Dynamical properties of discrete breathers in curved chains with first and second neighbor interaction

We present the study of discrete breather dynamics in curved polymerlike chains consisting of masses connected via nonlinear springs. The polymer chains are one dimensional but not rectilinear and their motion takes place on a plane. After constructing breathers following numerically accurate procedures, we launch them in the chains and investigate properties of their propagation dynamics. We find that breather motion is strongly affected by the presence of curved regions of polymers, while the breathers themselves show a very strong resilience and remarkable stability in the presence of geometrical changes. For chains with strong angular rigidity we find that breathers either pass through bent regions or get reflected while retaining their frequency. Their motion is practically lossless and seems to be determined through local energy conservation. For less rigid chains modeled via second neighbor interactions, we find similarly that chain geometry typically does not destroy the localized breather states but, contrary to the angularly rigid chains, it induces some small but constant energy loss. Furthermore, we find that a curved segment acts as an active gate reflecting or refracting the incident breather and transforming its velocity to a value that depends on the discrete breathers frequency. We analyze the physical reasoning behind these seemingly general breather properties.

Confinement of discrete breathers in inhomogeneously profiled nonlinear chains

We investigate numerically the scattering of a moving discrete breather on a pair of junctions in a Fermi-Pasta-Ulam chain. These junctions delimit an extended region with different masses of the particles. We consider (i) a rectangular trap, (ii) a wedge shaped trap, and (iii) a smoothly varying convex or concave mass profile. All three cases lead to DB confinement, with the ease of trapping depending on the profile of the trap. We also study the collision and trapping of two DBs within the profile as a function of trap width, shape, and approach time at the two junctions. The latter controls whether one or both DBs are trapped.

Ordered structures in rotating ultracold Bose gases

Two-dimentional systems of trapped samples of few cold bosonic atoms submitted to strong rotation around the perpendicular axis may be realized in optical lattices and microtraps. We investigate theoretically the evolution of ground state structures of such systems as the rotational frequency Omega increases. Various kinds of ordered structures are observed. In some cases, hidden interference patterns exhibit themselves only in the pair correlation function; in some other cases explicit broken-symmetry structures appear that modulate the density. For N < 10 atoms, the standard scenario, valid for large sytems is absent, and is only gradually recovered as N increases. On the one hand, the Laughlin state in the strong rotational regime contains ordered structures much more similar to a Wigner molecule than to a fermionic quantum liquid. On the other hand, in the weak rotational regime, the possibility to obtain equilibrium states, whose density reveals an array of vortices, is restricted to the vicinity of some critical values of the rotational frequency Omega.

Controlled-intensity detection peaks in a binary joint transform correlator

In multiobject pattern recognition the height of the correlation peaks should be controlled when the power spectrum of ajoint transform correlator is binarized. In this paper a method to predetermine the value of detection peaks is demonstrated. The technique is based on a frequency-variant threshold in order to remove the intraclass terms and on a suitable factor to normalize the binary joint power spectrum. Digital simulations and experimental hybrid implementation of this method were carried out.

Estimation of the parameters of the gravitational-wage signal of a coalescing binary system

The statistical theory of signal detection and the estimation of its parameters are reviewed and applied to the case of detection of the gravitational-wave signal from a coalescing binary by a laser interferometer. The correlation integral and the covariance matrix for all possible static configurations are investigated numerically. Approximate analytic formulas are derived for the case of narrow band sensitivity configuration of the detector.

Long-range-interactions induced ordered structures in deposition processes

We present a new model of sequential adsorption in which the adsorbing particles experience dipolar interactions. We show that in the presence of these long-range interactions, highly ordered structures in the adsorbed layer may be induced at low temperatures. The new phenomenology is manifest through significant variations of the pair correlation function and the jamming limit, with respect to the case of noninteracting particles. Our study could be relevant in understanding the adsorption of magnetic colloidal particles in the presence of a magnetic field.

Self and cross-velocity correlation functions and diffusion coefficients in liquids: a molecular dynamics study of binary mixtures of soft spheres

Molecular dynamics simulation is applied to the study of the diffusion properties in binary liquid mixtures made up of soft-sphere particles with different sizes and masses. Self- and distinct velocity correlation functions and related diffusion coefficients have been calculated. Special attention has been paid to the dynamic cross correlations which have been computed through recently introduced relative mean molecular velocity correlation functions which are independent on the reference frame. The differences between the distinct velocity correlations and diffusion coefficients in different reference frames (mass-fixed, number-fixed, and solvent-fixed) are discussed.

Variational localized-site cluster expansions. X. Dimerization in linear Heisenberg chains

Ground-state instability to bond alternation in long linear chains is considered from the point of view of valence-bond (VB) theory. This instability is viewed as the consequence of a long-range order (LRO) which is expected if the ground state is reasonably described in terms of the Kekulé states (with nearest-neighbor singlet pairing). It is argued that the bond alternation and associated LRO predicted by this simple, VB picture is retained for certain linear Heisenberg models; many-body VB calculations on spin s=1 / 2 and s=1 chains are carried out in a test of this argument.

A comparison of three methods of Mendelian randomization when the genetic instrument, the risk factor and the outcome are all binary.

The method of instrumental variable (referred to as Mendelian randomization when the instrument is a genetic variant) has been initially developed to infer on a causal effect of a risk factor on some outcome of interest in a linear model. Adapting this method to nonlinear models, however, is known to be problematic. In this paper, we consider the simple case when the genetic instrument, the risk factor, and the outcome are all binary. We compare via simulations the usual two-stages estimate of a causal odds-ratio and its adjusted version with a recently proposed estimate in the context of a clinical trial with noncompliance. In contrast to the former two, we confirm that the latter is (under some conditions) a valid estimate of a causal odds-ratio defined in the subpopulation of compliers, and we propose its use in the context of Mendelian randomization. By analogy with a clinical trial with noncompliance, compliers are those individuals for whom the presence/absence of the risk factor X is determined by the presence/absence of the genetic variant Z (i.e., for whom we would observe X = Z whatever the alleles randomly received at conception). We also recall and illustrate the huge variability of instrumental variable estimates when the instrument is weak (i.e., with a low percentage of compliers, as is typically the case with genetic instruments for which this proportion is frequently smaller than 10%) where the inter-quartile range of our simulated estimates was up to 18 times higher compared to a conventional (e.g., intention-to-treat) approach. We thus conclude that the need to find stronger instruments is probably as important as the need to develop a methodology allowing to consistently estimate a causal odds-ratio.