Boundary Condition for the Distribution Function of a Gas of Linear Molecules

1974 ◽  
Vol 29 (12) ◽  
pp. 1723-1735
Author(s):  
J. Halbritter
Keyword(s):  
Boundary Condition ◽  
Wave Function ◽  
Distribution Function ◽  
Angular Momentum ◽  
Interaction Potential ◽  
Transition Probability ◽  
Center Of Mass ◽  
Solid Surfaces ◽  
Molecular Axis ◽  
Linear Molecules

The scattering of linear molecules by a potential wall is studied. It is assumed that the interaction potential between the molecule and the wall depends on the distance of the center of mass of the molecule from the wall and on the orientation of the molecular axis. From the wave function of the reflected molecule an expression for the transition probability for scattering into the various final molecular states is obtained. Together with a modification of Maxwell's assumption for the interaction of atoms with solid surfaces, this transition probability is used to derive a boundary condition for the distribution function of a gas of linear rotating molecules. This also takes into account the change of rotational angular momentum in the collision with the wall.

On the Nonspherical Scattering Amplitude for Inelastic Molecular Collisions

1970 ◽  
Vol 25 (3) ◽  
pp. 336-350 ◽  
Author(s):  
W. E. Köhler ◽  
S. Hess ◽  
L. Waldmann
Keyword(s):  
Angular Momentum ◽  
Bulk Viscosity ◽  
Interaction Potential ◽  
Scattering Amplitude ◽  
Inelastic Collisions ◽  
Momentum Dependence ◽  
Molecular Collisions ◽  
Molecular Scattering ◽  
Polarized Beam ◽  
Linear Molecules

The rotational angular momentum dependence of the nonspherical scattering amplitude is investigated for inelastic collisions of linear molecules. As far as the approximation of small nonsphericity can be applied, this dependence is obtained from the angular momentum dependence of the nonspherical interaction potential. The connection between the nonspherical scattering amplitude and observables that can be measured by molecular scattering experiments involving a polarized beam is discussed. Some qualitative remarks are made on collision brackets occurring in the theoretical expressions for the bulk viscosity and for the Senftleben-Beenakker effect for H2 and HD

Hydrodynamic slippage of water at surfaces

2017 ◽  
Author(s):  
E. Charlaix ◽  
L. Bocquet
Keyword(s):  
Boundary Condition ◽  
Molecular Mechanisms ◽  
Slip Length ◽  
Molecular Simulations ◽  
Short Review ◽  
Solid Surfaces ◽  
Experimental Investigations

The boundary condition (B.C.) for hydrodynamic flows at solid surfaces is usually assumed to be that of no slip. However a number of molecular simulations and experimental investigations over the last two decades have demonstrated violations of the no-slip B.C., leading to hydrodynamic slippage at solid surfaces. In this short review, we explore the molecular mechanisms leading to hydrodynamic slippage of water at various surfaces and discuss experimental investigations allowing us to measure the so-called slip length

scholarly journals Infrared effects in the late stages of black hole evaporation

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Éanna É. Flanagan
Keyword(s):  
Black Hole ◽  
Angular Momentum ◽  
Center Of Mass ◽  
Planck Scale ◽  
Black Hole Mass ◽  
Order Unity ◽  
Intrinsic Angular Momentum ◽  
Hole Position ◽  
Late Stages ◽  
Shear Tensor

