Biomedical subjects

A R Bishop

Publications and source records attributed to A R Bishop.

At least 37 records · Page 2Linked to original sources

PubMed2004

Nonlinearity from geometric interactions: a case example.

We propose a ladder model wherein dynamical nonlinearity arises from geometry. It includes two strings of particles which are set along rigid rails of a "railroad" and coupled by linear springs. Physical realizations of the model include dust-particle strings in plasma sheaths and chains of microparticles trapped in a strong optical lattice. The transverse couplings between the strings, along with the motion constraint imposed by the rails, generate nonlinearity. It gives rise to robust solitary waves, which are found analytically in the long-wavelength limit, and are obtained in simulations of the full system.

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PubMed2004

Multipeaked polarons in soft potentials.

We consider a minimal coupled charge / excitation-lattice model capturing a competition between linear polaronic self-trapping and the self-focusing effects of a soft nonlinear on-site potential. The standard single-humped polaron ceases to exist above a critical value of the coupling strength, closely related to the inflection point in the nonlinear potential. For couplings beyond this critical value, we find that successive multihumped polaronic solutions correspond to the lowest-energy stationary states of the system, which may admit interesting quantum resonance behavior.

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PubMed2004

Strain-induced metal-insulator phase coexistence in perovskite manganites.

The coexistence of distinct metallic and insulating electronic phases within the same sample of a perovskite manganite, such as La(1-x-y)Pr(y)Ca(x)MnO3, presents researchers with a tool for tuning the electronic properties in materials. In particular, colossal magnetoresistance in these materials--the dramatic reduction of resistivity in a magnetic field--is closely related to the observed texture owing to nanometre- and micrometre-scale inhomogeneities. Despite accumulated data from various high-resolution probes, a theoretical understanding for the existence of such inhomogeneities has been lacking. Mechanisms invoked so far, usually based on electronic mechanisms and chemical disorder, have been inadequate to describe the multiscale, multiphase coexistence within a unified picture. Moreover, lattice distortions and long-range strains are known to be important in the manganites. Here we show that the texturing can be due to the intrinsic complexity of a system with strong coupling between the electronic and elastic degrees of freedom. This leads to local energetically favourable configurations and provides a natural mechanism for the self-organized inhomogeneities over both nanometre and micrometre scales. The framework provides a physical understanding of various experimental results and a basis for engineering nanoscale patterns of metallic and insulating phases.

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PubMed2004

Variational approach to the modulational instability.

We study the modulational stability of the nonlinear Schrödinger equation using a time-dependent variational approach. Within this framework, we derive ordinary differential equations (ODE's) for the time evolution of the amplitude and phase of modulational perturbations. Analyzing the ensuing ODE's, we rederive the classical modulational instability criterion. The case (relevant to applications in optics and Bose-Einstein condensation) where the coefficients of the equation are time dependent, is also examined.

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PubMed2004

Fibrillar templates and soft phases in systems with short-range dipolar and long-range interactions.

We analyze the thermal fluctuations of particles that have a short-range dipolar attraction and a long-range repulsion. In an inhomogeneous particle density region, or "soft phase," filamentary patterns appear which are destroyed only at very high temperatures. The filaments act as a fluctuating template for correlated percolation in which low-energy excitations can move through the stable pattern by local rearrangements. At intermediate temperatures, dynamically averaged checkerboard states appear. We discuss possible implications for doped cuprate oxides and related materials.

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PubMed2004

Nonintegrable Schrodinger discrete breathers.

In an extensive numerical investigation of nonintegrable translational motion of discrete breathers in nonlinear Schrödinger lattices, we have used a regularized Newton algorithm to continue these solutions from the limit of the integrable Ablowitz-Ladik lattice. These solutions are shown to be a superposition of a localized moving core and an excited extended state (background) to which the localized moving pulse is spatially asymptotic. The background is a linear combination of small amplitude nonlinear resonant plane waves and it plays an essential role in the energy balance governing the translational motion of the localized core. Perturbative collective variable theory predictions are critically analyzed in the light of the numerical results.

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PubMed2003

Elasticity-driven nanoscale electronic structure in superconductors.

The effects of long-range anisotropic elastic deformations on electronic structure in superconductors are analyzed within the framework of the Bogoliubov-de Gennes equations. Cases of twin boundaries and isolated defects are considered as illustrations. We find that the superconducting order parameter is depressed in the regions where pronounced lattice-deformation occurs. The calculated local density of states suggests that the electronic structure is strongly modulated in response to lattice deformations, and propagates to longer distances. In particular, this allows the trapping of low-lying quasiparticle states around defects. Some of our predictions can be directly tested by scanning tunneling microscopy experiments.

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PubMed2003

Coupling fields and underlying space curvature: an augmented Lagrangian approach.

