On the critical infection rate of the one-dimensional basic contact process: numerical results

1988 ◽  
Vol 25 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Herbert Ziezold ◽  
Christian Grillenberger
Keyword(s):  
Markov Process ◽  
Infected Cell ◽  
Infection Rate ◽  
Lower Bounds ◽  
Contact Process ◽  
Critical Value ◽  
Critical Values ◽  
One Dimensional ◽  
The One ◽  
The Right

Instead of the basic contact process on with infection rate λ we consider for m ≧ 0 the Markov process starting with ξ0(k) = 1 for k ≧ 0 and ξ0(k)= 0 for k < 0 and with changing only those k which are at most m places to the right of the left-most infected cell. For m = 0, 1,· ··, 14 direct computations give critical values which are lower bounds for the critical value of the original basic contact process.

On the critical infection rate of the one-dimensional basic contact process: numerical results

1988 ◽  
Vol 25 (01) ◽  
pp. 1-8 ◽  
Author(s):  
Herbert Ziezold ◽  
Christian Grillenberger
Keyword(s):  
Markov Process ◽  
Infected Cell ◽  
Infection Rate ◽  
Lower Bounds ◽  
Contact Process ◽  
Critical Value ◽  
Critical Values ◽  
One Dimensional ◽  
The One ◽  
The Right

Instead of the basic contact process on with infection rate λ we consider for m ≧ 0 the Markov process starting with ξ 0(k) = 1 for k ≧ 0 and ξ 0(k)= 0 for k &lt; 0 and with changing only those k which are at most m places to the right of the left-most infected cell. For m = 0, 1,· ··, 14 direct computations give critical values which are lower bounds for the critical value of the original basic contact process.

CORRELATION IDENTITIES FOR NEAREST-PARTICLE SYSTEMS AND THEIR APPLICATIONS TO ONE-DIMENSIONAL CONTACT PROCESS

1991 ◽  
Vol 05 (02) ◽  
pp. 151-159 ◽  
Author(s):  
NORIO KONNO ◽  
MAKOTO KATORI
Keyword(s):  
Order Parameter ◽  
Particle System ◽  
Contact Process ◽  
Critical Value ◽  
Particle Systems ◽  
Approximation Formula ◽  
One Dimensional ◽  
Renewal Measure ◽  
First Approximation ◽  
The One

A series of identities of correlation functions K(n1, n2, …, nN) are given in the nearest-particle system. The above correlation identities are applied to the one-dimensional contact process. The decoupling induced by a renewal measure yields the first approximation: [Formula: see text] for the critical value and [Formula: see text] for the order parameter, which makes a rigorous bound as proved by Holley and Liggett. Furthermore, introducing a new decoupling procedure, improved estimations of [Formula: see text] and [Formula: see text] are calculated.

scholarly journals Graph Constructions for the Contact Process with a Prescribed Critical Rate

2021 ◽  
Author(s):  
Stein Andreas Bethuelsen ◽  
Gabriel Baptista da Silva ◽  
Daniel Valesin
Keyword(s):  
Contact Process ◽  
Critical Value ◽  
Critical Rate ◽  
Bounded Degree ◽  
One Dimensional ◽  
Local Survival ◽  
The One ◽  
Global And Local

AbstractWe construct graphs (trees of bounded degree) on which the contact process has critical rate (which will be the same for both global and local survival) equal to any prescribed value between zero and $$\lambda _c({\mathbb {Z}})$$ λ c ( Z ) , the critical rate of the one-dimensional contact process. We exhibit both graphs in which the process at this target critical value survives (locally) and graphs where it dies out (globally).

scholarly journals Role of thermal field in entanglement harvesting between two accelerated Unruh-DeWitt detectors

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Dipankar Barman ◽  
Subhajit Barman ◽  
Bibhas Ranjan Majhi
Keyword(s):  
Mutual Information ◽  
Critical Point ◽  
Thermal Field ◽  
Narrow Range ◽  
Critical Value ◽  
Critical Values ◽  
Parallel Motion ◽  
Field Temperature ◽  
The Right

Abstract We investigate the effects of field temperature T(f) on the entanglement harvesting between two uniformly accelerated detectors. For their parallel motion, the thermal nature of fields does not produce any entanglement, and therefore, the outcome is the same as the non-thermal situation. On the contrary, T(f) affects entanglement harvesting when the detectors are in anti-parallel motion, i.e., when detectors A and B are in the right and left Rindler wedges, respectively. While for T(f) = 0 entanglement harvesting is possible for all values of A’s acceleration aA, in the presence of temperature, it is possible only within a narrow range of aA. In (1 + 1) dimensions, the range starts from specific values and extends to infinity, and as we increase T(f), the minimum required value of aA for entanglement harvesting increases. Moreover, above a critical value aA = ac harvesting increases as we increase T(f), which is just opposite to the accelerations below it. There are several critical values in (1 + 3) dimensions when they are in different accelerations. Contrary to the single range in (1 + 1) dimensions, here harvesting is possible within several discrete ranges of aA. Interestingly, for equal accelerations, one has a single critical point, with nature quite similar to (1 + 1) dimensional results. We also discuss the dependence of mutual information among these detectors on aA and T(f).

