A SHORT NOTE ON THE BOUNDEDNESS ANALYSIS AND CONTROL OF THE SPATIAL FRACTAL SET FROM A KIND OF CHAIN COUPLING LOGISTIC TYPE MAP

Fractals ◽  
2020 ◽  
Vol 28 (04) ◽  
pp. 2050060
Author(s):  
DA WANG ◽  
YANG ZHAO ◽  
YI ZHANG ◽  
XIYU LIU
Keyword(s):  
Short Note ◽  
Upper Bounds ◽  
Coupled Systems ◽  
Strongly Coupled ◽  
Numerical Examples ◽  
Fractal Set ◽  
Coupling System ◽  
Preliminary Study ◽  
System Variables ◽  
And Control

This paper presents a preliminary study about a kind of chain coupling system, which we hope could have some enlightened effect for the research on the spatial fractal set of more strongly coupled systems. By analyzing the trajectories of system variables and applying the magnifying or reducing method, the upper bounds of the original and controlled Julia sets from the proposed system are given. Numerical examples are also included to verify the conclusions.

scholarly journals On the universality of AdS2 diffusion bounds and the breakdown of linearized hydrodynamics

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Ning Wu ◽  
Matteo Baggioli ◽  
Wei-Jia Li
Keyword(s):  
Quantum Chaos ◽  
Short Note ◽  
Diffusion Constant ◽  
Coupled Systems ◽  
Recent Analysis ◽  
Spontaneous Breaking ◽  
Hydrodynamic Mode ◽  
Translational Invariance ◽  
Strongly Coupled ◽  
Track Record

Abstract The chase of universal bounds on diffusivities in strongly coupled systems and holographic models has a long track record. The identification of a universal velocity scale, independent of the presence of well-defined quasiparticle excitations, is one of the major challenges of this program. A recent analysis, valid for emergent IR fixed points exhibiting local quantum criticality, and dual to IR AdS2 geometries, suggests to identify such a velocity using the time and length scales at which hydrodynamics breaks down — the equilibration velocity. The latter relates to the radius of convergence of the hydrodynamic expansion and it is extracted from a collision between a hydrodynamic diffusive mode and a non-hydrodynamic mode associated to the IR AdS2 region. In this short note, we confirm this picture for holographic systems displaying the spontaneous breaking of translational invariance. Moreover, we find that, at zero temperature, the lower bound set by quantum chaos and the upper one defined by causality and hydrodynamics exactly coincide, determining uniquely the diffusion constant. Finally, we comment on the meaning and universality of this newly proposed prescription.

scholarly journals Fundamental limitations of the mode temperature concept in strongly coupled systems

2020 ◽  
Vol 75 (8) ◽  
pp. 803-807
Author(s):  
Svend-Age Biehs ◽  
Achim Kittel ◽  
Philippe Ben-Abdallah
Keyword(s):  
Heat Transfer ◽  
Heat Exchange ◽  
Strong Coupling ◽  
Quantum Systems ◽  
Coupled Systems ◽  
Strong Coupling Limit ◽  
Strongly Coupled ◽  
Fundamental Limitations ◽  
Temperature Concept ◽  
Vacuum Gap

AbstractWe theoretically analyze heat exchange between two quantum systems in interaction with external thermostats. We show that in the strong coupling limit the widely used concept of mode temperatures loses its thermodynamic foundation and therefore cannot be employed to make a valid statement on cooling and heating in such systems; instead, the incorrectly applied concept may result in a severe misinterpretation of the underlying physics. We illustrate these general conclusions by discussing recent experimental results reported on the nanoscale heat transfer through quantum fluctuations between two nanomechanical membranes separated by a vacuum gap.

Article

1999 ◽  
Vol 77 (11) ◽  
pp. 1810-1812 ◽  
Author(s):  
Alex D Bain
Keyword(s):  
Spin System ◽  
Coupled System ◽  
Coupled Systems ◽  
Physical Reason ◽  
Strongly Coupled ◽  
System Combination ◽  
First Order ◽  
Weakly Coupled ◽  
Quantum Transitions ◽  
Weakly Coupled Systems

