Diffusion growth

To this point, we have examined diffusion growth in terms of nucleatlon and embryo formation. Let us now explore the actual species which diffuse in the lattice. 

As is well known (Chirikov, 1979 Izrailev, 1990), the phase-space evolution of the norelativistic classical kicked rotor is described by nonrelativistic standard map. The analysis of this map shows that the motion of the nonrelativistic kicked rotor is accompanied by unlimited diffusion in the energy and momentum. However, this diffusion is suppressed in the quantum case (Casati et.al., 1979 Izrailev, 1990). Such a suppression of diffusive growth of the energy can be observed when one considers the (classical) relativistic extention of the classical standard map (Nomura et.al., 1992) which was obtained recently by considering the motion of the relativistic electron in the field of an electrostatic wave packet. The relativistic generalization of the standard map is obtained recently (Nomura et.al., 1992)... 

In the resonance case the diffusive growth of the energy can be observed while it is highly suppressed for the value of (3 = 0.1 which is less than (3 = 1/2-7T. However, the diffusion is not unlimited even for the resonance case. 

The main feature of the quantum kicked rotor is the quantum localization phenomenon, which implies suppression of the diffusive growth of energy of the quantum kicked rotor compared to the energy of the classical rotor (Izrailev, 1990). The time dependence of the energy can be calculated as... 

One-dimensional diffusive growth of a crystal of fixed composition For constant... 

After solving a from the above equation, the growth rate is known (Equation 4-47), and the growth distance is Hence, the diffusion-growth problem... 

Diffusive growth of a singie sphericai bubbie in an infinite liquid reservoir... 

Diffusive growth of many equai-size sphericai hubbies... 

The growth of relatively large single crystals has been facilitated by the development of a three-chamber apparatus (Fig. 1) that uses a diffusion-growth method.19,20 The chambers each have a capacity of about 50 mL and are separ-... 

Developing the idea of de Vries, New [28] has supposed that the diffusion growth of larger bubbles is directly proportional to their surface area. This assumption is also rather approximate. Another approach, first proposed by Clark and Blackman [29] and further developed by Lemlich [30,31] proves to be more correct. 

Fig. 7.2. The structure of the translocation pathway in mycelial cords. (A) Hyphae fanning out at the distal end of a cord of Phanerochaete velutina (scanning electron microscopy by A. Yarwood) (B) Internal structure of a cord of Serpula lacrymans, showing vessels and cytoplasm-filled hyphae and extracellular matrix material. (C) Diagram of the components of the translocation pathway (adapted from Cairney, 1992) V, vessel hypha f, foraging front a, anastomosis (D) A cord system in beech woodland showing both corded mycelium and diffuse growth in contact with the wood substrate.

Many growth factors that become soluble after having been processed arc not shed and remain anchored to the membrane. Therefore, the distinction between membrane-anchored and diffusible growth factors is somewhat ambiguous. In malignant transformed cells, diffusible factors may be retained in the membrane of the same cell where they are S3tithesized and processed. This can stimulate the cell in an autocrine fashion with deleterious effects. 

Diffusive Growth of a Cavitation Bubble in an Ultrasonic Field..115... 

One of the most interesting problems of ultrasonic cavitation is the existence of the diffusive growth of bubbles in a sound field. As, without any field, a gas bubble should slowly dissolute due to gas diffusion from the bubble to a liquid, directional gas diffusion from liquid to the bubble arises under conditions of the bubble surface... 

They lack the primitive stroma and Leydig cells that are present in Sertoli-Leydig cell tumors. Oxyphilic and lipid-rich variants have been described, and Sertoli cell tumors can contain areas of diffuse growth. Immu-nohistochemistry can help to confirm the diagnosis and to differentiate a Sertoli cell tumor from such differential diagnostic considerations as Sertoliform endometrioid... 

For sufficiently large particles (the so-called continuum regime) and assuming unity accommodation coefficient, /(Kn, a) = 1, the continuum diffusion growth law based on particle diameter is... 

The Solid State Mechanisms of Nucleation, Solid State Diffusion, Growth of Particles and Measurement of Solid State Reactions... 

Nucleation, diffusion, growth of particles and measurement of solid state... 

Nucleation, diffusion, growth of particles and measurement of solid state By suitable manipulation, we can get (by Taylor Series expansion) ... 

Referring to 3.1.17., we see that the shape factor, 0, has a major effect uponr and the exponent of time, t, as well as on the aetivation energies. El in the table is the activation energy for nuclei formation, whereas E2 is that for nuclei growth. Ed is the activation energy for diffusion growth. This is the first time we have mentioned diffusion as a mechanism in nuclei formation. 

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