Connectivity Influences on Nonlinear Dynamics in Weakly-Synchronized Networks: Insights from Rössler Systems, Electronic Chaotic Oscillators, Model and Biological Neurons

Natural and engineered networks, such as interconnected neurons, ecological and social networks, coupled oscillators, wireless terminals and power loads, are characterized by an appreciable heterogeneity in the local connectivity around each node. For instance, in both elementary structures such as stars and complex graphs having scale-free topology, a minority of elements are linked to the rest of the network disproportionately strongly. While the effect of the arrangement of structural connections on the emergent synchronization pattern has been studied extensively, considerably less is known about its influence on the temporal dynamics unfolding within each node. Here, we present a comprehensive investigation across diverse simulated and experimental systems, encompassing star and complex networks of Rössler systems, coupled hysteresis-based electronic oscillators, microcircuits of leaky integrate-and-fire model neurons, and finally recordings from in-vitro cultures of spontaneously-growing neuronal networks. We systematically consider a range of dynamical measures, including the correlation dimension, nonlinear prediction error, permutation entropy, and other information-theoretical indices. The empirical evidence gathered reveals that under situations of weak synchronization, wherein rather than a collective behavior one observes significantly differentiated dynamics, denser connectivity tends to locally promote the emergence of stronger signatures of nonlinear dynamics. In deterministic systems, transition to chaos and generation of higher-dimensional signals were observed; however, when the coupling is stronger, this relationship may be lost or even inverted. In systems with a strong stochastic component, the generation of more temporally-organized activity could be induced. These observations have many potential implications across diverse fields of basic and applied science, for example, in the design of distributed sensing systems based on wireless coupled oscillators, in network identification and control, as well as in the interpretation of neuroscientific and other dynamical data

Short-time Critical Dynamics of the 3-Dimensional Ising Model

Comprehensive Monte Carlo simulations of the short-time dynamic behaviour are reported for the three-dimensional Ising model at criticality. Besides the exponent $\theta$ of the critical initial increase and the dynamic exponent $z$, the static critical exponents $\nu$ and $\beta$ as well as the critical temperature are determined from the power-law scaling behaviour of observables at the beginning of the time evolution. States of very high temperature as well as of zero temperature are used as initial states for the simulations.Comment: 8 pages with 7 figure

Intrinsic Structural Disorder and the Magnetic Ground State in Bulk EuTiO3

The magnetic properties of single-crystal EuTiO3 are suggestive of nanoscale disorder below its cubic-tetragonal phase transition. We demonstrate that electric field cooling acts to restore monocrystallinity, thus confirming that emergent structural disorder is an intrinsic low-temperature property of this material. Using torque magnetometry, we deduce that tetragonal EuTiO3 enters an easy-axis antiferromagnetic phase at 5.6 K, with a first-order transition to an easy-plane ground state below 3 K. Our data is reproduced by a 3D anisotropic Heisenberg spin model.Comment: 5 pages, 4 figure

Impurity Effects on Superconductivity on Surfaces of Topological Insulators

A two-dimensional superconductor (SC) on surfaces of topological insulators (TIs) is a mixture of s-wave and helical p-wave components when induced by s-wave interactions, since spin and momentum are correlated. On the basis of the Abrikosov-Gor'kov theory, we reveal that unconventional SCs on the surfaces of TIs are stable against time-reversal symmetric (TRS) impurities within a region of small impurity concentration. Moreover, we analyze the stability of the SC on the surfaces of TIs against impurities beyond the perturbation theory by solving the real-space Bogoliubov-de Gennes equation for an effective tight-binding model of a TI. We find that the SC is stable against strong TRS impurities. The behaviors of bound states around an impurity suggest that the SC on the surfaces of TIs is not a topological SC.Comment: 17 pages, 14 figures, to appear in J. Phys. Soc. Jp

A New Solid Deuterium Source of Ultra-Cold Neutrons

In polarized neutron decay, the angular correlation between the neutron spin and the direction of emission of the electron is characterized by the coefficient A. Measuring A involves determining the forward-backward asymmetry of the decay beta with respect to the direction of the neutron polarization. The value of A, when combined with measurements of the neutron lifetime, determines the values of the vector and axial vector weak coupling constants, Gv and GA. The value of Gv can also be determined by measurements of superallowed nuclear beta decay and by requiring that the Cabibo-Kobayashi-Maskawi (CKM) mixing matrix be unitary along with the measured value of other elements of the CKM matrix

A high-field adiabatic fast passage ultracold neutron spin flipper for the UCNA experiment

The UCNA collaboration is making a precision measurement of the β asymmetry (A) in free neutron decay using polarized ultracold neutrons (UCN). A critical component of this experiment is an adiabatic fast passage neutron spin flipper capable of efficient operation in ambient magnetic fields on the order of 1 T. The requirement that it operate in a high field necessitated the construction of a free neutron spin flipper based, for the first time, on a birdcage resonator. The design, construction, and initial testing of this spin flipper prior to its use in the first measurement of A with UCN during the 2007 run cycle of the Los Alamos Neutron Science Center's 800 MeV proton accelerator is detailed. These studies determined the flipping efficiency of the device, averaged over the UCN spectrum present at the location of the spin flipper, to be ϵ(overbar) = 0.9985(4)

Inter-Intra Molecular Dynamics as an Iterated Function System

The dynamics of units (molecules) with slowly relaxing internal states is studied as an iterated function system (IFS) for the situation common in e.g. biological systems where these units are subjected to frequent collisional interactions. It is found that an increase in the collision frequency leads to successive discrete states that can be analyzed as partial steps to form a Cantor set. By considering the interactions among the units, a self-consistent IFS is derived, which leads to the formation and stabilization of multiple such discrete states. The relevance of the results to dynamical multiple states in biomolecules in crowded conditions is discussed.Comment: 7 pages, 7 figures. submitted to Europhysics Letter

Two-dimensional quantum interference contributions to the magnetoresistance of Nd{2-x}Ce{x}CuO{4-d} single crystals

The 2D weak localization effects at low temperatures T = (0.2-4.2)K have been investigated in nonsuperconducting sample Nd{1.88}Ce{0.12}CuO{4-d} and in the normal state of the superconducting sample Nd{1.82}Ce{0.18}CuO{4-d} for B>B_c2. The phase coherence time and the effective thickness $d$ of a conducting CuO_2 layer have been estimated by the fitting of 2D weak localization theory expressions to the magnetoresistivity data for the normal to plane and the in-plane magnetic fields.Comment: 5 pages, 4 postscript figure

Normal-state resistivity anisotropy in underdoped RBa_2Cu_3O_{6+x} crystals

We have revealed new features in the out-of-plane resistivity rho_c of heavily underdoped RBa_2Cu_3O_{6+x} (R=Tm,Lu) single crystals, which give evidence for two distinct mechanisms contributing the c-axis transport. We have observed a crossover towards "metal-like" (d rho_c/d T > 0) behavior at the temperature T_m which quickly increases with decreasing doping. The "metal-like" conductivity contribution dominates at T < T_m and provides a saturation of the resistivity anisotropy, rho_c / rho_{ab}. The antiferromagnetic ordering is found to block this "metal-like" part of the c-axis conductivity and complete decoupling of CuO_2 planes, which may be the reason of superconductivity disappearance.Comment: RevTex, 4 pages including 4 eps figures. To be published in Phys.Rev.Let