scholarly journals Instability of holographic superfluids in optical lattice

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Peng Yang ◽  
Xin Li ◽  
Yu Tian
Keyword(s):  
Optical Lattice ◽  
Equations Of Motion ◽  
Stable State ◽  
Bloch Wave ◽  
Linear Perturbation ◽  
Holographic Model ◽  
Chaotic State ◽  
Final State ◽  
Bloch Waves ◽  
Soliton Generation

Abstract The instability of superfluids in optical lattice has been investigated using the holographic model. The static and steady flow solutions are numerically obtained from the static equations of motion and the solutions are described as Bloch waves with different Bloch wave vector k. Based on these Bloch waves, the instability is investigated at two levels. At the linear perturbation level, we show that there is a critical kc above which the superflow is unstable. At the fully nonlinear level, the intermediate state and final state of unstable superflow are identified through numerical simulation of the full equations of motion. The results show that during the time evolution, the unstable superflow will undergo a chaotic state with soliton generation. The system will settle down to a stable state with k < kc eventually, with a smaller current and a larger condensate.

Phononic Band Gap Systems in Structural Mechanics: Finite Slender Elastic Structures and Infinite Periodic Waveguides

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
Michele Brun ◽  
Alexander B. Movchan ◽  
Ian S. Jones
Keyword(s):  
Equations Of Motion ◽  
Standing Waves ◽  
Tall Buildings ◽  
Bloch Wave ◽  
Elementary Cell ◽  
Mathematical Treatment ◽  
Asymptotic Model ◽  
Spectral Approach ◽  
Elastic Systems ◽  
Waveguide Problem

The paper presents a novel spectral approach, accompanied by an asymptotic model and numerical simulations for slender elastic systems such as long bridges or tall buildings. The focus is on asymptotic approximations of solutions by Bloch waves, which may propagate in a infinite periodic waveguide. Although the notion of passive mass dampers is conventional in the engineering literature, it is not obvious that an infinite waveguide problem is adequate for analysis of long but finite slender elastic systems. The formal mathematical treatment of a Bloch wave would reduce to a spectral analysis of equations of motion on an elementary cell of a periodic structure, with Bloch–Floquet quasi-periodicity conditions imposed on the boundary of the cell. Frequencies of some classes of standing waves can be estimated analytically. One of the applications discussed in the paper is the “dancing bridge” across the river Volga in Volgograd.

Bloch wave homogenisation of quasiperiodic media

2020 ◽  
pp. 1-21
Author(s):  
SISTA SIVAJI GANESH ◽  
VIVEK TEWARY
Keyword(s):  
Bloch Wave ◽  
Periodic Operator ◽  
Almost Periodic ◽  
Periodic Media ◽  
Direct Integral ◽  
Bloch Waves ◽  
Direct Integral Decomposition ◽  
Quasiperiodic Media ◽  
Integral Decomposition ◽  
Periodic Operators

Quasiperiodic media is a class of almost periodic media which is generated from periodic media through a ‘cut and project’ procedure. Quasiperiodic media displays some extraordinary optical, electronic and conductivity properties which call for the development of methods to analyse their microstructures and effective behaviour. In this paper, we develop the method of Bloch wave homogenisation for quasiperiodic media. Bloch waves are typically defined through a direct integral decomposition of periodic operators. A suitable direct integral decomposition is not available for almost periodic operators. To remedy this, we lift a quasiperiodic operator to a degenerate periodic operator in higher dimensions. Approximate Bloch waves are obtained for a regularised version of the degenerate operator. Homogenised coefficients for quasiperiodic media are obtained from the first Bloch eigenvalue of the regularised operator in the limit of regularisation parameter going to zero. A notion of quasiperiodic Bloch transform is defined and employed to obtain homogenisation limit for an equation with highly oscillating quasiperiodic coefficients.

Theory of bulk resonance diffraction in THEED

1993 ◽  
Vol 440 (1908) ◽  
pp. 95-115 ◽  
Keyword(s):  
Elastic Scattering ◽  
Incident Beam ◽  
Bloch Wave ◽  
Dynamical Theory ◽  
Zone Axis ◽  
Bloch Waves ◽  
Diffraction Geometry ◽  
Ewald Sphere ◽  
Lattice Images ◽  
New Type

A full dynamical theory has been developed for an off-axis diffraction geometry. A new type of resonance elastic scattering is found and discussed. This occurs when the Ewald sphere is almost tangential to one of the minus high order Laue zones, and is termed bulk resonance diffraction. It is shown that under certain diffraction conditions, i. e. bulk resonance diffraction conditions, effectively only a single distinct tightly bound Bloch wave localized around atom strings is excited within the crystal, and selection can be made of the particular bound Bloch waves by appropriately tilting the incident beam or the crystal. A new scheme for imaging individual tightly bound Bloch waves is proposed. Full dynamical calculations have been made for 1T–V Se 2 single crystals. It is demonstrated that chemical lattice images of V and Se atom strings can be obtained along the [0001] zone axis of a 1T–V Se 2 crystal for angles of incidence of 109.54 and 109.90 mrad respectively.

