On the theory of instabilities arising at quark-gluon plasma formation

Collisions of two degenerate quark Fermi liquids are studied. It is shown that there arise instabilities, which manifest themselves in propagation of growing oscillations corresponding to the modes existing in a Fermi liquid at rest. Quark jets are likely to appear in the directions of the growing oscillations propagation.

The instabilities studied in this work are similar to the beam instability in ordinary electron plasma.     

Stern-Brocot trees in cascades of mixed-mode oscillations and canards in the extended Bonhoeffer-van der Pol and the FitzHugh-Nagumo models of excitable systems

We report a systematic two-parameter study of the organization of mixed-mode oscillations and period-adding sequences observed in an extended Bonhoeffer-van der Pol and in a FitzHugh-Nagumo oscillator. For both systems, we construct isospike diagrams and show that the number of spikes of their periodic oscillations are organized in a remarkable hierarchical way, forming a Stern-Brocot tree. The Stern-Brocot tree is more general than the Farey tree. We conjecture the Stern-Brocot tree to also underlie the hierarchical structure of periodic oscillations of other systems supporting mixed-mode oscillations.     

Mixed-mode oscillations in a homogeneous pH-oscillatory chemical reaction system

We examine experimentally a chemical system in a flow-through stirred reactor, which is known to provide large-amplitude oscillations of the pH value. By systematic variation of the flow rate, we find that the system displays hysteresis between a steady state and oscillations, and more interestingly, a transition to chaos involving mixed-mode oscillations. The basic pattern of the measured pH in the mixed-mode regime includes a large-scale peak followed by a series of oscillations on a much smaller scale, which are usually highly irregular and of variable duration. The bifurcation diagram shows that chaos sets in via a period-doubling route observed on the large-amplitude scale, but simultaneously small-amplitude oscillations are involved. Beyond the apparent accumulation of period doubling bifurcations, a mixed-mode regime with irregular oscillations on both scales is observed, occasionally interrupted by windows of periodicity. As the flow rate is further increased, chaos turns into quasiperiodicity and later to a simple small-amplitude periodic regime. Dynamics of selected typical regimes were examined with the tools of nonlinear time-series analysis, which include phase space reconstruction of an attractor and calculation of the maximal Lyapunov exponent. The analysis points to deterministic chaos, which appears via a period doubling route from below and via a route involving quasiperiodicity from above, when the flow rate is varied.     

Complex mixed-mode periodic and chaotic oscillations in a simple three-variable model of nonlinear system

A detailed study of a generic model exhibiting new type of mixed-mode oscillations is presented. Period doubling and various period adding sequences of bifurcations are observed. New type of a family of 1D (one-dimensional) return maps is found. The maps are discontinuous at three points and consist of four branches. They are not invertible. The model describes in a qualitative way mixed-mode oscillations with two types of small amplitude oscillations at local maxima and local minima of large amplitude oscillations, which have been observed recently in the Belousov-Zhabotinsky system. (c) 2000 American Institute of Physics.     

Mixed-mode oscillations and chaos in a glow discharge

We present results from numerical simulations on mixed-mode oscillations and chaos excited in a glow discharge, where a model of one-dimensional fluid equations coupled with an external circuit is used. Long duration of high ion and electron densities and fast recharge of a capacitor after a breakdown contribute to the generation of mixed-mode oscillations. The chaotic behavior is characterized by a one-dimensional multibranched map.     

Zigzag and varicose instabilities of a localized stripe

A localized stripe solution to a reaction-diffusion equation can lose stability simultaneously to zigzag and varicose perturbations at a codimension-two point. The resulting mode interaction is described by O(2)xZ(2) equivariant amplitude equations. Stationary mixed-mode solutions are found which can undergo instabilities to breathing modes or to patterns which travel along the stripe.     

