42,477 research outputs found
The one-dimensional Stefan problem with non-Fourier heat conduction
We investigate the one-dimensional growth of a solid into a liquid bath,
starting from a small crystal, using the Guyer-Krumhansl and Maxwell-Cattaneo
models of heat conduction. By breaking the solidification process into the
relevant time regimes we are able to reduce the problem to a system of two
coupled ordinary differential equations describing the evolution of the
solid-liquid interface and the heat flux. The reduced formulation is in good
agreement with numerical simulations. In the case of silicon, differences
between classical and non-classical solidification kinetics are relatively
small, but larger deviations can be observed in the evolution in time of the
heat flux through the growing solid. From this study we conclude that the heat
flux provides more information about the presence of non-classical modes of
heat transport during phase-change processes.Comment: 29 pages, 6 figures, 2 tables + Supplementary Materia
Derivation of Delay Equation Climate Models Using the Mori-Zwanzig Formalism
Models incorporating delay have been frequently used to understand climate
variability phenomena, but often the delay is introduced through an ad-hoc
physical reasoning, such as the propagation time of waves. In this paper, the
Mori-Zwanzig formalism is introduced as a way to systematically derive delay
models from systems of partial differential equations and hence provides a
better justification for using these delay-type models. The Mori-Zwanzig
technique gives a formal rewriting of the system using a projection onto a set
of resolved variables, where the rewritten system contains a memory term. The
computation of this memory term requires solving the orthogonal dynamics
equation, which represents the unresolved dynamics. For nonlinear systems, it
is often not possible to obtain an analytical solution to the orthogonal
dynamics and an approximate solution needs to be found. Here, we demonstrate
the Mori-Zwanzig technique for a two-strip model of the El Nino Southern
Oscillation (ENSO) and explore methods to solve the orthogonal dynamics. The
resulting nonlinear delay model contains an additional term compared to
previously proposed ad-hoc conceptual models. This new term leads to a larger
ENSO period, which is closer to that seen in observations.Comment: Submitted to Proceedings of the Royal Society A, 25 pages, 10 figure
Computational statistics using the Bayesian Inference Engine
This paper introduces the Bayesian Inference Engine (BIE), a general
parallel, optimised software package for parameter inference and model
selection. This package is motivated by the analysis needs of modern
astronomical surveys and the need to organise and reuse expensive derived data.
The BIE is the first platform for computational statistics designed explicitly
to enable Bayesian update and model comparison for astronomical problems.
Bayesian update is based on the representation of high-dimensional posterior
distributions using metric-ball-tree based kernel density estimation. Among its
algorithmic offerings, the BIE emphasises hybrid tempered MCMC schemes that
robustly sample multimodal posterior distributions in high-dimensional
parameter spaces. Moreover, the BIE is implements a full persistence or
serialisation system that stores the full byte-level image of the running
inference and previously characterised posterior distributions for later use.
Two new algorithms to compute the marginal likelihood from the posterior
distribution, developed for and implemented in the BIE, enable model comparison
for complex models and data sets. Finally, the BIE was designed to be a
collaborative platform for applying Bayesian methodology to astronomy. It
includes an extensible object-oriented and easily extended framework that
implements every aspect of the Bayesian inference. By providing a variety of
statistical algorithms for all phases of the inference problem, a scientist may
explore a variety of approaches with a single model and data implementation.
Additional technical details and download details are available from
http://www.astro.umass.edu/bie. The BIE is distributed under the GNU GPL.Comment: Resubmitted version. Additional technical details and download
details are available from http://www.astro.umass.edu/bie. The BIE is
distributed under the GNU GP
Aversion to ambiguity and model misspecification in dynamic stochastic environments
Preferences that accommodate aversion to subjective uncertainty and its potential misspecification in dynamic settings are a valuable tool of analysis in many disciplines. By generalizing previous analyses, we propose a tractable approach to incorporating broadly conceived responses to uncertainty. We illustrate our approach on some stylized stochastic environments. By design, these discrete time environments have revealing continuous time limits. Drawing on these illustrations, we construct recursive representations of intertemporal preferences that allow for penalized and smooth ambiguity aversion to subjective uncertainty. These recursive representations imply continuous time limiting Hamilton–Jacobi–Bellman equations for solving control problems in the presence of uncertainty.Published versio
Unnatural Selection: A new formal approach to punctuated equilibrium in economic systems
Generalized Darwinian evolutionary theory has emerged as central to the description of economic process (e.g., Aldrich et. al., 2008). Here we demonstrate that, just as Darwinian principles provide necessary, but not sufficient, conditions for understanding the dynamics of social entities, in a similar manner the asymptotic limit theorems of information theory provide another set of necessary conditions that constrain the evolution of socioeconomic process. These latter constraints can, however, easily be formulated as a statistics-like analytic toolbox for the study of empirical data that is consistent with a generalized Darwinism, and this is no small thing
Experimental and Theoretical Challenges in the Search for the Quark Gluon Plasma: The STAR Collaboration's Critical Assessment of the Evidence from RHIC Collisions
We review the most important experimental results from the first three years
of nucleus-nucleus collision studies at RHIC, with emphasis on results from the
STAR experiment, and we assess their interpretation and comparison to theory.
