Biomedical subjects

A R Bishop

Publications and source records attributed to A R Bishop.

At least 19 recordsLinked to original sources

PubMed2002

Dynamical superfluid-insulator transition in a chain of weakly coupled bose-Einstein condensates.

We predict a dynamical classical superfluid-insulator transition in a Bose-Einstein condensate trapped in an optical and a magnetic potential. In the tight-binding limit, this system realizes an array of weakly coupled condensates driven by an external harmonic field. For small displacements of the parabolic trap about the equilibrium position, the condensates coherently oscillate in the array. For large displacements, the condensates remain localized on the side of the harmonic trap with a randomization of the relative phases. The superfluid-insulator transition is due to a discrete modulational instability, occurring when the condensate center of mass velocity is larger than a critical value.

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PubMed2002

Conformational dynamics of photoexcited conjugated molecules.

Time-dependent photoexcitation and optical spectroscopy of pi-conjugated molecules is described using a new method for the simulation of excited state molecular dynamics in extended molecular systems with sizes up to hundreds of atoms. Applications are made to poly(p-phenylene vinylene) oligomers. Our analysis shows self-trapping of excitations on about six repeat units in the course of photoexcitation relaxation, identifies specific slow (torsion) and fast (bond-stretch) nuclear motions strongly coupled to the electronic degrees of freedom, and predicts spectroscopic signatures of molecular conformations.

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PubMed2002

Spin and charge order around vortices and impurities in high-T(c) superconductors.

A comparative study is made for the spin and charge structure around superconducting vortices and unitary impurities, by solving self-consistently an effective Hamiltonian including interactions for both antiferromagnetic spin-density wave (SDW) and d-wave superconducting orderings. Around vortices, we show the induction of an SDW two-dimensionally modulated with a period of eight lattice constants (8a(0)) and an associated charge-density wave (CDW) with a period of 4a(0), which explains very well recent experimental observations. In the case of unitary impurities, an SDW modulation with identical periodicity, but without an associated CDW, is also predicted.

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PubMed2002

Targeted transfer of solitons in continua and lattices.

We propose a robust mechanism of targeted energy transfer along a line, as well as on a surface, in the form of transport of coherent solitary-wave structures, driven by a moving, spatially localized external ac field ("arm") in a lossy medium. The efficiency and robustness of the mechanism are demonstrated analytically and numerically in terms of the nonlinear Schrödinger (NLS) equation, and broad regions of stable operation are identified in the model's parameter space. Direct simulations show that the driving arm can manipulate solitons equally well in a lattice NLS model. A salient feature, which is revealed by simulations and explained analytically, is a resonant character of the operation of the driving arm in the lattice medium, both integer and fractional resonances being identified. Numerical experiments also demonstrate that the same solitary-wave-transport mechanism works well in two-dimensional lattice media.

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PubMed2002

Delocalizing transition of Bose-Einstein condensates in optical lattices.

A Bose-Einstein condensate trapped in a two-dimensional optical lattice exhibits an abrupt transition manifested by the macroscopic wave function changing character from spatially localized to extended. Resulting from a bifurcation, this irreversible transition takes place as the interwell potential barrier is adiabatically decreased below a critical value. This is in sharp contrast to the corresponding one-dimensional case where such a bifurcation is absent and the extent of a localized mode is continuously tunable. We demonstrate how these phenomena can be experimentally explored.

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PubMed2002

Effects of intrinsic base-pair fluctuations on charge transport in DNA.

We investigate propagation of a charge carrier along intrinsically dynamically disordered double-stranded DNA. This is realized by the semiclassical coupling of the charge with a nonlinear lattice model that can accurately describe the statistical mechanics of the large amplitude fluctuations of the base pairs leading to the thermal denaturation transition of DNA. We find that the fluctuating intrinsic disorder can trap the charge and inhibit polaronic charge transport. The dependence of the mean distance covered by the charge carrier until its trapping, as a function of the energy of the fluctuations of the base pairs is also presented.

Base Pairing↗

PubMed2002

Superfluidity versus disorder in the discrete nonlinear Schrödinger equation.

