Abhijit Sen

Chimera states: the existence criteria revisited.

Chimera states, representing a spontaneous breakup of a population of identical oscillators that are identically coupled, into subpopulations displaying synchronized and desynchronized behavior, have traditionally been found to exist in weakly coupled systems and with some form of nonlocal coupling between the oscillators. Here we show that neither the weak-coupling approximation nor nonlocal coupling are essential conditions for their existence. We obtain, for the first time, amplitude-mediated chimera states in a system of globally coupled complex Ginzburg-Landau oscillators. We delineate the dynamical origins for the formation of such states from a bifurcation analysis of a reduced model equation and also discuss the practical implications of our discovery of this broader class of chimera states.

Amplitude-mediated chimera states

We investigate the possibility of obtaining chimera state solutions of the nonlocal complex Ginzburg-Landau equation (NLCGLE) in the strong coupling limit when it is important to retain amplitude variations. Our numerical studies reveal the existence of a variety of amplitude-mediated chimera states (including stationary and nonstationary two-cluster chimera states) that display intermittent emergence and decay of amplitude dips in their phase incoherent regions. The existence regions of the single-cluster chimera state and both types of two-cluster chimera states are mapped numerically in the parameter space of C(1) and C(2), the linear and nonlinear dispersion coefficients, respectively, of the NLCGLE. They represent a new domain of dynamical behavior in the well-explored rich phase diagram of this system. The amplitude-mediated chimera states may find useful applications in understanding spatiotemporal patterns found in fluid flow experiments and other strongly coupled systems.

Nonlinear dynamics of magnetic islands imbedded in small-scale turbulence.

The nonlinear dynamics of magnetic tearing islands imbedded in a pressure gradient driven turbulence is investigated numerically in a reduced magnetohydrodynamic model. The study reveals regimes where the linear and nonlinear phases of the tearing instability are controlled by the properties of the pressure gradient. In these regimes, the interplay between the pressure and the magnetic flux determines the dynamics of the saturated state. A secondary instability can occur and strongly modify the magnetic island dynamics by triggering a poloidal rotation. It is shown that the complex nonlinear interaction between the islands and turbulence is nonlocal and involves small scales.

A Critique of Recent Semi-Classical Spin-Half Quantum Plasma Theories

Certain recent semi-classical theories of spin-half quant um plasmas are examined with regard to their internal consistency, physical applicabilit y and relevance to fusion, astrophysical and condensed matter plasmas. It is shown that the derivations and some of the results obtained in these theories are internally inconsistent and contradi ct well-established principles of quantum and statistical mechanics, especially in their treatment o f fermions and spin. Claims of large semiclassical effects of spin magnetic moments that could dominate the plasma dynamics are found to be invalid both for single-particles and collectively. Lar mor moments dominate at high temperature while spin moments cancel due to Pauli blocking at low temperatures. Explicit numerical estimates from a variety of plasmas are provided to demonstrate that spin effects are indeed much smaller than many neglected classical effects. The analysis presented suggests that the aforementioned ‘Spin Quantum Hydrodynamic’ theories are not rel evant to conventional laboratory or astrophysical plasmas.

A KdV-like advection-dispersion equation with some remarkable properties

Abstract We discuss a new non-linear PDE, u t + ( 2 u xx / u ) u x = ϵ u xxx , invariant under scaling of dependent variable and referred to here as SIdV. It is one of the simplest such translation and space–time reflection-symmetric first order advection–dispersion equations. This PDE (with dispersion coefficient unity) was discovered in a genetic programming search for equations sharing the KdV solitary wave solution. It provides a bridge between non-linear advection, diffusion and dispersion. Special cases include the mKdV and linear dispersive equations. We identify two conservation laws, though initial investigations indicate that SIdV does not follow from a polynomial Lagrangian of the KdV sort. Nevertheless, it possesses solitary and periodic travelling waves. Moreover, numerical simulations reveal recurrence properties usually associated with integrable systems. KdV and SIdV are the simplest in an infinite dimensional family of equations sharing the KdV solitary wave. SIdV and its generalizations may serve as a testing ground for numerical and analytical techniques and be a rich source for further explorations.