Strongly coupled spin systems provide many curious and interesting effects in NMR spectra, one of which is the presence of unexpected (from a first-order viewpoint) lines. A physical reason is given for the presence of these combination lines. The X part of the spectrum of an ABX spin system is analysed as an example. For an ABX system, it is well known that the AB nuclei give a spectrum consisting of two AB-type spectra, corresponding to the two orientations of the X nucleus. It can also be shown that the X part of the spectrum corresponds to the X nucleus undergoing a transition in the presence of an AB-like spin system. For weakly coupled systems, the four observed lines correspond to the four different orientations of the A and B nuclei. For a strongly coupled system, two additional lines may appear, the combination lines. The resulting six lines correspond to the four spin orientations, plus the two zero-quantum transitions. It is shown that these six lines are such that there is no net excitation of the AB-like spin system associated with the X transitions. There is no AB coherence created directly by a pulse applied to X. AB coherence is created as the system evolves, and this is responsible for many of the curious effects. This is shown to be true for all spin sub-systems, which are weakly coupled to a strongly coupled sub-system.Key words: NMR, strong coupling, second-order spectra, ABX spin system, combination lines, spectral analysis.

scholarly journals Closed expressions for coefficients in weighted Newton-Cotes quadratures

Filomat ◽  
2013 ◽  
Vol 27 (4) ◽  
pp. 649-658 ◽  
Author(s):  
Mohammad Masjed-Jamei ◽  
Gradimir Milovanovic ◽  
M.A. Jafari
Keyword(s):  
Short Note ◽  
Stirling Numbers ◽  
Quadrature Formulas ◽  
Numerical Examples ◽  
Quadrature Formulae ◽  
Equidistant Nodes

In this short note, we derive closed expressions for Cotes numbers in the weighted Newton-Cotes quadrature formulae with equidistant nodes in terms of moments and Stirling numbers of the first kind. Three types of equidistant nodes are considered. The corresponding program codes in Mathematica Package are presented. Finally, in order to illustrate the application of the obtained quadrature formulas a few numerical examples are included.

scholarly journals A Preliminary Study on The Prevention and Control of Seawater Intrusion in Northern Pingtan Island with Freshwater Recharge Curtain

2020 ◽  
Vol 199 ◽  
pp. 00012
Author(s):  
Mengyao Diao ◽  
Panlin Li ◽  
Weifang Ruan ◽  
Wanglin Li
Keyword(s):  
Seawater Intrusion ◽  
Effective Means ◽  
Northern Coast ◽  
Economic Activities ◽  
Intrusion Prevention ◽  
The North ◽  
Pingtan Island ◽  
Preliminary Study ◽  
Over Exploitation ◽  
And Control

Seawater intrusion caused by groundwater over-exploitation is a kind of geological disaster caused by human economic activities and natural environment changes. Using freshwater recharge curtain technology is an effective means to prevent seawater intrusion. Based on the analysis of the characteristics of seawater intrusion in Pingtan island, Fujian Province, and in view of the possible seawater intrusion problems in the construction of Luyangpu underground reservoir in Pingtan Island, this paper expounds the basic principle of seawater intrusion prevention with freshwater recharge curtain , the technical measures of installing a row of recharge wells in the northern coastal zone of Luyangpu plain in Pingtan Island and using freshwater recharge curtain are put forward to prevent seawater intrusion. Through groundwater numerical simulation, the dynamic distribution of groundwater level in the north of Pingtan Island in the next 20 years is analyzed and predicted. The results show that the seawater intrusion can be effectively prevented by installing freshwater curtain recharge wells in the northern coast of Luyangpu.

scholarly journals Preliminary Study, Risk Analysis and HACCP in Cold Chain System, Frozen Yellow Fin Tuna in Moluccas

2015 ◽  
Vol 3 (2) ◽  
pp. 248
Author(s):  
Grasiano Warakano Lailossa
Keyword(s):  
Risk Analysis ◽  
Field Observation ◽  
Hazard Analysis ◽  
Cold Chain ◽  
Chain System ◽  
System Risk ◽  
Paper Review ◽  
Preliminary Study ◽  
The One ◽  
And Control

The differences In cold chain system, Risk analysis and Hazard Analysis and Critical Crisis Point(HACCP) is a procedure for the identification, assessment and control of hazards in, and indirectly risks from, food. HACCP procedures focus on chemical, physical and microbiological hazards, Yellow Fin Tuna is the one of the most superior export fishery product of Moluccas, based on paper review and field observation in Molucass, this paper is a preliminary study to development HACCP framework of frozen Yellow Fin Tuna in Moluccas.

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