Drift velocity vector

The magnitude of the drift velocity vector v of conduction electrons can be calculated rather easily. It is surprisingly low. If we denote the number of conduction electrons per cubic meter n and the electronic charge as e, then... 

In this section, we begin the description of Brownian motion in terms of stochastic process. Here, we establish the link between stochastic processes and diffusion equations by giving expressions for the drift velocity and diffusivity of a stochastic process whose probability distribution obeys a desired diffusion equation. The drift velocity vector and diffusivity tensor are defined here as statistical properties of a stochastic process, which are proportional to the first and second moments of random changes in coordinates over a short time period, respectively. In Section VILA, we describe Brownian motion as a random walk of the soft generalized coordinates, and in Section VII.B as a constrained random walk of the Cartesian bead positions. 

Brownian motion of a constrained system of N point particles may also be described by an equivalent Markov process of the Cartesian bead positions R (f),..., R (f). The constrained diffusion of the Cartesian coordinates may be characterized by a Cartesian drift velocity vector and diffusivity tensor... 

The value of the drift coefficients required by each type of SDE may be obtained by comparing the value of the drift velocity generated by the SDE to that required by statistical mechanics. The desired drift velocity vector for a system of coordinates X, ..., X may be expressed in generic form as a sum... 

In an increase in sample ion concentration occurs due to a local decrease in the magnitude of the drift velocity of an ion. For drift velocity vector field Vd, stacking occurs when... 

D. Dynamical Reciprocal Vectors Drift Velocities and Diffusivities... 

Vj velocity (average drift) of particles i (iy = velocity vector)... 

Any particular ion starts off after a collision with a velocity that may be in any direction this is the randomness in its walk. The initial velocity can be ignored precisely because it can take place in any direction and therefore does not contribute to the drift (preferred motion) of the ion. But the ion is all the time under the influence of the applied-force field. This force imparts a component to the velocity of the ion, an extra velocity component in the same dkection as the force vector F. It is this additional velocity component due to the force F that is called the drift velocity Vj. What is its average value ... 

Moreover, the average relative velocity vector (10.105) is approximated by (10.113), as for the CPV model, because the drift velocity is neglected. 

The results (5.10.8) for the thermocapillary force Ft and (5.10.9) for the thermocapillary drift velocity, which were obtained under the assumption of a constant temperature gradient remote from the drop, prove to hold also for a varying gradient. These expressions can be rewritten in a vector form as follows [468] ... 

Fig. iO. Velocity vectors recorded for successive 20-min time intervals by a current meter 2 m above the bottom near the geometrical center of Long Island Sound. The rotary character of the tide and the net drift of bottom water due to the estuarine circulation are shown. 

To determine the drift velocity field for an arbitrarily shaped spatial domain, we divide it into a set of small subdomains. Each subdomain is treated as a one-point detector generating a feedback signal with a phase shift given by Eq. (9.46). Finally, the resulting drift velocity field is derived according to Eqs. (9.45) and (9.42) as the sum over all drift vectors induced by single subdomains. This superposition principle unifies and simplifies the study of different algorithms for continuous feedback control considerably. 

If a feedback can be considered as a sum of signals taken from different sources, the resulting drift direction is found to be the sum of particular drift vectors induced by each separate source. This superposition principle essentially simplifies the analysis of the drift velocity fields [47, 53]. 

The computational procedure for diffusion with drift is similar to that of the basic random walk procedure described above. At each time step, the values of loc and the drift velocity must be determined from the potential energy and the first and second derivatives of the trial wavefunction. The drift distance is given by the product of the vector drift velocity and the time step. Multiplication is based on the local energy. 

The longitudinal drift does not depend on the rotation direction of the spiral wave. On the contrary, the transverse drift is proportional to the vector product of the angular velocity vector and the gradient of the parameter, so the counter-rotating spirals drift in opposite directions. This drift has been demonstrated in mathematical models [42,43, 45,46] and in experiments in the BZ system [47, 48], and in preparations of myocardium [49, 50],... 

In the vertical distribution of the modules of mean current vectors (Fig. 3a), the highest vertical gradient (shear) is observed between 10 and 25 m (total mean values of 0.215 and 0.165 m s-1, respectively). This is probably related to the effect of the wind drift. In the layer 25-50 m, mean velocities are homogeneous and the main shear in their values takes place deeper down... 

L is the electrode spacing, the wave velocity and k the wave vector, each of which are given by the experimental configuration. A and B are attenuation coefficients and is the potential at the crystal surface, and these three parameters can also be calculated from the geometry and the material properties. The drift mobihty is measured in this experiment and is defined by... 

Meteorology the use of appropriate wind vectors to steer drift away from susceptible areas, awareness of the dangers of strongly stable and unstable atmospheric conditions and the selection of low-wind velocities for placement application. 

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