scholarly journals Bright Solitons in aPT-Symmetric Chain of Dimers

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Omar B. Kirikchi ◽  
Alhaji A. Bachtiar ◽  
Hadi Susanto
Keyword(s):  
Bright Solitons ◽  
Small Coupling ◽  
Complex Eigenvalues ◽  
Discrete Nonlinear Schrödinger Equations ◽  
Existence And Stability ◽  
A Chain ◽  
The Stability ◽  
Loss Term ◽  
Gain Loss ◽  
Antisymmetric Solutions

We study the existence and stability of fundamental bright discrete solitons in a parity-time- (PT-) symmetric coupler composed by a chain of dimers that is modelled by linearly coupled discrete nonlinear Schrödinger equations with gain and loss terms. We use a perturbation theory for small coupling between the lattices to perform the analysis, which is then confirmed by numerical calculations. Such analysis is based on the concept of the so-called anticontinuum limit approach. We consider the fundamental onsite and intersite bright solitons. Each solution has symmetric and antisymmetric configurations between the arms. The stability of the solutions is then determined by solving the corresponding eigenvalue problem. We obtain that both symmetric and antisymmetric onsite mode can be stable for small coupling, in contrast to the reported continuum limit where the antisymmetric solutions are always unstable. The instability is either due to the internal modes crossing the origin or the appearance of a quartet of complex eigenvalues. In general, the gain-loss term can be considered parasitic as it reduces the stability region of the onsite solitons. Additionally, we analyse the dynamic behaviour of the onsite and intersite solitons when unstable, where typically it is either in the form of travelling solitons or soliton blow-ups.

scholarly journals On the stability of Einstein universe in f(R, T, Rμν Tμν) gravity

2018 ◽  
Vol 33 (36) ◽  
pp. 1850216 ◽  
Author(s):  
M. Sharif ◽  
Arfa Waseem
Keyword(s):  
State Parameter ◽  
Big Bang ◽  
Graphical Analysis ◽  
Momentum Tensor ◽  
Field Equations ◽  
Einstein Universe ◽  
Existence And Stability ◽  
The Stability ◽  
The Big Bang ◽  
Big Bang Singularity

This paper investigates the existence and stability of Einstein universe in the context of f(R, T, Q) gravity, where Q = R[Formula: see text] T[Formula: see text]. Considering linear homogeneous perturbations around scale factor and energy density, we formulate static as well as perturbed field equations. We parametrize the stability regions corresponding to conserved as well as non-conserved energy–momentum tensor using linear equation of state parameter for particular models of this gravity. The graphical analysis concludes that for a suitable choice of parameters, stable regions of the Einstein universe are obtained which indicates that the big bang singularity can be avoided successfully by the emergent mechanism in non-minimal matter-curvature coupled gravity.

scholarly journals Study of Mechanical Behavior and Microstructure for Low-Hardness P92 Steel

2021 ◽  
Vol 2101 (1) ◽  
pp. 012074
Author(s):  
Weixin Yu ◽  
Zhen Dai ◽  
Jifeng Zhao ◽  
Lulu Fang ◽  
Yiwen Zhang
Keyword(s):  
Mechanical Properties ◽  
Grain Size ◽  
Tensile Strength ◽  
Maximum Size ◽  
Rapid Decrease ◽  
Laves Phases ◽  
P92 Steel ◽  
A Chain ◽  
The Stability ◽  
Evolution Of Microstructure

Abstract The strength of P92 steel (tensile strength, specified plastic elongation strength) will decrease after its hardness is reduced, ferrite and carbides forming the structure. Carbides of grain size 5-6 are precipitated in the grains and grain boundaries. The martensite lath shape has completely disappeared. M23C6 carbide coarsened obviously, with a maximum size of about 500nm; The Laves phase is also aggregated and coarsened, connecting in a chain shape with a maximum size of more than 500nm. Evolution of microstructure, namely the obvious coarsening of M23C6 carbides and the aggregation and connection of Laves phases in a chain shape, are the main causes for rapid decrease in the stability of the material substructure and evident decline in mechanical properties and hardness. In addition, the MX phase did not change significantly, hardly affecting the hardness reduction of P92 steel.

scholarly journals Non-Hermitian physics for optical manipulation uncovers inherent instability of large clusters

