11,429 research outputs found
Analysis of phase transitions in the mean-field Blume-Emery-Griffiths model
In this paper we give a complete analysis of the phase transitions in the
mean-field Blume-Emery-Griffiths lattice-spin model with respect to the
canonical ensemble, showing both a second-order, continuous phase transition
and a first-order, discontinuous phase transition for appropriate values of the
thermodynamic parameters that define the model. These phase transitions are
analyzed both in terms of the empirical measure and the spin per site by
studying bifurcation phenomena of the corresponding sets of canonical
equilibrium macrostates, which are defined via large deviation principles.
Analogous phase transitions with respect to the microcanonical ensemble are
also studied via a combination of rigorous analysis and numerical calculations.
Finally, probabilistic limit theorems for appropriately scaled values of the
total spin are proved with respect to the canonical ensemble. These limit
theorems include both central-limit-type theorems when the thermodynamic
parameters are not equal to critical values and non-central-limit-type theorems
when these parameters equal critical values.Comment: 33 pages, revtex
Fully nonlinear development of the most unstable goertler vortex in a three dimensional boundary layer
The nonlinear development is studied of the most unstable Gortler mode within a general 3-D boundary layer upon a suitably concave surface. The structure of this mode was first identified by Denier, Hall and Seddougui (1991) who demonstrated that the growth rate of this instability is O(G sup 3/5) where G is the Gortler number (taken to be large here), which is effectively a measure of the curvature of the surface. Previous researchers have described the fate of the most unstable mode within a 2-D boundary layer. Denier and Hall (1992) discussed the fully nonlinear development of the vortex in this case and showed that the nonlinearity causes a breakdown of the flow structure. The effect of crossflow and unsteadiness upon an infinitesimal unstable mode was elucidated by Bassom and Hall (1991). They demonstrated that crossflow tends to stabilize the most unstable Gortler mode, and for certain crossflow/frequency combinations the Gortler mode may be made neutrally stable. These vortex configurations naturally lend themselves to a weakly nonlinear stability analysis; work which is described in a previous article by the present author. Here we extend the ideas of Denier and Hall (1992) to the three-dimensional boundary layer problem. It is found that the numerical solution of the fully nonlinear equations is best conducted using a method which is essentially an adaption of that utilized by Denier and Hall (1992). The influence of crossflow and unsteadiness upon the breakdown of the flow is described
Recombination dramatically speeds up evolution of finite populations
We study the role of recombination, as practiced by genetically-competent
bacteria, in speeding up Darwinian evolution. This is done by adding a new
process to a previously-studied Markov model of evolution on a smooth fitness
landscape; this new process allows alleles to be exchanged with those in the
surrounding medium. Our results, both numerical and analytic, indicate that for
a wide range of intermediate population sizes, recombination dramatically
speeds up the evolutionary advance
Joint evolution of multiple social traits: a kin selection analysis
General models of the evolution of cooperation, altruism and other social behaviours have focused almost entirely on single traits, whereas it is clear that social traits commonly interact. We develop a general kin-selection framework for the evolution of social behaviours in multiple dimensions. We show that whenever there are interactions among social traits new behaviours can emerge that are not predicted by one-dimensional analyses. For example, a prohibitively costly cooperative trait can ultimately be favoured owing to initial evolution in other (cheaper) social traits that in turn change the cost-benefit ratio of the original trait. To understand these behaviours, we use a two-dimensional stability criterion that can be viewed as an extension of Hamilton's rule. Our principal example is the social dilemma posed by, first, the construction and, second, the exploitation of a shared public good. We find that, contrary to the separate one-dimensional analyses, evolutionary feedback between the two traits can cause an increase in the equilibrium level of selfish exploitation with increasing relatedness, while both social (production plus exploitation) and asocial (neither) strategies can be locally stable. Our results demonstrate the importance of emergent stability properties of multidimensional social dilemmas, as one-dimensional stability in all component dimensions can conceal multidimensional instability
An Allosteric Receptor by Simultaneous "Casting" and "Molding" in a Dynamic Combinatorial Library
