A Model for Solid 3^3He: II

We propose a simple Ginzburg-Landau free energy to describe the magnetic phase transition in solid $^3$He. The free energy is analyzed with due consideration of the hard first order transitions at low magnetic fields. The resulting phase diagram contains all of the important features of the experimentally observed ph ase diagram. The free energy also yields a critical field at which the transition from the disordered state to the high field state changes from a first order to a second order one.Comment: This paper has been accepted for publication in Journal of Low Temperature Physics. Use regular Tex, with the D. Eardley version of Macros called jnl.tex. 10 pages, 4 figs available from [email protected]

VPLanet: The Virtual Planet Simulator

We describe a software package called VPLanet that simulates fundamental aspects of planetary system evolution over Gyr timescales, with a focus on investigating habitable worlds. In this initial release, eleven physics modules are included that model internal, atmospheric, rotational, orbital, stellar, and galactic processes. Many of these modules can be coupled simultaneously to simulate the evolution of terrestrial planets, gaseous planets, and stars. The code is validated by reproducing a selection of observations and past results. VPLanet is written in C and designed so that the user can choose the physics modules to apply to an individual object at runtime without recompiling, i.e., a single executable can simulate the diverse phenomena that are relevant to a wide range of planetary and stellar systems. This feature is enabled by matrices and vectors of function pointers that are dynamically allocated and populated based on user input. The speed and modularity of VPLanet enables large parameter sweeps and the versatility to add/remove physical phenomena to assess their importance. VPLanet is publicly available from a repository that contains extensive documentation, numerous examples, Python scripts for plotting and data management, and infrastructure for community input and future development.Comment: 75 pages, 34 figures, 10 tables, accepted to the Proceedings of the Astronomical Society of the Pacific. Source code, documentation, and examples available at https://github.com/VirtualPlanetaryLaboratory/vplane

Epitaxial growth in dislocation-free strained alloy films: Morphological and compositional instabilities

The mechanisms of stability or instability in the strained alloy film growth are of intense current interest to both theorists and experimentalists. We consider dislocation-free, coherent, growing alloy films which could exhibit a morphological instability without nucleation. We investigate such strained films by developing a nonequilibrium, continuum model and by performing a linear stability analysis. The couplings of film-substrate misfit strain, compositional stress, deposition rate, and growth temperature determine the stability of film morphology as well as the surface spinodal decomposition. We consider some realistic factors of epitaxial growth, in particular the composition dependence of elastic moduli and the coupling between top surface and underlying bulk of the film. The interplay of these factors leads to new stability results. In addition to the stability diagrams both above and below the coherent spinodal temperature, we also calculate the kinetic critical thickness for the onset of instability as well as its scaling behavior with respect to misfit strain and deposition rate. We apply our results to some real growth systems and discuss the implications related to some recent experimental observations.Comment: 26 pages, 13 eps figure

Phase field modeling of electrochemistry I: Equilibrium

A diffuse interface (phase field) model for an electrochemical system is developed. We describe the minimal set of components needed to model an electrochemical interface and present a variational derivation of the governing equations. With a simple set of assumptions: mass and volume constraints, Poisson's equation, ideal solution thermodynamics in the bulk, and a simple description of the competing energies in the interface, the model captures the charge separation associated with the equilibrium double layer at the electrochemical interface. The decay of the electrostatic potential in the electrolyte agrees with the classical Gouy-Chapman and Debye-H\"uckel theories. We calculate the surface energy, surface charge, and differential capacitance as functions of potential and find qualitative agreement between the model and existing theories and experiments. In particular, the differential capacitance curves exhibit complex shapes with multiple extrema, as exhibited in many electrochemical systems.Comment: v3: To be published in Phys. Rev. E v2: Added link to cond-mat/0308179 in References 13 pages, 6 figures in 15 files, REVTeX 4, SIUnits.sty. Precedes cond-mat/030817

Order of the phase transition in models of DNA thermal denaturation

We examine the behavior of a model which describes the melting of double-stranded DNA chains. The model, with displacement-dependent stiffness constants and a Morse on-site potential, is analyzed numerically; depending on the stiffness parameter, it is shown to have either (i) a second-order transition with "nu_perpendicular" = - beta = 1, "nu_parallel" = gamma/2 = 2 (characteristic of short range attractive part of the Morse potential) or (ii) a first-order transition with finite melting entropy, discontinuous fraction of bound pairs, divergent correlation lengths, and critical exponents "nu_perpendicular" = - beta = 1/2, "nu_parallel" = gamma/2 = 1.Comment: 4 pages of Latex, including 4 Postscript figures. To be published in Phys. Rev. Let

Thermodynamic instabilities in one dimensional particle lattices: a finite-size scaling approach

One-dimensional thermodynamic instabilities are phase transitions not prohibited by Landau's argument, because the energy of the domain wall (DW) which separates the two phases is infinite. Whether they actually occur in a given system of particles must be demonstrated on a case-by-case basis by examining the (non-) analyticity properties of the corresponding transfer integral (TI) equation. The present note deals with the generic Peyrard-Bishop model of DNA denaturation. In the absence of exact statements about the spectrum of the singular TI equation, I use Gauss-Hermite quadratures to achieve a single-parameter-controlled approach to rounding effects; this allows me to employ finite-size scaling concepts in order to demonstrate that a phase transition occurs and to derive the critical exponents.Comment: 5 pages, 6 figures, subm. to Phys. Rev.

The spatiotemporal evolution of granular microslip precursors to laboratory earthquakes

Laboratory earthquake experiments provide important observational constraints for our understanding of earthquake physics. Here we leverage continuous waveform data from a network of piezoceramic sensors to study the spatial and temporal evolution of microslip activity during a shear experiment with synthetic fault gouge. We combine machine learning techniques with ray theoretical seismology to detect, associate, and locate tens of thousands of microslip events within the gouge layer. Microslip activity is concentrated near the center of the system but is highly variable in space and time. While microslip activity rate increases as failure approaches, the spatiotemporal evolution can differ substantially between stick-slip cycles. These results illustrate that even within a single, well-constrained laboratory experiment, the dynamics of earthquake nucleation can be highly complex