Testing multiple mapping conditioning mixing for Monte Carlo probability density function simulations

Mitarai [Phys. Fluids 17, 047101 (2005)] compared turbulent combustion models against homogeneous direct numerical simulations with extinction/recognition phenomena. The recently suggested multiple mapping conditioning (MMC) was not considered and is simulated here for the same case with favorable results. Implementation issues crucial for successful MMC simulations are also discussed.

On the inverse parabolicity of pdf equations in turbulent flows

The focus of the present work is the well-known feature of the probability density function (PDF) transport equations in turbulent flows-the inverse parabolicity of the equations. While it is quite common in fluid mechanics to interpret equations with direct (forward-time) parabolicity as diffusive (or as a combination of diffusion, convection and reaction), the possibility of a similar interpretation for equations with inverse parabolicity is not clear. According to Einstein's point of view, a diffusion process is associated with the random walk of some physical or imaginary particles, which can be modelled by a Markov diffusion process. In the present paper it is shown that the Markov diffusion process directly associated with the PDF equation represents a reasonable model for dealing with the PDFs of scalars but it significantly underestimates the diffusion rate required to simulate turbulent dispersion when the velocity components are considered.

Statistical tests of load-unload response ratio signals by lattice solid model: Implication to tidal triggering and earthquake prediction

Statistical tests of Load-Unload Response Ratio (LURR) signals are carried in order to verify statistical robustness of the previous studies using the Lattice Solid Model (MORA et al., 2002b). In each case 24 groups of samples with the same macroscopic parameters (tidal perturbation amplitude A, period T and tectonic loading rate k) but different particle arrangements are employed. Results of uni-axial compression experiments show that before the normalized time of catastrophic failure, the ensemble average LURR value rises significantly, in agreement with the observations of high LURR prior to the large earthquakes. In shearing tests, two parameters are found to control the correlation between earthquake occurrence and tidal stress. One is, A/(kT) controlling the phase shift between the peak seismicity rate and the peak amplitude of the perturbation stress. With an increase of this parameter, the phase shift is found to decrease. Another parameter, AT/k, controls the height of the probability density function (Pdf) of modeled seismicity. As this parameter increases, the Pdf becomes sharper and narrower, indicating a strong triggering. Statistical studies of LURR signals in shearing tests also suggest that except in strong triggering cases, where LURR cannot be calculated due to poor data in unloading cycles, the larger events are more likely to occur in higher LURR periods than the smaller ones, supporting the LURR hypothesis.

Matching conditional moments in PDF modelling of nonpremixed combustion

The rate of generation of fluctuations with respect to the scalar values conditioned on the mixture fraction, which significantly affects turbulent nonpremixed combustion processes, is examined. Simulation of the rate in a major mixing model is investigated and the derived equations can assist in selecting the model parameters so that the level of conditional fluctuations is better reproduced by the models. A more general formulation of the multiple mapping conditioning (MMC) model that distinguishes the reference and conditioning variables is suggested. This formulation can be viewed as a methodology of enforcing certain desired conditional properties onto conventional mixing models. Examples of constructing consistent MMC models with dissipation and velocity conditioning as well as of combining MMC with large eddy simulations (LES) are also provided. (c) 2005 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Population-based continuous optimization, probabilistic modelling and mean shift

Evolutionary algorithms perform optimization using a population of sample solution points. An interesting development has been to view population-based optimization as the process of evolving an explicit, probabilistic model of the search space. This paper investigates a formal basis for continuous, population-based optimization in terms of a stochastic gradient descent on the Kullback-Leibler divergence between the model probability density and the objective function, represented as an unknown density of assumed form. This leads to an update rule that is related and compared with previous theoretical work, a continuous version of the population-based incremental learning algorithm, and the generalized mean shift clustering framework. Experimental results are presented that demonstrate the dynamics of the new algorithm on a set of simple test problems.

Time-evolution of highly localized positive-energy states of the free Dirac electron

Highly localized positive-energy states of the free Dirac electron are constructed and shown to evolve in a simple way under the action of Dirac's equation. When the initial uncertainty in position is small on the scale of the Compton wavelength, there is an associated uncertainty in the mean energy that is large compared with the rest mass of the electron. However, this does not lead to any breakdown of the one-particle description, associated with the possibility of pair-production, but rather leads to a rapid expansion of the probability density outwards from the point of localization, at speeds close to the speed of light.

Structure and dynamics of ASC2, a pyrin domain-only protein that regulates inflammatory signaling

Pyrin domain (PYD)-containing proteins are key components of pathways that regulate inflammation, apoptosis, and cytokine processing. Their importance is further evidenced by the consequences of mutations in these proteins that give rise to autoimmune and hyperinflammatory syndromes. PYDs, like other members of the death domain ( DD) superfamily, are postulated to mediate homotypic interactions that assemble and regulate the activity of signaling complexes. However, PYDs are presently the least well characterized of all four DD subfamilies. Here we report the three-dimensional structure and dynamic properties of ASC2, a PYD-only protein that functions as a modulator of multidomain PYD-containing proteins involved in NF-KB and caspase-1 activation. ASC2 adopts a six-helix bundle structure with a prominent loop, comprising 13 amino acid residues, between helices two and three. This loop represents a divergent feature of PYDs from other domains with the DD fold. Detailed analysis of backbone N-15 NMR relaxation data using both the Lipari-Szabo model-free and reduced spectral density function formalisms revealed no evidence of contiguous stretches of polypeptide chain with dramatically increased internal motion, except at the extreme N and C termini. Some mobility in the fast, picosecond to nanosecond timescale, was seen in helix 3 and the preceding alpha 2-alpha 3 loop, in stark contrast to the complete disorder seen in the corresponding region of the NALP1 PYD. Our results suggest that extensive conformational flexibility in helix 3 and the alpha 2-alpha 3 loop is not a general feature of pyrin domains. Further, a transition from complete disorder to order of the alpha 2-alpha 3 loop upon binding, as suggested for NALP1, is unlikely to be a common attribute of pyrin domain interactions.

No relationship between low-density lipoproteins and endothelial function in hemodialysis patients

Background: Relationships between low-density lipoprotein cholesterol and endothelial function in hemodialysis patients have yet to be investigated. Furthermore, current reporting of endothelial function data using flow-mediated dilatation has recognised limitations. The aims of the study were to determine the relationship between low-density lipoproteins and endothelial function in hemodialysis patients and to investigate the validity of determining the area under the curve for data collected during the flow-mediated dilatation technique. Methods: Brachial artery responses to reactive hyperemia (endothelial-dependent) and glyceryl trinitrate (endothelial-independent) were assessed in 19 hemodialysis patients using high-resolution ultrasound. Lipid profiles and other factors known to effect brachial artery reactivity were also measured prior to the flow-mediated dilatation technique. Results: There were no significant relationships between serum low-density lipoproteins and endothelial-dependent or -independent vasodilation using absolute change (mm), relative change (%), time to peak change (s) or area under the curve (mm(.)s). In hemodialysis patients with atherosclerosis, area under the curve analysis showed a significantly (p < 0.05) decreased endothelial-dependent response (mean +/- S.D.: 19.2 +/- 17.4) compared to non-atherosclerotic patients (42.3 +/- 28.6). However, when analysing these data using absolute change, relative change or time to peak dilatation, there were no significant differences between the two groups. Conclusions: In summary, there was no relationship between low-density lipoproteins and endothelial function in hemodialysis patients. In addition, area under the curve analysis of flow-mediated vasodilatation data may be a useful method of determining the temporal vascular response during the procedure. (c) 2004 Elsevier Ireland Ltd. All rights reserved.