Sharp bounds on the critical stability radius for relativistic charged spheres

In a recent paper by Giuliani and Rothman \cite{GR}, the problem of finding a lower bound on the radius $R$ of a charged sphere with mass M and charge Q<M is addressed. Such a bound is referred to as the critical stability radius. Equivalently, it can be formulated as the problem of finding an upper bound on M for given radius and charge. This problem has resulted in a number of papers in recent years but neither a transparent nor a general inequality similar to the case without charge, i.e., M\leq 4R/9, has been found. In this paper we derive the surprisingly transparent inequality $$\sqrt{M}\leq\frac{\sqrt{R}}{3}+\sqrt{\frac{R}{9}+\frac{Q^2}{3R}}.$$ The inequality is shown to hold for any solution which satisfies $p+2p_T\leq\rho,$ where $p\geq 0$ and $p_T$ are the radial- and tangential pressures respectively and $\rho\geq 0$ is the energy density. In addition we show that the inequality is sharp, in particular we show that sharpness is attained by infinitely thin shell solutions.Comment: 20 pages, 1 figur

A large ungated TPC with GEM amplification

A Time Projection Chamber (TPC) is an ideal device for the detection of charged particle tracks in a large volume covering a solid angle of almost . The high density of hits on a given particle track facilitates the task of pattern recognition in a high-occupancy environment and in addition provides particle identification by measuring the specific energy loss for each track. For these reasons, TPCs with Multiwire Proportional Chamber (MWPC) amplification have been and are widely used in experiments recording heavy-ion collisions. A significant drawback, however, is the large dead time of the order of 1 ms per event generated by the use of a gating grid, which is mandatory to prevent ions created in the amplification region from drifting back into the drift volume, where they would severely distort the drift path of subsequent tracks. For experiments with higher event rates this concept of a conventional TPC operating with a triggered gating grid can therefore not be applied without a significant loss of data. A continuous readout of the signals is the more appropriate way of operation. This, however, constitutes a change of paradigm with considerable challenges to be met concerning the amplification region, the design and bandwidth of the readout electronics, and the data handling. A mandatory prerequisite for such an operation is a sufficiently good suppression of the ion backflow from the avalanche region, which otherwise limits the tracking and particle identification capabilities of such a detector. Gas Electron Multipliers (GEM) are a promising candidate to combine excellent spatial resolution with an intrinsic suppression of ions. In this paper we describe the design, construction and the commissioning of a large TPC with GEM amplification and without gating grid (GEM-TPC). The design requirements have driven innovations in the construction of a light-weight field-cage, a supporting media flange, the GEM amplification and the readout system, which are presented in this paper. We further describe the support infrastructure such as gas, cooling and slow control. Finally, we report on the operation of the GEM-TPC in the FOPI experiment, and describe the calibration procedures which are applied to achieve the design performance of the device.Peer reviewe

The Role of Dietary Approach in Irritable Bowel Syndrome

Irritable bowel syndrome (IBS) is a chronic functional disorder of the gastrointestinal tract and is one of the most frequent gastrointestinal diseases. In IBS multiple pathophysiological mechanisms including alterations in intestinal motility, permeability, nutrient absorption, and intestinal microbiota have been implicated. Foods are commonly reported by patients to be a trigger of symptoms and therefore are likely involved in the generation of symptoms in IBS. Among all possible therapeutic options, a first-line approach to IBS is dietary education and identification of foods potentially responsible for the onset or worsening of symptoms. Dietary approaches include reduction of gas-producing foods (i.e. fermentable oligo-, di-, and monosaccharides and polyols (FODMAPs)), lactose and gluten. Further studies are required to link the ultimate role of diets in different IBS subtypes

A universal modified van der Waals equation of state. Part I: Polymer and mineral glass formers

PVT data of glass formers (minerals and polymers) published in the literature are re-analyzed. All the polymer glass formers (PS, PVAc, PVME, PMMA, POMS, PBMA, PVC, PE, PP, PMPS, PMTS, PPG) present two main properties which have never been noted: a) the isobars P(V) have a fan structure characterized by the two parameters T* and V*; b) the isotherms verify the principle of temperature-pressure superposition for P < P *. From these properties we show that the Equation Of State (EOS) can be put on a modified van der Waals form (VW-EOS), (V − V *) = (V0 − V *)P */(P + P *) . The characteristic pressure P* and the covolume V* are T and P independent. In polymer glass formers P* and V* have same values in the α (melt) and β (glass) domains. The characteristic temperatures T * deduced from the Fan Structure of the Isobar (FSIb) above and below T g are different. The characteristic temperature T *(α) of the melt state is found near the Vogel temperature T 0 for linear polymers and more than 100 K below T 0 for atactic polymers (with pendent groups). This difference in atactic polymers (and in some low molecular weight compounds) is explained by the importance of the β motions due to the pendent groups. The independence of T 0 on P is discussed. A modified VFT equation (analogous to the compensation law and Meyer-Neldel rule) giving the relaxation time τ of the α motions as a function of P and T is proposed. The fan structure of the isotherm logτ versus P is explained. It is shown that organic non-polymeric liquids (C6H12, C6H14, DHIQ, OTP, Glycerol, Salol, PDE, DGEBA), mineral glass (SiO2, Se, GeSe4, GeSe2, GeO2, As2O3 and two metallic glasses (LaCe and CaAl alloys) verify this VW-EOS with similar accuracy. The relation P * = B 0/γ B among the characteristic pressure P *, the zero-pressure modulus B 0 and the Slatter-Grüneisen anharmonicity parameter γ B deduced from the VW-EOS, is observed in all the glass formers