Instabilities in Self-Focused Electron Beams

The appearance of large amplitude oscillations and attenuation of beam current have been observed in high perveance electrically self-focused beams. These phenomena are shown to be due to instabilities produced by the interaction of the beam with its self-generated plasma. The critical current which must be exceeded for the instabilities to appear and the frequencies of the oscillations have been related to beam and background parameters and the dimensions of the experimental system.     

On the theory of ion-beam plasma instability

High-and low-frequency convective instabilities of an ion beam in a longitudinal magnetic field in the presence of the gas entering the ion transportation channel from the plasma source are studied theoretically. Spatial growth rates of the beam instabilities are found and mechanisms for the nonlinear saturation of potential oscillations are investigated in the hydrodynamic approximation. The averaged (over the oscillation period) effective beam emittance associated with collective fast-ion heating is determined. The results obtained can be applied to calculating the dynamics of negative ion beams in the injectors of linear and cyclic accelerators.     

Voltage interval mappings for activity transitions in neuron models for elliptic bursters

We performed a thorough bifurcation analysis of a mathematical elliptic bursting model, using a computer-assisted reduction to equationless, one-dimensional Poincaré mappings for a voltage interval. Using the interval mappings, we were able to examine in detail the bifurcations that underlie the complex activity transitions between: tonic spiking and bursting, bursting and mixed-mode oscillations, and finally mixed-mode oscillations and quiescence in the FitzHugh–Nagumo–Rinzel model. We illustrate the wealth of information, qualitative and quantitative, that was derived from the Poincaré mappings, for the neuronal models and for similar (electro)chemical systems.     

Mixed-mode oscillations and cluster patterns in an electrochemical relaxation oscillator under galvanostatic control

We studied the dynamics of a prototypical electrochemical model, the electro-oxidation of hydrogen in the presence of poisons, under galvanostatic conditions. The lumped system exhibits relaxation oscillations, which develop mixed-mode oscillations (MMOs) for low preset currents. A fast-slow analysis of the homogeneous dynamics reveals that the MMOs arise from a fast oscillating subsystem and a one-dimensional slow manifold. In the spatially extended system, the galvanostatic constraint imposes a synchronizing global coupling that drives the system into cluster patterns. The properties of the cluster patterns (CPs) result from an intricate interplay of the nature of the local oscillators, the global constraint, and a nonlocal coupling through the electrolyte. In particular, we find that the global constraint suppresses small-amplitude oscillations of MMOs and prevents domains oscillating out of phase from occupying equal regions in phase space. The nonlocal coupling causes each individual clustered region to oscillate on a different limit cycle. Typically multistability of CPs is found. Coexisting patterns possess different oscillation periods and a different total fraction in space that occupies the in-phase or out-of-phase state, respectively.     

Nonlinear torsional oscillations in rotating systems

Torsional oscillations, temporal variations in the differential rotation in rotating systems, are a well-established phenomenon in the fluid regions of convective stars and planets. We show for the first time that nonlinear torsional oscillations can be generated and maintained by convective instabilities in rotating systems.     

General theory of microscopic dynamical response in surface probe microscopy: from imaging to dissipation

We present a general theory of atomistic dynamical response in surface probe microscopy when two solid surfaces move with respect to each other in close proximity, when atomic instabilities are likely to occur. These instabilities result in a bistable potential energy surface, leading to temperature dependent atomic scale topography and damping (dissipation) images. The theory is illustrated on noncontact atomic force microscopy and enables us to calculate, on the same footing, both the frequency shift and the excitation signal amplitude for tip oscillations. We show, using atomistic simulations, how dissipation occurs through reversible jumps of a surface atom between the minima when a tip is close to the surface, resulting in dissipated energies of 1.6 eV. We also demonstrate that atomic instabilities lead to jumps in the frequency shift that are smoothed out with increasing temperature.     

Statistical physics of a chemical reaction model

We give a nonlinear theory of fluctuations at chemical instabilities using the Prigogine-Lefever-Nicolis model. Our results apply to arbitrary dimensions, a mode-continuum and temporal oscillations. Striking analogies to laser phase-transitions and hydrodynamic instabilities are found.     

