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Intermittency route to chaos for the nuclear billiard - a qualitative study  [PDF]
D. Felea,I. V. Grossu,C. C. Bordeianu,C. Besliu,Al. Jipa,A. A. Radu,C. M. Mitu,E. Stan
Physics , 2009,
Abstract: We analyze on a simple classical billiard system the onset of chaotical behaviour in different dynamical states. A classical version of the "nuclear billiard" with a 2D deep Woods-Saxon potential is used. We take into account the coupling between the single-particle and the collective degrees of freedom in the presence of dissipation for several vibrational multipolarities. For the considered oscillation modes an increasing divergence of the nucleonic trajectories from the adiabatic to the resonance regime was observed. Also, a peculiar case of intermittency is reached in the vicinity of the resonance, for the monopole case. We examine the order-to-chaos transition by performing several types of qualitative analysis including sensitive dependence on the initial conditions, single-particle phase space maps, fractal dimensions of Poincare maps and autocorrelation functions.
Intermittency Route to Strange Nonchaotic Attractors  [PDF]
Awadhesh Prasad,Vishal Mehra,Ramakrishna Ramaswamy
Physics , 1997, DOI: 10.1103/PhysRevLett.79.4127
Abstract: Strange nonchaotic attractors (SNA) arise in quasiperiodically driven systems in the neighborhood of a saddle node bifurcation whereby a strange attractor is replaced by a periodic (torus) attractor. This transition is accompanied by Type-I intermittency. The largest nontrivial Lyapunov exponent $\Lambda$ is a good order-parameter for this route from chaos to SNA to periodic motion: the signature is distinctive and unlike that for other routes to SNA. In particular, $\Lambda$ changes sharply at the SNA to torus transition, as does the distribution of finite-time or N--step Lyapunov exponents, P(\Lambda_N).
Quantifying intermittency in the open drivebelt billiard  [PDF]
Carl P. Dettmann,Orestis Georgiou
Physics , 2011, DOI: 10.1063/1.3685522
Abstract: A "drivebelt" stadium billiard with boundary consisting of circular arcs of differing radius connected by their common tangents shares many properties with the conventional "straight" stadium, including hyperbolicity and mixing, as well as intermittency due to marginally unstable periodic orbits (MUPOs). Interestingly, the roles of the straight and curved sides are reversed. Here we discuss intermittent properties of the chaotic trajectories from the point of view of escape through a hole in the billiard, giving the exact leading order coefficient $\lim_{t\to\infty} t P(t)$ of the survival probability $P(t)$ which is algebraic for fixed hole size. However, in the natural scaling limit of small hole size inversely proportional to time, the decay remains exponential. The big distinction between the straight and drivebelt stadia is that in the drivebelt case there are multiple families of MUPOs leading to qualitatively new effects. A further difference is that most marginal periodic orbits in this system are oblique to the boundary, thus permitting applications that utilise total internal reflection such as microlasers.
Intermittency in Quantitative Finance  [PDF]
Laurent Schoeffel
Quantitative Finance , 2011,
Abstract: Factorial moments are convenient tools in nuclear physics to characterize the multiplicity distributions when phase-space resolution ($\Delta$) becomes small. For uncorrelated particle production within $\Delta$, Gaussian statistics holds and factorial moments $F_q$ are equal to unity for all orders $q$. Correlations between particles lead to a broadening of the multiplicity distribution and to dynamical fluctuations. In this case, the factorial moments increase above 1 with decreasing $\Delta$. This corresponds to what can be called intermittency. In this letter, we show that a similar analysis can be developed on financial price series, with an adequate definition of factorial moments. An intermittent behavior can be extracted using moments of order 2 ($F_2$), illustrating a sensitivity to non-Gaussian fluctuations within time resolution below 4 hours. This confirms that correlations between price returns start to play a role when the time resolution is below this threshold.