scholarly journals Analytical formulation of three-dimensional dynamic homogenization for periodic elastic systems

2012 ◽  
Vol 468 (2142) ◽  
pp. 1629-1651 ◽  
Author(s):  
A. N. Norris ◽  
A. L. Shuvalov ◽  
A. A. Kutsenko
Keyword(s):  
Effective Medium Theory ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Expansion Method ◽  
Bloch Wave ◽  
Dimensional System ◽  
Medium Theory ◽  
Material Parameters ◽  
Elastic Systems ◽  
Arbitrary Frequency

Homogenization of the equations of motion for a three-dimensional periodic elastic system is considered. Expressions are obtained for the fully dynamic effective material parameters governing the spatially averaged fields by using the plane wave expansion method. The effective equations are of Willis form with coupling between momentum and stress and tensorial inertia. The formulation demonstrates that the Willis equations of elastodynamics are closed under homogenization. The effective material parameters are obtained for arbitrary frequency and wavenumber combinations, including but not restricted to Bloch wave branches for wave propagation in the periodic medium. Numerical examples for a one-dimensional system illustrate the frequency dependence of the parameters on Bloch wave branches and provide a comparison with an alternative dynamic effective medium theory, which also reduces to Willis form but with different effective moduli.

Atomistic Simulation of Vapor-Phase Nanoparticle Formation

1994 ◽  
Vol 351 ◽  
Author(s):  
Michael R. Zachariah ◽  
Michael J. Carrier ◽  
Estela Blaisten-Barojas
Keyword(s):  
Atomistic Simulation ◽  
Equations Of Motion ◽  
Stable State ◽  
Dynamic Effects ◽  
Diffusion Constants ◽  
Large Heat ◽  
Dynamics Simulations ◽  
Three Body ◽  
The Impact ◽  
Weber Potential

ABSTRACTIn order to understand from a fundamental view how nanoparticles form and grow, classical molecular dynamics simulations of cluster growth and energy accommodation processes have been conducted for clusters of silicon (< 1000 atoms), over a wide temperature range. Simulations involved solution of the classical equations of motion constrained with the three body Stillinger-Weber potential. The results show the large heat release and resulting cluster heating during a cluster-cluster collision event, and the corresponding time evolution of the internal energy to a more stable state. Dynamic effects associated with the temperature of the cluster and the impact parameter are also clearly evident. In particular, clusters show a large sensitivity to temperature in the rate of coalescence, particularly at low temperature. Calculated diffusion coefficients are significantly larger than surface diffusion constants stated in the literature. Phonon density of states spectra do not seem to show size effects.

scholarly journals The Complex Dynamics of Sharing Platform Competition Game

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Jianli Xiao
Keyword(s):  
Feedback Control ◽  
Rapid Development ◽  
Stable State ◽  
Sharing Economy ◽  
System Stability ◽  
Largest Lyapunov Exponent ◽  
Platform Competition ◽  
Chaotic State ◽  
Price Increases ◽  
Adjustment Speed

With the rapid development of Internet technologies and online sharing platforms, sharing economy has become a major trend in economy. The entry of sharing economy leads to profound impacts on incumbent industry. We build a dynamic sharing platform competition model with which agents are bounded rational, and consumer side is heterogeneous. Then, we present the fixed points and the stability conditions of the bifurcation of the dynamic model. We simulate the adjustment speed of sharing platform, sharing platform price, and costs of traditional firm effects on system stability, and we present stable area, bifurcation diagram, the largest Lyapunov exponent, and strange attractor of different parameters, and we give a feedback control method at last. Our main results are as follows: (1) when adjustment speed of sharing platform increases, the system becomes bifurcation, and finally, the system goes into a chaotic state; when the system is stable, price of traditional firm and fee decision of sharing platform are constant. (2) When price of sharing platform increases, sharing platform is more stable while traditional firm is more vulnerable. Suppose the system is in the stable state; when sharing platform price increases, traditional firm price increases, while sharing platform fees decreases. (3) When traditional firm cost is small, the system would be more stable. When the system is stable, with traditional firm cost increasing, traditional firm price increases quicker than sharing platform consumer fee, while sharing platform seller fee decreases. (4) Feedback control can alleviate the chaotic state of system. With feedback control parameter increases, the system becomes more stable.

scholarly journals Non-modal stability analysis of miscible viscous fingering with non-monotonic viscosity profiles

2018 ◽  
Vol 856 ◽  
pp. 552-579
Author(s):  
Tapan Kumar Hota ◽  
Manoranjan Mishra
Keyword(s):  
Stability Analysis ◽  
Viscous Fluid ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Physical Mechanism ◽  
Stable State ◽  
Viscous Fingering ◽  
Linear Perturbation ◽  
Optimal Perturbation ◽  
Nonlinear Simulations

