Average lifetime and geometric properties for superlong chaotic transients in a hybrid optical bistable system

We study unusual chaotic transients towards the zero fixed point in the DAOD-map derived from differential equations of the delayed aperiodic oscillator [Rozhdestvensky et al., 1992; Struchkov, 1993], which is one of the simplest models of the radiophysical autogenerator with chaotic transients [Rozhdestvensky et al., 1992]. Unusual character of the observed chaotic transients manifests itself in near-linear increase of the Ln[τ(p)]-curve for its average lifetime τ(p) as a function of system’s parameter p. Parameter p is corresponding to the amplifying coefficient of the radio-physical autogenerator [Rozhdestvensky et al., 1992]. This curve includes lacunas when p belongs to the periodic windows (when p∈∆n). In small enough neighborhood of ∆nLn[τ(p)]-curve behaves itself like as in boundary crisis due to intermittency. Permanent presence of the transient chaos in the DAOD-map (even when p∈∆n) is caused by the existence in phase space of the Monotonous Descent Channel (MDCh), which is coming in a zero fixed point from infinity.

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Super persistent chaotic transients

Ergodic Theory and Dynamical Systems ◽

10.1017/s014338570000300x ◽

1985 ◽

Vol 5 (3) ◽

pp. 341-372 ◽

Cited By ~ 75

Author(s):

Celso Grebogi ◽

Edward Ott ◽

James A. Yorke

Keyword(s):

Bifurcation Point ◽

Average Length ◽

Asymptotic State ◽

Average Lifetime ◽

Bounded Noise ◽

Small Random Perturbations ◽

Image Position ◽

Chaotic Transients ◽

Parameter Values ◽

Chaotic Transient

AbstractThe unstable-unstable pair bifurcation is a bifurcation in which two unstable fixed points or periodic orbits of the same period coalesce and disappear as a system paremeter is raised. For parameter values just above that at which unstable orbits are destroyed there can be chaotic transients. Then, as the bifurcation is approached from above, the average length of a chaotic transient diverges, and, below the bifurcation point, the chaotic transient may be regarded as having been converted into a chaotic attractor. It is argued that unstable-unstable pair bifurcations should be expected to occur commonly in dynamical systems. This bifurcation is an example of the crisis route to chaos. The most striking fact about unstable-unstable pair bifurcation crises is that long chaotic transients persist even for parameter values relatively far from the bifurcation point. These long-lived chaotic transients may prevent the time asymptotic state from being reached during experiments. An expression giving a lower bound for the average lifetime of a chaotic transient is derived and shown to agree well with numerical experiments. In particular, this bound on the average lifetime, (τ), satisfiesfor α near α*, where k1 and k2 are constants and α* is the value of the parameter a at which the crisis occurs. Thus, as a approaches α* from above, (τ) increases more rapidly than any power of (α − α*)−1. Finally, we discuss the effect of adding bounded noise (small random perturbations) on these phenomena and argue that the chaotic transients should be lengthened by noise.

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DYNAMICAL STUDIES OF A HYBRID OPTICAL BISTABLE SYSTEM

Le Journal de Physique Colloques ◽

10.1051/jphyscol:19882100 ◽

1988 ◽

Vol 49 (C2) ◽

pp. C2-419-C2-422

Author(s):

B. J. HAWDON ◽

J. O'GORMAN ◽

D. M. HEFFERNAN

Keyword(s):

Bistable System

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Faculty Opinions recommendation of Age- and gender-related differences in the geometric properties and biomechanical significance of intracortical porosity in the distal radius and tibia.

Faculty Opinions – Post-Publication Peer Review of the Biomedical Literature ◽

10.3410/f.6737956.6902054 ◽

2010 ◽

Author(s):

Felix Wehrli ◽

Yusuf Bhagat

Keyword(s):

Distal Radius ◽

Age And Gender ◽

Geometric Properties ◽

And Gender

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Computation of Geometric Properties from the Medial Axis Transform in 0 (n logn) Time.

