Analytic solution for nonlinear shock acceleration in the Bohm limit

The selfconsistent steady state solution for a strong shock, significantly modified by accelerated particles is obtained on the level of a kinetic description, assuming Bohm-type diffusion. The original problem that is commonly formulated in terms of the diffusion-convection equation for the distribution function of energetic particles, coupled with the thermal plasma through the momentum flux continuity equation, is reduced to a nonlinear integral equation in one variable. Its solution provides selfconsistently both the particle spectrum and the structure of the hydrodynamic flow. A critical system parameter governing the acceleration process is found to be $\Lambda = M^{-3/4}\Lambda_1$, where $\Lambda_1 =\eta p_1/mc$, with a suitably normalized injection rate $\eta$, the Mach number M >> 1, and the cut-off momentum $p_1$. We particularly focus on an efficient solution, in which almost all the energy of the flow is converted into a few energetic particles. It was found that (i) for this efficient solution (or, equivalently, for multiple solutions) to exist, the parameter $\zeta =\eta\sqrt{p_0 p_1}/mc$ must exceed a critical value $\zeta_{cr} \sim 1$ ($p_0$ is the injection momentum), (ii) the total shock compression ratio r increases with M and saturates at a level that scales as $ r \propto \Lambda_1 (iii) the downstream power-law spectrum has the universal index q=3.5 over a broad momentum range. (iv) completely smooth shock transitions do not appear in the steady state kinetic description.Comment: 39 pages, 3 PostScript figures, uses aasms4.sty, to appear in Aug. 20, 1997 issue ApJ, vol. 48

Efficiency of Nonlinear Particle Acceleration at Cosmic Structure Shocks

We have calculated the evolution of cosmic ray (CR) modified astrophysical shocks for a wide range of shock Mach numbers and shock speeds through numerical simulations of diffusive shock acceleration (DSA) in 1D quasi- parallel plane shocks. The simulations include thermal leakage injection of seed CRs, as well as pre-existing, upstream CR populations. Bohm-like diffusion is assumed. We model shocks similar to those expected around cosmic structure pancakes as well as other accretion shocks driven by flows with upstream gas temperatures in the range $T_0=10^4-10^{7.6}$K and shock Mach numbers spanning $M_s=2.4-133$. We show that CR modified shocks evolve to time-asymptotic states by the time injected particles are accelerated to moderately relativistic energies (p/mc \gsim 1), and that two shocks with the same Mach number, but with different shock speeds, evolve qualitatively similarly when the results are presented in terms of a characteristic diffusion length and diffusion time. For these models the time asymptotic value for the CR acceleration efficiency is controlled mainly by shock Mach number. The modeled high Mach number shocks all evolve towards efficiencies $\sim 50$%, regardless of the upstream CR pressure. On the other hand, the upstream CR pressure increases the overall CR energy in moderate strength shocks ($M_s \sim {\rm a few}$). (abridged)Comment: 23 pages, 12 ps figures, accepted for Astrophysical Journal (Feb. 10, 2005

Cosmic Ray Electrons in Groups and Clusters of Galaxies: Primary and Secondary Populations from a Numerical Cosmological Simulation

We study the generation and distribution of high energy electrons in cosmic environment and their observational consequences by carrying out the first cosmological simulation that includes directly cosmic ray (CR) particles. Starting from cosmological initial conditions we follow the evolution of primary and secondary electrons (CRE), CR ions (CRI) and a passive magnetic field. CRIs and primary CREs are injected and accelerated at large scale structure shocks. Secondary CREs are continuously generated through inelastic p-p collisions. We include spatial transport, adiabatic expansion/compression, Coulomb collisions, bremsstrahlung, synchrotron (SE)and inverse Compton (IC) emission. We find that, from the perspective of cosmic shock energy and acceleration efficiency, the few detections of hard X-ray radiation excess could be explained in the framework of IC emission of primary CREs in clusters undergoing high accretion/merger phase. Instead, IC emission from both primary and secondary CREs accounts at most for a small fraction of the radiation excesses detected in the extreme-UV (except for the Coma cluster as reported by Bowyer et al.1999). Next, we calculate the SE after normalizing the magnetic field so that for a Coma-like cluster ^1/2~3 \muG. Our results indicate that the SE from secondary CREs reproduces several general properties of radio halos, including the recently found P_1.4GHz vs T relation, the morphology and polarization of the emitting region and, to some extent, the spectral index. Moreover, SE from primary CREs turns out sufficient to power extended regions resembling radio relics observed at the outskirts of clusters. Again we find striking resemblance between morphology, polarization and spectral index of our synthetic maps and those reported in the literature.Comment: emulateapj, 27 pages, 10 figures, 5 tables; ApJ in pres

