scholarly journals Crossover scaling functions in the asymmetric avalanche process

2021 ◽  
Author(s):  
Anastasiia Trofimova ◽  
Alexander M Povolotsky
Keyword(s):  
Power Law ◽  
Critical Density ◽  
Integral Form ◽  
Universality Class ◽  
System Size ◽  
Scaling Functions ◽  
Time Space ◽  
Perturbative Solution ◽  
Avalanche Process ◽  
Particle Current

Abstract We consider the particle current in the asymmetric avalanche process on a ring. It is known to exhibit a transition from the intermittent to continuous flow at the critical density of particles. The exact expressions for the first two scaled cumulants of the particle current are obtained in the large time limit t ! ∞ via the Bethe ansatz and a perturbative solution of the TQ-equation. The results are presented in an integral form suitable for the asymptotic analysis in the large system size limit N ! ∞. In this limit the first cumulant, the average current per site or the average velocity of the associated interface, is asymptotically finite below the critical density and grows linearly and exponentially times power law prefactor at the critical density and above, respectively. The scaled second cumulant per site, i.e. the diffusion coefficient or the scaled variance of the associated interface height, shows the O(N-1⁄2) decay expected for models in the Kardar-Parisi-Zhang universality class below the critical density, while it is growing as O(N3⁄2) and exponentially times power law prefactor at the critical point and above. Also, we identify the crossover regime and obtain the scaling functions for the uniform asymptotics unifying the three regimes. These functions are compared to the scaling functions describing crossover of the cumulants of the avalanche size, obtained as statistics of the first return area under the time space trajectory of the Vasicek random process.

scholarly journals Highlights from NA61/SHINE: Proton Intermittency Analysis

Universe ◽  
2019 ◽  
Vol 5 (5) ◽  
pp. 103
Author(s):  
Daria Prokhorova ◽  
Nikolaos Davis
Keyword(s):  
Critical Point ◽  
Power Law ◽  
Bootstrap Method ◽  
Critical Index ◽  
Universality Class ◽  
System Size ◽  
Density Fluctuations ◽  
Proton Density ◽  
Factorial Moments ◽  
Intermittent Behavior

The NA61/SHINE experiment at CERN SPS searches for the critical point of strongly interacting matter via scanning the phase diagram by changing beam momenta (13A–150A GeV/c) and system size (p + p, p + Pb, Be + Be, Ar + Sc, Xe + La). An observation of local proton-density fluctuations that scale as a power law of the appropriate universality class as a function of phase space bin size would signal the approach of the system to the vicinity of the possible critical point. An investigation of this phenomenon was performed in terms of the second-scaled factorial moments (SSFMs) of proton density in transverse momentum space with subtraction of a noncritical background. New NA61/SHINE preliminary analysis of Ar + Sc data at 150A GeV/c revealed a nontrivial intermittent behavior of proton moments. A similar effect was observed by NA49 in “Si” + Si data at 158A GeV/c. At the same time, no intermittency signal was detected in “C” + C and Pb + Pb events by NA49, as well as in Be + Be collisions by NA61/SHINE. EPOS1.99 also fails to describe the power-law scaling of SSFMs in Ar + Sc. Qualitatively, the effect is more pronounced with the increase of collision-peripherality and proton-purity thresholds, but a quantitative estimate is to be properly done via power-law exponent fit using the bootstrap method and compared to intermittency critical index ϕ 2 , derived from 3D-Ising effective action.

scholarly journals Entanglement marginal problems

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 589
Author(s):  
Miguel Navascués ◽  
Flavio Baccari ◽  
Antonio Acín
Keyword(s):  
Quantum State ◽  
System Size ◽  
Separable Extension ◽  
Translation Invariant ◽  
Time Space ◽  
Marginal Problem ◽  
Spatial Dimensions ◽  
A Chain ◽  
Reduced Density ◽  
Star Configuration

We consider the entanglement marginal problem, which consists of deciding whether a number of reduced density matrices are compatible with an overall separable quantum state. To tackle this problem, we propose hierarchies of semidefinite programming relaxations of the set of quantum state marginals admitting a fully separable extension. We connect the completeness of each hierarchy to the resolution of an analog classical marginal problem and thus identify relevant experimental situations where the hierarchies are complete. For finitely many parties on a star configuration or a chain, we find that we can achieve an arbitrarily good approximation to the set of nearest-neighbour marginals of separable states with a time (space) complexity polynomial (linear) on the system size. Our results even extend to infinite systems, such as translation-invariant systems in 1D, as well as higher spatial dimensions with extra symmetries.

scholarly journals Critical flow and dissipation in a quasi–one-dimensional superfluid

2015 ◽  
Vol 1 (4) ◽  
pp. e1400222 ◽  
Author(s):  
Pierre-François Duc ◽  
Michel Savard ◽  
Matei Petrescu ◽  
Bernd Rosenow ◽  
Adrian Del Maestro ◽  
...  
Keyword(s):  
Power Law ◽  
Capillary Flow ◽  
Three Dimensional ◽  
Universality Class ◽  
Superfluid State ◽  
One Dimensional ◽  
Flow Experiment ◽  
20 Nm ◽  
Bulk Behavior ◽  
Superfluid Velocity