We demonstrate a systematic implementation of coupling between a scalar field and the geometry of the space which carries the field. This naturally gives rise to a feedback mechanism between the field and the geometry. We develop a systematic model for the feedback in a general form, inspired by a specific implementation in the context of molecular dynamics (the so-called Rahman-Parrinello molecular dynamics, or RP-MD). We use a generalized Lagrangian that allows for the coupling of the space's metric tensor to the scalar field, and add terms motivated by RP-MD. We present two implementations of the scheme: one in which the metric is only time-dependent (which gives rise to an ordinary differential equation for its temporal evolution), and the other with spatiotemporal dependence (wherein the metric's evolution is governed by a partial differential equation). Numerical results are reported for the (1+1)-dimensional model with a nonlinearity of the sine-Gordon type.

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PubMed2003

Domain walls in two-component dynamical lattices.

We introduce domain-wall (DW) states in the bimodal discrete nonlinear Schrödinger equation, in which the modes are coupled by cross-phase modulation (XPM). The results apply to an array of nonlinear optical waveguides carrying two different polarizations of light, or two different wavelengths, with anomalous intrinsic diffraction controlled by direction of the light beam, and to a string of drops of a binary Bose-Einstein condensate, trapped in an optical lattice. By means of continuation from various initial patterns taken in the anticontinuum (AC) limit, we find a number of different solutions of the DW type, for which different stability scenarios are identified. In the case of strong-XPM coupling, DW configurations contain a single mode at each end of the chain. The most fundamental solution of this type is found to be always stable. Another solution, which is generated by a different AC pattern, demonstrates behavior which is unusual for nonlinear dynamical lattices: it is unstable for small values of the coupling constant C (which measures the ratio of the nonlinearity and coupling lengths), and becomes stable at larger C. Stable bound states of DWs are also found. DW configurations generated by more sophisticated AC patterns are identified as well, but they are either completely unstable, or are stable only at small values of C. In the case of weak XPM, a natural DW solution is the one which contains a combination of both polarizations, with the phase difference between them 0 and pi at the opposite ends of the lattice. This solution is unstable at all values of C, but the instability is very weak for large C, indicating stabilization as the continuum limit is approached. The stability of DWs is also verified by direct simulations, and the evolution of unstable DWs is simulated too; in particular, it is found that, in the weak-XPM system, the instability may give rise to a moving DW. The DW states can be observed experimentally in the same parameter range where discrete solitons have been found in the lattice setting.

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PubMed2003

Spin-polarized conductance induced by tunneling through a magnetic impurity.

Using the zero mode method, we compute the conductance of a wire consisting of a magnetic impurity coupled to two Luttinger liquid leads characterized by the Luttinger exponent alpha(>or=1). We find for resonance conditions, in which the Fermi energy of the leads is close to a single particle energy of the impurity, that the conductance as a function of temperature is G approximately equal (e(2)/h)(T/T(F))(2(alpha-2)), whereas for off-resonance conditions the conductance is G approximately equal (e(2)/h)(T/T(F))(2(alpha-1)). By applying either a gate voltage or a magnetic field or both, one of the spin components can be in resonance while the other is off resonance causing a strong asymmetry between the spin-up and spin-down conductances.

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PubMed2003

Photoexcited breathers in conjugated polyenes: an excited-state molecular dynamics study.

pi-conjugated polymers have become an important class of materials for electronic devices. Design of these devices requires understanding such processes as photochemical reactions, spatial dynamics of photoexcitations, and energy and charge transport, which in turn involve complex coupled electron-vibrational dynamics. Here we study nonlinear photoexcitation dynamics in the polyene oligomers by using a quantum-chemical method suitable for the simulation of excited-state molecular dynamics in extended molecular systems with sizes up to hundreds of atoms. The method is based on the adiabatic propagation of the ground-state and transition single-electron density matrices along the trajectory. The simulations reveal formation of a self-localized vibronic excitation ("breather" or multiquanta bound state) with a typical period of 34 fs and allows us to identify specific slow and fast nuclear motions strongly coupled to the electronic degrees of freedom. The effect of chain imperfections and chemical defects on the dynamics is also investigated. A complementary two-dimensional analysis of corresponding transition density matrices provides an efficient way to monitor time-dependent real-space localization of the photoexcitation by identifying the underlying changes in charge densities and bond orders. Possible correlated electronic and vibrational spectroscopic signatures of photoexcited breathers are predicted, and generalizations to energy localization in complex macromolecules are discussed.

Algorithms↗

PubMed2003

Thermal diffusion of supersonic solitons in an anharmonic chain of atoms.