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Xiao Li ◽  
Yineng Liu ◽  
Zhifang Lin ◽  
Jack Ng ◽  
C. T. Chan
Keyword(s):  
Large Scale ◽  
Critical Role ◽  
Optical Forces ◽  
Exceptional Points ◽  
Complex Eigenvalues ◽  
Microscopic World ◽  
The Stability ◽  
The Many ◽  
Large Clusters ◽  
Conventional Systems

AbstractIntense light traps and binds small particles, offering unique control to the microscopic world. With incoming illumination and radiative losses, optical forces are inherently nonconservative, thus non-Hermitian. Contrary to conventional systems, the operator governing time evolution is real and asymmetric (i.e., non-Hermitian), which inevitably yield complex eigenvalues when driven beyond the exceptional points, where light pumps in energy that eventually “melts” the light-bound structures. Surprisingly, unstable complex eigenvalues are prevalent for clusters with ~10 or more particles, and in the many-particle limit, their presence is inevitable. As such, optical forces alone fail to bind a large cluster. Our conclusion does not contradict with the observation of large optically-bound cluster in a fluid, where the ambient damping can take away the excess energy and restore the stability. The non-Hermitian theory overturns the understanding of optical trapping and binding, and unveils the critical role played by non-Hermiticity and exceptional points, paving the way for large-scale manipulation.

Dynamics of Two Van Der Pol Oscillators Coupled via a Bath

2003 ◽  
Author(s):  
Erika Camacho ◽  
Richard Rand ◽  
Howard Howland
Keyword(s):  
Software Package ◽  
Bifurcation Theory ◽  
Floquet Theory ◽  
Van Der Pol Oscillator ◽  
Direct Connection ◽  
Periodic Motions ◽  
Van Der Pol ◽  
Existence And Stability ◽  
Van Der Pol Oscillators ◽  
The Stability

In this work we study a system of two van der Pol oscillators, x and y, coupled via a “bath” z: x¨−ε(1−x2)x˙+x=k(z−x)y¨−ε(1−y2)y˙+y=k(z−y)z˙=k(x−z)+k(y−z) We investigate the existence and stability of the in-phase and out-of-phase modes for parameters ε > 0 and k > 0. To this end we use Floquet theory and numerical integration. Surprisingly, our results show that the out-of-phase mode exists and is stable for a wider range of parameters than is the in-phase mode. This behavior is compared to that of two directly coupled van der Pol oscillators, and it is shown that the effect of the bath is to reduce the stability of the in-phase mode. We also investigate the occurrence of other periodic motions by using bifurcation theory and the AUTO bifurcation and continuation software package. Our motivation for studying this system comes from the presence of circadian rhythms in the chemistry of the eyes. We present a simplified model of a circadian oscillator which shows that it can be modeled as a van der Pol oscillator. Although there is no direct connection between the two eyes, they can influence each other by affecting the concentration of melatonin in the bloodstream, which is represented by the bath in our model.

scholarly journals Probing the stability and magnetic properties of magnetosome chains in freeze-dried magnetotactic bacteria

2020 ◽  
Vol 2 (3) ◽  
pp. 1115-1121
Author(s):  
Philipp Bender ◽  
Lourdes Marcano ◽  
Iñaki Orue ◽  
Diego Alba Venero ◽  
Dirk Honecker ◽  
...  
Keyword(s):  
Magnetic Properties ◽  
Magnetite Nanoparticles ◽  
Magnetotactic Bacteria ◽  
Magnetic Compass ◽  
High Quality ◽  
Magnetospirillum Gryphiswaldense ◽  
Freeze Dried ◽  
A Chain ◽  
The Stability

Magnetospirillum gryphiswaldense biosynthesize high quality magnetite nanoparticles, called magnetosomes, and arrange them into a chain that behaves like a magnetic compass.

