Intersite Potential Research Articles

DNA Model with Non-Local Inter-Site Interaction in Collisional Thermostat

A modified Peyrard-Bishop-Dauxios model with non-local nature of the inter-site potential was studied in a collisional thermostat with a Maxwell velocity distribution of short-lived virtual particles at a temperature of 310 K. Introduction of non-locality to the inter-site potential was found to reduce significantly the equilibrium constants for the denaturation bubble formation reaction. This property improves the agreement of calculated data with experiments. The effect is especially pronounced for large bubbles. The end effects in the new version of the model are investigated. The significant contribution of entropy and the important role of the processes of transfer and localization of mechanical energy at the end sections of DNA are shown.

Investigation of DNA Breather Dynamics in A Model with Non-Local Inter-Site Interaction

A variant of the Peyrard-Bishop-Dauxois model is proposed, which takes account of the partially delocalized nature of DNA stacking interactions. It is shown that the nonlocal nature of the inter-site potential can lead to an increase in the local cooperativity of the base pairs' opening an increasing in the number of simultaneously opening adjacent nucleotide pairs during the denaturation bubble's nucleation. The process of the formation and propagation of mobile breathers excited by the initial displacements of a number of nucleotide pairs has been studied. It is revealed that taking account of the non-local coupling in the Peyrard-Bishop-Dauxois model, while maintaining the remaining parameters of the model, leads to a decrease in the speed of the mobile breather and an increase in the probability of nucleation of the denaturation bubble.

Stable and unstable periodic orbits in the one-dimensional lattice ϕ^{4} theory.

Periodic orbits for the classical ϕ^{4} theory on the one-dimensional lattice are systematically constructed by extending the normal modes of the harmonic theory, for periodic, free and fixed boundary conditions. Through the process, we investigate which normal modes of the linear theory can or cannot be extended to the full nonlinear theory and why. We then analyze the stability of these orbits, clarifying the link between the stability, parametric resonance, and Lyapunov spectra for these orbits. The construction of the periodic orbits and the stability analysis is applicable to theories governed by Hamiltonians with quadratic intersite potentials and a general on-site potential. We also apply the analysis to theories with on-site potentials that have qualitatively different behavior from the ϕ^{4} theory, with some concrete examples.

From solitons to discrete breathers

The excitation of solitons and discrete breathers (pinned or otherwise, also known as intrinsic localized modes, DB/ILM) in a one-dimensional lattice, also denoted as a chain, is considered when both on-site and inter-site vibrations, coupled together, are governed by the empirical Morse interaction. We focus attention on the transformation of the former into the latter as the relative strength of the on-site potential to that of the inter-site potential is increased.

Inductive intrinsic localized modes in a one-dimensional nonlinear electric transmission line.

The experimental properties of intrinsic localized modes (ILMs) have long been compared with theoretical dynamical lattice models that make use of nonlinear onsite and/or nearest-neighbor intersite potentials. Here it is shown for a one-dimensional lumped electrical transmission line that a nonlinear inductive component in an otherwise linear parallel capacitor lattice makes possible a new kind of ILM outside the plane wave spectrum. To simplify the analysis, the nonlinear inductive current equations are transformed to flux transmission line equations with analog onsite hard potential nonlinearities. Approximate analytic results compare favorably with those obtained from a driven damped lattice model and with eigenvalue simulations. For this mono-element lattice, ILMs above the top of the plane wave spectrum are the result. We find that the current ILM is spatially compressed relative to the corresponding flux ILM. Finally, this study makes the connection between the dynamics of mass and force constant defects in the harmonic lattice and ILMs in a strongly anharmonic lattice.

Wave motions along lattices with nonlinear on-site and inter-site potentials. Cooperation and/or competition leading to lattice solitons and/or discrete breathers

Wave motions along lattices with nonlinear on-site and inter-site potentials. Cooperation and/or competition leading to lattice solitons and/or discrete breathers

Oscillating multidromion excitations in higher-dimensional nonlinear lattice with intersite and external on-site potentials using symbolic computation

We show by an extensive method of quasi-discrete multiple-scale approximation that nonlinear multi-dimensional lattice waves subjected to intersite and external on-site potentials are found to be governed by (N + 1)-dimensional nonlinear Schrödinger (NLS) equation. In particular, the resonant mode interaction of (2+1)-dimensional NLS equation has been identified and the theory allows the inclusion of transverse effect. We apply the exponential function method to the (2+1)-dimensional NLS equation and obtain the class of soliton solutions with a purely algebraic computational method. Notably, we discuss in detail the effects of the external on-site potentials on the explicit form of the soliton solution generated recursively. Under the action of the external on-site potentials, the model presents a rich variety of oscillating multidromion patterns propagating in the system.

Different Kinds of Discrete Breathers in Three Types of One-Dimensional Models

The dynamics of different kinds of discrete breathers in three types of one-dimensional monatomic chains with on-site and inter-site potentials are investigated. The existence and evolution of symmetric breather, antisymmetric breather, and multibreather in one-dimensional models are proved by using rotating wave approximation, local anharmonic approximation, and the numerical method. The linear stability of these breathers is investigated by using Lyapunov stable analysis. The localization and stability of breathers in three types of models correlate closely to the system nonlinear parameter β.

