Ground States for Diffusion Dominated Free Energies with Logarithmic Interaction

Replacing linear diffusion by a degenerate diffusion of porous medium type is known to regularize the classical two-dimensional parabolic-elliptic Keller-Segel model. The implications of nonlinear diffusion are that solutions exist globally and are uniformly bounded in time. We analyse the stationary case showing the existence of a unique, up to translation, global minimizer of the associated free energy. Furthermore, we prove that this global minimizer is a radially decreasing compactly supported continuous density function which is smooth inside its support, and it is characterized as the unique compactly supported stationary state of the evolution model. This unique profile is the clear candidate to describe the long time asymptotics of the diffusion dominated classical Keller-Segel model for general initial data.Comment: 30 pages, 2 figure

Production of doubly charged scalars from the decay of singly charged scalars in the Higgs Triplet Model

The existence of doubly charged Higgs bosons (H^{\pm\pm}) is a distinctive feature of the Higgs Triplet Model (HTM), in which neutrinos obtain tree-level masses from the vacuum expectation value of a neutral scalar in a triplet representation of SU(2)_L. We point out that a large branching ratio for the decay of a singly charged Higgs boson to a doubly charged Higgs boson via H^\pm\to H^{\pm\pm}W^* is possible in a sizeable parameter space of the HTM. From the production mechanism q'qbar\to W^* \to H^{\pm\pm}H^\mp the above decay mode would give rise to pair production of H^{\pm\pm}, with a cross section which can be comparable to that of the standard pair-production mechanism qqbar\to \gamma^*,Z^* \to H^{++}H^{--}. We suggest that the presence of a sizeable branching ratio for H^\pm\to H^{\pm\pm}W^* could significantly enhance the detection prospects of H^{\pm\pm} in the four-lepton channel. Moreover, the decays H^0\to H^\pm W^* and A^0\to H^\pm W^* from production of the neutral triplet scalars H^0 and A^0 would also provide an additional source of H^\pm, which can subsequently decay to H^{\pm\pm}.Comment: 13 pages, 3 figures, two figures added in v2, to appear in Physical Review

Non-Oberbeck-Boussinesq effects in two-dimensional Rayleigh-Benard convection in glycerol

We numerically analyze Non-Oberbeck-Boussinesq (NOB) effects in two-dimensional Rayleigh-Benard flow in glycerol, which shows a dramatic change in the viscosity with temperature. The results are presented both as functions of the Rayleigh number (Ra) up to $10^8$ (for fixed temperature difference between the top and bottom plates) and as functions of "non-Oberbeck-Boussinesqness'' or "NOBness'' ($\Delta$) up to 50 K (for fixed Ra). For this large NOBness the center temperature $T_c$ is more than 5 K larger than the arithmetic mean temperature $T_m$ between top and bottom plate and only weakly depends on Ra. To physically account for the NOB deviations of the Nusselt numbers from its Oberbeck-Boussinesq values, we apply the decomposition of $Nu_{NOB}/Nu_{OB}$ into the product of two effects, namely first the change in the sum of the top and bottom thermal BL thicknesses, and second the shift of the center temperature $T_c$ as compared to $T_m$. While for water the origin of the $Nu$ deviation is totally dominated by the second effect (cf. Ahlers et al., J. Fluid Mech. 569, pp. 409 (2006)) for glycerol the first effect is dominating, in spite of the large increase of $T_c$ as compared to $T_m$.Comment: 6 pages, 7 figure

Mixings of 4-quark components in light non-singlet scalar mesons in QCD sum rules

Mixings of 4-quark components in the non-singlet scalar mesons are studied in the QCD sum rules. We propose a formulation to evaluate the cross correlators of q\bar q and qq\bar q \bar q operators and to define the mixings of different Fock states in the sum rule. It is applied to the non-singlet scalar mesons, a_0 and K_0^\ast. It is found that the 4-quark operators predict lower masses than the q\bar q operators and that the 4-quark states occupy about 70-90% of the lowest mass states.Comment: 8 pages, 9 figure

Cosmic Microwave Background-Weak Lensing Correlation: Analytical and Numerical Study of Nonlinearity and Implications for Dark Energy

