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

Unbinding Transition Induced by Osmotic Pressure in Relation to Unilamellar Vesicle Formation

Small-angle X-ray scattering and phase-contrast microscopy experiments were performed to investigate the effect of the osmotic pressure on vesicle formation in a dioleoylphosphatidylcholine (DOPC)/water/NaI system. Multi-lamellar vesicles were formed when a pure lipid film was hydrated with an aqueous solution of NaI. On the other hand, uni-lamellar vesicles (ULVs) were formed when a lipid film mixed with an enough amount of NaI was hydrated. To confirm the effect of the osmotic pressure due to NaI, a free-energy calculation was performed. This result showed that the osmotic pressure induced an unbinding transition on the hydration process, which resulted in ULV formation

Quantum System under Periodic Perturbation: Effect of Environment

In many physical situations the behavior of a quantum system is affected by interaction with a larger environment. We develop, using the method of influence functional, how to deduce the density matrix of the quantum system incorporating the effect of environment. After introducing characterization of the environment by spectral weight, we first devise schemes to approximate the spectral weight, and then a perturbation method in field theory models, in order to approximately describe the environment. All of these approximate models may be classified as extended Ohmic models of dissipation whose differences are in the high frequency part. The quantum system we deal with in the present work is a general class of harmonic oscillators with arbitrary time dependent frequency. The late time behavior of the system is well described by an approximation that employs a localized friction in the dissipative part of the correlation function appearing in the influence functional. The density matrix of the quantum system is then determined in terms of a single classical solution obtained with the time dependent frequency. With this one can compute the entropy, the energy distribution function, and other physical quantities of the system in a closed form. Specific application is made to the case of periodically varying frequency. This dynamical system has a remarkable property when the environmental interaction is switched off: Effect of the parametric resonance gives rise to an exponential growth of the populated number in higher excitation levels, or particle production in field theory models. The effect of the environment is investigated for this dynamical system and it is demonstrated that there existsComment: 55 pages, LATEX file plus 13 PS figures. A few calculational mistatkes and corresponding figure 1 in field theory model corrected and some changes made for publication in Phys. Rev.D (in press

Pressure-induced and Composition-induced Structural Quantum Phase Transition in the Cubic Superconductor (Sr/Ca)_3Ir_4Sn_{13}

We show that the quasi-skutterudite superconductor Sr_3Ir_4Sn_{13} undergoes a structural transition from a simple cubic parent structure, the I-phase, to a superlattice variant, the I'-phase, which has a lattice parameter twice that of the high temperature phase. We argue that the superlattice distortion is associated with a charge density wave transition of the conduction electron system and demonstrate that the superlattice transition temperature T* can be suppressed to zero by combining chemical and physical pressure. This enables the first comprehensive investigation of a superlattice quantum phase transition and its interplay with superconductivity in a cubic charge density wave system.Comment: 4 figures, 5 pages (excluding supplementary material). To be published in Phys. Rev. Let

Universality in heavy-fermion systems with general degeneracy

We discuss the relation between the T^{2}-coefficient of electrical resistivity $A$ and the T-linear specific-heat coefficient $\gamma$ for heavy-fermion systems with general $N$, where $N$ is the degeneracy of quasi-particles. A set of experimental data reveals that the Kadowaki-Woods relation; $A/\gamma^{2} = 1*10^{-5} {\mu\Omega}(K mol/mJ)^{2}$, collapses remarkably for large-N systems, although this relation has been regarded to be commonly applicable to the Fermi-liquids. Instead, based on the Fermi-liquid theory we propose a new relation; $\tilde{A}/\tilde{\gamma}^2=1\times10^{-5}$ with $\tilde{A} = A/(1/2)N(N-1)$ and $\tilde{\gamma} = \gamma/(1/2)N(N-1)$. This new relation exhibits an excellent agreement with the data for whole the range of degenerate heavy-fermions.Comment: 2 figures, to appear in Phys. Rev. Let

Relaxation of classical many-body hamiltonians in one dimension

The relaxation of Fourier modes of hamiltonian chains close to equilibrium is studied in the framework of a simple mode-coupling theory. Explicit estimates of the dependence of relevant time scales on the energy density (or temperature) and on the wavenumber of the initial excitation are given. They are in agreement with previous numerical findings on the approach to equilibrium and turn out to be also useful in the qualitative interpretation of them. The theory is compared with molecular dynamics results in the case of the quartic Fermi-Pasta-Ulam potential.Comment: 9 pag. 6 figs. To appear in Phys.Rev.

The Key Role of Heavy Precipitation Events in Climate Model Disagreements of Future Annual Precipitation Changes in California

Climate model simulations disagree on whether future precipitation will increase or decrease over California, which has impeded efforts to anticipate and adapt to human-induced climate change. This disagreement is explored in terms of daily precipitation frequency and intensity. It is found that divergent model projections of changes in the incidence of rare heavy (\u3e60 mm day−1) daily precipitation events explain much of the model disagreement on annual time scales, yet represent only 0.3% of precipitating days and 9% of annual precipitation volume. Of the 25 downscaled model projections examined here, 21 agree that precipitation frequency will decrease by the 2060s, with a mean reduction of 6–14 days yr−1. This reduces California\u27s mean annual precipitation by about 5.7%. Partly offsetting this, 16 of the 25 projections agree that daily precipitation intensity will increase, which accounts for a model average 5.3% increase in annual precipitation. Between these conflicting tendencies, 12 projections show drier annual conditions by the 2060s and 13 show wetter. These results are obtained from 16 global general circulation models downscaled with different combinations of dynamical methods [Weather Research and Forecasting (WRF), Regional Spectral Model (RSM), and version 3 of the Regional Climate Model (RegCM3)] and statistical methods [bias correction with spatial disaggregation (BCSD) and bias correction with constructed analogs (BCCA)], although not all downscaling methods were applied to each global model. Model disagreements in the projected change in occurrence of the heaviest precipitation days (\u3e60 mm day−1) account for the majority of disagreement in the projected change in annual precipitation, and occur preferentially over the Sierra Nevada and Northern California. When such events are excluded, nearly twice as many projections show drier future conditions