Allosteric synthetic receptors are difficult to access by design. Herein we report a dynamic combinatorial strategy towards such systems based on the simultaneous use of two different templates. Through a process of simultaneous casting (the assembly of a library member around a template) and molding (the assembly of a library member inside the binding pocket of a template), a Russian-doll-like termolecular complex was obtained with remarkable selectivity. Analysis of the stepwise formation of the complex indicates that binding of the two partners by the central macrocycle exhibits significant positive cooperativity. Such allosteric systems represent hubs that may have considerable potential in systems chemistry
Attitude Change in Response to an In-Service Teacher Education Programme
How can I tell how successful this course has been? is becoming an increasingly common question in tertiary education. This interest in tertiary teaching and learning is reflected in the fact that one-half of all Australian universities now have tertiary teaching units. There are a number of reasons why evaluation is important. Firstly, discrepancies between the actual and the ideal situation can be detected, causes identified and corrective measures instituted at all stages of the evaluative model, to serve the interests of increased efficiency and improved staff and student satisfaction. Secondly, courses which are continually being evaluated are better able to meet changing demands from students, from the society which the educational institution is serving, and also better able to adjust to internal changes in staff numbers and expertise. Thirdly, evaluation properly conducted can provide a statement of accountability
Dynamic Combinatorial Libraries: From Exploring Molecular Recognition to Systems Chemistry
Dynamic combinatorial chemistry (DCC) is a subset of combinatorial chemistry where the library members interconvert continuously by exchanging building blocks with each other. Dynamic combinatorial libraries (DCLs) are powerful tools for discovering the unexpected and have given rise to many fascinating molecules, ranging from interlocked structures to self-replicators. Furthermore, dynamic combinatorial molecular networks can produce emergent properties at systems level, which provide exciting new opportunities in systems chemistry. In this perspective we will highlight some new methodologies in this field and analyze selected examples of DCLs that are under thermodynamic control, leading to synthetic receptors, catalytic systems, and complex self-assembled supramolecular architectures. Also reviewed are extensions of the principles of DCC to systems that are not at equilibrium and may therefore harbor richer functional behavior. Examples include self-replication and molecular machines
CSF lactate dehydrogenase activity in patients with Creutzfeldt-Jakob disease exceeds that in other dementias
The diagnosis of Creutzfeldt- Jakob disease (CJD) is still made by exclusion of other dementias. We now evaluated lactate dehydrogenase (LDH) in the cerebrospinal fluid (CSF) as a possible additional diagnostic tool. CSF LDH levels of patients with CJD ( n = 26) were compared with those in other dementias ( n = 28). LDH isoenzymes were determined in a subset ( n = 9). Total LDH and isoenzyme LDH-1 were significantly higher, whereas the fractions of LDH-2 and LDH-3 were significantly lower in CJD patients. We conclude that in addition to established CSF parameters, LDH and its isoenzymes might serve as a further help to discriminate between CJD and other dementias. Copyright (C) 2004 S. Karger AG, Basel
Analytical study of the effect of recombination on evolution via DNA shuffling
We investigate a multi-locus evolutionary model which is based on the DNA
shuffling protocol widely applied in \textit{in vitro} directed evolution. This
model incorporates selection, recombination and point mutations. The simplicity
of the model allows us to obtain a full analytical treatment of both its
dynamical and equilibrium properties, for the case of an infinite population.
We also briefly discuss finite population size corrections
Microscopic dynamics of thin hard rods
Based on the collision rules for hard needles we derive a hydrodynamic
equation that determines the coupled translational and rotational dynamics of a
tagged thin rod in an ensemble of identical rods. Specifically, based on a
Pseudo-Liouville operator for binary collisions between rods, the Mori-Zwanzig
projection formalism is used to derive a continued fraction representation for
the correlation function of the tagged particle's density, specifying its
position and orientation. Truncation of the continued fraction gives rise to a
generalised Enskog equation, which can be compared to the phenomenological
Perrin equation for anisotropic diffusion. Only for sufficiently large density
do we observe anisotropic diffusion, as indicated by an anisotropic mean square
displacement, growing linearly with time. For lower densities, the Perrin
equation is shown to be an insufficient hydrodynamic description for hard
needles interacting via binary collisions. We compare our results to
simulations and find excellent quantitative agreement for low densities and
qualtitative agreement for higher densities.Comment: 21 pages, 6 figures, v2: clarifications and improved readabilit
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