scholarly journals Critical behavior of density-driven and shear-driven reversible–irreversible transitions in cyclically sheared vortices

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
S. Maegochi ◽  
K. Ienaga ◽  
S. Okuma
Keyword(s):  
Power Law ◽  
Critical Behavior ◽  
Particle Density ◽  
Universality Class ◽  
Time Dependent ◽  
Directed Percolation ◽  
Two Dimensional ◽  
Significant Drop ◽  
Cyclic Shear ◽  
Vortex Density

AbstractRandom assemblies of particles subjected to cyclic shear undergo a reversible–irreversible transition (RIT) with increasing a shear amplitude d or particle density n, while the latter type of RIT has not been verified experimentally. Here, we measure the time-dependent velocity of cyclically sheared vortices and observe the critical behavior of RIT driven by vortex density B as well as d. At the critical point of each RIT, $$B_{\mathrm {c}}$$ B c and $$d_{\mathrm {c}}$$ d c , the relaxation time $$\tau $$ τ to reach the steady state shows a power-law divergence. The critical exponent for B-driven RIT is in agreement with that for d-driven RIT and both types of RIT fall into the same universality class as the absorbing transition in the two-dimensional directed-percolation universality class. As d is decreased to the average intervortex spacing in the reversible regime, $$\tau (d)$$ τ ( d ) shows a significant drop, indicating a transition or crossover from a loop-reversible state with vortex-vortex collisions to a collisionless point-reversible state. In either regime, $$\tau (d)$$ τ ( d ) exhibits a power-law divergence at the same $$d_{\mathrm {c}}$$ d c with nearly the same exponent.

scholarly journals Critical behavior near the reversible-irreversible transition in periodically driven vortices under random local shear

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
S. Maegochi ◽  
K. Ienaga ◽  
S. Kaneko ◽  
S. Okuma
Keyword(s):  
Power Law ◽  
Critical Behavior ◽  
Amorphous Film ◽  
Universality Class ◽  
Initial Position ◽  
Directed Percolation ◽  
General Phenomenon ◽  
Periodically Driven ◽  
Local Shear ◽  
Absorbing Phase Transition

Abstract When many-particle (vortex) assemblies with disordered distribution are subjected to a periodic shear with a small amplitude $${\boldsymbol{d}}$$ d , the particles gradually self-organize to avoid next collisions and transform into an organized configuration. We can detect it from the time-dependent voltage $${\boldsymbol{V}}{\boldsymbol{(}}{\boldsymbol{t}}{\boldsymbol{)}}$$ V ( t ) (average velocity) that increases towards a steady-state value. For small $${\boldsymbol{d}}$$ d , the particles settle into a reversible state where all the particles return to their initial position after each shear cycle, while they reach an irreversible state for $${\boldsymbol{d}}$$ d above a threshold $${{\boldsymbol{d}}}_{{\boldsymbol{c}}}$$ d c . Here, we investigate the general phenomenon of a reversible-irreversible transition (RIT) using periodically driven vortices in a strip-shaped amorphous film with random pinning that causes local shear, as a function of $${\boldsymbol{d}}$$ d . By measuring $${\boldsymbol{V}}{\boldsymbol{(}}{\boldsymbol{t}}{\boldsymbol{)}}$$ V ( t ) , we observe a critical behavior of RIT, not only on the irreversible side, but also on the reversible side of the transition, which is the first under random local shear. The relaxation time $${\boldsymbol{\tau }}{\boldsymbol{(}}{\boldsymbol{d}}{\boldsymbol{)}}$$ τ ( d ) to reach either the reversible or irreversible state shows a power-law divergence at $${{\boldsymbol{d}}}_{{\boldsymbol{c}}}$$ d c . The critical exponent is determined with higher accuracy and is, within errors, in agreement with the value expected for an absorbing phase transition in the two-dimensional directed-percolation universality class. As $${\boldsymbol{d}}$$ d is decreased down to the intervortex spacing in the reversible regime, $${\boldsymbol{\tau }}{\boldsymbol{(}}{\boldsymbol{d}}{\boldsymbol{)}}$$ τ ( d ) deviates downward from the power-law relation, reflecting the suppression of intervortex collisions. We also suggest the possibility of a narrow smectic-flow regime, which is predicted to intervene between fully reversible and irreversible flow.

scholarly journals CRITICAL BEHAVIOR OF NONEQUILIBRIUM MODELS WITH INFINITELY MANY ABSORBING STATES

1994 ◽  
Vol 08 (23) ◽  
pp. 3299-3311 ◽  
Author(s):  
IWAN JENSEN
Keyword(s):  
Heterogeneous Catalysis ◽  
Critical Behavior ◽  
Critical Exponents ◽  
Lattice Model ◽  
Universality Class ◽  
Directed Percolation ◽  
Two Dimensional ◽  
Absorbing States ◽  
Nonequilibrium Models

I study the critical behavior of a two-dimensional dimer-trimer lattice model, introduced by Köhler and ben-Avraham,17a for heterogeneous catalysis of the reaction ½A2 + ⅓B3 → AB. The model possesses infinitely many absorbing states in which the lattice is saturated by adsorbed particles and reactions cease because only isolated vacancies are left. Results for various critical exponents show that the model exhibits the same critical behavior as directed percolation, contrary to earlier findings by Köhler and ben-Avraham. Together with several other studies, reviewed briefly in this article, this confirms that directed percolation is the generic universality class for models with infinitely many absorbing states.

