Non-universal Features Research Articles

Quantum decay into a non-flat continuum

We study the decay of a prepared state into non-flat continuum. We find that the survival probability P(t) might exhibit either stretched-exponential or power-law decay, depending on non-universal features of the model. Still there is a universal characteristic time t0 that does not depend on the functional form. It is only for a flat continuum that we get a robust exponential decay that is insensitive to the nature of the intra-continuum couplings. The analysis highlights the co-existence of perturbative and non-perturbative features in the local density of states, and the nonlinear dependence of 1/t0 on the strength of the coupling.

Universal and non-universal aspects of wet granular matter under vertical vibrations

The phase diagram of vertically vibrated wet granular matter is investigated by both experiments and molecular dynamics type simulations, with a focus on the coexistence regime of the fluid and gas phases. Phase diagrams measured at various parameters including the rupture energy of liquid bridges, are presented. While for elastic grains, the transition from the fluid to the fluid-gas coexistence phase is found to be determined only by the rupture energy of liquid bridges [Fingerle et al. New J. Phys. 10, 053020 (2008)], inelasticity is found to introduce non-universal features into the phase diagram, which are also affected by the grain size.

Topology-Induced Anomalous Defect Production by Crossing a Quantum Critical Point

We study the influence of topology on the quench dynamics of a system driven across a quantum critical point. We show how the appearance of certain edge states, which fully characterize the topology of the system, dramatically modifies the process of defect production during the crossing of the critical point. Interestingly enough, the density of defects is no longer described by the Kibble-Zurek scaling, but determined instead by the nonuniversal topological features of the system. Edge states are shown to be robust against defect production, which highlights their topological nature.

Analysis of the Entire Sequence of a Single Photon Experiment on a Flavin Protein

The large amount of statistical data collected by single biomolecule experiments often demonstrates complex and non-Markovian relaxation over many time scales. Analyzing and interpreting these data is a major challenge because of the inherently statistical noise and the lack of definite theoretical descriptions or computer simulations on biologically relevant time scales. This paper reports one of the first complete sequence analyses of a single photon experiment on the flavin protein to determine an underlying physical picture for protein motions on the millisecond to second regimes. The robustness of Bayesian information analysis combined with the nonparametric maximum entropy method (MEM) incorporates all available information of the single-molecule data sequence and maximizes our ability to test the legitimacy of possible models. Our analysis of the experimental data is consistent with the stochastic Gaussian diffusion model where the slow protein motions are modeled as a collection of over-damped diffusive normal modes and reveals non-universal and distinct dynamic features that are specific for protein functions.

Labat Lecture 2006. Regional Anesthesia: Aspects, Thoughts, and Some Honest Ethics; About Needle Bevels and Nerve Lesions, and Back Pain After Spinal Anesthesia

<h3>Abstract</h3> Long-range synchrony from short-range interactions is a familiar pattern in biological and physical systems, many of which share a common set of “universal” properties at the point of synchronization. Common biological systems of coupled oscillators have been shown to be members of the Ising universality class, meaning that the very simple Ising model replicates certain spatial statistics of these systems at stationarity. This observation is useful because it reveals which aspects of spatial pattern arise independently of the details governing local dynamics, resulting in both deeper understanding of and a simpler baseline model for biological synchrony. However, in many situations a system’s dynamics are of greater interest than their static spatial properties. Here, we ask whether a dynamical Ising model can replicate universal and non-universal features of ecological systems, using noisy coupled metapopulation models with two-cycle dynamics as a case study. The standard Ising model makes unrealistic dynamical predictions, but the Ising model with memory corrects this by using an additional parameter to reflect the tendency for local dynamics to maintain their phase of oscillation. By fitting the two parameters of the Ising model with memory to simulated ecological dynamics, we assess the correspondence between the Ising and ecological models in several of their features (location of the critical boundary in parameter space between synchronous and asynchronous dynamics, probability of local phase changes, and ability to predict future dynamics). We find that the Ising model with memory is reasonably good at representing these properties of ecological metapopulations. The correspondence between these models creates the potential for the simple and well-known Ising class of models to become a valuable tool for understanding complex biological systems.

Solution thermodynamics near the liquid–liquid critical point: I. First-order excess derivatives

We present a phenomenological approximation to the study of various non-universal features of liquid–liquid phase transitions in the framework of an approximate equation that relates the excess volume, the excess enthalpy, and the slope of the critical line. The mixtures under study are those containing 1-nitropropane (NP) or nitrobenzene (NB) and n-alkanes (C N H 2 N+2 ). The validity range of the above-mentioned equation is studied in detail for NP–C N H 2 N+2 systems. The consistency thus observed is within the experimental resolution limits, indicating that the equation can be extremely successful. The influence of effects at a molecular level on the slope of the critical line and on the critical amplitude of the isobaric thermal expansivity is analyzed from the microscopic interpretation of the excess volume and the excess enthalpy. This analysis is extended to NB–C N H 2 N+2 systems. The results reflect the importance of volumetric effects on critical behaviour, short-range anti-parallel ordering in NB appearing to be particularly relevant.

