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

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.

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

Scientific Reports ◽

10.1038/s41598-021-98959-w ◽

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.

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CRITICAL BEHAVIOR OF AN EPIDEMIC MODEL OF DRUG RESISTANT DISEASES

International Journal of Modern Physics C ◽

10.1142/s0129183104006704 ◽

2004 ◽

Vol 15 (09) ◽

pp. 1279-1290 ◽

Cited By ~ 5

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.

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CRITICAL BEHAVIOR OF NONEQUILIBRIUM MODELS WITH INFINITELY MANY ABSORBING STATES

International Journal of Modern Physics B ◽

10.1142/s021797929400138x ◽

1994 ◽

Vol 08 (23) ◽

pp. 3299-3311 ◽

Cited By ~ 13

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.

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NONEQUILIBRIUM PHASE TRANSITIONS IN CATALYSIS AND POPULATION MODELS

International Journal of Modern Physics C ◽

10.1142/s0129183193000288 ◽

1993 ◽

Vol 04 (02) ◽

pp. 271-277 ◽

Cited By ~ 22

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.

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EFFECT OF FIELD DIRECTION AND FIELD INTENSITY ON DIRECTED SPIRAL PERCOLATION

International Journal of Modern Physics C ◽

10.1142/s0129183106009072 ◽

2006 ◽

Vol 17 (09) ◽

pp. 1285-1302 ◽

Cited By ~ 1

Author(s):

SANTANU SINHA ◽

S. B. SANTRA

Keyword(s):

Phase Diagram ◽

Critical Behavior ◽

Disordered Systems ◽

Universality Class ◽

Two Dimensions ◽

Percolation Model ◽

Field Direction ◽

Critical Properties ◽

External Bias ◽

Directional Field

Directed spiral percolation (DSP) is a new percolation model with crossed external bias fields. Since percolation is a model of disorder, the effect of external bias fields on the properties of disordered systems can be studied numerically using DSP. In DSP, the bias fields are an in-plane directional field (E) and a field of rotational nature (B) applied perpendicular to the plane of the lattice. The critical properties of DSP clusters are studied here varying the direction of E field and intensities of both E and B fields in two-dimensions. The system shows interesting and unusual critical behavior at the percolation threshold. Not only the DSP model is found to belong in a new universality class compared to that of other percolation models but also the universality class remains invariant under the variation of E field direction. Varying the intensities of the E and B fields, a crossover from DSP to other percolation models has been studied. A phase diagram of the percolation models is obtained as a function of intensities of the bias fields E and B.

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

Science Advances ◽

10.1126/sciadv.1400222 ◽

2015 ◽

Vol 1 (4) ◽

pp. e1400222 ◽

Cited By ~ 12

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.

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NEW UNIVERSALITY CLASS OF IMPACT FRAGMENTATION

Fractals ◽

10.1142/s0218348x0300221x ◽

2003 ◽

Vol 11 (04) ◽

pp. 369-376 ◽

Cited By ~ 7

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.

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