We study the nonequilibrium diffusion dynamics of supersonic lattice solitons in a classical chain of atoms with nearest-neighbor interactions coupled to a heat bath. As a specific example we choose an interaction with cubic anharmonicity. The coupling between the system and a thermal bath with a given temperature is made by adding noise, delta correlated in time and space, and damping to the set of discrete equations of motion. Working in the continuum limit and changing to the sound velocity frame we derive a Korteweg-de Vries equation with noise and damping. We apply a collective coordinate approach which yields two stochastic ODEs which are solved approximately by a perturbation analysis. This finally yields analytical expressions for the variances of the soliton position and velocity. We perform Langevin dynamics simulations for the original discrete system which confirm the predictions of our analytical calculations, namely, noise-induced superdiffusive behavior which scales with the temperature and depends strongly on the initial soliton velocity. A normal diffusion behavior is observed for solitons with very low energy, where the noise-induced phonons also make a significant contribution to the soliton diffusion.

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PubMed2003

Discrete nonlinear Schrödinger equation with defects.

We investigate the dynamical properties of the one-dimensional discrete nonlinear Schrödinger equation (DNLS) with periodic boundary conditions and with an arbitrary distribution of on-site defects. We study the propagation of a traveling plane wave with momentum k: the dynamics in Fourier space mainly involves two localized states with momenta +/-k (corresponding to a transmitted and a reflected wave). Within a two-mode ansatz in Fourier space, the dynamics of the system maps on a nonrigid pendulum Hamiltonian. The several analytically predicted (and numerically confirmed) regimes include states with a vanishing time average of the rotational states (implying complete reflections and refocusing of the incident wave), oscillations around fixed points (corresponding to quasi-stationary states), and, above a critical value of the nonlinearity, self-trapped states (with the wave traveling almost undisturbed through the impurity). We generalize this treatment to the case of several traveling waves and time-dependent defects. The validity of the two-mode ansatz and the continuum limit of the DNLS are discussed.

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PubMed2003

Dynamical ordering of driven stripe phases in quenched disorder.

We examine the dynamics and stripe formation in a system with competing short and long-range interactions in the presence of both an applied dc drive and quenched disorder. Without disorder, the system forms stripes organized in a labyrinth state. We find that, when the disorder strength exceeds a critical value, an applied dc drive can induce a dynamical stripe ordering transition to a state that is more ordered than the originating undriven, unpinned pattern. We show that signatures in the structure factor and transport properties correspond to this dynamical reordering transition, and we present the dynamic phase diagram as a function of strengths of disorder and dc drive.

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PubMed2003

Underdamped commensurate dynamics in a driven Frenkel-Kontorova-type model.

The dynamics of a Frenkel-Kontorova chain subject to a substrate potential with a multiple-well structure and driven by an external dc force is studied in the underdamped regime. Making a rational choice among the three inherent length scales characterizing the system allows us to consider the possible formation of commensurate structures during sliding over the complex on-site potential. We comment both on the nature of the particle dynamics in the vicinity of the pinning-depinning transition point, and on the dynamical states displayed during the chain motion at different strengths of the dc driving. Varying the number of particles in the simulations allows us to consider, on a multiple-well substrate, the role played by the coverage variable on the depinning mechanism. The dependence of the minimal force required to initiate the chain motion (static friction) on the ratio of the model interaction strengths is analyzed and compared to the well-known case of the standard Frenkel-Kontorova model, which has only two inherent lengths.

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PubMed2003

Localization in physical systems described by discrete nonlinear Schrodinger-type equations.

Following a short introduction on localized modes in a model system, namely the discrete nonlinear Schrodinger equation, we present explicit results pertaining to three different physical systems described by similar equations. The applications range from the Raman scattering spectra of a complex electronic material through intrinsic localized vibrational modes, to the manifestation of an abrupt and irreversible delocalizing transition of Bose-Einstein condensates trapped in two-dimensional optical lattices, and to the instabilities of localized modes in coupled arrays of optical waveguides.

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PubMed2002

Simulations in the mathematical modeling of the spread of the Hantavirus.

The range of validity of a recently proposed deterministic (mean field) model of the spread of the Hantavirus infection is studied with the help of Monte Carlo simulations for the evolution of mice populations. The simulation is found to reproduce earlier results on the average but to display additional behavior stemming from discreteness in mice number and from fluctuations of the finite size system. It is shown that mice diffusion affects those additional features of the simulation in a physically understandable manner, higher diffusion constants leading to greater agreement with the mean field results.

Animals↗

PubMed2002

Discrete nonlinear model with substrate feedback.

We consider a prototypical model in which a nonlinear field (continuum or discrete) evolves on a flexible substrate which feeds back to the evolution of the main field. We identify the underlying physics and potential applications of such a model and examine its simplest one-dimensional Hamiltonian form, which turns out to be a modified Frenkel-Kontorova model coupled to an extra linear equation. We find static kink solutions and study their stability, and then examine moving kinks (the continuum limit of the model is studied too). We observe how the substrate effectively renormalizes properties of the kinks. In particular, a nontrivial finding is that branches of stable and unstable kink solutions may be extended beyond a critical point at which an effective intersite coupling vanishes; passing this critical point does not destabilize the kink. Kink-antikink collisions are also studied, demonstrating alternation between merger and transmission cases.

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