Diffusion ballistic

In a recent study, Huan et al. [25] performed NM R experiments in vibrofluidized beds of mustard seeds in which the small sample volume allowed pulses short enough that displacements in the ballistic phase were distinguishable from those in the diffusion phase. In this case, the average collision frequency is measured directly, bypassing the uncertainty of the multiplicative factor mentioned above. These workers also measured the height dependence of the granular temperature profile. 

The new model is called quasi-ballistic because the electron motion in the quasi-free state is partly ballistic—that is, not fully diffusive, due to fast trapping. It is intended to be applied to low- and intermediate-mobility liquids, where the mobility in the trapped state is negligible. According to this, the mean... 

Table 10.4 lists the values of trap density and binding energy obtained in the quasi-ballistic model for different hydrocarbon liquids by matching the calculated mobility with experimental determination at one temperature. The experimental data have been taken from Allen (1976) and Tabata et ah, (1991). In all cases, the computed activation energy slightly exceeds the experimental value, and typically for n-hexane, 0/Eac = 0.89. Some other details of calculation will be found in Mozumder (1995a). It is noteworthy that in low-mobility liquids ballistic motion predominates. Its effect on the mobility in n-hexane is 1.74 times greater than that of diffusive trap-controlled motion. As yet, there has been no calculation of the field dependence of electron mobility in the quasi-ballistic model. 

The connection between anomalous conductivity and anomalous diffusion has been also established(Li and Wang, 2003 Li et al, 2005), which implies in particular that a subdiffusive system is an insulator in the thermodynamic limit and a ballistic system is a perfect thermal conductor, the Fourier law being therefore valid only when phonons undergo a normal diffusive motion. More profoundly, it has been clarified that exponential dynamical instability is a sufRcient(Casati et al, 2005 Alonso et al, 2005) but not a necessary condition for the validity of Fourier law (Li et al, 2005 Alonso et al, 2002 Li et al, 2003 Li et al, 2004). These basic studies not only enrich our knowledge of the fundamental transport laws in statistical mechanics, but also open the way for applications such as designing novel thermal materials and/or... 

This relation connects heat conduction and diffusion, quantitatively. As expected, normal diffusion (a =1)corresponds to the size-independent (/ = 0) heat conduction obeying the Fourier law. Moreover, a ballistic motion (a = 2) implies that the thermal conductivity is proportional to... 

Figure 5. Comparison of prediction (4) with numerical data. Normal diffusion ( ). The ballistic motion ( ). Superdiffusion ID Ehrenfest gas channel (Li et al, 2005)(v) the rational triangle channel (Li et al, 2003) (empty box) the polygonal billiard channel with (i = (V > — 1)7t/4), and 2 = 7r/3 (Alonso et al, 2002)(A) the triangle-square channel gas(Li et al, 2005) (<>) / values are obtained from system size L e [192, 384] for all channels except Ehrenfest channel (Li et al, 2005). The FPU lattice model at high temperature regime (Li et al, 2005) ( ), and the single walled nanotubes at room temperature ( ). Subdiffusion model from Ref. (Alonso et al, 2002) (solid left triangle). The solid curve is f3 = 2 — 2/a.

It is important to note that Eqs. 5, 8, and 9 were derived entirely from a silicon material balance and the assumption that physical sputtering is the only silicon loss mechanism thus these equations are independent of the kinetic assumptions incorporated into Eqs. 1, 2, and 7. This is an important point because several of these kinetic assumptions are questionable for example, Eq. 2 assumes a radical dominated mechanism for X= 0, but bombardment-induced processes may dominate for small oxide thickness. Moreover, ballistic transport is not included in Eq. 1, but this may be the dominant transport mechanism through the first 40 A of oxide. Finally, the first 40 A of oxide may be annealed by the bombarding ions, so the diffusion coefficient may not be a constant throughout the oxide layer. In spite of these objections, Eq. 2 is a three parameter kinetic model (k, Cs, and D), and it should not be rejected until clear experimental evidence shows that a more complex kinetic scheme is required. 

Fig. 10.2 Diffusive versus ballistic transport of electrons (See Color Plates)...

Constraints may be introduced either into the classical mechanical equations of motion (i.e., Newton s or Hamilton s equations, or the corresponding inertial Langevin equations), which attempt to resolve the ballistic motion observed over short time scales, or into a theory of Brownian motion, which describes only the diffusive motion observed over longer time scales. We focus here on the latter case, in which constraints are introduced directly into the theory of Brownian motion, as described by either a diffusion equation or an inertialess stochastic differential equation. Although the analysis given here is phrased in quite general terms, it is motivated primarily by the use of constrained mechanical models to describe the dynamics of polymers in solution, for which the slowest internal motions are accurately described by a purely diffusive dynamical model. 

