Accurate multi-boson long-time dynamics in triple-well periodic traps

To solve the many-boson Schr\"odinger equation we utilize the Multiconfigurational time-dependent Hartree method for bosons (MCTDHB). To be able to attack larger systems and/or to propagate the solution for longer times, we implement a parallel version of the MCTDHB method thereby realizing the recently proposed [Streltsov {\it et al.} arXiv:0910.2577v1] novel idea how to construct efficiently the result of the action of the Hamiltonian on a bosonic state vector. We study the real-space dynamics of repulsive bosonic systems made of N=12, 51 and 3003 bosons in triple-well periodic potentials. The ground state of this system is three-fold fragmented. By suddenly strongly distorting the trap potential, the system performs complex many-body quantum dynamics. At long times it reveals a tendency to an oscillatory behavior around a threefold fragmented state. These oscillations are strongly suppressed and damped by quantum depletions. In spite of the richness of the observed dynamics, the three time-adaptive orbitals of MCTDHB(M=3) are capable to describe the many-boson quantum dynamics of the system for short and intermediate times. For longer times, however, more self-consistent time-adaptive orbitals are needed to correctly describe the non-equilibrium many-body physics. The convergence of the MCTDHB($M$) method with the number $M$ of self-consistent time-dependent orbitals used is demonstrated.Comment: 37 pages, 7 figure

Non-perturbative response: chaos versus disorder

Quantized chaotic systems are generically characterized by two energy scales: the mean level spacing $\Delta$, and the bandwidth $\Delta_b\propto\hbar$. This implies that with respect to driving such systems have an adiabatic, a perturbative, and a non-perturbative regimes. A "strong" quantal non-perturbative response effect is found for {\em disordered} systems that are described by random matrix theory models. Is there a similar effect for quantized {\em chaotic} systems? Theoretical arguments cannot exclude the existence of a "weak" non-perturbative response effect, but our numerics demonstrate an unexpected degree of semiclassical correspondence.Comment: 8 pages, 2 figures, final version to be published in JP

Articular human joint modelling

Copyright @ Cambridge University Press 2009.The work reported in this paper encapsulates the theories and algorithms developed to drive the core analysis modules of the software which has been developed to model a musculoskeletal structure of anatomic joints. Due to local bone surface and contact geometry based joint kinematics, newly developed algorithms make the proposed modeller different from currently available modellers. There are many modellers that are capable of modelling gross human body motion. Nevertheless, none of the available modellers offer complete elements of joint modelling. It appears that joint modelling is an extension of their core analysis capability, which, in every case, appears to be musculoskeletal motion dynamics. It is felt that an analysis framework that is focused on human joints would have significant benefit and potential to be used in many orthopaedic applications. The local mobility of joints has a significant influence in human motion analysis, in understanding of joint loading, tissue behaviour and contact forces. However, in order to develop a bone surface based joint modeller, there are a number of major problems, from tissue idealizations to surface geometry discretization and non-linear motion analysis. This paper presents the following: (a) The physical deformation of biological tissues as linear or non-linear viscoelastic deformation, based on spring-dashpot elements. (b) The linear dynamic multibody modelling, where the linear formulation is established for small motions and is particularly useful for calculating the equilibrium position of the joint. This model can also be used for finding small motion behaviour or loading under static conditions. It also has the potential of quantifying the joint laxity. (c) The non-linear dynamic multibody modelling, where a non-matrix and algorithmic formulation is presented. The approach allows handling complex material and geometrical nonlinearity easily. (d) Shortest path algorithms for calculating soft tissue line of action geometries. The developed algorithms are based on calculating minimum ‘surface mass’ and ‘surface covariance’. An improved version of the ‘surface covariance’ algorithm is described as ‘residual covariance’. The resulting path is used to establish the direction of forces and moments acting on joints. This information is needed for linear or non-linear treatment of the joint motion. (e) The final contribution of the paper is the treatment of the collision. In the virtual world, the difficulty in analysing bodies in motion arises due to body interpenetrations. The collision algorithm proposed in the paper involves finding the shortest projected ray from one body to the other. The projection of the body is determined by the resultant forces acting on it due to soft tissue connections under tension. This enables the calculation of collision condition of non-convex objects accurately. After the initial collision detection, the analysis involves attaching special springs (stiffness only normal to the surfaces) at the ‘potentially colliding points’ and motion of bodies is recalculated. The collision algorithm incorporates the rotation as well as translation. The algorithm continues until the joint equilibrium is achieved. Finally, the results obtained based on the software are compared with experimental results obtained using cadaveric joints

Subwavelength optical spatial solitons and three-dimensional localization in disordered ferroelectrics: towards metamaterials of nonlinear origin

We predict the existence of a novel class of multidimensional light localizations in out-of-equilibrium ferroelectric crystals. In two dimensions, the non-diffracting beams form at arbitrary low power level and propagate even when their width is well below the optical wavelength. In three dimensions, a novel form of subwavelength light bullets is found. The effects emerge when compositionally disordered crystals are brought to their metastable glassy state, and can have a profound impact on super-resolved imaging and ultra-dense optical storage, while resembling many features of the so-called metamaterials, as the suppression of evanescent waves.Comment: 4 pages, 3 figure

Tsallis non-extensive statistics, intermittent turbulence, SOC and chaos in the solar plasma. Part one: Sunspot dynamics

In this study, the nonlinear analysis of the sunspot index is embedded in the non-extensive statistical theory of Tsallis. The triplet of Tsallis, as well as the correlation dimension and the Lyapunov exponent spectrum were estimated for the SVD components of the sunspot index timeseries. Also the multifractal scaling exponent spectrum, the generalized Renyi dimension spectrum and the spectrum of the structure function exponents were estimated experimentally and theoretically by using the entropy principle included in Tsallis non extensive statistical theory, following Arimitsu and Arimitsu. Our analysis showed clearly the following: a) a phase transition process in the solar dynamics from high dimensional non Gaussian SOC state to a low dimensional non Gaussian chaotic state, b) strong intermittent solar turbulence and anomalous (multifractal) diffusion solar process, which is strengthened as the solar dynamics makes phase transition to low dimensional chaos in accordance to Ruzmaikin, Zeleny and Milovanov studies c) faithful agreement of Tsallis non equilibrium statistical theory with the experimental estimations of i) non-Gaussian probability distribution function, ii) multifractal scaling exponent spectrum and generalized Renyi dimension spectrum, iii) exponent spectrum of the structure functions estimated for the sunspot index and its underlying non equilibrium solar dynamics.Comment: 40 pages, 11 figure