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Harmonic Functions and Collision Probabilities

Christopher I. Connolly
1997 The international journal of robotics research  
In short, the hitting 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.  ... 
doi:10.1177/027836499701600404 fatcat:nb75znlkhfbi5d3su74qrffjue

Harmonic functions and collision probabilities

C.I. Connolly
Proceedings of the 1994 IEEE International Conference on Robotics and Automation  
There is a close relationship between 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.  ... 
doi:10.1109/robot.1994.351106 dblp:conf/icra/Connolly94 fatcat:vrroghglvzbunjmaij3ho2bp44

Ultrahigh Harmonics from Laser-Assisted Ion-Atom Collisions

Manfred Lein, Jan M. Rost
2003 Physical Review Letters  
These 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.  ... 
doi:10.1103/physrevlett.91.243901 pmid:14683120 fatcat:ooqk3ci72vhhfbyjqwfipcyacq

Quantum‐Mechanical Calculation of Harmonic Oscillator Transition Probabilities in a One‐Dimensional Impulsive Collision

Kurt E. Shuler, Robert Zwanzig
1960 Journal of Chemical Physics  
In the pres- 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  ... 
doi:10.1063/1.1731501 fatcat:devuxahpnfczvcwlbltmosdvyi

Review of Anisotropic Flow Correlations in Ultrarelativistic Heavy-Ion Collisions

You Zhou
2016 Advances in High Energy Physics  
Several new observables associated with correlations between anisotropic flow 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.  ... 
doi:10.1155/2016/9365637 fatcat:skvf4e2wardtbfuc5stp763ata

Counting hot/cold spots in quark-gluon plasma

Guang-You Qin, Berndt Müller
2012 Physical Review C  
such as the population of hot 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  ... 
doi:10.1103/physrevc.85.061901 fatcat:to54zrw6oncapeq2lgwsysypge

Multichannel atomic scattering and confinement-induced resonances in waveguides

Shahpoor Saeidian, Vladimir S. Melezhik, Peter Schmelcher
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.  ... 
doi:10.1103/physreva.77.042721 fatcat:qg6dqzgzxrahjb4zweoe25f47q

Harmonic Moments of the Gluon Density Distribution in AA Collisions

Yasushi Nara
2012 Progress of Theoretical Physics Supplement  
initial density distribution for both RHIC(Au+Au@200GeV) 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.  ... 
doi:10.1143/ptps.193.145 fatcat:uvwdndio7nbj3erqfnjjyibgrm

Particle Correlations from ALICE: Latest Results

Andrew M. Adare
2013 Nuclear Physics A  
The correlation between pairs or triplets of particles in relative angle 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.  ... 
doi:10.1016/j.nuclphysa.2013.01.074 fatcat:ldiuhny5knbtnc5bq26b4shvnm

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.  ... 

Energy dependent growth of the nucleon and hydrodynamic initial conditions

Ulrich Heinz, J. Scott Moreland
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 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  ... 
doi:10.1103/physrevc.84.054905 fatcat:haognsoozbd7thxnnov7pzepbm

Nonlinear enhancement of the multiphonon Coulomb excitation in relativistic heavy ion collisions

M. S. Hussein, A. F. R. de Toledo Piza, O. K. Vorov
1999 Physical Review C  
Enhancement of the Double Giant Resonance excitation 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).  ... 
doi:10.1103/physrevc.59.r1242 fatcat:vwjiwyyetnfg3obwkfpy7wupei

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.  ... 

Discrete-step evaporation of an atomic beam

T. Lahaye, D. Gu�ry-Odelin
2005 European Physical Journal D : Atomic, Molecular and Optical Physics  
First we derive the changes in flux 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.  ... 
doi:10.1140/epjd/e2005-00007-y fatcat:tjrjsgj6pve67gazymitayem5q

Anisotropic flow measured from multi-particle azimuthal correlations for Pb–Pb collisions at 2.76 TeV by ALICE at the LHC

Ante Bilandzic
2013 Nuclear Physics A  
We report on the measurement of various flow 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.  ... 
doi:10.1016/j.nuclphysa.2013.02.066 fatcat:cwgo3wkkhjb4vmjvgwcnq5cs2u
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