Stability of Subharmonic Oscillations in a Pipe Conveying Fluid under Harmonic Excitation

2013 ◽  
Vol 444-445 ◽  
pp. 796-800
Author(s):  
Yi Xiang Geng ◽  
Han Ze Liu
Keyword(s):  
Averaging Method ◽  
Melnikov Method ◽  
Equation Of Motion ◽  
Harmonic Excitation ◽  
Angle Variable ◽  
Galerkin Approach ◽  
Existence And Stability ◽  
The Stability ◽  
Action Angle Variable ◽  
Conveying Fluid

The existence and stability of subharmonic oscillations in a two end-fixed fluid conveying pipe whose base is subjected to a harmonic excitation are investigated. A Galerkin approach is utilized to reduce the equation of motion to a second order nonlinear differential equation. The conditions for the existence of subharmonic oscillations are given by using Melnikov method. The stability of subharmonic oscillations is discussed in detail by using action-angle variable and averaging method. It is shown that the velocity of fluid plays an important role in the stability of subharmonic oscillations.

scholarly journals Squeal Frequency of a Railway Disc Brake Evaluation by FE Analyses

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
F. Cascetta ◽  
F. Caputo ◽  
A. De Luca
Keyword(s):  
Sensitivity Analysis ◽  
Finite Element ◽  
Experimental Tests ◽  
Numerical Approach ◽  
System Stability ◽  
Brake System ◽  
Physical Parameters ◽  
Disc Brake ◽  
Complex Eigenvalues ◽  
The Stability

This paper deals with the development of a numerical model, based on the Finite Element (FE) theory for the prediction of the squeal frequency of a railway disc brake. The analytical background has been discussed and presented, as well as the most efficient methods for evaluating the system stability; the attention has been paid particularly to the complex eigenvalues method, which has been adopted within this paper to investigate the railway disc brake system. Numerical results have been compared with measurements from experimental tests in order to validate the proposed numerical approach. At the end of this work, a sensitivity analysis, aimed at understanding the effects of some physical parameters influencing the stability of the brake system and the squeal propensity, has been carried out.

THE EFFECT OF TIME DELAY ON SPATIOTEMPORAL DYNAMICS IN ONE-DIMENSIONAL DISCRETE EXCITABLE MEDIA

2001 ◽  
Vol 15 (02) ◽  
pp. 167-176
Author(s):  
TAE-HOON CHUNG ◽  
SEUNGWHAN KIM
Keyword(s):  
Time Delay ◽  
Spatiotemporal Dynamics ◽  
Excitable Media ◽  
Winding Number ◽  
One Dimensional ◽  
Circle Maps ◽  
Pattern Complexity ◽  
Existence And Stability ◽  
Spatiotemporal Intermittency ◽  
The Stability

We investigate the effect of time delay on spatiotemporal dynamics in one-dimensional discrete excitable media with local delayed-interactions using coupled sine circle-maps. With the help of the stability analysis and numerical calculation of the pattern complexity entropy, we construct the phase diagram in the parameter space time delay and the nonlinear coupling. We find that the time delay affects the existence and stability of various regular states including homogeneously phase-locked and checkerboard states. In particular, the time delay induces the breakup of the homogeneously phase-locked state into spatiotemporal intermittency and the occurrence of multi-stability that depends on the winding number.

scholarly journals Synchronization of Two Non-Identical Coupled Exciters in a Non-Resonant Vibrating System of Linear Motion. Part I: Theoretical Analysis

2009 ◽  
Vol 16 (5) ◽  
pp. 505-515 ◽  
Author(s):  
Chunyu Zhao ◽  
Hongtao Zhu ◽  
Ruizi Wang ◽  
Bangchun Wen
Keyword(s):  
Zero Solution ◽  
Moment Of Inertia ◽  
Moments Of Inertia ◽  
Vibrating System ◽  
Frequency Capture ◽  
Synchronization Problem ◽  
Small Parameters ◽  
Existence And Stability ◽  
Synchronous Operation ◽  
The Stability

In this paper an analytical approach is proposed to study the feature of frequency capture of two non-identical coupled exciters in a non-resonant vibrating system. The electromagnetic torque of an induction motor in the quasi-steady-state operation is derived. With the introduction of two perturbation small parameters to average angular velocity of two exciters and their phase difference, we deduce the Equation of Frequency Capture by averaging two motion equations of two exciters over their average period. It converts the synchronization problem of two exciters into that of existence and stability of zero solution for the Equation of Frequency Capture. The conditions of implementing frequency capture and that of stabilizing synchronous operation of two motors have been derived. The concept of torque of frequency capture is proposed to physically explain the peculiarity of self-synchronization of the two exciters. An interesting conclusion is reached that the moments of inertia of the two exciters in the Equation of Frequency Capture reduce and there is a coupling moment of inertia between the two exciters. The reduction of moments of inertia and the coupling moment of inertia have an effect on the stability of synchronous operation.

Sign in / Sign up

Export Citation Format

Share Document