Dispersion of particle systems in Brownian flows

1996 ◽  
Vol 28 (1) ◽  
pp. 53-74 ◽  
Author(s):  
Craig L. Zirbel ◽  
Erhan Çinlar
Keyword(s):  
Asymptotic Behavior ◽  
Incompressible Flows ◽  
Center Of Mass ◽  
Spatial Dimension ◽  
Two Dimensions ◽  
Separation Process ◽  
Particle Systems ◽  
Largest Lyapunov Exponent ◽  
Second Moments ◽  
Pair Separation

We study the dispersion of a collection of particles carried by an isotropic Brownian flow in Of particular interest are the center of mass and the centered spatial second moments. Their asymptotic behavior depends strongly on the spatial dimension and the largest Lyapunov exponent of the flow. We use estimates for the pair separation process to give a fairly complete picture of this behavior as t → ∞. In particular, for incompressible flows in two dimensions, we show that the variance of the center of mass grows sublinearly, while dispersion relative to the center of mass grows linearly.

Dispersion of particle systems in Brownian flows

1996 ◽  
Vol 28 (01) ◽  
pp. 53-74 ◽  
Author(s):  
Craig L. Zirbel ◽  
Erhan Çinlar
Keyword(s):  
Asymptotic Behavior ◽  
Incompressible Flows ◽  
Center Of Mass ◽  
Spatial Dimension ◽  
Two Dimensions ◽  
Separation Process ◽  
Particle Systems ◽  
Largest Lyapunov Exponent ◽  
Second Moments ◽  
Pair Separation

We study the dispersion of a collection of particles carried by an isotropic Brownian flow in Of particular interest are the center of mass and the centered spatial second moments. Their asymptotic behavior depends strongly on the spatial dimension and the largest Lyapunov exponent of the flow. We use estimates for the pair separation process to give a fairly complete picture of this behavior as t → ∞. In particular, for incompressible flows in two dimensions, we show that the variance of the center of mass grows sublinearly, while dispersion relative to the center of mass grows linearly.

scholarly journals Limit Theory for High Frequency Sampled MCARMA Models

2014 ◽  
Vol 46 (3) ◽  
pp. 846-877 ◽  
Author(s):  
Vicky Fasen
Keyword(s):  
Asymptotic Behavior ◽  
High Frequency ◽  
Lévy Process ◽  
Asymptotic Properties ◽  
Domain Of Attraction ◽  
Levy Process ◽  
Sample Variance ◽  
Limit Theory ◽  
Second Moments ◽  
Time Grid

We consider a multivariate continuous-time ARMA (MCARMA) process sampled at a high-frequency time grid {hn, 2hn,…, nhn}, where hn ↓ 0 and nhn → ∞ as n → ∞, or at a constant time grid where hn = h. For this model, we present the asymptotic behavior of the properly normalized partial sum to a multivariate stable or a multivariate normal random vector depending on the domain of attraction of the driving Lévy process. Furthermore, we derive the asymptotic behavior of the sample variance. In the case of finite second moments of the driving Lévy process the sample variance is a consistent estimator. Moreover, we embed the MCARMA process in a cointegrated model. For this model, we propose a parameter estimator and derive its asymptotic behavior. The results are given for more general processes than MCARMA processes and contain some asymptotic properties of stochastic integrals.

On a Voronoi aggregative process related to a bivariate Poisson process

1996 ◽  
Vol 28 (04) ◽  
pp. 965-981 ◽  
Author(s):  
S. G. Foss ◽  
S. A. Zuyev
Keyword(s):  
Asymptotic Behavior ◽  
Lower Bounds ◽  
Distribution Functions ◽  
Poisson Processes ◽  
Upper And Lower Bounds ◽  
Additive Functionals ◽  
Second Moments ◽  
Explicit Formulae ◽  
Bivariate Poisson Process ◽  
Sum Of Distances

