Critical exponents of Nikolaevskii turbulence

We study the spatial power spectra of Nikolaevskii turbulence in one-dimensional space. First, we show that the energy distribution in wavenumber space is extensive in nature. Then, we demonstrate that, when varying a particular parameter, the spectrum becomes qualitatively indistinguishable from that of Kuramoto-Sivashinsky turbulence. Next, we derive the critical exponents of turbulent fluctuations. Finally, we argue that in some previous studies, parameter values for which this type of turbulence does not appear were mistakenly considered, and we resolve inconsistencies obtained in previous studies.Comment: 9 pages, 6 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

Chemical turbulence equivalent to Nikolavskii turbulence

We find evidence that a certain class of reaction-diffusion systems can exhibit chemical turbulence equivalent to Nikolaevskii turbulence. The distinctive characteristic of this type of turbulence is that it results from the interaction of weakly stable long-wavelength modes and unstable short-wavelength modes. We indirectly study this class of reaction-diffusion systems by considering an extended complex Ginzburg-Landau (CGL) equation that was previously derived from this class of reaction-diffusion systems. First, we show numerically that the power spectrum of this CGL equation in a particular regime is qualitatively quite similar to that of the Nikolaevskii equation. Then, we demonstrate that the Nikolaevskii equation can in fact be obtained from this CGL equation through a phase reduction procedure applied in the neighborhood of a codimension-two Turing--Benjamin-Feir point.Comment: 10 pages, 3 figure

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.

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

The Kuramoto model with distributed shear

We uncover a solvable generalization of the Kuramoto model in which shears (or nonisochronicities) and natural frequencies are distributed and statistically dependent. We show that the strength and sign of this dependence greatly alter synchronization and yield qualitatively different phase diagrams. The Ott-Antonsen ansatz allows us to obtain analytical results for a specific family of joint distributions. We also derive, using linear stability analysis, general formulae for the stability border of incoherence.Comment: 6 page

Self-Consistent Perturbation Theory for Thermodynamics of Magnetic Impurity Systems

Integral equations for thermodynamic quantities are derived in the framework of the non-crossing approximation (NCA). Entropy and specific heat of 4f contribution are calculated without numerical differentiations of thermodynamic potential. The formulation is applied to systems such as PrFe4P12 with singlet-triplet crystalline electric field (CEF) levels.Comment: 3 pages, 2 figures, proc. ASR-WYP-2005 (JAERI

Spin-dependent neutrino-induced nucleon knockout

We study neutrino-induced nucleon knockout off atomic nuclei and examine the polarization properties of the ejectile. A detailed study of the spin dependence of the outgoing nucleon is presented. The numerical results are derived within a non-relativistic plane-wave impulse-approximation approach. Our calculations reveal large polarization asymmetries, and clear dissimilarities between neutrino- and antineutrino-induced reactions. They reflect the fact that neutrino-induced nucleon knockout is dominated by the transverse axial current and gains its major contributions from forward nucleon emission and backward lepton scattering.Comment: 9 pages, 7 figures, accepted for publication in Phys. Rev.

Dynamics of the Singlet-Triplet System Coupled with Conduction Spins -- Application to Pr Skutterudites

Dynamics of the singlet-triplet crystalline electric field (CEF) system at finite temperatures is discussed by use of the non-crossing approximation. Even though the Kondo temperature is smaller than excitation energy to the CEF triplet, the Kondo effect appears at temperatures higher than the CEF splitting, and accordingly only quasi-elastic peak is found in the magnetic spectra. On the other hand, at lower temperatures the CEF splitting suppresses the Kondo effect and inelastic peak develops. The broad quasi-elastic neutron scattering spectra observed in PrFe_4P_{12} at temperatures higher than the quadrupole order correspond to the parameter range where the CEF splittings are unimportant.Comment: 16 pages, 12 figures, 1 tabl

Excitonic Bound State in the Extended Anderson Model with c-f Coulomb Interaction

The Anderson model with the Coulomb interaction between the local and conduction electrons is studied in the semiconducting phase. Based on a perturbation theory from the atomic limit, leading contributions for the c-f Coulomb interaction are incorporated as a vertex correction to hybridization. An analytical solution shows that the effective attraction in the intermediate states leads to a bound state localized at the local electron site. Self-consistent equations are constructed as an extension of the non-crossing approximation (NCA) to include the vertex part yielding the bound state. A numerical calculation demonstrates the excitonic bound state inside the semiconducting gap for single-particle excitations, and a discontinuity at the gap edge for magnetic excitations.Comment: 15 pages, 20 figures, submitted to J. Phys. Soc. Jp