393 research outputs found
On the non-convergence of the Wang-Landau algorithms with multiple random walkers
This paper discusses some convergence properties in the entropic sampling
Monte Carlo methods with multiple random walkers, particularly in the
Wang-Landau (WL) and algorithms. The classical algorithms are modified by
the use of independent random walkers in the energy landscape to calculate
the density of states (DOS). The Ising model is used to show the convergence
properties in the calculation of the DOS, as well as the critical temperature,
while the calculation of the number by multiple dimensional integration
is used in the continuum approximation. In each case, the error is obtained
separately for each walker at a fixed time, ; then, the average over
walkers is performed. It is observed that the error goes as .
However, if the number of walkers increases above a certain critical value
, the error reaches a constant value (i.e. it saturates). This occurs
for both algorithms; however, it is shown that for a given system, the
algorithm is more efficient and accurate than the similar version of the WL
algorithm. It follows that it makes no sense to increase the number of walkers
above a critical value , since it does not reduces the error in the
calculation. Therefore, the number of walkers does not guarantee convergence.Comment: 10 pages, 12 figures, Regular Articl
Wang-Landau Algorithm: a Theoretical Analysis of the Saturation of the Error
In this work we present a theoretical analysis of the convergence of the
Wang-Landau algorithm [Phys. Rev. Lett. 86, 2050 (2001)] which was introduced
years ago to calculate the density of states in statistical models. We study
the dynamical behavior of the error in the calculation of the density of
states.We conclude that the source of the saturation of the error is due to the
decreasing variations of the refinement parameter. To overcome this limitation,
we present an analytical treatment in which the refinement parameter is scaled
down as a power law instead of exponentially. An extension of the analysis to
the N-fold way variation of the method is also discussed.Comment: 7 pages, 5 figure
Analysis of the convergence of the 1/t and Wang-Landau algorithms in the calculation of multidimensional integrals
In this communication, the convergence of the 1/t and Wang - Landau
algorithms in the calculation of multidimensional numerical integrals is
analyzed. Both simulation methods are applied to a wide variety of integrals
without restrictions in one, two and higher dimensions. The errors between the
exact and the calculated values of the integral are obtained and the efficiency
and accuracy of the methods are determined by their dynamical behavior. The
comparison between both methods and the simple sampling Monte Carlo method is
also reported. It is observed that the time dependence of the errors calculated
with 1/t algorithm goes as N^{-1/2} (with N the MC trials) in quantitative
agreement with the simple sampling Monte Carlo method. It is also showed that
the error for the Wang - Landau algorithm saturates in time evidencing the
non-convergence of the methods. The sources for the error are also determined.Comment: 8 pages, 5 figure
Thermal fluctuations of an interface near a contact line
The effect of thermal fluctuations near a contact line of a liquid interface
partially wetting an impenetrable substrate is studied analytically and
numerically. Promoting both the interface profile and the contact line position
to random variables, we explore the equilibrium properties of the corresponding
fluctuating contact line problem based on an interfacial Hamiltonian involving
a "contact" binding potential. To facilitate an analytical treatment we
consider the case of a one-dimensional interface. The effective boundary
condition at the contact line is determined by a dimensionless parameter that
encodes the relative importance of thermal energy and substrate energy at the
microscopic scale. We find that this parameter controls the transition from a
partially wetting to a pseudo-partial wetting state, the latter being
characterized by a thin prewetting film of fixed thickness. In the partial
wetting regime, instead, the profile typically approaches the substrate via an
exponentially thinning prewetting film. We show that, independently of the
physics at the microscopic scale, Young's angle is recovered sufficiently far
from the substrate. The fluctuations of the interface and of the contact line
give rise to an effective disjoining pressure, exponentially decreasing with
height. Fluctuations therefore provide a regularization of the singular contact
forces occurring in the corresponding deterministic problem.Comment: 40 Pages, 12 Figure
Fast Algorithm to Calculate Density of States
An algorithm to calculate the density of states, based on the well-known
Wang-Landau method, is introduced. Independent random walks are performed in
different restricted ranges of energy, and the resultant density of states is
modified by a function of time, F(t)=1/t, for large time. As a consequence, the
