The equivalence of the discretized equations resulting from both uctuation splitting and nite volume schemes is demonstrated in one dimension. Scalar equations are considered for advection, di usion, and combined advection/diffusion. Analysis of systems is performed for the Euler and Navier-Stokes equations of gas dynamics. Non-uniform mesh-point distributions are included in the analyses.

In the context of the dynamical evolution in a non-stationary thermal bath, we construct a family of uctuation relations for the entropy production that are not veri ed by the work performed on the system. We exhibit uctuation relations which are global versions either of the generalized Fluctuation-Dissipation Theorem around a non-equilibrium di usion or of the usual Fluctuation-Dissipation Th...

Eternally innating universes can contain large thermalized regions with different values of the constants of Nature and with diierent density uctuation spectra. To nd the probability for a `typical' observer to detect a certain set of constants, or a certain uctuation spectrum, one needs to compare the volumes occupied by diierent types of regions. If the volumes are taken on an equal-time hype...

This paper considers segregation in collisional granular shearing ows from the experimental, computational, and theoretical standpoints. We focus on a phenomenon of segregation where the separation of grains by size or mass is driven by spatial gradients in the uctuation energy of the grains. We report experiments carried out in microgravity with a shear cell shaped as a race track and containi...

An analysis of the chemical composition between 300 and 1000 TeV based on the uctuation of the shower maximum using data from the AIROBICC and scintillator array of the HEGRA installation is presented. Within the errors the composition is in agreement with the low energy composition over the whole energy range. The chemical composition beyond about 100 TeV will provide a decisive clue about cos...

In this paper, we extend the Maximum Likelihood (ML) training algorithm to the Minimum Classiica-tion Error (MCE) training algorithm for discriminatively estimating the state-dependent polynomial coeecients in the stochastic trajectory model or the trended HMM originally proposed in 2]. The main motivation of this extension is the new model space for smoothness-constrained, state-bound speech t...

In this paper, we extend the maximum likelihood (ML) training algorithm to the minimum classification error (MCE) training algorithm for discriminatively estimating the state-dependent polynomial coefficients in the stochastic trajectory model or the trended hidden Markov model (HMM) originally proposed in [2]. The main motivation of this extension is the new model space for smoothness-constrai...