Inorganic bonding of semiconductor strain gages

Inorganic bonding materials minimize outgassing and improve electrical and mechanical properties of semiconductor strain-gage transducers in high-vacuum and high-temperature operations. The two basic methods described are ceramic-glass-bonding and metallic bond formation between the strain gage and the substrate

Renormalisation-theoretic analysis of non-equilibrium phase transitions II: The effect of perturbations on rate coefficients in the Becker-Doring equations

We study in detail the application of renormalisation theory to models of cluster aggregation and fragmentation of relevance to nucleation and growth processes. In particular, we investigate the Becker-Doring (BD) equations, originally formulated to describe and analyse non-equilibrium phase transitions, but more recently generalised to describe a wide range of physicochemical problems. We consider here rate coefficients which depend on the cluster size in a power-law fashion, but now perturbed by small amplitude random noise. Power-law rate coefficients arise naturally in the theory of surface-controlled nucleation and growth processes. The noisy perturbations on these rates reflect the effect of microscopic variations in such mean-field coefficients, thermal fluctuations and/or experimental uncertainties. In the present paper we generalise our earlier work that identified the nine classes into which all dynamical behaviour must fall by investigating how random perturbations of the rate coefficients influence the steady-state and kinetic behaviour of the coarse-grained, renormalised system. We are hence able to confirm the existence of a set of up to nine universality classes for such BD systems.Comment: 30 pages, to appear in J Phys A Math Ge

Renormalisation-theoretic analysis of non-equilibrium phase transitions I: The Becker-Doring equations with power law rate coefficients

We study in detail the application of renormalisation theory to models of cluster aggregation and fragmentation of relevance to nucleation and growth processes. We investigate the Becker-Dorging equations, originally formulated to describe and analyse non-equilibrium phase transitions, and more recently generalised to describe a wide range of physicochemical problems. In the present paper we analyse how the systematic coarse-graining renormalisation of the \BD system of equations affects the aggregation and fragmentation rate coefficients. We consider the case of power-law size-dependent cluster rate coefficients which we show lead to only three classes of system that require analysis: coagulation-dominated systems, fragmentation-dominated systems and those where coagulation and fragmentation are exactly balanced. We analyse the late-time asymptotics associated with each class.Comment: 18 pages, to appear in J Phys A Math Ge

Effect of C. Parvum on immunization with irradiated tumour cells.

S.c. injection of tumour cells or small pieces of tumour irradiated to a dose of 22,000 rad evoked resistance to live challenge with the same tumour (a CBA strain fibrosarcoma induced with methylcholanthrene) 14 days later. This resistance was, however, over-ridden if the challenging inoculum was sufficiently large, and did not develop if the cells were irradiated to 100,000 rad. The resistance evoked by injection of 10(6) irradiated tumour cells was impaired by i.p. injection of 1-4 mg C. parvum 5 days before, and virtually abolished by a similar injection 11 days after, the irradiated cells. The effect of s.c. injection of a mixture of 10(6) irradiated cells and C. parvum 14 days before live challenge depended on the dose of C. parvum. With 0-7 mg the development of resistance was largely but not completely abrogated; 0-35 mg resulted in a lesser degree of abrogation, and 0-09 mg or 0-02 mg had little or no effect

The Renormalization Group and Singular Perturbations: Multiple-Scales, Boundary Layers and Reductive Perturbation Theory

Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary layers with technically difficult asymptotic matching, and WKB analysis. In contrast to conventional methods, the renormalization group approach requires neither {\it ad hoc\/} assumptions about the structure of perturbation series nor the use of asymptotic matching. Our renormalization group approach provides approximate solutions which are practically superior to those obtained conventionally, although the latter can be reproduced, if desired, by appropriate expansion of the renormalization group approximant. We show that the renormalization group equation may be interpreted as an amplitude equation, and from this point of view develop reductive perturbation theory for partial differential equations describing spatially-extended systems near bifurcation points, deriving both amplitude equations and the center manifold.Comment: 44 pages, 2 Postscript figures, macro \uiucmac.tex available at macro archives or at ftp://gijoe.mrl.uiuc.edu/pu

Renormalization Group Theory for Global Asymptotic Analysis

We show with several examples that renormalization group (RG) theory can be used to understand singular and reductive perturbation methods in a unified fashion. Amplitude equations describing slow motion dynamics in nonequilibrium phenomena are RG equations. The renormalized perturbation approach may be simpler to use than other approaches, because it does not require the use of asymptotic matching, and yields practically superior approximations.Comment: 13 pages, plain tex + uiucmac.tex (available from babbage.sissa.it), one PostScript figure appended at end. Or (easier) get compressed postscript file by anon ftp from gijoe.mrl.uiuc.edu (128.174.119.153), file /pub/rg_sing_prl.ps.

Influence of compressibility on scaling regimes of strongly anisotropic fully developed turbulence

Statistical model of strongly anisotropic fully developed turbulence of the weakly compressible fluid is considered by means of the field theoretic renormalization group. The corrections due to compressibility to the infrared form of the kinetic energy spectrum have been calculated in the leading order in Mach number expansion. Furthermore, in this approximation the validity of the Kolmogorov hypothesis on the independence of dissipation length of velocity correlation functions in the inertial range has been proved.Comment: REVTEX file with EPS figure

Dynamical Reduction of Discrete Systems Based on the Renormalization Group Method

The renormalization group (RG) method is extended for global asymptotic analysis of discrete systems. We show that the RG equation in the discretized form leads to difference equations corresponding to the Stuart-Landau or Ginzburg-Landau equations. We propose a discretization scheme which leads to a faithful discretization of the reduced dynamics of the original differential equations.Comment: LaTEX. 12pages. 1 figure include

Determination of the (3x3)-Sn/Ge(111) structure by photoelectron diffraction

At a coverage of about 1/3 monolayer, Sn deposited on Ge(111) below 550 forms a metastable (sqrt3 x sqrt3)R30 phase. This phase continuously and reversibly transforms into a (3x3) one, upon cooling below 200 K. The photoemission spectra of the Sn 4d electrons from the (3x3)-Sn/Ge(111) surface present two components which are attributed to inequivalent Sn atoms in T4 bonding sites. This structure has been explored by photoelectron diffraction experiments performed at the ALOISA beamline of the Elettra storage ring in Trieste (Italy). The modulation of the intensities of the two Sn components, caused by the backscattering of the underneath Ge atoms, has been measured as a function of the emission angle at fixed kinetic energies and viceversa. The bond angle between Sn and its nearest neighbour atoms in the first Ge layer (Sn-Ge1) has been measured by taking polar scans along the main symmetry directions and it was found almost equivalent for the two components. The corresponding bond lengths are also quite similar, as obtained by studying the dependence on the photoelectron kinetic energy, while keeping the photon polarization and the collection direction parallel to the Sn-Ge1 bond orientation (bond emission). A clear difference between the two bonding sites is observed when studying the energy dependence at normal emission, where the sensitivity to the Sn height above the Ge atom in the second layer is enhanced. This vertical distance is found to be 0.3 Angstroms larger for one Sn atom out of the three contained in the lattice unit cell. The (3x3)-Sn/Ge(111) is thus characterized by a structure where the Sn atom and its three nearest neighbour Ge atoms form a rather rigid unit that presents a strong vertical distortion with respect to the underneath atom of the second Ge layer.Comment: 10 pages with 9 figures, added reference