Working group report: Low energy and flavour physics

This is a report of the low energy and flavour physics working group at WHEPP-8, held at the Indian Institute of Technology, Mumbai, India, during 5–16 January 2004.     

Radiating Kerr particle in Einstein universe

A generalized Kerr-NUT type metric is considered in connection with Einstein field equations corresponding to perfect fluid plus a pure radiation field. A general scheme for obtaining the exact solutions of these field equations is developed. Two physically meaningful particular cases are investigated in detail. One gives the field of a radiating Kerr particle embedded in the Einstein universe. The other solution may probably represent a deSitter-like universe pervaded by a pure radiation field.     

The transition width and critical current density measurements on slow-cooled YBa2Cu3O7−x superconductor

It is shown that by adopting a very gradual programmed cooling procedure in oxygen environment one can obtain a sharp transition (ΔT _c⋍1 K) in YBa₂Cu₃O_7−x while retaining the high-T _c value (⋍105 K) of samples prepared by a semi-wet route. This is attributed to a maximum occupancy of oxygen at 0 1/2 0 sites and a near-perfect ordering of vacancies at 1/2 0 0 sites in the orthorhombic unit cell which maximizes the availability of conduction paths in the form of continuous CuO₄ chains. Critical current densities (J _c) of 204 A cm⁻² are obtained for bulk samples at 77 K. It is suggested that the intergrain coupling is weak and thus limits the transportJ _c-values.     

Embedding in higher dimensions causes ambiguity in determining equations from data

A linear system of dimension D can be embedded by D time-delay vectors. However, a nonlinear system often requires more vectors, almost always not more than 2D+1. This paper is regarding the consequence of such an embedding. We encountered this problem in an attempt to obtain a set of equations from the observed data. Our goal was to generate a system which is topologically conjugate to the original system. We found that many a times our efforts led to highly unstable systems. Now, we have an explanation. Embedding in higher dimensions causes a topological foliation and this foliation has a D-dimensional “leaf”. All the data were on this leaf and therefore we were unable to distinguish this foliated system from those where the foliation had collapsed. We illustrate the phenomenon by examples from numerically generated data and suggest possible remedies.     

A Nonlinear Generalization of Singular Value Decomposition and Its Applications to Mathematical Modeling and Chaotic Cryptanalysis

In this paper we are going to study the zero location and asymptotic behavior of extremal polynomials with respect to a generalized non-diagonal Sobolev norm in which the product of the function and its derivative appears. The orthogonal polynomials with respect to this Sobolev norm are a particular case of those extremal polynomials. The multiplication operator by the independent variable is the main tool in order to obtain our results.     

Speeding up Karmarkar's algorithm for multicommodity flows

We show how to speed up Karmarkar's linear programming algorithm for the case of multicommodity flows. The special structure of the constraint matrix is exploited to obtain an algorithm for the multicommodity flow problem which requires O(s ^3.5 v ^2.5 eL) arithmetic operations, each operation being performed to a precision of O (L) bits. Herev is the number of vertices ande is the number of edges in the given network,s is the number of commodities, andL is bounded by the number of bits in the input. We obtain a speed up of the order of (e ^0.5/v ^0.5)+(e ^2.5/v ^2.5s²) over Karmarkar's modified algorithm which is substantial for dense networks. The techniques in the paper can also be used to speed up any interior point algorithm for any linear programming problem whose constraint matrix is structurally similar to the one in the multicommodity flow problem. Research supported by a fellowship from the Shell Foundation. Research supported by NSF under grant NSF DCR-8404239.     

Column isoelectric focusing in natural pH gradients generated by biological buffers

Using 2 or 3 simple Good zwitterionic buffers at a 16 or 18 mmol/L final column concentration of the mixture, natural pH gradients of 4 to 8 and 3 to 9.5, respectively, were generated in a liquid LKB column. The pH gradients, stabilized by an anticonvective sucrose gradient, were linear, reproducible and stable in the electric field up to 5h. The pH gradients were used for isoelectric focusing of a number of impure proteins such as human hemoglobin, bovine serum albumin and chicken egg white lysozyme. The protein components could be well separated in the gradient, were easily recovered and appeared to be quite pure when analyzed by sodium dodecyl sulfate-gel electrophoresis. Furthermore, the pH gradient 4-8 was effectively used to isolate one of the acidic isozyme (pI 5.6) components of mouse liver alcohol dehydrogenase (EC 1.1.1.1) in an enzymatically active state, suggesting that the procedure does not denature proteins. The low cost, the ease with which the pH gradients are formed, their linearity, stability for a sufficient period to allow proteins to reach equilibrium and their subsequent recovery from buffer eluates should make the procedure interesting for electrofocusing of proteins.     

DNA attachment chemistry at the flexible silicone elastomer surface: toward disposable microarrays

This paper describes the preparation and surface characterization of maleimide-activated silicone elastomer (PDMS(MCC)) followed by covalent functionalization using thiol-terminated DNA sequences (primary oligo). The stability of this attachment chemistry was demonstrated by the retention of the primary oligo through the process of hybridization with a labeled complementary DNA sequence. In these studies, the hybridized labeled DNA oligomers were detected using confocal fluorescence microscopy. We have employed a vapor deposition technique in which a plasma-treated silicone elastomer (PDMS(OH)) was exposed to vapors of 3-(aminopropyl)triethoxysilane (APTS) under vacuum, to yield the amine-functionalized silicone elastomer (PDMS(NH)(2)). PDMS(NH)(2) was further coupled with a heterofunctional cross-linker, sulfosuccinimidyl-4-(N-maleimidomethyl)cyclohexane-1-carboxylate to obtain PDMS(MCC). The surface functionalities of the elastomers were characterized using contact angle measurements and X-ray photoelectron spectroscopy. Surface-modified silicone elastomers appear to be promising substrates for use as substrates for disposable microarrays.     

Adsorption and interaction of fibronectin and human serum albumin at the liquid-liquid interface

The goal of this work was to investigate the dynamics of human plasma fibronectin (HFN) at the oil-water interface and to characterize its interactions with human serum albumin (HSA) by total internal reflection fluorescence microscopy (TIRFM). Among key results, we observed that fibronectin adsorption at the oil-water interface is rapid and essentially irreversible, even over short time scales. This may be due to the highly flexible nature of the protein, which allows its various domains to quickly attain energetically favorable conformations. On the other hand, HSA adsorption at the oil-water interface is relatively reversible at short times, and the protein is readily displaced by fibronectin even after HSA has been adsorbed at the interface for as long as 2 h. At longer adsorption times, HSA is able to more effectively resist complete displacement by fibronectin, although we observed significant fibronectin adsorption even under those conditions. Displacement of adsorbed fibronectin by HSA was negligible under all conditions. Fibronectin also adsorbs preferentially from a mixture of HFN and HSA, even when the concentration of HSA is substantially higher. This study is relevant to such emerging research thrusts as the development of biomimetic interfaces for a variety of applications, where there is a clear need for better understanding of the effects of interfacial competition, adsorption time scales, and extent of adsorption irreversibility on interfacial dynamics.