We next consider the effective force balance for all >N variables, while treating the system as an unconstrained system. For simplicity, we consider the case in which the crossover from ballistic motion to diffusion occurs at a timescale much less than any characteristic relaxation time for vibrations of the hard coordinates, so that the vibrations are overdamped, but in which the vibrational relaxation times are much less than any timescale for the diffusion of the soft coordinates. In this case, we may assume local equilibration of all 3N momenta at timescales of order the vibration time. Repeating the analysis of the Section V.A, while now treating all 3N coordinates as unconstrained, yields an effective force balance... 

To obtain ballistite with a more progressive rate of burning, attempts were made to produce laminated flakes, with the two outer layers made of attenuated ballistite and an inner one, sandwiched between, made of ordinary ballistite. In the attenuated ballistite DNT was substituted for part of the nitroglycerine. However a powder of this type retained its ballistic characteristics for only a few months, since, due to diffusion, the composition of all three layers gradually became equal. 

Summary. We discuss how threshold detectors can be used for a direct measurement of the full counting statistics (FCS) of current fluctuations and how to implement Josephson junctions in this respect. We propose a scheme to characterize the full counting statistics from the current dependence of the escape rate measured. We illustrate the scheme with explicit results for tunnel, diffusive and quasi-ballistic mesoscopic conductors. 

Fig. 2. Escape rates versus Th/T for a tunnel (t), diffusive (d) and ballistic (b) mesoscopic conductor. refers to forward/backward bias respectively. Dashed...

In the past few years much attention has been drawn to the properties of shot noise in mesoscopic structures. So far experimental studies have been primarily concentrated on ballistic and diffusive systems, with only few exceptions [1, 2] where shot noise in electron tunneling or hopping was investigated. 

Transport of electrons along conducting wires surrounded by insulators have been studied for several decades mechanisms of the transport phenomena involved are nowadays well understood (see [1, 2, 3] for review). In the ballistic regime where the mean free path is much longer than the wire lengths, l 3> d, the conductance is given by the Sharvin expression, G = (e2/-jrh)N, where N (kpa)2 is the number of transverse modes, a, is the wire radius, a Fermi wave vector. For a shorter mean free path diffusion controlled transport is obtained with the ohmic behavior of the conductance, G (e2/ph)N /d, neglecting the weak localization interference between scattered electronic waves. With a further decrease in the ratio /d, the ohmic behavior breaks down due to the localization effects when /d < N-1 the conductance appears to decay exponentially [4]. 

The counter-intuitive behavior of the single-particle conductance Eq. (3) which increases with decreasing was first predicted by Andreev [10]. Comparing Eq. (3) with the ballistic ( d) expression Eq. (1) we see that disorder with d stimulates the single-particle transport by opening of new single-particle conducting modes that are blocked by Andreev reflections in the ballistic limit. The conductance reaches its maximum when the mean free path decreases down to a, after which the distinction between the usual and the Andreev diffusion is lost and Eq. (3) transforms into Eq. (4) for a dirty wire (see [11] for the particular case of vortex lines). 

The foundation for the development of these techniques is built on investigations into photon migration processes [2, 9]. Subsequent, detailed examination by Everall et al. [10, 11] demonstrated that the inelastically scattered (Raman) component decays substantially more slowly than its elastically scattered counterpart (i.e. the laser light) due to the regeneration of the Raman signal from the laser component. Discrimination between diffusely scattered photons and the ballistic and snake components is achieved by gating the detector in the temporal or spatial domain. 

Those who read this chapter may share with its authors the feelings expressed in Ref. 110 The dynamics in this particular problem space seems to have been rather more diffusive than ballistic. It is therefore wise to have some idea of where the ultimate destination is and to be familiar with the strategies that are most likely to take us there. 

G. Chen, Ballistic-diffusive heat-conduction equation, Phys. Rev. Lett. 86(11), 2297-2300 (2001). 

As a result, nearly perfect interfaces between the ferromagnetic material and the semiconductor are not a prerequisite for efficient spin injection. It is for example possible to insert a non-magnetic seed layer between the ferromagnetic base layer and the semiconductor collector. Since hot electrons retain their spin moment while traversing the thin non-magnetic layer this will not drastically reduce the spin polarization of the injected current. Finally, since electron injection is ballistic in SVT and MTT devices the spin injection efficiency is not fundamentally limited by a substantial conductivity mismatch between metals and semiconductors [161, 162], The latter is the case in diffusive ferromagnetic metal/semiconductor contacts [163],... 

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