calculated density of state, gm(E,t), approaches asymptotically the exact value
gex(E) as 1/sqrt(t), avoiding the saturation of the error. It is also shown
that the growth of the interface of the energy histogram belongs to the random
deposition universality class.Comment: 5 pages, 5 figure
Ricci-flat Metrics with U(1) Action and the Dirichlet Boundary-value Problem in Riemannian Quantum Gravity and Isoperimetric Inequalities
The Dirichlet boundary-value problem and isoperimetric inequalities for
positive definite regular solutions of the vacuum Einstein equations are
studied in arbitrary dimensions for the class of metrics with boundaries
admitting a U(1) action. We show that in the case of non-trivial bundles
Taub-Bolt infillings are double-valued whereas Taub-Nut and Eguchi-Hanson
infillings are unique. In the case of trivial bundles, there are two
Schwarzschild infillings in arbitrary dimensions. The condition of whether a
particular type of filling in is possible can be expressed as a limitation on
squashing through a functional dependence on dimension in each case. The case
of the Eguchi-Hanson metric is solved in arbitrary dimension. The Taub-Nut and
the Taub-Bolt are solved in four dimensions and methods for arbitrary dimension
are delineated. For the case of Schwarzschild, analytic formulae for the two
infilling black hole masses in arbitrary dimension have been obtained. This
should facilitate the study of black hole dynamics/thermodynamics in higher
dimensions. We found that all infilling solutions are convex. Thus convexity of
the boundary does not guarantee uniqueness of the infilling. Isoperimetric
inequalities involving the volume of the boundary and the volume of the
infilling solutions are then investigated. In particular, the analogues of
Minkowski's celebrated inequality in flat space are found and discussed
providing insight into the geometric nature of these Ricci-flat spaces.Comment: 40 pages, 3 figure
Synthesis, antitubercular activity and mechanism of resistance of highly effective thiacetazone analogues
Defining the pharmacological target(s) of currently used drugs and developing new analogues with greater potency are both important aspects of the search for agents that are effective against drug-sensitive and drug-resistant Mycobacterium tuberculosis. Thiacetazone (TAC) is an anti-tubercular drug that was formerly used in conjunction with isoniazid, but removed from the antitubercular chemotherapeutic arsenal due to toxic side effects. However, several recent studies have linked the mechanisms of action of TAC to mycolic acid metabolism and TAC-derived analogues have shown increased potency against M. tuberculosis. To obtain new insights into the molecular mechanisms of TAC resistance, we isolated and analyzed 10 mutants of M. tuberculosis that were highly resistant to TAC. One strain was found to be mutated in the methyltransferase MmaA4 at Gly101, consistent with its lack of oxygenated mycolic acids. All remaining strains harbored missense mutations in either HadA (at Cys61) or HadC (at Val85, Lys157 or Thr123), which are components of the bhydroxyacyl-ACP dehydratase complex that participates in the mycolic acid elongation step. Separately, a library of 31 new TAC analogues was synthesized and evaluated against M. tuberculosis. Two of these compounds, 15 and 16, exhibited minimal inhibitory concentrations 10-fold lower than the parental molecule, and inhibited mycolic acid biosynthesis in a dose-dependent manner. Moreover, overexpression of HadAB HadBC or HadABC in M. tuberculosis led to high level resistance to these compounds, demonstrating that their mode of action is similar to that of TAC. In summary, this study uncovered new mutations associated with TAC resistance and also demonstrated that simple structural optimization of the TAC scaffold was possible and may lead to a new generation of TAC-derived drug candidates for the potential treatment of tuberculosis as mycolic acid inhibitors
Wang-Landau study of the 3D Ising model with bond disorder
We implement a two-stage approach of the Wang-Landau algorithm to investigate
the critical properties of the 3D Ising model with quenched bond randomness. In
particular, we consider the case where disorder couples to the nearest-neighbor
ferromagnetic interaction, in terms of a bimodal distribution of strong versus
weak bonds. Our simulations are carried out for large ensembles of disorder
realizations and lattices with linear sizes in the range . We apply
well-established finite-size scaling techniques and concepts from the scaling
theory of disordered systems to describe the nature of the phase transition of
the disordered model, departing gradually from the fixed point of the pure
system. Our analysis (based on the determination of the critical exponents)
shows that the 3D random-bond Ising model belongs to the same universality
class with the site- and bond-dilution models, providing a single universality
class for the 3D Ising model with these three types of quenched uncorrelated
disorder.Comment: 7 pages, 7 figures, to be published in Eur. Phys. J.
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