We study the discrete nonlinear Schrödinger equation (DNLS) in an annular geometry with on-site defects. The dynamics of a traveling plane-wave maps onto an effective nonrigid pendulum Hamiltonian. The different regimes include the complete reflection and refocusing of the initial wave, solitonic structures, and a superfluid state. In the superfluid regime, which occurs above a critical value of nonlinearity, a plane wave travels coherently through the randomly distributed defects. This superfluidity criterion for the DNLS is analogous to (yet very different from) the Landau superfluidity criteria in translationally invariant systems. Experimental implications for the physics of Bose-Einstein condensate gases trapped in optical potentials and of arrays of optical fibers are discussed.

Mathematical Computing↗

PubMed2002

Continuum approach to discreteness.

We study analytically and numerically continuum models derived on the basis of Padé approximations and their effectiveness in modeling spatially discrete systems. We not only analyze features of the temporal dynamics that can be captured through these continuum approaches (e.g., shape oscillations, radiation effects, and trapping) but also point out ones that cannot be captured (such as Peierls-Nabarro barriers and Bloch oscillations). We analyze the role of such methods in providing an effective "homogenization" of spatially discrete, as well as of heterogeneous continuum equations. Finally, we develop numerical methods for solving such equations and use them to establish the range of validity of these continuum approximations, as well as to compare them with other semicontinuum approximations.

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PubMed2002

Dynamics of quantum phase transition in an array of Josephson junctions.

We study the dynamics of the Mott insulator-superfluid quantum phase transition in a periodic 1D array of Josephson junctions. We show that crossing the critical point at a finite rate with a quench time tau(Q) induces finite quantum fluctuations of the current around the loop proportional to tau(-1/6)(Q). This scaling could be experimentally verified with an array of weakly coupled Bose-Einstein condensates or superconducting grains.

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PubMed2002

Quantum instability of a Bose-Einstein condensate with attractive interaction.

We study the quantum and the mean-field Gross-Pitaevskii (GP) dynamics of a Bose-Einstein condensate gas confined in a toroidal trap. According to GP, if the interatomic interaction is attractive, the rotational states of the system can be dynamically stable or unstable depending on the strength of the mean-field energy. The full quantum analysis, however, reveals that the condensate is always unstable. Quantum fluctuations are particularly important close to the GP stability borderline, even for systems with a relatively large number of condensate atoms.

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PubMed2001

Hysteresis and metastability in the quenched turbulent dynamics of the complex Ginzburg-Landau equation.

We consider the quenched dynamics of the two-dimensional complex Ginzburg-Landau equation in its turbulent regime. We initialize the system in a frustrated state and observe how frustration affects the evolution towards the turbulent state. This process is performed for parameter values where, for random initial conditions, the system evolves into the turbulent state. We observe that the glassiness of the initial condition can inhibit the occurrence of the absolute instability close to the critical point for that instability in parameter space. Sufficiently far from the critical point, the turbulent state will develop, but only after spending considerable time in a transient metastable state of fixed vortex density. The parameter distance from the critical point is found to scale as an exponential of a power of the lifetime of the metastable state, and with a power exponent depending on the "depth" of the original quench. The limiting regimes of shallow and deep quench are identified by their respective values of the exponent, and the distinct mechanisms leading to the relaxation to turbulence in each case are highlighted.

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PubMed2001

Localized vortices with a semi-integer charge in nonlinear dynamical lattices.

The topological charge S of vortexlike configurations in two-dimensional (2D) dynamical lattices need not necessarily be integer, nor is it a dynamical invariant. Accordingly, we demonstrate that the discrete nonlinear Schrödinger (DNLS) equation in 2D has stationary solutions in the form of a vortex with S=1/2, which does not exist in the model's continuum counterpart. Analysis of the DNLS equation linearized about the vortex shows that it is stable except for, possibly, extremely weak instabilities (at the level of numerical precision). Direct simulations of the full DNLS model in 2D show that the S=1/2 vortex soliton is a stable oscillating solution. This behavior of classical dynamical lattices is in contrast with a recently reported result by Clay et al. [Phys. Rev. Lett. 86, 4085 (2001)], according to which fractional charges in quantum lattices are subject to dynamical rearrangement into integer charges. We also consider S=1 discrete vortices that may be built as a pair of S=1/2 ones. These are different from the cross-shaped S=1 vortices that were recently found in the same 2D model. The S=1 vortices found in this work have larger energy and a slightly smaller stability range. We also find an analog of the S=1/2 vortices in the 1D DNLS model, which also turns out to be a stable oscillating soliton, different from the twisted localized modes recently found in the 1D model.

