1. In this paper I compute explicitly the regulator map on K4(X) for an arbitrary curve X over a number field. Using this and Beilinson’s theorem about regulators for modular curves ([B2]) I prove a formula expressing the value of the L-function L(E, s) of a modular elliptic curve E over Q at s = 3 by the double Eisenstein-Kronecker series. It was conjectured by C. Deninger [D1]. 2. Generalized...

In this work we present a reactions module for “Chaos Many-Body Engine” (Grossu et al., 2010 [1]). Following our goal of creating a customizable, object oriented code library, the list of all possible reactions, including the corresponding properties (particle types, probability, cross-section, particles lifetime etc.), could be supplied as parameter, using a specific XML input file. Inspired b...

In a recent paper [A. D. Bailey et al., Phys. Rev. Lett. 34,3124 (1993)], the authors presented direct planar laser induced. fluorescence measurements of the oscillatory ion fluid velocity field in the presence of a large amplitude drift-Alfvenj wave. Surprisingly, the measured speeds were an order of magnitude lower than predicted by standard fluid theory, yet the flow pattern was consistent w...

In this paper, nonlinear dynamics of Duffing system with fractional order damping is investigated. The four order RungeKutta method and ten order CFE-Euler methods are introduced to simulate the fractional order Duffing equations. The effect of taking fractional order on the system dynamics is investigated using phase diagrams, bifurcation diagrams and Poincare map. The bifurcation diagram is a...