Many-Body Theory of Synchronization by Long-Range Interactions

Synchronization of coupled oscillators on a $d$-dimensional lattice with the power-law coupling $G(r) = g_0/r^\alpha$ and randomly distributed intrinsic frequency is analyzed. A systematic perturbation theory is developed to calculate the order parameter profile and correlation functions in powers of $\epsilon = \alpha/d-1$. For $\alpha \le d$, the system exhibits a sharp synchronization transition as described by the conventional mean-field theory. For $\alpha > d$, the transition is smeared by the quenched disorder, and the macroscopic order parameter \Av\psi decays slowly with $g_0$ as |\Av\psi| \propto g_0^2.Comment: 4 pages, 2 figure

Powder containing 2H-type silicon carbide produced by reacting silicon dioxide and carbon powder in nitrogen atmosphere in the presence of aluminum

The production of powder which contains silicon carbide consisting of 40% of 2H-type silicon carbide, beta type silicon carbide and less than 3% of nitrogen is discussed. The reaction temperature to produce the powder containing 40% of 2H-type silicon carbide is set at above 1550 degrees C in an atmosphere of aluminum or aluminum compounds and nitrogen gas or an antioxidation atmosphere containing nitrogen gas. The mixture ratio of silicon dioxide and carbon powder is 0.55 - 1:2.0 and the contents of aluminum or aluminum compounds within silicon dioxide is less than 3% in weight

Chimera and globally clustered chimera: Impact of time delay

Following a short report of our preliminary results [Phys. Rev. E 79, 055203(R) (2009)], we present a more detailed study of the effects of coupling delay in diffusively coupled phase oscillator populations. We find that coupling delay induces chimera and globally clustered chimera (GCC) states in delay coupled populations. We show the existence of multi-clustered states that act as link between the chimera and the GCC states. A stable GCC state goes through a variety of GCC states, namely periodic, aperiodic, long-- and short--period breathers and becomes unstable GCC leading to global synchronization in the system, on increasing time delay. We provide numerical evidence and theoretical explanations for the above results and discuss possible applications of the observed phenomena.Comment: 10 pages, 10 figures, Accepted in Phys. Rev.

To synchronize or not to synchronize, that is the question: finite-size scaling and fluctuation effects in the Kuramoto model

The entrainment transition of coupled random frequency oscillators presents a long-standing problem in nonlinear physics. The onset of entrainment in populations of large but finite size exhibits strong sensitivity to fluctuations in the oscillator density at the synchronizing frequency. This is the source for the unusual values assumed by the correlation size exponent $\nu'$. Locally coupled oscillators on a $d$-dimensional lattice exhibit two types of frequency entrainment: symmetry-breaking at $d > 4$, and aggregation of compact synchronized domains in three and four dimensions. Various critical properties of the transition are well captured by finite-size scaling relations with simple yet unconventional exponent values.Comment: 9 pages, 1 figure, to appear in a special issue of JSTAT dedicated to Statphys2

Hole Structures in Nonlocally Coupled Noisy Phase Oscillators

We demonstrate that a system of nonlocally coupled noisy phase oscillators can collectively exhibit a hole structure, which manifests itself in the spatial phase distribution of the oscillators. The phase model is described by a nonlinear Fokker-Planck equation, which can be reduced to the complex Ginzburg-Landau equation near the Hopf bifurcation point of the uniform solution. By numerical simulations, we show that the hole structure clearly appears in the space-dependent order parameter, which corresponds to the Nozaki-Bekki hole solution of the complex Ginzburg-Landau equation.Comment: 4 pages, 4 figures, to appear in Phys. Rev.

Synchronization Transition in the Kuramoto Model with Colored Noise

We present a linear stability analysis of the incoherent state in a system of globally coupled, identical phase oscillators subject to colored noise. In that we succeed to bridge the extreme time scales between the formerly studied and analytically solvable cases of white noise and quenched random frequencies.Comment: 4 pages, 2 figure

Hybridization effects and multipole orders in Pr skutterudites

Theoretical account is given of 4f-electron dynamics and multipole orders in Pr skutterudites with particular attention to (i) mechanism of the crystalline electric field (CEF) splitting leading to a pseudo-quartet ground state;(ii) Kondo effect due to exchange interactions involving the pseudo-quartet;(iii) multipole orders in the lattice of the pseudo-quartet in magnetic field.Competition between the point-charge interaction andhybridization between 4f and conduction electrons is identified as the key for controlling the CEF splitting. It is found that one of two pseudo-spins forming the pseudo-quartet has a ferromagnetic exchange, while the other has an antiferromagnetic exchange with conduction electrons. The Kondo effect is clearly seen in the resistivity calculated by the NCA, provided the low-lying triplet above the singlet is mainly composed of the $\Gamma_4$-type wave functions.If the weight of the $\Gamma_5$-type is large in the triplet, the Kondo effect does not appear.This difference caused by the nature of the triplet explains the presence of the Kondo effect inPrFe$_4$P$_{12}$, and its absence in PrOs$_4$Sb$_{12}$.By taking the minimal model with antiferro-quadrupole (AFQ) and ferro-type intersite interactions for dipoles and octupoles between nearest-neighbors,the mean-field theory reproduces the overall feature of the multiple ordered phases in PrFe$_4$P$_{12}$. The AFQ order with the $\Gamma_3$-type symmetry is found to be stable only as a mixture of $O_2^0$ and $O_2^2$ components.Comment: 21 pages, to be published in proc. YKIS200

Collective phase synchronization in locally-coupled limit-cycle oscillators

We study collective behavior of locally-coupled limit-cycle oscillators with scattered intrinsic frequencies on $d$-dimensional lattices. A linear analysis shows that the system should be always desynchronized up to $d=4$. On the other hand, numerical investigation for $d= 5$ and 6 reveals the emergence of the synchronized (ordered) phase via a continuous transition from the fully random desynchronized phase. This demonstrates that the lower critical dimension for the phase synchronization in this system is $d_{l}=4

Chimera States for Coupled Oscillators

Arrays of identical oscillators can display a remarkable spatiotemporal pattern in which phase-locked oscillators coexist with drifting ones. Discovered two years ago, such "chimera states" are believed to be impossible for locally or globally coupled systems; they are peculiar to the intermediate case of nonlocal coupling. Here we present an exact solution for this state, for a ring of phase oscillators coupled by a cosine kernel. We show that the stable chimera state bifurcates from a spatially modulated drift state, and dies in a saddle-node bifurcation with an unstable chimera.Comment: 4 pages, 4 figure

Globally clustered chimera states in delay--coupled populations

We have identified the existence of globally clustered chimera states in delay coupled oscillator populations and find that these states can breathe periodically, aperiodically and become unstable depending upon the value of coupling delay. We also find that the coupling delay induces frequency suppression in the desynchronized group. We provide numerical evidence and theoretical explanations for the above results and discuss possible applications of the observed phenomena.Comment: Accepted in Phys. Rev. E as a Rapid Communicatio