500 research outputs found
Diluted Networks of Nonlinear Resistors and Fractal Dimensions of Percolation Clusters
We study random networks of nonlinear resistors, which obey a generalized
Ohm's law, . Our renormalized field theory, which thrives on an
interpretation of the involved Feynman Diagrams as being resistor networks
themselves, is presented in detail. By considering distinct values of the
nonlinearity r, we calculate several fractal dimensions characterizing
percolation clusters. For the dimension associated with the red bonds we show
that at least to order {\sl O} (\epsilon^4),
with being the correlation length exponent, and , where d
denotes the spatial dimension. This result agrees with a rigorous one by
Coniglio. Our result for the chemical distance, d_{\scriptsize min} = 2 -
\epsilon /6 - [ 937/588 + 45/49 (\ln 2 -9/10 \ln 3)] (\epsilon /6)^2 + {\sl O}
(\epsilon^3) verifies a previous calculation by one of us. For the backbone
dimension we find D_B = 2 + \epsilon /21 - 172 \epsilon^2 /9261 + 2 (- 74639 +
22680 \zeta (3))\epsilon^3 /4084101 + {\sl O} (\epsilon^4), where , in agreement to second order in with a two-loop
calculation by Harris and Lubensky.Comment: 29 pages, 7 figure
Simulations of lattice animals and trees
The scaling behaviour of randomly branched polymers in a good solvent is
studied in two to nine dimensions, using as microscopic models lattice animals
and lattice trees on simple hypercubic lattices. As a stochastic sampling
method we use a biased sequential sampling algorithm with re-sampling, similar
to the pruned-enriched Rosenbluth method (PERM) used extensively for linear
polymers. Essentially we start simulating percolation clusters (either site or
bond), re-weigh them according to the animal (tree) ensemble, and prune or
branch the further growth according to a heuristic fitness function. In
contrast to previous applications of PERM, this fitness function is {\it not}
the weight with which the actual configuration would contribute to the
partition sum, but is closely related to it. We obtain high statistics of
animals with up to several thousand sites in all dimension 2 <= d <= 9. In
addition to the partition sum (number of different animals) we estimate
gyration radii and numbers of perimeter sites. In all dimensions we verify the
Parisi-Sourlas prediction, and we verify all exactly known critical exponents
in dimensions 2, 3, 4, and >= 8. In addition, we present the hitherto most
precise estimates for growth constants in d >= 3. For clusters with one site
attached to an attractive surface, we verify the superuniversality of the
cross-over exponent at the adsorption transition predicted by Janssen and
Lyssy. Finally, we discuss the collapse of animals and trees, arguing that our
present version of the algorithm is also efficient for some of the models
studied in this context, but showing that it is {\it not} very efficient for
the `classical' model for collapsing animals.Comment: 17 pages RevTeX, 29 figures include
Streaming instability of slime mold amoebae: An analytical model
During the aggregation of amoebae of the cellular slime mould Dictyostelium, the interaction of chemical waves of the signaling molecule cAMP with cAMP-directed cell movement causes the breakup of a uniform cell layer into branching patterns of cell streams. Recent numerical and experimental investigations emphasize the pivotal role of the cell-density dependence of the chemical wave speed for the occurrence of the streaming instability. A simple, analytically tractable, model of Dictyostelium aggregation is developed to test this idea. The interaction of cAMP waves with cAMP-directed cell movement is studied in the form of coupled dynamics of wave front geometries and cell density. Comparing the resulting explicit instability criterion and dispersion relation for cell streaming with the previous findings of model simulations and numerical stability analyses, a unifying interpretation of the streaming instability as a cAMP wave-driven chemotactic instability is proposed
Random Resistor-Diode Networks and the Crossover from Isotropic to Directed Percolation
By employing the methods of renormalized field theory we show that the
percolation behavior of random resistor-diode networks near the multicritical
line belongs to the universality class of isotropic percolation. We construct a
mesoscopic model from the general epidemic process by including a relevant
isotropy-breaking perturbation. We present a two-loop calculation of the
crossover exponent . Upon blending the -expansion result with
the exact value for one dimension by a rational approximation, we
obtain for two dimensions . This value is in agreement
with the recent simulations of a two-dimensional random diode network by Inui,
Kakuno, Tretyakov, Komatsu, and Kameoka, who found an order parameter exponent
different from those of isotropic and directed percolation.
