Langer

A fiill theory of micleation requires a dynamical description. In the late 1960s, the early theories of homogeneous micleation were generalized and made rigorous by Langer [47]. Here one starts with an appropriate Fokker-Planck... 

Within this general framework there have been many different systems modelled and the dynamical, statistical prefactors have been calculated. These are detailed in [42]. For a binary mixture, phase separating from an initially metastable state, the work of Langer and Schwartz [48] using die Langer theory [47] gives the micleation rate as... 

Berezhkovskii A M and Zitserman V Yu 1992 Generalization of the Kramers-Langer theory decay of the metastable state in the case of strongly anisotropic friction J. Phys. A Math. Gen. 25 2077-92... 

Berezhkovskii A M, Poliak E and Zitserman V Y 1992 Activated rate processes generalization of the Kramers-Grote-Hynes and Langer theories J. Chem. Phys. 97 2422... 

A. E. Halasa in A. W. Langer, ed., Polyamine-Chelated Alkali Metal Compounds, ACS Advances in Chemisty, No. 130, American Chemical Society, Washington, D.C., 1974. 

Neglecting flow nonuniformities, the contributions of molecular diffusion and turbulent mixing arising from stream sphtting and recombination around the sorbent particles can be considered additive [Langer et al., Int. ]. Heat and Mass Transfer, 21, 751 (1978)] thus, the axial dispersion coefficient is given by ... 

In addition to the trivial solutions, there is a /S-periodic upside-down barrier trajectory called instanton, or bounce [Langer 1969 Callan and Coleman 1977 Polyakov 1977]. At jS oo the instanton dwells mostly in the vicinity of the point x = 0, attending the barrier region (near x ) only during some finite time (fig. 20). When jS is raised, the instanton amplitude... 

Langer, who was the first to introduce the ImF method in his original paper [Langer 1969] on nucleation theory called it bubble . 

Recently, Langer (1999) has joined the debate. He at first sounds a distinct note of scepticism ... the term numerical simulation makes many of us uncomfortable. It is easy to build models on computers and watch what they do, but it is often unjustified to claim that we learn anything from such exercises. He continues by examining a number of actual simulations and points out, first, the value of... 

Langer, M., Silikone absolut verbindlich. Kleb-Dichtstoffe, 40(1), 26-31 (1996). 

Fig. 5. Electrical resistance as a function of the temperature at the indicated magnetic fields for a single microbundle of carbon nanotubes. The solid line is a fit using the two-band model for graphite (see inset) with an overlap A = 3.7 meV and a Fermi level right in the middle of the overlap (after Langer et at. l9 ).

Fig. 6. The magnetic field dependence of the magnetoresistance at different temperature for the same microbundle measured in Fig. 5 (after Langer et aL[ 9 ).

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