Abstract As a black hole evaporates, each outgoing Hawking quantum carries away some of the black holes asymptotic charges associated with the extended Bondi-Metzner-Sachs group. These include the Poincaré charges of energy, linear momentum, intrinsic angular momentum, and orbital angular momentum or center-of-mass charge, as well as extensions of these quantities associated with supertranslations and super-Lorentz transformations, namely supermomentum, superspin and super center-of-mass charges (also known as soft hair). Since each emitted quantum has fluctuations that are of order unity, fluctuations in the black hole’s charges grow over the course of the evaporation. We estimate the scale of these fluctuations using a simple model. The results are, in Planck units: (i) The black hole position has a uncertainty of $$ \sim {M}_i^2 $$ ∼ M i 2 at late times, where Mi is the initial mass (previously found by Page). (ii) The black hole mass M has an uncertainty of order the mass M itself at the epoch when M ∼ $$ {M}_i^{2/3} $$ M i 2 / 3 , well before the Planck scale is reached. Correspondingly, the time at which the evaporation ends has an uncertainty of order $$ \sim {M}_i^2 $$ ∼ M i 2 . (iii) The supermomentum and superspin charges are not independent but are determined from the Poincaré charges and the super center-of-mass charges. (iv) The supertranslation that characterizes the super center-of-mass charges has fluctuations at multipole orders l of order unity that are of order unity in Planck units. At large l, there is a power law spectrum of fluctuations that extends up to l ∼ $$ {M}_i^2/M $$ M i 2 / M , beyond which the fluctuations fall off exponentially, with corresponding total rms shear tensor fluctuations ∼ MiM−3/2.

Non-Lorentzian Shape of the Depolarized Rayleigh Line and the Correlation Function of the Tensor Polarization

1973 ◽  
Vol 28 (9) ◽  
pp. 1385-1388
Author(s):  
S. Hess ◽  
H. Vestner
Keyword(s):  
Distribution Function ◽  
Correlation Function ◽  
Rayleigh Line ◽  
Tensor Polarization ◽  
Pressure Broadening ◽  
Exponential Functions ◽  
Linear Molecules ◽  
Lorentzian Shape

The correlation function of the tensor polarization relevant for the depolarized Rayleigh line of a gas of rotating linear molecules is calculated for the pressure broadening regime. Point of depar­ture is the Waldmann-Snider equation for the distribution function of the gas. Due to the collisional coupling between the tensor polarization and other moments of the distribution function the cor­relation function turns out to be a sum of exponential functions. Consequently the depolarized Rayleigh line has a non-Lorentzian shape.

THE STEREODYNAMICS STUDY OF THE C(3P) + OH (X2 Π) → CO(X1Σ+) + H(2S) REACTION

2010 ◽  
Vol 09 (05) ◽  
pp. 935-943 ◽  
Author(s):  
PENG SONG ◽  
YONG-HUA ZHU ◽  
JIAN-YONG LIU ◽  
FENG-CAI MA
Keyword(s):  
Angular Momentum ◽  
Cross Sections ◽  
Collision Energy ◽  
Energy Surface ◽  
Center Of Mass ◽  
Title Reaction ◽  
High Collision Energy ◽  
Dependency Relationship ◽  
Energy Dependency ◽  
Mass Frame

The stereodynamics of the title reaction on the ground electronic state X2A' potential energy surface (PES)1 has been studied using the quasiclassical trajectory (QCT) method. The commonly used polarization-dependent differential cross-sections (PDDCSs) of the product and the angular momentum alignment distribution, P(θr) and P(Φr), are generated in the center-of-mass frame using QCT method to gain insight of the alignment and orientation of the product molecules. Influence of collision energy on the stereodynamics is shown and discussed. The results reveal that the distribution of P(θr) and P(Φr) is sensitive to collision energy. The PDDCSs exhibit different collision energy dependency relationship at low and high collision energy ranges.

scholarly journals WAVE FUNCTION AND PAIR DISTRIBUTION FUNCTION OF A DILUTE BOSE GAS

2009 ◽  
Vol 23 (15) ◽  
pp. 1843-1845
Author(s):  
BO-BO WEI
Keyword(s):  
Wave Function ◽  
Distribution Function ◽  
Low Temperatures ◽  
Hard Sphere ◽  
Pair Distribution Function ◽  
Bose Gas ◽  
Dilute Bose Gas

The wave function of a dilute hard sphere Bose gas at low temperatures is revisited. Errors in an early 1957 paper are corrected. The pair distribution function is calculated for two values of [Formula: see text].