Nonlinear Phase Dynamics in a Driven Bosonic Josephson Junction

We study the collective dynamics of a driven two-mode Bose-Hubbard model in the Josephson interaction regime. The classical phase space is mixed, with chaotic and regular components, which determine the dynamical nature of the fringe visibility. For a weak off-resonant drive, where the chaotic component is small, the many-body dynamics corresponds to that of a Kapitza pendulum, with the relative phase φ between the condensates playing the role of the pendulum angle. Using a master equation approach we show that the modulation of the intersite potential barrier stabilizes the φ=π "inverted pendulum" coherent state, and protects the fringe visibility.

Tuning the bond-order wave phase in the half-filled extended Hubbard model

Theoretical and computational studies of the quantum phase diagram of the one-dimensional half-filled extended Hubbard model (EHM) indicate a narrow bond-order wave (BOW) phase with finite magnetic gap E-m for on-site repulsion U < U-*, the critical point, and nearest-neighbor interaction V-c approximate to U/2 near the boundary of the charge-density wave (CDW) phase. Potentials with more extended interactions that retain the EHM symmetry are shown to have a less cooperative CDW transition with higher U-* and wider BOW phase. Density-matrix renormalization group is used to obtain E-m directly as the singlet-triplet gap, with finite E-m marking the BOW boundary V-s(U). The BOW/CDW boundary V-c(U) is obtained from exact finite-size calculations that are consistent with previous EHM determinations. The kinetic energy or bond order provides a convenient new estimate of U-* based on a metallic point at V-c(U) for U < U-*. Tuning the BOW phase of half-filled Hubbard models with different intersite potentials indicates a ground state with large charge fluctuations and magnetic frustration. The possibility of physical realizations of a BOW phase is raised for Coulomb interactions.

Discrete breathers and nonlinear normal modes in monoatomic chains

We consider a relation between discrete breathers (DBs) and nonlinear normal modes in some nonlinear monoatomic chains. The dependence of the breathers’ stability on the strength of interparticle interaction in the K 4 chain (the chain with uniform on-site and intersite potentials of the fourth order) is investigated. A general method for constructing DBs which provides the pair synchronization between the individual particles’ vibrations is discussed. Many-frequency breathers as DBs of a new type and quasibreathers [introduced in Physical Review E 74 (2006) 036608] are analyzed.

Stability change of intrinsic localized mode in finite nonlinear coupled oscillators

Intrinsic localized mode (ILM) is spatially localized and temporally periodic oscillation in nonlinear coupled oscillators. We numerically investigate the dynamical stability of ILMs in a microcantilever array, in which ILMs were experimentally observed by Sato et al. It is found that the stability change of ILMs is due to the ratio in nonlinear potentials. This phenomenon also occurs in the array without harmonic potentials. Consequently, the stability of ILMs substantially depends on the ratio in nonlinear on-site and inter-site potentials.

Multi-site Compact-Like Discrete Breather in Discrete One-Dimensional Monatomic Chains

Multi-site compact-like discrete breathers in discrete one-dimensional monatomic chains are investigated by discussing a generalized discrete one-dimensional monatomic model. We obtain that the two-site compact-like discrete breathers with codes σ = {0,…, 0,1,1, 0,…, 0} and codes σ = {0,…,0,1, - 1,0,…, 0} can exist in discrete one-dimensional monatomic chain with quartic on-site and inter-site potentials. However, the former can only exist in hard quartic on-site potential and cannot exist in soft quartic on-site potential, whereas the latter is just reversed. All of the two-site Compact-like discrete breathers with codes σ = {0,…, 0,1,1, 0,…, 0} and σ = {0,…, 0,1, - 1, 0,…, 0} cannot exist in a pure K4 chain.

Discrete nonlinear Schrödinger approximation of a mixed Klein–Gordon/Fermi–Pasta–Ulam chain: Modulational instability and a statistical condition for creation of thermodynamic breathers

We analyze certain aspects of the classical dynamics of a one-dimensional discrete nonlinear Schrödinger model with inter-site as well as on-site nonlinearities. The equation is derived from a mixed Klein–Gordon/Fermi–Pasta–Ulam chain of anharmonic oscillators coupled with anharmonic inter-site potentials, and approximates the slow dynamics of the fundamental harmonic of discrete small-amplitude modulational waves. We give explicit analytical conditions for modulational instability of travelling plane waves, and find in particular that sufficiently strong inter-site nonlinearities may change the nature of the instabilities from long-wavelength to short-wavelength perturbations. Further, we describe thermodynamic properties of the model using the grand-canonical ensemble to account for two conserved quantities: norm and Hamiltonian. The available phase space is divided into two separated parts with qualitatively different properties in thermal equilibrium: one part corresponding to a normal thermalized state with exponentially small probabilities for large-amplitude excitations, and another part typically associated with the formation of high-amplitude localized excitations, interacting with an infinite-temperature phonon bath. A modulationally unstable travelling wave may exhibit a transition from one region to the other as its amplitude is varied, and thus modulational instability is not a sufficient criterion for the creation of persistent localized modes in thermal equilibrium. For pure on-site nonlinearities the created localized excitations are typically pinned to particular lattice sites, while for significant inter-site nonlinearities they become mobile, in agreement with well-known properties of localized excitations in Fermi–Pasta–Ulam-type chains.

