Analytical calculation of the transition to complete phase synchronization in coupled oscillators

Here we present a system of coupled phase oscillators with nearest neighbors coupling, which we study for different boundary conditions. We concentrate at the transition to total synchronization. We are able to develop exact solutions for the value of the coupling parameter when the system becomes completely synchronized, for the case of periodic boundary conditions as well as for an open chain with fixed ends. We compare the results with those calculated numerically.Comment: 5 pages, 3 figure

CAUSALITY AND DYNAMICS OF ENERGY CONSUMPTION AND OUTPUT: EVIDENCE FROM NON-OECD ASIAN COUNTRIES

This article examines the short-run and long-run causal relationship between energy consumption and output in six non-OECD Asian developing countries. Standard time series econometrics is used for this purpose. Based on cointegration and vector error correction modeling, the empirical result shows a bi-directional causality between energy consumption and income in Malaysia, while a unidirectional causality from output to energy consumption in China and Thailand and energy consumption to output in India and Pakistan. Bangladesh remains as an energy neutral economy confirming the fact that it is one of the lowest energy consuming countries in Asia. Both the generalized variance decompositions and the impulse response functions confirm the direction of causality in these countries. These findings have important policy implications for concerned countries. Countries like China and Thailand may contribute to the fight against global warming directly implementing energy conservation measures whereas India and Pakistan may focus on technological developments and mitigation policies. For Malaysia, a balanced combination of alternative policies seems to be appropriate.Energy Conservation, Cointegration, Error Correction Model, Generalized Variance Decompositions, Generalized Impulse Response Functions

Cosmological solutions of massive gravity on de Sitter

In the framework of the recently proposed models of massive gravity, defined with respect to a de Sitter reference metric, we obtain new homogeneous and isotropic solutions for arbitrary cosmological matter and arbitrary spatial curvature. These solutions can be classified into three branches. In the first two, the massive gravity terms behave like a cosmological constant. In the third branch, the massive gravity effects can be described by a time evolving effective fluid with rather remarkable features, including the property to behave as a cosmological constant at late time.Comment: 6 pages, 1 figure; discussion extended, a few references added, improved analysis in Section

Synthesis of Triazolo and Pyrazolo Derivatives of Quinoline Nucleus

New heterocyclic derivatives of quinoline are reported. Reaction of quinoline-2-thiol 4 with hydrazine hydrate gave 2-hydrazionoquinoline 5. Treatment of  5 with CS2 in pyridine afforded 1,2,4-triazolo-[4,3-a]-quinolin-1-2H-thione 6, whereas the reaction of 5 with carboxylic acids namely formic acid or acetic acid, yielded the 1,2,4-triazol-[4,3-a]-quinolin 7 or 5-methyl-1,2,4-triazolo [4,3-a]-quinoline 8 through ring closure. Diazotization of 5 under acidic conditions produced the fused tetrazole compound 9, tetrzolo-[1,5-a]-quinoline. Moreover, treatment of 5 with active methlyene compounds gave two pyrazole derivatives 10 and 11. Azomethines 12a-e were prepared through condensation of 5 with aromatic aldehydes or ketones. Keyword: triazoloquinoline, tetrazoloquinoline, pyrazoloquinolines, azomethines.

Analytic Determination of the Critical Coupling for Oscillators in a Ring

We study a model of coupled oscillators with bidirectional first nearest neighbours coupling with periodic boundary conditions. We show that a stable phase-locked solution is decided by the oscillators at the borders between the major clusters, which merge to form a larger one of all oscillators at the stage of complete synchronization. We are able to locate these four oscillators as well as the size of major clusters in the vicinity of the stage of full synchronization which we show to depend only on the set of initial frequencies. Using the method presented here, we are able to obtain an analytic form of the critical coupling, at which the complete synchronization state occurs.Comment: 5 pages and 3 figure

Thermal quantum and classical correlations in two qubit XX model in a nonuniform external magnetic field

We investigate how thermal quantum discord (QD) and classical correlations (CC) of a two-qubit one-dimensional XX Heisenberg chain in thermal equilibrium depend on the temperature of the bath as well as on nonuniform external magnetic fields applied to two qubits and varied separately. We show that the behavior of QD differs in many unexpected ways from the thermal entanglement (EOF). For the nonuniform case (B1 = -B2), we find that QD and CC are equal for all values of (B1 = -B2) and for different temperatures. We show that, in this case, the thermal states of the system belong to a class of mixed states and satisfy certain conditions under which QD and CC are equal. The specification of this class and the corresponding conditions are completely general and apply to any quantum system in a state in this class satisfying these conditions. We further find that the relative contributions of QD and CC can be controlled easily by changing the relative magnitudes of B1 and B2. Finally, we connect our results with the monogamy relations between the EOF, CC and the QD of two qubits and the environment.Comment: 8 pages, 13 figures. We connect our results with the monogamy relations between the EOF, CC and the QD of two qubits and the environmen