Spectral properties of Bunimovich mushroom billiards

Properties of a quantum mushroom billiard in the form of a superconducting microwave resonator have been investigated. They reveal unexpected nonuniversal features such as, e.g., a supershell effect in the level density and a dip in the nearest-neighbor spacing distribution. Theoretical predictions for the quantum properties of mixed systems rely on the sharp separability of phase space--an unusual property met by mushroom billiards. We however find deviations which are ascribed to the presence of dynamic tunneling.

Universal and nonuniversal features in a model of city traffic

The complex behavior that occurs when traffic lights are synchronized is studied. Two strategies are considered: all lights in phase, and a "green wave" with a propagating green signal. It is found that traffic variables such as traveling time, velocity, and fuel consumption, near resonance, follow critical scaling laws. For the green wave, it is shown that time and velocity scaling laws hold even for random separation between traffic lights. These results suggest the concept of transient resonances, which can be induced by adaptively changing the phase of traffic lights. This may be important to consider when designing strategies for traffic control in cities, where short trajectories, and thus transient solutions, are likely to be relevant.

Universal and non-universal features of the dynamic susceptibility of supercooledliquids

We discuss the dynamics of the glass-forming liquids glycerol, propylene carbonate, andbenzophenone, as revealed in their dielectric behaviour and in depolarized light scattering(DLS) data. Above the melting point, the liquids exhibit two-step stretched relaxationbehaviour typical of ‘glassy dynamics’ at all attainable temperatures . There is no sign of a transition to exponential relaxation; rather, the stretching depends onlyweakly on the temperature. The spectral change, in first approximation, amounts to shifting theα-relaxation peak with the temperature. This behaviour is in contrast with thetemperature-dependent spectral shapes observed in the low-temperature state close toTg. Analysing corresponding dielectric spectroscopic (DS) data for comparisons, similartendencies are observed, except that the stretching parameters are different. Belowa certain temperature in glycerol, the tail of the excess wing, which is clearlypronounced in the DS data, appears also in the DLS spectra, with the same ratio ofthe wing exponents in DLS versus DS as of the stretching exponents at higherT. In propylene carbonate, the presence of a wing in the DLS data is not immediatelyobvious. However, its low-temperature DLS spectra are fully compatible with an empiricalmodel for the temperature-dependent spectral shape that adequately describes theDS data of both materials and includes the wing. We were however unable toreconcile the DLS results of glycerol with this model. This, together with thepronounced difference in DLS and DS spectral widths of glycerol, cast doubtsover the general validity of universal scaling procedures for different techniques.

Universal and nonuniversal features in the crossover from linear to nonlinear interface growth

We study a restricted solid-on-solid model involving deposition and evaporation with probabilities p and 1 - p, respectively, in one-dimensional substrates. It presents a crossover from Edwards-Wilkinson (EW) to Kardar-Parisi-Zhang (KPZ) scaling for p approximately 0.5. The associated KPZ equation is analytically derived, exhibiting a coefficient lambda of the nonlinear term proportional to q identical with p - 1/2, which is confirmed numerically by calculation of tilt-dependent growth velocities for several values of p. This linear lambda - q relation contrasts to the apparently universal parabolic law obtained in competitive models mixing EW and KPZ components. The regions where the interface roughness shows pure EW and KPZ scaling are identified for 0.55< or =p< or =0.8, which provides numerical estimates of the crossover times tc. They scale as tc approximately lambda -phi with phi=4.1+/-0.1, which is in excellent agreement with the theoretically predicted universal value phi=4 and improves previous numerical estimates, which suggested phi approximately 3.

Critical Binder cumulant in two-dimensional anisotropic Ising models

The Binder cumulant at the phase transition of Ising models on square lattices with various ferromagnetic nearest and next-nearest neighbour couplings is determined using mainly Monte Carlo techniques. We discuss the possibility to relate the value of the critical cumulant in the isotropic, nearest neighbour and in the anisotropic cases to each other by means of a scale transformation in rectangular geometry, to pinpoint universal and nonuniversal features.

Non-universal features of forced 2D turbulence in the energy and enstrophy ranges

Analysis of energy spectra and fluxes of 2D forced incompressible turbulence in the energy range reveals marked departures from the $-5/3$ law and the idea of spectral locality. Departures from the locality could also be diagnosed in the enstrophy interval, and in the energy range of beta-plane turbulence.

Universality in nontrivial continuum limits: A model calculation

We study numerically the continuum limit corresponding to the non-trivial fixed point of Dyson's hierarchical model. We discuss the possibility of using the critical amplitudes as input parameters. We determine numerically the leading and subleading critical amplitudes of the zero-momentum $2l$-point functions in the symmetric phase up to l=10 for randomly chosen local measures. In the infinite cutoff limit, the dimensionless renormalized coupling constants are in very good approximation universal (independent of the choice of the local measure). In addition, ratios of subleading amplitudes also appear to be universal. If we neglect very small log-periodic corrections, the non-universal features of the 2l-point functions appear to depend only the non-universal features of the 2-point function. We infer that when 2l becomes large, the dimensionless renormalized couplings grow as (2l)! despite the non-perturbative nature of our calculation, while the universal ratios of subleading amplitudes grow linearly.

