Superradiant laser: First-order phase transition and non-stationary regime

We solve the superradiant laser model in two limiting cases. First the stationary low-pumping regime is considered where a first-order phase transition in the semiclassical solution occurs. This discontinuity is smeared out in the quantum regime. Second, we solve the model in the non-stationary regime where we find a temporally periodic solution. For a certain parameter range well-separated pulses may occur. Received: 19 June 1998 / Accepted: 19 October 1998     

On chemiluminescent emission from an infiltrated chiral sculptured thin film

The theory describing the far-field emission from a dipole source embedded inside a chiral sculptured thin film (CSTF), based on a spectral Green function formalism, was further developed to allow for infiltration of the void regions of the CSTF by a fluid. In doing so, the extended Bruggeman homogenization formalism — which accommodates constituent particles that are small compared to wavelength but not vanishingly small — was used to estimate the relative permittivity parameters of the infiltrated CSTF. For a numerical example, we found that left circularly polarized (LCP) light was preferentially emitted through one face of the CSTF while right circularly polarized (RCP) light was preferentially emitted through the opposite face, at wavelengths within the Bragg regime. The centre wavelength for the preferential emission of LCP/RCP light was red shifted as the refractive index of the infiltrating fluid increased from unity, and this red shift was accentuated when the size of the constituent particles in our homogenization model was increased. Also, the bandwidth of the preferential LCP/RCP emission regime decreased as the refractive index of the infiltrating fluid increased from unity.     

Topological phase transition in a network model with preferential attachment and node removal

Preferential attachment is a popular model of growing networks. We consider a generalized model with random node removal, and a combination of preferential and random attachment. Using a high-degree expansion of the master equation, we identify a topological phase transition depending on the rate of node removal and the relative strength of preferential vs. random attachment, where the degree distribution goes from a power law to one with an exponential tail.     

A random covering interpretation for the phase transition of the random energy model

The random energy model is related to a random covering of the real line. The phase transition is interpreted as the passage from a regime where a family of random intervals covers the line (high temperature) to a noncovering regime (low temperature).     

Monte Carlo study of phase transitions in the bond-diluted 3D 4-state Potts model

Large-scale Monte Carlo simulations of the bond-diluted three-dimensional 4-state Potts model are performed. The phase diagram and the physical properties at the phase transitions are studied using finite-size scaling techniques. Evidences are given for the existence of a tricritical point dividing the phase diagram into a regime where the transitions remain of first order and a second regime where the transitions are softened to continuous ones by the influence of disorder. In the former regime, the nature of the transition is essentially clarified through an analysis of the energy probability distribution. In the latter regime critical exponents are estimated. Rare and typical events are identified and their role is qualitatively discussed in both regimes.     

Spreading processes on dynamically changing contact networks

We develop and analyze an agent-based model for the study of information propagation in dynamic contact networks. We represent information as a state of a node in a network that can be probabilistically transferred to an adjacent node within a single time step. The model is based on a closed (yet sufficiently large) population that can support processes of link generation and annihilation using different contact regimes. Our study is confined to the case of homogeneous contacts, where each agent establishes and breaks contacts in the same way. We consider information to be available for spreading in a fixed time window (i.e. finite memory). We find, surprisingly, that information transmission (measured as the proportion of informed nodes after a fixed number of time steps) is identical for dynamic preferential and random networks, but radically different for the associate mixing contact regime. We also find that the probability of transmission is, similarly counterintuitively, not a main driver of the process as opposed the the main network par maters determining contact lifetime and the turnover rate on connections. We discuss the explanation and the significance of these results in the light of the fundamental difference between dynamic and static (cumulative) networks.     

Active transport and cluster formation on 2D networks

We introduce a model for active transport on inhomogeneous networks embedded in a diffusive environment which is motivated by vesicular transport on actin filaments. In the presence of a hard-core interaction, particle clusters are observed that exhibit an algebraically decaying distribution in a large parameter regime, indicating the existence of clusters on all scales. The scale-free behavior can be understood by a mechanism promoting preferential attachment of particles to large clusters. The results are compared with a diffusion-limited aggregation model and active transport on a regular network. For both models we observe aggregation of particles to clusters which are characterized by a finite size scale if the relevant time scales and particle densities are considered.     

