Classification of Dynamical Systems with Invertible Cosymmetry in a Neighborhood of a Cosymmetric Equilibrium and an Equilibrium Line

Global gyrokinetic simulations of ion temperature gradient turbulent transport with piecewise-flat profiles are given to illustrate the breaking of gyro-Bohm scaling by a nonlocal mechanism. The nonlocal drainage of the turbulence from unstable regions spreading into stable (or less unstable) regions breaks the gyro-Bohm scaling toward Bohm in unstable regions and toward super-gyro-Bohm in stable (or less unstable) regions. A heuristic model for this nonlocal process is formulated in terms of a nonlocal growth rate resulting from a locally weighted radial average of the local linear ballooning mode growth rate. A nonlocality length L measured in ion gyroradii provides the exponential scale for the local weighting. The nonlocal growth rate can be incorporated into a local gyro-Bohm-scaled transport model in place of the local growth rate. The resulting nonlocal transport model will provide some transport in stable regions. A heuristic theory of this nonlocal transport mechanism based on the partial formation of global modes in toroidal geometry is detailed. The theory argues that the nonlocality length L increases with relative gyroradius and decreases with the linear growth rate.

Steam jet injector is a prospective device with advantages of impact volume, strong heat transfer, without moving part, which can be applied in various industrial fields such as nuclear/conventional power plant, heat-supply system and heat recovery system, etc. However, as the steam jet injector is driven by high speed steam jet condensation in subcooled water flow in the mix chamber, the instability of steam-water direct contact condensation will lead to loud noise and severe vibration. Thus, loud noise will evolve into environmental pollution, and vibration will endanger the equipment, which prevent the promotion of this device in induatrial applications. Moreover, the published works generally involved in the pressure oscillation caused by steam jet condensation in large space water pool, where the water was considered to be stagnant. However, the case becomes more complex when direct contact condensation occurs in a confined channel like in a steam jet injector, where the effect of turbulence on water side and wall can not be ignored. Thus, the reported results can not be applied in the present condition. So it is necessary to study the mechanism of the instability of steam-water direct contact condensation in a confined channel. In this paper, experimental investigation was performed on the amplitude characteristics of pressure oscillation caused by direct contact condensation in a confined channel, aiming at revealing the mechanism of noise and vibration and providing some guidance for the design and operation of the steam jet injector. In order to better observe the behavior of the steam-water interface, a special visualized test section was designed and a high speed camera was applied. The dynamic pressure data was obtained by a dynamic pressure transducer arranged on the wall of channel. Three main inlet parameters, including steam mass flux, water mass flux and water temperatures were tested in the ranges of 150–600 kg/m2s, 6×103–18×103 kg/m2s and 15–40°C, respectively. The results indicated that when direct contact condensation occurred in a confined channel, flow patterns could be divided into two categories-unstable and stable flow patterns with respect to the interface behavior. The effect of the inlet parameters on amplitude characteristics of pressure oscillation was discussed. With the increase of water mass flux, the amplitude altered slightly in stable flow pattern region, but increased suddenly and dramatically in unstable region. With the increase of steam mass flux, the amplitude increased a little in unstable region, but decreased suddenly in stable region and then increased again. And the increase of water temperature leaded to the increasing of amplitude in all flow pattern regions. In a word, the equipment would bear stronger impact load when operating in unstable flow pattern region.

Instead of relying on the usual, long-range shelf-test for determining emulsion stability, a technique utilizing the light scattering property of emulsions was developed to allow the determination within a short period of time.In the previous report (Part 1), the oil phase was restricted to mineral oil and the concentration of the oil phase was kept constant in determining the effects of surfactant type and surfactant concentration on the stability index. It was found that the stable region was below stability index, R=0.33 and the unstable region was above R=0.46 Between these two R values, the stability was ambiguous.In this report, four different oils, including a higher alcohol (hexadecyl alcohol), ester (isopropylmyristate), triglyceride (castor oil) and four different surfactants were studied at varying oil phase concentrations to determine the effects on stability indices.The experimental data indicated that for isopropylmyristate, the stable region was below R=0.157 and the unstable region was above R=0.203. The stability was ambiguous between these two values. For hexadecyl alcohol, the stable region was below R=0.163 and the unstable region was above 0.211. For castor oil, the stable region was below R=0.177 and the unstable region was above 0.22. The values for the lanolin system were 0.209 and 0.251 respectively.It is clear that the boundaries for the stable and unstable regions varied somewhat depending on the type of oils employed. The reason for the variation will be clarified in the future research work.

