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51.
An energy-transport model is rigorously derived from the Boltzmann transport equation of semiconductors under the hypothesis that the energy gain or loss of the electrons by the phonon collisions is weak. Retaining at leading order electron-electron collisions and elastic collisions (i.e., impurity scattering and the elastic part of phonon collisions), a rigorous diffusion limit of the Boltzmann equation can be carried over, which leads to a set of diffusion equations for the electron density and temperature. The derivation is given in both the degenerate and nondegenerate cases. 相似文献
52.
Using a new graph counting technique suitable for self-similar fractals, exact 18th-order series expansions for SAWs on some Sierpinski carpets are generated. From them, the critical fugacityx
c and critical exponents SAW and SAW are obtained. The results show a linear dependence of the critical fugacity with the average number of bonds per site of the lattices studied. We find for some carpets with low lacunarity that SAW<0.75, thus violating the relation SAW(fractal) > SAW (d) for SAWs on the fractals which are embedded in ad-dimensional Euclidean space. 相似文献
53.
E. Brézin E. Korutcheva Th. Jolicoeur J. Zinn-Justin 《Journal of statistical physics》1993,70(3-4):583-598
Prompted by a recent article of Chakravarty, we reexamine theO(N) vector model with twisted boundary conditions ind dimensions in the various frameworks of the =d–2 expansion, the =4–d expansion, and the large-N expansion. These continuum models describe the physics below the critical temperatureT
c and nearT
c of a latticeO(N) spin model. We determine the effect of the twisting on finite-size scaling functions, for various geometries.On leave from G. Nadjakov Institute of Solid State Physics, 1784 Sofia, Bulgaria. 相似文献
54.
Summary The members of the power divergence family of statistics
all have an asymptotically equivalent χ2 distribution (Cressie and Read [1]). An asymptotic expansion for the distribution function is derived which shows that the
speed of convergence to this asymptotic limit is dependent on λ. Known results for Pearson'sX
2 statistic and the log-likelihood ratio statistic then appear as special cases in a continuum rather than as separate (unrelated)
expansions. 相似文献
55.
Carl M. Bender Fred Cooper Gerald Guralnik Harvey A. Rose David H. Sharp 《Journal of statistical physics》1980,22(6):647-660
We discuss the simple, randomly driven systemdx/dt = –x –x3 +f(t), wheref(t) is a Gaussian random function or stirring force with f(t)f(t) = (t – t). We show how to obtain approximately the coefficients of the expansion of the equal-time Green's functions as power series in (1/R)n, whereR is the internal Reynolds number ()1/2/, by using a new expansion for the path integral representation of the generating functional for the correlation functions. Exploiting the fact that the action for the randomly driven system is related to that of a quantum mechanical anharmonic oscillator with Hamiltonianp
2/2 +m
2
x
2/2 +vx
4 +x
6/2, we evaluate the path integral on a lattice by assuming that thex
6 term dominates the action. This gives an expansion of the lattice theory Green's functions as power series in 1/(a)1/3, wherea is the lattice spacing. Using Padé approximants to extrapolate toa = 0, we obtain the desired large-Reynolds-number expansion of the two-point function.Supported financially by the National Science Foundation and the U.S. Department of Energy. 相似文献
56.
Giorgio Parisi 《Journal of statistical physics》1980,23(1):49-82
We review the physical principles which are at the basis of recent field-theoretic computations of the critical exponents in two- and three-dimensional systems. We concentrate on those points that do not show up explicitly in the more standard-expansion: they must be discussed with care if one uses a perturbative approach at fixed space dimensions (the loop expansion). We present in detail simple computations of the critical exponents, while we summarize the results of longer and more accurate computations. 相似文献
57.
Exact renormalization group equations are derived for a position-space renormalization of spin systems with weak long-range forces. It is shown how an apparent dependence of the critical exponents on the choice of the renormalization group can be resolved via the mechanism of dangerous irrelevant variables and that this same mechanism is responsible for the breakdown of hyperscaling. The dimensiond=4 can be seen to be a borderline dimension above which classical critical exponents are expected. 相似文献
58.
The reaction of 1-alkynylcyclobutanols with aryl iodides in the presence of Pd(OAc)2 and Et3N in acetonitrile at 80°C for 24 h gives 2-disubstituted methylenecyclopentan-1-ones in modest to good yields. The tandem insertion-ring expansion process proceeds via the formation of an alkynyl π-complex, followed by migration of a carbon-carbon bond of the tert-alkanol to form the cyclopentanones stereoselectively. 相似文献
59.
This paper concerns the application of excess adsorption isotherms, measured for solvent mixture/adsorbent systems, to the characterization of TLC data. For this purpose the excess adsorption isotherms for three liquid mixtures: cyclohexane/ benzene, benzene/acetone, and carbon tetrachloride/ethyl acetate on silica gel at 20°C have been measured. These mixtures have been used as binary mobile phases in TLC measurements. It has been shown for a given solute in binary mobile phase that the quantity RM is a simple function of the excess adsorption. Parameters of this function have been used to characterize chromatographic systems with binary mobile phases. 相似文献
60.
C. Marhag H. Said P. Satre C. Favotto J. Rogez 《Journal of Thermal Analysis and Calorimetry》2003,74(1):275-285
Study of solid-liquid phase diagram of LiPO3-Pb(PO3)2 binary system, in certain calcination conditions, shows the existence of several metastable phasis. When heated at a temperature
of 723 K the binary mixtures lead uncompletely to a defined compound Pb2Li(PO3). On heating these ternary solid mixtures, three eutectic reactions have been observed: LiPO3+Pb(PO3)2→Liquid at a temperature of 793 K(1) LiPO3+Pb2Li(PO3)5→Liquid at a temperature of 843 K (2) Pb2Li(PO3)5+Pb(PO3)2→Liquid at a temperature of 891 K (3) The metastable liquid phase appears in the system at temperature of 793 K. DTA experiments
performed on the binary LiPO3-Pb(PO3)2 mixtures, show a superposition of two diagrams. The first one is metastable and the second represents the stable equilibrium
phase diagram. Measurements of liquid enthalpy of binary LiPO3-Pb(PO3)2 system at temperature of 979.65 K were reported. The corresponding values were very small and so the binary system can be
considered as athermal. Assuming an ideal behaviour, the liquidus curves in the metastable diagram were calculated and the
eutectic reaction (LiPO3-Pb(PO3)2→Liquid) was confirmed at 793 K.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献