10.21236/ada158934 ◽

1985 ◽

Author(s):

A. Y. Wu ◽

S. K. Bhaskar ◽

A. Rosenfeld

Keyword(s):

Medial Axis ◽

Medial Axis Transform ◽

Geometric Properties

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Statistical approach for describing failures and lifetimes of water mains

Water Science & Technology ◽

10.2166/wst.1998.0254 ◽

1998 ◽

Vol 38 (6) ◽

pp. 209-217 ◽

Cited By ~ 5

Author(s):

Jianhua Lei ◽

Sveinung Sægrov

Keyword(s):

Data Base ◽

Ductile Iron ◽

Counting Process ◽

Statistical Approach ◽

Process Models ◽

Average Lifetime ◽

Maintenance Practice ◽

Water Mains ◽

Near Future

This paper demonstrates the statistical approach for describing failures and lifetimes of water mains. The statistical approach is based on pipe inventory data and the maintenance data registered in the data base. The approach consists of data pre-processing and statistical analysis. Two classes of statistical models are applied, namely counting process models and lifetime models. With lifetime models, one can estimate the probability which a pipe will fail within a time horizon. With counting process models one can see the deteriorating (or improving) trend in time of a group of “identical” pipes and their rates of occurrence of failure (ROCOF). The case study with the data base from Trondheim municipality (Norway) demonstrates the applicability of the statistical approach and leads to the following results: 1). In the past 20 years, Trondheim municipality has experienced approximately 250 to 300 failures per year. However, the number of failures per year will significantly increase in the near future unless better maintenance practice is implemented now. 2). Unprotected ductile iron pipes have a higher probability of failures than other materials. The average lifetime of unprotected ductile iron pipes is approximately 30 to 40 years shorter than the lifetime of a cast iron pipe. 3). Pipes installed 1963 and 1975 are most likely to fail in the future; 4) The age of a pipe does not play a significant role for the remaining lifetime of the pipe; 5). After 2 to 3 failures, a pipe enters a fast-failure stage (i.e., frequent multiple between failures).

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Some Properties of Para-Sasakian Manifolds

Science & Technology Journal ◽

10.22232/stj.2017.05.02.01 ◽

2017 ◽

Vol 5 (2) ◽

pp. 73-78

Author(s):

Jay Prakash Singh ◽

Keyword(s):

Vector Field ◽

Killing Vector ◽

Sasakian Manifold ◽

Subject Classification ◽

Killing Vector Field ◽

Sasakian Manifolds ◽

Geometric Properties ◽

Paper Author

In this paper author present an investigation of some differential geometric properties of Para-Sasakian manifolds. Condition for a vector field to be Killing vector field in Para-Sasakian manifold is obtained. Mathematics Subject Classification (2010). 53B20, 53C15.

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Effect of 12 months of creatine supplementation and whole-body resistance training on measures of bone, muscle and strength in older males

Nutrition and Health ◽

10.1177/0260106020975247 ◽

2020 ◽

pp. 026010602097524

Author(s):

Darren G Candow ◽

Philip D Chilibeck ◽

Julianne Gordon ◽

Emelie Vogt ◽

Tim Landeryou ◽

...

Keyword(s):

Bone Mineral Density ◽

Resistance Training ◽

Bone Mineral ◽

Creatine Supplementation ◽

Whole Body ◽

Mineral Density ◽

Geometric Properties ◽

Section Modulus ◽

Body Resistance ◽

Older Males

Background: The combination of creatine supplementation and resistance training (10–12 weeks) has been shown to increase bone mineral content and reduce a urinary indicator of bone resorption in older males compared with placebo. However, the longer-term effects (12 months) of creatine and resistance training on bone mineral density and bone geometric properties in older males is unknown. Aim: To assess the effects of 12 months of creatine supplementation and supervised, whole-body resistance training on bone mineral density, bone geometric properties, muscle accretion, and strength in older males. Methods: Participants were randomized to supplement with creatine ( n = 18, 49–69 years, 0.1 g·kg-1·d-1) or placebo ( n = 20, 49–67 years, 0.1 g·kg-1·d-1) during 12 months of supervised, whole-body resistance training. Results: After 12 months of training, both groups experienced similar changes in bone mineral density and geometry, bone speed of sound, lean tissue and fat mass, muscle thickness, and muscle strength. There was a trend ( p = 0.061) for creatine to increase the section modulus of the narrow part of the femoral neck, an indicator of bone bending strength, compared with placebo. Adverse events did not differ between creatine and placebo. Conclusions: Twelve months of creatine supplementation and supervised, whole-body resistance training had no greater effect on measures of bone, muscle, or strength in older males compared with placebo.

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Remarkable Classes of Almost 3-Contact Metric Manifolds

Axioms ◽

10.3390/axioms10010008 ◽

2021 ◽

Vol 10 (1) ◽

pp. 8

Author(s):

Giulia Dileo

Keyword(s):

Geometric Properties ◽

New Class ◽

Contact Metric Manifolds ◽

Cosymplectic Manifolds ◽

Sasaki Manifolds

We introduce a new class of almost 3-contact metric manifolds, called 3-(0,δ)-Sasaki manifolds. We show fundamental geometric properties of these manifolds, analyzing analogies and differences with the known classes of 3-(α,δ)-Sasaki (α≠0) and 3-δ-cosymplectic manifolds.

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