Multipole Gravitational Lensing and High-order Perturbations on the Quadrupole Lens

An arbitrary surface mass density of gravitational lens can be decomposed into multipole components. We simulate the ray-tracing for the multipolar mass distribution of generalized SIS (Singular Isothermal Sphere) model, based on the deflection angles which are analytically calculated. The magnification patterns in the source plane are then derived from inverse shooting technique. As have been found, the caustics of odd mode lenses are composed of two overlapping layers for some lens models. When a point source traverses such kind of overlapping caustics, the image numbers change by \pm 4, rather than \pm 2. There are two kinds of images for the caustics. One is the critical curve and the other is the transition locus. It is found that the image number of the fold is exactly the average value of image numbers on two sides of the fold, while the image number of the cusp is equal to the smaller one. We also focus on the magnification patterns of the quadrupole (m = 2) lenses under the perturbations of m = 3, 4 and 5 mode components, and found that one, two, and three butterfly or swallowtail singularities can be produced respectively. With the increasing intensity of the high-order perturbations, the singularities grow up to bring sixfold image regions. If these perturbations are large enough to let two or three of the butterflies or swallowtails contact, eightfold or tenfold image regions can be produced as well. The possible astronomical applications are discussed.Comment: 24 pages, 6 figure

Neutrino Oscillations and Lepton Flavor Mixing

In view of the recent announcement on non-zero neutrino mass from Super-Kamiokande experiment, it would be very timely to investigate all the possible scenarios on masses and mixings of light neutrinos. Recently suggested mass matrix texture for the quark CKM mixing, which can be originated from the family permutation symmetry and its suitable breakings, is assumed for the neutrino mass matrix and determined by the four combinations of solar, atmospheric and LSND neutrino data and cosmological hot dark matter bound as input constraints. The charged-lepton mass matrix is assumed to be diagonal so that the neutrino mixing matrix can be identified directly as the lepton flavor mixing matrix and no CP invariance violation originates from the leptonic sector. The results favor hierarchical patterns for the neutrino masses, which follow from the case when either solar-atmospheric data or solar-HDM constraints are used.Comment: Latex, 9 page

A novel interdigitated capacitor based biosensor for detection of cardiovascular risk marker

C-reactive protein (CRP) is a potential biomarker whose elevated levels in humans determine cardiovascular disease risk and inflammation. In this study, we have developed a novel capacitive biosensor for detection of CRP-antigen using capacitor with interdigitated gold (GID) electrodes on nanocrystalline diamond (NCD) surface. The NCD surface served as a dielectric layer between the gold electrodes. GID-surface was functionalized by antibodies and the immobilization was confirmed by Fourier transform spectroscopy (FT-IR) and contact angle measurements. The CRP-antigen detection was performed by capacitive/dielectric-constant measurements. The relaxation time and polarizability constants were estimated using Cole-Cole model. Our results showed that the relaxation time constant (tau) of only CRP-antibody was within 10(-16)-10(-13) s, which was increased to 10(-11) s after the incubation with CRP-antigen, suggesting that the CRP-antigen was captured by the antibodies on GID-surface. In addition, polarizability constant(m) of CRP was also increased upon incubation with increasing concentration of CRP-antigen. Our results showed that the response of GID-NCD-based capacitive biosensor for CRP-antigen was dependent on both concentration (25-800 ng/ml) as well as frequency (50-350 MHz). Furthermore, using optimized conditions, the GID-NCD based capacitive biosensor developed in this study can potentially be used for detection of elevated levels of protein risk markers in suspected subjects for early diagnosis of disease

