Synchronization and structure in an adaptive oscillator network

We analyze the interplay of synchronization and structure evolution in an evolving network of phase oscillators. An initially random network is adaptively rewired according to the dynamical coherence of the oscillators, in order to enhance their mutual synchronization. We show that the evolving network reaches a small-world structure. Its clustering coefficient attains a maximum for an intermediate intensity of the coupling between oscillators, where a rich diversity of synchronized oscillator groups is observed. In the stationary state, these synchronized groups are directly associated with network clusters.     

Competition between phase separation and "Classical" intermediate valence in an exactly solved model

The exact solution of the spin-1 / 2 Falicov-Kimball model on an infinite-coordination Bethe lattice is analyzed in the regime of "classical" intermediate valence. We find that (i) either phase separation or a direct metal-insulator transition precludes intermediate valence over a large portion of the phase diagram, and (ii) within the intermediate valence phase, only continuous transitions are found as functions of the localized f-electron energy or temperature.     

Exactly solvable models of adaptive networks

A satisfiability-unsatisfiability (SAT-UNSAT) transition takes place for many optimization problems when the number of constraints, graphically represented by links between variables nodes, is brought above some threshold. If the network of constraints is allowed to adapt by redistributing its links, the SAT-UNSAT transition may be delayed and preceded by an intermediate phase where the structure self-organizes to satisfy the constraints. We present an analytic approach, based on the recently introduced cavity method for large deviations, which exactly describes the two phase transitions delimiting this adaptive intermediate phase. We give explicit results for random bond models subject to the connectivity or rigidity percolation transitions, and compare them with numerical simulations.     

Structure of blue phase III of cholesteric liquid crystals

We report large scale simulations of the blue phases of cholesteric liquid crystals. Our results suggest a structure for blue phase III, the blue fog, which has been the subject of a long debate in liquid crystal physics. We propose that blue phase III is an amorphous network of disclination lines, which is thermodynamically and kinetically stabilized over crystalline blue phases at intermediate chiralities. This amorphous network becomes ordered under an applied electric field, as seen in experiments.     

A geometrical interpretation of the chaotic state of inhomogeneous deterministic cellular automata

We propose a geometrical interpretation of the chaotic state of inhomogeneous cellular automata. From the rules of the cellular automaton we construct a network. The percolating phase of this network coincides with the chaotic phase of the cellular automaton. We also report numerical tests of these ideas on several cellular automata.     

"Bending to stretching" transition in disordered networks

From polymer gels to cytoskeletal structures, random networks of elastic material are commonly found in both materials science and biology. We present a three-dimensional micromechanical model of these networks and identify a "bending-to-stretching" transition. We characterize this transition in terms of concentration scaling laws, the stored elastic energy, and affinity measurements. Understanding the relationship between microscopic geometry and macroscopic mechanics will elucidate, for example, the mechanical properties of polymer gel networks or the role of semiflexible network mechanics in cells.     

Chaotic transmission of waves and "cooling" of signals

Ray dynamics in waveguide media exhibits chaotic motion. For a finite length of propagation, the large distance asymptotics is not uniform and represents a complicated combination of bunches of rays with different intermediate asymptotics. The origin of the phenomena that we call "chaotic transmission," lies in the nonuniformity of the phase space with sticky domains near the boundary of islands. We demonstrate different fractal properties of ray propagation using underwater acoustics as an example. The phenomenon of the kind of Levy flights can occur and it can be used as a mechanism of cooling of signals when the width of spatial spectra dispersion is significantly reduced. (c) 1997 American Institute of Physics.     

Associative memory on a small-world neural network

We study a model of associative memory based on a neural network with small-world structure. The efficacy of the network to retrieve one of the stored patterns exhibits a phase transition at a finite value of the disorder. The more ordered networks are unable to recover the patterns, and are always attracted to non-symmetric mixture states. Besides, for a range of the number of stored patterns, the efficacy has a maximum at an intermediate value of the disorder. We also give a statistical characterization of the spurious attractors for all values of the disorder of the network.Received: 12 January 2004, Published online: 28 May 2004PACS: 84.35. + i Neural networks - 89.75.Hc Networks and genealogical trees - 87.18.Sn Neural networks     

Synchronization in interdependent networks

We explore the synchronization behavior in interdependent systems, where the one-dimensional (1D) network (the intranetwork coupling strength J(I)) is ferromagnetically intercoupled (the strength J) to the Watts-Strogatz (WS) small-world network (the intranetwork coupling strength J(II)). In the absence of the internetwork coupling (J=0), the former network is well known not to exhibit the synchronized phase at any finite coupling strength, whereas the latter displays the mean-field transition. Through an analytic approach based on the mean-field approximation, it is found that for the weakly coupled 1D network (J(I)?1) the increase of J suppresses synchrony, because the nonsynchronized 1D network becomes a heavier burden for the synchronization process of the WS network. As the coupling in the 1D network becomes stronger, it is revealed by the renormalization group (RG) argument that the synchronization is enhanced as J(I) is increased, implying that the more enhanced partial synchronization in the 1D network makes the burden lighter. Extensive numerical simulations confirm these expected behaviors, while exhibiting a reentrant behavior in the intermediate range of J(I). The nonmonotonic change of the critical value of J(II) is also compared with the result from the numerical RG calculation.     

