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Simulations are performed to investigate the nonlinear dynamics of a (2 + 1)-dimensional chemotaxis model of Keller-Segel (KS) type, with a logistic growth term. Because of its ability to display auto-aggregation, the KS model has been widely used to simulate self-organization in many biological systems. We show that the corresponding dynamics may lead to steady-states, to divergencies in a finite time as well as to the formation of spatiotemporal irregular patterns. The latter, in particular, appears to be chaotic in part of the range of bounded solutions, as demonstrated by the analysis of wavelet power spectra. Steady-states are achieved with sufficiently large values of the chemotactic coefficient (chi) and/or with growth rates r below a critical value r(c). For r > r(c), the solutions of the differential equations of the model diverge in a finite time. We also report on the pattern formation regime, for different values of chi, r and of the diffusion coefficient D. (C) 2011 Elsevier B.V. All rights reserved.

We consider the nonlinear propagation of electrostatic wave packets in an ultra-relativistic (UR) degenerate dense electron-ion plasma, whose dynamics is governed by the nonlocal two-dimensional nonlinear Schrodinger-like equations. The coupled set of equations is then used to study the modulational instability (MI) of a uniform wave train to an infinitesimal perturbation of multidimensional form. The condition for the MI is obtained, and it is shown that the nondimensional parameter, beta proportional to lambda(C)n(0)(1/3) (where lambda(C) is the reduced Compton wavelength and n(0) is the particle number density) associated with the UR pressure of degenerate electrons, shifts the stable (unstable) regions at n(0) similar to 10(30)cm(-3) to unstable (stable) ones at higher densities, i.e., n(0) greater than or similar to 7 x 10(33). It is also found that the higher the values of n(0), the lower is the growth rate of MI with cut-offs at lower wave numbers of modulation. Furthermore, the dynamical evolution of the wave packets is studied numerically. We show that either they disperse away or they blowup in a finite time, when the wave action is below or above the threshold. The results could be useful for understanding the properties of modulated wave packets and their multidimensional evolution in UR degenerate dense plasmas, such as those in the interior of white dwarfs and/or pre-Supernova stars.

In this paper we calculate the contribution to the ponderomotive force in a plasma from the electron spin using a recently developed model. The spin-fluid model used in the present paper contains spin-velocity correlations, in contrast to previous models used for the same purpose. Is its then found that previous terms for the spin-ponderomotive force are recovered, but also that additional terms appear. Furthermore, the results due to the spin-velocity correlations are confirmed using the spin-kinetic theory. The significance of our results is discussed.

The nonlinear propagation of two-dimensional (2D) quantum ion-acoustic waves (QIAWs) is studied in a quantum electron–ion plasma. By using a 2D quantum hydrodynamic model and the method of multiple scales, a new set of coupled nonlinear partial differential equations is derived which governs the slow modulation of the 2D QIAW packets. The oblique modulational instability (MI) is then studied by means of a corresponding nonlinear Schrödinger equation derived from the coupled nonlinear partial differential equations. It is shown that the quantum parameter H (ratio of the plasmon energy density to Fermi energy) shifts the MI domains around the kθ -plane, where k is the carrier wave number and θ is the angle of modulation. In particular, the ion-acoustic wave (IAW), previously known to be stable under parallel modulation in classical plasmas, is shown to be unstable in quantum plasmas. The growth rate of the MI is found to be quenched by the obliqueness of modulation. The modulation of 2D QIAW packets along the wave vector k is shown to be described by a set of Davey–Stewartson-like equations. The latter can be studied for the 2D wave collapse in dense plasmas. The predicted results, which could be important to look for stable wave propagation in laboratory experiments as well as in dense astrophysical plasmas, thus generalize the theory of MI of IAW propagations both in classical and quantum electron–ion plasmas.

Optical chaos is a topic of current research characterized by high-dimensional nonlinearity which is attributed to the delay-induced dynamics, high bandwidth and easy modular implementation of optical feedback. In light of these facts, which add enough confusion and diffusion properties for secure communications, we explore the synchronization phenomena in spatiotemporal semiconductor laser systems. The novel system is used in a two-phase colored image encryption process. The high-dimensional chaotic attractor generated by the system produces a completely randomized chaotic time series, which is ideal in the secure encoding of messages. The scheme thus illustrated is a two-phase encryption method, which provides sufficiently high confusion and diffusion properties of chaotic cryptosystem employed with unique data sets of processed chaotic sequences. In this novel method of cryptography, the chaotic phase masks are represented as images using the chaotic sequences as the elements of the image. The scheme drastically permutes the positions of the picture elements. The next additional layer of security further alters the statistical information of the original image to a great extent along the three-color planes. The intermediate results during encryption demonstrate the infeasibility for an unauthorized user to decipher the cipher image. Exhaustive statistical tests conducted validate that the scheme is robust against noise and resistant to common attacks due to the double shield of encryption and the infinite dimensionality of the relevant system of partial differential equations.

