Optical calibration of photoviscoelastic materials on a microsecond time scale

The short-time behavior of viscoelastic materials has been traditionally studied on the millisecond time scale using steady sinusoidal excitation to measure the complex modulus and optical functions. A technique has now been developed for determining the short-time inverse optical-creep function on the microsecond time scale, using wave propagation in a rod. The method is demonstrated by characterizing an epoxy material in the time regime from 1 μs to 100μs.     

On the asymptotic stability of a neural network on a time scale

We establish sufficient conditions for the global asymptotic stability of an equilibrium state of a neural network on a time scale. We give new sufficient conditions for the function of the system to be regressive and new sufficient conditions for the existence and uniqueness of an equilibrium state of a neural network.     

Elements of Lyapunov stability theory for dynamic equations on time scale

Stability of dynamic equations on time scale is analyzed. The main results are new conditions of stability, uniform stability, and uniform asymptotic stability for quasilinear and nonlinear systems On the occasion of the 150th birthday of A. M. Lyapunov __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 9, pp. 3–27, September 2007.     

Estimation of local scale exponents for heartbeat time series based on DFA

The paper mainly introduces a method combining detrended fluctuation analysis (DFA) with moving fitting window to analyze the heartbeat time series in different pathologic states. Compared to traditional approaches, the estimation of the local scale exponent method shows more details of scale properties and provides a reliable analysis. We also quantify the effects of outliers, subseries length and gender on scale spectrum α(s). Comparing the results of the healthy subjects, patients with congestive heart failure (CHF), and patients with atrial fibrillation (AF) indicate clearly that at small scales, the exponents show great volatility and they all have their own scale pattern. In addition, the length of the series should be relatively longer to avoid properties losing. For the effect of gender, contrary to healthy results, the scale exponents of CHF male subjects are continuously greater than female. The spectrum of DFA scale exponents provides a new way to measure the heartbeat series and distinguishes healthy and pathologic groups.     

Material surface treatment using microsecond plasma opening switch

This paper is concerned with the surface treatment of steels by a high power ion beam generated in microsecond plasma opening switch (MPOS). Investigated are modified surface properties of stainless steel, carbon steel, and pure iron whereby the optimal regimes for irradiation were defined. An increase in microhardness up to 1.5–2 times was obtained. The numerical calculations and theoretical estimates of the ion beam-matter interaction were also made.     

Two time scale solution for an unsteady MHD duct flow

The investigation deals with unsteady laminar flow of a viscous, incompressible, electrically conducting fluid between conducting or nonconducting flat plates. A constant magnetic field is suddenly applied perpendicular to the plates and the created electromagnetic effects modify the motion. An approximate solution is obtained using time scales t and t/ε, where ε is the small magnetic Prandtl number.     

Turbulent time and length scale measurements in high-velocity open channel flows

In high-velocity open channel flows, the measurements of air–water flow properties are complicated by the strong interactions between the flow turbulence and the entrained air. In the present study, an advanced signal processing of traditional single- and dual-tip conductivity probe signals is developed to provide further details on the air–water turbulent level, time and length scales. The technique is applied to turbulent open channel flows on a stepped chute conducted in a large-size facility with flow Reynolds numbers ranging from 3.8E+5 to 7.1E+5. The air water flow properties presented some basic characteristics that were qualitatively and quantitatively similar to previous skimming flow studies. Some self-similar relationships were observed systematically at both macroscopic and microscopic levels. These included the distributions of void fraction, bubble count rate, interfacial velocity and turbulence level at a macroscopic scale, and the auto- and cross-correlation functions at the microscopic level. New correlation analyses yielded a characterisation of the large eddies advecting the bubbles. Basic results included the integral turbulent length and time scales. The turbulent length scales characterised some measure of the size of large vortical structures advecting air bubbles in the skimming flows, and the data were closely related to the characteristic air–water depth Y ₉₀. In the spray region, present results highlighted the existence of an upper spray region for C > 0.95–0.97 in which the distributions of droplet chord sizes and integral advection scales presented some marked differences with the rest of the flow.     