Magnetic field amplification and electron acceleration to near-energy equipartition with ions by a mildly relativistic quasi-parallel plasma protoshock

The prompt emissions of gamma-ray bursts are seeded by radiating ultrarelativistic electrons. Internal shocks propagating through a jet launched by a stellar implosion, are expected to amplify the magnetic field & accelerate electrons. We explore the effects of density asymmetry & a quasi-parallel magnetic field on the collision of plasma clouds. A 2D relativistic PIC simulation models the collision of two plasma clouds, in the presence of a quasi-parallel magnetic field. The cloud density ratio is 10. The densities of ions & electrons & the temperature of 131 keV are equal in each cloud. The mass ratio is 250. The peak Lorentz factor of the electrons is determined, along with the orientation & strength of the magnetic field at the cloud collision boundary. The magnetic field component orthogonal to the initial plasma flow direction is amplified to values that exceed those expected from shock compression by over an order of magnitude. The forming shock is quasi-perpendicular due to this amplification, caused by a current sheet which develops in response to the differing deflection of the incoming upstream electrons & ions. The electron deflection implies a charge separation of the upstream electrons & ions; the resulting electric field drags the electrons through the magnetic field, whereupon they acquire a relativistic mass comparable to the ions. We demonstrate how a magnetic field structure resembling the cross section of a flux tube grows in the current sheet of the shock transition layer. Plasma filamentation develops, as well as signatures of orthogonal magnetic field striping. Localized magnetic bubbles form. Energy equipartition between the ion, electron & magnetic energy is obtained at the shock transition layer. The electronic radiation can provide a seed photon population that can be energized by secondary processes (e.g. inverse Compton).Comment: 12 pages, 15 Figures, accepted to A&

Contribution to van der Waerden's conjecture

AbstractIn this paper, we give two different elementary proofs for the inequality which states that the permanent of doubly stochastic matrices is greater than or equal to (n!/nn). This inequality was proved earlier by the author, and independently by Egorychev and Falikman

Sex differences in mathematics and reading achievement are inversely related: within- and across-nation assessment of 10 years of PISA data

We analyzed one decade of data collected by the Programme for International Student Assessment (PISA), including the mathematics and reading performance of nearly 1.5 million 15 year olds in 75 countries. Across nations, boys scored higher than girls in mathematics, but lower than girls in reading. The sex difference in reading was three times as large as in mathematics. There was considerable variation in the extent of the sex differences between nations. There are countries without a sex difference in mathematics performance, and in some countries girls scored higher than boys. Boys scored lower in reading in all nations in all four PISA assessments (2000, 2003, 2006, 2009). Contrary to several previous studies, we found no evidence that the sex differences were related to nations’ gender equality indicators. Further, paradoxically, sex differences in mathematics were consistently and strongly inversely correlated with sex differences in reading: Countries with a smaller sex difference in mathematics had a larger sex difference in reading and vice versa. We demonstrate that this was not merely a between-nation, but also a within-nation effect. This effect is related to relative changes in these sex differences across the performance continuum: We did not find a sex difference in mathematics among the lowest performing students, but this is where the sex difference in reading was largest. In contrast, the sex difference in mathematics was largest among the higher performing students, and this is where the sex difference in reading was smallest. The implication is that if policy makers decide that changes in these sex differences are desired, different approaches will be needed to achieve this for reading and mathematics. Interventions that focus on high-achieving girls in mathematics and on low achieving boys in reading are likely to yield the strongest educational benefits