Scaling and universality of inherent structure simulations.

In this paper we explore the inherent structures (IS) approach to the dynamics of the East constrained kinetic Ising model. The inherent structures do not capture the nature of the dynamics of many quantities, including the spin autocorrelation function. Simply monitoring the quenched energy fluctuations, i.e., IS energy, results in an oversimplified single order-parameter description of the system's dynamics, but examining other features, such as domain dynamics or normal modes, may give a more complete and useful picture of the dynamics. The universality in the behavior of the IS energy of this model does not reveal nonuniversal features of the kinetics that determine long-time relaxation of the system. As a result, popular functional forms, such as the stretched exponential relaxation or Gaussian distribution of energies, may be a numerical fit to data with little physical justification. Filtering data can be shown to erase features of the system and the resulting quantities resemble more universal functional forms that lack physical insight. These results for the East model have implications for IS simulations of realistic systems and suggest careful analysis including the examination of other potential order parameters is necessary to evaluate the validity of applications of universal and scaling arguments to IS simulations.

Ellipsometric Study of Superfluid Onset in Thin Liquid4Helium Films

We have developed a modulated null ellipsometer capable of measuring single layers of adsorbed 4He films at 1.4 K. The small optical index of liquid helium, the extreme sensitivity to temperature gradients, and the requirement of sub-monolayer stability over many hours presents significant experimental challenges, which will be briefly discussed. The main goal of our experiments is to independently measure the superfluid and normal coverage in thin adsorbed 4He films. This is a particularly important issue for helium films on intermediate strength substrates such as rubidium and thin cesium, where previous measurements indicate that prewetting and the Kosterlitz-Thouless transition interact strongly, and the K-T transition appears to have nonuniversal features. Independent determination of the superfluid and normal fraction can be accomplished by using the ellipsometer in conjunction with a quartz crystal micro balance (QCM). QCM measurements rely on viscous coupling of the fluid layers, and therefore respond only to the normal component of a 4He film. In contrast, the ellipsometer is sensitive to the total thickness, independent of the state (superfluid or normal) of the film. By combining the QCM and ellipsometric measurements we can determine the total coverage, the normal fluid component and thus the superfluid fraction.

Universal and nonuniversal features in shadowing dynamics of nonhyperbolic chaotic systems with unstable-dimension variability.

An important quantity characterizing the shadowability of computer-generated trajectories in nonhyperbolic chaotic system is the shadowing time, which measures for how long a numerical trajectory remains valid. This time depends sensitively on an initial condition. Here, we show that for nonhyperbolic systems with unstable-dimension variability, the probability distribution of the shadowing time contains two distinct scaling behaviors: an algebraic scaling for short times and an exponential scaling for long times. The exponential behavior depends on the system details but the small-time algebraic behavior appears to be universal.

Surface critical behavior of thin Ising films at the ‘special point’

The critical surface phenomena of a magnetic thin Ising film is studied using numerical Monte-Carlo method based on Wolff cluster algorithm. With varying the surface coupling, j s = J s / J, the phase diagram exhibits a special surface coupling j sp at which all the films have a unique critical temperature T c for an arbitrary thickness n. In spite of this, the critical exponent of the surface magnetization at the special point is found to increase with n. Moreover, non-universal features as well as dimensionality crossover from two- to three-dimensional behavior are found at this point.

Persistence in an antiferromagnetic Ising system with conserved magnetisation

We obtain the persistence exponents for an antiferromagnetic Ising system in which the magnetisation is kept constant. This system belongs to model C (system with non-conserved order parameter with a conserved density) and is expected to have persistence exponents different from that of model A (system with no conservation) but independent of the conserved density. Our numerical results for both local persistence at zero temperature and global persistence at the critical temperature however indicate that the exponents are dependent on the conserved magnetisation in both two and three dimensions. This non-universal feature is attributed to the presence of the conserved field and is special to the persistence phenomena.

Exact and scaling approaches to nonequilibrium models

Nonequilibrium phase transitions in simple lattice-based interacting-particle models are considered. Exact methods to treat these systems in low dimensions are discussed and the development of new more widely applicable scaling methods is outlined, which may be used to extract universal and nonuniversal features of the steady-state and dynamical critical behaviour.

Forced two-dimensional turbulence in spectral and physical space.

Two-dimensional (2D) turbulence in the energy range exhibits nonuniversal features, manifested in the departure (at low k) from the k(-5/3) energy spectrum law, variable energy flux, and irregular, nonlocal transfers. To unravel the underlying mechanism we conducted a detailed study of the 2D turbulence in spectral and physical space. It revealed complex multiscale organization of vorticity field and dynamic processes, ranging from large-scale meandering jets to strong localized vortices. The latter bear prime responsibility for the nonuniversal behavior of 2D turbulence, and we examined their statistical features and the growth mechanism. Our results are based on the numeric simulation of 2D turbulence on the 512 grid under different forcing-dissipation conditions.