Microswimmers near surfaces

Both, in their natural environment and in a controlled experimental setup, microswimmers regularly interact with surfaces. These surfaces provide a steric boundary, both for the swimming motion and the hydrodynamic flow pattern. These effects typically imply a strong accumulation of microswimmers near surfaces. While some generic features can be derived, details of the swimmer shape and propulsion mechanism matter, which give rise to a broad range of adhesion phenomena and have to be taken into account to predict the surface accumulation for a given swimmer. We show in this minireview how numerical simulations and analytic theory can be used to predict the accumulation statistics for different systems, with an emphasis on swimmer shape, hydrodynamics interactions, and type of noisy dynamics.     

Synchronisation of chaos and its applications

Dynamical networks are important models for the behaviour of complex systems, modelling physical, biological and societal systems, including the brain, food webs, epidemic disease in populations, power grids and many other. Such dynamical networks can exhibit behaviour in which deterministic chaos, exhibiting unpredictability and disorder, coexists with synchronisation, a classical paradigm of order. We survey the main theory behind complete, generalised and phase synchronisation phenomena in simple as well as complex networks and discuss applications to secure communications, parameter estimation and the anticipation of chaos.     

Oscillator Synchronisation under Arbitrary Quasi-periodic Forcing

We study the problem of existence of response solutions for a real-analytic one-dimensional system, consisting of a rotator subject to a small quasi-periodic forcing with Bryuno frequency vector. We prove that at least one response solution always exists, without any assumption on the forcing besides smallness and analyticity. This strengthens the results available in the literature, where generic non-degeneracy conditions are assumed. The proof is based on a diagrammatic formalism and relies on renormalisation group techniques, which exploit the formal analogy with problems of quantum field theory; a crucial role is played by remarkable identities between classes of diagrams.     

Synchronisation of canonical measures for hyperbolic attractors

Under suitable conditions it is shown how to change the velocity of aC ² AxiomA attractor so that the Sinai-Ruelle-Bowen measure coincides with the measure of maximal entropy. These measures are obtained as limits of certain closed orbital measures.     

Overlap Synchronisation in Multipartite Random Energy Models

In a multipartite random energy model, made of a number of coupled generalised random energy models (GREMs), we determine the joint law of the overlaps in terms of the ones of the single GREMs. This provides the simplest example of the so-called overlap synchronisation.     

Hydrodynamic and Kinetic Model of Laser-Stimulated Homogenization of Volume-Structured Media

The paper is devoted to a theoretical investigation of laser-stimulated homogenization of regularly volume-structured and porous media with near-critical average density (close to the density corresponding to plasma resonance for the wavelength of the incident laser radiation). A concept of two-stage homogenization is proposed and theoretically substantiated: the first stage of fast partial smoothing of the mass distribution due to collisions of plasma flows in laser-heated and evaporated solid elements of the material structure and the second stage of slow complete smoothing of the density distribution due to viscosity dissipation of hydrodynamic perturbations. The properties of laser radiation absorption in a porous material are discussed and the high efficiency of internal “ volume” absorption of a laser pulse in porous media of average density significantly (by an order of magnitude) higher than the critical density is predicted.     

Transient and Stationary Simulations for a Quantum Hydrodynamic Model

The transient and stationary characteristics of a one-dimensional quantum hydrodynamic model are comparatively studied for semiconductor charge transport in a resonant tunnelling diode. When the bias is not small, our numerical results show a deviation of the asymptotic transient solutions from the stationary ones. A dynamic instability accounts for such deviation. The stationary quantum hydrodynamic model is therefore unsuitable in general for simulating quantum devices.     

对光滑粒子流体动力学模型π源的视像分析

∈利用光滑粒子流体动力学模型,研究了NN=200 GeV Au+Au碰撞产生的介子发射源的视像结果。 碰撞后的演化图显示, 系统在演化过程中呈现出明显的非均匀性颗粒集团分布。 这种发射源所得到的视像分析结果表明, 即使在相同的碰撞参数下, 不同事件的相对发射源函数也会存在差异。 这种差异在大碰撞参数下表现得尤为明显。 We investigate the imaging of pion emitting source produced in NN=200 GeV Au+Au collisions with NeXSPheRIO model. The pictures of the system evolution show that there is obvious inhomogeneous structure of granular lumps. The results of imaging analysis indicate that the relative source functions for the various events of the granular sources are different even though the events are with the same impact parameter. This difference is more evident for the events with large impact parameter.     

Hydrodynamic Limit for an Evolutional Model of Two-Dimensional Young Diagrams

We construct dynamics of two-dimensional Young diagrams, which are naturally associated with their grandcanonical ensembles, by allowing the creation and annihilation of unit squares located at the boundary of the diagrams. The grandcanonical ensembles, which were introduced by Vershik [17], are uniform measures under conditioning on their size (or equivalently, area). We then show that, as the averaged size of the diagrams diverges, the corresponding height variable converges to a solution of a certain non-linear partial differential equation under a proper hydrodynamic scaling. Furthermore, the stationary solution of the limit equation is identified with the so-called Vershik curve. We discuss both uniform and restricted uniform statistics for the Young diagrams.     

Synchronisation conventions in test theories of special relativity

The Mansouri-Sexl class of test theories of special relativity has motivated various experiments to observe or limit the difference between slow clock transport and Einstein synchronisation. These do not constitute tests of the isotropy of the one-way speed of light, since the latter is conventional. We discuss the effects of the conventionality of synchrony in the preferred frame, as well as the laboratory frame, within the Mansouri-Sexl formalism. We also consider the mutual inter-relationships of both synchrony conventions with measurements of the one-way speed of light and of time dilation factors.     