Staggered Phases in Diluted Systems with Continuous Spins

We consider systems with continuous spins and annealed dilution. We show that, as in the discrete case, such systems often undergo a phase transition, which is manifested in the appearance of a staggered intermediate phase. In particular, these phases appear in systems such as the massive Gaussian model where there is no phase transition in the undiluted system. Received: 2 January 1997 / Accepted: 1 February 1997     

Polyamorphism of ice at low temperatures from constant-pressure simulations

We report results of molecular dynamics simulations of amorphous ice in the pressure range 0-22.5 kbar. The high-density amorphous (HDA) ice prepared by compression of Ih ice at T=80 K is annealed to T=170 K at intermediate pressures in order to generate relaxed states. We confirm the existence of recently observed phenomena, the very high-density amorphous ice, and a continuum of HDA forms. We suggest that both phenomena have their origin in the evolution of the network topology of the annealed HDA phase with decreasing volume, resulting at low temperatures in the metastability of a range of densities.     

Intermediate structures in two-dimensional molecular self-assembly

We discuss the occurrence of transition structures observed in molecular self-assembly at surfaces. The increasing surface coverage transitions from low coverage structures to high coverage structures are a common phenomenon. However, often observed and not perfectly understood is the formation of intermediate structures, sometimes with lower lateral density than the initial phase. We will present different examples from our recent work and discuss the possible mechanisms of intermediate phase formation. In addition, we present intermediate structures occurring due to temperature-controlled reversible phase transitions.     

1H-13C polarization transfer in membranes: a tool for probing lipid dynamics and the effect of cholesterol

Phospholipid bilayers with over 20% cholesterol can form a liquid-ordered (l(o)) phase, which can be found in lateral domains, called rafts, in biomembranes. We show here that high-resolution (13)C and (1)H solid-state NMR are well suited to explore this phase, intermediate between gel and fluid. This approach can be applied to artificial or natural membranes, with no isotopic enrichment and with the help of magic-angle spinning (MAS), taking advantage of the high resolution and sensitivity of these nuclei. The sensitivity of magnetization transfer schemes to different lipid states has allowed us here to discriminate between various phases. We show that the phase composed of unsaturated phospholipids and cholesterol differs, in terms of lipid dynamics, both from the previously described l(o) phase and from the liquid-disordered phase.     

Possibility of a distortion induced gap in intermediate valence compounds

It is shown that in some stoichiometric intermediate valence compounds a symmetry breaking distortion leading to a hybridization gap in the electronic density of states can exist. We study this possibility for the high pressure phase of SmS and the paramagnetic phase of TmSe.     

A hierarchical model exhibiting the Kosterlitz-Thouless fixed point

We present a new hierarchical model for 2D Coulomb gases and investigate its behavior under renormalization group transformations. Unlike all previous hierarchical models (including the Migdal-Kadanoff version) for this system our model displays a line of stable fixed points describing the Kosterlitz-Thouless phase transition. For Coulomb gases corresponding to Z_N models these fixed points are stable in an intermediate range of temperatures.     

High-pressure molecular phases of solid carbon dioxide

We present a theoretical study of solid CO2 up to 50 GPa and 1500 K using first-principles calculations. In this pressure-temperature range, interpretations of recent experiments have suggested the existence of CO2 phases which are intermediate between molecular and covalent-bonded solids. We reexamine the concept of intermediate phases in the CO2 phase diagram and propose instead molecular structures, which provide an excellent agreement with measurements.     

Further insights into the “ρπ puzzle”

Based on a systematic investigation of J/ψ(ψ) → VP,where V and P stand for light vector and pseudoscalar mesons,we identify the role played by the electromagnetic(EM) transitions and intermediate meson loop transitions,which are essential ingredients for understanding the J/ψ and ψ couplings to VP.We show that on the one hand,the EM transitions have relatively larger interferences in ψ→ρπ and K*K+c.c.as explicitly shown by vector meson dominance(VMD).On the other hand,the strong decay of ψ receives relatively larger destructive interferences from the intermediate meson loop transitions.By identifying these mechanisms in an overall study of J/ψ(ψ)→VP,we provide a coherent understanding of the so-called "ρπ puzzle".     

Synchronization and information transmission in spatio-temporal networks of deformable units

We study the relationship between synchronization and the rate with which information is exchanged between nodes in a spatio-temporal network that describes the dynamics of classical particles under a substrate Remoissenet-Peyrard potential. We also show how phase and complete synchronization can be detected in this network. The difficulty in detecting phase synchronization in such a network appears due to the highly non-coherent character of the particle dynamics which unables a proper definition of the phase dynamics. The difficulty in detecting complete synchronization appears due to the spatio character of the potential which results in an asymptotic state highly dependent on the initial state.      

Viscoelastic phase separation of protein solutions

In addition to the known behavior of normal phase separation and gelation, we report novel phase-separation behavior of protein solutions as their intermediate case. A network structure of the protein-rich phase may be formed even if it is the minority phase, contrary to the conventional wisdom. This behavior is characteristic of viscoelastic phase separation found in polymer solutions. This kinetic pathway may play crucial roles in the complex phase ordering of protein solutions, in particular, protein network formation in biological systems and foods.     

Synchronizability of dynamical scale-free networks subject to random errors

In this paper the robustness of network synchronizability against random deletion of nodes, i.e. errors, in dynamical scale-free networks was studied. To this end, two measures of network synchronizability, namely, the eigenratio of the Laplacian and the order parameter quantifying the degree of phase synchrony were adopted, and the synchronizability robustness on preferential attachment scale-free graphs was investigated. The findings revealed that as the network size decreases, the robustness of its synchronizability against random removal of nodes declines, i.e. the more the number of randomly removed nodes from the network, the worse its synchronizability. We also showed that this dependence of the synchronizability on the network size is different with that in the growing scale-free networks. The profile of a number of network properties such as clustering coefficient, efficiency, assortativity, and eccentricity, as a function of the network size was investigated in these two cases, growing scale-free networks and those with randomly removed nodes. The results showed that these processes are also different in terms of these metrics.