CRITICAL BEHAVIOR OF A FOUR-STATE IRREVERSIBLE MODEL WITH POTTS SYMMETRY

1999 ◽  
Vol 13 (14) ◽  
pp. 471-477 ◽  
Author(s):  
A. BRUNSTEIN ◽  
T. TOMÉ
Keyword(s):  
Monte Carlo ◽  
Phase Transitions ◽  
Critical Behavior ◽  
Potts Model ◽  
Present Model ◽  
Universality Class ◽  
Two Dimensional ◽  
Dynamical Phase ◽  
Dynamical Phase Transitions ◽  
Symmetry Operations

We analyze the critical behavior of a two-dimensional irreversible cellular automaton whose dynamic rules are invariant under the same symmetry operations as those of the three-state Potts model. We study the dynamical phase transitions that take place in the model and obtain the static and dynamical critical exponents through Monte Carlo simulations. Our results indicate that the present model is in the same universality class as the three-state Potts model.

scholarly journals CRITICAL BEHAVIOR OF AN EPIDEMIC MODEL OF DRUG RESISTANT DISEASES

2004 ◽  
Vol 15 (09) ◽  
pp. 1279-1290 ◽  
Author(s):  
C. R. DA SILVA ◽  
U. L. FULCO ◽  
M. L. LYRA ◽  
G. M. VISWANATHAN
Keyword(s):  
Critical Behavior ◽  
Finite Size ◽  
Universality Class ◽  
Active Phase ◽  
Propagation Model ◽  
Mutation Rates ◽  
Scaling Analysis ◽  
Directed Percolation ◽  
Drug Resistant ◽  
Finite Size Scaling

In this work, we study the critical behavior of an epidemic propagation model that considers individuals that can develop drug resistance. In our lattice model, each site can be found in one of the four states: empty, healthy, normally infected (not drug resistant) and strain infected (drug resistant) states. The most relevant parameters in our model are related to the mortality, cure and mutation rates. This model presents two distinct stationary active phases: a phase with co-existing normal and drug resistant infected individuals, and an intermediate active phase with only drug resistant individuals. We employed a finite-size scaling analysis to compute the critical points and the critical exponents, β/ν and 1/ν, governing the phase transitions between these active states and the absorbing inactive state. Our results are consistent with the hypothesis that these transitions belong to the directed percolation universality class.

NONEQUILIBRIUM PHASE TRANSITIONS IN CATALYSIS AND POPULATION MODELS

1993 ◽  
Vol 04 (02) ◽  
pp. 271-277 ◽  
Author(s):  
RONALD DICKMAN
Keyword(s):  
Phase Transitions ◽  
Chemical Reactions ◽  
Critical Behavior ◽  
Universality Class ◽  
Population Models ◽  
Directed Percolation ◽  
Nonequilibrium Phase Transitions ◽  
Absorbing State ◽  
Surface Catalysis ◽  
Far From Equilibrium

A wide variety of far-from-equilibrium models, arising in fields such as surface catalysis, autocatalytic chemical reactions, and epidemic or population models, exhibit phase transitions into an absorbing state. When continuous, these transitions typically belong to the universality class of directed percolation, but unusual phase diagrams and new kinds of critical behavior have also been identified.

scholarly journals Integrable unsteady motion with an application to ocean eddies

1998 ◽  
Vol 5 (3) ◽  
pp. 145-151
Author(s):  
A. D. Kirwan, Jr. ◽  
B. L. Lipphardt, Jr.
Keyword(s):  
Potential Vorticity ◽  
Particle Motion ◽  
Gulf Stream ◽  
Incompressible Flows ◽  
Unsteady Motion ◽  
Ring System ◽  
Time Dependent ◽  
Two Dimensional ◽  
Ocean Eddies ◽  
Multilayered Systems

Abstract. Application of the Brown-Samelson theorem, which shows that particle motion is integrable in a class of vorticity-conserving, two-dimensional incompressible flows, is extended here to a class of explicit time dependent dynamically balanced flows in multilayered systems. Particle motion for nonsteady two-dimensional flows with discontinuities in the vorticity or potential vorticity fields (modon solutions) is shown to be integrable. An example of a two-layer modon solution constrained by observations of a Gulf Stream ring system is discussed.

scholarly journals Universality class of the motility-induced critical point in large scale off-lattice simulations of active particles.

Soft Matter ◽  
2021 ◽  
Author(s):  
Claudio Maggi ◽  
Matteo Paoluzzi ◽  
Andrea Crisanti ◽  
Emanuela Zaccarelli ◽  
Nicoletta Gnan
Keyword(s):  
Phase Separation ◽  
Critical Point ◽  
Computer Simulations ◽  
Large Scale ◽  
Universality Class ◽  
Critical Behaviour ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Active Particles ◽  
Two Dimensional Model

We perform large-scale computer simulations of an off-lattice two-dimensional model of active particles undergoing a motility-induced phase separation (MIPS) to investigate the systems critical behaviour close to the critical point...

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