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Harmonic Functions and Collision Probabilities

1997
*
The international journal of robotics research
*

In short, the hitting

doi:10.1177/027836499701600404
fatcat:nb75znlkhfbi5d3su74qrffjue
*probabilities*for random walks can be cast as a Dirichlet problem for*harmonic**functions*, in much the same way as in path planning. ... This paper describes a relationship between*harmonic**functions*{ which have recently been proposed for path planning {*and*recent work on randomization*and*learning in robotics. ... In this case, the resulting*harmonic**function*is the*collision**probability**function*over the workspace. ...##
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Harmonic functions and collision probabilities

*
Proceedings of the 1994 IEEE International Conference on Robotics and Automation
*

There is a close relationship between

doi:10.1109/robot.1994.351106
dblp:conf/icra/Connolly94
fatcat:vrroghglvzbunjmaij3ho2bp44
*harmonic**functions*{ which have recently been proposed f o r p ath planning {*and*hitting*probabilities*for random processes. ... The hitting*probabilities*for random walks can be c ast as a Dirichlet problem for*harmonic**functions*, in much the same way as in path planning. ... In particular, the equivalence of*harmonic**functions**and**collision**probabilities*has been illustrated. ...##
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Ultrahigh Harmonics from Laser-Assisted Ion-Atom Collisions

2003
*
Physical Review Letters
*

These

doi:10.1103/physrevlett.91.243901
pmid:14683120
fatcat:ooqk3ci72vhhfbyjqwfipcyacq
*harmonics*are due to two different mechanisms: (i)*collisional*electron capture*and*subsequent laser-driven transfer of an electron between projectile*and*target atom; (ii) reflection of a laser-driven ... We present a theoretical analysis of high-order*harmonic*generation from ion-atom*collisions*in the presence of linearly polarized intense laser pulses. ... Figure 3 (a) displays the final capture*probability*as a*function*of b, with*and*without laser field. Ionization reduces the capture*probability*significantly. ...##
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Quantum‐Mechanical Calculation of Harmonic Oscillator Transition Probabilities in a One‐Dimensional Impulsive Collision

1960
*
Journal of Chemical Physics
*

In the pres-

doi:10.1063/1.1731501
fatcat:devuxahpnfczvcwlbltmosdvyi
*HARMONIC*OSCILLATOR TRANSITION*PROBABILITIES*Fic. 1. The vibrational transition*probability*per*collision*Pj.s(€) = [(eti—f) /e}il B; |? ... This is to expand the wave*function*along the boundary in*harmonic*oscillator states V(R, R) = Den (R) +-co a= / dRy,*(R)W(R, R) (10) Since ¥(R, R) vanishes identically,*and*since the*functions*¥,(R) form ...##
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Review of Anisotropic Flow Correlations in Ultrarelativistic Heavy-Ion Collisions

2016
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Advances in High Energy Physics
*

Several new observables associated with correlations between anisotropic flow

doi:10.1155/2016/9365637
fatcat:skvf4e2wardtbfuc5stp763ata
*harmonics*are developed, which are expected to be sensitive to the initial fluctuations*and*transport properties of the created ... matter in heavy-ion*collisions*. ... Ollitrault,*and*H. Song for the comments on the manuscript 10 Advances in High Energy Physics*and*fruitful discussions. ...##
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Counting hot/cold spots in quark-gluon plasma

2012
*
Physical Review C
*

such as the population of hot

doi:10.1103/physrevc.85.061901
fatcat:to54zrw6oncapeq2lgwsysypge
*and*cold spots that are produced in high energy nuclear*collisions*. ... We study how local fluctuations in the initial states of relativistic heavy-ion*collisions*manifest themselves in the correlations between different orders of*harmonic*moments of the density profiles, ... The relative*probabilities*of hot*and*cold spots are taken as P si (1) = 35%*and*P si (−1) = 65% by comparing to the values of the correlation*functions*C (3) , e.g., The effects of the hot spots on these ...##
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Multichannel atomic scattering and confinement-induced resonances in waveguides

2008
*
Physical Review A. Atomic, Molecular, and Optical Physics
*

*Collisions*of identical bosonic

*and*fermionic as well as distinguishable atoms in

*harmonic*traps with a single frequency ω permitting the center-of-mass (c.m.) separation are explored in depth. ... Possible applications include, e.g., cold

*and*ultracold atom-atom

*collisions*in atomic waveguides

*and*electron-impurity scattering in quantum wires. ...

*and*the transition

*probabilities*characterizing the two-body

*collisions*in the trap. ...