The Hidden Variables Theory

2021 ◽  
Author(s):  
Israel Fried
Keyword(s):  
Wave Function ◽  
Magnetic Flux ◽  
W Boson ◽  
Energy Levels ◽  
Center Of Mass ◽  
Hidden Variables ◽  
Bound State ◽  
Electron Mass ◽  
Charged Mesons ◽  
New Variables

The book presents a new concept on several physics topics. The initial values are non-relativistic quantities of subatomic particles which the values obtained in experiments are actually their relativistic reflection. The subjects in the book are presented in such order that each new topic is based on the development of its predecessor that explains where it stems from. The book presents methods of analyzing traditional physics concepts to extract hidden embedded information that reveals new variables which are combined with those known. The new formulas yield results that match experiments accurately. It presents discoveries as: The electric charge of subatomic particle results directly from its OAM (Orbital Angular Momentum). OAM Offset exhibits neutral state. The electron mass is a magnitude that expresses quantitatively the square of its magnetic flux quantum, hence this mass in the Wave Function yields solutions that their squared values represent the flow pattern of magnetic flux surrounding electrons at energy levels, contrary to probability density describing odds of locating electron in atom. In calculation of hydrogen's wave function the electron and proton constitute one entity. Hence zero OAM at ground state determined by computational and experimental means is due to OAM offset of electron and proton rotation in opposite directions at center of mass. The proton, neutron and all baryons consist of three energy levels on which the quarks are orbiting. The third energy level of 80.5Gev plays a major role in the weak force while it is filled by charged mesons that are emitted thru W boson while acquiring the level's energy. The OAM of the orbiting quarks are third or two thirds of the reduced Planck constant. The proton missing spin is resolved by the OAM of quarks. The Electron is bound state composition of a negative Pion and an Electron's neutrino. The theory predicts a neutral boson of 160Gev (Accompanied by W+ boson from 240Gev decaying particle).

The Hidden Variables Theory

2021 ◽  
Author(s):  
Israel Fried
Keyword(s):  
Wave Function ◽  
Magnetic Flux ◽  
W Boson ◽  
Energy Levels ◽  
Center Of Mass ◽  
Hidden Variables ◽  
Bound State ◽  
Electron Mass ◽  
Charged Mesons ◽  
New Variables

The book presents a new concept on several physics topics. The initial values are non-relativistic quantities of subatomic particles which the values obtained in experiments are actually their relativistic reflection. The subjects in the book are presented in such order that each new topic is based on the development of its predecessor that explains where it stems from. The book presents methods of analyzing traditional physics concepts to extract hidden embedded information that reveals new variables which are combined with those known. The new formulas yield results that match experiments accurately. It presents discoveries as: The electric charge of subatomic particle results directly from its OAM (Orbital Angular Momentum). OAM Offset exhibits neutral state. The electron mass is a magnitude that expresses quantitatively the square of its magnetic flux quantum, hence this mass in the Wave Function yields solutions that their squared values represent the flow pattern of magnetic flux surrounding electrons at energy levels, contrary to probability density describing odds of locating electron in atom. In calculation of hydrogen's wave function the electron and proton constitute one entity. Hence zero OAM at ground state determined by computational and experimental means is due to OAM offset of electron and proton rotation in opposite directions at center of mass. The proton, neutron and all baryons consist of three energy levels on which the quarks are orbiting. The third energy level of 80.5Gev plays a major role in the weak force while it is filled by charged mesons that are emitted thru W boson while acquiring the level's energy. The OAM of the orbiting quarks are third or two thirds of the reduced Planck constant. The proton missing spin is resolved by the OAM of quarks. The Electron is bound state composition of a negative Pion and an Electron's neutrino. The theory predicts a neutral boson of 160Gev (Accompanied by W+ boson from 240Gev decaying particle).

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