It is widely accepted that knowing the composition and the orbital evolution of asteroids might help us to understand the process of formation of the Solar system. It is also known that asteroids can represent a threat to our planet. Such an important role has made space missions to asteroids a very popular topic in current astrodynamics and astronomy studies. Taking into account the increasing interest in space missions to asteroids, especially to multiple systems, we present a study that aims to characterize the stable and unstable regions around the triple system of asteroids (45) Eugenia. The goal is to characterize the unstable and stable regions of this system and to make a comparison with the system 2001 SN263, which is the target of the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) mission. A new concept was used for mapping orbits, by considering the disturbance received by the spacecraft from all perturbing forces individually. This method has also been applied to (45) Eugenia. We present the stable and unstable regions for particles with relative inclination between 0° and 180°. We found that (45) Eugenia presents larger stable regions for both prograde and retrograde cases. This is mainly because the satellites of this system are small when compared to the primary body, and because they are not close to each other. We also present a comparison between these two triple systems, and we discuss how these results can guide us in the planning of future missions.

This paper shows that the August 10, 1996-WECC blackout originated from negative damping arising from sin6 nonlinearity. The proof is based on keeping the nonlinearity in the dynamic equation of a turbine-generator swinging against an infinite bus. Small signal perturbation linearization can predict the occurrence of negative damping. But the linear approach cannot produce the negatively damped waveform of the WECC blackout. Therefore, the graphical Phase Plane method is resorted to. As MatLab, MATHEMATICA, Wolfram MathWorld, etc. offer software plotters, the phase plane method is not difficult to use. Phase portraits show that the “Swing Equation” has stable and unstable regions. The WECC blackout happened because the initial states fell in the unstable region. Although dismissed as being limited to two-dimensions, the paper makes a contribution by showing that phase plane can be used to study the impact of 3 independent controllers. A worked-example shows when the independent controllers (turbine torque, the generator counter-torque and the damping torque) cannot meet the Transient Stability Limit after a line short circuit fault, local blackout occurs. The global WECC blackout is considered to be a scaled up local blackout. Instead of a turbine-generator swinging against an infinite bus, the last stage of the August 10, 1996-WECC blackout is assumed to be the Seattle-area swinging against the California-area. A phase portrait is found in the unstable region whose trajectory unravels in several cycles. Time-domain simulation shows a waveform oscillating with same number of cycles, which qualitatively matches the waveform of the August 10, 1996-WECC blackout.

Current patterns of biodiversity distribution result from a combination of historical and contemporary processes. Here, we compiled checklists of amphibian species to assess the roles of long-term climate stability (Quaternary oscillations), contemporary environmental gradients and geographical distance as determinants of change in amphibian taxonomic and phylogenetic composition in the Brazilian Atlantic Forest. We calculated beta diversity as both variation in species composition (CBD) and phylogenetic differentiation (PBD) among the assemblages. In both cases, overall beta diversity was partitioned into two basic components: species replacement and difference in species richness. Our results suggest that the CBD and PBD of amphibians are determined by spatial turnover. Geographical distance, current environmental gradients and long-term climatic conditions were complementary predictors of the variation in CBD and PBD of amphibian species. Furthermore, the turnover components between sites from different regions and between sites within the stable region were greater than between sites within the unstable region. On the other hand, the proportion of beta-diversity due to species richness difference for both CBD and PBD was higher between sites in the unstable region than between sites in the stable region. The high turnover components from CBD and PBD between sites in unstable vs stable regions suggest that these distinct regions have different biogeographic histories. Sites in the stable region shared distinct clades that might have led to greater diversity, whereas sites in the unstable region shared close relatives. Taken together, these results indicate that speciation, environmental filtering and limited dispersal are complementary drivers of beta-diversity of amphibian assemblages in the Brazilian Atlantic Forest.

