Localization Phenomenon In Some Random Classical Systems.

1994 ◽  
Author(s):  
Alexander Figotin
Keyword(s):  
Classical Systems ◽  
Localization Phenomenon

scholarly journals Efficient Numerical Evaluation of Thermodynamic Quantities on Infinite (Semi-)classical Chains

2021 ◽  
Vol 182 (3) ◽  
Author(s):  
Christian B. Mendl ◽  
Folkmar Bornemann
Keyword(s):  
Transfer Operator ◽  
Classical System ◽  
Free Energy Density ◽  
Classical Particle ◽  
Thermodynamic Quantities ◽  
Nls Equation ◽  
Classical Systems ◽  
Particle Chain ◽  
Dynamics Simulations ◽  
Good Agreement

AbstractThis work presents an efficient numerical method to evaluate the free energy density and associated thermodynamic quantities of (quasi) one-dimensional classical systems, by combining the transfer operator approach with a numerical discretization of integral kernels using quadrature rules. For analytic kernels, the technique exhibits exponential convergence in the number of quadrature points. As demonstration, we apply the method to a classical particle chain, to the semiclassical nonlinear Schrödinger (NLS) equation and to a classical system on a cylindrical lattice. A comparison with molecular dynamics simulations performed for the NLS model shows very good agreement.

Nonlinear Vibrations of Two-Span Composite Laminated Plates with Equal and Unequal Subspan Lengths

2017 ◽  
Vol 9 (6) ◽  
pp. 1485-1505
Author(s):  
Lingchang Meng ◽  
Fengming Li
Keyword(s):  
Multiple Scales ◽  
Equations Of Motion ◽  
Primary Resonance ◽  
Laminated Plates ◽  
Laminated Plate ◽  
Composite Laminated Plate ◽  
Vibration Localization ◽  
Composite Laminated Plates ◽  
Localization Phenomenon ◽  
Harmonic Resonance

AbstractThe nonlinear transverse vibrations of ordered and disordered two-dimensional (2D) two-span composite laminated plates are studied. Based on the von Karman's large deformation theory, the equations of motion of each-span composite laminated plate are formulated using Hamilton's principle, and the partial differential equations are discretized into nonlinear ordinary ones through the Galerkin's method. The primary resonance and 1/3 sub-harmonic resonance are investigated by using the method of multiple scales. The amplitude-frequency relations of the steady-state responses and their stability analyses in each kind of resonance are carried out. The effects of the disorder ratio and ply angle on the two different resonances are analyzed. From the numerical results, it can be concluded that disorder in the length of the two-span 2D composite laminated plate will cause the nonlinear vibration localization phenomenon, and with the increase of the disorder ratio, the vibration localization phenomenon will become more obvious. Moreover, the amplitude-frequency curves for both primary resonance and 1/3 sub-harmonic resonance obtained by the present analytical method are compared with those by the numerical integration, and satisfactory precision can be obtained for engineering applications and the results certify the correctness of the present approximately analytical solutions.

scholarly journals Nonlinear quantization of integrable classical systems

1997 ◽  
Vol 38 (8) ◽  
pp. 4073-4085
Author(s):  
Antonio Scotti ◽  
Alexander Ushveridze
Keyword(s):  
Classical Systems ◽  
Nonlinear Quantization

Nonadiabatic reaction rates for dissipative quantum-classical systems

2003 ◽  
Vol 119 (24) ◽  
pp. 12776-12783 ◽  
Author(s):  
Alessandro Sergi ◽  
Raymond Kapral
Keyword(s):  
Reaction Rates ◽  
Classical Systems

Recent advances in the technologies of connection for panel structures: Design and cost analysis of different solutions with X-shaped dissipative connectors

2016 ◽  
Vol 20 (3) ◽  
pp. 299-315
Author(s):  
Massimo Latour
Keyword(s):  
Finite Element ◽  
Cost Reduction ◽  
Design Criterion ◽  
Classical Solutions ◽  
Finite Element Analyses ◽  
Seismic Damper ◽  
Classical Systems ◽  
Cyclic Behaviour ◽  
Energy Dissipation Capacity ◽  
The Cost

In this work, a recently patented seismic damper to be applied to structures composed by systems of panels is presented. In particular, the article is devoted to characterize the behaviour of the proposed connector by means of an experimental and numerical analysis and to provide some information about the cost of the elements needed to realize the damper, accounting for the manufacturing process. The experimental analysis has regarded five specimens tested under different loading conditions, and it has been used as a term of comparison with the classical systems of connection currently employed in these structures. Afterwards, in the article, a design criterion able to control the capacity and ductility of the device by simply varying the shape of the damper is presented and its accuracy is evaluated by performing finite element analyses. The results of the experimental and finite element analyses are very promising in terms of cyclic behaviour and energy dissipation capacity and reveal that the design of the element can be accurately controlled by means of the proposed approach. Furthermore, the cost estimate has revealed that the proposed damper is also cheaper than the classical solutions with a cost reduction of about 40%.

On a localization phenomenon in two types of bio-inspired hierarchically organized oscillatory systems

2019 ◽  
Vol 99 (1) ◽  
pp. 679-706 ◽  
Author(s):  
Ivana Kovacic ◽  
Miodrag Zukovic ◽  
Dragi Radomirovic
Keyword(s):  
Oscillatory Systems ◽  
Localization Phenomenon
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