Rotational Brownian motion of an asymmetric top

Ford, G. W.; Lewis, J. T.; McConnell, James R.

doi:10.1103/physreva.19.907

Cited by 54 publications

(34 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This dynamics takes place on a generalization of the upper half-plane, the space of univalent functions. A much more elementary example would be rigid body motion; random motion of rigid bodies have been used to model dust grains in astronomy [8]. We will now give a general framework for this theory.…”

Section: Stochastic Geodesic Motion On Groupsmentioning

confidence: 98%

The Langevin equation on Lie algebras: Maxwell–Boltzmann is not always the equilibrium

Rajeev

2009

Annals of Physics

View full text Add to dashboard Cite

Section: Stochastic Geodesic Motion On Groupsmentioning

confidence: 98%

The Langevin equation on Lie algebras: Maxwell–Boltzmann is not always the equilibrium

Rajeev

2009

Annals of Physics

View full text Add to dashboard Cite

“…(7, t) = -Q53c (7, t) -zG(7, t) + Z J dT(7 + 7)G? (7, t) (17) 8tG_ (7,t) = -i7c(7, t) -ZC (7, t) -z J dT(7 + 7)G (7,t) (18) After the expansion of t) in the Taylor series near the "point" 7, Eq. (17) permits pansage to the 1imit z -+ , -4 -1, z(1 + y) -f = in the same manner as in case of the derivation of the standard FPE from the KS kinetic equation (6) (see e.g.…”

Section: Ocfs In Case 01? Angular Momentum Reorientationmentioning

confidence: 99%

“…Eq. (6) contains, as a special case, the .3-diffusion (JD) model [2,5,[11][12][13][14][15] ('y = 0) and the FPE [2,5,12,[16][17][18][19] (z -00, y -' 1, z(1 -) -i = const). When --1, t' -, 2z, yE 0 and Eq.…”

Section: Ocfs In Case 01? Angular Momentum Reorientationmentioning

confidence: 99%

Orientational relaxation of spherical top molecules in gases and liquids: effect of collision intensity

Блохин¹,

Gelin²

1997

SPIE Proceedings

View full text Add to dashboard Cite

ABSTRACrIn order to study the influence of ccre1ation of the angular momenta before and after collision on the course of orientational relaxation of spherical top mo1ecu1, a Markovian maer equation with the collision kernel by Keilson and Storer is considered. The equation is solved analytically i_n case of the complete angular momentum reorientation due to a collision. The results obtained allow one to establish the upper and the lower limit of the time development of the orientational correlation functions. THE KEILSON-STORER KERNELIt is natural to imply that the rate of the angular momentum change due to an instantaneous encounter is determined by the intensity of intermolecular interactions. This statement can be put on the reliable mathematical ground by invoking the Keibon-Storer (KS) collision kernel [1,2J.(1) The kernel is the conditional probabifity density of the angular momentum change due to a collision.Here 7 and 7 are molecuiar anguiar momenta before and after a single collision, and parameter -1 1 determines efficiency of encounters. It drib a large variety of collision events. When --'7 = 1, the angular momentum and rotational energy are conserved, and T( J -y .1') reduc to 5(7 -P). Provided ' = 0, intermolecular interactions are so strong that a single collision is enough to establish a Boltzmann equilibrium distribution in the molecular ensemble. By letting 'y = -1, -one also arrives at the delta-function, but ofthe kind 6( J + .1'). So, the magnitude of the angular momentum is preserved but its direction reversed due to a collision. When 'y -1, the angular momentum change is quite strong, but that of the rotational ener, on the contrary, is quite weak.In the range 0 < -y < 1, the KS model interpolates smoothly between the extremes of strong and weak collisions, and allows one to investigate a physical situation when -1 'y < 0. The latter situation corresponds to a preferential reorientation of the angular momentum due to a collision. This can be attributed to the so-called "cage effects" that are characteristic ofthe molecular rotation in liquids.One can invoke the KS kernel to calculate various coelation functions (CFB). By substituting kernel (1) into the conventional Markovian kinetic equation, it is the standard routine to derive exact formulas far the angular momentum and rotational energy CFs E2,31:CE(t) =< J (O)J (t) >< J4 >= 3/5 + 2/5 exp{_zjEt}.(3) The effective frequencies of decay of these CF8 are expreed through the KS kernel parameters as follows v=z(l-7), vE=z(1_y2) (4) with Z being the collision frequency. 277 SPIE Vol. 3090 • 0277-786X/971$10.00 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 06/20/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx

show abstract

“…The matrix X has the same form with (6). But elements of X matrix are equal to µ x = sin θ, i.e., X θ = sin θ.…”

mentioning

confidence: 99%

“…Here that equation is the Smoluchowski equation, which is an approximate Fokker-Planck equation in the space of angular coordinates for the distribution function of the orientations of the dipoles on the surface of the unit sphere when the influence of the inertia of the molecules on the relaxation process is ignored. Following years many generalizations of Debye model have been extensively studied [3,4,5,6,7,8,9,10,11]. However, Debye theory cannot explain relaxation phenomena in strongly interacting systems.…”

mentioning

confidence: 99%

Rotational Brownian Motion on Sphere Surface and Rotational Relaxation

Aydıner

2006

Chinese Phys. Lett.

View full text Add to dashboard Cite

The spatial components of the autocorrelation function of noninteracting dipoles are analytically obtained in terms of rotational Brownian motion on the surface of a unit sphere using multi-level jumping formalism based on Debye's rotational relaxation model, and the rotational relaxation functions are evaluated.PACS numbers: 77.22. Gm, 05.40.Jc, Rotational Brownian motion and rotational relaxation phenomena has received considerable interest in the literature for a long time. Historically, the problem of isotropic rotational Brownian motion arose in connection with the work of Purcell on spin relaxation in systems with more than two spins in the same molecule. The dynamics of rotational Brownian motion of a sphere around a given axis was discussed briefly by Einstein [1] in one of his early papers. Later, Debye [2] proceeded by extending Einsteins treatment of the translational Brownian motion to rotational Brownian motion of noninteracting permanent dipoles in the presence of an external timevarying field and solving the appropriate Fokker-Planck equation. Here that equation is the Smoluchowski equation, which is an approximate Fokker-Planck equation in the space of angular coordinates for the distribution function of the orientations of the dipoles on the surface of the unit sphere when the influence of the inertia of the molecules on the relaxation process is ignored. Following years many generalizations of Debye model have been extensively studied [3,4,5,6,7,8,9,10,11]. However, Debye theory cannot explain relaxation phenomena in strongly interacting systems. The relaxation behavior in strongly interacting systems such as amorphous polymers, spin glasses, glass forming liquids, etc., deviates considerably from the exponential (Debye) pattern Φ ∼ exp [−t/τ ] and is characterized by a broad distribution of relaxation times. The relaxation in strongly interacting systems obey to the stretched exponential relaxation function experimentally Φ ∼ exp [−(t/τ ) α ] with 0 < α < 1, which often referred to as the KohlrauschWilliam-Watts (KWW) function [12,13].In this Letter our aim is to obtain rotational relaxation function in terms of autocorrelation function of rotational Brownian motion using multi-level jumping process (MJP) formalism based on historical Debye rotational relaxation scenario. The MJP is the generalization of the two-level jumping process (TJP) formalism. The TJP and MJP have been used to obtain the relaxation function [14,15,16,17]. Recently, the non-exponential relaxation function in complex systems has been obtained using MJP formalism [18]. * Electronic address: ekrem.aydiner@deu.edu.tr Autocorrelation function φ is simply given by( 1) where µ(0) and µ(t) denote values of fluctuation variable µ, i.e. dipole, at time zero and the same variable at a later time t, respectively. Physically, it measures the time over which the variable µ retains its own memory until this memory is averaged out by statistical randomness.If it is assumed that the external field has been applied in the z-direction, the...

show abstract

Rotational Brownian motion of an asymmetric top

Cited by 54 publications

References 18 publications

The Langevin equation on Lie algebras: Maxwell–Boltzmann is not always the equilibrium

The Langevin equation on Lie algebras: Maxwell–Boltzmann is not always the equilibrium

Orientational relaxation of spherical top molecules in gases and liquids: effect of collision intensity

Rotational Brownian Motion on Sphere Surface and Rotational Relaxation

Contact Info

Product

Resources

About