Experimental study on pressure pulse generated by condensing subsonic/supersonic steam jet in a horizontal channel

Periodic processes of gene network functioning are described with good precision by periodic trajectories (limit cycles) of multidimensional systems of kinetic-type differential equations. In the literature, such systems are often called dynamical, they are composed according to schemes of positive and negative feedback between components of these networks. The variables in these equations describe concentrations of these components as functions of time. In the preparation of numerical experiments with such mathematical models, it is useful to start with studies of qualitative behavior of ensembles of trajectories of the corresponding dynamical systems, in particular, to estimate the highest likelihood domain of the initial data, to solve inverse problems of parameter identification, to list the equilibrium points and their characteristics, to localize cycles in the phase portraits, to construct stratification of the phase portraits to subdomains with different qualities of trajectory behavior, etc. Such an à priori geometric analysis of the dynamical systems is quite analogous to the basic section “Investigation of functions and plot of their graphs” of Calculus, where the methods of qualitative studies of shapes of curves determined by equations are exposed. In the present paper, we construct ensembles of trajectories in phase portraits of some dynamical systems. These ensembles are 2-dimensional surfaces invariant with respect to shifts along the trajectories. This is analogous to classical construction in analytic mechanics, i. e. the level surfaces of motion integrals (energy, kinetic moment, etc.). Such surfaces compose foliations in phase portraits of dynamical systems of Hamiltonian mechanics. In contrast with this classical mechanical case, the foliations considered in this paper have singularities: all their leaves have a non-empty intersection, they contain limit cycles on their boundaries. Description of the phase portraits of these systems at the level of their stratifications, and that of ensembles of trajectories allows one to construct more realistic gene network models on the basis of methods of statistical physics and the theory of stochastic differential equations.

Stochastic characteristics for the vortical structure of a 5-MW wind turbine wake

The Au-to-Au micro/nano-contact behavior in unstable contact region during the initial stage of contact formation has been experimentally investigated under low contact force. The experimental results reveal that the asperity deformation process, which is conventionally observed in the stable region, could start from the early stage of contact formation in the unstable region. The fundamental mechanism for the instability of electrical conductance in the unstable region can be explained under a framework of trap-assisted tunneling at the contact interface.

The electrical contact behavior of metal micro-contacts is of significant importance in various fields of science and engineering, and it has not yet been adequately understood compared to the bulk metal contacts. Specifically, in DC contact type of microelectromechanical (MEMS) or nanoelectromechanical (NEMS) devices, the metal contact is one of the most crucial parts, as it determines the device performance and is closely related to the reliability issues. In order to investigate the degradation mechanism of the metal contacts under different testing conditions, load cycling tests have been performed using MEMS switches. The micro-contact behavior during a single load test has also been intensively studied. The electrical contact resistance (Rc) as a key parameter was characterized and analyzed to understand the contact behavior. In general, the relation between Rc and contact force Fc can be divided into three regions for a typical contact cycle. It starts from an unstable contact region (Region I) with drastic fluctuations of Rc, followed by a stable but gradual reduction of Rc in Region II and reaches a steady state with low Rc in Region III. A minimum contact force Fmin is required to establish the stable electrical contact. When the contact force exceeds Fmin (in Region II), the gradual reduction of Rc could be attributed to plastic deformation of surface asperities until the high force region (Region III), in which Rc is determined by film thickness effects on a macroscopic scale. The metal-to-metal contact behaviors have been widely studied by many different research groups. However, the unstable electrical contact behavior under low contact force (Region I) remains unexamined. In conventional MEMS switches, the contact force is believed to be larger than Fmin for most cases. Therefore, past studies of contact behavior mainly focused on the stable region, including the load cycling tests. On the other hand, there is an ongoing demand to scale down the MEMS components towards sub-micrometer and nanometer dimensions, in which the contact force could be drastically reduced. Therefore, it becomes necessary to look into the unstable contact region of metal micro-contacts. In this thesis, the electrical contact instability is investigated. A nanoindentation stage was utilized for the contact tests under precisely controlled experiential conditions (various combinations of applied voltage, contact material, surface treatment, etc.). X-ray photoelectron spectroscopy (XPS) techniques were used to characterize the sample surface. The results reveal that the contamination film on the metal contact surface, which may originate from the residues of microfabrication process or absorption of air-borne species such as hydrocarbons and carbon dioxide, plays a critical role in determining the micro-contact behavior under low contact force. The rapid fluctuations of contact resistance in the unstable region could be explained under the framework of electron tunneling through the alien contamination film. The asperity…

