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A R Bishop

Publications and source records attributed to A R Bishop.

At least 19 recordsLinked to original sources
PubMed2006

Discrete solitons and vortices in the two-dimensional Salerno model with competing nonlinearities.

An anisotropic lattice model in two spatial dimensions, with on-site and intersite cubic nonlinearities (the Salerno model), is introduced, with emphasis on the case in which the intersite nonlinearity is self-defocusing, competing with on-site self-focusing. The model applies, for example, to a dipolar Bose-Einstein condensate trapped in a deep two-dimensional (2D) optical lattice. Soliton families of two kinds are found in the model: ordinary ones and cuspons, with peakons at the border between them. Stability borders for the ordinary solitons are found, while all cuspons (and peakons) are stable. The Vakhitov-Kolokolov criterion does not apply to cuspons, but for the ordinary solitons it correctly identifies the stability limits. In direct simulations, unstable solitons evolve into localized pulsons. Varying the anisotropy parameter, we trace a transition between the solitons in 1D and 2D versions of the model. In the isotropic model, we also construct discrete vortices of two types, on-site and intersite centered (vortex crosses and squares, respectively), and identify their stability regions. In simulations, unstable vortices in the noncompeting model transform into regular solitons, while in the model with the competing nonlinearities they evolve into localized vortical pulsons, which maintain their topological character. Bound states of regular solitons and vortices are constructed too, and their stability is identified.

Journal Article↗
PubMed2006

Statics and dynamics of an inhomogeneously nonlinear lattice.

We introduce an inhomogeneously nonlinear Schrödinger lattice, featuring a defocusing segment, a focusing segment and a transitional interface between the two. We illustrate that such inhomogeneous settings present vastly different dynamical behavior in the vicinity of the interface than the one expected in their homogeneous counterparts. We analyze the relevant stationary states, as well as their stability, by means of perturbation theory and linear stability analysis. We find good agreement with the numerical findings in the vicinity of the anticontinuum limit. For larger values of the coupling, we follow the relevant branches numerically and show that they terminate at values of the coupling strength which are larger for more extended solutions. The dynamical development of relevant instabilities is also monitored in the case of unstable solutions.

Journal Article↗
PubMed2006

Probing the mechanical unzipping of DNA.

A study of the micromechanical unzipping of DNA in the framework of the Peyrard-Bishop-Dauxois model is presented. We introduce a Monte Carlo technique that allows accurate determination of the dependence of the unzipping forces on unzipping speed and temperature. Our findings agree quantitatively with experimental results for homogeneous DNA, and for lamda-phage DNA we reproduce the recently obtained experimental force-temperature phase diagram. Finally, we argue that there may be fundamental differences between in vivo and in vitro DNA unzipping.

Bacteriophage lambda↗
PubMed2006

Ultra-violet light induced changes in DNA dynamics may enhance TT-dimer recognition.

Short-wave ultra-violet light promotes the formation of DNA dimers between adjacent thymine bases, and if unrepaired these dimers may induce skin cancer. Living cells have a very robust repair system capable of repairing hundreds of lesions every day. Although many of the details of the dimer repair mechanism are known, it is still a mystery how the dimers are recognized. Because the dimers are hidden from repair proteins diffusing in the cell nucleus, it has been surmised that dimer recognition is indirect. In this paper, a new recognition signal is suggested by a theory of the dimer-induced large amplitude, prolonged oscillations in the motion of the two strands in double-stranded DNA molecules. These large amplitude oscillations of the two DNA strands, localized around the dimer will unveil the dimer allowing the repair proteins to bind to the dimer site. The temperature dependence of the recognition rate is correlated with the inter-strand fluctuations and must decrease with decreasing temperature according to the findings in this paper. Moreover the probability for finding a large opening is localized to the dimer neighbourhood and these large openings may play an important role in dimer-repair protein biochemistry.

DNA↗
PubMed2006

Healing length and bubble formation in DNA.

It has been suggested that thermally induced separations ("bubbles") of the DNA double-strand may play a role in the initiation of gene transcription, and an accurate understanding of the sequence dependence of thermal strand separation is therefore desirable. Based on the Peyrard-Bishop-Dauxois model, we show here that the bubble forming ability of DNA can be quantified in terms of a healing length L(n), defined as the length (number of base-pairs) over which a base-pair defect affects bubbles involving n consecutive base-pairs. The probability for a bubble of size n is demonstrated to be proportional to the number of adenine-thymine base-pairs found within this length. The method for calculating bubble probabilities in a given sequence derived from this notion requires several order of magnitude less numerical effort than direct evaluation.

