a timed Petri net model of an emergency call center which
processes calls with different levels of priority. The counter variables of the
Petri net represent the cumulated number of events as a function of time. We
show that these variables are determined by a piecewise linear dynamical
system. We also prove that computing the stationary regimes of the associated
fluid dynamics reduces to solving a polynomial system over a tropical
(min-plus) semifield of germs. This leads to explicit formul{\ae} expressing
the throughput of the fluid system as a piecewise linear function of the
resources, revealing the existence of different congestion phases. Numerical
experiments show that the analysis of the fluid dynamics yields a good
approximation of the real throughput.Comment: 21 pages, 4 figures. A shorter version can be found in the
proceedings of the conference FORMATS 201
Finite average lengths in critical loop models
A relation between the average length of loops and their free energy is
obtained for a variety of O(n)-type models on two-dimensional lattices, by
extending to finite temperatures a calculation due to Kast. We show that the
(number) averaged loop length L stays finite for all non-zero fugacities n, and
in particular it does not diverge upon entering the critical regime n -> 2+.
Fully packed loop (FPL) models with n=2 seem to obey the simple relation L = 3
L_min, where L_min is the smallest loop length allowed by the underlying
lattice. We demonstrate this analytically for the FPL model on the honeycomb
lattice and for the 4-state Potts model on the square lattice, and based on
numerical estimates obtained from a transfer matrix method we conjecture that
this is also true for the two-flavour FPL model on the square lattice. We
present in addition numerical results for the average loop length on the three
critical branches (compact, dense and dilute) of the O(n) model on the
honeycomb lattice, and discuss the limit n -> 0. Contact is made with the
predictions for the distribution of loop lengths obtained by conformal
invariance methods.Comment: 20 pages of LaTeX including 3 figure
Unraveling the acoustic electron-phonon interaction in graphene
Using a first-principles approach we calculate the acoustic electron-phonon
couplings in graphene for the transverse (TA) and longitudinal (LA) acoustic
phonons. Analytic forms of the coupling matrix elements valid in the
long-wavelength limit are found to give an almost quantitative description of
the first-principles based matrix elements even at shorter wavelengths. Using
the analytic forms of the coupling matrix elements, we study the acoustic
phonon-limited carrier mobility for temperatures 0-200 K and high carrier
densities of 10^{12}-10^{13} cm^{-2}. We find that the intrinsic effective
acoustic deformation potential of graphene is \Xi_eff = 6.8 eV and that the
temperature dependence of the mobility \mu ~ T^{-\alpha} increases beyond an
\alpha = 4 dependence even in the absence of screening when the full coupling
matrix elements are considered. The large disagreement between our calculated
deformation potential and those extracted from experimental measurements (18-29
eV) indicates that additional or modified acoustic phonon-scattering mechanisms
are at play in experimental situations.Comment: 7 pages, 3 figure
Exact enumeration of Hamiltonian circuits, walks, and chains in two and three dimensions
We present an algorithm for enumerating exactly the number of Hamiltonian
chains on regular lattices in low dimensions. By definition, these are sets of
k disjoint paths whose union visits each lattice vertex exactly once. The
well-known Hamiltonian circuits and walks appear as the special cases k=0 and
k=1 respectively. In two dimensions, we enumerate chains on L x L square
lattices up to L=12, walks up to L=17, and circuits up to L=20. Some results
for three dimensions are also given. Using our data we extract several
quantities of physical interest
Dense loops, supersymmetry, and Goldstone phases in two dimensions
Loop models in two dimensions can be related to O(N) models. The
low-temperature dense-loops phase of such a model, or of its reformulation
using a supergroup as symmetry, can have a Goldstone broken-symmetry phase for
N<2. We argue that this phase is generic for -2< N <2 when crossings of loops
are allowed, and distinct from the model of non-crossing dense loops first
studied by Nienhuis [Phys. Rev. Lett. 49, 1062 (1982)]. Our arguments are
supported by our numerical results, and by a lattice model solved exactly by
Martins et al. [Phys. Rev. Lett. 81, 504 (1998)].Comment: RevTeX, 5 pages, 3 postscript figure
Simulations of energetic beam deposition: from picoseconds to seconds
We present a new method for simulating crystal growth by energetic beam
deposition. The method combines a Kinetic Monte-Carlo simulation for the
thermal surface diffusion with a small scale molecular dynamics simulation of
every single deposition event. We have implemented the method using the
effective medium theory as a model potential for the atomic interactions, and
present simulations for Ag/Ag(111) and Pt/Pt(111) for incoming energies up to
35 eV. The method is capable of following the growth of several monolayers at
realistic growth rates of 1 monolayer per second, correctly accounting for both
energy-induced atomic mobility and thermal surface diffusion. We find that the
energy influences island and step densities and can induce layer-by-layer
growth. We find an optimal energy for layer-by-layer growth (25 eV for Ag),
which correlates with where the net impact-induced downward interlayer
transport is at a maximum. A high step density is needed for energy induced
layer-by-layer growth, hence the effect dies away at increased temperatures,
where thermal surface diffusion reduces the step density. As part of the
development of the method, we present molecular dynamics simulations of single
atom-surface collisions on flat parts of the surface and near straight steps,
we identify microscopic mechanisms by which the energy influences the growth,
and we discuss the nature of the energy-induced atomic mobility
Single Electrode Heat Effects:I. Peltier Entropies of Gas Electrodes in Carbonate Paste Electrolytes
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