scholarly journals Sharpness of the Phase Transition for the Orthant Model

2021 ◽  
Vol 24 (4) ◽  
Author(s):  
Thomas Beekenkamp
Keyword(s):  
Phase Transition ◽  
Random Walk ◽  
Critical Value ◽  
Percolation Model ◽  
Critical Threshold ◽  
Directed Percolation ◽  
Sharp Threshold ◽  
Shape Theorem ◽  
Exponentially Small

AbstractThe orthant model is a directed percolation model on $\mathbb {Z}^{d}$ ℤ d , in which all clusters are infinite. We prove a sharp threshold result for this model: if p is larger than the critical value above which the cluster of 0 is contained in a cone, then the shift from 0 that is required to contain the cluster of 0 in that cone is exponentially small. As a consequence, above this critical threshold, a shape theorem holds for the cluster of 0, as well as ballisticity of the random walk on this cluster.

The flattening phase transition in systems of trapped ions

2009 ◽  
Vol 87 (10) ◽  
pp. 1425-1435 ◽  
Author(s):  
Taunia L. L. Closson ◽  
Marc R. Roussel
Keyword(s):  
Phase Transition ◽  
Critical Exponent ◽  
Order Parameter ◽  
Ion Trap ◽  
Anisotropy Parameter ◽  
Critical Value ◽  
Trapped Ions ◽  
Dimensional Structure ◽  
Flattening Process ◽  
Second Order Phase Transition

When the anisotropy of a harmonic ion trap is increased, the ions eventually collapse into a two-dimensional structure consisting of concentric shells of ions. This collapse generally behaves like a second-order phase transition. A graph of the critical value of the anisotropy parameter vs. the number of ions displays substructure closely related to the inner-shell configurations of the clusters. The critical exponent for the order parameter of this phase transition (maximum extent in the z direction) was found computationally to have the value β = 1/2. A second critical exponent related to displacements perpendicular to the z axis was found to have the value δ = 1. Using these estimates of the critical exponents, we derive an equation that relates the amplitudes of the displacements of the ions parallel to the x–y plane to the amplitudes along the z axis during the flattening process.

Laser-Induced Pretransitional Ordering And Nonlinear Optical Properties Of Rigid-Rod Polymer Suspensions

1993 ◽  
Vol 328 ◽  
Author(s):  
Boris E. Vugmeister ◽  
Michelle S. Malcuit ◽  
John C. Kralik ◽  
Colleen Stevens
Keyword(s):  
Phase Transition ◽  
Colloidal Particles ◽  
Volume Fraction ◽  
Orientational Order ◽  
Critical Value ◽  
Orientational Relaxation ◽  
First Order ◽  
First Order Phase Transition ◽  
Rigid Rod ◽  
First Order Phase

ABSTRACTWe investigate the pretransitional behavior in laser-induced alignment of rigid rod-like polytetraflouroethylene (PTFE) suspensions. Using a laser-induced birefringence experiment, we measure both the orientational order parameter and the orientational relaxation time. We find that both increase as the volume fraction of colloidal particles approaches the critical value for the isotropic-nematic phase transition. Experimental results are compared with theory which takes into account the possibility of a first-order phase transition induced by a laser electric field.

Nonequilibrium Phenomena in Globally Coupled Phase Oscillators: Noise-Induced Bifurcations, Clustering, and Switching

1997 ◽  
Vol 07 (04) ◽  
pp. 917-922
Author(s):  
Seon Hee Park ◽  
Seunghwan Kim ◽  
Seung Kee Han
Keyword(s):  
Phase Transition ◽  
Noise Intensity ◽  
Multiplicative Noise ◽  
Additive Noise ◽  
Critical Value ◽  
Phase Oscillators ◽  
Deterministic Systems ◽  
Nonequilibrium Phenomena ◽  
Noise Models ◽  
Coupled Phase Oscillators

