A fundamental constraint on quantum mechanical diffusion coefficients

A general quantum mechanical master equation for the damped oscillator, which can be represented as a phase space Fokker-Planck equation for the Wigner function, will be investigated with respect to the uncertainty principle. This leads to a condition to be imposed on the diffusion coefficients, which (i) is not fulfilled by an often quoted quasi-classical choice, and (ii) provides a uniqueness criterium in Dekker's theory.     

A method for extracting gluon-fragmentation functions from jet-events

A simple algorithm to extract gluon fragmentation functions from two- and three-jet events ine ⁺ e ^?-annihilation is discussed.     

A Monte Carlo model for determination of binary diffusion coefficients in gases

A Monte Carlo method has been developed for the calculation of binary diffusion coefficients in gas mixtures. The method is based on the stochastic solution of the linear Boltzmann equation obtained for the transport of one component in a thermal bath of the second one. Anisotropic scattering is included by calculating the classical deflection angle in binary collisions under isotropic potential. Model results are compared to accurate solutions of the Chapman–Enskog equation in the first and higher orders. We have selected two different cases, H₂ in H₂ and O in O₂, assuming rigid spheres or using a model phenomenological potential. Diffusion coefficients, calculated in the proposed approach, are found in close agreement with Chapman–Enskog results in all the cases considered, the deviations being reduced using higher order approximations.     

Comparison of methods for calculating turbulent diffusion coefficients

Different methods for calculating the turbulent diffusion coefficient D _T of a passive scalar impurity in an infinite homogeneous isotropic stationary turbulent medium are examined. The values of D _T calculated by these methods are compared for two limiting types of turbulence, viz., turbulence with a δ-function spectrum and turbulence with a Kolmogorov-type spectrum. The temporal dependence of the velocity correlators is assumed to be exponential. It is shown that the most accurate method is based on the use of the solution of the nonlinear equation for the averaged Green’s function with consideration of the contribution from the four-point turbulent velocity correlators. A comparison with the results of other methods that are simpler from the mathematical standpoint shows that some of them also permit the calculation of D _T with relatively good accuracy. Zh. éksp. Teor. Fiz. 111, 871–881 (March 1997)     

On optical diffusion coefficients for step-index multimode guides

Optical diffusion coefficients, computed from ray-tracing in step-index slab guides with small continuous width perturbations, show an angular dependence which does not in general correspond well with the mechanical deformation spectrum. This contrasts with assumptions of a one-to-one correspondence in earlier reports. The results indicate that, in a fibre having a steep cut-off in the perturbation spectrum at high mechanical frequencies, the corresponding diffusion coefficient will have a significantly less pronounced cut-off. It is also shown that, in a cylindrical guide with diameter perturbations, the effect of skew rays is to further reduce the cut-off rate in the diffusion coefficient.An immediate consequence of these findings is that, in a perturbed fibre without appreciable cladding loss, the loss penalty (due to radiation) may be much higher than would be predicted by the mechanical spectrum alone.As a prelude to the above ray-tracing studies, a derivation of the optical diffusion equation is given from the analogy with Brownian motion.     

Method for measuring chemical diffusion coefficients in solids

Experiments were performed with temperature programmed desorption of hydrogen and deuterium adsorbates on small platinum spheres. Beyond the expected desorption peak of these adsorbates at around 300 K sample temperature an additional desorption peak at higher temperatures was observed. This additional peak is explained by the diffusion of hydrogen or deuterium atoms from the inside of the spheres to their surfaces with final desorption from these surfaces. The visibility of this second high temperature desorption peak is supported by a small diameter of the platinum spheres. Platinum spheres with diameters around 64 μm were used. The sample temperature at which the second peak was observed depends on the parameters: diameter of the platinum spheres, heating rate of the sample and chemical diffusion coefficient of hydrogen or deuterium in platinum. A theory, which assumes that the chemical diffusion coefficient can be described with an Arrhenius ansatz, was developed to simulate the occurrence of the second peak. The combination of these kinds of experiments with the theory gives a method to measure chemical diffusion coefficients. This method can be called temperature programmed diffusion. At 510 K sample temperature the diffusion coefficient 1.61×10⁻¹² m²/s of hydrogen in platinum and the diffusion coefficient 1.40×10⁻¹² m²/s of deuterium in platinum was measured.     

