Extended Diffusion Models Research Articles

Opinion-aware information diffusion model based on multivariate marked Hawkes process

Currently, information diffusion on online platforms plays an important role in social governance. Opinions contained in information have a significant influence on information diffusion. However, both classic and extended diffusion models lack consideration of the influence of opinions. Therefore, in this study, we propose an opinion-aware information diffusion model based on the multivariate marked Hawkes process to simulate the information diffusion process with effect of opinions. In addition, to simulate this process more accurately, we consider various endogenous and exogenous stimuli apart from the opinion. Simulation results show that the diffusion trend prediction evaluation metrics of our model are 31.4% (on average) better than the contemporary models tested. Moreover, the effects of internal and external factors are found to be qualitatively similar to the real information diffusion process; hence, we gain useful inspiration for social network research and public opinion guidance.

The femtosecond birefringence of CO2: from the high pressure gas to the liquid phase

The optical heterodyne detected (OHD) birefringence of CO2 gas in the reduced density range from ρ/ρc = 0.09–0.82 and in the room temperature liquid are reported. Each birefringent response is separated into an electronic, rotational diffusion and non-diffusive nuclear component. The CO2 rotational relaxation times in the gas phase scale inversely with density in accordance with extended diffusion models of rotational reorientation. The rotational diffusion component of CO2 liquid (τD = 0.34 ps) appears to obey Debye–Stokes–Einstein behavior. The non-diffusive nuclear responses of the vapor samples exhibit only very modest changes with density and closely resemble the response function of the classical linear free rotor. The dominant, but not exclusive, contribution to the decay of the Raman anisotropy of high-pressure CO2 gas is inertial motion. The spectral density of the non-diffusive nuclear response of liquid CO2 is broader and has higher frequency components than the corresponding gas-phase spectral densities, indicating the relative importance of interaction induced effects. The greater extent of collision-induced effects is clearly evident for CS2 liquid compared with liquid CO2 when the spectral densities of the non-diffusive nuclear responses of liquid CO2 and CS2 are compared as a function of reduced frequency. Inertial motion clearly makes a much larger contribution to the birefringence of liquid CO2 than to that of liquid CS2 (at room temperature). Copyright © 2000 John Wiley & Sons, Ltd.

On extended diffusion models for asymmetric top molecules in liquids

The extended rotational diffusion models are generalized to treat liquids composed of asymmetric top molecules. The correlation functions and their Fourier transforms are determined by both an analytical mechanics approach and a memory function approach. The limit of very short angular momentum correlation time is examined and is compared with the Debye anisotropic rotational diffusion model. The results are applied to infrared and Raman spectroscopy. A series of representative band profiles is presented. For asymmetric top molecules, the J-model is shown to be more realistic than the M-model.

Model for infrared and Raman studies of molecular rotations in liquids and gases

Experimental infrared and Raman data for molecular rotations in dense phases often lie in between the results predicted by theJ- andM-diffusion models of Gordon. In this paper, we present a theory which is similar in its basic approach to Gordon’s extended diffusion models (EDM) but in which the restrictions of theJ andM limits are removed. The outcome is a scheme which allows one to describe situations which fall between the two extreme pictures of theJ andM models. Application of this scheme to experiments is discussed.

Application of field theoretical methods to the calculation of spectroscopic band shapes of molecules in strongly interacting solvents. IV. Microscopic interpretation of the extended rotational diffusion model

Methods of field theory have been used to derive exact formal expressions for the frequency Fourier transforms of spectroscopic memory functions. In particular these functions for free- and environment-interacting rotors have been obtained. The nature of the parameter τJ that appears in the extended diffusion models has been identified as being the imaginary part of the self energy. All theoretical methods based upon the memory function techniques must use approximations to the exact formal memory functions derived in this paper. In those regions in which hydrodynamic treatments are no longer valid, the parameter τJ must appear as a frequency dependent quantity; we have demonstrated this frequency dependence. Finally by using the finite temperature Green’s function method we have derived two expressions for τJ, one of which is of second order in the solute–solvent interaction potential and the other is a far more exact infinite order result. Both of these results show temperature dependence.

