Reducing the number of time delays in coupled dynamical systems

When several dynamical systems interact, the transmission of the information between them necessarily implies a time delay. When the time delay is not negligible, the study of the dynamics of these interactions deserve a special treatment. We will show here that under certain assumptions, it is possible to set to zero a significant amount of time-delayed connections without altering the global dynamics. We will focus on graphs of interactions with identical time delays and bidirectional connections. With these premises, it is possible to find a configuration where a number $n_z$ of time delays have been removed with $n_v-1 \leq n_z \leq n_v^2/4$, where $n_v$ is the number of dynamical systems on a connected graph

Chaotic dynamics and fractal structures in experiments with cold atoms

We use tools from nonlinear dynamics to the detailed analysis of cold atom experiments. A powerful example is provided by the recent concept of basin entropy which allows to quantify the final state unpredictability that results from the complexity of the phase space geometry. We show here that this enables one to reliably infer the presence of fractal structures in phase space from direct measurements. We illustrate the method with numerical simulations in an experimental configuration made of two crossing laser guides that can be used as a matter wave splitter

Using the basin entropy to explore bifurcations

Bifurcation theory is the usual analytic approach to study the parameter space of a dynamical system. Despite the great power of prediction of these techniques, fundamental limitations appear during the study of a given problem. Nonlinear dynamical systems often hide their secrets and the ultimate resource is the numerical simulations of the equations. This paper presents a method to explore bifurcations by using the basin entropy. This measure of the unpredictability can detect transformations of phase space structures as a parameter evolves. We present several examples where the bifurcations in the parameter space have a quantitative effect on the basin entropy. Moreover, some transformations, such as the basin boundary metamorphoses, can be identified with the basin entropy but are not reflected in the bifurcation diagram. The correct interpretation of the basin entropy plotted as a parameter extends the numerical exploration of dynamical systems

Solubilities of some new refrigerants in water

Solubility data for the refrigerants HFC23 (CHF3), HFC32 (CH2F2) and HFC125 (C2HF5) in water have been determined as a function of the temperature in the range of temperatures 288-303 K at atmospheric pressure. These hydrofluorocarbons (HFCs) are good substitutes of the chlorofluorocarbons (CFCs), which have significant impact to stratospheric ozone depletion.http://www.sciencedirect.com/science/article/B6TG2-4177PK4-7/1/12019e8daebba6ccc7515753953406a

Period-doubling bifurcations and islets of stability in two-degree-of-freedom Hamiltonian systems

In this paper, we show that the destruction of the main KAM islands in two-degree-of-freedom Hamiltonian systems occurs through a cascade of period-doubling bifurcations. We calculate the corresponding Feigenbaum constant and the accumulation point of the period-doubling sequence. By means of a systematic grid search on exit basin diagrams, we find the existence of numerous very small KAM islands ('islets') for values below and above the aforementioned accumulation point. We study the bifurcations involving the formation of islets and we classify them in three different types. Finally, we show that the same types of islets appear in generic two-degree-of-freedom Hamiltonian systems and in area-preserving maps