553 research outputs found
Intermittent dislocation density fluctuations in crystal plasticity from a phase-field crystal model
Plastic deformation mediated by collective dislocation dynamics is
investigated in the two-dimensional phase-field crystal model of sheared single
crystals. We find that intermittent fluctuations in the dislocation population
number accompany bursts in the plastic strain-rate fluctuations. Dislocation
number fluctuations exhibit a power-law spectral density at high
frequencies . The probability distribution of number fluctuations becomes
bimodal at low driving rates corresponding to a scenario where low density of
defects alternate at irregular times with high population of defects. We
propose a simple stochastic model of dislocation reaction kinetics that is able
to capture these statistical properties of the dislocation density fluctuations
as a function of shear rate
Critical Scaling Properties at the Superfluid Transition of He in Aerogel
We study the superfluid transition of He in aerogel by Monte Carlo
simulations and finite size scaling analysis. Aerogel is a highly porous silica
glass, which we model by a diffusion limited cluster aggregation model. The
superfluid is modeled by a three dimensional XY model, with excluded bonds to
sites on the aerogel cluster. We obtain the correlation length exponent
, in reasonable agreement with experiments and with previous
simulations. For the heat capacity exponent , both experiments and
previous simulations suggest deviations from the Josephson hyperscaling
relation . In contrast, our Monte Carlo results support
hyperscaling with . We suggest a reinterpretation of
previous experiments, which avoids scaling violations and is consistent with
our simulation results.Comment: 4 pages, 3 figure
Non-linear elastic effects in phase field crystal and amplitude equations: Comparison to ab initio simulations of bcc metals and graphene
We investigate non-linear elastic deformations in the phase field crystal
model and derived amplitude equations formulations. Two sources of
non-linearity are found, one of them based on geometric non-linearity expressed
through a finite strain tensor. It reflects the Eulerian structure of the
continuum models and correctly describes the strain dependence of the
stiffness. In general, the relevant strain tensor is related to the left
Cauchy-Green deformation tensor. In isotropic one- and two-dimensional
situations the elastic energy can be expressed equivalently through the right
deformation tensor. The predicted isotropic low temperature non-linear elastic
effects are directly related to the Birch-Murnaghan equation of state with bulk
modulus derivative for bcc. A two-dimensional generalization suggests
. These predictions are in agreement with ab initio results for
large strain bulk deformations of various bcc elements and graphene. Physical
non-linearity arises if the strain dependence of the density wave amplitudes is
taken into account and leads to elastic weakening. For anisotropic deformations
the magnitudes of the amplitudes depend on their relative orientation to the
applied strain.Comment: 16 page
Renormalization Group Theory for Global Asymptotic Analysis
We show with several examples that renormalization group (RG) theory can be
used to understand singular and reductive perturbation methods in a unified
fashion. Amplitude equations describing slow motion dynamics in nonequilibrium
phenomena are RG equations. The renormalized perturbation approach may be
simpler to use than other approaches, because it does not require the use of
asymptotic matching, and yields practically superior approximations.Comment: 13 pages, plain tex + uiucmac.tex (available from babbage.sissa.it),
one PostScript figure appended at end. Or (easier) get compressed postscript
file by anon ftp from gijoe.mrl.uiuc.edu (128.174.119.153), file
/pub/rg_sing_prl.ps.
On computational irreducibility and the predictability of complex physical systems
Using elementary cellular automata (CA) as an example, we show how to
coarse-grain CA in all classes of Wolfram's classification. We find that
computationally irreducible (CIR) physical processes can be predictable and
even computationally reducible at a coarse-grained level of description. The
resulting coarse-grained CA which we construct emulate the large-scale behavior
of the original systems without accounting for small-scale details. At least
one of the CA that can be coarse-grained is irreducible and known to be a
universal Turing machine.Comment: 4 pages, 2 figures, to be published in PR
Short-Time Critical Dynamics of Damage Spreading in the Two-Dimensional Ising Model
The short-time critical dynamics of propagation of damage in the Ising
ferromagnet in two dimensions is studied by means of Monte Carlo simulations.