In one of the most celebrated examples of the theory of universal critical phenomena, the phase transition to the superfluid state of 4He belongs to the same three-dimensional (3D) O(2) universality class as the onset of ferromagnetism in a lattice of classical spins with XY symmetry. Below the transition, the superfluid density ρs and superfluid velocity vs increase as a power law of temperature described by a universal critical exponent that is constrained to be identical by scale invariance. As the dimensionality is reduced toward 1D, it is expected that enhanced thermal and quantum fluctuations preclude long-range order, thereby inhibiting superfluidity. We have measured the flow rate of liquid helium and deduced its superfluid velocity in a capillary flow experiment occurring in single 30-nm-long nanopores with radii ranging down from 20 to 3 nm. As the pore size is reduced toward the 1D limit, we observe the following: (i) a suppression of the pressure dependence of the superfluid velocity; (ii) a temperature dependence of vs that surprisingly can be well-fitted by a power law with a single exponent over a broad range of temperatures; and (iii) decreasing critical velocities as a function of decreasing radius for channel sizes below R ≃ 20 nm, in stark contrast with what is observed in micrometer-sized channels. We interpret these deviations from bulk behavior as signaling the crossover to a quasi-1D state, whereby the size of a critical topological defect is cut off by the channel radius.

NEW UNIVERSALITY CLASS OF IMPACT FRAGMENTATION

Fractals ◽  
2003 ◽  
Vol 11 (04) ◽  
pp. 369-376 ◽  
Author(s):  
HAJIME INAOKA ◽  
MAREKAZU OHNO
Keyword(s):  
Size Distribution ◽  
Power Law ◽  
Fragment Size ◽  
Universality Class ◽  
Fragment Size Distribution ◽  
Space Filling ◽  
Impact Fragmentation

We conducted a set of experiments of impact fragmentation of samples with voids, such as pumice stones and bricks. We discovered that the fragment size distribution follows a power law, but that the exponent of the distribution is different from that of the distribution by the fragmentation of a space-filling sample like a gypsum ball. The value of the exponent is about 0.9. And the value seems universal for samples with voids.

scholarly journals Three-dimensional universality class of the Ising model with power-law correlated critical disorder

2019 ◽  
Vol 100 (14) ◽  
Author(s):  
Wenlong Wang ◽  
Hannes Meier ◽  
Jack Lidmar ◽  
Mats Wallin
Keyword(s):  
Ising Model ◽  
Power Law ◽  
Three Dimensional ◽  
Universality Class

Critical exponents and the universality class of a minesweeper percolation model

2020 ◽  
Vol 31 (09) ◽  
pp. 2050129
Author(s):  
Yuqi Qing ◽  
Wen-Long You ◽  
Maoxin Liu
Keyword(s):  
Phase Transition ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Critical Exponents ◽  
Critical Density ◽  
Universality Class ◽  
Percolation Model ◽  
System Configuration ◽  
Percolation Transition ◽  
Second Order Phase Transition

We introduce a minesweeper percolation model, in which the system configuration is obtained via an automatic minesweeper process. For a variety of candidate networks with different lattice configurations, our process gives rise to a second-order phase transition. Using Monte Carlo simulation, we identify the critical points implied by giant components. A set of critical exponents are extracted to characterize the nature of the minesweeper percolation transition. The determined universality class shows a clear difference from the traditional percolation transition. A proper mine density of the minesweeper game should be set around the critical density.

EXTREME FLUCTUATIONS IN SMALL-WORLD-COUPLED AUTONOMOUS SYSTEMS WITH RELAXATIONAL DYNAMICS

2005 ◽  
Vol 05 (01) ◽  
pp. L43-L62 ◽  
Author(s):  
H. GUCLU ◽  
G. KORNISS
Keyword(s):  
Power Law ◽  
Fundamental Problem ◽  
Discrete Event ◽  
Autonomous Systems ◽  
Small World ◽  
System Size ◽  
Discrete Event Simulations ◽  
Synchronization Problem ◽  
Parallel Discrete Event ◽  
Average Size

Synchronization is a fundamental problem in natural and artificial coupled multi-component systems. We investigate to what extent small-world couplings (extending the original local relaxational dynamics through the random links) lead to the suppression of extreme fluctuations in the synchronization landscape of such systems. In the absence of the random links, the steady-state landscape is "rough" (strongly de-synchronized state) and the average and the extreme height fluctuations diverge in the same power-law fashion with the system size (number of nodes). With small-world links present, the average size of the fluctuations becomes finite (synchronized state). For exponential-like noise the extreme heights diverge only logarithmically with the number of nodes, while for power-law noise they diverge in a power-law fashion. The statistics of the extreme heights are governed by the Fisher–Tippett–Gumbel and the Fréchet distribution, respectively. We illustrate our findings through an actual synchronization problem in parallel discrete-event simulations.

scholarly journals UNIVERSAL SCALING BEHAVIOR OF NON-EQUILIBRIUM PHASE TRANSITIONS

