scholarly journals Shadowing Homoclinic Chains to a Symplectic Critical Manifold

2021 ◽  
Vol 37 (1) ◽  
pp. 1-23
Author(s):  
global sci
Keyword(s):  
Critical Manifold

Multiple-S-Shaped Critical Manifold and Jump Phenomena in Low Frequency Forced Vibration with Amplitude Modulation

2019 ◽  
Vol 29 (05) ◽  
pp. 1930012 ◽  
Author(s):  
Yue Yu ◽  
Qianqian Wang ◽  
Qinsheng Bi ◽  
C. W. Lim
Keyword(s):  
Amplitude Modulation ◽  
Large Amplitude ◽  
Low Frequency ◽  
Slow Variable ◽  
Critical Manifold ◽  
Singular Orbit ◽  
Modulation Control ◽  
Cycle Oscillation ◽  
Tuning Frequency ◽  
Complex Mechanical Systems

Motivated by the forced harmonic vibration of complex mechanical systems, we analyze the dynamics involving different waves in a double-well potential oscillator coupling amplitude modulation control of low frequency. The combination of amplitude modulation factor significantly enriches the dynamical behaviors on the formation of multiple-S-shaped manifold and multiple jumping phenomena that alternate between epochs of slow and fast motion. We can conduct bifurcation analysis to identify two harmonic vibrations. One is that the singular orbit makes multiple jumps to a fast trajectory segment from one attracting equilibrium to another as the expression of slow variable by using the DeMoivre formula. With the increase of tuning frequency, the system exhibits relaxation-type oscillations whose small amplitude oscillations are produced by nonlinear local cycles together with a distinct large amplitude cycle oscillation accounting for the Melnikov threshold values. The tuning frequency may not only affect the asymptotic expressions for the solution curves near fold singularities but also allow for the large amplitude orbit vibrations near fold-cycle singularities. Numerical analysis for computing critical manifolds and their intersections is used to detect the dynamical features in this paper.

scholarly journals Finite-size transitions in complex membranes

2020 ◽  
Author(s):  
M. Girard ◽  
T. Bereau
Keyword(s):  
Experimental Evidence ◽  
Critical Point ◽  
Finite Size ◽  
Underlying Mechanism ◽  
Large Temperature ◽  
Strong Argument ◽  
Biological Regulation ◽  
Critical Manifold ◽  
Critical Composition ◽  
Dynamics Simulations

ABSTRACTThe lipid raft hypothesis postulates that cell membranes possess some degree of lateral organization. The last decade has seen a large amount of experimental evidence for rafts. Yet, the underlying mechanism remains elusive. One hypothesis that supports rafts relies on the membrane to lie near a critical point. While supported by experimental evidence, the role of regulation is unclear. Using both a lattice model and molecular dynamics simulations, we show that lipid regulation of a many-component membrane can lead to critical behavior over a large temperature range. Across this range, the membrane displays a critical composition due to finite-size effects. This mechanism provides a rationale as to how cells tune their composition without the need for specific sensing mechanisms. It is robust and reproduces important experimentally verified biological trends: membrane-demixing temperature closely follows cell growth temperature, and the composition evolves along a critical manifold. The simplicity of the mechanism provides a strong argument in favor of the critical membrane hypothesis.SIGNIFICANCEWe show that biological regulation of a large amount of phospholipids in membranes naturally leads to a critical composition for finite-size systems. This suggests that regulating a system near a critical point is trivial for cells. These effects vanish logarithmically and therefore can be present in micron-sized systems.

scholarly journals Adaptive Estimation of Biological Rhythm in Crassulacean Acid Metabolism with Critical Manifold

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Takami Matsuo ◽  
Yusuke Totoki ◽  
Haruo Suemitsu
Keyword(s):  
Continuous Time ◽  
Crassulacean Acid Metabolism ◽  
Acid Metabolism ◽  
Adaptive Estimation ◽  
Nonlinear Function ◽  
Slow Manifold ◽  
Adaptive Observer ◽  
Critical Manifold ◽  
Wide Range ◽  
Time Differential

The mechanism of endogenous circadian photosynthesis oscillations of plants performing crassulacean acid metabolism (CAM) is investigated in terms of a nonlinear theoretical model. Blasius et al. used throughout continuous time differential equations which adequately reflect the CAM dynamics. The model shows regular endogenous limit cycle oscillations that are stable for a wide range of temperatures in a manner that complies well with experimental data. In this paper, we pay attention to the approximation of the fast modes of the CAM dynamics. Using the zero-epsilon approximation of the slow manifold, we derive the critical manifold that is defined by two algebraic nonlinear equations. The critical manifold allows us to give the algebraic estimate of the order of the tonoplast membrane. The dynamic equation of the order of the tonoplast membrane includes the nonlinear function that gives the equilibrium value of the lipid order of tonoplast functions as a hysteresis switch. We identify the nonlinear function with the measurement signals. Using the basis function expansion of the nonlinear and the critical manifold, we propose an adaptive observer to estimate the tonoplast order and the nonlinear function.