State-dependent diffusion coefficients and free energies for nucleation processes from Bayesian trajectory analysis

ABSTRACT

The rate of nucleation processes such as the freezing of a supercooled liquid or the condensation of supersaturated vapour is mainly determined by the height of the nucleation barrier and the diffusion coefficient for the motion across it. Here, we use a Bayesian inference algorithm for Markovian dynamics to extract simultaneously the free energy profile and the diffusion coefficient in the nucleation barrier region from short molecular dynamics trajectories. The specific example we study is the nucleation of vapour bubbles in liquid water under strongly negative pressures, for which we use the volume of the largest bubble as a reaction coordinate. Particular attention is paid to the effects of discretisation, the implementation of appropriate boundary conditions and the optimal selection of parameters. We find that the diffusivity is a linear function of the bubble volume over wide ranges of volumes and pressures, and is mainly determined by the viscosity of the liquid, as expected from the Rayleigh–Plesset theory for macroscopic bubble dynamics. The method is generally applicable to nucleation processes and yields important quantities for the estimation of nucleation rates in classical nucleation theory.     

A Hamilton-Jacobi formalism for thermodynamics

We show that classical thermodynamics has a formulation in terms of Hamilton-Jacobi theory, analogous to mechanics. Even though the thermodynamic variables come in conjugate pairs such as pressure/volume or temperature/entropy, the phase space is odd-dimensional. For a system with n thermodynamic degrees of freedom it is 2n+1-dimensional. The equations of state of a substance pick out an n-dimensional submanifold. A family of substances whose equations of state depend on n parameters define a hypersurface of co-dimension one. This can be described by the vanishing of a function which plays the role of a Hamiltonian. The ordinary differential equations (characteristic equations) defined by this function describe a dynamical system on the hypersurface. Its orbits can be used to reconstruct the equations of state. The ‘time’ variable associated to this dynamics is related to, but is not identical to, entropy. After developing this formalism on well-grounded systems such as the van der Waals gases and the Curie-Weiss magnets, we derive a Hamilton-Jacobi equation for black hole thermodynamics in General Relativity. The cosmological constant appears as a constant of integration in this picture.     

A high accuracy diffusion kinetics formalism for random multicomponent alloys: application to high entropy alloys

In this paper, a new, lighter, version of the highly accurate Moleko, Allnatt and Allnatt formalism for describing both tracer (self) and collective diffusion kinetics in multicomponent random alloys is presented. Verification of the resulting expressions is performed by means of kinetic Monte Carlo simulation. The accuracy of the new formalism is much higher than that of the combined Manning and Holdsworth and Elliott formalism discussed recently. Using this formalism the possible range of the tracer diffusion ratio of the highest to the lowest atomic component is examined for equiatomic (or near equiatomic) binary, ternary, quaternary and quinary alloys. It is shown that in the random alloy model, the correlation effect is the highest with a reduction of the fastest tracer diffusion by 40–55%, when moving from two pure metals to their equiatomic binary alloy. By adding the third component (with an intermediate mobility) this effect can be further increased with a possible total reduction of the fastest tracer diffusion by up to 70% (depending on the combinations of mobilities), while adding the fourth component brings this reduction up to 80% and with a possible maximum of up to 85% reduction for the 5-component alloy (again depending on the combinations of mobilities). But the slowest diffusing components are not affected by this. This suggests that kinetics arguments alone are not enough for explaining the sluggish diffusion observed of all atomic components in (equiatomic) high-entropy alloys.     