2004 ◽  
Vol 18 (31n32) ◽  
pp. 3977-4118 ◽  
Author(s):  
SVEN LÜBECK
Keyword(s):  
Renormalization Group ◽  
Phase Transitions ◽  
Critical Phenomena ◽  
Equilibrium Phase ◽  
Finite Size ◽  
Universality Class ◽  
Scaling Functions ◽  
Universal Scaling ◽  
Universality Classes ◽  
Non Equilibrium

Non-equilibrium critical phenomena have attracted a lot of research interest in the recent decades. Similar to equilibrium critical phenomena, the concept of universality remains the major tool to order the great variety of non-equilibrium phase transitions systematically. All systems belonging to a given universality class share the same set of critical exponents, and certain scaling functions become identical near the critical point. It is known that the scaling functions vary more widely between different universality classes than the exponents. Thus, universal scaling functions offer a sensitive and accurate test for a system's universality class. On the other hand, universal scaling functions demonstrate the robustness of a given universality class impressively. Unfortunately, most studies focus on the determination of the critical exponents, neglecting the universal scaling functions. In this work a particular class of non-equilibrium critical phenomena is considered, the so-called absorbing phase transitions. Absorbing phase transitions are expected to occur in physical, chemical as well as biological systems, and a detailed introduction is presented. The universal scaling behavior of two different universality classes is analyzed in detail, namely the directed percolation and the Manna universality class. Especially, directed percolation is the most common universality class of absorbing phase transitions. The presented picture gallery of universal scaling functions includes steady state, dynamical as well as finite size scaling functions. In particular, the effect of an external field conjugated to the order parameter is investigated. Incorporating the conjugated field, it is possible to determine the equation of state, the susceptibility, and to perform a modified finite-size scaling analysis appropriate for absorbing phase transitions. Focusing on these equations, the obtained results can be applied to other non-equilibrium continuous phase transitions observed in numerical simulations or experiments. Thus, we think that the presented picture gallery of universal scaling functions is valuable for future work. Additionally to the manifestation of universality classes, universal scaling functions are useful in order to check renormalization group results quantitatively. Since the renormalization group theory is the basis of our understanding of critical phenomena, it is of fundamental interest to examine the accuracy of the obtained results. Due to the continuing improvement of computer hardware, accurate numerical data have become available, resulting in a fruitful interplay between numerical investigations and renormalization group analyzes.

Creep rupture due to thermally induced cracking

2013 ◽  
Vol 1535 ◽  
Author(s):  
Naoki Yoshioka ◽  
Ferenc Kun ◽  
Nobuyasu Ito
Keyword(s):  
Power Law ◽  
Crack Nucleation ◽  
Waiting Times ◽  
System Size ◽  
Thermal Fluctuations ◽  
Average Lifetime ◽  
Thermally Induced ◽  
Thermally Activated ◽  
Structural Entropy ◽  
Stochastic Time Series

ABSTRACTWe study sub-critical fracture driven by thermally activated crack nucleation in the framework of a fiber bundle model. Based on analytic calculations and computer simulations we show that in the presence of stress inhomogeneities, thermally activated cracking results in an anomalous size effect, i.e. the average lifetime of the system decreases as a power law of the system size, where the exponent depends on the external load and on the temperature. We propose a modified form of the Arrhenius law which provides a comprehensive description of the load, temperature, and size dependence of the lifetime of the system. On the micro-level, thermal fluctuations trigger bursts of breaking events which form a stochastic time series as the system evolves towards failure. Numerical and analytical calculations revealed that both the size of bursts and the waiting times between consecutive events have power law distributions, however, the exponents depend on the load and temperature. Analyzing the structural entropy and the location of consecutive bursts we show that in the presence of stress concentration the acceleration of the rupture process close to failure is the consequence of damage localization.

scholarly journals Symmetry in Self-Similarity in Space and Time—Short Time Transients and Power-Law Spatial Asymptotes

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1489
Author(s):  
Ken Sekimoto ◽  
Takahiko Fujita
Keyword(s):  
Power Law ◽  
Late Stage ◽  
Scaling Function ◽  
Early Stage ◽  
The Self ◽  
Scaling Functions ◽  
Self Similarity ◽  
Simple Diffusion ◽  
Early Stages ◽  
Space And Time

The self-similarity in space and time (hereafter self-similarity), either deterministic or statistical, is characterized by similarity exponents and a function of scaled variable, called the scaling function. In the present paper, we address mainly the self-similarity in the limit of early stage, as opposed to the latter one, and also consider the scaling functions that decay or grow algebraically, as opposed to the rapidly decaying functions such as Gaussian or error function. In particular, in the case of simple diffusion, our symmetry analysis shows a mathematical mechanism by which the rapidly decaying scaling functions are generated by other polynomial scaling functions. While the former is adapted to the self-similarity in the late-stage processes, the latter is adapted to the early stages. This paper sheds some light on the internal structure of the family of self-similarities generated by a simple diffusion equation. Then, we present an example of self-similarity for the late stage whose scaling function has power-law tail, and also several cases of self-similarity for the early stages. These examples show the utility of self-similarity to a wider range of phenomena other than the late stage behaviors with rapidly decaying scaling functions.

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