1,023 research outputs found
Numerical Modeling of Contaminant Transport in a Porous Medium; The Uncertainty in the Solution Arising from Uncertainty in Model Parameters.
A Model for Solid He: II
We propose a simple Ginzburg-Landau free energy to describe the magnetic
phase transition in solid 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
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
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
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
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