On the First Moment Relaxation Equation of Anharmonic Oscillators

1970 ◽  
Vol 53 (10) ◽  
pp. 4107-4108 ◽  
Author(s):  
C. T. Hsu ◽  
L. D. McMillen
Keyword(s):  
Anharmonic Oscillators ◽  
Relaxation Equation ◽  
First Moment

VIBRATIONAL RELAXATION IN DISSOCIATING DIATOMIC GASES

1963 ◽  
Vol 41 (5) ◽  
pp. 717-723 ◽  
Author(s):  
M. McChesney
Keyword(s):  
Vibrational Relaxation ◽  
Vibrational Excitation ◽  
Thermal Dissociation ◽  
Boltzmann Distribution ◽  
Anharmonic Oscillators ◽  
Distribution Law ◽  
Relaxation Equation ◽  
Vibrational Levels ◽  
Equilibrium Level ◽  
Theoretical Analyses

This article questions the available theoretical analyses relating to the vibrational excitation of a dissociating gas which assume that the gas dissociates from vibrational level populations given by the Maxwell–Boltzmann distribution law. The two theories of thermal dissociation are briefly outlined and it is shown that either theory gives non-equilibrium-level populations. Furthermore, the use of a simple relaxation equation to describe the vibrational excitation of anharmonic oscillators in high vibrational levels is questioned.

The role of differential phase contrast in electron microscopy

1978 ◽  
Vol 36 (1) ◽  
pp. 176-177
Author(s):  
E.M. Waddell ◽  
J.N. Chapman ◽  
R.P. Ferrier
Keyword(s):  
Phase Contrast ◽  
Practical Method ◽  
Position Vector ◽  
Differential Phase ◽  
Pure Phase ◽  
Differential Phase Contrast ◽  
The Difference ◽  
Image Position ◽  
First Moment

Dekkers and de Lang (1977) have discussed a practical method of realising differential phase contrast in a STEM. The method involves taking the difference signal from two semi-circular detectors placed symmetrically about the optic axis and subtending the same angle (2α) at the specimen as that of the cone of illumination. Such a system, or an obvious generalisation of it, namely a quadrant detector, has the characteristic of responding to the gradient of the phase of the specimen transmittance. In this paper we shall compare the performance of this type of system with that of a first moment detector (Waddell et al.1977).For a first moment detector the response function R(k) is of the form R(k) = ck where c is a constant, k is a position vector in the detector plane and the vector nature of R(k)indicates that two signals are produced. This type of system would produce an image signal given bywhere the specimen transmittance is given by a (r) exp (iϕ (r), r is a position vector in object space, ro the position of the probe, ⊛ represents a convolution integral and it has been assumed that we have a coherent probe, with a complex disturbance of the form b(r-ro) exp (iζ (r-ro)). Thus the image signal for a pure phase object imaged in a STEM using a first moment detector is b2 ⊛ ▽ø. Note that this puts no restrictions on the magnitude of the variation of the phase function, but does assume an infinite detector.

Perturbative-variational calculations in two-well anharmonic oscillators

1990 ◽  
Vol 42 (9) ◽  
pp. 5073-5078 ◽  
Author(s):  
F. Arias de Saavedra ◽  
E. Buenda
Keyword(s):  
Anharmonic Oscillators ◽  
Variational Calculations

scholarly journals A new proof for the generalized law of large numbers under Choquet expectation

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Jing Chen ◽  
Zengjing Chen
Keyword(s):  
Probability Theory ◽  
Law Of Large Numbers ◽  
Moment Condition ◽  
Large Numbers ◽  
Choquet Expectation ◽  
The Law ◽  
Linear Probability ◽  
First Moment ◽  
Independent And Identically Distributed

Abstract In this article, we employ the elementary inequalities arising from the sub-linearity of Choquet expectation to give a new proof for the generalized law of large numbers under Choquet expectations induced by 2-alternating capacities with mild assumptions. This generalizes the Linderberg–Feller methodology for linear probability theory to Choquet expectation framework and extends the law of large numbers under Choquet expectation from the strong independent and identically distributed (iid) assumptions to the convolutional independence combined with the strengthened first moment condition.

scholarly journals The First Moment of Azimuthal Anisotropy in Nuclear Collisions from AGS to LHC Energies

2016 ◽  
Vol 2016 ◽  
pp. 1-16 ◽  
Author(s):  
Subhash Singha ◽  
Prashanth Shanmuganathan ◽  
Declan Keane
Keyword(s):  
Quark Gluon Plasma ◽  
Charged Particles ◽  
Theoretical Work ◽  
Heavy Ion ◽  
Gluon Plasma ◽  
Azimuthal Anisotropy ◽  
Flow Focusing ◽  
Nuclear Collisions ◽  
Ion Collisions ◽  
First Moment

We review topics related to the first moment of azimuthal anisotropy (v1), commonly known as directed flow, focusing on both charged particles and identified particles from heavy-ion collisions. Beam energies from the highest available, at the CERN LHC, down to projectile kinetic energies per nucleon of a few GeV per nucleon, as studied in experiments at the Brookhaven AGS, fall within our scope. We focus on experimental measurements and on theoretical work where direct comparisons with experiment have been emphasized. The physics addressed or potentially addressed by this review topic includes the study of Quark Gluon Plasma and, more generally, investigation of the Quantum Chromodynamics phase diagram and the equation of state describing the accessible phases.

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