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Harmonic Moments of the Gluon Density Distribution in AA Collisions

2012
*
Progress of Theoretical Physics Supplement
*

initial density distribution for both RHIC(Au+Au@200GeV)

doi:10.1143/ptps.193.145
fatcat:uvwdndio7nbj3erqfnjjyibgrm
*and*LHC(Pb+Pb@2.76TeV)*collisions*. ... By using Monte-Carlo implementations of k_T-factorization formula with running-coupling BK unintegrated gluon distributions for nucleus-nucleus*collisions*, we compute higher order*harmonic*moments of the ... Figure 2 shows the*harmonic*moments for Au+Au*collisions*at √ s NN = 200 GeV*and*Pb+Pb*collisions*at √ s NN = 2.76 TeV from the MCrcBK model. ...##
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Particle Correlations from ALICE: Latest Results

2013
*
Nuclear Physics A
*

The correlation between pairs or triplets of particles in relative angle

doi:10.1016/j.nuclphysa.2013.01.074
fatcat:ldiuhny5knbtnc5bq26b4shvnm
*and*momentum provides a valuable means of accessing the physics of particle production in heavy ion*collisions*. ... A selection of recent results from two*and*three particle correlations measured by the ALICE experiment are presented,*and*some brief interpretations of their implications are offered. ... Peaks in a correlation*function*indicate a relatively high*probability*for particle coincidence in a particular region of phase space for the pair; accordingly, depletions indicate a lower*probability*. ...##
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Page 68 of The Journal of Chemical Physics Vol. 25, Issue 1
[page]

1956
*
The Journal of Chemical Physics
*

*harmonic*oscillator

*collisional*transition

*probabilities*in studying the relaxation behavior of our model. ... The Effect of the

*Collisional*Transition

*Probabilities*on the Relaxation Behavior RoBErT J. Rusinft

*AND*Kurt E. ...

##
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Energy dependent growth of the nucleon and hydrodynamic initial conditions

2011
*
Physical Review C
*

We study this effect for fluctuating initial conditions generated with the Monte Carlo Kharzeev-Levin-Nardi (MC-KLN) model for Au+Au

doi:10.1103/physrevc.84.054905
fatcat:haognsoozbd7thxnnov7pzepbm
*collisions*at the Relativistic Heavy Ion Collider (RHIC)*and*the Large ... This leads to a natural smoothing of the initial energy density distribution in the transverse plane of the matter created near midrapidity in heavy-ion*collisions*. ... Acknowledgments We gratefully acknowledge clarifying discussions with Adrian Dumitru, Tetsu Hirano, Will Horowitz, Yuri Kovchegov, Mike Lisa, Yasushi Nara, Zhi Qiu,*and*Chun Shen,*and*thank Genya Levin ...##
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Nonlinear enhancement of the multiphonon Coulomb excitation in relativistic heavy ion collisions

1999
*
Physical Review C
*

Enhancement of the Double Giant Resonance excitation

doi:10.1103/physrevc.59.r1242
fatcat:vwjiwyyetnfg3obwkfpy7wupei
*probabilities*in relativistic ion*collisions*scales as (2 k +1)(2k)^-1 for the degree of nonlinearity (2k)^-1*and*is able to reach values 1.5-2 compatible ... [KEYWORDS: Relativistic Heavy Ion*Collisions*,Double Giant Resonance] ... The*functions*α(t)*and*φ(t) can be found from simple differential equations which relate the unknown α(t)*and*φ(t) with the*function*v 1 (t) in the Hamiltonian H(t). ...##
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Page 243 of The Journal of Chemical Physics Vol. 30, Issue 1
[page]

1959
*
The Journal of Chemical Physics
*

Quantum transition

*probabilities*of the*harmonic*oscillator, as*functions*of incident momentum, in the limit uO, n> @, p fixed. ... ONE-DIMENSIONAL INELASTIC*COLLISIONS*Gi J. 2 ( / 1)? Fic. 2. Quantum transition*probabilities*of the string os- cillator, as*functions*of incident momentum, in the limit u—0, n>, p fixed. ...##
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Discrete-step evaporation of an atomic beam

2005
*
European Physical Journal D : Atomic, Molecular and Optical Physics
*

First we derive the changes in flux

doi:10.1140/epjd/e2005-00007-y
fatcat:tjrjsgj6pve67gazymitayem5q
*and*temperature, as well as in*collision*rate*and*phase-space density, for a single evaporation step. ... Next we show how the occurrence of*collisions*during the propagation between two successive antennas can be probed. ... Kozlowski*and*the ENS laser cooling group. We thank D. Roberts for careful reading of the manuscript. ...##
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Anisotropic flow measured from multi-particle azimuthal correlations for Pb–Pb collisions at 2.76 TeV by ALICE at the LHC

2013
*
Nuclear Physics A
*

We report on the measurement of various flow

doi:10.1016/j.nuclphysa.2013.02.066
fatcat:cwgo3wkkhjb4vmjvgwcnq5cs2u
*harmonics*, v_n, with multi-particle cumulants,*and*present the results from a study of the inter-correlation among different order symmetry planes Ψ_n via multi-particle ... mixed*harmonic*correlations. ... The*probability*density*function*of event-by-event flow fluctuations was studied with multi-particle cumulants,*and*was found to be consistent with a Bessel-Gaussian distribution. ...
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