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PubMed2001

Effects of transport memory and nonlinear damping in a generalized Fisher's equation.

Memory effects in transport require, for their incorporation into reaction-diffusion investigations, a generalization of traditional equations. The well-known Fisher's equation, which combines diffusion with a logistic nonlinearity, is generalized to include memory effects, and traveling wave solutions of the equation are found. Comparison is made with alternative generalization procedures.

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PubMed2001

Ring solitons on vortices.

Interaction of a ring dark or antidark soliton (RDS and RADS, respectively) with a vortex is considered in the defocusing nonlinear Schrödinger equation with cubic (for RDS) or saturable (for RADS) nonlinearities. By means of direct simulations, it is found that the interaction gives rise to either an almost isotropic or a spiral-like pattern. A transition between them occurs at a critical value of the RDS or RADS amplitude, the spiral pattern appearing if the amplitude exceeds the critical value. An initial ring soliton created on top of the vortex splits into a pair of rings moving inward and outward. In the subcritical case, the inbound ring reverses its polarity, bouncing from the vortex core, without conspicuous effect on the core. In the transcritical case, the bounced ring soliton suffers a spiral deformation, while the vortex changes its position and structure and also loses its axial symmetry. Through a variational-type approach to the system's Hamiltonian, we additionally find that the vortex-RDS and vortex-RADS interactions are, respectively, attractive and repulsive. Simulations with the vortex placed eccentrically with respect to the RDS or RADS reveal the generation of strongly localized multispot dark and/or antidark coherent structures. The occurrence of spiral-like patterns in many numerical experiments prompted an attempt to generate a spiral dark soliton, but the latter is found to suffer a core instability that converts it into a rotating dipole emitting waves in the outward direction.

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PubMed2001

Effects of competing short- and long-range dispersive interactions on discrete breathers.

The discrete nonlinear Schrödinger equation with competing short-range and long-range interactions is considered in spatial dimensions d> or =2. This model equation is derived for a situation of two linearly coupled excitations (independently of dimension), and we analytically and numerically study its properties in 2+1 dimensions. We analyze theoretically and demonstrate numerically the dependence of the discrete breather solutions on the amplitude and range of the interactions. We find that complete suppression of the existence thresholds obtained recently for short-range interactions can be achieved beyond a critical value of the amplitude or of the range of the long-range kernel. For supercritical values of the corresponding parameters, staggered branches of solutions are obtained both in theory as well as in the numerical experiment.

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PubMed2001

Interaction between sine-Gordon breathers.

Using the exact breather lattice solution of the sine-Gordon equation, we obtain the asymptotic interaction between two breathers. We identify the exponential dependence of the interaction on the breather separation as well as its power-law dependence on the breather frequency. Numerical simulation of the breather lattice demonstrates its instability. However, stabilization of such structures is found to be feasible through ac driving and damping. Finally, other limits of the original periodic solution are traced, obtaining the leading-order terms in the interaction between "pseudosphere" solutions and kink-antikink pairs.

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PubMed2001

Three-dimensional elastic compatibility and varieties of twins in martensites.

We model a cubic-to-tetragonal martensitic transition by a Ginzburg-Landau free energy in the symmetric strain tensor. We show in three dimensions (3D) that solving the St. Venant compatibility relations for strain, treated as independent field equations, generates three anisotropic long-range potentials between the two order parameter components. These potentials encode 3D discrete symmetries, express the energetics of lattice integrity, and determine 3D textures. Simulation predictions include twins with temperature-varying orientation, helical twins, competing metastable states, and compatibility-induced elastic frustration. Our approach also applies to improper ferroelastics.

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PubMed2001

Anomalous relaxation and self-organization in nonequilibrium processes.

We study thermal relaxation in ordered arrays of coupled nonlinear elements with external driving. We find that our model exhibits dynamic self-organization manifested in a universal stretched-exponential form of relaxation. We identify two types of self-organization, cooperative and anticooperative, which lead to fast and slow relaxation, respectively. We give a qualitative explanation for the behavior of the stretched exponent in different parameter ranges. We emphasize that this is a system exhibiting stretched-exponential relaxation without explicit disorder or frustration.

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