1,737 research outputs found
Fluctuation Pressure of a Stack of Membranes
We calculate the universal pressure constants of a stack of N membranes
between walls by strong-coupling theory. The results are in very good agreement
with values from Monte-Carlo simulations.Comment: Author Information under
http://www.physik.fu-berlin.de/~kleinert/institution.html Latest update of
paper also at http://www.physik.fu-berlin.de/~kleinert/31
Optimal Energy Estimation in Path-Integral Monte Carlo Simulations
We investigate the properties of two standard energy estimators used in
path-integral Monte Carlo simulations. By disentangling the variance of the
estimators and their autocorrelation times we analyse the dependence of the
performance on the update algorithm and present a detailed comparison of
refined update schemes such as multigrid and staging techniques. We show that a
proper combination of the two estimators leads to a further reduction of the
statistical error of the estimated energy with respect to the better of the two
without extra cost.Comment: 45 pp. LaTeX, 22 Postscript Figure
Two-State Folding, Folding through Intermediates, and Metastability in a Minimalistic Hydrophobic-Polar Model for Proteins
Within the frame of an effective, coarse-grained hydrophobic-polar protein
model, we employ multicanonical Monte Carlo simulations to investigate
free-energy landscapes and folding channels of exemplified heteropolymer
sequences, which are permutations of each other. Despite the simplicity of the
model, the knowledge of the free-energy landscape in dependence of a suitable
system order parameter enables us to reveal complex folding characteristics
known from real bioproteins and synthetic peptides, such as two-state folding,
folding through weakly stable intermediates, and glassy metastability.Comment: 10 pages, 1 figur
Condensation of vortices in the X-Y model in 3d: a disorder parameter
A disorder parameter is constructed which signals the condensation of
vortices. The construction is tested by numerical simulations.Comment: 9 pages, 5 postscript figures, typset using REVTE
Multicanonical Study of Coarse-Grained Off-Lattice Models for Folding Heteropolymers
We have performed multicanonical simulations of hydrophobic-hydrophilic
heteropolymers with two simple effective, coarse-grained off-lattice models to
study the influence of specific interactions in the models on conformational
transitions of selected sequences with 20 monomers. Another aspect of the
investigation was the comparison with the purely hydrophobic homopolymer and
the study of general conformational properties induced by the "disorder" in the
sequence of a heteropolymer. Furthermore, we applied an optimization algorithm
to sequences with up to 55 monomers and compared the global-energy minimum
found with lowest-energy states identified within the multicanonical
simulation. This was used to find out how reliable the multicanonical method
samples the free-energy landscape, in particular for low temperatures.Comment: 11 pages, RevTeX, 10 Postscript figures, Author Information under
http://www.physik.uni-leipzig.de/index.php?id=2
Monte Carlo study of the evaporation/condensation transition on different Ising lattices
In 2002 Biskup et al. [Europhys. Lett. 60, 21 (2002)] sketched a rigorous
proof for the behavior of the 2D Ising lattice gas, at a finite volume and a
fixed excess \delta M of particles (spins) above the ambient gas density
(spontaneous magnetisation). By identifying a dimensionless parameter \Delta
(\delta M) and a universal constant \Delta_c, they showed in the limit of large
system sizes that for \Delta < \Delta_c the excess is absorbed in the
background (``evaporated'' system), while for \Delta > \Delta_c a droplet of
the dense phase occurs (``condensed'' system).
To check the applicability of the analytical results to much smaller,
practically accessible system sizes, we performed several Monte Carlo
simulations for the 2D Ising model with nearest-neighbour couplings on a square
lattice at fixed magnetisation M. Thereby, we measured the largest minority
droplet, corresponding to the condensed phase, at various system sizes (L=40,
>..., 640). With analytic values for for the spontaneous magnetisation m_0, the
susceptibility \chi and the Wulff interfacial free energy density \tau_W for
the infinite system, we were able to determine \lambda numerically in very good
agreement with the theoretical prediction.