Multiple time scale analysis of aircraft longitudinal dynamics with aerodynamic vectoring

The paper analyzes the longitudinal dynamics of sustained high angle-of-attack flights performed by a small agile Unmanned Aerial Vehicle (UAV) equipped with an aerodynamic vectoring feature. This unique feature is achieved through variable-incidence wing that allows the angle of incidence of the wing with respect to fuselage to be decoupled. The aerodynamics of the UAV is estimated through wind-tunnel experiments. Subsequently, the dynamics of the UAV motion are studied for trim conditions across the complete spectrum of velocity between hover and forward cruise flight. The short-period eigenvalue migration, as the trimmed flight conditions are changed, studied, and the peculiarities observed from this linear analysis are highlighted. Further, the Multiple Time Scales method in conjunction with bifurcation theory is used to obtain the approximate solutions of the multiple degree-of-freedom nonlinear equations of motion. The explicit analytical results obtained are useful to identify the key parameters affecting the dynamics and stability of the aircraft??s longitudinal motion. The conditions leading to limit cycle responses in the vicinity of the stall regime are also highlighted.     

Concerning time and length scale estimates made from burst-mode LDA autocorrelation measurements

 An investigation was performed in grid-generated turbulence to highlight the difficulties in estimating integral and microscales from discrete autocorrelation measurements made using a burst-mode laser Doppler anemometer (LDA). Comparison was made to hot-wire results and the theoretical growth laws determined by the decay of turbulent energy. The chief concern was the presence of a spike in the measured autocorrelation coefficient functions at t=0. It was found that renormalizing the autocorrelation to a value at t=0 determined by “backfitting” a quadratic equation to the slots near t=0 led to microscale estimates that showed the same trend as the decay law and were in agreement with those determined using a hot-wire. Additionally, practical guidelines are presented for making accurate autocorrelation measurements by LDA. Received: 12 January 1995/Accepted: 9 June 1997     

Moderate time scale finite amplitude analysis of large stefan number convection in a gravity modulated mushy layer during the solidification of binary alloys

We investigate the convection amplitude in a binary alloy mushy layer subjected to a vibration body force that is collinear with the gravitational acceleration. The analysis shows that the convection amplitude decreases over time for all vibration frequencies tested. The analysis further reveals that as the vibration frequency increases, the convection amplitude subsequently decreases until a critical vibration frequency; at which the amplitude reaches the lowest value. Further increases in the vibration frequency increase the convection amplitude but gradually.     

Flow visualization in a scanning electron microscope scale

This paper describes a method of visualizing the two-dimensional flow around small bodies by means of a scanning electron microscope (SEM). The advantages, compared to light microscopic methods, are, for example, a greater distance between objective lens and object, a higher depth of focus and the possibility of observing smaller details. The disadvantages are the restriction to certain fluids and the expensive equipment. The described method may be important for the investigation of stationary objects as well as that of unsteady flow. In the near future we shall try to visualize three dimensional flow in a scanning electron microscope scale.     

Tomographic and time resolved PIV measurements on a finite cylinder mounted on a flat plate

Tomographic and time resolved PIV measurements were performed to examine the 3D flow topology and the flow dynamic above the upper surface of a low-aspect ratio cylinder at Re ≈ 1 ×  10⁵. This generic experiment is of fundamental interest because it represents flow features which are relevant to many applications such as laminar separation bubbles and turbulent reattachment. At Re  ≈ 1 × 10⁵, laminar separation bubbles arise on the side of the cylinder. Furthermore, on the top of the cylinder a separation with reattachment is of major interest. The tomographic PIV measurement, which allows to determine all three velocity components in a volume instantaneously, was applied to examine the flow topology and interaction between the boundary layer and wake structures on the top of the finite cylinder. In the instantaneous flow fields the tip vortices and the recirculation region becomes visible. However, it is also observed that the flow is quite unsteady due to the large separation occurring on the top of the cylinder. In order to study the temporal behaviour of the separation, time resolved PIV was applied. This technique allows capturing the dynamic processes in detail. The development of vortices in the separated shear layer is observed and in addition regions with different dominant frequencies are identified.     

Effects of polymer additives on the large scale structure of a two-dimensional submerged jet

The large structures on the boundary of a two-dimensional submerged jet were examined. In the first experiment, a jet of a 100 ppm aqueous polyacrylamid solution was fed into pure water (P/W). In the second experiment, the jet as well as the ambient fluid were pure water (W/W), whereas in the third experiment, polymer solution (W/P) was in the ambient only.The large structures were found to be of the same size for all three experiments. The spread-angle was lowest for P/W and highest for W/P. These effects are attributed to a strong flow which stretches the polymer molecules in the mixing layer.     