Kink-like periodic travelling waves for lattice equations with on-site and inter-site potentials

The existence of travelling generalized kinks with oscillation tails is studied for a class of 1D lattice equations with both onsite and intersite potential. The travelling wave equation of the corresponding discrete nonlin- ear equation is formulated as an advanced{delay dieren tial equation which is reduced by a center manifold method to a 4-dimensional singular ODE with certain symmetries and with a symmetric heteroclinic structure. Bifurcations of solutions from the heteroclinic ones are investigated for the singular per- turbation systems of autonomous o.d.eqns in R4. This gives the existence of generalized kink solutions with co{propagating oscillation tails.

Discrete gap breathers in a diatomic Klein-Gordon chain: Stability and mobility

A one-dimensional diatomic chain with harmonic intersite potential and nonlinear external potential is considered (the Klein-Gordon model). Localized solutions of the corresponding nonlinear differential equations with frequencies inside the gap of the linear wave spectrum--"gap breathers"--are studied numerically. The linear stability analysis for these solutions is performed while changing the system parameters from the anticontinuous to the continuous limit. Two different types of solutions are considered: symmetric centered at a heavy atom and antisymmetric centered at a light atom, respectively. Different mechanisms of instability, oscillatory as well as nonoscillatory, of the gap breathers are studied, and the influence of the instabilities on the breather solutions is investigated in the dynamics simulations. In particular, the presence of an "inversion of stability" regime, with simultaneous nonoscillatory instabilities of symmetric and antisymmetric solutions with respect to antisymmetric perturbations, is found, yielding practically radiationless mobility.

Pattern formation and localization in the forced-damped Fermi-Pasta-Ulam lattice.

We study spatial pattern formation and energy localization in the dynamics of an anharmonic chain with quadratic and quartic intersite potential, subject to an optical, sinusoidally oscillating field and a weak damping. The zone-boundary mode is stable and locked to the driving field below a critical forcing that we determine analytically using an approximate model, which describes mode interactions. Above such a forcing, a standing modulated wave forms for driving frequencies below the band edge, while a "multibreather" state develops at higher frequencies. Of the former, we give an explicit approximate analytical expression, which compares well with numerical data. At higher forcing, space-time chaotic patterns are observed.

Memory effects and heat transport in one-dimensional insulators

We study the dynamical correlation functions and heat conduction for the simplest model of quasi one-dimensional (1d) dielectric crystal i.e. a chain of classical particles coupled by quadratic and cubic intersite potential. Even in the weakly nonlinear regime, numerical simulation on long enough chains reveal sizeable deviations from the perturbative results in the form of a slower decay of correlations in equilibrium. Their origin can be traced back to the subtle nonlinear effects described by mode-coupling theories. Measures of thermal conductivity with nonequilibrium molecular-dynamics method confirm the relevance of such effects for low-dimensional lattices even at very low temperatures.

Dynamics of coupled gap solitons in diatomic lattices with cubic and quartic nonlinearities

The dynamics of coupled gap solitons in diatomic lattices with cubic and quartic nonlinearities is considered analytically based on an extended quasidiscreteness approach. For various mass differences (and thus different gap widths of the phonon spectrum), the coupled gap solitons are shown to display very rich dynamical behavior and their properties are strongly dependent on the force-constant ratio K(2)(3)/(K2K4), where K(j)(j=1,2,3) are the force constants for the quadratic, cubic, and quartic parts of the intersite interaction potential, respectively. Several previous theoretical approaches for studying gap soliton dynamics in diatomic lattices are recovered in our scheme, and the relations between these methods are elucidated in a systematic way.

Determination of an ethane intermolecular potential model for use in molecular simulations from ab initio calculations

Counterpoise-corrected, supermolecule, ab initio energies obtained at the MP2/6-311+G(2df,2pd) level were computed for 22 different relative orientations of two ethane molecules as a function of the separation distance between the molecular centers. These energies were used to regress the parameters in several simple, analytical, interatomic or site–site models that can be used for implementation in molecular simulations. Sensitivity analysis indicates that the intermolecular potential surface is insensitive to C–C interactions and that the parameters in the C–C model are coupled and unobtainable from the dimer energies. Representation of the potential surface can be made in terms of C–H and H–H interatomic potentials if the C–C interactions are treated as shielded. Simple Lennard-Jones and exp-6 models do not adequately represent the potential surface using these shielded models, nor do they produce the anticipated physics for the interatomic potentials. The exp-6 model with a damping function and the modified-Morse interatomic potentials both reproduce the intermolecular potential surface well with physically realistic intersite potentials suitable for use in molecular dynamics simulations.