Discrete filter operators for large‐eddy simulation using high‐order spectral difference methods

The combination of a high‐order unstructured spectral difference (SD) spatial discretization scheme with sub‐grid scale (SGS) modeling for large‐eddy simulation is investigated with particular focus on the consistent implementation of a structural mixed model based on the scale similarity hypothesis. The difficult task of deriving a consistent formulation for the discrete filter within the SD element of arbitrary order led to the development of a new class of three‐dimensional constrained discrete filters. The discrete filters satisfy a set of selected criteria and are completely local within the SD element. Their weights can be automatically computed at run time from the number of solution points within each element and the expected filter cutoff length scale. The novel discrete filters can be applied to any SGS model involving explicit filtering and to a broad class of high‐order discontinuous finite element numerical schemes. The code is applied to the computation of turbulent channel flows at three Reynolds numbers, namely Re_τ = 180, 395, and 590 (based on the friction velocity u_τ and channel half‐width δ). Results from computations with and without the SGS model are compared against results from direct numerical simulation. The numerical experiments suggest that the results are sensitive to the use of the SGS model, even when a high‐order numerical scheme is used, especially when the grid resolution is kept relatively low and mostly in terms of resolved Reynolds stresses. Results obtained using existing filters based on the projection of the solution over lower‐order polynomial bases are also shown and demonstrate that these filters are inadequate for SGS modeling purposes, mostly because of their inability to enforce the selected cutoff length scale with sufficient accuracy. The use of the similarity mixed formulation proved to be particularly accurate in reproducing SGS interactions, confirming that its well‐known potential can be realized in conjunction with state‐of‐the‐art high‐order numerical schemes.Copyright © 2012 John Wiley & Sons, Ltd.     

Uniform persistence for population interaction models with time delay

In this paper uniform persistence is establised for kolmogorov type Prey‐Predator and competion models with per capitals ent growth rates that are dependent on time‐lagged population densities.     

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Homogeneity of variance and correlation coefficients is one of assumptions in the analysis of longitudinal data.However, the assumption can be challenged. In this paper, we mainly propose and analyze nonlinear mixed effects models for longitudinal data with exponential correlation covariance structure, intend to introduce Huber's function in the log likelihood function and get robust estimation (M-estimation) by Fisher scoring method. Score test statistics for homogeneity of variance and correlation coefficient based on M-estimation are then studied. A simulation study is carried to assess the performance of test statistics and the method we proposed in the paper is illustrated by an actual data example.     

Ratio-conjugation tool and its application in linear optimization models†

The ratio-conjugation-tool (RC) is constructed systematically, and its applicability for analysis of economic models is demonstrated. One of the main results establishes a general formula for RC of aggregative function. This tool is applied to the analysis of linear economic dynamics models of Neumann–Gale type which can be solved by a dynamic programming method: for each direct problem we construct the corresponding dual RC-problem. Moreover, we consider three examples of the most important economic dynamics models and look at these now from a unified general position.     

Verification of the Usefulness of Radiotracing Methods in Hydrodynamic Investigations

In the paper comparison of accuracy of two methods used for investigations of hydrodynamic in continuous flow tanks has been made. Basis for the comparison is the experimental work performed for big industrial wastewater concentration equalization tank. The first method is based on the radiotracer experiment while the second one uses the analysis of response on sudden change of the technological parameters. The radiotracer method has better accuracy connected with the shorter sampling period.

Ks wird die Genauigkeit zweier Methoden zur Untersuchting der Hydrodynamik von kontinuierlich arbeitenden Flüssigkeitsbehältern verglichen. Grundlage dafür sind experimentelle Untersuchungen an groβen Industrieabwasser-Ausgleichsbehältern. Die erste Methode bedient sich der Radiotracertechnik, während die zweite Methode auf einer plötzlichen Veränderung der technologischcn Parameter beruht. Es zeigt sich, daβ die Radiotracermethoden die besseren Ergebnisse liefert, wobei auβerdem noch kürzere Probenaltmeperioden von Vorteil sind.     

Motzkin numbers out of Random Domino Automaton

Motzkin numbers are derived from a special case of Random Domino Automaton – recently proposed a slowly driven system being a stochastic toy model of earthquakes. It is also a generalisation of 1D Drossel–Schwabl forest-fire model. A solution of the set of equations describing stationary state of Random Domino Automaton in inverse-power case is presented. A link with Motzkin numbers allows to present explicit form of asymptotic behaviour of the automaton.     

Computation of the hindrance factor for the diffusion for nanoconfined ions: molecular dynamics simulations versus continuum-based models

We report the self-diffusion coefficients and hindrance factor for the diffusion of ions into cylindrical hydrophilic silica nanopores (hydrated silica) determined from molecular dynamics (MD) simulations. We make a comparison with the hindered diffusion coefficients used in continuum-based models of nanofiltration (NF). Hindrance factors for diffusion estimated from the macroscopic hydrodynamic theory were found to be in fair quantitative agreement with MD simulations for a protonated pore, but they strongly overestimate diffusion inside a deprotonated pore.     

A dynamic process interpretation of the sparse ERGM reference model

Exponential family random graph models (ERGMs) can be understood in terms of a set of structural biases that act on an underlying reference distribution. This distribution determines many aspects of the behavior and interpretation of the ERGM families incorporating it. One important innovation in this area has been the development of an ERGM reference model that produces realistic behavior when generalized to sparse networks of varying sizes. Here, we show that this model can be derived from a latent dynamic process in which tie formation takes place within small local settings between which individuals move. This derivation provides one possible micro-process interpretation of the sparse ERGM reference model and sheds light on the conditions under which constant mean degree scaling can emerge.