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

Optical properties of current carrying molecular wires

We consider several fundamental optical phenomena involving single molecules in biased metal-molecule-metal junctions. The molecule is represented by its highest occupied and lowest unoccupied molecular orbitals, and the analysis involves the simultaneous consideration of three coupled fluxes: the electronic current through the molecule, energy flow between the molecule and electron-hole excitations in the leads and the incident and/or emitted photon flux. Using a unified theoretical approach based on the non-equilibrium Green function method we derive expressions for the absorption lineshape (not an observable but a ueful reference for considering yields of other optical processes) and for the current induced molecular emission in such junctions. We also consider conditions under which resonance radiation can induce electronic current in an unbiased junction. We find that current driven molecular emission and resonant light induced electronic currents in single molecule junctions can be of observable magnitude under appropriate realizable conditions. In particular, light induced current should be observed in junctions involving molecular bridges that are characterized by strong charge transfer optical transitions. For observing current induced molecular emission we find that in addition to the familiar need to control the damping of molecular excitations into the metal substrate the phenomenon is also sensitive to the way in which the potential bias si distributed on the junction.Comment: 56 pages, 8 figures; submitted to JC

Effect Of Environmental Hydrogen Pressure On The Hydrogen Yield From X‐irradiated Polyethylenes

An experimental assembly incorporating a capacitance‐type, differential pressure transducer, which provides resolutions of 3 x 10−4 torr at pressures extending to 30 torr, has been employed to monitor the effect of hydrogen environmental pressure on the hydrogen yield from x‐irradiated polyethylene\u27s. Contrary to the observations of previous investigators, the hydrogen yield is found to be independent of hydrogen environmental pressures extending over the critical range up to at least 30 torr. It is demonstrated that neglecting the temperature and density gradients inherent in closed‐volume irradiation assemblies employing cryogenic traps to separate liberated gases into condensable and non condensable fractions may lead to erroneous conclusions with respect to gas yields arising from the irradiation of materials. A homogeneous, variable‐plate separation ion chamber consisting of a polyethylene body and utilizing flowing ethylene as the cavity gas was employed to obtain total volatile G values of 3.6 ± 0.4, 3.8 ± 0.4, and 4.0 ± 0.4 molecules/100 e.v., for Marlex 6002, Dow Ziegler (Q 917.5), and DuPont A‐1410 polyethylene\u27s, respectively. A hydrogen contribution of approximately 98 mole‐% was obtained with this experimental method. Copyright © 1967 John Wiley & Sons, Inc

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

Development of an Integrated Governance Strategy for the Voluntary and Community Sector

This report on governance provides a framework for thinking about how policy makers, funders,regulators and advisers can all work with Board members and staff to enhance the effectiveness of nonprofit organisations. It was commissioned by the Active Community Unit (ACU) of the Home Office, in parallel with other reviews designed to improve the capacity of the voluntary and community sector, at a time when the sector plays an increasingly important role in the delivery of services using public funds. That role has recently been investigated in two Government reports, the Cross Cutting Review carried out by the Treasury, and the Strategy Unit review of charities and nonprofits. Our report proposes actions of three types: some that can be taken immediately, some that require further discussion with key interests, and some integration with the other ACU reviews. Taken together they provide the starting point for an evolving strategy to improve governance across the sector. We recommend ACU chairs a group charged with the responsibility for planning and implementing this. Our focus is on governance as 'the systems and processes concerned with ensuring the overall direction, supervision and accountability of an organisation'. This is often taken to mean the way that a Board, management committee or other governing body steers the overall development of an organisation, where day-to-day management is in the hands of staff or volunteers. Sometimes, of course, the committee and volunteers are the same. They – like all governing bodies – have to balance the interests of the organisation and those they are trying to serve, while being conscious of financial and legal responsibilities, and the requirements of funders and other supporters

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

Parametric Fokker-Planck equation

We derive the Fokker-Planck equation on the parametric space. It is the Wasserstein gradient flow of relative entropy on the statistical manifold. We pull back the PDE to a finite dimensional ODE on parameter space. Some analytical example and numerical examples are presented

A variable time step self-consistent mean field DSMC model for three-dimensional environments

A self-consistent mean field direct simulation Monte Carlo (SCMFD) algorithm was recently proposed for simulating collision environments for a range of one-dimensional model systems. This work extends the one-dimensional SCMFD approach to three dimensions and introduces a variable time step (3D-vt-SCMFD), enabling the modeling of a considerably wider range of different collision environments. We demonstrate the performance of the augmented method by modeling a varied set of test systems: ideal gas mixtures, Poiseuille flow of argon, and expansion of gas into high vacuum. For the gas mixtures, the 3D-vt-SCMFD method reproduces the properties (mean free path, mean free time, collision frequency, and temperature) in excellent agreement with theoretical predictions. From the Poiseuille flow simulations, we extract flow profiles that agree with the solution to the Navier–Stokes equations in the high-density limit and resemble free molecular flow at low densities, as expected. The measured viscosity from 3D-vt-SCMF is ∼15% lower than the theoretical prediction from Chapman–Enskog theory. The expansion of gas into vacuum is examined in the effusive regime and at the hydrodynamic limit. In both cases, 3D-vt-SCMDF simulations produce gas beam density, velocity, and temperature profiles in excellent agreement with analytical models. In summary, our tests show that 3D-vt-SCMFD is robust and computationally efficient, while also illustrating the diversity of systems the SCMFD model can be successfully applied to