Diffusion-Limited Aggregation Processes with 3-Particle Elementary Reactions

A diffusion-limited aggregation process, in which clusters coalesce by means of 3-particle reaction, A+A+A->A, is investigated. In one dimension we give a heuristic argument that predicts logarithmic corrections to the mean-field asymptotic behavior for the concentration of clusters of mass $m$ at time $t$, $c(m,t)~m^{-1/2}(log(t)/t)^{3/4}$, for $1 << m << \sqrt{t/log(t)}$. The total concentration of clusters, $c(t)$, decays as $c(t)~\sqrt{log(t)/t}$ at $t --> \infty$. We also investigate the problem with a localized steady source of monomers and find that the steady-state concentration $c(r)$ scales as $r^{-1}(log(r))^{1/2}$, $r^{-1}$, and $r^{-1}(log(r))^{-1/2}$, respectively, for the spatial dimension $d$ equal to 1, 2, and 3. The total number of clusters, $N(t)$, grows with time as $(log(t))^{3/2}$, $t^{1/2}$, and $t(log(t))^{-1/2}$ for $d$ = 1, 2, and 3. Furthermore, in three dimensions we obtain an asymptotic solution for the steady state cluster-mass distribution: $c(m,r) \sim r^{-1}(log(r))^{-1}\Phi(z)$, with the scaling function $\Phi(z)=z^{-1/2}\exp(-z)$ and the scaling variable $z ~ m/\sqrt{log(r)}$.Comment: 12 pages, plain Te

Review on carbon-derived, solid-state, micro and nano sensors for electrochemical sensing applications

The aim of this review is to summarize the most relevant contributions in the development of electrochemical sensors based on carbon materials in the recent years. There have been increasing numbers of reports on the first application of carbon derived materials for the preparation of an electrochemical sensor. These include carbon nanotubes, diamond like carbon films and diamond film-based sensors demonstrating that the particular structure of these carbon material and their unique properties make them a very attractive material for the design of electrochemical biosensors and gas sensors. Carbon nanotubes (CNT) have become one of the most extensively studied nanostructures because of their unique properties. CNT can enhance the electrochemical reactivity of important biomolecules and can promote the electron-transfer reactions of proteins (including those where the redox center is embedded deep within the glycoprotein shell). In addition to enhanced electrochemical reactivity, CNT-modified electrodes have been shown useful to be coated with biomolecules (e.g., nucleic acids) and to alleviate surface fouling effects (such as those involved in the NADH oxidation process). The remarkable sensitivity of CNT conductivity with the surface adsorbates permits the use of CNT as highly sensitive nanoscale sensors. These properties make CNT extremely attractive for a wide range of electrochemical sensors ranging from amperometric enzyme electrodes to DNA hybridization biosensors. Recently, a CNT sensor based fast diagnosis method using non-treated blood assay has been developed for specific detection of hepatitis B virus (HBV) (human liver diseases, such as chronic hepatitis, cirrhosis, and hepatocellular carcinoma caused by hepatitis B virus). The linear detection limits for HBV plasma is in the range 0.5–3.0 μL−1 and for anti- HBVs 0.035–0.242 mg/mL in a 0.1 M NH4H2PO4 electrolyte solution. These detection limits enables early detection of HBV infection in suspected serum samples. Therefore, non-treated blood serum can be directly applied for real-time sensitive detection in medical diagnosis as well as in direct in vivo monitoring. Synthetic diamond has been recognized as an extremely attractive material for both (bio-) chemical sensing and as an interface to biological systems. Synthetic diamond have outstanding electrochemical properties, superior chemical inertness and biocompatibility. Recent advances in the synthesis of highly conducting nanocrystalline-diamond thin films and nano wires have lead to an entirely new class of electrochemical biosensors and bio-inorganic interfaces. In addition, it also combines with development of new chemical approaches to covalently attach biomolecules on the diamond surface also contributed to the advancement of diamond-based biosensors. The feasibility of a capacitive field-effect EDIS (electrolyte-diamond-insulatorsemiconductor) platform for multi-parameter sensing is demonstrated with an O-terminated nanocrystalline-diamond (NCD) film as transducer material for the detection of pH and penicillin concentration. This has also been extended for the label-free electrical monitoring of adsorption and binding of charged macromolecules. One more recent study demonstrated a novel bio-sensing platform, which is introduced by combination of a) geometrically controlled DNA bonding using vertically aligned diamond nano-wires and b) the superior electrochemical sensing properties of diamond as transducer material. Diamond nanowires can be a new approach towards next generation electrochemical gene sensor platforms. This review highlights the advantages of these carbon materials to promote different electron transfer reactions specially those related to biomolecules. Different strategies have been applied for constructing carbon material-based electrochemical sensors, their analytical performance and future prospects are discussed

Is the Number of Giant Arcs in LCDM Consistent With Observations?

