scholarly journals Chaotic dynamics in Parkfield region, California and characteristics earthquakes

MAUSAM ◽  
2021 ◽  
Vol 50 (1) ◽  
pp. 99-104
Author(s):  
H. N. SRIVASTAVA ◽  
K. C. SINHA RAY
Keyword(s):  
Lyapunov Exponent ◽  
Chaotic Dynamics ◽  
Initial Conditions ◽  
Strong Dependence ◽  
Plate Boundary ◽  
Deterministic Chaos ◽  
Himalayan Region ◽  
Positive Lyapunov Exponent ◽  
Collision Type ◽  
Earthquake Predictability

Based on about 75000 earthquakes in the California region detected through Parkfield network during the years 1969-1987, the occurrence of chaos was examined by two different approaches, namely, strange at tractor dimension and the Lyapunov exponent. The strange at tractor dimension was found as 6.3 in this region suggesting atleast 7 parameters for earthquake predictability. Small positive Lyapunov exponent of 0.045 provided further evidence for deterministic chaos in the region which showed strong dependence on the initial conditions. Implications of chaotic dynamics on characteristic Parkfield earthquakes has been discussed. The strange at tractor dimension in the region could be representative for the Transform type of plate boundary which is lower than that reported for continent collision type of plate boundary which is lower than that reported for continent collision type of plate boundary near Hindukush northwest Himalayan region.

FINITE TIME BEHAVIOR OF SMALL ERRORS IN DETERMINISTIC CHAOS AND LYAPUNOV EXPONENTS

1993 ◽  
Vol 03 (05) ◽  
pp. 1339-1342 ◽  
Author(s):  
C. NICOLIS ◽  
G. NICOLIS
Keyword(s):  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Finite Time ◽  
Initial Conditions ◽  
Deterministic Chaos ◽  
Time Behavior ◽  
Error Growth ◽  
Extended Formulation ◽  
Sensitivity To Initial Conditions

An extended formulation of sensitivity to initial conditions applicable to (small) finite errors and finite times is developed. It is shown that the first stages of error growth are neither exponential nor driven by the Lyapunov exponent.

scholarly journals Strange attractor in earthquake swarms near Valsad (Gujarat), India

MAUSAM ◽  
2021 ◽  
Vol 58 (4) ◽  
pp. 543-550
Author(s):  
H. N. SRIVASTAVA ◽  
S. N. BHATTACHARYA ◽  
D. T. RAO ◽  
S. SRIVASTAVA
Keyword(s):  
Lyapunov Exponent ◽  
Strange Attractor ◽  
Deterministic Chaos ◽  
Largest Lyapunov Exponent ◽  
Earthquake Swarms ◽  
Western Coast ◽  
Peninsular India ◽  
Earthquake Predictability ◽  
Daily Frequency ◽  
Low Dimension

Valsad district in south Gujarat near the western coast of the peninsular India experienced earthquake swarms since early February 1986.  Seismic monitoring through a network of micro earthquake seismographs showed a well concentrated seismic activity over an area of 7 × 10 km2 with the depth of foci extending from 1 to 15 km.  A total number of 21,830 earthquakes were recorded during March 1986 to June 1988.  The daily frequency of earthquakes for this period was utilized to examine deterministic chaos through evaluation of dimension of strange attractor and Lyapunov exponent.  The low dimension of 2.1 for the strange attractor and positive value of the largest Lyapunov exponent suggest chaotic dynamics in Valsad earthquake swarms with at least 3 parameters for earthquake predictability.  The results indicate differences in the characteristics of deterministic chaos in intraplate and interplate regions of India.

DETERMINISTIC CHAOS IN AN INTERPHASE LAYER OF A LIQUID–VAPOR SYSTEM

2004 ◽  
Vol 14 (10) ◽  
pp. 3671-3678
Author(s):  
G. P. BYSTRAI ◽  
S. I. IVANOVA ◽  
S. I. STUDENOK
Keyword(s):  
Phase Transitions ◽  
Chaotic Dynamics ◽  
Deterministic Chaos ◽  
Second Order ◽  
Homogeneous Layer ◽  
Time Interval ◽  
Evaporation And Condensation ◽  
Starting Conditions ◽  
Kolmogorov's Entropy ◽  
Dimensional Mapping

A second-order nonlinear differential equation with an aftereffect for the density of a thin homogeneous layer on a liquid and vapor interface is considered. The acts of evaporation and condensation of molecules, which are regarded as periodic "impacts", excite the layer. The mentioned NDE is integrated over a finite time interval to find a 2D (two-dimensional) mapping whose numerical solution describes the chaotic dynamics of density and pressure in time. The algorithms of constructing bifurcation diagrams, Lyapunov's exponents and Kolmogorov's entropy for systems with first-order, second-order phase transitions and Van der Waals' systems were elaborated. This approach allows to associate such concepts as phase transition, deterministic chaos and nonlinear processes. It also allows to answer a question whether deterministic chaos occurs in systems with phase transitions and how fast the information about starting conditions is lost within them.

scholarly journals EXACT SOLUTION OF AN IRREVERSIBLE ONE-DIMENSIONAL MODEL WITH FULLY BIASED SPIN EXCHANGES

1996 ◽  
Vol 10 (25) ◽  
pp. 3451-3459 ◽  
Author(s):  
ANTÓNIO M.R. CADILHE ◽  
VLADIMIR PRIVMAN
Keyword(s):  
Exact Solution ◽  
Domain Wall ◽  
Nearest Neighbor ◽  
Spin Exchange ◽  
Initial Conditions ◽  
Strong Dependence ◽  
Zero Temperature ◽  
Dimensional Model ◽  
One Dimensional ◽  
Temperature Dynamics

We introduce a model with conserved dynamics, where nearest neighbor pairs of spins ↑↓ (↓↑) can exchange to assume the configuration ↓↑ (↑↓), with rate β(α), through energy decreasing moves only. We report exact solution for the case when one of the rates, α or β, is zero. The irreversibility of such zero-temperature dynamics results in strong dependence on the initial conditions. Domain wall arguments suggest that for more general, finite-temperature models with steady states the dynamical critical exponent for the anisotropic spin exchange is different from the isotropic value.