Modeling curvature effects in turbulent autoigniting non-premixed flames using tabulated chemistry

Turbulent flames are intrinsically curved. In the presence of preferential diffusion, curvature effects either enhance or suppress molecular diffusion, depending on the diffusivity of the species and the direction of the flame curvature. When a tabulated chemistry type of modeling is employed, curvature-preferential diffusion interactions have to be taken into consideration in the construction of manifolds. In this study, we employ multistage stage flamelet generated manifolds (MuSt-FGM) method to model autoigniting non-premixed turbulent flames with preferential diffusion effects included. The conditions for the modeled flame are in MILD combustion regime. To model the above-mentioned curvature-preferential diffusion interactions, a new mixture fraction which has a non-unity Lewis number is defined and used as a new control variable in the manifold generation. 1D curved flames are simulated to create the necessary flamelets. The resulting MuSt-FGM tables are used in the simulation of 1D laminar flames, and then also applied to turbulent flames using 2D direct numerical simulations (DNS). It was observed that when the curvature effects are included in the manifold, the MuSt-FGM results agree well with the detailed chemistry results; whereas the results become unsatisfactory when the curvature effects are ignored.     

A self-consistent approach to measure preferential attachment in networks and its application to an inherent structure network

Preferential attachment is one possible way to obtain a scale-free network. We develop a self-consistent method to determine whether preferential attachment occurs during the growth of a network, and to extract the preferential attachment rule using time-dependent data. Model networks are grown with known preferential attachment rules to test the method, which is seen to be robust. The method is then applied to a scale-free inherent structure (IS) network, which represents the connections between minima via transition states on a potential energy landscape. Even though this network is static, we can examine the growth of the network as a function of a threshold energy (rather than time), where only those transition states with energies lower than the threshold energy contribute to the network. For these networks we are able to detect the presence of preferential attachment, and this helps to explain the ubiquity of funnels on potential energy landscapes. However, the scale-free degree distribution shows some differences from that of a model network grown using the obtained preferential attachment rules, implying that other factors are also important in the growth process.     

Force spectroscopy of single multidomain biopolymers: A master equation approach

Experiments using atomic force microscopy for unfolding single multidomain biopolymers cover a broad range of time scales from equilibrium to non-equilibrium. A master equation approach allows to identify and treat coherently three dynamical regimes for increasing linear ramp velocity: i) an equilibrium regime, ii) a transient regime where refolding events still occur, and iii) a saw-tooth regime without any refolding events. For each regime, analytical approximations are derived and compared to numerically investigated examples. We analyze in the framework of this model also a periodic experimental protocol instead of a linear ramp. In this case, a major simplification arises if the dynamics can be restricted to an effectively two-dimensional subspace. For transitions with an intermediate meta-stable state, like Immunoglobulin27, a refined model allows to extract previously unknown molecular parameters related to this meta-stable state.     

Elasticity of stiff polymer networks

We study the elasticity of a two-dimensional random network of rigid rods ("Mikado model"). The essential features incorporated into the model are the anisotropic elasticity of the rods and the random geometry of the network. We show that there are three distinct scaling regimes, characterized by two distinct length scales on the elastic backbone. In addition to a critical rigidity percolation region and a homogeneously elastic regime we find a novel intermediate scaling regime, where the elasticity is dominated by bending deformations.     

Sand ripple dynamics in the case of out-of-equilibrium aeolian regimes

From a phenomenological hydrodynamical model, we analyze the aeolian sand ripple evolution in an out-of-equilibrium aeolian regime where erosion exceeds accretion (and vice versa). We find, in particular, that the ripple structure can be destroyed in favor of a flat sand bed. In the ripple regime we report on a new class of generic dynamics described by the Benney equation. This equation reveals either order or disorder depending on whether wave dispersion is strong or weak. In both cases, the average wavelength of the pattern is fixed in time. This markedly contrasts with the regime of equilibrium aeolian regime -reached when erosion balances deposition- where ripples undergo a coarsening process at long time (i.e., the wavelength increases indefinitely with time).Received: 4 August 2003, Published online: 5 February 2004PACS: 81.05.Rm Porous materials; granular materials     

Inverse cascade regime in shell models of two-dimensional turbulence

We consider shell models that display an inverse energy cascade similar to two-dimensional turbulence (together with a direct cascade of an enstrophylike invariant). Previous attempts to construct such models ended negatively, stating that shell models give rise to a "quasiequilibrium" situation with equipartition of the energy among the shells. We show analytically that the quasiequilibrium state predicts its own disappearance upon changing the model parameters in favor of the establishment of an inverse cascade regime with Kolmogorov scaling. The latter regime is found where predicted, offering a useful model to study inverse cascades.     