Quantum effects in classical chaos through intermittency  [PDF]
T. S. Nag,P. Banerjee
Physics , 2012,
Abstract: The semi-quantal dynamics is applied to investigate the influence of quantum fluctuations on problems in classical chaos through intermittency involving bifurcations. The results of the numerical calculations indicate that quantum effects enhance the tendency to chaos in both the problems of inverted pitchfork and saddle-node bifurcations discussed here.
Classical and Quantum Chaos in the Diamond Shaped Billiard  [PDF]
R. Salazar,G. Téllez,D. Jaramillo,D. L. González
Physics , 2012,
Abstract: We analyse the classical and quantum behaviour of a particle trapped in a diamond shaped billiard. We defined this billiard as a half stadium connected with a triangular billiard. A parameter $\xi$ which gradually change the shape of the billiard from a regular equilateral triangle ($\xi=1$) to a diamond ($\xi=0$) was used to control the transition between the regular and chaotic regimes. The classical behaviour is regular when the control parameter $\xi$ is one; in contrast, the system is chaotic when $\xi \neq 1$ even for values of $\xi$ close to one. The entropy grows fast as $\xi$ is decreased from 1 and the Lyapunov exponent remains positive for $\xi<1$. The Finite Difference Method was implemented in order to solve the quantum problem. The energy spectrum and eigenstates were numerically computed for different values of the control parameter. The nearest-neighbour spacing distribution is analysed as a function of $\xi$, finding a Poisson and a Gaussian Orthogonal Ensemble(GOE) distribution for regular and chaotic regimes respectively. Several scars and bouncing ball states are shown with their corresponding classical periodic orbits. Along the document the classical chaos identifiers are computed to show that system is chaotic. On the other hand, the quantum counterpart is in agreement with the Bohigas-Giannoni-Schmit conjecture and exhibits the standard features for chaotic billiard such as the scarring of the wavefunction.
Experimental observation of chaos-chaos intermittency types in spherical Couette flow  [PDF]
Dmitry Zhilenko,Olga Krivonosova
Physics , 2013, DOI: 10.1134/S102833581401011X
Abstract: Flows between concentric, counter rotating spherical boundaries are under investigation in the gap with size equal to inner sphere radius. Outer sphere rotational rate is fixed, while inner sphere rotational rate has time periodic variations. The amplitudes and frequencies of these variations are small relative to both spheres averaged rotational rates. With amplitude increase transition from initial periodical flow to chaos is occurred. To determine state of the flow time series of azimuthal velocity, taken with laser Doppler anemometry, were used. We demonstrate appearance of flow states in the form of chaos-chaos and cycle-chaos-chaos intermittency. A procedure is considered which allow quantitatively confirm distinct properties of different patterns of time alternating flow state with intermittency.
Chaos of the logistic equation with piecewise constant argument  [PDF]
Marat Akhmet,Derya Altintan,Tanil Ergenc
Physics , 2010,
Abstract: We consider the logistic equation with different types of the piecewise constant argument. It is proved that the equation generates chaos and intermittency. Li-Yorke chaos is obtained as well as the chaos through period-doubling route. Basic plots are presented to show the complexity of the behavior.
Classical and quantum chaos in a circular billiard with a straight cut  [PDF]
Suhan Ree,L. E. Reichl
Physics , 1998, DOI: 10.1103/PhysRevE.60.1607
Abstract: We study classical and quantum dynamics of a particle in a circular billiard with a straight cut. This system can be integrable, nonintegrable with soft chaos, or nonintegrable with hard chaos, as we vary the size of the cut. We use a quantum web to show differences in the quantum manifestations of classical chaos for these three different regimes.
On the Intermittency and Chaos in High Energy Collisions  [PDF]
Jinghua Fu,Lianshou Liu,Yuanfang Wu
Physics , 1999,
Abstract: It is shown that an event sample from the Monte Carlo simulation of a random cascading \alpha model with fixed dynamical fluctuation strength is intermittent but not chaotic, while the variance of dynamical fluctuation strength in different events will result in both the intermittency and the chaotic behavior. This shows that fractality and chaoticity are two connected but different features of non-linear dynamics in high energy collisions.
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