We use high-resolution N-body simulations to study the galaxy-cluster cross-sections and the abundance of giant arcs in the $\Lambda$CDM model. Clusters are selected from the simulations using the friends-of-friends method, and their cross-sections for forming giant arcs are analyzed. The background sources are assumed to follow a uniform ellipticity distribution from 0 to 0.5 and to have an area identical to a circular source with diameter 1\arcsec. We find that the optical depth scales as the source redshift approximately as \tau_{1''} = 2.25 \times 10^{-6}/[1+(\zs/3.14)^{-3.42}] (0.6<\zs<7). The amplitude is about 50% higher for an effective source diameter of 0.5\arcsec. The optimal lens redshift for giant arcs with the length-to-width ratio ($L/W$) larger than 10 increases from 0.3 for \zs=1, to 0.5 for \zs=2, and to 0.7-0.8 for \zs>3. The optical depth is sensitive to the source redshift, in qualitative agreement with Wambsganss et al. (2004). However, our overall optical depth appears to be only $\sim$ 10% to 70% of those from previous studies. The differences can be mostly explained by different power spectrum normalizations ($\sigma_8$) used and different ways of determining the $L/W$ ratio. Finite source size and ellipticity have modest effects on the optical depth. We also found that the number of highly magnified (with magnification $|\mu|>10$) and ``undistorted'' images (with $L/W<3$) is comparable to the number of giant arcs with $|\mu|>10$ and $L/W>10$. We conclude that our predicted rate of giant arcs may be lower than the observed rate, although the precise `discrepancy' is still unclear due to uncertainties both in theory and observations.Comment: Revised version after the referee's reports (32 pages,13figures). The paper has been significantly revised with many additions. The new version includes more detailed comparisons with previous studies, including the effects of source size and ellipticity. New discussions about the redshift distribution of lensing clusters and the width of giant arcs have been adde

Nanocrystalline diamond film for biosensor applications

In this study, we have developed a novel capacitive biosensor based oil interdigitated gold nanodiamond (GID-NCD) electrode for detection of C-reactive protein (CRP) antigen. CRP is one of the plasma proteins known as acute-phase proteins and its levels rise dramatically during inflammatory processes occurring in the body. It has been reported that CRP in serum can be used for risk assessment of cardiovascular diseases. The antibodies immobilization were confirmed by Fourier transform spectroscopy (FTIR) and contact angle measurements. In this capacitive biosensor, nanocrystalline diamond acting as a dielectric layer between the electrodes. The CRP antigen detection was performed by capacitive/dielectric-constant measurements. Our results showed that the response of NCD-based capacitive-based biosensor for CRP antigen was dependent on both concentration (25-800 ng/ml) as well as frequency (50-350 MHz). Furthermore, using optimized conditions, the biosensors developed in this study can be potentially used for detection of elevated level of risk markers protein in suspected subjects for early diagnosis of disease

Reaction-diffusion with a time-dependent reaction rate: the single-species diffusion-annihilation process

We study the single-species diffusion-annihilation process with a time-dependent reaction rate, lambda(t)=lambda_0 t^-omega. Scaling arguments show that there is a critical value of the decay exponent omega_c(d) separating a reaction-limited regime for omega > omega_c from a diffusion-limited regime for omega < omega_c. The particle density displays a mean-field, omega-dependent, decay when the process is reaction limited whereas it behaves as for a constant reaction rate when the process is diffusion limited. These results are confirmed by Monte Carlo simulations. They allow us to discuss the scaling behaviour of coupled diffusion-annihilation processes in terms of effective time-dependent reaction rates.Comment: 11 pages, 9 figures, minor correction