Relaxation-Induced Suppression of Vortex Disturbances in a Molecular Gas

The influence of thermal excitation on a finite-amplitude vortex disturbance in a shear flow of a molecular gas is studied in a model problem. The evolution of such vortex structures is typical of both the nonlinear stage of the laminar–turbulent transition and for developed turbulence. Since the excitation level was assumed to be comparatively low, full Navier–Stokes equations for a compressible heat-conducting gas were used in calculations; nonequilibrium was taken into account by the coefficient of bulk viscosity. As the bulk viscosity increases in the range of realistic values, the disturbance-energy damping rate in a weakly compressible flow increases approximately by 10%. The increase in the Mach number enhances the effect of disturbance suppression.     

Reachable set bounding for nonlinear perturbed time-delay systems: The smallest bound

In this letter, we propose a new approach to obtain the smallest box which bounds all reachable sets of a class of nonlinear time-delay systems with bounded disturbances. A numerical example is studied to illustrate the obtained result.     

Transition to turbulence, small disturbances, and sensitivity analysis I: A motivating problem

For over 100 years, researchers have attempted to predict transition to turbulence in fluid flows by analyzing the spectrum of the linearized Navier-Stokes equations. However, for many simple flows this approach fails to match experimental results. Recently, new scenarios for transition have been proposed that are based on the interaction of the linearized equations of motion with small disturbances to the flow system. These new “mostly linear” theories have increased our understanding of the transition process, but the role of nonlinearity has not been explored in detail. This paper is the first of a two part work in which sensitivity analysis is used to study the effects of small disturbances on transition to turbulence. In this part, we study a highly sensitive one-dimensional Burgers' equation as a motivating problem. Sensitivity analysis is used to predict the large changes in solutions in the presence of a small disturbance. Also, sensitivity analysis is shown to provide more information about the disturbed nonlinear problem than a purely linear analysis of the problem. In the second part of this work, this analysis will be extended to the three-dimensional Navier-Stokes equations to show that small disturbances have great potential to trigger transition to turbulence.     

Time-average holographic interferometry with a sinusoidally modulated laser diode

Laser diodes have the features of a single-mode operation and a frequency tunability. Holographic interferometry is described for investigating the vibrating amplitude and phase with a frequency-modulated laser diode. Sinusoidal wavelength change by varying laser injection current produces the sinusoidal phase modulation of relative phase difference between the reference and vibrating object paths. Holograms are made by time-average exposure of three-type recording modes with a laser diode. The phase of vibrating object is extracted from the measurements of Bessel-type fringe irradiances in three kinds of time-average holographic reconstruction. Experimental results of phase and amplitude for a vibrating cantilever object are shown.     

Measurement of diameter of metal cylinders using a sinusoidally vibrating interference pattern

A method for measuring external diameters of metal cylinders is proposed in which a sinusoidally vibrating interference pattern (SVIP) of 100-μm period is used as an exact scale. Lights from the end-points of a metal cylinder are extracted with a spatial filtering in an imaging system to form a cross-sectional image of the metal cylinder. On the image a sinusoidally phase-modulated signal owing to the SVIP is detected with a CCD image sensor to measure the phases of the SVIP at the two end-points of the cylinder. The coordinates of the two end-points are obtained from the phases at the two end-points, the phase distribution of the SVIP, and the coordinates of the pixels of the CCD image sensor. Metal cylinder diameters of 7.99, 8.00, and 9.00 mm are measured along their length directions with an error less than 1 μm.     

两种群非自治Lotka-Volterra竞争扩散系统的概周期解

本文讨论两种群概周期竞争扩散系统，利用微分不等式，证明了系统概周期解的存在、唯一性及其在壳扰动下的稳定性．     

Discriminant Analysis for Regression Models with Stationary Long-Memory Disturbances

We shall consider the problems of classifying an observation from regression model with stationary long-memory or short-memory disturbances into one of two populations described by the mean functions of the model. We use the log-likelihood ratio as a discrimant statistic which is optimal in the sense of its minimizing the misclassification probabilities. Then we confirm the theoretical results by some simple polynomial regression models.     

A stochastic optimal control approach to a class of production and inventory problems

A comprehensible and unified system control approach is presented to solve a class of production/inventory smoothing problems. A nonstationary, non-Gaussian, finite-time linear optimal solution with an attractive computation scheme is obtained for a general quadratic and linear cost structure. A complete solution to a classical production/inventory control problem is given as an example. A general solution to the discrete-time optimal regulator with arbitrary but known disturbance is provided and discussed in detail. A computationally attractive closed-loop suboptimal scheme is presented for problems with constraints or nonquadratic costs. Implementation and interpretation of the results are discussed.     

Numerical modeling of the disturbances of the separated flow in a rounded compression corner

Numerical modeling of the time-dependent supersonic flow over a compression corner with different roundness radii is performed on the basis of the solution of the two-dimensional Navier-Stokes equations in the regimes corresponding to local boundary layer separation. The development of unstable disturbances generated by local periodic injection/suction in the preseparated boundary layer is calculated. The results are compared with those of similar calculations for a flat plate. It is shown that the natural oscillations of the boundary-layer second mode stabilize in the separation zone and grow intensely downstream of the reattachment point. The acoustic modes excited within a separation bubble are studied using numerical calculations and an asymptotic analysis.     

Effect of acoustic disturbances on a free convective flow

A gas-dynamic flow in an axisymmetric convective jet is studied experimentally. It is demonstrated that the jet flow with Grashof numbers Gr = (0.4–2.0) · 10⁶ is self-similar. Acoustic oscillations directed perpendicular to the axis of symmetry transform the profiles of the gas-flow parameters; two temperature maximums located outside the axis can appear. The results obtained indicate that flow instability is generated in high-gradient regions. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 5, pp. 27–33, September–October, 2006.