Large-density fluctuations for the one-dimensional supercritical contact process

1989 ◽  
Vol 55 (3-4) ◽  
pp. 639-648 ◽  
Author(s):  
Antonio Galves ◽  
Fabio Martinelli ◽  
Enzo Olivieri
Keyword(s):  
Contact Process ◽  
Density Fluctuations ◽  
One Dimensional ◽  
Large Density ◽  
The One

Lower Bounds to the Eigenvalues in One-Dimensional Problems by a Shift in the Weight Function

1970 ◽  
Vol 37 (2) ◽  
pp. 267-270 ◽  
Author(s):  
D. Pnueli
Keyword(s):  
Lower Bound ◽  
Weight Function ◽  
Lower Bounds ◽  
Variational Formulation ◽  
Ritz Method ◽  
The Other ◽  
One Dimensional ◽  
Systematic Shift ◽  
The One ◽  
Detailed Computation

A method is presented to obtain both upper and lower bound to eigenvalues when a variational formulation of the problem exists. The method consists of a systematic shift in the weight function. A detailed procedure is offered for one-dimensional problems, which makes improvement of the bounds possible, and which involves the same order of detailed computation as the Rayleigh-Ritz method. The main contribution of this method is that it yields the “other bound;” i.e., the one which cannot be obtained by the Rayleigh-Ritz method.

Hanna Yablonka, Yeladim beseder gamur: biyografiyah dorit shel yelidei haaretz 1948–1955 (Children by the Book, Biography of a Generation: The First Native Israelis Born 1948–1955). Rishon Letziyon: Miskal, 2018. 430 pp.

2021 ◽  
pp. 310-312
Keyword(s):  
Educational System ◽  
Historical Consciousness ◽  
The State ◽  
Historical Experience ◽  
One Dimensional ◽  
The People ◽  
Native Identity ◽  
The One ◽  
State Educational ◽  
The Right

This chapter examines Hanna Yablonka's Children by the Book, Biography of a Generation: The First Native Israelis Born 1948–1955 (2018). This book is unique in that it is neither politically committed to nationalist political slogans that are thrown daily into the arena of Israeli politics in the days of Netanyahu nor connected to the one-dimensional, sweeping condemnation of critics of the Israeli enterprise on the Right and Left. Instead, it suggests to set aside, even if only for a moment, what Yablonka calls “the current Israeli discourse, which furiously shatters everything that has happened in the state since it was established, brutally erasing all the achievements of Little Israel.” Yabonka is guided by Karl Mannheim's concept of a “historical generation”: a group in which there is a shared historical consciousness derived from historical experience. She shows how the state educational system fashioned the image of the new Israeli, endowing children with a local, native identity and imbuing them with the consciousness of belonging both to the people and to the land.

A Note on Hidden Transient Chaos in the Lorenz System

2017 ◽  
Vol 18 (5) ◽  
pp. 427-434 ◽  
Author(s):  
Quan Yuan ◽  
Fang-Yan Yang ◽  
Lei Wang
Keyword(s):  
Rayleigh Number ◽  
Lorenz System ◽  
Critical Value ◽  
Transient Chaos ◽  
Topological Horseshoe ◽  
One Dimensional ◽  
Dynamical Behaviors ◽  
The Lorenz System ◽  
The One

AbstractIn this paper, the classic Lorenz system is revisited. Some dynamical behaviors are shown with the Rayleigh number $\rho $ somewhat smaller than the critical value 24.06 by studying the basins characterization of attraction of attractors and tracing the one-dimensional unstable manifold of the origin, indicating some interesting clues for detecting the existence of hidden transient chaos. In addition, horseshoes chaos is verified in the famous system for some parameters corresponding to the hidden transient chaos by the topological horseshoe theory.

NOTES ON THE DISTRIBUTION OF PHASE SHIFTS

2008 ◽  
Vol 22 (23) ◽  
pp. 2163-2175 ◽  
Author(s):  
MIKLÓS HORVÁTH
Keyword(s):  
Inverse Scattering ◽  
Lower Bounds ◽  
Three Dimensional ◽  
Variational Formula ◽  
Phase Shifts ◽  
Upper And Lower Bounds ◽  
One Dimensional ◽  
Fixed Energy ◽  
Symmetrical Potential ◽  
The One

We consider three-dimensional inverse scattering with fixed energy for which the spherically symmetrical potential is nonvanishing only in a ball. We give exact upper and lower bounds for the phase shifts. We provide a variational formula for the Weyl–Titchmarsh m-function of the one-dimensional Schrödinger operator defined on the half-line.

On a semilinear equation in ℝ2 involving bounded measures

1983 ◽  
Vol 95 (3-4) ◽  
pp. 181-202 ◽  
Author(s):  
Juan L. Vazquez
Keyword(s):  
Real Function ◽  
Radon Measure ◽  
Existence Of Solutions ◽  
Critical Value ◽  
Existence Of A Solution ◽  
One Dimensional ◽  
Semilinear Equation ◽  
The One

SynopsisWe study the semilinear equation –Δu + β(u) = f in ℝ2, where β is a continuous increasing real function with β(0) = 0 and f is a bounded Radon measure. We show the existence of a solution, which is unique in the appropriate class, provided that each of the point masses contained in f does not exceed some critical value denned in terms of the growth of (β at ∞ This condition is shown to be necessary for the existence of solutions, even locally. The one-dimensional situation is also discussed.

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