Furthermore, we reconsider the theory of the full crossover from isotropic to
directed percolation by Frey, T\"{a}uber, and Schwabl and clear up some minor
shortcomings.Comment: 24 pages, 2 figure
Intermediate temperature dynamics of one-dimensional Heisenberg antiferromagnets
We present a general theory for the intermediate temperature (T) properties
of Heisenberg antiferromagnets of spin-S ions on p-leg ladders, valid for 2Sp
even or odd. Following an earlier proposal for 2Sp even (Damle and Sachdev,
cond-mat/9711014), we argue that an integrable, classical, continuum model of a
fixed-length, 3-vector applies over an intermediate temperature range; this
range becomes very wide for moderate and large values of 2Sp. The coupling
constants of the effective model are known exactly in terms of the energy gap
above the ground state (for 2Sp even) or a crossover scale (for 2Sp odd).
Analytic and numeric results for dynamic and transport properties are obtained,
including some exact results for the spin-wave damping. Numerous quantitative
predictions for neutron scattering and NMR experiments are made. A general
discussion on the nature of T>0 transport in integrable systems is also
presented: an exact solution of a toy model proves that diffusion can exist in
integrable systems, provided proper care is taken in approaching the
thermodynamic limit.Comment: 38 pages, including 12 figure
New Dynamic Monte Carlo Renormalization Group Method
The dynamical critical exponent of the two-dimensional spin-flip Ising model
is evaluated by a Monte Carlo renormalization group method involving a
transformation in time. The results agree very well with a finite-size scaling
analysis performed on the same data. The value of is
obtained, which is consistent with most recent estimates
Cluster Hybrid Monte Carlo Simulation Algorithms
We show that addition of Metropolis single spin-flips to the Wolff cluster
flipping Monte Carlo procedure leads to a dramatic {\bf increase} in
performance for the spin-1/2 Ising model. We also show that adding Wolff
cluster flipping to the Metropolis or heat bath algorithms in systems where
just cluster flipping is not immediately obvious (such as the spin-3/2 Ising
model) can substantially {\bf reduce} the statistical errors of the
simulations. A further advantage of these methods is that systematic errors
introduced by the use of imperfect random number generation may be largely
healed by hybridizing single spin-flips with cluster flipping.Comment: 16 pages, 10 figure
Interfacial adsorption phenomena of the three-dimensional three-state Potts model
We study the interfacial adsorption phenomena of the three-state
ferromagnetic Potts model on the simple cubic lattice by the Monte Carlo
method. Finite-size scaling analyses of the net-adsorption yield the evidence
of the phase transition being of first-order and .Comment: 14 page
Piscicultura de água doce: análise da capacitação de multiplicadores.
A experiência aqui sistematizada é resultado de um trabalho realizado a partir de uma parceria entre o Serviço Nacional de Aprendizagem Rural (Senar) e a Embrapa Pesca e Aquicultura, que resultou na realização do Curso de Capacitação de Multiplicadores em Piscicultura de Água Doce, realizado em 2011 no Município de Palmas, TO. A sistematização de experiências abarca diversas percepções dos atores envolvidos no processo para tal descrição, diferentemente de um relato de experiência que é unidirecional, sob apenas uma percepção. A presente sistematização foi coordenada por colaboradores do setor de transferência de tecnologia (TT) da Embrapa Pesca e Aquicultura.bitstream/item/176437/1/CNPASA-2017-se16.pd
Nonequilibrium relaxation of the two-dimensional Ising model: Series-expansion and Monte Carlo studies
We study the critical relaxation of the two-dimensional Ising model from a
fully ordered configuration by series expansion in time t and by Monte Carlo
simulation. Both the magnetization (m) and energy series are obtained up to
12-th order. An accurate estimate from series analysis for the dynamical
critical exponent z is difficult but compatible with 2.2. We also use Monte
Carlo simulation to determine an effective exponent, z_eff(t) = - {1/8} d ln t
/d ln m, directly from a ratio of three-spin correlation to m. Extrapolation to
t = infinity leads to an estimate z = 2.169 +/- 0.003.Comment: 9 pages including 2 figure
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