The nonlinear dynamics of coupled electrostatic upper-hybrid (UH) and Alfven waves (AWs) is revisited in a magnetized electron-ion plasma with charged dust impurities. A pair of nonlinear equations that describe the interaction of UH wave envelopes (including the relativistic electron mass increase) and the density as well as the compressional magnetic field perturbations associated with the AWs are solved numerically to show that many coherent solitary patterns can be excited and saturated due to modulational instability of unstable UH waves. The evolution of these solitary patterns is also shown to appear in the states of spatiotemporal coherence, temporal as well as spatiotemporal chaos, due to collision and fusion among the patterns in stochastic motion. Furthermore, these spatiotemporal features are demonstrated by the analysis of wavelet power spectra. It is found that a redistribution of wave energy takes place to higher harmonic modes with small wavelengths, which, in turn, results in the onset of Alfvenic turbulence in dusty magnetoplasmas. Such a scenario can occur in the vicinity of Saturn's magnetosphere as many electrostatic solitary structures have been observed there by the Cassini spacecraft.

The influence of the intrinsic spin of electrons on the propagation of circularly polarized waves in a magnetized plasma is considered. New eigenmodes are identified, one of which propagates below the electron cyclotron frequency, one above the spin-precession frequency, and another close to the spin-precession frequency. The latter corresponds to the spin modes in ferromagnets under certain conditions. In the non-relativistic motion of electrons, the spin effects become noticeable even when the external magnetic field B₀ is below the quantum critical magnetic field strength, i.e. B₀ < B_Q = 4.4138 × 10⁹T and the electron density satisfies n₀ ≫ n_c ≃ 10³²m⁻³. The importance of electron spin (paramagnetic) resonance (ESR) for plasma diagnostics is discussed.

The formation of small but finite amplitude electrostatic shocks in the propagation of quantum ion-acoustic waves obliquely to an external magnetic field is reported in a quantum electron-positron-ion plasma. Such shocks are seen to have double-layer (DL) structures composed of the compressive and accompanying rarefactive slow-wave fronts. Existence of such DL shocks depends critically on the quantum coupling parameter H associated with the Bohm potential and the positron to electron density ratio delta. The profiles may, however, steepen initially and reach a steady state with a number of solitary waves in front of the shocks. Such novel DL shocks could be a good candidate for particle acceleration in intense laser-solid density plasma interaction experiments as well as in compact astrophysical objects, e.g., magnetized white dwarfs.

The excitation of electrostatic wakefields in a magnetized spin quantum plasma by the classical and the spin-induced ponderomotive force (CPF and SPF, respectively) due to whistler waves is reported. The nonlinear dynamics of the whistlers and the wakefields is shown to be governed by a coupled set of nonlinear Schrodinger and driven Boussinesq-like equations. It is found that the quantum force associated with the Bohm potential introduces two characteristic length scales, which lead to the excitation of multiple wakefields in a strongly magnetized dense plasma (with a typical magnetic field strength B(0)greater than or similar to 10(9) T and particle density n(0)greater than or similar to 10(36) m(-3)), where the SPF strongly dominates over the CPF. In other regimes, namely, B(0)less than or similar to 10(8) T and n(0)less than or similar to 10(35) m(-3), where the SPF is comparable to the CPF, a plasma wakefield can also be excited self-consistently with one characteristic length scale. Numerical results reveal that the wakefield amplitude is enhanced by the quantum tunneling effect; however, it is lowered by the external magnetic field. Under appropriate conditions, the wakefields can maintain high coherence over multiple plasma wavelengths and thereby accelerate electrons to extremely high energies. The results could be useful for particle acceleration at short scales, i.e., at nanometer and micrometer scales, in magnetized dense plasmas where the driver is the whistler wave instead of a laser or a particle beam.

The nonlinear propagation of small but finite amplitude dust ion-acoustic waves (DIAWs) in an ion-beam driven plasma consisting of Boltzmannian electrons, positive ions, and stationary negatively charged dust grains is studied by using the standard reductive perturbation technique. It is shown that there exist two critical values (γ_c1) and (γ_c2) of ion beam to ion phase velocity ratio (γ), above and below which the beam generated solitons are not possible. The effects of the parameters, namely, γ, the ratio of the ion beam to plasma ion density (μ_i), the dust to ion density ratio (μ_d), and the ion beam to plasma ion mass ratio (μ) on both the amplitude and width of the stationary DIAWs, are analyzed numerically, and applications of the results to laboratory ion beam as well as space plasmas (e.g., auroral plasmas) are explained.