The Nonequilibrium phenomena in a class of globally coupled phase oscillators systems with multiplicative noise are studied. It is shown that at the critical value of the noise intensity the systems undergo a phase transition and converge to clustered states. We also show that the time delay in the interaction between oscillators gives rise to the switching phenomena of clusters. These phenomena are noise-induced effects which cannot be seen in the deterministic systems or in the simple additive noise models.

scholarly journals A phase transition in the random transposition random walk

2005 ◽  
Vol 136 (2) ◽  
pp. 203-233 ◽  
Author(s):  
Nathanaël Berestycki ◽  
Rick Durrett
Keyword(s):  
Phase Transition ◽  
Random Walk ◽  
Random Transposition

scholarly journals ANALYTIC STUDY OF FIRST-ORDER PHASE TRANSITION IN HOLOGRAPHIC SUPERCONDUCTOR AND SUPERFLUID

2013 ◽  
Vol 28 (28) ◽  
pp. 1350140 ◽  
Author(s):  
WUNG-HONG HUANG
Keyword(s):  
Phase Transition ◽  
Order Phase Transition ◽  
Critical Value ◽  
Analytic Study ◽  
Matching Method ◽  
Holographic Superconductor ◽  
First Order ◽  
Numerical Result ◽  
First Order Phase Transition ◽  
First Order Phase

We use the matching method to investigate the first-order phase transition in holographic superconductor and superfluid. We first use the simple holographic superconductor model to describe the matching method and mention how to see the first-order phase transition. Next, we study the holographic superconductor with Stückelberg term and see that the analytic results indicate the existence of first-order phase transition. Finally, we study the holographic superfluid and show that the first-order phase transition can be found for some values of parameters. We determine the critical value analytically and compare it with the previous numerical result.

Random-walk model of the phase transition of hydrocarbon chains on a lattice

1981 ◽  
Vol 23 (2) ◽  
pp. 897-907 ◽  
Author(s):  
Sofia D. Merajver ◽  
Ellen D. Yorke ◽  
Andrew G. De Rocco
Keyword(s):  
Phase Transition ◽  
Random Walk ◽  
Random Walk Model ◽  
Hydrocarbon Chains

Formation of Periodic Ripples in a Surface Skin

1977 ◽  
Vol 32 (1) ◽  
pp. 33-39
Author(s):  
Fred Fischer
Keyword(s):  
Phase Transition ◽  
Order Parameter ◽  
Liquid Surface ◽  
Compressive Strain ◽  
Critical Value ◽  
Skin Thickness ◽  
Skin Area ◽  
Ripple Formation ◽  
Elastic Skin ◽  
Second Order Phase Transition

Abstract A solid elastic skin on a liquid surface aquires a periodic ripple formation when a compressive strain surpasses a critical value. From a calculation the ripple wavelength is found to be proportional to the 3/4th power of the skin thickness. This instability can be described as a kind of second order phase transition, where a relative amplitude of the ripple wave is the order parameter. In addition, when the skin area is abruptly compressed the ripple wavelength depends on the magnitude of the compressive strain. Examples for skin rippling with wavelengths between 10 μm and 100 m are discussed.

scholarly journals Type Transition of Simple Random Walks on Randomly Directed Regular Lattices

2014 ◽  
Vol 51 (4) ◽  
pp. 1065-1080 ◽  
Author(s):  
Massimo Campanino ◽  
Dimitri Petritis
Keyword(s):  
Random Walk ◽  
Periodic Function ◽  
Random Walks ◽  
Power Law ◽  
Random Perturbation ◽  
Simple Random Walk ◽  
Critical Value ◽  
Absolute Value ◽  
Horizontal Orientation ◽  
Regular Lattices

Simple random walks on a partially directed version ofZ2are considered. More precisely, vertical edges between neighbouring vertices ofZ2can be traversed in both directions (they are undirected) while horizontal edges are one-way. The horizontal orientation is prescribed by a random perturbation of a periodic function; the perturbation probability decays according to a power law in the absolute value of the ordinate. We study the type of simple random walk that is recurrent or transient, and show that there exists a critical value of the decay power, above which it is almost surely recurrent and below which it is almost surely transient.

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