46,859 research outputs found
On Blowup for time-dependent generalized Hartree-Fock equations
We prove finite-time blowup for spherically symmetric and negative energy
solutions of Hartree-Fock and Hartree-Fock-Bogoliubov type equations, which
describe the evolution of attractive fermionic systems (e. g. white dwarfs).
Our main results are twofold: First, we extend the recent blowup result of
[Hainzl and Schlein, Comm. Math. Phys. \textbf{287} (2009), 705--714] to
Hartree-Fock equations with infinite rank solutions and a general class of
Newtonian type interactions. Second, we show the existence of finite-time
blowup for spherically symmetric solutions of a Hartree-Fock-Bogoliubov model,
where an angular momentum cutoff is introduced. We also explain the key
difficulties encountered in the full Hartree-Fock-Bogoliubov theory.Comment: 24 page
Some Key Developments in Computational Electromagnetics and their Attribution
Key developments in computational electromagnetics are proposed. Historical highlights are summarized concentrating on the two main approaches of differential and integral methods. This is seen as timely as a retrospective analysis is needed to minimize duplication and to help settle questions of attribution
Fitting Effective Diffusion Models to Data Associated with a "Glassy Potential": Estimation, Classical Inference Procedures and Some Heuristics
A variety of researchers have successfully obtained the parameters of low
dimensional diffusion models using the data that comes out of atomistic
simulations. This naturally raises a variety of questions about efficient
estimation, goodness-of-fit tests, and confidence interval estimation. The
first part of this article uses maximum likelihood estimation to obtain the
parameters of a diffusion model from a scalar time series. I address numerical
issues associated with attempting to realize asymptotic statistics results with
moderate sample sizes in the presence of exact and approximated transition
densities. Approximate transition densities are used because the analytic
solution of a transition density associated with a parametric diffusion model
is often unknown.I am primarily interested in how well the deterministic
transition density expansions of Ait-Sahalia capture the curvature of the
transition density in (idealized) situations that occur when one carries out
simulations in the presence of a "glassy" interaction potential. Accurate
approximation of the curvature of the transition density is desirable because
it can be used to quantify the goodness-of-fit of the model and to calculate
asymptotic confidence intervals of the estimated parameters. The second part of
this paper contributes a heuristic estimation technique for approximating a
nonlinear diffusion model. A "global" nonlinear model is obtained by taking a
batch of time series and applying simple local models to portions of the data.
I demonstrate the technique on a diffusion model with a known transition
density and on data generated by the Stochastic Simulation Algorithm.Comment: 30 pages 10 figures Submitted to SIAM MMS (typos removed and slightly
shortened
Fluid dynamic aspects of cardiovascular behavior during low-frequency whole-body vibration
The behavior of the cardiovascular system during low frequency whole-body vibration, such as encountered by astronauts during launch and reentry, is examined from a fluid mechanical viewpoint. The vibration characteristics of typical manned spacecraft and other vibration environments are discussed, and existing results from in vivo studies of the hemodynamic aspects of this problem are reviewed. Recent theoretical solutions to related fluid mechanical problems are then used in the interpretation of these results and in discussing areas of future work. The results are included of studies of the effects of vibration on the work done by the heart and on pulsatile flow in blood vessels. It is shown that important changes in pulse velocity, the instantaneous velocity profile, mass flow rate, and wall shear stress may occur in a pulsatile flow due to the presence of vibration. The significance of this in terms of changes in peripheral vascular resistance and possible damage to the endothelium of blood vessels is discussed
Structure of the Yang-Mills vacuum in the zero modes enhancement quantum model
We have formulated new quantum model of the QCD vacuum using the effective
potential approach for composite operators. It is based on the existence and
importance of such kind of the nonperturbative, topologically nontrivial
excitations of gluon field configurations, which can be effectively correctly
described by the -type behavior of the full gluon propagator in the
deep infrared domain. The ultraviolet part of the full gluon propagator was
approximated by the asymptotic freedom to-leading order perturbative logarithm
term of the running coupling constant. Despite the vacuum energy density
remains badly divergent, we have formulated a method how to establish a finite
(in the ultraviolet limit) relation between the two scale parameters of our
model. We have expressed the asymptotic scale parameter as times
the nonperturbative scale, which is inevitably contained in any realistic
Ansatz for the full gluon propagator.Comment: 16 pages, no figures, no tables, to appear in Phys. Lett.
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Econometrics: A bird's eye view
As a unified discipline, econometrics is still relatively young and has been transforming and expanding very rapidly over the past few decades. Major advances have taken place in the analysis of cross sectional data by means of semi-parametric and non-parametric techniques. Heterogeneity of economic relations across individuals, firms and industries is increasingly acknowledge and attempts have been made to take them into account either by integrating out their effects or by modeling the sources of heterogeneity when suitable panel data exists. The counterfactual considerations that underlie policy analysis and treatment evaluation have been given a more satisfactory foundation. New time series econometric techniques have been developed and employed extensively in the areas of macroeconometrics and finance. Non-linear econometric techniques are used increasingly in the analysis of cross section and time series observations. Applications of Bayesian techniques to econometric problems have been given new impetus largely thanks to advances in computer power and computational techniques. The use of Bayesian techniques have in turn provided the investigators with a unifying framework where the tasks and forecasting, decision making, model evaluation and learning can be considered as parts of the same interactive and iterative process; thus paving the way for establishing the foundation of the "real time econometrics". This paper attempts to provide an overview of some of these developments
Krylov subspace approximations for the exponential Euler method: error estimates and the harmonic Ritz approximant
We study Krylov subspace methods for approximating the matrix-function vector product φ(tA)b where φ(z) = [exp(z) - 1]/z. This product arises in the numerical integration of large stiff systems of differential equations by the Exponential Euler Method, where A is the Jacobian matrix of the system. Recently, this method has found application in the simulation of transport phenomena in porous media within mathematical models of wood drying and groundwater flow. We develop an a posteriori upper bound on the Krylov subspace approximation error and provide a new interpretation of a previously published error estimate. This leads to an alternative Krylov approximation to φ(tA)b, the so-called Harmonic Ritz approximant, which we find does not exhibit oscillatory behaviour of the residual error
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