Home About us Contact
|
Home About us Contact | ||
|
|
||
Ensemble Averages (ensemble + average)
Selected AbstractsDiffractive imaging for periodic samples: retrieving one-dimensional concentration profiles across microfluidic channelsACTA CRYSTALLOGRAPHICA SECTION A, Issue 4 2007Oliver Bunk A technique has been developed that allows determination of the concentration profiles of colloidal solutions or any kind of fluid under confinement. Currently, submicrometre-wide channels are sampled with a resolution in the 10,nm range. The method comprises regular arrays of microfluidic channels and one-dimensional X-ray phase-retrieval techniques for the analysis of small-angle X-ray diffraction from the array structures. Recording the X-ray diffraction data requires a low dose on each individual channel since the sum of the signals from all channels is detected. The determined concentration profiles represent the ensemble average rather than individual entities and are obtained in a model-independent way. As an example, amplitude and phase of the exit field and concentration profiles for a colloidal fluid within confining channels of different widths are shown. [source] Tropical-cyclone intensification and predictability in three dimensionsTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 632 2008Nguyen Van Sang Abstract We present numerical-model experiments to investigate the dynamics of tropical-cyclone amplification and its predictability in three dimensions. For the prototype amplification problem beginning with a weak-tropical-storm-strength vortex, the emergent flow becomes highly asymmetric and dominated by deep convective vortex structures, even though the problem as posed is essentially axisymmetric. The asymmetries that develop are highly sensitive to the boundary-layer moisture distribution. When a small random moisture perturbation is added in the boundary layer at the initial time, the pattern of evolution of the flow asymmetries is changed dramatically, and a non-negligible spread in the local and azimuthally-averaged intensity results. We conclude, first, that the flow on the convective scales exhibits a degree of randomness, and only those asymmetric features that survive in an ensemble average of many realizations can be regarded as robust; and secondly, that there is an intrinsic uncertainty in the prediction of maximum intensity using either maximum-wind or minimum-surface-pressure metrics. There are clear implications for the possibility of deterministic forecasts of the mesoscale structure of tropical cyclones, which may have a major impact on the intensity and on rapid intensity changes. Some other aspects of vortex structure are addressed also, including vortex-size parameters, and sensitivity to the inclusion of different physical processes or higher spatial resolution. We investigate also the analogous problem on a ,-plane, a prototype problem for tropical-cyclone motion. A new perspective on the putative role of the wind--evaporation feedback process for tropical-cyclone intensification is offered also. The results provide new insight into the fluid dynamics of the intensification process in three dimensions, and at the same time suggest limitations of deterministic prediction for the mesoscale structure. Larger-scale characteristics, such as the radius of gale-force winds and ,-gyres, are found to be less variable than their mesoscale counterparts. Copyright © 2008 Royal Meteorological Society [source] A field-scale infiltration model accounting for spatial heterogeneity of rainfall and soil saturated hydraulic conductivityHYDROLOGICAL PROCESSES, Issue 7 2006Renato Morbidelli Abstract This study first explores the role of spatial heterogeneity, in both the saturated hydraulic conductivity Ks and rainfall intensity r, on the integrated hydrological response of a natural slope. On this basis, a mathematical model for estimating the expected areal-average infiltration is then formulated. Both Ks and r are considered as random variables with assessed probability density functions. The model relies upon a semi-analytical component, which describes the directly infiltrated rainfall, and an empirical component, which accounts further for the infiltration of surface water running downslope into pervious soils (the run-on effect). Monte Carlo simulations over a clay loam soil and a sandy loam soil were performed for constructing the ensemble averages of field-scale infiltration used for model validation. The model produced very accurate estimates of the expected field-scale infiltration rate, as well as of the outflow generated by significant rainfall events. Furthermore, the two model components were found to interact appropriately for different weights of the two infiltration mechanisms involved. Copyright © 2005 John Wiley & Sons, Ltd. [source] Stochastic computational modelling of highly heterogeneous poroelastic media with long-range correlationsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 1 2004Diego G. Frias Abstract The compaction of highly heterogeneous poroelastic reservoirs with the geology characterized by long-range correlations displaying fractal character is investigated within the framework of the stochastic computational modelling. The influence of reservoir heterogeneity upon the magnitude of the stresses induced in the porous matrix during fluid withdrawal and rock consolidation is analysed by performing ensemble averages over realizations of a log-normally distributed stationary random hydraulic conductivity field. Considering the statistical distribution of this parameter characterized by a coefficient of variation governing the magnitude of heterogeneity and a correlation function which decays with a power-law scaling behaviour we show that the combination of these two effects result in an increase in the magnitude of effective stresses of the rock during reservoir depletion. Further, within the framework of a perturbation analysis we show that the randomness in the hydraulic conductivity gives rise to non-linear corrections in the upscaled poroelastic equations. These corrections are illustrated by a self-consistent recursive hierarchy of solutions of the stochastic poroelastic equations parametrized by a scale parameter representing the fluctuating log-conductivity standard deviation. A classical example of land subsidence caused by fluid extraction of a weak reservoir is numerically simulated by performing Monte Carlo simulations in conjunction with finite elements discretizations of the poroelastic equations associated with an ensemble of geologies. Numerical results illustrate the effects of the spatial variability and fractal character of the permeability distribution upon the evolution of the Mohr,Coulomb function of the rock. Copyright © 2004 John Wiley & Sons, Ltd. [source] On the clustering phase transition in self-gravitating N -body systemsMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 1 2001Monica Cerruti-Sola The thermodynamic behaviour of self-gravitating N -body systems has been worked out by borrowing a standard method from molecular dynamics. The link between dynamics and thermodynamics is made in the microcanonical ensemble of statistical mechanics. Through the computation of basic thermodynamic observables and of the equation of state in the plane, the clustering phase transition appears to be of the second-order type. The dynamical,microcanonical averages are compared with their corresponding canonical ensemble averages, obtained through standard Monte Carlo computations. The latter seem to have completely lost any information about the phase transition. Finally, our results , obtained in a ,microscopic' framework , are compared with some existing theoretical predictions , obtained in a ,macroscopic' (thermodynamic) framework: qualitative and quantitative agreement is found, with an interesting exception. [source] The role of ,-, 310 -, and ,-helix in helix,coil transitionsPROTEIN SCIENCE, Issue 6 2003Roger Armen Abstract The conformational equilibrium between 310 - and ,-helical structure has been studied via high-resolution NMR spectroscopy by Millhauser and coworkers using the MW peptide Ac-AMAAKAWAAKA AAARA-NH2. Their 750-MHz nuclear Overhauser effect spectroscopy (NOESY) spectra were interpreted to reflect appreciable populations of 310 -helix throughout the peptide, with the greatest contribution at the N and C termini. The presence of simultaneous ,N(i,i + 2) and ,N(i,i + 4) NOE cross-peaks was proposed to represent conformational averaging between 310 - and ,-helical structures. In this study, we describe 25-nsec molecular dynamics simulations of the MW peptide at 298 K, using both an 8 Å and a 10 Å force-shifted nonbonded cutoff. The ensemble averages of both simulations are in reasonable agreement with the experimental helical content from circular dichroism (CD), the 3JHN, coupling constants, and the 57 observed NOEs. Analysis of the structures from both simulations revealed very little formation of contiguous i , i + 3 hydrogen bonds (310 -helix); however, there was a large population of bifurcated i , i + 3 and i , i + 4 ,-helical hydrogen bonds. In addition, both simulations contained considerable populations of ,-helix (i , i + 5 hydrogen bonds). Individual turns formed over residues 1,9, which we predict contribute to the intensities of the experimentally observed ,N(i,i + 2) NOEs. Here we show how sampling of both folded and unfolded structures can provide a structural framework for deconvolution of the conformational contributions to experimental ensemble averages. [source] | |||||||||||||