Base Pairing↗
PubMed2006

Solitons in the Salerno model with competing nonlinearities.

We consider a lattice equation (Salerno model) combining onsite self-focusing and intersite self-defocusing cubic terms, which may describe a Bose-Einstein condensate of dipolar atoms trapped in a strong periodic potential. In the continuum approximation, the model gives rise to solitons in a finite band of frequencies, with sechlike solitons near one edge, and an exact peakon solution at the other. A similar family of solitons is found in the discrete system, including a peakon; beyond the peakon, the family continues in the form of cuspons. Stability of the lattice solitons is explored through computation of eigenvalues for small perturbations, and by direct simulations. A small part of the family is unstable (in that case, the discrete solitons transform into robust pulsonic excitations); both peakons and cuspons are stable. The Vakhitov-Kolokolov criterion precisely explains the stability of regular solitons and peakons, but does not apply to cuspons. In-phase and out-of-phase bound states of solitons are also constructed. They exchange their stability at a point where the bound solitons are peakons. Mobile solitons, composed of a moving core and background, exist up to a critical value of the strength of the self-defocusing intersite nonlinearity. Colliding solitons always merge into a single pulse.

Journal Article↗
PubMed2006

Pinning frequencies of the collective modes in alpha-uranium.

Uranium is the only known element that features a charge-density wave (CDW) and superconductivity. We report a comparison of the specific heat of single-crystal and polycrystalline alpha-uranium. In the single crystal we find excess contributions to the heat capacity at 41 K, 38 K, and 23 K, with a Debye temperature ThetaD = 265 K. In the polycrystalline sample the heat capacity curve is thermally broadened (ThetaD = 184 K), but no excess heat capacity was observed. The excess heat capacity Cphi (taken as the difference between the single-crystal and polycrystal heat capacities) is well described in terms of collective-mode excitations above their respective pinning frequencies. This attribution is represented by a modified Debye spectrum with two cutoff frequencies, a pinning frequency V0 for the pinned CDW (due to grain boundaries in the polycrystal), and a normal Debye acoustic frequency occurring in the single crystal.

Journal Article↗
PubMed2006

Sequencing DNA by dynamic force spectroscopy: limitations and prospects.

Using a well established model, we systematically analyze fundamental limitations on the viability of using mechanical unzipping of DNA as a fast and inexpensive sequencing method. Standard unzipping techniques, where double-stranded DNA is unzipped through the application of a force at one end of the molecule, are shown to be inadequate. Emerging techniques that unzip DNA by local force application are more promising, and we establish the necessary experimental requirements that must be met for these techniques to succeed as single molecule sequencing tools.

Microscopy, Atomic Force↗
PubMed2005

Discrete solitons and vortices on anisotropic lattices.

We consider the effects of anisotropy on solitons of various types in two-dimensional nonlinear lattices, using the discrete nonlinear Schrödinger equation as a paradigm model. For fundamental solitons, we develop a variational approximation that predicts that broad quasicontinuum solitons are unstable, while their strongly anisotropic counterparts are stable. By means of numerical methods, it is found that, in the general case, the fundamental solitons and simplest on-site-centered vortex solitons ("vortex crosses") feature enhanced or reduced stability areas, depending on the strength of the anisotropy. More surprising is the effect of anisotropy on the so-called "super-symmetric" intersite-centered vortices ("vortex squares"), with the topological charge equal to the square's size : we predict in an analytical form by means of the Lyapunov-Schmidt theory, and confirm by numerical results, that arbitrarily weak anisotropy results in dramatic changes in the stability and dynamics in comparison with the degenerate, in this case, isotropic, limit.

Journal Article↗
PubMed2005

Nondissipative diffusion of lattice solitons out of thermal equilibrium.

We perform Langevin dynamics simulations for pulse solitons on atomic chains with anharmonic nearest-neighbor interactions. After switching off noise and damping after a sufficiently long time, the solitons are only influenced by the thermal phonon bath which had been created by the noise. The soliton diffusion constant D is considerably smaller than before the switch-off, and it is proportional to the square of the temperature T , in contrast to the diffusion due to the noise which is proportional to T . We derive a diffusion equation for a soliton which is scattered elastically in an ensemble of phonons and derive general expressions for D and for the drift velocity v(d) . These expressions can be evaluated for the case of the Toda lattice for which the soliton shift due to the phonon scattering is known explicitly. D is indeed proportional to T2 and agrees well with the simulation results, while v(d) is much smaller than the soliton velocity and cannot be measured in the simulations due to the large fluctuations of the soliton position. We express D in terms of soliton characteristics which are known also for solitons on other anharmonic chains in the continuum limit: namely, velocity, amplitude, and width. The results agree well with the simulations if the soliton shape is the same as in the Toda case. If the shape is different, only an estimate of the order of magnitude can be given.

