2,583 research outputs found
An inviscid dyadic model of turbulence: the fixed point and Onsager's conjecture
Properties of an infinite system of nonlinearly coupled ordinary differential
equations are discussed. This system models some properties present in the
equations of motion for an inviscid fluid such as the skew symmetry and the
3-dimensional scaling of the quadratic nonlinearity. It is proved that the
system with forcing has a unique equilibrium and that every solution blows up
in finite time in -norm. Onsager's conjecture is confirmed for the
model system
Hybrid Deterministic-Stochastic Methods for Data Fitting
Many structured data-fitting applications require the solution of an
optimization problem involving a sum over a potentially large number of
measurements. Incremental gradient algorithms offer inexpensive iterations by
sampling a subset of the terms in the sum. These methods can make great
progress initially, but often slow as they approach a solution. In contrast,
full-gradient methods achieve steady convergence at the expense of evaluating
the full objective and gradient on each iteration. We explore hybrid methods
that exhibit the benefits of both approaches. Rate-of-convergence analysis
shows that by controlling the sample size in an incremental gradient algorithm,
it is possible to maintain the steady convergence rates of full-gradient
methods. We detail a practical quasi-Newton implementation based on this
approach. Numerical experiments illustrate its potential benefits.Comment: 26 pages. Revised proofs of Theorems 2.6 and 3.1, results unchange
Analysis of nuclear waste disposal in space, phase 3. Volume 2: Technical report
The options, reference definitions and/or requirements currently envisioned for the total nuclear waste disposal in space mission are summarized. The waste form evaluation and selection process is documented along with the physical characteristics of the iron nickel-base cermet matrix chosen for disposal of commercial and defense wastes. Safety aspects of radioisotope thermal generators, the general purpose heat source, and the Lewis Research Center concept for space disposal are assessed as well as the on-pad catastrophic accident environments for the uprated space shuttle and the heavy lift launch vehicle. The radionuclides that contribute most to long-term risk of terrestrial disposal were determined and the effects of resuspension of fallout particles from an accidental release of waste material were studied. Health effects are considered. Payload breakup and rescue technology are discussed as well as expected requirements for licensing, supporting research and technology, and safety testing
Analysis of nuclear waste disposal in space, phase 3. Volume 1: Executive summary of technical report
The objectives, approach, assumptions, and limitations of a study of nuclear waste disposal in space are discussed with emphasis on the following: (1) payload characterization; (2) safety assessment; (3) health effects assessment; (4) long-term risk assessment; and (5) program planning support to NASA and DOE. Conclusions are presented for each task
To the modification of methods of nuclear chronometry in astrophysics and geophysics
In practically all known till now methods of nuclear chronometry there were
usually taken into account the life-times of only fundamental states of
-radioactive nuclei. But in the processes of nuclear synthesis in stars
and under the influence of the constant cosmic radiation on surfaces of planets
the excitations of the -radioactive nuclei are going on. Between them
there are the states with the excited -particles inside the parent
nuclei and so with much smaller life-times. And inside the large masses of
stellar, terrestrial and meteoric substances the transitions between different
internal conditions of radioactive nuclei are accompanied by infinite chains of
the -radiations with the subsequent -absorptions, the further
-radiations etc. For the description of the -decay evolution
with considering of such excited states and multiple -radiations and
-absorptions inside stars and under the influence of the cosmic
radiation on the earth surface we present the quantum-mechanical approach,
which is based on the generalized Krylov-Fock theorem.
Some simple estimations are also presented. They bring to the conclusion that
the usual (non-corrected) "nuclear clocks" do really indicate not to realistic
values but to the \emph{upper limits} of the durations of the -decay
stellar and planet processes.Comment: 6 pages, Standard LaTeX v.2
The fundamental solution and Strichartz estimates for the Schr\"odinger equation on flat euclidean cones
We study the Schr\"odinger equation on a flat euclidean cone of cross-sectional radius , developing
asymptotics for the fundamental solution both in the regime near the cone point
and at radial infinity. These asymptotic expansions remain uniform while
approaching the intersection of the "geometric front", the part of the solution
coming from formal application of the method of images, and the "diffractive
front" emerging from the cone tip. As an application, we prove Strichartz
estimates for the Schr\"odinger propagator on this class of cones.Comment: 21 pages, 4 figures. Minor typos corrected. To be published in Comm.
Math. Phy
Nonlinear Instability for the Critically Dissipative Quasi-Geostrophic Equation
We prove that linear instability implies non-linear instability in the energy
norm for the critically dissipative quasi-geostrophic equation.Comment: 16 pages, corrected typos, a global bound that was obtained for the
unforced equation by Kiselev-Nazarov-Volberg obtained for the forced equation
and utilized in the paper
Hadamard States and Adiabatic Vacua
Reversing a slight detrimental effect of the mailer related to TeXabilityComment: 10pages, LaTeX (RevTeX-preprint style
Inexact restoration method for derivative-free optimization with smooth constraints
Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)A new method is introduced for solving constrained optimization problems in which the derivatives of the constraints are available but the derivatives of the objective function are not. The method is based on the inexact restoration framework, by means of which each iteration is divided in two phases. In the first phase one considers only the constraints, in order to improve feasibility. In the second phase one minimizes a suitable objective function subject to a linear approximation of the constraints. The second phase must be solved using derivative-free methods. An algorithm introduced recently by Kolda, Lewis, and Torczon for linearly constrained derivative-free optimization is employed for this purpose. Under usual assumptions, convergence to stationary points is proved. A computer implementation is described and numerical experiments are presented.A new method is introduced for solving constrained optimization problems in which the derivatives of the constraints are available but the derivatives of the objective function are not. The method is based on the inexact restoration framework, by means of23211891213CNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOFAPERJ - FUNDAÇÃO CARLOS CHAGAS FILHO DE AMPARO À PESQUISA DO ESTADO DO RIO DE JANEIROFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)CNPq [E-26/171.164/2003-APQ1]FAPESP [FAPESP 2011-51305-0]FAPESP [03/09169-6, 06/53768-0, 07/06663-0, 08/00468-4]E-26/171.164/2003–APQ12011-51305-0; 03/09169-6; 06/53768-0; 07/06663-0; 08/00468-4sem informaçãoWe are indebted to associate editor Prof. Margaret Wright and two anonymous referees for many useful comments and remarks that led to significant improvement of this pape
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