Integrals involving an exponential integral function and exponentials arising in the solution of radiation transfer

The solution of the equation of radiative transfer for a participating medium generally results in the evaluation of integrals involving a product of an exponential integral function or an exponential with a polynomial. Although expressions are available in the literature for the evaluation of such integrals, which appear to be structurally easy and simple to program, they are found to be not so accurate for certain parameters involved. To overcome such difficulties, alternative, computationally more accurate, analytic expressions are presented, and numerical techniques for their evaluation are discussed.     

Bleidner vapour phase extraction technique for the determination of organochlorine compounds in lake sediments

Summary The vapour phase extraction technique according to Bleidner has been applied to the trace analysis of organochlorine pesticides and PCB in water sediments. This method eliminates time consuming drying, extracting, and clean-up steps in comparison with the conventional (Soxhlet) methods. The method developed is sufficiently sensitive and shows satisfying recovery results — with the exception of -HCH. Low yields of the DDT family are not caused by artifacts but are rather due to irreversible adsorption to sediment and fast metabolizing power of this substrate.Dedicated to Prof. Dr. E. Lahmann, Institut für Wasser-, Boden-, und Lufthygiene, D-1000 Berlin 33, on the occasion of his 65th birthday     

Optimization of Gold Nanoparticle-Based DNA Detection for Microarrays

DNA microarrays are promising tools for fast and highly parallel DNA detection by means of fluorescence or gold nanoparticle labeling. However, substrate modification with silanes (as a prerequisite for capture DNA binding) often leads to inhomogeneous surfaces and/or nonspecific binding of the labeled DNA. We examined both different substrate cleaning and activating protocols and also different blocking strategies for optimizing the procedures, especially those for nanoparticle labeling. Contact angle measurements as well as fluorescence microscopy, atomic force microscopy (AFM), and a flatbed scanner were used to analyze the multiple-step process. Although the examined different cleaning and activating protocols resulted in considerably different contact angles, meaning different substrate wettability, silanization led to similar hydrophobic surfaces which could be revealed as smooth surfaces of about 2–4 nm roughness. The two examined silanes (3-glycidoxypropyltrimethoxysilane (GOPS) and 3-aminopropyltriethoxysilane (APTES)) differed in their DNA binding homogeneity, maximum signal intensities, and sensitivity. Nonspecific gold binding on APTES/PDC surfaces could be blocked by treatment in 3% bovine serum albumin (BSA).     

Are the New Physics Contributions from the Left-Right Symmetric Model Important for the Indirect CP Violation in the Neutral B Mesons?

No Heading Several works analyzing the new physics contributions from the Left-Right Symmetric Model to the CP violation phenomena in the neutral B mesons can be found in the literature. These works exhibit interesting and experimentally sensible deviations from the Standard Model predictions but at the expense of considering a low right scale υ_R around 1 TeV. However, when we stick to the more conservative estimates for υ_R, which say that it must be at least 10⁷ GeV, no experimentally sensible deviations from the Standard Model appear for indirect CP violation. This estimate for υ_R arises when the generation of neutrino masses is considered. In spite of the fact that this scenario is much less interesting and says nothing new about both the CP violation phenomenon and the structure of the Left-Right Symmetric Model, this possibility must be taken into account for the sake of completeness and when considering the see-saw mechanism that provides masses to the neutrino sector. ¹ Associate researcher of the Centro Internacional de Física, Ciudad Universitaria, Bogotá D.C., Colombia.     

Axiomatic Geometric Formulation of Electromagnetism with Only One Axiom: The Field Equation for the Bivector Field <Emphasis Type="Italic">F</Emphasis> with an Explanation of the Trouton-Noble Experiment

In this paper we present an axiomatic, geometric, formulation of electromagnetism with only one axiom: the field equation for the Faraday bivector field F. This formulation with F field is a self-contained, complete and consistent formulation that dispenses with either electric and magnetic fields or the electromagnetic potentials. All physical quantities are defined without reference frames, the absolute quantities, i.e., they are geometric four-dimensional (4D) quantities or, when some basis is introduced, every quantity is represented as a 4D coordinate-based geometric quantity comprising both components and a basis. The new observer-independent expressions for the stress-energy vector T(n) (1-vector), the energy density U (scalar), the Poynting vector S and the momentum density g (1-vectors), the angular momentum density M (bivector) and the Lorentz force K ((1-vector) are directly derived from the field equation for F. The local conservation laws are also directly derived from that field equation. The 1-vector Lagrangian with the F field as a 4D absolute quantity is presented; the interaction term is written in terms of F and not, as usual, in terms of A. It is shown that this geometric formulation is in a full agreement with the Trouton-Noble experiment.     

Can a Circulating Light Beam Produce a Time Machine

In a recent paper, Mallett found a solution of the Einstein equations in which closed timelike curves (CTC’s) are present in the empty space outside an infinitely long cylinder of light moving in circular paths around an axis. Here we show that, for physically realistic energy densities, the CTC’s occur at distances from the axis greater than the radius of the visible universe by an immense factor. We then show that Mallett’s solution has a curvature singularity on the axis, even in the case where the intensity of the light vanishes. Thus it is not the solution one would get by starting with Minkowski space and establishing a cylinder of light.     

The Difference Between the Standard and The Lorentz Transformations of the Electric and the Magnetic Fields

In this paper it is shown by using the Clifford algebra formalism that the usual Lorentz transformations of the three-dimensional (3D) vectors of the electric and magnetic fields E and B (which will be named as standard transformations (ST)) are different than the Lorentz transformations (LT) of well-defined quantities from the 4D spacetime. This difference between the ST and the LT is obtained regardless of the used algebraic objects (1-vectors or bivectors) for the representation of the electric and magnetic fields in the usual observer dependent decompositions of F. The LT correctly transform the whole 4D quantity, e.g., E_f : F · γ₀, whereas the ST are the result of the application of the LT only to the part of E_f, i.e., to F, but leaving γ₀ unchanged. The new decompositions of F in terms of 4D quantities that are defined without reference frames, i.e., the absolute quantities, are introduced and discussed. It is shown that the LT of the 4D quantities representing electric and magnetic fields correctly describe the motional electromotive force (emf) for all relatively moving inertial observers, whereas it is not the case with the ST of the 3D E and B.