On New Aspects of Nested Carbon Nanotubes as Gigahertz Oscillators

2011 ◽  
Vol 133 (5) ◽  
Author(s):  
R. Ansari ◽  
B. Motevalli
Keyword(s):  
Carbon Nanotubes ◽  
Initial Velocity ◽  
Initial Conditions ◽  
Strong Dependence ◽  
Interaction Force ◽  
Arbitrary Length ◽  
Oscillatory Frequency ◽  
Analytical Expression ◽  
System Parameters ◽  
The Core

Nested carbon nanotubes exhibit telescopic oscillatory motion with frequencies in the gigahertz range. In this paper, our previously proposed semi-analytical expression for the interaction force between two concentric carbon nanotubes is used to solve the equation of motion. That expression also enables a new semi-analytical expression for the precise evaluation of oscillation frequency to be introduced. Alternatively, an algebraic frequency formula derived based on the simplifying assumption of constant van der Waals force is also given. Based on the given formulas, a thorough study on different aspects of operating frequencies under various system parameters is conducted, which permits fresh insight into the problem. Some notable improvements over the previously drawn conclusions are made. The strong dependence of oscillatory frequency on system parameters including the extrusion distance and initial velocity of the core as initial conditions for the motion is shown. Interestingly, our results indicate that there is a special initial velocity at which oscillatory frequency is unique for any arbitrary length of the core. A particular relationship between the escape velocity (the minimum initial velocity beyond which the core will leave the outer nanotube) and this specific initial velocity is also revealed.

scholarly journals Chaos and the (un)predictability of evolution in a changing environment

2017 ◽  
Author(s):  
Artur Rego-Costa ◽  
Florence Débarre ◽  
Luis-Miguel Chevin
Keyword(s):  
Evolutionary Dynamics ◽  
Initial Conditions ◽  
Strong Dependence ◽  
Environmental Stochasticity ◽  
Phenotypic Evolution ◽  
Evolutionary System ◽  
Chaotic Oscillations ◽  
Changing Environment ◽  
Environmental Forcing ◽  
Evolutionary Trajectories

Among the factors that may reduce the predictability of evolution, chaos, characterized by a strong dependence on initial conditions, has received much less attention than randomness due to genetic drift or environmental stochasticity. It was recently shown that chaos in phenotypic evolution arises commonly under frequency-dependent selection caused by competitive interactions mediated by many traits. This result has been used to argue that chaos should often make evolutionary dynamics unpredictable. However, populations also evolve largely in response to external changing environments, and such environmental forcing is likely to influence the outcome of evolution in systems prone to chaos. We investigate how a changing environment causing oscillations of an optimal phenotype interacts with the internal dynamics of an eco-evolutionary system that would be chaotic in a constant environment. We show that strong environmental forcing can improve the predictability of evolution, by reducing the probability of chaos arising, and by dampening the magnitude of chaotic oscillations. In contrast, weak forcing can increase the probability of chaos, but it also causes evolutionary trajectories to track the environment more closely. Overall, our results indicate that, although chaos may occur in evolution, it does not necessarily undermine its predictability.

Dripping instability of a two-dimensional liquid film under an inclined plate

2021 ◽  
Vol 932 ◽  
Author(s):  
Guangzhao Zhou ◽  
Andrea Prosperetti
Keyword(s):  
Liquid Film ◽  
Initial Conditions ◽  
Strong Dependence ◽  
Bond Number ◽  
Quasi Equilibrium ◽  
Two Dimensional ◽  
Inclined Plate ◽  
Maximum Value ◽  
Critical Curvature ◽  
Rayleigh Taylor Instability

It is known that the dripping of a liquid film on the underside of a plate can be suppressed by tilting the plate so as to cause a sufficiently strong flow. This paper uses two-dimensional numerical simulations in a closed-flow framework to study several aspects of this phenomenon. It is shown that, in quasi-equilibrium conditions, the onset of dripping is closely associated with the curvature of the wave crests approaching a well-defined maximum value. When dynamic effects become significant, this connection between curvature and dripping weakens, although the critical curvature remains a useful reference point as it is intimately related to the short length scales promoted by the Rayleigh–Taylor instability. In the absence of flow, when the film is on the underside of a horizontal plate, the concept of a limit curvature is relevant only for small liquid volumes close to a critical value. Otherwise, the drops that form have a smaller curvature and a large volume. The paper also illustrates the peculiarly strong dependence of the dripping transition on the initial conditions of the simulations. This feature prevents the development of phase maps dependent only on the governing parameters (Reynolds number, Bond number, etc.) similar to those available for film flow on the upper side of an inclined plate.

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