Singularity formation in three-dimensional vortex sheets

We study singularity formation of three-dimensional (3-D) vortex sheets without surface tension using a new approach. First, we derive a leading order approximation to the boundary integral equation governing the 3-D vortex sheet. This leading order equation captures the most singular contributions of the integral equation. By introducing an appropriate change of variables, we show that the leading order vortex sheet equation degenerates to a two-dimensional vortex sheet equation in the direction of the tangential velocity jump. This change of variables is guided by a careful analysis based on properties of certain singular integral operators, and is crucial in identifying the leading order singular behavior. Our result confirms that the tangential velocity jump is the physical driving force of the vortex sheet singularities. We also show that the singularity type of the three-dimensional problem is similar to that of the two-dimensional problem. Moreover, we introduce a model equation for 3-D vortex sheets. This model equation captures the leading order singularity structure of the full 3-D vortex sheet equation, and it can be computed efficiently using fast Fourier transform. This enables us to perform well-resolved calculations to study the generic type of 3-D vortex sheet singularities. We will provide detailed numerical results to support the analytic prediction, and to reveal the generic form of the vortex sheet singularity

From spacetime foam to holographic foam cosmology

Due to quantum fluctuations, spacetime is foamy on small scales. For maximum spatial resolution of the geometry of spacetime, the holographic model of spacetime foam stipulates that the uncertainty or fluctuation of distance $l$ is given, on the average, by $(l l_P^2)^{1/3}$ where $l_P$ is the Planck length. Applied to cosmology, it predicts that the cosmic energy is of critical density and the cosmic entropy is the maximum allowed by the holographic principle. In addition, it requires the existence of unconventional (dark) energy/matter and accelerating cosmic expansion in the present era. We will argue that a holographic foam cosmology of this type has the potential to become a full fledged competitor (with distinct testable consequences) for scalar driven inflation.Comment: 8 pages, TeX; dedicated to Rafael Sorki

Constraints on the Neutrino Mass from SZ Surveys

Statistical measures of galaxy clusters are sensitive to neutrino masses in the sub-eV range. We explore the possibility of using cluster number counts from the ongoing PLANCK/SZ and future cosmic-variance-limited surveys to constrain neutrino masses from CMB data alone. The precision with which the total neutrino mass can be determined from SZ number counts is limited mostly by uncertainties in the cluster mass function and intracluster gas evolution; these are explicitly accounted for in our analysis. We find that projected results from the PLANCK/SZ survey can be used to determine the total neutrino mass with a (1\sigma) uncertainty of 0.06 eV, assuming it is in the range 0.1-0.3 eV, and the survey detection limit is set at the 5\sigma significance level. Our results constitute a significant improvement on the limits expected from PLANCK/CMB lensing measurements, 0.15 eV. Based on expected results from future cosmic-variance-limited (CVL) SZ survey we predict a 1\sigma uncertainty of 0.04 eV, a level comparable to that expected when CMB lensing extraction is carried out with the same experiment. A few percent uncertainty in the mass function parameters could result in up to a factor \sim 2-3 degradation of our PLANCK and CVL forecasts. Our analysis shows that cluster number counts provide a viable complementary cosmological probe to CMB lensing constraints on the total neutrino mass.Comment: Replaced with a revised version to match the MNRAS accepted version. arXiv admin note: text overlap with arXiv:1009.411

Determination of Rare Earth Element Isotopic Compositions Using Sample-Standard Bracketing and Double-Spike Approaches

Rare earth elements (REEs) have been found to have numerous uses to trace geological and cosmochemical processes through analyses of elemental patterns, radioactive decay, nucleosynthetic anomalies, and cosmogenic effects. Stable isotopic fractionation is one aspect of REE geochemistry that has been seldom studied, with most publications focusing on the development of analytical methodologies for individual REEs, and most applications concerning terrestrial igneous rocks. In this study, we present a method to systematically analyze stable isotopic fractionations of 8 REEs, including Ce, Nd, Sm, Eu, Gd, Dy, Er, and Yb, using sample-standard bracketing (SSB) and double-spike (DS) approaches. All REEs are separated and purified using a fluoropolymer pneumatic liquid chromatography (FPLC) system. We introduce procedures for identifying and correcting some isobaric interferences in double-spike data reduction. Several geostandards, including igneous rocks and sediments, are analyzed using SSB and DS methods. The results indicate that REE isotopic fractionation in igneous processes is limited, except for Eu. Other REEs can still be isotopically fractionated by low-temperature processes and kinetic effects at a high temperature

Oral Perfluorooctane Sulfonate (PFOS) Lessens Tumor Development In The APCmin Mouse Model of Spontaneous Familial Adenomatous Polyposis

Colorectal cancer is the second most common cause of cancer deaths for both men and women, and the third most common cause of cancer in the U.S. Toxicity of current chemotherapeutic agents for colorectal cancer, and emergence of drug resistance underscore the need to develop new, potentially less toxic alternatives. Our recent cross-sectional study in a large Appalachian population, showed a strong, inverse, dose–response association of serum perfluorooctane sulfonate (PFOS) levels to prevalent colorectal cancer, suggesting PFOS may have therapeutic potential in the prevention and/or treatment of colorectal cancer. In these preliminary studies using a mouse model of familial colorectal cancer, the APCmin mouse, and exposures comparable to those reported in human populations, we assess the efficacy of PFOS for reducing tumor burden, and evaluate potential dose–response effects