Dimensional analysis of pore scale and field scale immiscible displacement

A basic re-examination of the traditional dimensional analysis of microscopic and macroscopic multiphase flow equations in porous media is presented. We introduce a macroscopic capillary number which differs from the usual microscopic capillary number Ca in that it depends on length scale, type of porous medium and saturation history. The macroscopic capillary number is defined as the ratio between the macroscopic viscous pressure drop and the macroscopic capillary pressure. can be related to the microscopic capillary number Ca and the LeverettJ-function. Previous dimensional analyses contain a tacit assumption which amounts to setting = 1. This fact has impeded quantitative upscaling in the past. Our definition for , however, allows for the first time a consistent comparison between macroscopic flow experiments on different length scales. Illustrative sample calculations are presented which show that the breakpoint in capillary desaturation curves for different porous media appears to occur at 1. The length scale related difference between the macroscopic capillary number for core floods and reservoir floods provides a possible explanation for the systematic difference between residual oil saturations measured in field floods as compared to laboratory experiment.     

Small scale intermittency in a rough wall turbulent boundary layer

Relatively good quality isotropy is observed in the central region of a turbulent boundary layer developing over a mesh screen rough wall. Spectra of velocity and, more especially, vorticity fluctuations satisfy isotropy over a significant wavenumber range. Inertial range scaling exponents ζ _u2 (p) and ζ _u3 (p) of moments of order p(?8) of increments of the transverse velocity fluctuations u ₂ and u ₃ are significantly smaller than the exponents ζ _u1 (p) of increments of the longitudinal velocity fluctuation u ₁. Exponents inferred from the locally averaged values of squared transverse vorticity fluctuations are only slightly smaller than ζ _u1 (p). The difference between ζ _u1 (p) and ζ _u2 (p) [or ζ _u3 (p)] more likely reflects the departure from isotropy of inertial range scales. There is evidence to suggest that the difference decreases with an increase in the Reynolds number and/or a decrease in the magnitude of the mean shear.     

Effect of scale on the onset of detonations

Critical conditions for onset of detonations are compared at (1) two significantly different scales, (2) for a range of -air mixtures diluted with C, O, and (3) for two types of geometry – one a long obstructed channel and the other a room with a relatively small aspect ratios. For the range of scales, mixtures, and initial conditions tested, the detonation cell size was shown to be a reliable scaling parameter for characterization of detonation onset conditions. An experimental correlation is suggested for the critical detonation onset conditions. This correlation is based on a wide variety of available experimental data on DDT in mixtures of hydrogen and hydrocarbon fuels with air and on the use of detonation cell size as a scaling parameter characterizing the mixture. Received 14 November 1999 / Accepted 16 February 2000     

Multiscale time irreversibility analysis of financial time series based on segmentation

Time irreversibility is a subject of increasing interest in an unbalanced system of various time series. Taking into account dynamic basic concepts, we provide multiscale time irreversibility analysis of financial time series based on segmentation which quantifies the time asymmetry in multiscales and is applied to several different forms of financial time series. Specifically, we adopt four distinct time irreversibility indices—Porta’s, Guzik’s and Ehler’s indices (P%, G% and E) and \(\gamma _{2,1} (k)\), respectively, derived from data segments on various timescales. We investigate the performance of our statistical tests for local financial time series from segmented series system with known time reversal properties and find out that it can help classify the partially representative financial markets finally. Particularly, the smaller the scale factor L is the better the ability to distinguish data. Statistical analysis shows a close relationship between G% and E. On the contrary, the connection between P% and G% or P% and E is not proven. In addition, we define a new metric \(\gamma _{2,1} (k)\) to measure the degree of time irreversibility. By further observing the results of the proposed method for computing the degree of irreversibility of the time series, we confirm that the asymmetry is an inherent property of the financial time series, which can be extended to a wide range of scales. Finally, we apply this method to the recurrence plot and multiscale recurrence quantification analysis, to compare effectiveness of the segmentation method.