Starting with equilibrium configurations at and magnetization
, an initial damage is created by flipping a small amount of spins in one
of the two replicas studied. In this way, the initial damage is proportional to
the initial magnetization in one of the configurations upon quenching the
system at , the Onsager critical temperature of the
ferromagnetic-paramagnetic transition. It is found that, at short times, the
damage increases with an exponent , which is much larger
than the exponent characteristic of the initial increase of the
magnetization . Also, an epidemic study was performed. It is found that
the average distance from the origin of the epidemic ()
grows with an exponent , which is the same,
within error bars, as the exponent . However, the survival
probability of the epidemics reaches a plateau so that . On the other
hand, by quenching the system to lower temperatures one observes the critical
spreading of the damage at , where all the measured
observables exhibit power laws with exponents , , and .Comment: 11 pages, 9 figures (included). Phys. Rev. E (2010), in press
A simple topological model with continuous phase transition
In the area of topological and geometric treatment of phase transitions and
symmetry breaking in Hamiltonian systems, in a recent paper some general
sufficient conditions for these phenomena in -symmetric systems
(i.e. invariant under reflection of coordinates) have been found out. In this
paper we present a simple topological model satisfying the above conditions
hoping to enlighten the mechanism which causes this phenomenon in more general
physical models. The symmetry breaking is testified by a continuous
magnetization with a nonanalytic point in correspondence of a critical
temperature which divides the broken symmetry phase from the unbroken one. A
particularity with respect to the common pictures of a phase transition is that
the nonanalyticity of the magnetization is not accompanied by a nonanalytic
behavior of the free energy.Comment: 17 pages, 7 figure
Universal Scaling in Non-equilibrium Transport Through a Single-Channel Kondo Dot
Scaling laws and universality play an important role in our understanding of
critical phenomena and the Kondo effect. Here we present measurements of
non-equilibrium transport through a single-channel Kondo quantum dot at low
temperature and bias. We find that the low-energy Kondo conductance is
consistent with universality between temperature and bias and characterized by
a quadratic scaling exponent, as expected for the spin-1/2 Kondo effect. The
non-equilibrium Kondo transport measurements are well-described by a universal
scaling function with two scaling parameters.Comment: v2: improved introduction and theory-experiment comparsio
Coarse-graining of cellular automata, emergence, and the predictability of complex systems
We study the predictability of emergent phenomena in complex systems. Using
nearest neighbor, one-dimensional Cellular Automata (CA) as an example, we show
how to construct local coarse-grained descriptions of CA in all classes of
Wolfram's classification. The resulting coarse-grained CA that we construct are
capable of emulating the large-scale behavior of the original systems without
accounting for small-scale details. Several CA that can be coarse-grained by
this construction are known to be universal Turing machines; they can emulate
any CA or other computing devices and are therefore undecidable. We thus show
that because in practice one only seeks coarse-grained information, complex
physical systems can be predictable and even decidable at some level of
description. The renormalization group flows that we construct induce a
hierarchy of CA rules. This hierarchy agrees well with apparent rule complexity
and is therefore a good candidate for a complexity measure and a classification
method. Finally we argue that the large scale dynamics of CA can be very
simple, at least when measured by the Kolmogorov complexity of the large scale
update rule, and moreover exhibits a novel scaling law. We show that because of
this large-scale simplicity, the probability of finding a coarse-grained
description of CA approaches unity as one goes to increasingly coarser scales.
We interpret this large scale simplicity as a pattern formation mechanism in
which large scale patterns are forced upon the system by the simplicity of the
rules that govern the large scale dynamics.Comment: 18 pages, 9 figure
Thermodynamics of Born-Infeld-anti-de Sitter black holes in the grand canonical ensemble
The main objective of this paper is to study thermodynamics and stability of
static electrically charged Born-Infeld black holes in AdS space in D=4. The
Euclidean action for the grand canonical ensemble is computed with the
appropriate boundary terms. The thermodynamical quantities such as the Gibbs
free energy, entropy and specific heat of the black holes are derived from it.
The global stability of black holes are studied in detail by studying the free
energy for various potentials. For small values of the potential, we find that
there is a Hawking-Page phase transition between a BIAdS black hole and the
thermal-AdS space. For large potentials, the black hole phase is dominant and
are preferred over the thermal-AdS space. Local stability is studied by
computing the specific heat for constant potentials. The non-extreme black
holes have two branches: small black holes are unstable and the large black
holes are stable. The extreme black holes are shown to be stable both globally
as well as locally. In addition to the thermodynamics, we also show that the
phase structure relating the mass and the charge of the black holes is
similar to the liquid-gas-solid phase diagram.Comment: Accepted to be published in Physical Review D. Minor change
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