Chromatic polynomials and whitney's broken circuits

The theorem of Hassler Whitney, which gives the chromatic polynomial of a graph in terms of “broken circuits,” is used to derive a new formula for the coefficients of chromatic polynomials.     

Covariant conservation laws from the palatini formalism

Covariant conservation laws in the Palatini formalism are derived. The result indicates that the gravitational part of conserved charges in general relativity should be calculated from a combination of Komar's strongly conserved current and the Einstein tensor. This implies that the set of complete diffeomorphism charges of a gravitating system consisting of scalar matter is described by Komar's vector density, and that the identification of gravitational energy and momentum reduces to two choices: a choice of relative weights of the contributions resulting from Komar's current and from the Einstein tensor, and a choice of preferred vector fields in space-time. A proposal is made which yields energy and momentum as scalars under diffeomorphisms and as a Lorentz vector in tangent space. Furthermore, the result can be used to identify covariant conservation laws holding separately for the matter contributions to diffeomorphism charges.     

A multigrid method for steady incompressible navier-stokes equations based on flux difference splitting

The steady Navier–Stokes equations in primitive variables are discretized in conservative form by a vertex-centred finite volume method Flux difference splitting is applied to the convective part to obtain an upwind discretization. The diffusive part is discretized in the central way. In its first-order formulation, flux difference splitting leads to a discretization of so-called vector positive type. This allows the use of classical relaxation methods in collective form. An alternating line Gauss–Seidel relaxation method is chosen here. This relaxation method is used as a smoother in a multigrid method. The components of this multigrid method are: full approximation scheme with F-cycles, bilinear prolongation, full weighting for residual restriction and injection of grid functions. Higher-order accuracy is achieved by the flux extrapolation method. In this approach the first-order convective fluxes are modified by adding second-order corrections involving flux limiting. Here the simple MinMod limiter is chosen. In the multigrid formulation the second-order discrete system is solved by defect correction. Computational results are shown for the well known GAMM backward-facing step problem and for a channel with a half-circular obstruction.     

The mass detector: A new detection system for carbohydrate and lipid analyses

Summary The mass detector was investigated as an alternative to RI detection for carbohydrate and lipid analyses with high pressure liquid chromatography. The instrument was found to be more sensitive than most RI detectors and, as gradient elution could also be carried out, the resulting chromatograms showed improved resolution.     

An Adsorption Isotherm from a Micro-state Model

The present study is dedicated to the derivation of an alternative adsorption isotherm for liquid-solid interfaces from a micro-state model, where adsorption is predominantly of a chemical nature. We describe adsorption-desorption on a liquid-solid interface starting from a partition function. In the new model the surface site occupation number is controlled by the Pauli principle (monolayer condition) and additional an attractive or repulsive surface potential, which depends on the overall surface coverage (nonlinearity). The effective potential represents adsorbate adsorbent interaction, as well as an influence of adsorbate adsorbate interactions on the surface potential. A Langmuir equivalent isotherm is recovered in the limit of a weak potential. The proposed model and Langmuirs isotherm are compared using data of humic acid (HA) adsorption on Brazilian Oxisol soil samples. Both models parameterize the experimental data well, but only the new model seems to be self-consistent.     

Probing segmental order in lipid bilayers at variable hydration levels by amplitude- and phase-modulated cross-polarization NMR

The conformational response of dimyristoylphosphatidylcholine bilayers in the liquid crystalline phase to hydration is investigated by a novel magic-angle spinning cross-polarization NMR technique.     

Impact ionization wavefront in ϱ-InSb

An impact ionization wavefront if found to cause avalanching in ?-InSb at 77 K. The front velocity of 3 × 10⁸cm/sec, is measured by a simple but accurate technique. Injected electrons initiate the front immediately after penetrating past the cathode or after drifting some distance beyond it, depending on the magnitude of the electric field strength.