Synchronisation in networks of delay-coupled type-I excitable systems

We use a generic model for type-I excitability (known as the SNIPER or SNIC model) to describe the local dynamics of nodes within a network in the presence of non-zero coupling delays. Utilising the method of the Master Stability Function, we investigate the stability of the zero-lag synchronised dynamics of the network nodes and its dependence on the two coupling parameters, namely the coupling strength and delay time. Unlike in the FitzHugh-Nagumo model (a model for type-II excitability), there are parameter ranges where the stability of synchronisation depends on the coupling strength and delay time. One important implication of these results is that there exist complex networks for which the adding of inhibitory links in a small-world fashion may not only lead to a loss of stable synchronisation, but may also restabilise synchronisation or introduce multiple transitions between synchronisation and desynchronisation. To underline the scope of our results, we show using the Stuart-Landau model that such multiple transitions do not only occur in excitable systems, but also in oscillatory ones.     

Zero Debye Length Asymptotic of the Quantum Hydrodynamic Model for Semiconductors

In the present paper we consider the zero Debye length asymptotic of solutions of isentropic quantum hydrodynamic equations for semiconductors at nano-size and show that the current density consists of the divergence free vector field involved in the incompressible Euler equation and highly oscillating gradient vector field caused by the highly electric fields for small Debye length. This means that the quantum effects possibly may not dominate the charge transport within the channel of semiconductor devices (for instance MOSFET) of nano-size for isentropic quantum fluids.Dedicated to Professor Tai-Ping Liu on his sixtieth birthday     

Numerical Validation of Brenner's Hydrodynamic Model by Force Driven Poiseuille Flow

Recently Brenner [Physica A 349, 60 (2005)] proposed a modified Navier-Stokes set of equations. Based on some theoretical arguments and some limited experiments, the model is expected to be able to describe flows with a finite Knudsen number. In this work, we apply this model to the plane Poiseuille flow driven by a force, and compare the results with the Direct Simulation Monte Carlo (DSMC) measurements. It is found that Brenner's model is inadequate for flows with a finite Knudsen number.     

Hydrodynamic Model and Its Computational Code for Thermal Self-focusing

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The Thermal Equilibrium Solution of a Generic Bipolar Quantum Hydrodynamic Model

The thermal equilibrium state of a bipolar, isothermic quantum fluid confined to a bounded domain ,d = 1,2 or d = 3 is entirely described by the particle densities n, p, minimizing the energy

Synaptic Plasticity and Spike Synchronisation in Neuronal Networks

Brain plasticity, also known as neuroplasticity, is a fundamental mechanism of neuronal adaptation in response to changes in the environment or due to brain injury. In this review, we show our results about the effects of synaptic plasticity on neuronal networks composed by Hodgkin-Huxley neurons. We show that the final topology of the evolved network depends crucially on the ratio between the strengths of the inhibitory and excitatory synapses. Excitation of the same order of inhibition revels an evolved network that presents the rich-club phenomenon, well known to exist in the brain. For initial networks with considerably larger inhibitory strengths, we observe the emergence of a complex evolved topology, where neurons sparsely connected to other neurons, also a typical topology of the brain. The presence of noise enhances the strength of both types of synapses, but if the initial network has synapses of both natures with similar strengths. Finally, we show how the synchronous behaviour of the evolved network will reflect its evolved topology.     

Synchronisation of fractional-order time delayed chaotic systems with ring connection

In this paper, synchronisation of fractional-order time delayed chaotic systems in ring networks is investigated. Based on Lyapunov stability theory, a new generic synchronisation criterion for N-coupled chaotic systems with time delay is proposed. The synchronisation scheme is applied to N-coupled fractional-order time delayed simplified Lorenz systems, and the Adomian decomposition method (ADM) is developed for solving these chaotic systems. Performance analysis of the synchronisation network is carried out. Numerical experiments demonstrate that synchronisation realises in both state variables and intermediate variables, which verifies the effectiveness of the proposed method.     

New Feedback Control Model in the Lattice Hydrodynamic Model Considering the Historic Optimal Velocity Difference Effect

A feedback control model of lattice hydrodynamic model is proposed by taking the information of the historic optimal velocity into account for the traffic system. The modern control theory is applied for the linear stability condition with feedback control signal. The result shows that the stability of traffic flow is closely related to the information of the historic optimal velocity. Furthermore, numerical simulations conform that the new feedback control did increase the stability of traffic flow efficiently, which is in accord with theoretical analysis.     

A Hydrodynamic Model of the Interaction of Picosecond Laser Pulses with Condensed Targets

We consider a physical model of the interaction of highpower laser pulses with plasma created upon irradiation of condensed targets. The model is based on the equations of singlefluid, twotemperature hydrodynamics taking into account the ponderomotive force, and the Maxwell equations for laser radiation at oblique incidence in the cases of s and ppolarizations. The model takes into account the generation of fast electrons in the conditions of plasma resonance at the critical surface, and their transport with consideration for the friction force, caused by the ionization losses. Heating of ions in the plasma due to beats of the ponderomotive potential is considered. The results of numerical modeling of the interaction of a picosecond laser pulse, containing a prepulse, with a deuterium target at power densities of 10¹⁶–10¹⁷ W/cm² are presented. It is shown that the neutron yield of the DDreaction decreases with increase in prepulse energy, because the plasma created inhibits heating of the dense region of the target where a high rate of the reactions can be realized. It is also shown that the laser radiation losses caused by the stimulated scattering increase with increase in prepulse energy.