We consider two independent homogeneous Poisson processes Π0 and Π1 in the plane with intensities λ0 and λ1, respectively. We study additive functionals of the set of Π0-particles within a typical Voronoi Π1-cell. We find the first and the second moments of these variables as well as upper and lower bounds on their distribution functions, implying an exponential asymptotic behavior of their tails. Explicit formulae are given for the number and the sum of distances from Π0-particles to the nucleus within a typical Voronoi Π1-cell.

scholarly journals TAJALLIYAH ASH-SHIRA' FI AL-ADAB AL-'ARABI AL-MU'ASHIR WA ATSARIHI FI HARB AL-'ARAB تجليات الصراع في الأدب العربي المعاصر وأثره في حرب العرب (من الصراع والصدام إلى ثقافة الحرب في شعر سوريا نموذجا)

2018 ◽  
Vol 20 (2) ◽  
pp. 305
Author(s):  
Halimi Halimi ◽  
M. Faisol ◽  
Muhammad Majed Al-Dakhiel
Keyword(s):  
Arab World ◽  
Strong Relationship ◽  
Spatial Dimension ◽  
Two Dimensions ◽  
Spiritual Dimension ◽  
The Social ◽  
History Of ◽  
The Revolution

<p>لقد عبر شعر الصراع (المقاومة والثورة والحرب) في بلاد الجزيرة العربية مفردات متنوعة طوال تاريخها من خلال البعدين، منهما البعد المكاني متمثلا في الأرض التي حملها الشعر دلالات ومعان تتجاوز ملامحها المادية لتكتسب بعدا روحيا وقيما عليا. والبعد الثاني يتمثل في البعد التراثي والتاريخي. فشعر الصراعات لا ينفصل من الواقع الاجتماعي، وليس هو الشعر الانعزالي، بل هو الشعر الاجتماعي الذي له علاقة متينة بواقعه، والذي يحمل رموزا تاريخية كثيرة نتيجة لامتداد العمر الزمني لهذا المجتمع من العصور القديمة، وكان المجتمع والأرض تصنع تقاليد تتطور إلى رموز، فهناك رمز للكرام وللمروءة ولمعاناة المجتمع وللصراع، وفي الرمز أسلوب فيه تلميح ومداره.</p><p><br />Throughout the history of the Arab world, the poetry of the struggle (the resistance, the revolution and the war) has been a varied vocabulary throughout its history through the two dimensions, including the spatial dimension, in the land where poetry carries meanings and meanings that transcend its physical texture to acquire a spiritual dimension and supreme value. It is the social poetry that has a strong relationship to its reality, which carries many historical symbols as a result of the extension of the temporal age of this society from antiquity. The society and the land made traditions that evolve into symbols. And the suffering of society and the conflict and the virus, and in the code style in which the tip and orbit.</p>

Estimation in Dynamic Linear Regression Models with Infinite Variance Errors

1993 ◽  
Vol 9 (4) ◽  
pp. 570-588 ◽  
Author(s):  
Keith Knight
Keyword(s):  
Asymptotic Behavior ◽  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Regression Models ◽  
Infinite Variance ◽  
Linear Regression Models ◽  
Asymptotically Normal ◽  
Second Moments ◽  
True Values

This paper considers the asymptotic behavior of M-estimates in a dynamic linear regression model where the errors have infinite second moments but the exogenous regressors satisfy the standard assumptions. It is shown that under certain conditions, the estimates of the parameters corresponding to the exogenous regressors are asymptotically normal and converge to the true values at the standard n−½ rate.

scholarly journals The two dimensions of Italian academics’ public engagement

2020 ◽  
Author(s):  
Monia Anzivino ◽  
Flavio A. Ceravolo ◽  
Michele Rostan
Keyword(s):  
Data Analysis ◽  
Public Engagement ◽  
Local Community ◽  
Response Rate ◽  
Common Factors ◽  
Political Engagement ◽  
Spatial Dimension ◽  
Two Dimensions ◽  
Academic Rank ◽  
Third Mission

