Impact of osmotic pressure on the stability of Taylor vortices

We use linear stability analysis and direct numerical simulations to investigate the coupling between centrifugal instabilities, solute transport and osmotic pressure in a Taylor–Couette configuration that models rotating dynamic filtration devices. The geometry consists of a Taylor–Couette cell with a superimposed radial throughflow of solvent across two semi-permeable cylinders. Both cylinders totally reject the solute, inducing the build-up of a concentration boundary layer. The solute retroacts on the velocity field via the osmotic pressure associated with the concentration differences across the semi-permeable cylinders. Our results show that the presence of osmotic pressure strongly alters the dynamics of the centrifugal instabilities and substantially reduces the critical conditions above which Taylor vortices are observed. It is also found that this enhancement of the hydrodynamic instabilities eventually plateaus as the osmotic pressure is further increased. We propose a mechanism to explain how osmosis and instabilities cooperate and develop an analytical criterion to bound the parameter range for which osmosis fosters the hydrodynamic instabilities.

The Study of Generalized Synchronization between Two Identical Neurons Based on the Laplace Transform Method

In this paper, a new method is proposed based on the auxiliary system approach to investigate generalized synchronization between two identical neurons with unidirectional coupling. Different from other studies, the synchronization error system between the response and auxiliary systems is converted into a set of Volterra integral equations according to the Laplace transform method and convolution theorem. By using the successive approximation method in the theory of integral equations, an analytical criterion for the detection of generalized synchronization between two identical neurons is obtained. It is found that there is a time difference between two signals of neurons when the generalized synchronization between them is achieved. Furthermore, the value of the time difference has no relation to the generalized synchronization condition but depends on the coupling function between two neurons. The study in this paper shows that one can construct a coupling function between two identical neurons using the current signal of the drive system to predict its future signal or make its past signal reappear.

Relativistic Dynamical Stability Criterion of Multiplanet Systems with a Distant Companion

Multiplanetary systems are prevalent in our Galaxy. The long-term stability of such systems may be disrupted if a distant inclined companion excites the eccentricity and inclination of the inner planets via the eccentric Kozai–Lidov mechanism. However, the star–planet and the planet–planet interactions can help stabilize the system. In this work, we extend the previous stability criterion that only considered the companion–planet and planet–planet interactions by also accounting for short-range forces or effects, specifically, relativistic precession induced by the host star. A general analytical stability criterion is developed for planetary systems with N inner planets and a relatively distant inclined perturber by comparing precession rates of relevant dynamical effects. Furthermore, we demonstrate as examples that in systems with two and three inner planets, the analytical criterion is consistent with numerical simulations using a combination of Gauss’s averaging method and direct N-body integration. Finally, the criterion is applied to observed systems, constraining the orbital parameter space of a possible undiscovered companion. This new stability criterion extends the parameter space in which an inclined companion of multiplanet systems can inhabit.

The role of sliding in ice stream formation

Ice streams are bands of fast-flowing ice in ice sheets. We investigate their formation as an example of spontaneous pattern formation, based on positive feedbacks between dissipation and basal sliding. Our focus is on temperature-dependent subtemperate sliding, where faster sliding leads to enhanced dissipation and hence warmer temperatures, weak- ening the bed further, and on a similar feedback driven by basal melt water production. Using a novel thermomechanical model, we show that formation of a steady pattern of fast and slow flow can occur through the downstream amplification of noise in basal conditions. This process can lead to the establishment of a clearly defined ice stream separated from slowly flowing, cold-based ice ridges by narrow shear margins. Our model is also able to predict the downstream widening of ice streams due to dissipation and heat transport in these margins. We also show that downward advection of cold ice induced by accelerated sliding is the primary stabilizing mechanism that can suppress ice steam formation altogether, and give an approximate, analytical criterion for pattern formation.

Efficient Design Strategy for Optimizing the Settling Time in Three-Stage Amplifiers Including Small- and Large-Signal Behavior

An analytical criterion for the optimization of the small-signal settling time in three-stage amplifiers is carried out. The criterion is based on making equal the two exponential decays of the step response. Including slew-rate effects, a useful design strategy for the design of three-stage operational transconductance amplifier is provided. Extensive time-domain simulations on a transistor-level design in a 65-nm CMOS process confirm the validity of the proposed approach.

