scholarly journals Spatial bifurcations of fixed points and limit cycles during the electrochemical oxidation of H2 on Pt ring-electrodes

2001 ◽  
Vol 120 ◽  
pp. 165-178 ◽  
Author(s):  
Peter Grauel ◽  
Hamilton Varela ◽  
Katharina Krischer
Keyword(s):  
Fixed Points ◽  
Electrochemical Oxidation ◽  
Limit Cycles ◽  
Oxidation Of H2

Electrochemical oxidation of H2 catalyzed by ruthenium hydride complexes bearing P2N2 ligands with pendant amines as proton relays

2014 ◽  
Vol 7 (11) ◽  
pp. 3630-3639 ◽  
Author(s):  
Tianbiao Liu ◽  
Mary Rakowski DuBois ◽  
Daniel L. DuBois ◽  
R. Morris Bullock
Keyword(s):  
Electrochemical Oxidation ◽  
Chemical Bond ◽  
Bond Energy ◽  
Diphosphine Ligands ◽  
Ruthenium Hydride ◽  
Hydride Complexes ◽  
New Class ◽  
Oxidation Of H2

A new class of Ru electrocatalysts containing P2N2 diphosphine ligands with pendant amines converts the chemical bond energy of H2 to electricity.

scholarly journals Tiling Efflorescence of Expanding Kernels in a Fixed Periodic Array

2021 ◽  
Vol 3 (1) ◽  
pp. 13-34
Author(s):  
Robert J Marks II
Keyword(s):  
Fourier Analysis ◽  
Fixed Points ◽  
Limit Cycles ◽  
Circular Cone ◽  
Two Dimensional ◽  
Periodic Functions ◽  
Fundamental Properties ◽  
Art And Architecture ◽  
The Trinity ◽  
Func Tion

Continually expanding periodically translated kernels on the two dimensional grid can yield interesting, beau- tiful and even familiar patterns. For example, expand- ing circular pillbox shaped kernels on a hexagonal grid, adding when there is overlap, yields patterns includ- ing maximally packed circles and a triquetra-type three petal structure used to represent the trinity in Chris- tianity. Continued expansion yields the flower-of-life used extensively in art and architecture. Additional expansion yields an even more interesting emerging ef- florescence of periodic functions. Example images are given for the case of circular pillbox and circular cone shaped kernels. Using Fourier analysis, fundamental properties of these patterns are analyzed. As a func- tion of expansion, some effloresced functions asymp- totically approach fixed points or limit cycles. Most interesting is the case where the efflorescence never repeats. Video links are provided for viewing efflores- cence in real time.

LIMIT CYCLES OF A DOUBLE OSCILLATOR EXCITED BY DRY FRICTION

2011 ◽  
Vol 21 (10) ◽  
pp. 3043-3046 ◽  
Author(s):  
SERGEY STEPANOV
Keyword(s):  
Fixed Points ◽  
Numerical Method ◽  
Limit Cycles ◽  
Dry Friction ◽  
Coulomb Friction ◽  
Three Dimensional ◽  
Slip Mode ◽  
Two Dimensional ◽  
Parametric Investigation ◽  
Friction Laws

A two-mass oscillator with one mass lying on the driving belt with dry Coulomb friction is considered. A numerical method for finding all limit cycles and their parametric investigation, based on the analysis of fixed points of a two-dimensional map, is suggested. As successive points for the map we chose points of friction transferred from stick mode to slip mode. These transfers are defined by two equalities and yield a two-dimensional map, in contrast to three-dimensional maps that we can construct for regularized continuous dry friction laws.

Exploiting the controlled responses of chaotic elements to design configurable hardware

2006 ◽  
Vol 364 (1846) ◽  
pp. 2483-2494 ◽  
Author(s):  
Sudeshna Sinha ◽  
William L Ditto
Keyword(s):  
Fixed Points ◽  
Chaotic System ◽  
Limit Cycles ◽  
Chaotic Systems ◽  
Dynamic Logic ◽  
Logic Gates ◽  
Threshold Level ◽  
Experimental Realization ◽  
Configurable Hardware ◽  
Simple Manipulation

We discuss how threshold mechanisms can be effectively employed to control chaotic systems onto stable fixed points and limit cycles of widely varying periodicities. Then, we outline the theory and experimental realization of fundamental logic-gates from a chaotic system, using thresholding to effect control. A key feature of this implementation is that a single chaotic ‘processor’ can be flexibly configured (and re-configured) to emulate different fixed or dynamic logic gates through the simple manipulation of a threshold level.

