Basic Perturbations Research Articles

Построение базового закона движения материальной точки и реализующего его программного управления при наличии фазовых ограничений

The article presents a solved problem about a material point motion basic kinematic law in a homogeneousgravity field, taking into account the resistance of the medium, which proportional to the velocity in the second degree. A point bypasses the specified restricted zones and does not leave the specified vertical strip above the earth's surface during the flight according to proposed law. A program control has been developed that implements a point motion proposed law. Differential equations describing the dynamics of the basic motion perturbations are compiled in the article.

Compare of Transient Quality in Automatic Control Systems with Classic PID Algorithm and Optimal Regulator

Currently, about 90–95% of generic controllers use the PID algorithm to generate control actions, while 64% of the PID controllers are used in single-circuit automatic control systems. Most of industries (power industry among them) use hundreds of automatic control systems. The quality of their work is the basis of economic efficiency of technical processes, ensuring safety, reliability, durability and environmental friendliness of both technological equipment and automation equipment. There are different modifications of PID-controller structure implementation. In practice the ideal PID controller with a filter and the classic PID regulator (serial connection of the ideal PI controller and the real PD regulator as the direct action elements) are widely used. The problem of choosing a rational structure and a method of parametric optimization of PID controllers, which provide the best direct indicatives of the quality in the development of the main effects in single-circuit automatic control systems, becomes urgent. However, only for the classical PID controllers, which are widely used at present, there are more than three hundred methods for adjusting the three parameters of the optimal dynamic adjustment, as well as the ballast time constant. This results in arising a problem of substantiation of the best structure and method of parametric optimization of classical PID regulators. As a basic option, one of the simplest and most obvious one, viz. the method of automated adjustment of the controller in the Simulink MatLab environment had been chosen, which was compared with the method of full compensation in general for objects with a transfer function in the form of an inertial link with a conditional delay. Two variants of control action realization on the basis of the structural scheme of the optimal regulator developed by the Belarusian national technical University were also offered. In contrast with the classic PID controller, the optimal controller has one parameter of dynamic adjustment setting. The results of simulation of transients at basic perturbations confirmed that the best direct indicatives of the quality are provided with an optimal regulator, which makes it possible to recommend it for wide implementation instead of the classic PID controllers.

An insight into drought stress and signal transduction of abscisic acid

The sustainable crop production is one of the major issue in the era of urbanization, industrialization, and globalization. In the environment, there are number of abiotic and biotic factors which are hampering the sustainable production of crops. The drought is one of the constraints which directly/indirectly affects the crop yield. It has various negative effects on the normal physiology and biochemistry of the plants. Therefore, researchers must have to work in the field of developing drought-tolerant crop plants to meet the food needs of the exponentially growing population of the world. The present study is the outcome of an extensive literature survey on the basic perturbations of drought to the crops, role of abscisic acid (ABA) in stressful conditions and its signal transduction.

Influence of thermal load on the characteristics of a flow with evaporation

The two-layer flows of a liquid and a gas in a horizontal channel are investigated under condition of given gas flow rate. Evaporation on the thermocapillary interface is taken into account. An exact solution is constructed of the Navier–Stokes equations in the Boussinesq approximation, taking into account the Dufour effect in the gas-vapor layer. Within the framework of linear theory, the stability of the obtained solutions and the characteristics of the arising perturbations are studied. The influence is considered of the thickness of the liquid layer and the magnitude of the longitudinal temperature gradient on the structure of the basic flow and perturbations.

Dynamical stability of Minkowski space in higher order gravity

We discuss the Minkowski stability problem in modified gravity by using dynamical system approach. The method to investigate dynamical stability of Minkowski space is proposed. This method was applied for some modified gravity theories, such as f(R) gravity, f(R)+αR□R gravity and scalar–tensor gravity models with non-minimal kinetic coupling. It was shown that in the case of f(R) gravity Minkowski solution is asymptotically stable in ghost-free (f′ > 0) and tachyon-free (f″ > 0) theories in expanding Universe with respect to isotropic and basic anisotropic perturbations. In the case of higher order gravity with αR□R correction conditions of Minkowski stability with respect to isotropic perturbations are significantly different: f′(0) < 0, f″(0) < 0 and 3f′(0) + f″(0)2/α > 0. And in the case of scalar-tensor gravity with non-minimal kinetic coupling Minkowski solution is asymptotically stable in expanding Universe with respect to isotropic perturbations of metric. Moreover, the developed method may be used for finding additional restrictions on parameters of different modified gravity theories.

Linear stability analysis of the convective flow in a spherical gap withη=0.714

A linear stability analysis has been performed of the buoyancy-driven flow of a Boussinesq fluid in a spherical gap where the inner shell is warmer than the outer one (T1>T2) for the radii ratio η=R1R2=0.714. We show that the two-dimensional axisymmetric basic flow becomes unstable with respect to non-axisymmetric perturbations. The stability diagrams, critical Grashof number Grc and wave number mc versus the Prandtl number Pr are presented for both the steady and the oscillatory instabilities. In this way, the results bridge the gap to recent three-dimensional simulations performed in Scurtu et al. (2010), Feldman and Colonius (2013) for air in this η. Furthermore we investigate the energy exchange between the basic flow and perturbations in terms of a Reynolds–Orr-equation.