Ice stream formation

<div>Ice streams are the arteries through which a large fraction of the ice lost from Antarctica is discharged. With the introduction of "higher order" mechanics, the representation of ice streams in ice sheet models appears to have become more robust, eliminating previously ubiquitous grid effects. The detailed processes that control ice stream formation --- and the minimal ingredients that a model requires to represent them faithfully --- remain incompletely explored. Here we focus on "pure" ice streams, not confined to topographic troughs. We study two mechanisms that can cause their formation through feedbacks between enhanced dissipation and faster sliding, and study the minimal model capable of reproducing both mechanisms. In the first mechanism, increased dissipation raises basal temperature before the melting point is reached, and subtemperate sliding is in turn facilitated by these higher temperatures, leading to yet more dissipation. This mechanism has received very limited attention in the literature, and is not fully incorporated in at least some commonly used ice sheet model. The second, better-studied mechanism involves basal effective pressure rather than temperature as the degree of freedom that creates a positive feedback: increased dissipation produces additional meltwater. Draining that excess water requires a lower effective pressure in typical "distributed" draiange ssytems. Reduced effective pressure in turn leads to faster sliding, and yet more dissipation. The two mechanisms are distinct and one can operate in the absence of the other, but both can cause the formation of ice streams whose trunks have very similar features. Using a novel, hybrid `shallow/"full Stokes" flow' model derived from first principles, we show how accelerated flow due to either feedback leads to advection of cold ice to the bed, and demonstrate that this is the key negative feedback that controls ice steam formation due to its role in cooling the bed. Downward advection occurs both along the axis of the incipient ice stream, and in the transverse plane. There, a significant secondary flow towards the ice stream centre develops, which is of equal importance to along-flow advection in controlling heat transport. Our model is unique in its ability to fully resolve that secondary flow while still using the "shallowness" of the flow to simplify computations of ice stream physics. The formation of ice streams can be understood as "spatial" instabilities in which small-scale structure is amplified in the downflow direction, for which we derive an analytical criterion. Our model self-consistently predicts the formation of a sharply-defined ice stream margin and very cold-bedded ice ridges over a relatively short downstream distance from the onset of patterning for both mechanisms. The model also shows how basal dissipation in the margin leads to appreciable stream widening in the downstream direction, while englacial dissipation in combination with advection can lead to a pronounced peak in basal water supply some distance inside the margins. We demonstrate additionally that the emergent patterns can be unstable in time, and identify the properties required of a model that can handle such temporal instabilities.</div>

A Synchronization Criterion for Two Hindmarsh-Rose Neurons with Linear and Nonlinear Coupling Functions Based on the Laplace Transform Method

In this paper, an analytical criterion is proposed to investigate the synchronization between two Hindmarsh-Rose neurons with linear and nonlinear coupling functions based on the Laplace transform method. Different from previous works, the synchronization error system is expressed in its integral form, which is more convenient to analyze. The synchronization problem of two HR coupled neurons is ultimately converted into the stability problem of roots to a nonlinear algebraic equation. Then, an analytical criterion for synchronization between the two HR neurons can be given by using the Routh-Hurwitz criterion. Numerical simulations show that the synchronization criterion derived in this paper is valid, regardless of the periodic spikes or burst-spike chaotic behavior of the two HR neurons. Furthermore, the analytical results have almost the same accuracy as the conditional Lyapunov method. In addition, the calculation quantities always are small no matter the linear and nonlinear coupling functions, which show that the approach presented in this paper is easy to be developed to study synchronization between a large number of HR neurons.

Пики термодесорбции водорода: моделирование и интерпретация

Various models of hydrogen thermal desorption peaks are analyzed. The dynamics model of the volume-averaged concentration with a continuum parameter allows integrally taking into account the degree of dominance of the limiting factors (diffusion and recombination of atoms into molecules during desorption). An analytical criterion for peaks symmetry is proposed in the context of comparison with the method of decomposing the component spectrum into the sum of Gaussian. Modifications of the Kissinger method for estimating the activation energy of desorption in experiments with several heating rates and procedures for solving the inverse problem of parametric identification of a unimodal peak using only one heating rate are presented. A comparative with a diffusion model with dynamic boundary conditions is performed. It is shown that the cause of local peaks can be not only capture with different binding energies but also the dynamics of interaction of bulk and surface processes, change in the surface structure during heating.