CHAOTIC BEHAVIOR AND DYNAMICS OF MAPS USED IN A METHOD OF SCRAMBLING SIGNALS

2010 ◽  
Vol 20 (12) ◽  
pp. 4097-4101
Author(s):  
REZA MAZROOEI-SEBDANI ◽  
MEHDI DEHGHAN
Keyword(s):  
Fixed Points ◽  
Limit Cycles ◽  
Secure Communication ◽  
Chaotic Behavior ◽  
Initial Conditions ◽  
Chaotic Encryption ◽  
Input And Output ◽  
Sensitive Dependence ◽  
Close Relationship ◽  
Existence And Stability

The close relationship between chaos and cryptography makes chaotic encryption a natural candidate for secure communication and cryptography. In this manuscript, we prove that a class of maps that have been proposed as suitable for scrambling signals possess the property of sensitive dependence on initial conditions (s.d.i.c.) necessary for chaos and cryptography. Our result can also be used for generating other maps with s.d.i.c., through a suitable semiconjugacy between their input and output parts. Using the condition of semiconjugacy we also establish for this class of maps rigorous criteria for the existence and stability of their fixed points and limit cycles.

scholarly journals Power Laws, Scale Invariance and the Generalized Frobenius Series: Applications to Newtonian and TOV Stars Near Criticality

2003 ◽  
Vol 18 (20) ◽  
pp. 3433-3468 ◽  
Author(s):  
Matt Visser ◽  
Nicolas Yunes
Keyword(s):  
Fixed Point ◽  
Power Series ◽  
Fixed Points ◽  
Limit Cycles ◽  
Power Laws ◽  
Series Solutions ◽  
Scale Invariant ◽  
Core Mass ◽  
Relativistic Case ◽  
Power Series Solutions

We present a self-contained formalism for calculating the background solution, the linearized solutions and a class of generalized Frobenius-like solutions to a system of scale-invariant differential equations. We first cast the scale-invariant model into its equidimensional and autonomous forms, find its fixed points, and then obtain power-law background solutions. After linearizing about these fixed points, we find a second linearized solution, which provides a distinct collection of power laws characterizing the deviations from the fixed point. We prove that generically there will be a region surrounding the fixed point in which the complete general solution can be represented as a generalized Frobenius-like power series with exponents that are integer multiples of the exponents arising in the linearized problem. While discussions of the linearized system are common, and one can often find a discussion of power-series with integer exponents, power series with irrational (indeed complex) exponents are much rarer in the extant literature. The Frobenius-like series we encounter can be viewed as a variant of the rarely-discussed Liapunov expansion theorem (not to be confused with the more commonly encountered Liapunov functions and Liapunov exponents). As specific examples we apply these ideas to Newtonian and relativistic isothermal stars and construct two separate power series with the overlapping radius of convergence. The second of these power series solutions represents an expansion around "spatial infinity," and in realistic models it is this second power series that gives information about the stellar core, and the damped oscillations in core mass and core radius as the central pressure goes to infinity. The power-series solutions we obtain extend classical results; as exemplified for instance by the work of Lane, Emden, and Chandrasekhar in the Newtonian case, and that of Harrison, Thorne, Wakano, and Wheeler in the relativistic case. We also indicate how to extend these ideas to situations where fixed points may not exist — either due to "monotone" flow or due to the presence of limit cycles. Monotone flow generically leads to logarithmic deviations from scaling, while limit cycles generally lead to discrete self-similar solutions.

scholarly journals Integration of Freeplay-Induced Limit Cycles Based On a State Space Iterating Scheme

2021 ◽  
Vol 11 (2) ◽  
pp. 741
Author(s):  
Xiangyu Wang ◽  
Zhigang Wu ◽  
Chao Yang
Keyword(s):  
Fixed Points ◽  
State Space ◽  
Limit Cycle ◽  
Limit Cycles ◽  
Initial Conditions ◽  
Time Integration ◽  
Integration Time ◽  
Aeroelastic System ◽  
System States ◽  
Short Integration Time

Time integration is commonly used to obtain accurate system responses, such as the limit cycle oscillations (LCOs) for an aeroelastic system with freeplay. However, the integrations that start with various initial conditions (I.C.s) are usually studied case by case, so only a few system states can possibly be focused on. This paper proposes a state space iterating (SSI) scheme to find LCO solutions using time integration by using another method. First, a large number of arbitrary I.C. cases are used for time integrations, but only a very short integration time is required for each I.C. case. Second, system behaviors are depicted visually through a method that combines a modified Poincaré map and Lorenz map, in which the LCO solutions are found as fixed points via visual inspections. To verify the SSI scheme’s ability to find LCOs, a typical plunge–pitch wing section is established numerically. Time integrations with both the classic scheme and the proposed SSI scheme are carried out. The LCO results of the SSI scheme are well-aligned with those from the classic scheme. The SSI scheme visualizes the patterns of system responses using arbitrary I.C. cases and analyzes the LCO stability, which provides more mathematical insights into an aeroelastic system with freeplay.

scholarly journals Quantum signatures of transitions from stable fixed points to limit cycles in optomechanical systems

2020 ◽  
Vol 101 (2) ◽  
Author(s):  
Qing Xia Meng ◽  
Zhi Jiao Deng ◽  
Zhigang Zhu ◽  
Liang Huang
Keyword(s):  
Fixed Points ◽  
Limit Cycles ◽  
Optomechanical Systems
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