Oscillatory-rotational processes in the Earth motion about the center of mass: Interpolation and forecast

The celestial-mechanics approach (the spatial version of the problem for the Earth-Moon system in the field of gravity of the Sun) is used to construct a mathematical model of the Earth’s rotational-oscillatory motions. The fundamental aspects of the processes of tidal inhomogeneity in the Earth rotation and the Earth’s pole oscillations are studied. It is shown that the presence of the perturbing component of gravitational-tidal forces, which is orthogonal to the Moon’s orbit plane, also allows one to distinguish short-period perturbations in the Moon’s motion. The obtained model of rotational-oscillatory motions of the nonrigid Earth takes into account both the basic perturbations of large amplitudes and the more complicated small-scale properties of the motion due to the Moon short-period perturbations with combination frequencies.

Physiological influence of basic perturbations assessed by non-invasive optical techniques in humans

New non-invasive techniques enabling frequent or continuous assessments of various pathophysiological conditions might be used to improve in-hospital outcome by enabling earlier and more reliable bedside detection of medical deterioration. In this preclinical study, three modern non-invasive optical techniques, laser Doppler imaging (LDI), near-infrared spectroscopy (NIRS), and tissue viability imaging (TVI), were all evaluated with respect to the influence of basic physiological perturbations (including local changes in arm positioning, skin temperature, and regional blood flow conditions) on quasi simultaneously obtained values of skin perfusion, muscle tissue oxygenation (StO₂), and skin blood volume, recorded in eighteen healthy volunteers. Skin perfusion measured by LDI responded prominently to changes in positioning of the arm, whereas muscle StO₂ measured by NIRS did not change significantly. Total haemoglobin count (HbT) measured by NIRS and blood volume estimated by TVI both increased significantly on lowering of the limb. On local cooling, the perfusion and blood volume were both found to increase considerably, while StO₂ and HbT did not change. Local heating induced a more than 10-fold increase in skin perfusion and a small increase in blood volume. On progressive venoarterial occlusion, the perfusion, StO₂, HbT, and blood volume values decreased, after transient increases in HbT and blood volume before full arterial occlusion occurred, and all values approached the baseline level on release of the occlusion with a slight overshoot of the StO₂. The results obtained have potential bearing on future utilization of these non-invasive techniques in the management of severely injured and (or) critically ill patients.

Mesoscale barotropic instability of vortex Rossby waves in tropical cyclones

In this study, the barotropic stability of vortex Rossby waves (VRWs) in 2D inviscid tropical cyclone (TC)-like vortices is explored in the context of rotational dynamics on an f-plane. Two necessary instable conditions are discovered: (a) there must be at least one zero point of basic vorticity gradient in the radial scope; and (b) the relative propagation velocity of perturbations must be negative to the basic vorticity gradient, which reflects the restriction relationship of instable energy. The maximum growth rate of instable waves depends on the peak radial gradient of the mean vorticity and the tangential wavenumber (WN). The vortex-semicircle theorem is also derived to provide bounds on the growth rates and phase speeds of VRWs. The typical basic states and different WN perturbations in a tropical cyclone (TC) are obtained from a high resolution simulation. It is shown that the first necessary condition for vortex barotropic instability can be easily met at the radius of maximum vorticity (RMV). The wave energy tends to decay (grow) inside (outside) the RMV due mainly to the negative (positive) sign of the radial gradient of the mean absolute vorticity. This finding appears to help explain the developemnt of strong vortices in the eyewall of TCs.

Invariance of Picard Dimensions Under Basic Perturbations

The Picard dimension dim μ of a signed Radon measure μ on the punc- tured closed unit ball 0 < |x| 1 in the d-dimensional euclidean space with d 2 is the cardinal number of the set of extremal rays of the cone of positive continuous distributional solutions u of the Schrodinger equation (−� + μ)u = 0 on the punc- tured open unit ball 0 < |x| < 1 with vanishing boundary values on the unit sphere |x |= 1. If the Green function of the above equation on 0 < |x| < 1 characterized as the minimal positive continuous distributional solution of (−� + μ)u = δy ,t he Dirac measure supported by the point y, exists for every y in 0 < |x| < 1 ,t henμ is referred to as being hyperbolic on 0 < |x| < 1. A basic perturbation γ is a radial Radon measure which is both positive and absolutely continuous with respect to the d-dimensional Lebesgue measure dx whose Radon-Nikodym density d γ( x)/dx is bounded by a positive constant multiple of |x| −2 . The purpose of this paper is to show that the Picard dimensions of hyperbolic radial Radon measures μ are invariant under basic perturbations γ : dim(μ + γ) = dim μ. Three applications of this invariance are also given.