The differential drive assist steering (DDAS) system improves the handiness of steering by torque difference between two-side wheels. However, the DDAS and the vehicle stability control (VSC) will interfere with each other due to the same actuators. This paper proposes a hierarchical coordination control approach for the DDAS and VSC. The system is divided into four layers: the parameter estimation layer, the control region division layer, the coordination decision layer, and the control allocation layer. In the control region division layer, the stable area is firstly determined on the $\beta - \dot{\beta }$ phase portrait, and the coordinated control region is obtained by applying the simulated annealing algorithm inwardly and outwardly to the boundary of the stable area. In the coordination decision layer, the direct control strategy of steering hand wheel torque is used to establish the controller of the DDAS based on the fuzzy adaptive PID algorithm. At the same time, the controller of yaw moment is established based on the sliding mode control theory. In the stable region, the DDAS works separately. The VSC works separately in the unstable region. In the coordination region, the Sigmoid function is used to adjust the weight coefficient of the DDAS dynamically. Besides, the control allocation layer includes torque distribution controller and vehicle slip ratio controller. Finally, the vehicle model is established in CarSim, the control strategy, and the wheel motor model are established in Simulink. The joint simulation results of several typical conditions show that the designed control strategy can improve the handling stability of the vehicle effectively while DDAS working even in severe driving condition.

Although used extensively for object recognition, texture has for the most part been ignored as a feature used for background modelling and object segmentation. The complexity of working with texture descriptors for segmentation in videos is two-fold: the descriptive features cannot be calculated in real time and features extracted based on arbitrarily chosen regions or blocks in the frame are not stable enough to allow for building models sufficiently accurate, yet simple enough to be used for real-time segmentation. The paper proposes an approach that can be used to detect regions of texture, stable enough to be modelled using probabilistic models commonly used for foreground segmentation. Based on the evaluated stable texture regions, a discriminative texture descriptor is proposed that can be evaluated in real time. When video is captured from a stationary camera, the background is expected to be stationary to a degree and an adaptive model can be built to serve as basis for segmentation. For reasons of efficiency most adaptive models are learnt on a per pixel basis [4]. Joint domain-space modelling [3], as well as modelling of the sequence at two different scales, has been suggested as a way to enhance the segmentation and escape the limitations of single-pixel-based models[1]. The improved approaches still fail to consider the texture properties of the objects in the background and suffer from the noise introduced by neighboring objects being modelled as one. Texture of the background can be used to build models in a more informed way. Large stable regions in the texture of the background allow for larger scale modelling and more precise extraction of texture related features. Conversely, unstable regions in terms of texture correspond to transitions between different objects in the background, and the features should be extracted for each of the objects separately. An approach to background modelling and foreground segmentation derived form these principles is proposed in the paper. In each frame of the sequence stable texture regions are determined, texture descriptor (feature) values extracted using the stable regions information and used to model the background and segment the foreground using standard probabilistic approaches. The process is illustrated in Fig. 1, where the brighter patches in the stability map correspond to more stable regions, in terms of texture. Once the size of the stable-texture region at each location is determined, arbitrary descriptive features can be extracted from the frames of the sequence. In addition, one can choose any of a number of probabilistic methods [4][2] to learn the statistics of the features. The size of the stable texture regions can be determined online, using integral images [6]. Observe that:

An investigation of the mixing position in the recuperators on the performance of an auto-cascade refrigerator operating with a rectifying column

The paper reports the simplest 4-D dissipative autonomous chaotic system with line of equilibria and many unique properties. The dynamics of the new system contains a total of eight terms with one nonlinear term. It has one bifurcation parameter. Therefore, the proposed chaotic system is the simplest compared with the other similar 4-D systems. The Jacobian matrix of the new system has rank less than four. However, the proposed system exhibits four distinct Lyapunov exponents with $$(+, 0, -, -)$$ sign for some values of parameter and thus confirms the presence of chaos. Further, the system shows chaotic 2-torus $$(+,0,0,-)$$ , quasi-periodic $$[(0,0,-,-), (0,0,0,-)]$$ and multistability behaviour. Bifurcation diagram, Lyapunov spectrum, phase portrait, instantaneous phase plot, Poincare map, frequency spectrum, recurrence analysis, 0–1 test, sensitivity to initial conditions and circuit simulation are used to analyse and describe the complex and rich dynamic behaviour of the proposed system. The hardware circuit realisation of the new system validates the MATLAB simulation results. The new system is developed from the well-known Rossler type-IV 3-D chaotic system.