Evolution of an elliptical bubble in an accelerating extensional flow

Mathematical models that describe the dynamical behavior of a thin gas bubble embedded in a glass fiber during a fiber drawing process have been discussed and analyzed. The starting point for the mathematical modeling was the equations presented in [1] for a glass fiber with a hole undergoing extensional flow. These equations were reconsidered here with the additional reduction that the hole, i.e. the gas bubble, was thin as compared to the radius of the fiber and of finite extent. The primary model considered was one in which the mass of the gas inside the bubble was fixed. This fixed-mass model involved equations for the axial velocity and fiber radius, and equations for the radius of the bubble and the gas pressure inside the bubble. The model equations assumed that the temperature of the furnace of the drawing tower was known. The governing equations of the bubble are hyperbolic and predict that the bubble cannot extend beyond the limiting characteristics specified by the ends of the initial bubble shape. An analysis of pinch-off was performed, and it was found that pinch-off can occur, depending on the parameters of the model, due to surface tension when the bubble radius is small. In order to determine the evolution of a bubble, a numerical method of solution was presented. The method was used to study the evolution of two different initial bubble shapes, one convex and the other non-convex. Both initial bubble shapes had fore-aft symmetry, and it was found that the bubbles stretched and elongated severely during the drawing process. For the convex shape, fore-aft symmetry was lost in the middle of the drawing process, but the symmetry was re-gained by the end of the drawing tower. A small amount of pinch-off was observed at each end for this case, so that the final bubble length was slightly shorter than its theoretical maximum length. For the non-convex initial shape, pinch-off occurred in the middle of the bubble resulting in two bubbles by the end of the fiber draw. The two bubbles had different final pressures and did not have fore-aft symmetry. An extension of the fixed-mass model was considered in which the gas in the bubble was allowed to diffuse into the surrounding glass. The governing equations for this leaky-mass model were developed and manipulated into a form suitable for a numerical treatment

On bilinear estimates and critical uniqueness classes for Navier-Stokes equations

We are concerned with bilinear estimates and uniqueness of mild solutions for the Navier-Stokes equations in critical persistence spaces. For that, we construct general settings in which estimates for the bilinear term of the mild formulation hold true without using auxiliary norms such as Kato time-weighted ones. We first obtain necessary conditions in abstract critical spaces and after consider settings with further structure to obtain the estimates in general classes of Besov, Morrey and Besov-Morrey spaces based on Banach spaces. We then give examples and applications of the abstract theory, which contribute with different proofs for some known estimates, and consequently for the corresponding uniqueness property, and contain (as far as we know) a new bilinear estimate in Besov-weak-Herz spaces. Some ingredients of our approach are characterizations and estimates on the corresponding predual spaces. In addition, we present applications of the theory to other PDEs.Comment: 36 page

Annihilation of Dipolar Dark Matter to Photons

In this work we study the annihilation of fermionic dark matter, considering it as a neutral particle with nonvanishing magnetic ($M$) and electric ($D$) dipole moments. Effective cross-section of the process $\chi \overline{\chi} \rightarrow \gamma \gamma$ is computed starting from a general form of coupling $\chi \overline{\chi} \gamma$ in the framework of an extension of the Standard Model. By taking into account annihilation of DM pairs into mono-energetic photons, we found that for small masses, $m_\chi \leq 10\,\textrm{GeV}$, an electric dipole moment $\sim 10^{-16}\, \textrm{e cm}$ is required to satisfy the current residual density inferences. Additionally, in order to pin down models viable to describe the physics of dark matter at the early Universe we also constrain our model according to recent measurements of the temperature anisotropies of the cosmic background radiation, we report constraints to the electric and magnetic dipole moments for a range of masses within our model.Comment: 20 pages, 6 figure

Fragile Heterosexuality

Previous research demonstrates that membership of majority groups is often perceived as more fragile than membership of minority groups. Four studies (N1=90, N2=247, N3=500, N4=1176) investigated whether this was the case for heterosexual identity, relative to gay identity. Support for fragile heterosexuality was found using various methods: sexual orientation perceptions of a target who engaged in incongruent behaviour, free-responses concerning behaviours required to change someone’s mind about a target’s sexual orientation, agreement with statements about men/women’s sexual orientation and agreement with gender neutral statements about sexual orientation. Neither participant nor target gender eliminated or reversed this effect. Additionally, we investigated multiple explanations (moderators) of the perceived difference in fragility between heterosexual identity and gay identity and found that higher estimates of the gay/lesbian population decreased the difference between the (higher) perceived fragility of heterosexual identity and the (lower) perceived fragility of gay identity

Annihilation of Dipolar Dark Matter: χχ→γγ

In this work we study the annihilation of dark matter, considering it as a neutral particle with magnetic and/or electric moments not null. The calculation of the effective section of the process χχbar→γγ is made starting from a general form of coupling χ χbar γ in the framework of an extension of the Standard Model. We found, when taking into account an annihilation of DDM-antiDDM to monoenergetic photons, that for small masses, mχ ≤ 0 GeV, an electric dipole moment ~10–6 e cm is required to satisfy the current residual density, while for the range of greater sensitivity of HAWC, 10 TeV < Eg < 20 TeV, the electrical dipole moment must be of the order of 10–8 e cm

Analysis of DDM into Gamma Radiation

We are interested in the purpose of a dipolar fermionic particle as a viable candidate of Dark Matter (DDM). Then, we study the annihilation of dark matter into photons, considering it as a neutral particle with non-vanishing magnetic (M) and electric (D) dipolar moments. The total annihilation cross section σ(χ → γ) is computed by starting from a general form of coupling χγ in a framework beyond to Standard Model (BSM). We found that candidates with O(mχ )∽102GeV, D≈10−16 e cm are required in order to satisfy the current cosmic relic density

The Large Aperture GRB Observatory

The Large Aperture GRB Observatory (LAGO) is aiming at the detection of the high energy (around 100 GeV) component of Gamma Ray Bursts, using the single particle technique in arrays of Water Cherenkov Detectors (WCD) in high mountain sites (Chacaltaya, Bolivia, 5300 m a.s.l., Pico Espejo, Venezuela, 4750 m a.s.l., Sierra Negra, Mexico, 4650 m a.s.l). WCD at high altitude offer a unique possibility of detecting low gamma fluxes in the 10 GeV - 1 TeV range. The status of the Observatory and data collected from 2007 to date will be presented.Comment: 4 pages, proceeding of 31st ICRC 200

Water Cherenkov Detectors response to a Gamma Ray Burst in the Large Aperture GRB Observatory

In order to characterise the behaviour of Water Cherenkov Detectors (WCD) under a sudden increase of 1 GeV - 1 TeV background photons from a Gamma Ray Burst (GRB), simulations were conducted and compared to data acquired by the WCD of the Large Aperture GRB Observatory (LAGO). The LAGO operates arrays of WCD at high altitude to detect GRBs using the single particle technique. The LAGO sensitivity to GRBs is derived from the reported simulations of the gamma initiated particle showers in the atmosphere and the WCD response to secondaries.Comment: 5 pages, proceeding of the 31st ICRC 200