64 research outputs found
Adiabatic-Nonadiabatic Transition in the Diffusive Hamiltonian Dynamics of a Classical Holstein Polaron
We study the Hamiltonian dynamics of a free particle injected onto a chain
containing a periodic array of harmonic oscillators in thermal equilibrium. The
particle interacts locally with each oscillator, with an interaction that is
linear in the oscillator coordinate and independent of the particle's position
when it is within a finite interaction range. At long times the particle
exhibits diffusive motion, with an ensemble averaged mean-squared displacement
that is linear in time. The diffusion constant at high temperatures follows a
power law D ~ T^{5/2} for all parameter values studied. At low temperatures
particle motion changes to a hopping process in which the particle is bound for
considerable periods of time to a single oscillator before it is able to escape
and explore the rest of the chain. A different power law, D ~ T^{3/4}, emerges
in this limit. A thermal distribution of particles exhibits thermally activated
diffusion at low temperatures as a result of classically self-trapped polaronic
states.Comment: 15 pages, 4 figures Submitted to Physical Review
Rheological Model for Wood
Wood as the most important natural and renewable building material plays an
important role in the construction sector. Nevertheless, its hygroscopic
character basically affects all related mechanical properties leading to
degradation of material stiffness and strength over the service life.
Accordingly, to attain reliable design of the timber structures, the influence
of moisture evolution and the role of time- and moisture-dependent behaviors
have to be taken into account. For this purpose, in the current study a 3D
orthotropic elasto-plastic, visco-elastic, mechano-sorptive constitutive model
for wood, with all material constants being defined as a function of moisture
content, is presented. The corresponding numerical integration approach, with
additive decomposition of the total strain is developed and implemented within
the framework of the finite element method (FEM). Moreover to preserve a
quadratic rate of asymptotic convergence the consistent tangent operator for
the whole model is derived.
Functionality and capability of the presented material model are evaluated by
performing several numerical verification simulations of wood components under
different combinations of mechanical loading and moisture variation.
Additionally, the flexibility and universality of the introduced model to
predict the mechanical behavior of different species are demonstrated by the
analysis of a hybrid wood element. Furthermore, the proposed numerical approach
is validated by comparisons of computational evaluations with experimental
results.Comment: 37 pages, 13 figures, 10 table
An Extended Network Model with a Packages Diffusion Process
The dynamics of a packages diffusion process within a selforganized network
is analytically studied by means of an extended % -spin facilitated kinetic
Ising model (Fredrickson-Andersen model) using a Fock-space representation for
the master equation. To map the three component system (active, passive and
packages cells) onto a lattice we apply two types of second quantized
operators. The active cells correspond to mobile states whereas the passive
cells correspond to immobile states of the Fredrickson-Andersen model. An
inherent cooperativity is included assuming that the local dynamics and
subsequently the local mobilities are restricted by the occupation of
neighboring cells. Depending on a temperature-like parameter
(interconnectivity) the diffusive process of the packages (information) can be
almost stopped, thus we get a well separation of the time regimes and a
quasi-localization for the intermediate range at low temperatures.Comment: 13 pages and 1 figur
Finite-size critical scaling in Ising spin glasses in the mean-field regime
We study in Ising spin glasses the finite-size effects near the spin-glass
transition in zero field and at the de Almeida-Thouless transition in a field
by Monte Carlo methods and by analytical approximations. In zero field, the
finite-size scaling function associated with the spin-glass susceptibility of
the Sherrington-Kirkpatrick mean-field spin-glass model is of the same form as
that of one-dimensional spin-glass models with power-law long-range
interactions in the regime where they can be a proxy for the Edwards-Anderson
short-range spin-glass model above the upper critical dimension. We also
calculate a simple analytical approximation for the spin-glass susceptibility
crossover function. The behavior of the spin-glass susceptibility near the de
Almeida-Thouless transition line has also been studied, but here we have only
been able to obtain analytically its behavior in the asymptotic limit above and
below the transition. We have also simulated the one-dimensional system in a
field in the non-mean-field regime to illustrate that when the Imry-Ma droplet
length scale exceeds the system size one can then be erroneously lead to
conclude that there is a de Almeida-Thouless transition even though it is
absent.Comment: 10 pages, 7 figure
Asymptotic properties of free monoid morphisms
Motivated by applications in the theory of numeration systems and
recognizable sets of integers, this paper deals with morphic words when erasing
morphisms are taken into account. Cobham showed that if an infinite word is the image of a fixed point of a morphism under another
morphism , then there exist a non-erasing morphism and a coding
such that .
Based on the Perron theorem about asymptotic properties of powers of
non-negative matrices, our main contribution is an in-depth study of the growth
type of iterated morphisms when one replaces erasing morphisms with non-erasing
ones. We also explicitly provide an algorithm computing and
from and .Comment: 25 page
Front propagation in laminar flows
The problem of front propagation in flowing media is addressed for laminar
velocity fields in two dimensions. Three representative cases are discussed:
stationary cellular flow, stationary shear flow, and percolating flow.
Production terms of Fisher-Kolmogorov-Petrovskii-Piskunov type and of Arrhenius
type are considered under the assumption of no feedback of the concentration on
the velocity. Numerical simulations of advection-reaction-diffusion equations
have been performed by an algorithm based on discrete-time maps. The results
show a generic enhancement of the speed of front propagation by the underlying
flow. For small molecular diffusivity, the front speed depends on the
typical flow velocity as a power law with an exponent depending on the
topological properties of the flow, and on the ratio of reactive and advective
time-scales. For open-streamline flows we find always , whereas for
cellular flows we observe for fast advection, and for slow advection.Comment: Enlarged, revised version, 37 pages, 14 figure
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