2,414 research outputs found
Assessing stochastic algorithms for large scale nonlinear least squares problems using extremal probabilities of linear combinations of gamma random variables
This article considers stochastic algorithms for efficiently solving a class
of large scale non-linear least squares (NLS) problems which frequently arise
in applications. We propose eight variants of a practical randomized algorithm
where the uncertainties in the major stochastic steps are quantified. Such
stochastic steps involve approximating the NLS objective function using
Monte-Carlo methods, and this is equivalent to the estimation of the trace of
corresponding symmetric positive semi-definite (SPSD) matrices. For the latter,
we prove tight necessary and sufficient conditions on the sample size (which
translates to cost) to satisfy the prescribed probabilistic accuracy. We show
that these conditions are practically computable and yield small sample sizes.
They are then incorporated in our stochastic algorithm to quantify the
uncertainty in each randomized step. The bounds we use are applications of more
general results regarding extremal tail probabilities of linear combinations of
gamma distributed random variables. We derive and prove new results concerning
the maximal and minimal tail probabilities of such linear combinations, which
can be considered independently of the rest of this paper
Solid rocket technology advancements for space tug and IUS applications
In order for the shuttle tug or interim upper stage (IUS) to capture all the missions in the current mission model for the tug and the IUS, an auxiliary or kick stage, using a solid propellant rocket motor, is required. Two solid propellant rocket motor technology concepts are described. One concept, called the 'advanced propulsion module' motor, is an 1800-kg, high-mass-fraction motor, which is single-burn and contains Class 2 propellent. The other concept, called the high energy upper stage restartable solid, is a two-burn (stop-restartable on command) motor which at present contains 1400 kg of Class 7 propellant. The details and status of the motor design and component and motor test results to date are presented, along with the schedule for future work
AdS rotating non-Abelian black holes
We present arguments for the existence of charged, rotating black holes with
equal magnitude angular momenta in Einstein-Yang-Mills theory with
negative cosmological constant. These solutions posses a regular horizon of
spherical topology and approach asymptotically the Anti-de Sitter spacetime
background. The black hole solutions have also an electric charge and a
nonvanishing magnetic flux through the sphere at infinity. Different from the
static case, no regular solution with a nonvanishing angular momenta is found
for a vanishing event horizon radius.Comment: 14 pages, 7 figure
Gravitating Semilocal strings
We discuss the properties of semilocal strings minimally coupled to gravity.
Semilocal strings are solutions of the bosonic sector of the Standard Model in
the limit (where is the Weinberg angle) and
correspond to embedded Abelian-Higgs strings for a particular choice of the
scalar doublet. We focus on the limit where the gauge boson mass is equal to
the Higgs boson mass such that the solutions fulfill the
Bogomolnyi-Prasad-Sommerfield (BPS) bound.Comment: Contribution to the Proceedings of the Spanish Relativity Meeting
(ERE) 2009, Bilbao, Spai
Modeling planar degenerate wetting and anchoring in nematic liquid crystals
We propose a simple surface potential favoring the planar degenerate
anchoring of nematic liquid crystals, i.e., the tendency of the molecules to
align parallel to one another along any direction parallel to the surface. We
show that, at lowest order in the tensorial Landau-de Gennes order-parameter,
fourth-order terms must be included. We analyze the anchoring and wetting
properties of this surface potential. In the nematic phase, we find the desired
degenerate planar anchoring, with positive scalar order-parameter and some
surface biaxiality. In the isotropic phase, we find, in agreement with
experiments, that the wetting layer may exhibit a uniaxial ordering with
negative scalar order-parameter. For large enough anchoring strength, this
negative ordering transits towards the planar degenerate state
Regularization-robust preconditioners for time-dependent PDE constrained optimization problems
In this article, we motivate, derive and test �effective preconditioners to be used with the Minres algorithm for solving a number of saddle point systems, which arise in PDE constrained optimization problems. We consider the distributed control problem involving the heat equation with two diff�erent functionals, and the Neumann boundary control problem involving Poisson's equation and the heat equation. Crucial to the eff�ectiveness of our preconditioners in each case is an eff�ective approximation of the Schur complement of the matrix system. In each case, we state the problem being solved, propose the preconditioning approach, prove relevant eigenvalue bounds, and provide numerical results which demonstrate that our solvers are eff�ective for a wide range of regularization parameter values, as well as mesh sizes and time-steps
Fast iterative solution of reaction-diffusion control problems arising from chemical processes
PDE-constrained optimization problems, and the development of preconditioned iterative methods for the efficient solution of the arising matrix system, is a field of numerical analysis that has recently been attracting much attention. In this paper, we analyze and develop preconditioners for matrix systems that arise from the optimal control of reaction-diffusion equations, which themselves result from chemical processes. Important aspects in our solvers are saddle point theory, mass matrix representation and effective Schur complement approximation, as well as the outer (Newton) iteration to take account of the nonlinearity of the underlying PDEs
Experimental investigation of the effects of cooling on friction and on boundary-layer transition for low-speed gas flow at the entry of a tube
Orbits in the Field of a Gravitating Magnetic Monopole
Orbits of test particles and light rays are an important tool to study the
properties of space-time metrics. Here we systematically study the properties
of the gravitational field of a globally regular magnetic monopole in terms of
the geodesics of test particles and light. The gravitational field depends on
two dimensionless parameters, defined as ratios of the characteristic mass
scales present. For critical values of these parameters the resulting metric
coefficients develop a singular behavior, which has profound influence on the
properties of the resulting space-time and which is clearly reflected in the
orbits of the test particles and light rays.Comment: 24 pages, 15 figures. Accepted for publication in GR
Spherically symmetric Yang-Mills solutions in a (4+n)- dimensional space-time
We consider the Einstein-Yang-Mills Lagrangian in a (4+n)-dimensional
space-time. Assuming the matter and metric fields to be independent of the n
extra coordinates, a spherical symmetric Ansatz for the fields leads to a set
of coupled ordinary differential equations. We find that for n > 1 only
solutions with either one non-zero Higgs field or with all Higgs fields
constant exist. We construct the analytic solutions which fulfill this
conditions for arbitrary n, namely the Einstein-Maxwell-dilaton solutions. We
also present generic solutions of the effective 4-dimensional
Einstein-Yang-Mills-Higgs-dilaton model, which possesses n Higgs triplets
coupled in a specific way to n independent dilaton fields. These solutions are
the abelian Einstein-Maxwell- dilaton solutions and analytic non-abelian
solutions, which have diverging Higgs fields. In addition, we construct
numerically asymptotically flat and finite energy solutions for n=2.Comment: 15 Latex pages, 4 eps figures; v2: discussion of results revisite
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