Furthermore, we did simulations for the spin-1/2 Ising model on a triangular
lattice and with next-nearest-neighbour couplings on a square lattice. Again,
finding a very good agreement with the analytic formula, we demonstrate the
universal aspects of the theory with respect to the underlying lattice. For the
case of the next-nearest-neighbour model, where \tau_W is unknown analytically,
we present different methods to obtain it numerically by fitting to the
distribution of the magnetisation density P(m).Comment: 14 pages, 17 figures, 1 tabl
Application of Multicanonical Multigrid Monte Carlo Method to the Two-Dimensional -Model: Autocorrelations and Interface Tension
We discuss the recently proposed multicanonical multigrid Monte Carlo method
and apply it to the scalar -model on a square lattice. To investigate
the performance of the new algorithm at the field-driven first-order phase
transitions between the two ordered phases we carefully analyze the
autocorrelations of the Monte Carlo process. Compared with standard
multicanonical simulations a real-time improvement of about one order of
magnitude is established. The interface tension between the two ordered phases
is extracted from high-statistics histograms of the magnetization applying
histogram reweighting techniques.Comment: 49 pp. Latex incl. 14 figures (Fig.7 not included, sorry) as
uuencoded compressed tar fil
Error estimation and reduction with cross correlations
Besides the well-known effect of autocorrelations in time series of Monte
Carlo simulation data resulting from the underlying Markov process, using the
same data pool for computing various estimates entails additional cross
correlations. This effect, if not properly taken into account, leads to
systematically wrong error estimates for combined quantities. Using a
straightforward recipe of data analysis employing the jackknife or similar
resampling techniques, such problems can be avoided. In addition, a covariance
analysis allows for the formulation of optimal estimators with often
significantly reduced variance as compared to more conventional averages.Comment: 16 pages, RevTEX4, 4 figures, 6 tables, published versio
Monte Carlo Study of Cluster-Diameter Distribution: A New Observable to Estimate Correlation Lengths
We report numerical simulations of two-dimensional -state Potts models
with emphasis on a new quantity for the computation of spatial correlation
lengths. This quantity is the cluster-diameter distribution function
, which measures the distribution of the diameter of
stochastically defined cluster. Theoretically it is predicted to fall off
exponentially for large diameter , , where
is the correlation length as usually defined through the large-distance
behavior of two-point correlation functions. The results of our extensive Monte
Carlo study in the disordered phase of the models with , 15, and on
large square lattices of size , , and , respectively, clearly confirm the theoretically predicted behavior.
Moreover, using this observable we are able to verify an exact formula for the
correlation length in the disordered phase at the first-order
transition point with an accuracy of about for all considered
values of . This is a considerable improvement over estimates derived from
the large-distance behavior of standard (projected) two-point correlation
functions, which are also discussed for comparison.Comment: 20 pages, LaTeX + 13 postscript figures. See also
http://www.cond-mat.physik.uni-mainz.de/~janke/doc/home_janke.htm
Coarse-Grained Modeling of Genetic Circuits as a Function of the Inherent Time Scales
From a coarse-grained perspective the motif of a self-activating species,
activating a second species which acts as its own repressor, is widely found in
biological systems, in particular in genetic systems with inherent oscillatory
behavior. Here we consider a specific realization of this motif as a genetic
circuit, in which genes are described as directly producing proteins, leaving
out the intermediate step of mRNA production. We focus on the effect that
inherent time scales on the underlying fine-grained scale can have on the
bifurcation patterns on a coarser scale in time. Time scales are set by the
binding and unbinding rates of the transcription factors to the promoter
regions of the genes. Depending on the ratio of these rates to the decay times
of the proteins, the appropriate averaging procedure for obtaining a
coarse-grained description changes and leads to sets of deterministic
equations, which differ in their bifurcation structure. In particular the
desired intermediate range of regular limit cycles fades away when the binding
rates of genes are of the same order or less than the decay time of at least
one of the proteins. Our analysis illustrates that the common topology of the
widely found motif alone does not necessarily imply universal features in the
dynamics.Comment: 29 pages, 16 figure
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