The theory-experiment comparison suggests that central Au+Au collisions at RHIC
produce dense, rapidly thermalizing matter characterized by: (1) initial energy
densities above the critical values predicted by lattice QCD for establishment
of a Quark-Gluon Plasma (QGP); (2) nearly ideal fluid flow, marked by
constituent interactions of very short mean free path, established most
probably at a stage preceding hadron formation; and (3) opacity to jets. Many
of the observations are consistent with models incorporating QGP formation in
the early collision stages, and have not found ready explanation in a hadronic
framework. However, the measurements themselves do not yet establish
unequivocal evidence for a transition to this new form of matter. The
theoretical treatment of the collision evolution, despite impressive successes,
invokes a suite of distinct models, degrees of freedom and assumptions of as
yet unknown quantitative consequence. We pose a set of important open
questions, and suggest additional measurements, at least some of which should
be addressed in order to establish a compelling basis to conclude definitively
that thermalized, deconfined quark-gluon matter has been produced at RHIC.Comment: 101 pages, 37 figures; revised version to Nucl. Phys.
A High-Low Model of Daily Stock Price Ranges
We observe that daily highs and lows of stock prices do not diverge over time and, hence, adopt the cointegration concept and the related vector error correction model (VECM) to model the daily high, the daily low, and the associated daily range data. The in-sample results attest the importance of incorporating high-low interactions in modeling the range variable. In evaluating the out-of-sample forecast performance using both mean-squared forecast error and direction of change criteria, it is found that the VECM-based low and high forecasts offer some advantages over some alternative forecasts. The VECM-based range forecasts, on the other hand, do not always dominate –the forecast rankings depend on the choice of evaluation criterion and the variables being forecasted.daily high, daily low, VECM model, forecast performance, implied volatility
Cooling Rates for Relativistic Electrons Undergoing Compton Scattering in Strong Magnetic Fields
For inner magnetospheric models of hard X-ray and gamma-ray emission in
high-field pulsars and magnetars, resonant Compton upscattering is anticipated
to be the most efficient process for generating continuum radiation. This is
due in part to the proximity of a hot soft photon bath from the stellar surface
to putative radiation dissipation regions in the inner magnetosphere. Moreover,
because the scattering process becomes resonant at the cyclotron frequency, the
effective cross section exceeds the classical Thomson value by over two orders
of magnitude, thereby enhancing the efficiency of continuum production and the
cooling of relativistic electrons. This paper presents computations of the
electron cooling rates for this process, which are needed for resonant Compton
models of non-thermal radiation from such highly-magnetized pulsars. The
computed rates extend previous calculations of magnetic Thomson cooling to the
domain of relativistic quantum effects, sampled near and above the quantum
critical magnetic field of 44.13 TeraGauss. This is the first exposition of
fully relativistic, quantum magnetic Compton cooling rates for electrons, and
it employs both the traditional Johnson and Lippman cross section, and a newer
Sokolov and Ternov (ST) formulation of Compton scattering in strong magnetic
fields. Such ST formalism is formally correct for treating spin-dependent
effects that are important in the cyclotron resonance, and has not been
addressed before in the context of cooling by Compton scattering. The QED
effects are observed to profoundly lower the rates below extrapolations of the
familiar magnetic Thomson results, as expected, when recoil and Klein-Nishina
reductions become important.Comment: 33 pages, 11 figures, accepted for publication in The Astrophysical
Journa
Matter in extremis: ultrarelativistic nuclear collisions at RHIC
We review the physics of nuclear matter at high energy density and the
experimental search for the Quark-Gluon Plasma at the Relativistic Heavy Ion
Collider (RHIC). The data obtained in the first three years of the RHIC physics
program provide several lines of evidence that a novel state of matter has been
created in the most violent, head-on collisions of nuclei at
GeV. Jet quenching and global measurements show that the initial
energy density of the strongly interacting medium generated in the collision is
about two orders of magnitude larger than that of cold nuclear matter, well
above the critical density for the deconfinement phase transition predicted by
lattice QCD. The observed collective flow patterns imply that the system
thermalizes early in its evolution, with the dynamics of its expansion
consistent with ideal hydrodynamic flow based on a Quark-Gluon Plasma equation
of state.Comment: 93 pages, 46 figures; final version for journal incorporating minor
changes and correction
- …