Robin conditions on the Euclidean ball

Techniques are presented for calculating directly the scalar functional determinant on the Euclidean d-ball. General formulae are given for Dirichlet and Robin boundary conditions. The method involves a large mass asymptotic limit which is carried out in detail for d=2 and d=4 incidentally producing some specific summations and identities. Extensive use is made of the Watson-Kober summation formula.Comment: 36p,JyTex, misprints corrected and a section on the massive case adde

Polyhedral Cosmic Strings

Quantum field theory is discussed in M\"obius corner kaleidoscopes using the method of images. The vacuum average of the stress-energy tensor of a free field is derived and is shown to be a simple sum of straight cosmic string expressions, the strings running along the edges of the corners. It does not seem possible to set up a spin-half theory easily.Comment: 15 pages, 4 text figures not include

The hybrid spectral problem and Robin boundary conditions

The hybrid spectral problem where the field satisfies Dirichlet conditions (D) on part of the boundary of the relevant domain and Neumann (N) on the remainder is discussed in simple terms. A conjecture for the C_1 coefficient is presented and the conformal determinant on a 2-disc, where the D and N regions are semi-circles, is derived. Comments on higher coefficients are made. A hemisphere hybrid problem is introduced that involves Robin boundary conditions and leads to logarithmic terms in the heat--kernel expansion which are evaluated explicitly.Comment: 24 pages. Typos and a few factors corrected. Minor comments added. Substantial Robin additions. Substantial revisio

Membranes by the Numbers

Many of the most important processes in cells take place on and across membranes. With the rise of an impressive array of powerful quantitative methods for characterizing these membranes, it is an opportune time to reflect on the structure and function of membranes from the point of view of biological numeracy. To that end, in this article, I review the quantitative parameters that characterize the mechanical, electrical and transport properties of membranes and carry out a number of corresponding order of magnitude estimates that help us understand the values of those parameters.Comment: 27 pages, 12 figure

Impedance Analysis of Complex Formation Equilibria in Phosphatidylcholine Bilayers Containing Decanoic Acid or Decylamine

Bilayer lipid membranes composed of phosphatidylcholine and decanoic acid or phosphatidylcholine and decylamine were investigated using electrochemical impedance spectroscopy. Interaction between membrane components causes significant deviations from the additivity rule. Area, capacitance, and stability constant values for the complexes were calculated based on the model assuming 1:1 stoichiometry, and the model was validated by comparison of these values to experimental results. We established that phosphatidylcholine and decylamine form highly stable 1:1 complexes. In the case of decanoic acid-modified phosphatidylcholine membranes, complexes with stoichiometries other than 1:1 should be taken into consideration

Enzymes immobilized in Langmuir-Blodgett films: Why determining the surface properties in Langmuir monolayer is important?

ABSTRACT In this review we discuss about the immobilization of enzymes in Langmuir-Blodgett films in order to determine the catalytic properties of these biomacromolecules when adsorbed on solid supports. Usually, the conformation of enzymes depends on the environmental conditions imposed to them, including the chemical composition of the matrix, and the morphology and thickness of the film. In this review, we show an outline of manuscripts that report the immobilization of enzymes as LB films since the 1980’s, and also some examples of how the surface properties of the floating monolayer prepared previously to the transfer to the solid support are important to determine the efficiency of the resulting device

Live-Load Test and Computer Modeling of a Pre-Cast Concrete Deck, Steel Girder Bridge, and a Cast-in-Place Concrete Box Girder Bridge

The scheduled replacement of the 8th North Bridge, in Salt Lake City, UT, presented a unique opportunity to test a pre-cast concrete deck, steel girder bridge. A live-load test was performed under the directions of Bridge Diagnostic Inc (BDI) and Utah State University. Six different load paths were chosen to be tested. The recorded data was used to calibrate a finite-element model of this superstructure, which was created using solid, shell, and frame elements. A comparison between the measured and finite-element response was performed and it was determined that the finite-element model replicated the measured results within 3.5% of the actual values. This model was later used to obtain theoretical live-load distribution factors, which were compared with the AASHTO LRFD Specifications estimations. The analysis was performed for the actual condition of the bridge and the original case of the bridge, which included sidewalks on both sides. The comparison showed that the code over predicted the behavior of the actual structure by 10%. For the original case, the code\u27s estimation differed by as much as 45% of the theoretical values. Another opportunity was presented to test the behavior of a cast-in-place concrete box girder bridge in Joaquin County, CA. The Walnut Grove Bridge was tested by BDI at the request of Utah State University. The test was performed with six different load paths and the recorded data was used to calibrate a finite-element model of the structure. The bridge was modeled using shell elements and the supports were modeled using solid elements. The model was shown to replicate the actual behavior of the bridge to within 3% of the measured values. The calibrated model was then used to calculate the theoretical live-load distribution factors, which allowed a comparison of the results with the AASHTOO LRFD Specifications equations. This analysis was performed for the real conditions of the bridge and a second case where intermediate diaphragms were not included. It was determined that the code\u27s equations estimated the behavior of the interior girder more accurately for the second model (within 10%) than the real model of the bridge (within 20%)