Smoluchowski Equation for Networks: Merger Induced Intermittent Giant Node Formation and Degree Gap

The dynamical phase diagram of a network undergoing annihilation, creation, and coagulation of nodes is found to exhibit two regimes controlled by the combined effect of preferential attachment for initiator and target nodes during coagulation and for link assignment to new nodes. The first regime exhibits smooth dynamics and power law degree distributions. In the second regime, giant degree nodes and gaps in the degree distribution are formed intermittently. Data for the Japanese firm network in 1994 and 2014 suggests that this network is moving towards the intermittent switching region.     

Effective boundary field theory for a Josephson junction chain with a weak link

We show that a finite Josephson junction (JJ) chain, ending with two bulk superconductors, and with a weak link at its center, may be regarded as a condensed matter realization of a two-boundary sine-Gordon model. Computing the partition function yields a remarkable analytic expression for the DC Josephson current as a function of the phase difference across the chain. We show that, in a suitable range of the chain parameters, there is a crossover of the DC Josephson current from a sinusoidal to a sawtooth behavior, which signals a transition from a regime where the boundary term is an irrelevant operator to a regime where it becomes relevant.     

Controlling polarization dynamics in a liquid environment: from localized to macroscopic switching in ferroelectrics

The effect of disorder on polarization switching in ferroelectric materials is studied using piezoresponse force microscopy in a liquid environment. The spatial extent of the electric field created by a biased tip is controlled by the choice of medium, resulting in a transition from localized switching dictated by tip radius, to uniform switching across the film. In the localized regime, the formation of fractal domains has been observed with dimensionality controlled by the length scale of the frozen disorder. In the nonlocal regime, preferential nucleation at defect sites and the presence of long-range correlations has been observed.     

Low-energy D scattering from Cs and CsCl adsorbed on the Si(100)2 × 1 surface

On the basis of neutralization and inelastic scattering of low-energy D⁺ ions, the bond nature of Cs and CsCl adsorbed on the Si(100)2 × 1 surface has been investigated. In a low-coverage regime ( < 0.2 ML), Cs is adsorbed ionically on Si(100) and subsequent oxygen adsorption readily causes the ionic Cs---O bond. CsCl is dissociatively adsorbed on the surface in a low-coverage regime due to the preferential reaction of Cl with the Si dangling bond and the resultant Cs is ionically bonded to Si.     

Slow dynamics in a turbulent von Kármán swirling flow

An experimental study of a turbulent von Kármán flow in a cylinder is presented. The mean flow is stationary up to a Reynolds number Re=10(4) where a bifurcation takes place. The new regime breaks some symmetries of the problem and becomes time dependent because of equatorial vortices moving with a precession movement. In the exact counterrotating case, a bistable regime appears and spontaneous reversals of the azimuthal velocity are registered. A three-well potential model with additive noise reproduces this dynamic. A regime of periodic response is observed when a very weak forcing is applied.     

Bosonic superfluid-insulator transition in continuous space

We investigate the zero-temperature phase diagram of interacting Bose gases in the presence of a simple cubic optical lattice, going beyond the regime where the mapping to the single-band Bose-Hubbard model is reliable. Our computational approach is a new hybrid quantum Monte?Carlo method which combines algorithms used to simulate homogeneous quantum fluids in continuous space with those used for discrete lattice models of strongly correlated systems. We determine the critical interaction strength and optical lattice intensity where the superfluid-to-insulator transition takes place, considering also the regime of shallow optical lattices and strong interatomic interactions. The implications of our findings for the supersolid state of matter are discussed.     

Loss of atom interference due to a random phase

We suggest a model where the influence of an environment on the atom interference is associated with a random phase. The model consists of sending a two-level state atom through two cavities, both containing a standing wave field in the Bragg regime and Raman–Nath regime, respectively. In view of this model, we can visualize the loss of interference fringes if the randomness of the phase increases, and the restoration of the pattern when it decreases, as which-path information. Then, the controllable random noise acts as a decoherence that would destroy the quantum features.