The matrix formalism for generalised gradients with time-varying orientation in diffusion NMR

Protein backbone 15N NMR spin relaxation rates are useful in characterizing the protein dynamics and structures. To observe the protein nuclear-spin resonances a pulse sequence has to include a water suppression scheme. There are two commonly employed methods, saturating or dephasing the water spins with pulse field gradients and keeping them unperturbed with flip-back pulses. Here different water suppression methods were incorporated into pulse sequences to measure 15N longitudinal T1 and transversal rotating-frame T1ρ spin relaxation. Unexpectedly the 15N T1 relaxation time constants varied significantly with the choice of water suppression method. For a 25-kDa Escherichiacoli. glutamine binding protein (GlnBP) the T1 values acquired with the pulse sequence containing a water dephasing gradient are on average 20% longer than the ones obtained using a pulse sequence containing the water flip-back pulse. In contrast the two T1ρ data sets are correlated without an apparent offset. The average T1 difference was reduced to 12% when the experimental recycle delay was doubled, while the average T1 values from the flip-back measurements were nearly unchanged. Analysis of spectral signal to noise ratios (s/n) showed the apparent slower 15N relaxation obtained with the water dephasing experiment originated from the differences in 1HN recovery for each relaxation time point. This in turn offset signal reduction from 15N relaxation decay. The artifact becomes noticeable when the measured 15N relaxation time constant is comparable to recycle delay, e.g., the 15N T1 of medium to large proteins. The 15N relaxation rates measured with either water suppression schemes yield reasonable fits to the structure. However, data from the saturated scheme results in significantly lower Model-Free order parameters (=0.81) than the non-saturated ones (=0.88), indicating such order parameters may be previously underestimated.     

Scaling laws for diffusion coefficients in mixtures of alkanes

Natural fluids, such as crude oils, are often mixtures of a broad range of different molecules, and in situ measurement of their composition is highly desirable. Furthermore, the relationship between their composition and their physical properties has always been a challenge for such mixtures. We have analyzed diffusion in alkane mixtures to find a power law for the self-diffusion coefficient in terms of molecular sizes. We demonstrate that this power law can be used to obtain the molecular size distribution of crude oils using noninvasive measurements of diffusion distributions.     

Surface diffusion coefficients for room acoustics: free-field measures

A surface diffusion coefficient is needed in room acoustics to enable the quality of diffusing surfaces to be evaluated. It may also facilitate more accurate geometric room acoustic models. This paper concentrates on diffusion coefficients derived from free-field polar responses. An extensive set of two- and three-dimensional measurements and predictions was used to test the worth of different diffusion coefficient definitions. The merits and problems associated with these types of coefficients are discussed, and past parameters reviewed. Two new coefficients are described. The new measure based on the autocorrelation function is forwarded as the best free-field coefficient. The strengths and weaknesses of the coefficient are defined.     

在不同扩散系数下反应扩散平面波的折射

在二维复金兹堡-朗道方程描述的反应扩散振荡系统中,就扩散对平面波折射率的影响进行了数值研究,从Snell定律出发导出了折射率的解析表达式,数值和理论结果表明：在纯扩散情况下,平面波的折射满足Snell折射定律,扩散只影响着平面波折射率的大小;在同时存在反应扩散情况下,只有在适当的扩散系数和系统参数下,平面波的折射才满足Snell折射定律.这些结果表明扩散系数对折射规律和折射率都有影响. 关键词： 复金兹堡-朗道方程 扩散 折射率     

Renormalized diffusion coefficients for electron-hole plasmas in crossed fields

The diffusion and drift of an excess plasma in a semiconductor is described with magnetohydrodynamic two-fluid equations including the fluctuating electric field produced by the equilibrium plasma in the sample. Using the weak coupling limit an equation of motion for the mean density of the excess plasma is established with renormalized drift and diffusion coefficients. With the aid of the fluctuation dissipation theorem these coefficients are expressed in terms of the dielectric function and discussed in detail for stable systems. The renormalized diffusion coefficient differs from the bare one by an additional term with thet ^–3/2-long time dependence. It is shown that this term in addition represents an anomalous diffusion rate proportionalB ^–1 which overweights the classical ambipolar diffusion for sufficiently strong fields, but decreases with increasing external electric field. The results are compared with experimental data.