Scaling properties in the production range of shear dominated flows

In large Reynolds number turbulence, isotropy is recovered as the scale is reduced and homogeneous-isotropic scalings are eventually observed. This picture is violated in many cases, e.g., wall bounded flows, where, due to the shear, different scaling laws emerge. This effect has been ascribed to the contamination of the inertial range by the larger anisotropic scales. The issue is addressed here by analyzing both numerical and experimental data for a homogeneous shear flow. In fact, under strong shear, the alteration of the scaling exponents is not induced by the contamination from the anisotropic sectors. Actually, the exponents are universal properties of the isotropic component of the structure functions of shear dominated flows. The implications are discussed in the context of turbulence near solid walls, where improved closure models would be advisable.     

Scaling analysis of phase fluctuations in experimental three-phase flows

The characterization of complex patterns arising from three-phase (e.g., oil-gas-water) flows is an important problem with significant engineering and industrial applications. Based solely on measured conductance fluctuation signals from experimental three-phase flows, we propose a method to characterize and distinguish three commonly observed flow patterns. Using the phase characterization method, we first calculate the instantaneous phase from the signals. Then, through performing a scaling analysis, detrended fluctuation analysis (DFA), we extract scaling behaviors associated with the phase fluctuations and find that the DFA scaling exponent is sensitive to the transition among different flow patterns, which can be used to characterize nonlinear dynamics of the three-phase flow. From a novel perspective, we investigate the three-phase flow in terms of phase characterization and scaling analysis. The results indicate that our method can provide new insights into the exploration of complex mechanism in flow pattern transition. The effectiveness of the method is demonstrated and its broader applicability is articulated.     

Heat exchange at laminar flow in rectangular channels

Numerical modeling of heat exchange at a laminar stationary and pulsatile flow in rectangular channels with different aspect ratios of side lengths γ has been carried out by a finite difference method for two boundary conditions: a constant wall temperature and a constant heat flux density on the wall. For the boundary condition of the first kind, the similarity of distributions of the heat flux density and shear stress on the walls over the channel perimeter has been established. The reasons for a nonmonotonous dependence of the initial thermal interval length on γ are discussed. For the boundary condition of the second kind, the difference of the Nusselt number averaged over the perimeter at γ → 0 from its value for a flow in a flat channel has been explained. An increase in the Nusselt number averaged over the perimeter and the period of oscillations has been revealed for a pulsatile flow in the quasi-stationary regime at large amplitudes of the oscillations of the velocity averaged over the cross section.     

Modeling two-phase flows in channels and nozzles

The gas dynamics of the flow of a two-phase mixture, consisting of a gaseous phase and polydisperse liquid particles of oxides suspended in it, plays a major role in determining the thrust parameters of rocket engines and the power characteristics of MHD stations based on metallized fuels. A number of monographs and reviews have now been published that reflect the current state in this branch of continuum mechanics. Here we give the results of a numerical investigation of certain features of two-phase streams in combustion chambers, Laval nozzles, and MHD generators.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 71–81, August, 1992.     

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基于感应电磁场方程发展了低磁雷诺数条件下充分发展液态金属管道流的数值模拟程序。为了校正程序,分别计算了两种工况：液态金属在全绝缘管道和部分绝缘管道中的流动,数值结果与Hunt和Shercliff的解析解吻合的很好,表明该程序具有很高的精度。最后利用发展的程序对液态金属钠钾合金在管壁材料为304不锈钢的全导电管道中的流动进行了数值模拟,并对流速分布和MHD压降结果与实验结果进行了比较,结果表明数值与实验结果吻合较好。     

Scaling properties of switching pulses

We investigate analytically the switching process of a bistable system which is described near each limit point by a single ordinary nonlinear differential equation. For a holding beam near the limit point and a rectangular switching pulse, we prove that the requirement of switching imposes a constraint on the pulse area. This results hold for bistability in general and is applied to purely dispersive optical bistability.     