AbstractThe article aims at investigating Italian academics’ Public Engagement highlighting its two dimensions, namely “Local Community Engagement” (LCE) and “General Political Engagement” (GPE). It is based on the results of a national survey on academics’ third mission activities carried out in the year 2015/2016 collecting information from a representative sample of 5,123 respondents working at 62 universities, with a response rate of 34.2%. In addition to detecting distinct dimensions of academics’ Public Engagement, data analysis shows that Italian academics are much more involved in LCE activities than in GPE ones. Although both LCE and GPE are influenced by many common factors, such as academic rank, discipline and being involved in other third mission activities, they also display peculiar traits: LCE activities are more likely to involve academic women while GPE are more likely to be carried out by older academics; LCE activities appear to be context-dependent while GPE activities are not. Hence, the article offers a contribution to a better understanding of the different goals of Public Engagement activities and of their spatial dimension.

Partial Euler Products on the Critical Line

2005 ◽  
Vol 57 (2) ◽  
pp. 267-297 ◽  
Author(s):  
Keith Conrad
Keyword(s):  
Asymptotic Behavior ◽  
Elliptic Curve ◽  
Riemann Hypothesis ◽  
Critical Line ◽  
Function Fields ◽  
Number Fields ◽  
Euler Product ◽  
Second Moments ◽  
Precise Sense ◽  
Euler Products

AbstractThe initial version of the Birch and Swinnerton-Dyer conjecture concerned asymptotics for partial Euler products for an elliptic curve L-function at s = 1. Goldfeld later proved that these asymptotics imply the Riemann hypothesis for the L-function and that the constant in the asymptotics has an unexpected factor of. We extend Goldfeld's theorem to an analysis of partial Euler products for a typical L-function along its critical line. The general phenomenon is related to second moments, while the asymptotic behavior (over number fields) is proved to be equivalent to a condition that in a precise sense seemsmuch deeper than the Riemann hypothesis. Over function fields, the Euler product asymptotics can sometimes be proved unconditionally.

Cooper Pairing and Ladder Correlations in a BCS Ground State

2003 ◽  
Vol 17 (18n20) ◽  
pp. 3304-3309
Author(s):  
V. C. Aguilera-Navarro ◽  
M. Fortes ◽  
M. de Llano
Keyword(s):  
Ground State ◽  
Center Of Mass ◽  
Two Dimensions ◽  
Einstein Condensation ◽  
Positive Energy ◽  
Cooper Pairs ◽  
Linear Dispersion ◽  
Bose Einstein Condensation ◽  
Leading Term ◽  
Bose Einstein

A Bethe–Salpeter treatment of Cooper pairs (CPs) based on an ideal Fermi gas (IFG) "sea" produces unstable CPs if holes are not ignored. Stable CPs with damping emerge when the BCS ground state replaces the IFG, and are positive-energy, finite-lifetime resonances for nonzero center-of-mass momentum with a linear dispersion leading term. Bose–Einstein condensation of such pairs may thus occur in exactly two dimensions as it cannot with quadratic dispersion.

Accurate calculation of the bound states of the quantum dipole problem in two dimensions

Open Physics ◽  
2012 ◽  
Vol 10 (1) ◽  
Author(s):  
Paolo Amore
Keyword(s):  
Asymptotic Behavior ◽  
Upper Bound ◽  
Ground State ◽  
Bound States ◽  
Two Dimensions ◽  
Accurate Calculation ◽  
Perfect Agreement

AbstractWe present an accurate calculation of the energies of the bound states of the quantumdipole problemin two dimensions using a Rayleigh-Ritz approach. We obtain an upper bound for the energy of the ground state, which is by far the most precise in the literature for this problem. We also obtain an alternative estimate of the fundamental energy of the model performing an extrapolation of the results corresponding to different subspaces. Finally, our calculation of the energies of the first 500 states shows a perfect agreement with the expected asymptotic behavior.

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