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Inter-molecular multiple quantum coherence (iMQC) has important applications in NMR and MRI. However, the current theoretical methods still have some difficulties in analyzing the behavior of iMQC signal attenuation of pulsed field gradient diffusion experiments. In this paper, the iMQC diffusion experiments were analyzed by an effective phase shift diffusion equation (EPSDE) method, which is based on the idea that the accumulating phase shift (APS) can be viewed as the result of a diffusion process in virtual phase space (VPS) with effective diffusion coefficient K²(t)D (rad²/s) where K(t) = t0 g(t')dt' is a wavenumber and D is the physical diffusion coefficient of the spin carrier in the real space. The term K(ttot)z1 needs to be added to the APS when K(ttot) is not zero. Most of the time, K(ttot) equals zero. However, in iMQC experiments, the condition K(ttot) equaling zero or being non-zero for each spin depends on the gradient pulse setting. The signal attenuations of these two types of iMQC, zero or non-zero K(ttot), were analyzed in detail for free and restricted diffusions, which shows that there are significant differences between these two types of iMQC. Particularly, if an apparent diffusion coefficient Dapp is used to analyze the signal attenuation, it equals nD for zero K(ttot) which agrees with current theoretical and experimental reports, while for non-zero K(ttot), it equals (2n - 1)D which agrees with experimental results from the literature; there are no similar theoretical results reported for comparison. The result that Dapp equals (2n - 1)D is important because the higher value of Dapp means that non-zero K(ttot) iMQC can potentially provide more contrast and measure slower diffusion rates than zero K(ttot) iMQC. The EPSDE method provides a new way to analyze iMQC diffusion experiments. [ABSTRACT FROM AUTHOR]

The disagreement between two different studies of the diffusion equation for two hard disks to diffuse past each other in a narrow channel remains unresolved. Two different values for the divergence exponent of the mean first passage time (MFPT) were obtained. This has motivated the proposal that the difference arises from the use of different and nonequivalent definitions for the MFPT. Doubt was raised regarding the validity of the numerical solution of the diffusion equation as an explanation for the disagreement with the dimensional reduction method. In this paper, a one disk model which partially mimics the two disks problem is studied in the infinitely anisotropic diffusion limits. Although analytical arguments predict the exact exponent to be 1/2, it has not been probed in numerical studies. Using the two algorithms, we obtain exponents from numerical solutions which are consistent with each other and the proposed exact value. [ABSTRACT FROM AUTHOR]

Within a concept of the fractional diffusion equation and subordination, the paper examines the influence of a competition between long waiting times and long jumps on the escape from the potential well. Applying analytical arguments and numerical methods, we demonstrate that the presence of long waiting times distributed according to a power-law distribution with a diverging mean leads to very general asymptotic properties of the survival probability. The observed survival probability asymptotically decays like a power law whose form is not affected by the value of the exponent characterizing the power law jump length distribution. It is demonstrated that this behavior is typical of and generic for systems exhibiting long waiting times. We also show that the survival probability has a universal character not only asymptotically, but also at small times. Finally, it is indicated which properties of the first passage time density are sensitive to the exact value of the exponent characterizing the jump length distribution. [ABSTRACT FROM AUTHOR]

The Green–Kubo formula for discrete hydrodynamic variables involves information about not only the fluid transport coefficients but also about discrete versions of the differential operators that govern the evolution of the discrete variables. This gives an intimate connection between discretization procedures in fluid dynamics and coarse-graining procedures used to obtain hydrodynamic behavior of molecular fluids. We observed that a natural definition of discrete hydrodynamic variables in terms of Voronoi cells leads to a Green–Kubo formula which is divergent, rendering the full coarse-graining strategy useless. In order to understand this subtle issue, in the present paper we consider the coarse graining of noninteracting Brownian particles. The discrete hydrodynamic variable for this problem is the number of particles within Voronoi cells. Thanks to the simplicity of the model we spot the origin of the singular behavior of the correlation functions. We offer an alternative definition, based on the concept of a Delaunay cell that behaves properly, suggesting the use of the Delaunay construction for the coarse graining of molecular fluids at the discrete hydrodynamic level. [ABSTRACT FROM AUTHOR]

Collisional energy transfer in unimolecular systems is often described using a master equation. The lack of detailed knowledge of energy transfer events combined with the computationally intensive nature of this approach makes approximate methods attractive, especially for parametrizing experimental results. One such approximation is based on the diffusion equation. In this paper a number of diffusion equation approximations is examined. Troe and Nikitin have derived such approximations by truncation of the Kramers–Moyal expansion of the master equation. A new approximation, using a similar approach is presented here. The diffusion equation can also be obtained as the limit of a sequence of master equations as the collision energy transfer becomes infinitely small and frequent. The derivation of such a limiting diffusion equation is presented. A further set of approximations in which the energy transfer process is imbedded in a diffusion process is also examined. The accuracy of all approximations is assessed by comparison with full solutions of the corresponding master equations for energy transfer in azulene and ethane, and for the kinetics of methane dissociation. [ABSTRACT FROM AUTHOR]