Synchronizations in small-world networks of spiking neurons: Diffusive versus sigmoid couplings

By using a semi-analytical dynamical mean-field approximation previously proposed by the author [H. Hasegawa, Phys. Rev. E, {\bf 70}, 066107 (2004)], we have studied the synchronization of stochastic, small-world (SW) networks of FitzHugh-Nagumo neurons with diffusive couplings. The difference and similarity between results for {\it diffusive} and {\it sigmoid} couplings have been discussed. It has been shown that with introducing the weak heterogeneity to regular networks, the synchronization may be slightly increased for diffusive couplings, while it is decreased for sigmoid couplings. This increase in the synchronization for diffusive couplings is shown to be due to their local, negative feedback contributions, but not due to the shorten average distance in SW networks. Synchronization of SW networks depends not only on their structure but also on the type of couplings.Comment: 17 pages, 8 figures, accepted in Phys. Rev. E with some change

Classical small systems coupled to finite baths

We have studied the properties of a classical $N_S$-body system coupled to a bath containing $N_B$-body harmonic oscillators, employing an $(N_S+N_B)$ model which is different from most of the existing models with $N_S=1$. We have performed simulations for $N_S$-oscillator systems, solving $2(N_S+N_B)$ first-order differential equations with $N_S \simeq 1 - 10$ and $N_B \simeq 10 - 1000$, in order to calculate the time-dependent energy exchange between the system and the bath. The calculated energy in the system rapidly changes while its envelope has a much slower time dependence. Detailed calculations of the stationary energy distribution of the system $f_S(u)$ ($u$: an energy per particle in the system) have shown that its properties are mainly determined by $N_S$ but weakly depend on $N_B$. The calculated $f_S(u)$ is analyzed with the use of the $\Gamma$ and $q$-$\Gamma$ distributions: the latter is derived with the superstatistical approach (SSA) and microcanonical approach (MCA) to the nonextensive statistics, where $q$ stands for the entropic index. Based on analyses of our simulation results, a critical comparison is made between the SSA and MCA. Simulations have been performed also for the $N_S$-body ideal-gas system. The effect of the coupling between oscillators in the bath has been examined by additional ($N_S+N_B$) models which include baths consisting of coupled linear chains with periodic and fixed-end boundary conditions.Comment: 30 pages, 16 figures; the final version accepted in Phys. Rev.

NMR Knight shifts and linewidths in the Ni‐Pd‐P and Ni‐Pt‐P metallic glasses: Composition and temperature dependences

NMR Knight shift and linewidth measurements are reported for the ^(31)P nuclei in the metallic glasses (Ni_(0.50)Pd_(0.50))100−_xP_x (where x=16 to 26.5) and (Ni_yPd_(1−y))_(80)P_(20) (where y=0.20 to 0.80), and both the ^(31)P and 195Pt nuclei in the metallic glass (Ni_yPt_(1−y))_(75)P_(25) (where y=0.20 to 0.68). The results are discussed in terms of the amorphous structure, electronic structure, and stability of transition metal + metalloid metallic glasses

Fast accretion of small planetesimals by protoplanetary cores

We explore the dynamics of small planetesimals coexisting with massive protoplanetary cores in a gaseous nebula. Gas drag strongly affects the motion of small bodies leading to the decay of their eccentricities and inclinations, which are excited by the gravity of protoplanetary cores. Drag acting on larger ($\gtrsim 1$ km), high velocity planetesimals causes a mere reduction of their average random velocity. By contrast, drag qualitatively changes the dynamics of smaller ($\lesssim 0.1-1$ km), low velocity objects: (1) small planetesimals sediment towards the midplane of the nebula forming vertically thin subdisk; (2) their random velocities rapidly decay between successive passages of the cores and, as a result, encounters with cores typically occur at the minimum relative velocity allowed by the shear in the disk. This leads to a drastic increase in the accretion rate of small planetesimals by the protoplanetary cores, allowing cores to grow faster than expected in the simple oligarchic picture, provided that the population of small planetesimals contains more than roughly 1% of the solid mass in the nebula. Fragmentation of larger planetesimals ($\gtrsim 1$ km) in energetic collisions triggered by the gravitational scattering by cores can easily channel this amount of material into small bodies on reasonable timescales ($< 1$ Myr in the outer Solar System), providing a means for the rapid growth (within several Myr at 30 AU) of rather massive protoplanetary cores. Effects of inelastic collisions between planetesimals and presence of multiple protoplanetary cores are discussed.Comment: 17 pages, 8 figures, additional clarifications, 1 more figure and table adde

Quasi Markovian behavior in mixing maps

We consider the time dependent probability distribution of a coarse grained observable Y whose evolution is governed by a discrete time map. If the map is mixing, the time dependent one-step transition probabilities converge in the long time limit to yield an ergodic stochastic matrix. The stationary distribution of this matrix is identical to the asymptotic distribution of Y under the exact dynamics. The nth time iterate of the baker map is explicitly computed and used to compare the time evolution of the occupation probabilities with those of the approximating Markov chain. The convergence is found to be at least exponentially fast for all rectangular partitions with Lebesgue measure. In particular, uniform rectangles form a Markov partition for which we find exact agreement.Comment: 16 pages, 1 figure, uses elsart.sty, to be published in Physica D Special Issue on Predictability: Quantifying Uncertainty in Models of Complex Phenomen