1,110 research outputs found
Group Leaders Optimization Algorithm
We present a new global optimization algorithm in which the influence of the
leaders in social groups is used as an inspiration for the evolutionary
technique which is designed into a group architecture. To demonstrate the
efficiency of the method, a standard suite of single and multidimensional
optimization functions along with the energies and the geometric structures of
Lennard-Jones clusters are given as well as the application of the algorithm on
quantum circuit design problems. We show that as an improvement over previous
methods, the algorithm scales as N^2.5 for the Lennard-Jones clusters of
N-particles. In addition, an efficient circuit design is shown for two qubit
Grover search algorithm which is a quantum algorithm providing quadratic
speed-up over the classical counterpart
Deceptive signals of phase transitions in small magnetic clusters
We present an analysis of the thermodynamic properties of small transition
metal clusters and show how the commonly used indicators of phase transitions
like peaks in the specific heat or magnetic susceptibility can lead to
deceptive interpretations of the underlying physics. The analysis of the
distribution of zeros of the canonical partition function in the whole complex
temperature plane reveals the nature of the transition. We show that signals in
the magnetic susceptibility at positive temperatures have their origin at zeros
lying at negative temperatures.Comment: 4 pages, 5 figures, revtex4, for further information see
http://www.smallsystems.d
Structural Transitions and Global Minima of Sodium Chloride Clusters
In recent experiments on sodium chloride clusters structural transitions
between nanocrystals with different cuboidal shapes were detected. Here we
determine reaction pathways between the low energy isomers of one of these
clusters, (NaCl)35Cl-. The key process in these structural transitions is a
highly cooperative rearrangement in which two parts of the nanocrystal slip
past one another on a {110} plane in a direction. In this way the
nanocrystals can plastically deform, in contrast to the brittle behaviour of
bulk sodium chloride crystals at the same temperatures; the nanocrystals have
mechanical properties which are a unique feature of their finite size. We also
report and compare the global potential energy minima for (NaCl)NCl- using two
empirical potentials, and comment on the effect of polarization.Comment: extended version, 13 pages, 8 figures, revte
Discrete Breathers in a Realistic Coarse-Grained Model of Proteins
We report the results of molecular dynamics simulations of an off-lattice
protein model featuring a physical force-field and amino-acid sequence. We show
that localized modes of nonlinear origin (discrete breathers) emerge naturally
as continuations of a subset of high-frequency normal modes residing at
specific sites dictated by the native fold. In the case of the small
-barrel structure that we consider, localization occurs on the turns
connecting the strands. At high energies, discrete breathers stabilize the
structure by concentrating energy on few sites, while their collapse marks the
onset of large-amplitude fluctuations of the protein. Furthermore, we show how
breathers develop as energy-accumulating centres following perturbations even
at distant locations, thus mediating efficient and irreversible energy
transfers. Remarkably, due to the presence of angular potentials, the breather
induces a local static distortion of the native fold. Altogether, the
combination of this two nonlinear effects may provide a ready means for
remotely controlling local conformational changes in proteins.Comment: Submitted to Physical Biolog
Symmetries of microcanonical entropy surfaces
Symmetry properties of the microcanonical entropy surface as a function of
the energy and the order parameter are deduced from the invariance group of the
Hamiltonian of the physical system. The consequences of these symmetries for
the microcanonical order parameter in the high energy and in the low energy
phases are investigated. In particular the breaking of the symmetry of the
microcanonical entropy in the low energy regime is considered. The general
statements are corroborated by investigations of various examples of classical
spin systems.Comment: 15 pages, 5 figures include
Slow relaxation to equipartition in spring-chain systems
In this study, one-dimensional systems of masses connected by springs, i.e.,
spring-chain systems, are investigated numerically. The average kinetic energy
of chain-end particles of these systems is larger than that of other particles,
which is similar to the behavior observed for systems made of masses connected
by rigid links. The energetic motion of the end particles is, however,
transient, and the system relaxes to thermal equilibrium after a while, where
the average kinetic energy of each particle is the same, that is, equipartition
of energy is achieved. This is in contrast to the case of systems made of
masses connected by rigid links, where the energetic motion of the end
particles is observed in equilibrium. The timescale of relaxation estimated by
simulation increases rapidly with increasing spring constant. The timescale is
also estimated using the Boltzmann-Jeans theory and is found to be in quite
good agreement with that obtained by the simulation
Classification of phase transitions in small systems
We present a classification scheme for phase transitions in finite systems
like atomic and molecular clusters based on the Lee-Yang zeros in the complex
temperature plane. In the limit of infinite particle numbers the scheme reduces
to the Ehrenfest definition of phase transitions and gives the right critical
indices. We apply this classification scheme to Bose-Einstein condensates in a
harmonic trap as an example of a higher order phase transitions in a finite
system and to small Ar clusters.Comment: 12 pages, 4 figures, accepted for publication in Phys. Rev. Let
Phase transitions and configuration space topology
Equilibrium phase transitions may be defined as nonanalytic points of
thermodynamic functions, e.g., of the canonical free energy. Given a certain
physical system, it is of interest to understand which properties of the system
account for the presence of a phase transition, and an understanding of these
properties may lead to a deeper understanding of the physical phenomenon. One
possible approach of this issue, reviewed and discussed in the present paper,
is the study of topology changes in configuration space which, remarkably, are
found to be related to equilibrium phase transitions in classical statistical
mechanical systems. For the study of configuration space topology, one
considers the subsets M_v, consisting of all points from configuration space
with a potential energy per particle equal to or less than a given v. For
finite systems, topology changes of M_v are intimately related to nonanalytic
points of the microcanonical entropy (which, as a surprise to many, do exist).
In the thermodynamic limit, a more complex relation between nonanalytic points
of thermodynamic functions (i.e., phase transitions) and topology changes is
observed. For some class of short-range systems, a topology change of the M_v
at v=v_t was proved to be necessary for a phase transition to take place at a
potential energy v_t. In contrast, phase transitions in systems with long-range
interactions or in systems with non-confining potentials need not be
accompanied by such a topology change. Instead, for such systems the
nonanalytic point in a thermodynamic function is found to have some
maximization procedure at its origin. These results may foster insight into the
mechanisms which lead to the occurrence of a phase transition, and thus may
help to explore the origin of this physical phenomenon.Comment: 22 pages, 6 figure
Feedback-optimized parallel tempering Monte Carlo
We introduce an algorithm to systematically improve the efficiency of
parallel tempering Monte Carlo simulations by optimizing the simulated
temperature set. Our approach is closely related to a recently introduced
adaptive algorithm that optimizes the simulated statistical ensemble in
generalized broad-histogram Monte Carlo simulations. Conventionally, a
temperature set is chosen in such a way that the acceptance rates for replica
swaps between adjacent temperatures are independent of the temperature and
large enough to ensure frequent swaps. In this paper, we show that by choosing
the temperatures with a modified version of the optimized ensemble feedback
method we can minimize the round-trip times between the lowest and highest
temperatures which effectively increases the efficiency of the parallel
tempering algorithm. In particular, the density of temperatures in the
optimized temperature set increases at the "bottlenecks'' of the simulation,
such as phase transitions. In turn, the acceptance rates are now temperature
dependent in the optimized temperature ensemble. We illustrate the
feedback-optimized parallel tempering algorithm by studying the two-dimensional
Ising ferromagnet and the two-dimensional fully-frustrated Ising model, and
briefly discuss possible feedback schemes for systems that require
configurational averages, such as spin glasses.Comment: 12 pages, 14 figure
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