Abstract:
Small-scale magnetic features are present everywhere in the solar photosphere. Theoretical models, numerical calculations, and simulations describing the formation of these features have existed for a few decades, but there are only a few observational studies in direct support of the simulations. In this study we present the evolution of small-scale magnetic features with a spatial resolution close to 0.15 arcsecond and compare these observations with those predicted by numerical simulations and also with previous observational work of a similar nature. We analyze a 40 min time sequence of full Stokes spectropolarimetric 630.25 nm data from a plage region near the Sun center. We use line-of-sight velocities and magnetic field measurements obtained using Milne-Eddington inversion techniques with and without stray-light compensation along with measured continuum and line minimum intensities. We discuss the results in relation to earlier observations and simulations. We present eight cases involving strong downflows and magnetic field intensification. All cases studied are associated with the formation of a bright point in the continuum. In three out of the eight cases we find the presence of weak opposite polarity field in close proximity to the downflow. Our data are consistent with earlier simulations describing flux tube collapse, but the transition to a state with stronger field appears transient and short-lived, rather than resulting in a permanent field intensification. Three cases of weak opposite polarity field found adjacent to the downflows do not appear related to reconnection but may be related to overturning convection pulling down some field lines and leading to up/down "serpentine" field, as seen in some simulations.

Abstract:
In this work, we study and quantify properties of strong-field small-scale convection and compare observed properties with those predicted by numerical simulations. We analyze spectropolarimetric 630.25 nm data from a unipolar ephemeral region near sun center. We use line-of-sight velocities and magnetic field measurements obtained with Milne-Eddington inversion techniques along with measured continuum intensities and Stokes V amplitude asymmetry at a spatial resolution of 0.15 arcseconds to establish statistical relations between the measured quantities. We also study these properties for different types of distinct magnetic features, such as micropores, bright points, ribbons, flowers and strings. We present the first direct observations of a small-scale granular magneto-convection pattern within extended regions of strong (more than 600 G average) magnetic field. Along the boundaries of the flux concentrations we see mostly downflows and asymmetric Stokes V profiles, consistent with synthetic line profiles calculated from MHD simulations. We note the frequent occurrence of bright downflows along these boundaries. In the interior of the flux concentrations, we observe an up/down flow pattern that we identify as small-scale magnetoconvection, appearing similar to that of field-free granulation but with scales 4 times smaller. Measured RMS velocities are 70% of those of nearby field-free granulation, even though the average radiative flux is not reduced. The interiors of these flux concentrations are dominated by upflows.

Abstract:
We generate random Gaussian turbulent velocity fields with a Kolmogorov spectrum and use these to obtain synthetic line-of-sight velocity profiles. The profiles are found to be similar to line profiles observed in molecular clouds. We suggest methods for analysing measured line profiles to test whether they might arise from Gaussian Kolmogorov turbulence.

Abstract:
We analyze the atmospheric neutrino data in the context of three flavor neutrino oscillations taking account of the matter effects in the earth. With the hierarchy among the vacuum mass eigenvalues $\mu_3^2 \gg \mu_2^2 \geq \mu_1^2$, the solution of the atmospheric neutrino problem depends on $\delta_{31}=\mu_3^2 - \mu_1^2$ and the $13$ and $23$ mixing angles $\phi$ and $\psi$. Whereas the sub-GeV atmospheric neutrino data imposes only a lower limit on $\delta_{31} > 10^{-3} eV^2$, the zenith angle dependent suppression observed in the multi-GeV data limits $\delta_{31}$ from above also. The allowed regions of the parameter space are strongly constrained by the multi-GeV data. Combined with our earlier solution to the solar neutrino problem which depends on $\delta_{21}= \mu_2^2-\mu_1^2$ and the $12$ and $13$ mixing angles $\omega$ and $\phi$, we have obtained the ranges of values of the five neutrino parameters which solve both the solar and the atmospheric neutrino problems simultaneously.

Abstract:
We investigate the time-of-night variation of solar neutrino rate which will be of relevance to Super-Kamioka and Sudbury neutrino detectors in the framework of oscillations among the three flavors. An analytical method of computing the regeneration in the earth is presented. If day-night effect is seen, we show how the study of the time-of-night variation will allow the determination of the neutrino parameters.

Abstract:
It is pointed out that the enhancement of the solar neutrino rate in a real time detector like Super-Kamioka, SNO or Borexino due to neutrino oscillations in the moon during a partial or total solar eclipse may be observable. The enhancement is calculated as a function of the neutrino parameters in the case of three flavor mixing. This enhancement if seen, can further help to determine the neutrino parameters.

Abstract:
We analyze the recent result of the CHOOZ collaboration in the context of mixing and oscillations between all the three neutrino flavors. If one assumes a hierarchy among the vacuum mass eigenvalues (\delta_{21} \ll \delta_{31}), then the CHOOZ result limits the (13) mixing angle \phi to quite small values. This in turn limits the contribution of the \nu_e <--> \nu_\mu oscillation channel to the atmospheric neutrino anomaly to less than 10 percent. It also implies that the solution to the solar neutrino problem is effectively \nu_e <--> \nu_\mu oscillation and that of the atmospheric neutrino problem is effectively \nu_\mu <--> \nu_\tau.

Abstract:
Recently it was suggested that two very different mass-squared differences play a role in atmospheric neutrino oscillations. The larger of these also accounts for the LSND result and the smaller of these also drives the solar neutrino oscillations. We consider the predictions of this scheme for long-baseline experiments. We find that high statistics experiments, such as MINOS, can observe a clean signal for this scheme, which is clearly distinguishable from the usual scheme of atmospheric neutrino oscillations driven by a single mass-squared difference.

Abstract:
Recent simulation results on heat conduction in a one-dimensional chain with an asymmetric inter-particle interaction potential and no onsite potential found non-anomalous heat transport in accordance to Fourier's law. This is a surprising result since it was long believed that heat conduction in one-dimensional systems is in general anomalous in the sense that the thermal conductivity diverges as the system size goes to infinity. In this paper we report on detailed numerical simulations of this problem to investigate the possibility of a finite temperature phase transition in this system. Our results indicate that the unexpected results for asymmetric potentials is a result of insufficient chain length, and does not represent the asymptotic behavior.

Abstract:
It has recently been proved that the popular nonlocal means (NLM) denoising algorithm does not optimally denoise images with sharp edges. Its weakness lies in the isotropic nature of the neighborhoods it uses to set its smoothing weights. In response, in this paper we introduce several theoretical and practical anisotropic nonlocal means (ANLM) algorithms and prove that they are near minimax optimal for edge-dominated images from the Horizon class. On real-world test images, an ANLM algorithm that adapts to the underlying image gradients outperforms NLM by a significant margin.