SDP vs. LP Relaxations for the Moment Approach in Some Performance Evaluation Problems

2004 ◽  
Vol 20 (4) ◽  
pp. 439-456 ◽  
Author(s):  
Jean-Bernard Lasserre ◽  
Tomás Prieto-Rumeau
Keyword(s):  
Performance Evaluation ◽  
Moment Approach ◽  
The Moment

THE LANGEVIN OR KRAMERS APPROACH TO BIOLOGICAL MODELING

2004 ◽  
Vol 14 (10) ◽  
pp. 1561-1583 ◽  
Author(s):  
KARL P. HADELER ◽  
THOMAS HILLEN ◽  
FRITHJOF LUTSCHER
Keyword(s):  
Wave Equations ◽  
Space Variable ◽  
Linear Partial Differential Equation ◽  
Reaction Diffusion ◽  
Nonlinear Problems ◽  
Kramers Equation ◽  
Moment Approach ◽  
The Moment ◽  
Nonlinear Damped Wave Equations ◽  
And Diffusion

In the Langevin or Ornstein–Uhlenbeck approach to diffusion, stochastic increments are applied to the velocity rather than to the space variable. The density of this process satisfies a linear partial differential equation of the general form of a transport equation which is hyperbolic with respect to the space variable but parabolic with respect to the velocity variable, the Klein–Kramers or simply Kramers equation. This modeling approach allows for a more detailed description of individual movement and orientation dependent interaction than the frequently used reaction diffusion framework.For the Kramers equation, moments are computed, the infinite system of moment equations is closed at several levels, and telegraph and diffusion equations are derived as approximations. Then nonlinearities are introduced such that the semi-linear reaction Kramers equation describes particles which move and interact on the same time-scale. Also for these nonlinear problems a moment approach is feasible and yields nonlinear damped wave equations as limiting cases.We apply the moment method to the Kramers equation for chemotactic movement and obtain the classical Patlak–Keller–Segel model. We discuss similarities between chemotactic movement of bacteria and gravitational movement of physical particles.

scholarly journals Improving the moment approach for astrometric binaries: possible application to Cygnus X-1

2014 ◽  
Vol 66 (5) ◽  
Author(s):  
Kei Yamada ◽  
Masaki S. Yamaguchi ◽  
Hideki Asada ◽  
Naoteru Gouda
Keyword(s):  
Moment Approach ◽  
The Moment ◽  
Astrometric Binaries

scholarly journals Derivation of Hydrodynamics for Multi-Relaxation Time Lattice Boltzmann using the Moment Approach

2013 ◽  
Vol 13 (3) ◽  
pp. 614-628 ◽  
Author(s):  
Goetz Kaehler ◽  
Alexander J. Wagner
Keyword(s):  
Relaxation Time ◽  
Lattice Boltzmann ◽  
Collision Operator ◽  
Significant Degree ◽  
Space Representation ◽  
Peculiar Velocities ◽  
Lattice Boltzmann Simulation ◽  
Moment Approach ◽  
The Moment ◽  
Lattice Boltzmann Models

AbstractA general analysis of the hydrodynamic limit of multi-relaxation time lattice Boltzmann models is presented. We examine multi-relaxation time BGK collision operators that are constructed similarly to those for the MRT case, however, without explicitly moving into a moment space representation. The corresponding ‘moments’ are derived as left eigenvectors of said collision operator in velocity space. Consequently we can, in a representation independent of the chosen base velocity set, generate the conservation equations. We find a significant degree of freedom in the choice of the collision matrix and the associated basis which leaves the collision operator invariant. We explain why MRT implementations in the literature reproduce identical hydrodynamics despite being based on different orthogonalization relations. More importantly, however, we outline a minimal set of requirements on the moment base necessary to maintain the validity of the hydrodynamic equations. This is particularly useful in the context of position and time-dependent moments such as those used in the context of peculiar velocities and some implementations of fluctuations in a lattice-Boltzmann simulation.

scholarly journals A new approach of estimating the galactic thermal dust and synchrotron polarized emission template in the microwave bands

2021 ◽  
Vol 507 (3) ◽  
pp. 4618-4637
Author(s):  
Debabrata Adak
Keyword(s):  
Expansion Method ◽  
Component Separation ◽  
Simultaneous Estimation ◽  
Microwave Background ◽  
New Approach ◽  
Constraint Equations ◽  
Multiple Frequencies ◽  
Moment Approach ◽  
The Moment ◽  
Complex Coefficients

ABSTRACT The Internal Linear Combination (ILC) method has been extensively used to extract the cosmic microwave background (CMB) anisotropy map from foreground contaminated multifrequency maps. However, the performance of simple ILC is limited and can be significantly improved by heavily constraint equations, dubbed constrained ILC (cILC). The standard ILC and cILC work on spin-0 fields. Recently, a generalised version of ILC has been developed, named polarization ILC (PILC), in which Q ± iU at multiple frequencies are combined using complex coefficients to estimate Stokes Q and U maps. A statistical moment expansion method has recently been developed for high-precision modelling of the galactic foregrounds. This paper develops a semiblind component separation method combining the moment approach of foreground modelling with a generalised version of the PILC method for heavily constraint equations. The algorithm is developed in pixel space over a spin-2 field. We demonstrate the performance of the method on three sets of absolutely calibrated simulated maps at WMAP and Planck frequencies with varying foreground models. We apply this component separation technique in simultaneous estimation of Stokes Q and U maps of the thermal dust at 353 GHz and synchrotron at 30 GHz. We also recover both dust and synchrotron maps at 100 and 143 GHz, where separating two components is challenging.

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