Exponential rate for the contact process extinction time

In this paper we prove lower and upper bounds for the extinction time of the contact process on random geometric graphs with connection radius tending to infinity. We obtain that for any infection rate λ > 0, the contact process on these graphs survives a time super-exponential in the number of vertices.

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The extinction time of a general birth and death process with catastrophes

Journal of Applied Probability ◽

10.1017/s0021900200116031 ◽

1986 ◽

Vol 23 (04) ◽

pp. 851-858 ◽

Cited By ~ 1

Author(s):

P. J. Brockwell

Keyword(s):

Laplace Transform ◽

Size Distribution ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Death Process ◽

Extinction Time ◽

Birth And Death Process ◽

Different Types ◽

The Laplace Transform ◽

Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

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ChemInform Abstract: DEACTIVATION BEHAVIOR OF ARENES AND HETEROARENES. XIII. EXTINCTION TIME BEHAVIOR IN PHOTODIMERIZATION

Chemischer Informationsdienst ◽

10.1002/chin.198001138 ◽

1980 ◽

Vol 11 (1) ◽

Author(s):

J. BENDIG ◽

D. KREYSIG

Keyword(s):

Time Behavior ◽

Extinction Time

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Emergence of disconnected clusters in heterogeneous complex systems

Scientific Reports ◽

10.1038/s41598-020-78769-2 ◽

2020 ◽

Vol 10 (1) ◽

Author(s):

István A. Kovács ◽

Róbert Juhász

Keyword(s):

Complex Systems ◽

Percolation Theory ◽

Contact Process ◽

Heterogeneous Systems ◽

Critical Dynamics ◽

Magnetic Domains ◽

3 Dimensional ◽

Quantum Ising Model ◽

Highly Correlated ◽

Exact Renormalization Group

AbstractPercolation theory dictates an intuitive picture depicting correlated regions in complex systems as densely connected clusters. While this picture might be adequate at small scales and apart from criticality, we show that highly correlated sites in complex systems can be inherently disconnected. This finding indicates a counter-intuitive organization of dynamical correlations, where functional similarity decouples from physical connectivity. We illustrate the phenomenon on the example of the disordered contact process (DCP) of infection spreading in heterogeneous systems. We apply numerical simulations and an asymptotically exact renormalization group technique (SDRG) in 1, 2 and 3 dimensional systems as well as in two-dimensional lattices with long-ranged interactions. We conclude that the critical dynamics is well captured by mostly one, highly correlated, but spatially disconnected cluster. Our findings indicate that at criticality the relevant, simultaneously infected sites typically do not directly interact with each other. Due to the similarity of the SDRG equations, our results hold also for the critical behavior of the disordered quantum Ising model, leading to quantum correlated, yet spatially disconnected, magnetic domains.

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Functional Inequalities for Two-Level Concentration

Potential Analysis ◽

10.1007/s11118-021-09900-9 ◽

2021 ◽

Author(s):

Franck Barthe ◽

Michał Strzelecki

Keyword(s):

Sobolev Inequality ◽

Poincaré Inequality ◽

Logarithmic Sobolev Inequality ◽

Probability Measures ◽

Exponential Rate ◽

Functional Inequalities ◽

Concentration Inequality ◽

Poincare Inequality ◽

Free Concentration ◽

Concentration Property

AbstractProbability measures satisfying a Poincaré inequality are known to enjoy a dimension-free concentration inequality with exponential rate. A celebrated result of Bobkov and Ledoux shows that a Poincaré inequality automatically implies a modified logarithmic Sobolev inequality. As a consequence the Poincaré inequality ensures a stronger dimension-free concentration property, known as two-level concentration. We show that a similar phenomenon occurs for the Latała–Oleszkiewicz inequalities, which were devised to uncover dimension-free concentration with rate between exponential and Gaussian. Motivated by the search for counterexamples to related questions, we also develop analytic techniques to study functional inequalities for probability measures on the line with wild potentials.

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Self‐aligned contact process for Nb/Al‐AlOx/Nb Josephson junctions

Applied Physics Letters ◽

10.1063/1.96573 ◽

1986 ◽

Vol 48 (3) ◽

pp. 254-256 ◽

Cited By ~ 37

Author(s):

Shin’ichi Morohashi ◽

Shinya Hasuo ◽

Toyoshi Yamaoka

Keyword(s):

Josephson Junctions ◽

Contact Process

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Experimental Investigation of the Effects of Irradiating Schemes in Laser Tube Bending Process

Metals ◽

10.3390/met11071123 ◽

2021 ◽

Vol 11 (7) ◽

pp. 1123

Author(s):

Mehdi Safari ◽

Ricardo J. Alves de Sousa ◽

Jalal Joudaki

Keyword(s):

Laser Beam ◽

Contact Process ◽

Steel Tube ◽

Thickness Variation ◽

Tube Bending ◽

Lateral Bending ◽

Bending Angle ◽

Laser Tube ◽

Bending Process ◽

Thickness Variations

The laser tube bending process (LTBP) process is a thermal non-contact process for bending tubes with less springback and less thinning of the tube. In this paper, the laser tube bending process will be studied experimentally. The length of irradiation and irradiation scheme are two main affecting process parameters in the LTBP process. For this purpose, different samples according to two main irradiation schemes (Circular irradiating scheme (CIS) and axial irradiating scheme (AIS)) and different lengths of laser beam irradiation (from 4.7 to 28.2 mm) are fabricated. The main bending angle of laser-bent tube, lateral bending angle, ovality, and thickness variations is measured experimentally, and the effects of the irradiating scheme and the length of irradiation are investigated. An 18 mm diameter, 1 mm thick mild steel tube was bent with 1100 Watts laser beam. The results show that for both irradiating schemes, by increasing the irradiating length of the main and lateral bending angle, the ovality and thickness variation ratio of the bent tube are increased. In addition, for a similar irradiating length, the main bending angle with AIS is considerably higher than CIS. The lateral bending angle by AIS is much less than the lateral bending angle with CIS. The results demonstrate that the ovality percentage and the thickness variation ratio for the laser-bent tube obtained by CIS are much more than the values associated with by AIS laser-bent tube.

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