Shear-induced rotations in a weakly anchored nematic liquid crystal

We analyse the instability dynamics of a nematic liquid crystal under steady plane Couette flow. Weak anchoring for molecules of the nematic at the boundaries with an easy axis perpendicular to the flow plane is assumed. Orientation of the director along the easy axis is our basic state. Previously (Tarasov et al., 2001, Liq. Cryst. 28, 833), it was found that the critical shear rate of the primary instability of the basic state strongly decreases with anchoring strength. In the present study our interest was to examine the effect of the anchoring strength on the nematic dynamics in the regime with a slightly supercritical shear rate. It was found that for weaker anchoring the director rotates more strongly and the relaxation time of the amplitude of the basic state perturbations significantly increases. Results obtained can be used for experimental measurements of the anchoring strengths.

Linear Stability Analysis of a Viscous Liquid Sheet in a High-Speed Viscous Gas

Air-assisted atomizers in which a thin liquid sheet is deformed under the action of a high-speed air flow are extensively used in industrial applications, e.g., in aircraft turbojet injectors. Primary atomization in these devices is a consequence of the onset and growth of instabilities on the air/liquid interfaces. To better understand this process, a temporal linear instability analysis is applied to a thin planar liquid sheet flowing between two semi-infinite streams of a high-speed viscous gas. This study includes the full viscous effects both in the liquid and gas basic states and perturbations. The relevant dimensionless groups entering the non-dimensional Orr-Sommerfeld equations and boundary conditions are the liquid and gas stream Reynolds numbers, the gas to liquid momentum flux ratio, the gas/liquid velocity ratio, the Weber number and the equivalent gas boundary layer to liquid sheet thickness ratio. Growth rates and temporal frequencies as a function of the wavenumber, varying the different dimensionless parameters are presented, together with neutral stability curves. From the results of this parametric study it is concluded that when the physical properties of gas and liquid are fixed, the momentum flux ratio is especially relevant to determine the instability conditions. It is also observed that the gas boundary layer thickness strongly influences the wave propagation, and acts by damping sheet oscillation frequency and growth. This is especially important because viscosity in the basic gas velocity profile has always been ignored in instability analysis applied to the geometry under study.

How phase and amplitude aberrations destabilize the phase singularities in the focal field of a lens

The output field of a uniformly illuminated lens contains points of zero intensity on the optical axis and zero-intensity Airy rings in the focal plane, as formed by diffraction. These intensity zeros have been recognized as phase singularities or wave dislocations. Recently it was shown that, under the influence of a perturbation, the axial singularities may transform into rings or disappear and that the Airy rings may split into triplets. Starting from optical diffraction theory, we identify the physical perturbations that can induce such topological transformations. The basic perturbations are phase and amplitude aberrations of the wave front that is incident on the lens; we show that their different natures have consequences for the possible dislocation reactions.

Thermal Deformations in a Satellite Telescope Mirror

Basic thermal perturbations are considered for a fused-silica primary mirror in an orbiting space telescope within 800 km of the earth’s surface. In such an orbit, the change of thermal environment with pointing direction leads almost inevitably to an axial temperature gradient dT/dz through the primary mirror, and to a consequent bending of the mirror and a change ΔF of focal length. If ΔF is constant across the mirror to within about ±3 f2λ, where f is the focal ratio and λ the wavelength, the rms deviation of the mirror surface from a paraboloid will not exceed λ/50, and diffraction-limited performance is possible. Nonuniformities of ΔF can result either from lateral changes of dT/dz across the face of the mirror or from axial changes of dT/dz, i.e., from nonlinear gradients. A numerical analysis of the radiation transfer in the telescope tube, when this is illuminated from one side, shows that even in the unfavorable case of a two-dimensional telescope the lateral variation of dT/dz can be kept sufficiently small if the telescope tube is substantially longer than the mirror diameter, and if the sunlit earth does not shine directly on the mirror at any time. Analysis of the thermal distortion near the edge of a flat disk subject to a nonlinear axial gradient and of a spherical cap subject to a radial gradient dT/dR indicates that the likely distortions are certainly within optical tolerance for a 1-m telescope and probably also for a 3-m telescope. Deviations from uniformity resulting from the mirror supports or from inhomogeneities in the mirror itself are not considered.

Fundamental Satellite Perturbations

A brief exposition, from an elementary point of view, is given for some basic satellite perturbations. The t reatment serves to generate independent checks of formal results from more elaborate analyses and to establish a direct relation of these results to physical principles. Attention is given to in-plane and precessional perturbations of circular orbits resulting from oblateness, luni-solar gravitation and radiation pressure. The derivations have quantitative validity and may be extended to more general situations.

A METHOD FOR QUANTITATIVE DETERMINATION OF LONG WAVES

In an effort to find tools for the description of long waves in the upper troposphere in addition to those already available, the total field of motion aloft is divided into a nondivergent basic current and perturbations, following standard hydrodynamical methods of wave treatment. After this division the long waves appear in the form of closed perturbation centers so that latitude is added to longitude as a coordinate for defining long waves. Moreover, since the intensity of these centers is also given, the deepening and filling which they experience, as well as their displacements from day to day can be followed, much as in the case of highs and lows on the sea-level chart. Several other measurements that can be made with use of perturbation charts are also indicated. Two examples of the suggested technique are given, and some synoptic consequences are also discussed.