Saddle-point approximations and space-time Martin boundary for nearest-neighbor random walk on a homogeneous tree

1991 ◽  
Vol 4 (4) ◽  
pp. 701-723 ◽  
Author(s):  
Steven P. Lalley
Keyword(s):  
Random Walk ◽  
Saddle Point ◽  
Nearest Neighbor ◽  
Martin Boundary ◽  
Space Time ◽  
Homogeneous Tree ◽  
Saddle Point Approximations

Kinetic Monte Carlo Simulations of Strain-Induced Nanopatterning on Hexagonal Surfaces

2002 ◽  
Vol 731 ◽  
Author(s):  
M.I. Larsson ◽  
B. Lee ◽  
R. Sabiryanov ◽  
K. Cho ◽  
W. Nix ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Saddle Point ◽  
Self Assembly ◽  
Nearest Neighbor ◽  
Kinetic Monte Carlo ◽  
Research Field ◽  
Surface Strain ◽  
Manufacturing Cost ◽  
Component Size ◽  
Quantum Mechanical Effects

AbstractGuided self assembly of periodic arrays of quantum dots has recently emerged as an important research field not only to reduce component size and manufacturing cost but also to explore and apply quantum mechanical effects in novel nanodevices. The intention of this kinetic Monte Carlo (KMC) simulation study is to investigate self-organized nanopatterning on hexagonal surfaces for relaxed periodic surface strain fields applied to Pt(111) epitaxy. The KMC model is a full diffusion bond-counting model including nearest neighbor as well as second-nearest neighbor interactions with an event catalogue consisting of 8989 events modeling the effect of the biaxial surface strain field. The strain dependence of the fcc site and the saddle point for a Pt adatom migrating on top of the Pt(111) surface is calculated using the embedded atom method. Both the valley and the saddle point energies show an excellent linear dependence on the strain. These results are applied in the KMC model. The surface strain in this study is caused by a hexagonal network of dislocations at the interface between the substrate and a mismatched epitaxial layer. How the selforganization of deposited atoms is influenced by the surface strain will be addressed.

Enahancing the detail on low-level seismicity and swarms in central-southern Italy by template matching

2021 ◽  
Author(s):  
Luca Carbone ◽  
Rita de Nardis ◽  
Giusy Lavecchia ◽  
Laura Peruzza ◽  
Enrico Priolo ◽  
...  
Keyword(s):  
Template Matching ◽  
Nearest Neighbor ◽  
Matched Filter ◽  
Central Italy ◽  
Total Duration ◽  
Space Time ◽  
Risk Area ◽  
Low Level ◽  
Seismic Catalogue ◽  
Completeness Magnitude

<p> </p><p>During the seismic sequence which followed the devastating L’Aquila 2009 earthquake, on 27 May 2009 the OGS (Istituto Nazionale di Oceanografia e di Geofisica Sperimentale) and the GeosisLab (Laboratorio di Geodinamica e Sismogenesi, Chieti-Pescara University) installed a temporary seismometric network around the Sulmona Basin, a high seismic risk area of Central Italy located right at SE of the epicentral one. This area of the central Apennines is generally characterized by low level seismicity organized in low energy clusters, but it experienced destructive earthquakes both in historical and in early instrumental time (Fucino 1915 =XI MCS, Majella 1706 =X-XI MCS, Barrea 1984 =VIII MCS).</p><p>From the 27 May 2009 to 22 November 2011, the temporary network provided a huge amount of continuous seismic recordings, and a seismic catalogue covering the first seven months of network operation (-1.5≤M<sub>L</sub>≤3.7, with a completeness magnitude of 1.1) and a spatial area that stretches from the Sulmona Basin to Marsica-Sora area. Aiming to enhance the detection of microearthquakes reported in this catalogue, we applied the matched-filter technique (MFT) to continuous waveforms properly integrated with data from permanent stations belonging to the national seismic network. Specifically, we used the open-source seismological package PyMPA to detect microseismicity from the cross-correlation of continuous data and templates. As templates we used only the best relocated events of the available seismic catalogue. Starting from 366 well located earthquakes<strong> </strong>we obtain a new seismic catalogue of 6084 new events (-2<M<sub>L</sub><4) lowering the completeness magnitude to 0.2. To these new seismic locations, we applied a declustering method to separate background seismicity from clustered seismicity in the area. All the seismicity shows a bimodal behaviour in term of distribution of the nearest-neighbor distance/time with the presence of two statistically distinct earthquake populations. We focused the attention on two of these clusters (C1 and C2) that numerically represent the 60% of the catalogue. They consist in 2619 and 995 events, respectively, with magnitude -2.0<M<sub>L</sub><3.6 and -0.5<M<sub>L</sub><3.2 occurred in Marsica-Sora area. C1 shows the typical characteristics of a seismic swarm, without a clear mainshock, but with 8 more energetic events (3.0≤M<sub>L</sub>≤3.5); the temporal evolution is very articulated with a total duration of one month with different bursts of seismicity and characteristic time extension of approximately one week. C2 instead has a different space-time evolution and consists of different swarm-like seismic sequences more discontinuous in comparison with C1. These swarms are described in greater detail to investigate the influence of overpressurized fluids and their space-time distribution.</p>