Coherent instabilities in the NICA collider

The thresholds of coherent beam instabilities in the NICA collider are analyzed in the present work. Studies were limited on the coherent oscillations in one of the rings due to the weakness of the beam-beam interaction forces when compared to the single-beam Coulomb forces. The thresholds of the single-beam and multiple-beam instabilities are estimated for the chosen collider operation scenario. Measures that have to be taken to suppress the instabilities are discussed.     

Numerical Study of Instabiities in Magnetized Inhomogeneous Plasmas under the Effect of Ionization

Influence of ionization is studied on two stream instability (TSI) in an inhomogeneous plasma in the presence of obliquely applied magnetic field. In addition to the usual TSI, a new type of instability is found to occur in this system, which is driven by the magnetic field and survives for relatively longer wavelength of oscillations. The growth rates of both the instabilities are enhanced by the magnetic field but their magnitudes attain a minimum value at certain angles of the wave propagation depending upon the wavelength of oscillations. At a critical value of ionization rate there is a sudden fall in the growth of both the instabilities, the reason of which is understood as the Landau damping. A further enhancement in the ionization suppresses the usual TSI whereas the magnetic field‐driven instability attains much lower growth. This new type of instability grows faster in the plasma having heavier ions, but shows a weak dependence on the charge of the ions. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Potential-Well Distortion Effect and Coherent Instabilities of Electron Bunches in Storage Rings

The effect of electromagnetic interaction between electron bunches and the vacuum chamber of a storage ring on the longitudinal motion of bunches is studied. Specifically, the potential-well distortion effect and the so-called coherent instabilities of coupled bunches are considered. An approximate analytical solution for the frequencies of incoherent oscillations of bunches distributed arbitrarily within the ring is obtained for a distorted potential well. A new approach to determining frequencies of coherent oscillations and an approximate analytical relation for estimating the stability of a system of bunches as a function of their distribution in the accelerator orbit are presented.     

Increasing spatial complexity toward near-resonant regimes of quadratic media

Near-resonant conditions lead to a strong interaction between saddle node and modulational instabilities in diffractive optical frequency down-conversion systems. The study of such an interaction reveals a new type of stable phase-locked mixed-mode hexagonal structure below the lasing threshold. Without this interaction, hexagonal structures do not exist. The analytical expression of the threshold associated with these structures is derived. Numerical solutions of the governing equations are in close agreement with analytical predictions.     

Recombination waves in CdS induced by optical quenching

Low-frequency current oscillations induced by optical quenching were observed in highly photosensitive CdS crystals. No evidence of a negative differential resistivity was found. The current oscillations were observed at room temperature at electric field strengths of 100–800 V/cm. As shown by probe measurements, the instabilities resulted from a bulk phenomenon. The oscillations are related to the excitation of recombination waves, predicted by Konstantinov and Perel.     

Chaotic oscillations associated with the breakup of polarization entangled coherent states in a microchip solid-state laser

We demonstrate the breakup of spatial-polarization entangled lasing patterns, which possess vector phase singularities, and the resultant dynamic instabilities featuring chaotic oscillations. The frequency splitting between a pair of Ince-Gauss (IG) lasing modes, originally forming a coherent entanglement state, and a self-excited additional nonorthogonal IG mode through a new class of transverse effect of self-injection pattern seeding, is shown to result in modal-interference-induced modulation at the beat frequency, leading to chaotic oscillations.     

On the instability of longitudinal oscillations in an inhomogeneous isotropic plasma

The stability of forced nonlinear longitudinal oscillations in isotropic plasma is investigated. It is demonstrated that at certain ratio between the parameters of the plasma and the external force there arise parametric-like instabilities, and both harmonics and subharmonic oscillations of the order of 1/3 become unstable. The growth rate of the unstable oscillations and conditions under which they occur are defined.