A non-modal linear stability analysis (NMA) of the miscible viscous fingering in a porous medium is studied for a toy model of non-monotonic viscosity variation. The onset of instability and its physical mechanism are captured in terms of the singular values of the propagator matrix corresponding to the non-autonomous linear equations. We discuss two types of non-monotonic viscosity profiles, namely, with unfavourable (when a less viscous fluid displaces a high viscous fluid) and with favourable (when a more viscous fluid displaces a less viscous fluid) endpoint viscosities. A linear stability analysis yields instabilities for such viscosity variations. Using the optimal perturbation structure, we are able to show that an initially unconditional stable state becomes unstable corresponding to the most unstable initial disturbance. In addition, we also show that to understand the spatio-temporal evolution of the perturbations it is necessary to analyse the viscosity gradient with respect to the concentration and the location of the maximum concentration $c_{m}$. For the favourable endpoint viscosities, a weak transient instability is observed when the viscosity maximum moves close to the pure invading or defending fluid. This instability is attributed to an interplay between the sharp viscosity gradient and the favourable endpoint viscosity contrast. Further, the usefulness of the non-modal analysis demonstrating the physical mechanism of the quadruple structure of the perturbations from the optimal concentration disturbances is discussed. We demonstrate the dissimilarity between the quasi-steady-state approach and NMA in finding the correct perturbation structure and the onset, for both the favourable and unfavourable viscosity profiles. The correctness of the linear perturbation structure obtained from the non-modal stability analysis is validated through nonlinear simulations. We have found that the nonlinear simulations and NMA results are in good agreement. In summary, a non-monotonic variation of the viscosity of a miscible fluid pair is seen to have a larger influence on the onset of fingering instabilities than the corresponding Arrhenius type relationship.

scholarly journals Bose–Hubbard Hamiltonian: Quantum chaos approach

2016 ◽  
Vol 30 (10) ◽  
pp. 1630009 ◽  
Author(s):  
Andrey R. Kolovsky
Keyword(s):  
Optical Lattice ◽  
Quantum Chaos ◽  
Quantum Physics ◽  
Cold Atoms ◽  
Equations Of Motion ◽  
Many Body ◽  
Bloch Oscillations ◽  
Classical Counterpart ◽  
Hubbard Hamiltonian ◽  
Quantum Analysis

We discuss applications of the theory of quantum chaos to one of the paradigm models of many-body quantum physics — the Bose–Hubbard (BH) model, which describes, in particular, interacting ultracold Bose atoms in an optical lattice. After preliminary, pure quantum analysis of the system we introduce the classical counterpart of the BH model and the governing semiclassical equations of motion. We analyze these equations for the problem of Bloch oscillations (BOs) of cold atoms where a number of experimental results are available. The paper is written for nonexperts and can be viewed as an introduction to the field.

Energy Loss Analysis in Bloch Waves

1974 ◽  
Vol 29 (6) ◽  
pp. 955-956
Author(s):  
F. Fujimoto ◽  
G. Lehmpfuhl
Keyword(s):  
Electron Diffraction ◽  
Energy Loss ◽  
Single Crystal ◽  
Bloch Wave ◽  
Diffraction Spot ◽  
Loss Peak ◽  
Bloch Waves ◽  
Loss Analysis ◽  
Partial Waves

In electron diffraction experiments with a single-crystal wedge Bloch waves can be analyzed directly because of their separation into partial waves when leaving the crystal. In a two-beam case the diffraction spot is split into a double representing two partial waves of the two Bloch waves. The energy-loss spectrum in the 220 doublet of MgO was investigated with a Möllenstedt velocity-analyzer. Two loss peaks at about 14 and 22 eV were found in each Bloch wave. Thermal losses were identified as a background in the no-loss peak.

DISSIPATIVE STRUCTURES IN A DOUBLE PLASMA ON AN EXCITED SEMICONDUCTOR: NEAR ONE-DIMENSIONAL SYSTEMS

1995 ◽  
Vol 09 (09) ◽  
pp. 1099-1112
Author(s):  
A.S.C. ESPERIDIÃO ◽  
R.F.S. ANDRADE
Keyword(s):  
Infinite System ◽  
Equations Of Motion ◽  
Stable State ◽  
Operator Method ◽  
Dissipative Structures ◽  
Continuous Laser ◽  
One Dimensional ◽  
Unstable Node ◽  
Eigen Values ◽  
Kinetics Of

The formation of dissipative structures in a double plasma of electron and holes, generated on a semiconductor sample by submitting it to a continuous laser beam, is investigated. The equations of motion for the quasi-particles are obtained after the nonequilibrium statistical operator method and constitute an infinite system of coupled differential equations. When the kinetics of the system is one-dimensional, the search for the eigen-values of the linear stability analysis matrix, in the [Formula: see text] limit, reduces to an equation of 8th degree. The results show that the doped system is intrinsically unstable with respect to the intensity of the laser and that the bifurcation from the stable state to the dissipative structure is from a stable to an unstable node.

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