0000000000590356
AUTHOR
J. Ros
Coexistence of periods in a bisecting bifurcation
The inner structure of the attractor appearing when the Varley-Gradwell-Hassell population model bifurcates from regular to chaotic behaviour is studied. By algebraic and geometric arguments the coexistence of a continuum of neutrally stable limit cycles with different periods in the attractor is explained.
Statistical geometric affinity in human brain electric activity
10 pages, 9 figures.-- PACS nrs.: 87.19.La; 05.45.Tp.-- ISI Article Identifier: 000246890100105
Effects of the axial isoscalar neutral current for solar neutrino detection
Abstract An essential assumption in the analysis of all the large solar neutrino experiments sensitive to neutral currents has been that the axial transitions are purely isovector. The recent results on the spin structure of the proton suggest the presence of an axial isoscalar neutral-current interaction. This would modify the assumed transition strengths for the neutral-current detection of solar neutrinos. We demonstrate that in the long wavelength limit a deuterium target is insensitive to such a mechanism. Our results for the situation of the planned BOREX experiment show that the suggested isoscalar strength would increase the observed rate by 30–40%, depending on the transition.
Double precision errors in the logistic map: statistical study and dynamical interpretation.
The nature of the round-off errors that occur in the usual double precision computation of the logistic map is studied in detail. Different iterative regimes from the whole panoply of behaviors exhibited in the bifurcation diagram are examined, histograms of errors in trajectories given, and for the case of fully developed chaos an explicit formula is found. It is shown that the statistics of the largest double precision error as a function of the map parameter is characterized by jumps whose location is determined by certain boundary crossings in the bifurcation diagram. Both jumps and locations seem to present geometric convergence characterized by the two first Feigenbaum constants. Even…
Strong-coupling expansion for the anharomonic oscillators −d2/dx 2+x 2+λx 2N
A perturbation expansion based on a modified and scaled harmonic oscillator combined with Pade extrapolation techniques has been used to determine the expansion of the ground-state energy in fractional and negative powers of the coupling constant, valid for large values of λ.
Coexistence of periods in a bifurcation
Abstract A particular type of order-to-chaos transition mediated by an infinite set of coexisting neutrally stable limit cycles of different periods is studied in the Varley–Gradwell–Hassell population model. We prove by an algebraic method that this kind of transition can only happen for a particular bifurcation parameter value. Previous results on the structure of the attractor at the transition point are here simplified and extended.
Chaotic Scattering in the Gaussian Potential
It is well known that general classical Hamiltonian dynamical systems have as a rule chaotic behaviour. By such a term one usually understands a sensitive dependence on initial conditions which manifests itself in the topology of phase space. For the most studied case of bounded motions this behaviour is detected, for example, by analysing the Poincare surfaces of section and by calculating Lyapunov characteristic exponents. The question then naturally arises of what are the effects of this complexity on the unbounded motions, i.e., on scattering phenomena. The signature of chaotic dynamics in these scattering regions of phase space has been the object of several papers appeared mainly in t…
Families of piecewise linear maps with constant Lyapunov exponent
We consider families of piecewise linear maps in which the moduli of the two slopes take different values. In some parameter regions, despite the variations in the dynamics, the Lyapunov exponent and the topological entropy remain constant. We provide numerical evidence of this fact and we prove it analytically for some special cases. The mechanism is very different from that of the logistic map and we conjecture that the Lyapunov plateaus reflect arithmetic relations between the slopes.
A pedagogical approach to the Magnus expansion
Time-dependent perturbation theory as a tool to compute approximate solutions of the Schrodinger equation does not preserve unitarity. Here we present, in a simple way, how the Magnus expansion (also known as exponential perturbation theory) provides such unitary approximate solutions. The purpose is to illustrate the importance and consequences of such a property. We suggest that the Magnus expansion may be introduced to students in advanced courses of quantum mechanics.
Why Magnus expansion
A short story about the origins of Magnus Expansion, why we got involved and how it led us to meet Geometric Integration. We present a biographical draft of Wilhelm Magnus, a sketchy discussion of ...
Charge and current distributions in elastic electron scattering by 1P shell nuclei
The authors study the charge and magnetic form factors appearing in elastic electron scattering by 1p shell nuclei. The question that the form factors may be obtained from simple nuclear models by simply introducing a scaling factor has been examined using the j-j coupling, the L-S coupling and the intermediate coupling of Cohen-Kurath (CK) resulting from effective interactions. Results for /sup 6/Li, /sup 7 /Li, /sup 9/Be and /sup 13/C are given and the q/sup 2/ dependences of their form factors are compared in the three models and with experiment. The CK scheme gives similar results to the L-S coupling for /sup 6/Li and /sup 7/Li in agreement with experiment, whereas it is intermediate be…