27,071 research outputs found
Break-up fragment topology in statistical multifragmentation models
Break-up fragmentation patterns together with kinetic and configurational
energy fluctuations are investigated in the framework of a microcanonical model
with fragment degrees of freedom over a broad excitation energy range. As far
as fragment partitioning is approximately preserved, energy fluctuations are
found to be rather insensitive to both the way in which the freeze-out volume
is constrained and the trajectory followed by the system in the excitation
energy - freeze-out volume space. Due to hard-core repulsion, the freeze-out
volume is found to be populated un-uniformly, its highly depleted core giving
the source a bubble-like structure. The most probable localization of the
largest fragments in the freeze-out volume may be inferred experimentally from
their kinematic properties, largely dictated by Coulomb repulsion
Continuous phase transitions with a convex dip in the microcanonical entropy
The appearance of a convex dip in the microcanonical entropy of finite
systems usually signals a first order transition. However, a convex dip also
shows up in some systems with a continuous transition as for example in the
Baxter-Wu model and in the four-state Potts model in two dimensions. We
demonstrate that the appearance of a convex dip in those cases can be traced
back to a finite-size effect. The properties of the dip are markedly different
from those associated with a first order transition and can be understood
within a microcanonical finite-size scaling theory for continuous phase
transitions. Results obtained from numerical simulations corroborate the
predictions of the scaling theory.Comment: 8 pages, 7 figures, to appear in Phys. Rev.
Theoretical investigation of finite size effects at DNA melting
We investigated how the finiteness of the length of the sequence affects the
phase transition that takes place at DNA melting temperature. For this purpose,
we modified the Transfer Integral method to adapt it to the calculation of both
extensive (partition function, entropy, specific heat, etc) and non-extensive
(order parameter and correlation length) thermodynamic quantities of finite
sequences with open boundary conditions, and applied the modified procedure to
two different dynamical models. We showed that rounding of the transition
clearly takes place when the length of the sequence is decreased. We also
performed a finite-size scaling analysis of the two models and showed that the
singular part of the free energy can indeed be expressed in terms of an
homogeneous function. However, both the correlation length and the average
separation between paired bases diverge at the melting transition, so that it
is no longer clear to which of these two quantities the length of the system
should be compared. Moreover, Josephson's identity is satisfied for none of the
investigated models, so that the derivation of the characteristic exponents
which appear, for example, in the expression of the specific heat, requires
some care
Finite-size behaviour of the microcanonical specific heat
For models which exhibit a continuous phase transition in the thermodynamic
limit a numerical study of small systems reveals a non-monotonic behaviour of
the microcanonical specific heat as a function of the system size. This is in
contrast to a treatment in the canonical ensemble where the maximum of the
specific heat increases monotonically with the size of the system. A
phenomenological theory is developed which permits to describe this peculiar
behaviour of the microcanonical specific heat and allows in principle the
determination of microcanonical critical exponents.Comment: 15 pages, 7 figures, submitted to J. Phys.
The value of improved (ERS) information based on domestic distribution effects of U.S. agriculture crops
The value of improving information for forecasting future crop harvests was investigated. Emphasis was placed upon establishing practical evaluation procedures firmly based in economic theory. The analysis was applied to the case of U.S. domestic wheat consumption. Estimates for a cost of storage function and a demand function for wheat were calculated. A model of market determinations of wheat inventories was developed for inventory adjustment. The carry-over horizon is computed by the solution of a nonlinear programming problem, and related variables such as spot and future price at each stage are determined. The model is adaptable to other markets. Results are shown to depend critically on the accuracy of current and proposed measurement techniques. The quantitative results are presented parametrically, in terms of various possible values of current and future accuracies
Statistical mechanics of non-hamiltonian systems: Traffic flow
Statistical mechanics of a small system of cars on a single-lane road is
developed. The system is not characterized by a Hamiltonian but by a
conditional probability of a velocity of a car for the given velocity and
distance of the car ahead. Distribution of car velocities for various densities
of a group of cars are derived as well as probabilities of density fluctuations
of the group for different velocities. For high braking abilities of cars
free-flow and congested phases are found. Platoons of cars are formed for
system of cars with inefficient brakes. A first order phase transition between
free-flow and congested phase is suggested.Comment: 12 pages, 6 figures, presented at TGF, Paris, 200
Emergent bipartiteness in a society of knights and knaves
We propose a simple model of a social network based on so-called
knights-and-knaves puzzles. The model describes the formation of networks
between two classes of agents where links are formed by agents introducing
their neighbours to others of their own class. We show that if the proportion
of knights and knaves is within a certain range, the network self-organizes to
a perfectly bipartite state. However, if the excess of one of the two classes
is greater than a threshold value, bipartiteness is not observed. We offer a
detailed theoretical analysis for the behaviour of the model, investigate its
behaviou r in the thermodynamic limit, and argue that it provides a simple
example of a topology-driven model whose behaviour is strongly reminiscent of a
first-order phase transitions far from equilibrium.Comment: 12 pages, 5 figure
Generalized canonical ensembles and ensemble equivalence
This paper is a companion article to our previous paper (J. Stat. Phys. 119,
1283 (2005), cond-mat/0408681), which introduced a generalized canonical
ensemble obtained by multiplying the usual Boltzmann weight factor of the canonical ensemble with an exponential factor involving a continuous
function of the Hamiltonian . We provide here a simplified introduction
to our previous work, focusing now on a number of physical rather than
mathematical aspects of the generalized canonical ensemble. The main result
discussed is that, for suitable choices of , the generalized canonical
ensemble reproduces, in the thermodynamic limit, all the microcanonical
equilibrium properties of the many-body system represented by even if this
system has a nonconcave microcanonical entropy function. This is something that
in general the standard () canonical ensemble cannot achieve. Thus a
virtue of the generalized canonical ensemble is that it can be made equivalent
to the microcanonical ensemble in cases where the canonical ensemble cannot.
The case of quadratic -functions is discussed in detail; it leads to the
so-called Gaussian ensemble.Comment: 8 pages, 4 figures (best viewed in ps), revtex4. Changes in v2: Title
changed, references updated, new paragraph added, minor differences with
published versio
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