We survey conditions for rapid mixing of certain Markov chains, called Gibbs samplers, and uniqueness of certain probability measures with prescribed finite dimensional conditional distributions, called Gibbs measures...
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ISBN:
(纸本)9781604237924
We survey conditions for rapid mixing of certain Markov chains, called Gibbs samplers, and uniqueness of certain probability measures with prescribed finite dimensional conditional distributions, called Gibbs measures. By Tatikonda and Jordan's [1] sufficiency result, these criteria translate into conditions for convergence of the Sum-Product algorithm. The basic idea, which goes back to Dobrushin [2], is to show that the transition kernels (in the Gibbs sampler case) or the prescribed conditional distributions (in the Gibbs measure case) act as contractions on spaces of functions or measures, provided they are weakly influenced by neighboring sites. The contributions of this paper are as follows: We compare various notions of influence, unifying notation and terminology currently scattered across a large body of literature. We survey, generalize and extend existing proof techniques which fall in three broad categories: analytic arguments, coupling arguments, and arguments using path coupling. In particular, we extend all arguments from single sites to finite blocks and from total variation to Wasserstein distance;we introduce new matrix methods;we answer an open question by Weitz [3];and we provide evidence to support the superiority of path coupling, addressing a question raised by Sokal [4] regarding the dual relationship of analytic and coupling techniques.
A three-dimensional wave packet generated by a local disturbance in a two-dimensional hypersonic boundary layer flow is studied with the aid of the previously solved initialvalue problem. The solution can be presented...
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ISBN:
(纸本)1563478102
A three-dimensional wave packet generated by a local disturbance in a two-dimensional hypersonic boundary layer flow is studied with the aid of the previously solved initialvalue problem. The solution can be presented as a sum of modes consisting of continuous and discrete spectra of temporal stability theory. Two discrete modes, known as Mode S and Mode F, are of interest in high-speed flows since they may be involved in a laminar-turbulent transition scenario. The continuous and discrete spectra are analyzed numerically for a hypersonic flow. A comprehensive study of the spectrum is performed, including Reynolds number, Mach number and temperature factor effects. A specific disturbance consisting of an initial temperature spot is considered, and the receptivity to this initial temperature spot is computed for both the two-dimensional and three-dimensional cases. Using the analysis of the discrete and continuous spectrum, the inverse Fourier transform is computed numerically. The two-dimensional inverse Fourier transform is calculated for Mode F and Mode S. The Mode S result is compared with an asymptotic approximation of the Fourier integral, which is obtained using a Gaussian model as well as the method of steepest descent. Additionally, the three-dimensional inverse Fourier transform is found using an asymptotic approximation. Using the inverse Fourier transform computations, the development of the wave packet is studied, including effects due to Reynolds number, Mach number and temperature factor.
Using a coarse molecular-dynamics (CMD) approach with an appropriate choice of coarse variable (order parameter), we map the underlying effective free-energy landscape for the melting of a crystalline solid. Implement...
Using a coarse molecular-dynamics (CMD) approach with an appropriate choice of coarse variable (order parameter), we map the underlying effective free-energy landscape for the melting of a crystalline solid. Implementation of this approach provides a means for constructing effective free-energy landscapes of structural transitions in condensed matter. The predictions of the approach for the thermodynamic melting point of a model silicon system are in excellent agreement with those of “traditional” techniques for melting-point calculations, as well as with literature values.
A number of research groups and companies have succeeded in employing various SLS schemes to create low defect-density Si films on glass substrates for making high performance TFTs, In this paper, we first point out t...
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A number of research groups and companies have succeeded in employing various SLS schemes to create low defect-density Si films on glass substrates for making high performance TFTs, In this paper, we first point out that SLS can be utilized to just as effectively handle crystallization of thin Si films on polymer substrates, and then present preliminary results on high-performance circuits that are built using the materials.
This paper is concerned with the effect on the bulk motion of applying torque by external means to the particles of a suspension. Our investigation is based upon theoretical consideration of the motion of a dilute sus...
This paper is concerned with the effect on the bulk motion of applying torque by external means to the particles of a suspension. Our investigation is based upon theoretical consideration of the motion of a dilute suspension of permanently magnetized spheroids, in the presence of a uniform magnetic field, for cases in which the motion of a Newtonian fluid would be uni-directional. For convenience, we have divided the work into two parts: in the first, the particles are assumed to be perfectly spherical and the magnetic field strength to be arbitrary; in the second, the particles are taken as arbitrary spheroids (with their magnetic dipole axis coincident with the axis of revolution), but the magnetic field is assumed to be strong enough to ensure that the magnetic dipole axis of each particle is effectively aligned with the field vector H. We concentrate attention on the development of general criteria which allow an a priori determination as to whether the bulk motion remains uni-directional in the presence of particle couples, and (when the motion is uni-directional) whether the resultant velocity profile has the same form as for a Newtonian fluid. In addition, we evaluate the effective viscosity of the suspension for several representative cases in which the velocity field is Newtonian in form. Finally, as an example of the general situation in which the bulk velocity field does not remain uni-directional, we obtain the solution for the motion through a circular tube when the magnetic particles are spherical and the magnetic field is applied at right angles to the tube axis.
We present an equation-free computational approach to the study of the coarse-grained dynamics of finite assemblies of nonidentical coupled oscillators at and near full synchronization. We use coarse-grained observabl...
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We present an equation-free computational approach to the study of the coarse-grained dynamics of finite assemblies of nonidentical coupled oscillators at and near full synchronization. We use coarse-grained observables which account for the (rapidly developing) correlations between phase angles and natural frequencies. Exploiting short bursts of appropriately initialized detailed simulations, we circumvent the derivation of closures for the long-term dynamics of the assembly statistics.
In this paper we apply a multiobjective optimization model of Smart Growth to land development. The term Smart Growth is meant to describe development strategies-that do not promote urban sprawl. However, the term is ...
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Scattering theory for anisotropic media is a useful but mathematically very demanding subject. Previous work on scalar scattering in anisotropic media is presently extended to cover the effects of anisotropy on the en...
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A mathematical model for bioleaching at the agglomerate scale is developed. The agglomerate is defined as a unit volume of a heap which contains a solid phase (a size distribution of ore particles), a liquid phase (st...
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