Controlling an oscillating Jackson-type network having state-dependent service rates

We consider a Jackson-type network comprised of two queues having state-dependent service rates, in which the queue lengths evolve periodically, exhibiting noisy cycles. To reduce this noise a certain heuristic, utilizing regions in the phase space in which the system behaves almost deterministically, is applied. Using this heuristic, we show that in order to decrease the probability of a customers overflow in one of the queues in the network, the server in that same queue – contrary to intuition – should be shut down for a short period of time. Further noise reduction is obtained if the server in the second queue is briefly shut down as well, when certain conditions hold.     

Damping of Crank–Nicolson error oscillations

The Crank–Nicolson (CN) simulation method has an oscillatory response to sharp initial transients. The technique is convenient but the oscillations make it less popular. Several ways of damping the oscillations in two types of electrochemical computations are investigated. For a simple one-dimensional system with an initial singularity, subdivision of the first time interval into a number of equal subintervals (the Pearson method) works rather well, and so does division with exponentially increasing subintervals, where however an optimum expansion parameter must be found. This method can be computationally more expensive with some systems. The simple device of starting with one backward implicit (BI, or Laasonen) step does damp the oscillations, but not always sufficiently. For electrochemical microdisk simulations which are two-dimensional in space and using CN, the use of a first BI step is much more effective and is recommended. Division into subintervals is also effective, and again, both the Pearson method and exponentially increasing subintervals methods are effective here. Exponentially increasing subintervals are often considerably more expensive computationally. Expanding intervals over the whole simulation period, although capable of satisfactory results, for most systems will require more cpu time compared with subdivision of the first interval only.     

The formation of an oscillating system during the sputtering of sapphire single crystal with pulsed glow discharge

Sapphire (α-Al₂O₃, transparent corundum) single crystals were analyzed with pulsed direct current glow discharge mass spectrometry. Combined hollow cathode was used as a discharge cell. To obtain stable sputtering of dielectric material, a formation of initial surface conductivity via preliminary vacuum deposition of thin metallic layer was proposed. Al and Ta film of different thickness (30–200 nm) were considered for this purpose. The approach was found to provide the effective sputtering of dielectrics. The formation of an oscillating system was shown during the sputtering of sapphire samples in a tantalum combined hollow cathode cell. For oriented sapphire single crystals, periodic oscillations of ²⁷Al⁺ intensity were acquired. This phenomenon was observed only for dielectric single crystals and not for other dielectric samples, e.g. alumina ceramic or fused quartz. The linear dependence of oscillation period on the duration of discharge pulse was found. The origin of these oscillations seems to be attributed to periodic fluctuations of surface conductivity. Oscillation periods calculated for two different orientations of sapphire single crystals (001 and 012) were found to be proportional to the main period of sapphire lattice. Therefore, an assumption that the crystal internal structure of the sample might be the cause of the oscillations is discussed.     

Resonant Leading Term Geometric Optics Expansions with Boundary Layers for Quasilinear Hyperbolic Boundary Problems

We construct and justify leading order weakly nonlinear geometric optics expansions for nonlinear hyperbolic initial value problems, including the compressible Euler equations. The technique of simultaneous Picard iteration is employed to show approximate solutions tend to the exact solutions in the small wavelength limit. Recent work [2 Coulombel, J.-F., Gues, O., and Williams, M., 2011. Resonant leading order geometric optics expansions for quasilinear hyperbolic fixed and free boundary problems, Comm. Part. Diff. Eqs. 36 (2011), pp. 1797–1859.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]] by Coulombel et al. studied the case of reflecting wave trains whose expansions involve only real phases. We treat generic boundary frequencies by incorporating into our expansions both real and nonreal phases. Nonreal phases introduce difficulties such as approximately solving complex transport equations and result in the addition of boundary layers with exponential decay. This also prevents us from doing an error analysis based on almost periodic profiles as in [2 Coulombel, J.-F., Gues, O., and Williams, M., 2011. Resonant leading order geometric optics expansions for quasilinear hyperbolic fixed and free boundary problems, Comm. Part. Diff. Eqs. 36 (2011), pp. 1797–1859.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]].     

Ellipsometric and microwave reflectivity studies of current oscillations during anodic dissolution of p-Si in fluoride solutions

Periodic current oscillations during anodic dissolution of monocrystalline p-Si(100) in buffered ammonium fluoride solutions (0.1 mol dm⁻³ fluoride, pH 4.5) were investigated using a flow cell in order to eliminate mass transport limitations. The flow cell was designed to permit simultaneous in-situ ellipsometry, impedance and potential modulated microwave reflectivity measurements. Analysis of the ellipsometric response showed that the current oscillations are accompanied by a synchronous variation of the overall oxide thickness with an amplitude of 4.5±0.1 nm. Analysis of the relationship between the total oxide thickness and the current during the oscillation cycle shows that to a first approximation the rate of chemical dissolution of anodic oxide remains constant. Oscillations of the electrode admittance and potential modulated microwave reflectivity were also measured. The imaginary component of the admittance is related to the oscillation in thickness of a narrow inner region of ‘dry’ oxide and to changes in the accumulation capacitance. The oscillation in the potential modulated microwave reflectivity is interpreted in terms of the changes in the density of holes accumulated at the p-Si SiO₂ interface.     