Critical Manifolds in Polycrystalline Grain Structures

2004 ◽  
Vol 467-470 ◽  
pp. 1039-1044 ◽  
Author(s):  
Elizabeth A. Holm ◽  
J.H. Meinke ◽  
E.S. McGarrity ◽  
P.M. Duxbury
Keyword(s):  
Grain Boundaries ◽  
Optimization Algorithm ◽  
Network Optimization ◽  
Three Dimensional ◽  
Critical Length ◽  
Short Length ◽  
Length Scale ◽  
Length Scales ◽  
Critical Manifold ◽  
Grain Structures

With the development of new, fully three-dimensional metallographic techniques, there is considerable interest in characterizing three-dimensional microstructures in ways that go beyond twodimensional stereology. One characteristic of grain structures is the surface of lowest energy across the microstructure, termed the critical manifold (CM). When the grain boundaries are sufficiently weak, the CM lies entirely on grain boundaries, while when the grain boundaries are strong, cleavage occurs. A scaling theory for the cleavage to intergranular transition of CMs is developed. We find that a critical length scale exists, so that on short length scales cleavage is observed, while at long length scales the CM is rough. CMs for realistic polycrystalline grain structures, determined by a network optimization algorithm, are used to verify the analysis.

scholarly journals Mathematical Simulation of Using a Combination of Mesh and Porous Materials as a Phase Separator

2019 ◽  
pp. 4-16 ◽  
Author(s):  
N.I. Avraamov ◽  
A.V. Korolkov ◽  
V.A. Maslov ◽  
V.B. Sapozhnikov
Keyword(s):  
Fluid Flow ◽  
Porous Materials ◽  
Mathematical Simulation ◽  
Critical Pressure ◽  
Critical Manifold ◽  
Capillary Inlet ◽  
Propellant Tank ◽  
Phase Separator

A combination of mesh and porous materials featuring bulk capillary properties is used as a phase separator in in-tank capillary inlet devices. These bulk capillary properties ensure a non-zero fluid flow into the interior of the in-tank inlet device after critical pressure has been reached. This quality makes it possible to reduce residual propellant volume in spacecraft engine tanks. We developed a mathematical simulation of an in-tank capillary inlet device comprising a phase separator made of a combination of mesh and porous materials. We represented a combination of mesh and porous materials as an array of "closely packed" transverse and longitudinal capillaries. Our mathematical simulation describes the operation of an in-tank inlet device after the critical manifold pressure has been reached. The fluid enters the interior of the in-tank inlet device one portion at a time. We determined the volume and arrival frequency of these portions and estimated the residual propellant volume in the propellant tank.

Change of the Most Probable Escape Path in a Fast-Slow Insect Outbreak System Under Different Noise Amplitude Ratios

2021 ◽  
Author(s):  
Qing Yu ◽  
Xianbin Liu
Keyword(s):  
Structural Changes ◽  
Domain Of Attraction ◽  
Relaxation Method ◽  
Noise Amplitude ◽  
Amplitude Ratios ◽  
Insect Outbreak ◽  
Full System ◽  
Critical Manifold ◽  
Escape Path ◽  
Complete Investigation

Abstract In the present paper, noise-induced escape from the domain of attraction of a stable fixed point of a fast-slow insect outbreak system is investigated. According to Dannenberg's theory(Dannenberg PH, Neu JC, 2014)[1], different noise amplitude ratios μ lead to the change of the Most Probable Escape Path(MPEP). Therefore, the research emphasis of this paper is to extend their study and discuss the changes of the MPEPs in more detail. Firstly, the case for μ=1, wherein the MPEP almost traces out the critical manifold, is considered. Via projecting the full system onto the critical manifold, a reduced system is obtained and the quasi-potential of the full system can be partly evaluated by that of this reduced system. In order to test the accuracy of the computed MPEP, a new relaxation method is then presented. Then, as μ converges to zero, an improved analytical method is given, through which a better approximation for the MPEP at the turning point is obtained. And then, in the case that the value of μ is moderate, wherein the MPEP will peel off the critical manifold, to determine the changing point of the MPEP on the critical manifold, an effective numerical algorithm is given. In brief, in this paper, a complete investigation on the structural changes of the MPEPs of a fast-slow insect outbreak system under different values of μ is given, and the results of the numerical simulations match well with the analytical ones.

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