Infrared study of diluted solutions of polyatomic molecules. I. Band shape of fundamentals associated with nondegenerate normal modes

A theory is proposed to analyze the band shapes of the simplest class of ir band profiles of polyatomic molecule solutions. The following theoretical points are explored in detail: dependence of vibrational correlation functions on the nature of normal modes involved, calculation of vectorial correlation functions for a classical ensemble of free asymmetric rotators, construction of extended diffusion models for asymmetric tops, and use of the ordered cumulant expansion techniques to study anisotropic rotational diffusion in liquids. The theory predicts a large variety of complex, often highly irregular, band profiles. A catalogue of representative band profiles is presented which orders them according to the symmetry of the active molecule.

On the theory of generalized rotational diffusion models

A new Volterra type equation is described from which correlation functions can be derived. A “memory kernel”, in contrast to the memory function is shown to arise more naturally out of the extended diffusion models suggested by Gordon.

Molecular dynamics of the rough sphere fluid. I. Rotational relaxation

A systematic study is made of rotational relaxation in rough sphere fluids for densities ranging from 0.1 to 0.666 of the closest packed density. Many of the current models of rotational relaxation are tested against the results of molecular dynamics. It is found that for densities higher than 0.40 of the closest packed density only the Fokker–Planck model is consistent with experiment. The various extended diffusion models, the jump diffusion model, and the rotational diffusion model are not only internally inconsistent, but also do not agree with experiment. No theory is consistent with experiment at intermediate densities where the collisional and the inertial time scales are comparable. In addition to the foregoing, it appears that the rough spheres tumble more freely in the solid state than they do in the fluid state at the melting density.

Cross-correlation functions for angular momentum and orientation

A general expression is derived that relates the generalized second moment of a rotational spectral band to an angular momentum−orientation time−correlation function for the ensemble of molecules. It is demonstrated that previous equations relating these spectral transforms to angular momentum correlation functions are recovered in the limit of short times. The extended diffusion models proposed by Gordon are used to calculate cross−correlation functions as a function of time, and the results are compared with several approximations, including the decoupling assumption widely used in spin−rotation relaxation. The cross correlations that appear in the spin−rotation problem are considered in detail. In contrast to the behavior of the spectral transform cross−correlation functions, it is explicitly demonstrated that the spin−rotation correlations for the extended diffusion models vanish after one collision.

Simulation of Diatomic Homonuclear Liquids

The molecular-dynamic method was used to simulate a fluid of 500 rigid diatomic homo-nuclear molecules interacting by a double Lennard-Jones potential. The equilibrium and time-dependent properties are calculated in the liquid phase. The computed pressure and the internal energy agree quantitatively to a few percent with experimental values for nitrogen. The reorientational and the velocity of the center-of-gravity self-correlation functions are also discussed. The memory-function formalism and the extended-diffusion models are used to interpret the reorientational self-correlation functions. The analysis reveals that these self-correlation functions have an exponential behavior for times larger than 5 \ifmmode\times\else\texttimes\fi{} 1${0}^{\ensuremath{-}13}$ sec. In this model, considering present computing precision, there is no observable hydrodynamic-type relaxation in the reorientational self-correlation functions.

Rotational Diffusion of Symmetric Top Molecules in Liquids

The extended M- and J-diffusion models previously proposed to describe the reorientation of linear and spherical molecules are used to treat liquids composed of symmetric top molecules. The reorientational correlation functions and their Fourier transforms are determined and shown to reduce, in the J-diffusion model in the limit of very short angular momentum correlation times τJ, to the results obtained by solution of the anisotropic diffusion equation. The applicability of the diffusion equation results, outside the domain of validity of the diffusion equation, are examined in detail. Magnetic spin relaxation due to motional modulation of spin-rotational interactions is also considered within the framework of the extended diffusion models, and the inertial motion of the molecules and the precessional motion of the angular momentum are shown to influence the contributions due to the modulation of the anisotropic part of the spin-rotational interactions.