Dissipative oscillations in spatially restricted ecosystems due to long range migration

An ecosystem containing three interacting species is studied using both Mean Field approach and Kinetic Monte Carlo simulations on a lattice substrate. The so called 3rd order LLV model involves birth, death and reaction processes with 3rd order nonlinearities and feedbacks. At the mean field level this system exhibits conservative oscillations; the analytic form of the constant of motion is presented. The stochastic simulations show that the density oscillations disappear for sufficiently large lattices, while they are present locally, on small lattice windows. Introduction of mixing via long range migration in the two reacting species changes this picture. For small migration rates p, the behavior remains as with p = 0 and the system is divided into local asynchronous oscillators. As p increases the system passes through a phase transition and exhibits a weak disorder limit cycle through a supercritical Hopf-like bifurcation. The amplitude of the limit cycle depends on the rate p, on the range of migration r and on the system kinetic rates k₁, k₂ and k₃.     

Self-organization in nonlinear dynamical systems and its relation to the materials science

This review paper presents briefly the main concepts of nonlinear dynamics and their exemplary manifestations in selected systems, including those important from the point of view of materials science. It is an extended version of the conference presentation. The conditions of instabilities leading to spontaneous formation of dissipative structures are given. Principles of nonlinear dynamics are illustrated with several examples from the homogeneous and heterogeneous and physical and chemical systems: pattern formation in the convective motion of fluids subject to various kinds of driving forces, periodic precipitation phenomena, oscillations, and pattern formation in the Belousov–Zhabotinski (BZ) reaction and the catalytic oxidation of thiocyanate ions with hydrogen peroxide, as well as bistability and tristability in the electrochemical reduction of azide complexes of nickel(II). The application of nonlinear dynamics in materials science is first exemplified by its role in polymerization reactions. Such processes can either exhibit internal couplings leading to oscillations or can be coupled with the chemical oscillatory process through, e.g., the covalent bonding of its catalyst to the polymer network. Other selected examples of the application of nonlinear dynamics in materials science, referring to electrochemical processes, were briefly reviewed. Nonlinear dynamics appears to be useful for designing new materials, including those at the nanoscale.

Artificial graphenes: Dirac matter beyond condensed matter

After the discovery of graphene and of its many fascinating properties, there has been a growing interest for the study of “artificial graphenes”. These are totally different and novel systems that bear exciting similarities with graphene. Among them are lattices of ultracold atoms, microwave or photonic lattices, “molecular graphene” or new compounds like phosphorene. The advantage of these structures is that they serve as new playgrounds for measuring and testing physical phenomena that may not be reachable in graphene, in particular the possibility of controlling the existence of Dirac points (or Dirac cones) existing in the electronic spectrum of graphene, of performing interference experiments in reciprocal space, of probing geometrical properties of the wave functions, of manipulating edge states, etc. These cones, which describe the band structure in the vicinity of the two connected energy bands, are characterized by a topological “charge”. They can be moved in the reciprocal space by appropriate modification of external parameters (pressure, twist, sliding, stress, etc.). They can be manipulated, created or suppressed under the condition that the total topological charge be conserved. In this short review, I discuss several aspects of the scenarios of merging or emergence of Dirac points as well as the experimental investigations of these scenarios in condensed matter and beyond.     

Modelling Spatial Variations of the Speed of Light

We extend a new method to measure possible variation of the speed of light by using Baryon Acoustic Oscillations and the Hubble function onto an inhomogeneous pressure model of the universe. The method relies on the fact that there is a simple relation between the angular diameter distance maximum and the Hubble function (H) evaluated at the same maximum‐condition redshift, which includes the speed of light c. One limit of such a method was the assumption of the vanishing of spatial curvature (though, as it has been shown, a non‐zero curvature has negligible effect). In this paper, apart from taking into account an inhomogeneity, we consider non‐zero spatial curvature and calculate an exact relation between and H. Our main result is the evaluation if current or future missions such as Square Kilometer Array (SKA) can be sensitive enough to detect any spatial variation of c which can in principle be related to the recently observed spatial variation of the fine structure constant (an effect known as α‐dipole).     

Explicit Solutions of Nonconvex Variational Problems in Dimension One

We propose a method of finding the generalized solutions of nonconvex variational problems by solving an appropriate differential inclusion that is motivated by necessary conditions of optimality for such generalized minimizers. Accepted 28 September 1998