Thermal diffusivity measurements in porous ceramics by photothermal methods

Received: 16 September 1996/Accepted: 6 January 1997     

A branching process model for sand avalanches

An analytically solvable model for sand avalanches of noninteracting grains of sand, based on the Chapman-Kolmogorov equations, is presented. For a single avalanche, distributions of lifetimes, sizes of overflows and avalanches, and correlation functions are calculated. Some of these are exponentials, some are power laws. Spatially homogeneous distributions of avalanches are also studied. Computer simulations of avalanches of interacting grains of sand are compared to the solutions to the Chapman-Kolmogorov equations. We find that within the range of parameters explored in the simulation, the approximation of noninteracting grains of sand is a good one.     

Rational approximation of vertical segments

In many applications, observations are prone to imprecise measurements. When constructing a model based on such data, an approximation rather than an interpolation approach is needed. Very often a least squares approximation is used. Here we follow a different approach. A natural way for dealing with uncertainty in the data is by means of an uncertainty interval. We assume that the uncertainty in the independent variables is negligible and that for each observation an uncertainty interval can be given which contains the (unknown) exact value. To approximate such data we look for functions which intersect all uncertainty intervals. In the past this problem has been studied for polynomials, or more generally for functions which are linear in the unknown coefficients. Here we study the problem for a particular class of functions which are nonlinear in the unknown coefficients, namely rational functions. We show how to reduce the problem to a quadratic programming problem with a strictly convex objective function, yielding a unique rational function which intersects all uncertainty intervals and satisfies some additional properties. Compared to rational least squares approximation which reduces to a nonlinear optimization problem where the objective function may have many local minima, this makes the new approach attractive.     

Reactions on the dimethylphenylbenzacridinones. VI. Hydrogenation of ortho-nitrophenyl derivatives

Catalytic hydrogenation of o-nitrophenylbenz[a], benz[c], dibenz[a,h] and dibenz[a,g]acridinones using Pd/C as catalyst, at 60 psi of pressure, gave the hiterto unknown benzoquinoacridine N-oxides and benzo-pyranonaphthyridine N-oxides. The structure of all products was corroborated by ir, ¹H- and ¹³C-nmr and mass spectra data.     

Constants of Motion for Several One-Dimensional Systems and Problems Associated with Getting Their Hamiltonians

The constants of motion of the following systems are deduced: a relativistic particle with linear dissipation; a no-relativistic particle with a time explicitly depending force; a no-relativistic particle with a constant force and time depending mass; and a relativistic particle under a conservative force with position depending mass. The Hamiltonian for these systems, which is determined by getting the velocity as a function of position and generalized linear momentum, can be found explicitly at first approximation for the first system. The Hamiltonians for the other systems are kept implicitly in their expressions for their constants of motion.     

Conductive polyethylene-carbon black composites by elongational-flow injection molding Part 3. Study of the structure and morphology

The morphology and structure of high molecular weight linear polyethylene (M _w 450000) filled with carbon black and processed using molds that introduce an elongational flow component during injection molding has been examined using electron microscopy and x-ray diffraction techniques. The study of fracture surfaces reveals the display of shish-kebabs oriented along the injection direction with segregated longitudinal channels of carbon black particles. Molecular and lamellar changes in orientation are, furthermore, studied across the thickness of the moldings. It is shown that addition of carbon black particles to injection-molded polyethylene induces significant changes in lamellar orientation. Thus, while lamellar overgrowth proceeds perpendicular to the fiber axes within carbon free channels, lamellae grow randomly within carbon-enriched regions where flow is less pronounced.     

Intramolecular hydrogen abstraction. Iodosobenzene diacetate,an efficient and convenient reagent for alkoxy radical generation

Photolysis of several hydroxy compounds in presence of iodosobenzene diacetate and iodine leads to alkoxy radical derivatives which undergo intramolecular hydrogen abstraction to produce cyclic ethers in good yield.     

Type-D vacuum solutions with cosmological constant

All type-D vacuum (nonnull orbit and null orbit) solutions with are exhibited in canonical coordinates. The nonnull orbit metrics with contain four families of solutions: the static Levi-Cività metrics, the nondivergingD's, the divergingD's, and the diverging and twisting solutions. The null orbit metrics subdivide into two subclasses of solutions: the divergenceless null orbitD's, and the diverging and twisting null orbit solution.