Journal Article↗
PubMed2005

Theory of slow-light solitons.

In the framework of the nonlinear lambda model we investigate propagation of solitons in atomic vapors and Bose-Einstein condensates. We show how the complicated nonlinear interplay between fast solitons and slow-light solitons in the lambda-type media points to the possibility to create optical gates and, thus, to control the optical transparency of the lambda-type media. We provide an exact analytic description of decelerating, stopping and reaccelerating of slow-light solitons in atomic media in the nonadiabatic regime. Dynamical control over slow-light solitons is realized via a controlling field generated by an auxiliary laser. For a rather general time dependence of the field; we find the dynamics of the slow-light soliton inside the medium. We provide an analytical description for the nonlinear dependence of the velocity of the signal on the controlling field. If the background field is turned off at some moment of time, the signal stops. We find the location and shape of the spatially localized memory bit imprinted into the medium. We discuss physically interesting features of our solution, which are in a good agreement with recent experiments.

Journal Article↗
PubMed2005

ac conductivity in a DNA charge transport model.

We present the ac response of a DNA charge transport model, where the charge in the pi-stack interacts with the base-pair opening dynamics of the double strand. The calculated ac conductivity exhibits prominent peaks at polaron normal modes with electronic character, while weaker response appears at lower frequencies in the vibrational part of the polaron normal mode spectrum. Examples of the former, strong peaks, show redshifts as the amplitude of the ac field increases.

Computer Simulation↗
PubMed2005

Persistent spin currents without spin-orbit coupling in a spin-1/2 ring.

We show that a spatially dependent magnetic field can induce a persistent spin current in a spin-1/2 Heisenberg antiferromagnetic ring, proportional to the solid angle subtended by the magnetic field on a unit sphere. The magnitude of the spin current is determined by the ratio of longitudinal and transverse exchange interactions J(parallel)/J(perpendicular) and by the magnetic field magnitude.

Journal Article↗
PubMed2005

Adaptability and "intermediate phase" in randomly connected networks.

We present a simple model that enables us to analytically characterize a floppy to rigid transition and an associated self-adaptive intermediate phase in a random bond network. In this intermediate phase, the network adapts itself to lower the stress due to constraints. Our simulations verify this picture. We use these insights to identify applications of these ideas in computational problems such as vertex cover and K-satisfiability.

Complex Mixtures↗
PubMed2005

Local structure fluctuations as a signature of an inhomogeneous ground state in high-Tc superconductors.

In-plane polarized Cu K-edge XAFS on La2CuO4.1 is presented, which indicates a radial in-plane Cu-O distribution function that is not a single Gaussian. Fits to the isolated Cu-O XAFS signal show the presence of a two-site radial distribution function, similar to that found in other La-based cuprate superconductors at temperatures below the temperature associated with the pseudogap appearance, T*. The appearance of the two-site distribution is interpreted as evidence of a non-homogeneous ground state, preceding the superconducting transition. Similar results found in other copper-oxide superconductors indicate that this non-homogeneous ground state is a general feature of these materials.

Journal Article↗
PubMed2005

Bubble nucleation and cooperativity in DNA melting.

The onset of intermediate states (denaturation bubbles) and their role during the melting transition of DNA are studied using the Peyrard-Bishop-Dauxois model by Monte Carlo simulations with no adjustable parameters. Comparison is made with previously published experimental results finding excellent agreement. Melting curves, critical DNA segment length for stability of bubbles, and the possibility of a two-state transition are studied.

Base Sequence↗
PubMed2004

Rich example of geometrically induced nonlinearity: from rotobreathers and kinks to moving localized modes and resonant energy transfer.

We present an experimentally realizable, simple mechanical system with linear interactions whose geometric nature leads to nontrivial, nonlinear dynamical equations. The equations of motion are derived and their ground state structures are analyzed. Selective "static" features of the model are examined in the context of nonlinear waves including rotobreathers and kinklike solitary waves. We also explore "dynamic" features of the model concerning the resonant transfer of energy and the role of moving intrinsic localized modes in the process.

Journal Article↗