Directed polymer in a random medium of dimension 1+1 and 1+3: weights statistics in the low-temperature phase

We consider the low-temperature $T<T_c$ disorder-dominated phase of the directed polymer in a random potentiel in dimension 1+1 (where $T_c=\infty$) and 1+3 (where $T_c<\infty$). To characterize the localization properties of the polymer of length $L$, we analyse the statistics of the weights $w_L(\vec r)$ of the last monomer as follows. We numerically compute the probability distributions $P_1(w)$ of the maximal weight $w_L^{max}= max_{\vec r} [w_L(\vec r)]$, the probability distribution $\Pi(Y_2)$ of the parameter $Y_2(L)= \sum_{\vec r} w_L^2(\vec r)$ as well as the average values of the higher order moments $Y_k(L)= \sum_{\vec r} w_L^k(\vec r)$. We find that there exists a temperature $T_{gap}<T_c$ such that (i) for $T<T_{gap}$, the distributions $P_1(w)$ and $\Pi(Y_2)$ present the characteristic Derrida-Flyvbjerg singularities at $w=1/n$ and $Y_2=1/n$ for $n=1,2..$. In particular, there exists a temperature-dependent exponent $\mu(T)$ that governs the main singularities $P_1(w) \sim (1-w)^{\mu(T)-1}$ and $\Pi(Y_2) \sim (1-Y_2)^{\mu(T)-1}$ as well as the power-law decay of the moments $\bar{Y_k(i)} \sim 1/k^{\mu(T)}$. The exponent $\mu(T)$ grows from the value $\mu(T=0)=0$ up to $\mu(T_{gap}) \sim 2$. (ii) for $T_{gap}<T<T_c$, the distribution $P_1(w)$ vanishes at some value $w_0(T)<1$, and accordingly the moments $\bar{Y_k(i)}$ decay exponentially as $(w_0(T))^k$ in $k$. The histograms of spatial correlations also display Derrida-Flyvbjerg singularities for $T<T_{gap}$. Both below and above $T_{gap}$, the study of typical and averaged correlations is in full agreement with the droplet scaling theory.Comment: 13 pages, 29 figure

Neutrino Mass Inference from SZ Surveys

The growth of structure in the universe begins at the time of radiation-matter equality, which corresponds to energy scales of $\sim 0.4 eV$. All tracers of dark matter evolution are expected to be sensitive to neutrino masses on this and smaller scales. Here we explore the possibility of using cluster number counts and power spectrum obtained from ongoing SZ surveys to constrain neutrino masses. Specifically, we forecast the capability of ongoing measurements with the PLANCK satellite and the ground-based SPT experiment, as well as measurements with the proposed EPIC satellite, to set interesting bounds on neutrino masses from their respective SZ surveys. We also consider an ACT-like CMB experiment that covers only a few hundred ${\rm deg^{2}}$ also to explore the tradeoff between the survey area and sensitivity and what effect this may have on inferred neutrino masses. We find that for such an experiment a shallow survey is preferable over a deep and low-noise scanning scheme. We also find that projected results from the PLANCK SZ survey can, in principle, be used to determine the total neutrino mass with a ($1\sigma$) uncertainty of $0.28 eV$, if the detection limit of a cluster is set at the $5\sigma$ significance level. This is twice as large as the limits expected from PLANCK CMB lensing measurements. The corresponding limits from the SPT and EPIC surveys are $\sim 0.44 eV$ and $\sim 0.12 eV$, respectively. Mapping an area of 200 deg$^{2}$, ACT measurements are predicted to attain a $1\sigma$ uncertainty of 0.61 eV; expanding the observed area to 4,000 deg$^{2}$ will decrease the uncertainty to 0.36 eV.Comment: 14 pages, 1 figure, 6 table

Onsager-symmetric constitutive laws for 3D granular flow in the inertial regime

This paper introduces a new mathematical technique for deriving continuum rheological models of granular matter. Specifically, it is shown that, under the hypothesis of Onsager symmetry, 3D dynamic constitutive laws for general strain rates can be derived from a 3D yield condition plus steady-state empirical data of quasi-2D flow. To illustrate the technique, a new rate-dependent 3D yield condition,suitable for dry granular materials in the inertial regime, is proposed and combined with DEM particle simulation data of simple-shear flow. In combination with Onsager symmetry, this generates a complete 3D viscoplastic model for such materials. Despite the simplicity of the inputs, the resulting constitutive laws agree very well with the pioneering non-planar DEM simulations of Clemmer et al. Phys. rev. lett. 127 (2021). Unlike several previous theories, the novel Onsager-symmetric constitutive relations incorporate a nonzero second normal stress difference in simple shear and are able to distinguish between general triaxial deformations via dependence on the Lode angle

Colossal Positive Magnetoresistance in a Doped Nearly Magnetic Semiconductor

We report on a positive colossal magnetoresistance (MR) induced by metallization of FeSb$_{2}$, a nearly magnetic or "Kondo" semiconductor with 3d ions. We discuss contribution of orbital MR and quantum interference to enhanced magnetic field response of electrical resistivity.Comment: 5 pages, 5 figure