scholarly journals Martin boundary of a killed random walk on a quadrant

2010 ◽  
Vol 38 (3) ◽  
pp. 1106-1142 ◽  
Author(s):  
Irina Ignatiouk-Robert ◽  
Christophe Loree
Keyword(s):  
Random Walk ◽  
Martin Boundary

Saddle Point Approximations

2006 ◽  
Author(s):  
George H. Weiss
Keyword(s):  
Saddle Point ◽  
Saddle Point Approximations

scholarly journals Space–time random walk loop measures

2020 ◽  
Vol 130 (4) ◽  
pp. 2086-2126
Author(s):  
Stefan Adams ◽  
Quirin Vogel
Keyword(s):  
Random Walk ◽  
Space Time

scholarly journals Local and Global Survival for Nonhomogeneous Random Walk Systems on Z

2014 ◽  
Vol 46 (01) ◽  
pp. 256-278 ◽  
Author(s):  
Daniela Bertacchi ◽  
Fábio Prates Machado ◽  
Fabio Zucca
Keyword(s):  
Random Walk ◽  
Nearest Neighbor ◽  
Sufficient Conditions ◽  
Local Extinction ◽  
Active Particle ◽  
Translation Invariant ◽  
Local Survival ◽  
Global Survival ◽  
Starting Location ◽  
The Right

We study an interacting random walk system on ℤ where at time 0 there is an active particle at 0 and one inactive particle on each site n ≥ 1. Particles become active when hit by another active particle. Once activated, the particle starting at n performs an asymmetric, translation invariant, nearest neighbor random walk with left-jump probability l n . We give conditions for global survival, local survival, and infinite activation both in the case where all particles are immortal and in the case where particles have geometrically distributed lifespan (with parameter depending on the starting location of the particle). More precisely, once activated, the particle at n survives at each step with probability p n ∈ [0, 1]. In particular, in the immortal case, we prove a 0-1 law for the probability of local survival when all particles drift to the right. Besides that, we give sufficient conditions for local survival or local extinction when all particles drift to the left. In the mortal case, we provide sufficient conditions for global survival, local survival, and local extinction (which apply to the immortal case with mixed drifts as well). Analysis of explicit examples is provided: we describe completely the phase diagram in the cases ½ - l n ~ ± 1 / n α, p n = 1 and ½ - l n ~ ± 1 / n α, 1 - p n ~ 1 / n β (where α, β > 0).

The nearest neighbor random walk on subspaces of a vector space and rate of convergence

1995 ◽  
Vol 8 (2) ◽  
pp. 321-346 ◽  
Author(s):  
Anthony J. D'Aristotile
Keyword(s):  
Random Walk ◽  
Vector Space ◽  
Rate Of Convergence ◽  
Nearest Neighbor

scholarly journals FROM PERSISTENT RANDOM WALK TO THE TELEGRAPH NOISE

2010 ◽  
Vol 10 (02) ◽  
pp. 161-196 ◽  
Author(s):  
S. HERRMANN ◽  
P. VALLOIS
Keyword(s):  
Random Walk ◽  
Markov Process ◽  
Random Walks ◽  
Poisson Process ◽  
Counting Process ◽  
Telegraph Equation ◽  
Space Time ◽  
Persistent Random Walks ◽  
Persistent Random Walk ◽  
Telegraph Noise

We study a family of memory-based persistent random walks and we prove weak convergences after space-time rescaling. The limit processes are not only Brownian motions with drift. We have obtained a continuous but non-Markov process (Zt) which can be easily expressed in terms of a counting process (Nt). In a particular case the counting process is a Poisson process, and (Zt) permits to represent the solution of the telegraph equation. We study in detail the Markov process ((Zt, Nt); t ≥ 0).

Comparison of a nearest neighbor and other approaches to the detection of space-time clustering

1984 ◽  
Vol 2 (2) ◽  
pp. 125-142 ◽  
Author(s):  
Timothy L. McAuliffe ◽  
A.A. Afifi
Keyword(s):  
Nearest Neighbor ◽  
Space Time
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