Scaling properties of universal tetramers

We evidence the existence of a universal correlation between the binding energies of successive four-boson bound states (tetramers), for large two-body scattering lengths (a), related to an additional scale not constrained by three-body Efimov physics. Relevant to ultracold atom experiments, the atom-trimer relaxation peaks for |a|→∞ when the ratio between the tetramer and trimer energies is ?4.6 and a new tetramer is formed. The new scale is also revealed for a < 0 by the prediction of a correlation between the positions of two successive peaks in the four-atom recombination process.     

Scaling properties of geometric parallelization

We present a universal scaling law for all geometrically parallelized computer simulation algorithms. For algorithms with local interaction laws we calculate the scaling exponents for zero and infinite lattice size. The scaling is tested on local (cellular automata, Metropolis Ising) as well as cluster (Swendsen-Wang) algorithms. The practical aspects of the scaling properties lead to a simple recipe for finding the optimum number of processors to be used for the parallel simulation of a particular system.     

Scaling properties in temporal patterns of schizophrenia

Investigations into the patterns of schizophrenia reveal evidence of scaling properties in temporal behaviour. This is shown in the spectral properties of mid-range and long-range (up to two years) daily recordings from a sample of patients drawn at the therapeutic dwelling SOTERIA (Ambühl et al., in: Springer Series in Synergetics, Vol. 58, eds. Tschacher et al. (Springer, Berlin, 1992) pp. 195–203 and references therein) of the Psychiatric University Hospital in Bern. The therapeutic setting is unique in that it tries to avoid treatment by medication.

Power law behaviour has been found within fractal walk analysis and Fourier spectra for the daily fluctuations. A simple dynamic principle, based on a generic intermittency model, is put in relation to these time series thus predicting an additional scaling law for the distribution P(T) of time spans T between successive hospitalizations. Testing this hypothesis with our data shows only insignificant deviations. A possible role of this dynamic principle in the risk assignment of psychotic phases is explored with the help of an example.     

Scaling properties of fluctuations in stationary turbulence

Turbulent fluctuations are treated using a stationary distribution functionw _st for an order parameter field representing a fluid. Naive scale invariance ofw _st yields thek ^–5/3 spectral law in three dimensions andk ^–3 in two dimensions. The noise parameter of the stationary distribution is connected with energy flow or enstrophy conservation, respectively. In order to include fluctuations of the local energy dissipation a grand distribution function is introduced.     

Subsonic non-steady-state gas flows in channels with inner cavities

A set of gasdynamic equations is given in the general form for matter with an arbitrary equation of state in the case when the entropy equation is used instead of the energy equation. In the ideal gas approximation in view of viscosity, a numerical investigation is performed of non-steady-state two-dimensional flows in a channel with a cavity. The calculation results have demonstrated that, given the flow velocity and the geometry of channel and cavity, pressure pulsations arise that are due to the departure of vortices from the cavity into the main flow. The values of the amplitude and frequency of pressure pulsations are determined. If measures are taken aimed at limiting the departure of vortices from the cavity, for example, a baffle is installed to restrict the interaction between the main flow and gas in the cavity, one can considerably increase the flow velocity in the channel, unaffected by the cavity. Such non-steady-state flows may be realized in MHD-generator channels, resonators of gas flow lasers, gas ducts for ventilation and gas transport systems, mufflers, whistles, etc.     

Scaling properties of simple limiter control

"Simple limiter control" of chaotic systems is analytically and numerically investigated, proceeding from the one-dimensional case to higher dimensions. The properties of the control method are fully described by the one-parameter one-dimensional flat-top map family, implying that orbits are stabilized in exponential time, independent of the periodicity and without the need for targeting. Fine-tuning of the control is limited by superexponential scaling in the control space, where orbits of the uncontrolled system are obtained for a set of zero Lebesgue measure. In higher dimensions, simple limiter control is a highly efficient control method, provided that the proper limiter form and placement are chosen.