New Modeling of the Lensing Galaxy and Cluster of Q0957+561: Implications for the Global Value of the Hubble Constant

The gravitational lens 0957+561 is modeled utilizing recent observations of the galaxy and the cluster as well as previous VLBI radio data which have been re-analyzed recently. The galaxy is modeled by a power-law elliptical mass density with a small core while the cluster is modeled by a non-singular power-law sphere as indicated by recent observations. Using all of the current available data, the best-fit model has a reduced chi-squared of approximately 6 where the chi-squared value is dominated by a small portion of the observational constraints used; this value of the reduced chi-squared is similar to that of the recent FGSE best-fit model by Barkana et al. However, the derived value of the Hubble constant is significantly different from the value derived from the FGSE model. We find that the value of the Hubble constant is given by H_0 = 69 +18/-12 (1-K) and 74 +18/-17 (1-K) km/s/Mpc with and without a constraint on the cluster's mass, respectively, where K is the convergence of the cluster at the position of the galaxy and the range for each value is defined by Delta chi-squared = reduced chi-squared. Presently, the best achievable fit for this system is not as good as for PG 1115+080, which also has recently been used to constrain the Hubble constant, and the degeneracy is large. Possibilities for improving the fit and reducing the degeneracy are discussed.Comment: 22 pages in aaspp style including 6 tables and 5 figures, ApJ in press (Nov. 1st issue

Hamiltonian formalism and the Garrett-Munk spectrum of internal waves in the ocean

Wave turbulence formalism for long internal waves in a stratified fluid is developed, based on a natural Hamiltonian description. A kinetic equation appropriate for the description of spectral energy transfer is derived, and its self-similar stationary solution corresponding to a direct cascade of energy toward the short scales is found. This solution is very close to the high wavenumber limit of the Garrett-Munk spectrum of long internal waves in the ocean. In fact, a small modification of the Garrett-Munk formalism includes a spectrum consistent with the one predicted by wave turbulence.Comment: 4 pages latex fil

Values of H_0 from Models of the Gravitational Lens 0957+561

The lensed double QSO 0957+561 has a well-measured time delay and hence is useful for a global determination of H0. Uncertainty in the mass distribution of the lens is the largest source of uncertainty in the derived H0. We investigate the range of \hn produced by a set of lens models intended to mimic the full range of astrophysically plausible mass distributions, using as constraints the numerous multiply-imaged sources which have been detected. We obtain the first adequate fit to all the observations, but only if we include effects from the galaxy cluster beyond a constant local magnification and shear. Both the lens galaxy and the surrounding cluster must depart from circular symmetry as well. Lens models which are consistent with observations to 95% CL indicate H0=104^{+31}_{-23}(1-\kthirty) km/s/Mpc. Previous weak lensing measurements constrain the mean mass density within 30" of G1 to be kthirty=0.26+/-0.16 (95% CL), implying H0=77^{+29}_{-24}km/s/Mpc (95% CL). The best-fitting models span the range 65--80 km/s/Mpc. Further observations will shrink the confidence interval for both the mass model and \kthirty. The range of H0 allowed by the full gamut of our lens models is substantially larger than that implied by limiting consideration to simple power law density profiles. We therefore caution against use of simple isothermal or power-law mass models in the derivation of H0 from other time-delay systems. High-S/N imaging of multiple or extended lensed features will greatly reduce the H0 uncertainties when fitting complex models to time-delay lenses.Comment: AASTEX, 48 pages 4 figures, 2 tables. Also available at: http://www.astro.lsa.umich.edu:80/users/philf/www/papers/list.htm

A Proof of Concept Study on Utilising a Non-invasive Microwave Analysis Technique to Characterise Silver Based Materials in Aqueous Solution

This paper reports on the feasibility of using a novel and robust microwave sensing technique to analyse and detect silver materials in an aqueous solution. Two products are tested, namely: silver chloride and silver oxide. The study mainly focused on indicating the difference between them and also any change in the size/size distribution of the sample. A microwave sensor designed previously is utilised to identify the potential of the technique to carry out the analysis. The results are presented as microwave spectrums that are the material response to microwaves. The results have shown that the technique has reasonably indicated the change in material type as well as size distribution. The results also show that these curves are distinguishable and can be related to the material and the change in its size. It is concluded that there is a potential of extending this technique to determine various other properties of silver products. The study suggests a design and development of a bespoke unit as a dedicated analysis tool and to address any anomalies arising from the current feasibility. This will have a huge industrial benefit in terms of cost reduction and time associated with the industrial analysis of silver material

Elastic energy of proteins and the stages of protein folding

We propose a universal elastic energy for proteins, which depends only on the radius of gyration $R_{g}$ and the residue number $N$. It is constructed using physical arguments based on the hydrophobic effect and hydrogen bonding. Adjustable parameters are fitted to data from the computer simulation of the folding of a set of proteins using the CSAW (conditioned self-avoiding walk) model. The elastic energy gives rise to scaling relations of the form $R_{g}\sim N^{\nu}$ in different regions. It shows three folding stages characterized by the progression with exponents $\nu = 3/5, 3/7, 2/5$, which we identify as the unfolded stage, pre-globule, and molten globule, respectively. The pre-globule goes over to the molten globule via a break in behavior akin to a first-order phase transition, which is initiated by a sudden acceleration of hydrogen bonding

Bound states of magnons in the S=1/2 quantum spin ladder

We study the excitation spectrum of the two-leg antiferromagnetic S=1/2 Heisenberg ladder. Our approach is based on the description of the excitations as triplets above a strong-coupling singlet ground state. The quasiparticle spectrum is calculated by treating the excitations as a dilute Bose gas with infinite on-site repulsion. We find singlet (S=0) and triplet (S=1) two-particle bound states of the elementary triplets. We argue that bound states generally exist in any dimerized quantum spin model.Comment: 4 REVTeX pages, 4 Postscript figure

Feasibility study on using microwave sensing technique to analyse silver-based products

This paper reports on the feasibility of using a novel and robust microwave sensing technology to detect and analyse various silverbased products such as silver nitrate and silver oxide. The focus of the investigation is to differentiate between the two products, identify the contamination and change in the sample size. A microwave sensor designed previously in house has been utilised to carry out this initial study to analyse the capability of microwave sensing technique to carry out the analysis. The change in the microwave spectra are used as an indicator of the difference in the silver products and any contamination they may have. The results and their detailed repeatability confirm the viability of using microwave sensing technique as a potential method to analyse various silver products. The curves obtained from the material response to microwaves are distinguishable and can be related to the materials’ properties. The study suggests a design and development of a bespoke unit as a dedicated analysis tool and to address any anomalies arising from the current feasibility. This will have a huge industrial benefit in terms of cost reduction and time associated with the industrial analysis