Driven response of time delay coupled limit cycle oscillators

We study the periodic forced response of a system of two limit cycle oscillators that interact with each other via a time delayed coupling. Detailed bifurcation diagrams in the parameter space of the forcing amplitude and forcing frequency are obtained for various interesting limits using numerical and analytical means. In particular, the effects of the coupling strength, the natural frequency spread of the two oscillators and the time delay parameter on the size and nature of the entrainment domain are delineated. For an appropriate choice of time delay, synchronization can occur with infinitesimal forcing amplitudes even at off-resonant driving. The system is also found to display a nonlinear response on certain critical contours in the space of the coupling strength and time delay. Numerical simulations with a large number of coupled driven oscillators display similar behavior. Time delay offers a novel tuning knob for controlling the system response over a wide range of frequencies and this may have important practical applications. 2003 Elsevier B.V. All rights reserved.

Comment on "Spin-gradient-driven light amplification in a quantum plasma".

A comment on the Letter by S. Braun, F. A. Asenjo and S. M. Mahajan, Phys. Rev. Lett., 109, 175003 (2012). We show that recent arguments for light amplification driven by inhomogeneous quantum spin fields in low temperature electron plasmas in metals are invalid. In essence, a neglect of Pauli `blocking led the authors to over-estimate the effects of intrinsic spin.

Nonlinear viscoresistive dynamics of the m=1 tearing instability

A numerical investigation of the viscoresistive evolution of the m=1 tearing instability is presented. Its linear growth rate is found to have various power law scalings in different viscoresistive regimes, in agreement with the theoretical results of Porcelli [Phys. Fluids 30, 1734 (1987)]. Our principal focus is on the nonlinear behavior of this instability at a high value of the stability parameter Δ′ and for different values of the Prandtl number Pm. It is found that, depending on the Prandtl regime, and in association with a poloidal oscillation of the magnetic structure, a quadrupolar flow can be generated and/or destroyed outside the current sheet. The reconnection process appears to be influenced by the generation/inhibition dynamics of this external quadrupolar flow. At large enough times, this nonlinear quadrupolar flow can be partially advected in the poloidal direction at the Alfven velocity. However at high Pm values, such an advection is inhibited by viscosity and, as a consequence, the latt...

Microscopic origin of shear relaxation in a model viscoelastic liquid.

An atomistic description of shear stress relaxation in a viscoelastic liquid is developed from first principles through accurate molecular dynamic simulations in a model Yukawa system. It is shown that the relaxation time τ(M)(ex) of the excess part of the shear stress autocorrelation function provides a correct measure of the relaxation process. Below a certain critical value Γ(c) of the Coulomb coupling strength, the lifetime of local atomic connectivity τ(LC) converges to τ(M)(ex) and is the microscopic origin of the relaxation. At Γ≫Γ(c), i.e., in the potential energy dominated regime, τ(M)(ex)→τ(M) (the Maxwell relaxation time) and can, therefore, fully account for the elastic or solidlike behavior. Our results can help provide a better fundamental understanding of viscoelastic behavior in a variety of strongly coupled systems such as dusty plasmas, colloids, and non-Newtonian fluids.

A sniffer technique for an efficient deduction of model dynamical equations using genetic programming

A novel heuristic technique that enhances the search facility of the standard genetic programming (GP) algorithm is presented. The method provides a dynamic sniffing facility to optimize the local search in the vicinity of the current best chromosomes that emerge during GP iterations. Such a hybrid approach, that combines the GP method with the sniffer technique, is found to be very effective in the solution of inverse problems where one is trying to construct model dynamical equations from either finite time series data or knowledge of an analytic solution function. As illustrative examples, some special function ordinary differential equations (ODEs) and integrable nonlinear partial differential equations (PDEs) are shown to be efficiently and exactly recovered from known solution data. The method can also be used effectively for solution of model equations (the direct problem) and as a tool for generating multiple dynamical systems that share the same solution space.