Evolution of density fluctuations yields secondary anisotropies in the cosmic microwave background ( CMB), which are correlated with the same density fluctuations that can be measured by weak lensing (WL) surveys. We study the CMB-WL correlation induced by the integrated Sachs-Wolfe (ISW) effect and its nonlinear extension, the Rees-Sciama (RS) effect, using analytical models as well as N-body simulations. We show that an analytical model based on the time derivative of matter power spectrum agrees with simulations. All-sky cosmic-variance-limited CMB and WL surveys allow us to measure the correlation from the nonlinear RS effect with high significance (50 sigma) for l(max) = 10(4) whereas forthcoming missions such as Planck and LSST are expected to yield 4 l p 10 1.5 sigma detections, on the assumption of that the point-source contributions are negligible. We find that the CMB-WL correlation has a characteristic scale which is sensitive to the nature of dark energy.Alfred P. Sloan FellowshipAstronom

Tumor Biology and Racial Disparities in Reconstruction After Mastectomy: A SEER Database Analysis

Introduction: Significant disparities in immediate breast reconstruction after mastectomy have persisted, and may even be increasing, despite large-scale efforts to minimize them, such as the Women’s Health and Cancer Rights Act of 1998. Immediate breast reconstruction has been shown to lead to higher rates of surgical satisfaction, minimize delay in post-operative cancer treatment, and improve the quality of life and overall well-being of mastectomy patients. However only 25-40% of eligible women in the United States receive reconstruction. The rate of reconstruction is even lower in African American and Hispanic women compared to White women. To better understand this disparity, this study uses national population-based data to examine how demographic factors, socioeconomic factors, and disease characteristics interact and affect the rate of immediate breast reconstruction (IBR) after mastectomy. Methods: Women with AJCC7 Stage 0-III breast cancer who underwent mastectomy from 2010 to 2012 were identified in the Surveillance, Epidemiology and End Results Program (SEER) database. Race, Hispanic ethnicity, age, marital status, insurance status, tumor grade, AJCC7 stage and hormone receptor/ Her2Neu profile were compared between women undergoing mastectomy with IBR and mastectomy alone using univariate and multivariate analysis. Results: We identified 51,115 women who underwent mastectomy for Stage 0-III breast cancer from 2010-2012, of whom 15,389 (30.1%) received IBR. On multivariate analysis, age (p Conclusion: The decision to undergo reconstruction after mastectomy is influenced by many factors. Our results show that even after adjusting for tumor characteristics, socioeconomic factors are independently associated with receiving IBR after mastectomy. Further research is needed to elucidate the factors that influence the decision to undergo IBR in order to eliminate these persistent disparities

Magnetic order and frustrated dynamics in Li(Ni0.8Co0.1Mn0.1)O2: a study by {\mu}+SR and SQUID magnetometry

Recently, the mixed transition metal oxides of the form Li(Ni1-y-zCoyMnz)O2, have become the center of attention as promising candidates for novel battery material. These materials have also revealed very interesting magnetic properties due to the alternate stacking of planes of metal oxides on a 2D triangular lattice and the Li-layers. The title compound, Li(Ni0.8Co0.1Mn0.1)O2, has been investigated by both magnetometry and measurements and {\mu}+SR. We find the evolution of localized magnetic moments with decreasing temperature below 70 K. The magnetic ground state (T = 2 K) is, however, shown to be a frustrated system in 3D, followed by a transition into a possible 2D spinglass above 22 K. With further increasing temperature the compound show the presence of remaining correlations with increasing effective dimensionality all the way up to the ferrimagnetic transition at TC = 70 K.Comment: Accepted for publication in Physics Procedia (muSR2011 Conference

Patchy He II reionization and the physical state of the IGM

We present a Monte-Carlo model of He II reionization by QSOs and its effect on the thermal state of the clumpy intergalactic medium (IGM). The model assumes that patchy reionization develops as a result of the discrete distribution of QSOs. It includes various recipes for the propagation of the ionizing photons, and treats photo-heating self-consistently. The model provides the fraction of He III, the mean temperature in the IGM, and the He II mean optical depth -- all as a function of redshift. It also predicts the evolution of the local temperature versus density relation during reionization. Our findings are as follows: The fraction of He III increases gradually until it becomes close to unity at $z\sim 2.8-3.0$. The He II mean optical depth decreases from $\tau\sim 10$ at $z\geq 3.5$ to $\tau\leq 0.5$ at $z\leq 2.5$. The mean temperature rises gradually between $z\sim 4$ and $z\sim 3$ and declines slowly at lower redshifts. The model predicts a flattening of the temperature-density relation with significant increase in the scatter during reionization at $z\sim 3$. Towards the end of reionization the scatter is reduced and a tight relation is re-established. This scatter should be incorporated in the analysis of the Ly$\alpha$ forest at $z\leq 3$. Comparison with observational results of the optical depth and the mean temperature at moderate redshifts constrains several key physical parameters.Comment: 18 pages, 9 figures; Changed content. Accepted for publication in MNRA