Supramolecular complex formation in cell signaling and disease: An update on a recurrent theme in cell life and death

In summary, this limited discussion of recent developments concerning a few signaling pathways and associated cellular systems hopefully underscores the importance of multiprotein complex formation in cellular signaling, the major theme of an international symposium held September 2002 in Santiago, Chile. Perhaps the most fascinating emerging subject is the importance of membranes in many aspects of signaling. Some 25 years ago, the observation that DAG serves as a physiologically-relevant activator of PKC gave rise to the concept of lipid second messengers, thereby completely changing the way lipids were viewed (reviewed in Quest, et al., 1996). Now, with the description of membrane microdomains (rafts, caveolae), we are beginning to appreciate the complexity of lipid: organization within membranes and the role these highly-dynamic surfaces play as platforms for the assembly of many of the protein complexes employed in signaling. Indeed, such surface-bound complex assembly is not lim

The relationship between smoking and quality of life in advanced lung cancer patients: a prospective longitudinal study.

PURPOSE: Smoking is a major cause of lung cancer, and continued smoking may compromise treatment efficacy and quality of life (health-related quality of life (HRQoL)) in patients with advanced lung cancer. Our aims were to determine (i) preference for treatments which promote quality over length of life depending on smoking status, (ii) the relationship between HRQoL and smoking status at diagnosis (T1), after controlling for demographic and clinical variables, and (iii) changes in HRQoL 6 months after diagnosis (T2) depending on smoking status. METHODS: Two hundred ninety-six patients with advanced lung cancer were given questionnaires to assess HRQoL (EORTC QLQ-C30), time-trade-off for life quality versus quantity (QQQ) and smoking history (current, former or never smoker) at diagnosis (T1) and 6 months later (T2). Medical data were extracted from case records. RESULTS: Questionnaires were returned by 202 (68.2 %) patients at T1 and 114 (53.3 %) at T2. Patients favoured treatments that would enhance quality of life over increased longevity. Those who continued smoking after diagnosis reported worse HRQoL than former smokers or those who never smoked. Smoking status was a significant independent predictor of coughing in T1 (worse in smokers) and cognitive functioning in T2 (better in never smokers). CONCLUSIONS: Smoking by patients with advanced lung cancer is associated with worse symptoms on diagnosis and poorer HRQoL for those who continue smoking. The results have implications to help staff explain the consequences of smoking to patients

The effect of disgust-related side-effects on symptoms of depression and anxiety in people treated for cancer: a moderated mediation model

As maladaptive disgust responses are linked to mental health problems, and cancer patients may experience heightened disgust as a result of treatments they receive, we explored the associations between disgust-related side-effects and symptoms of depression and anxiety in people treated for cancer. One hundred and thirty two (83 women, Mage = 57.48 years) participants answered questions about their treatments, side-effects, disgust responding, and mental health. Experiencing bowel and/or bladder problems, sickness and/or nausea (referred to here as “core” disgust-related side-effects) was significantly related to greater symptoms of depression and borderline increased anxiety. Further, these links were explained by a moderated mediation model, whereby the effects of core disgust side-effects on depression and anxiety were mediated by (physical and behavioural) self-directed disgust, and disgust propensity moderated the effect of core disgust side-effects on self-disgust. These findings stress the importance of emotional responses, like disgust, in psychological adaptation to the side-effects of cancer treatments

Countries with Higher Levels of Gender Equality Show Larger National Sex Differences in Mathematics Anxiety and Relatively Lower Parental Mathematics Valuation for Girls.

Despite international advancements in gender equality across a variety of societal domains, the underrepresentation of girls and women in Science, Technology, Engineering, and Mathematics (STEM) related fields persists. In this study, we explored the possibility that the sex difference in mathematics anxiety contributes to this disparity. More specifically, we tested a number of predictions from the prominent gender stratification model, which is the leading psychological theory of cross-national patterns of sex differences in mathematics anxiety and performance. To this end, we analyzed data from 761,655 15-year old students across 68 nations who participated in the Programme for International Student Assessment (PISA). Most importantly and contra predictions, we showed that economically developed and more gender equal countries have a lower overall level of mathematics anxiety, and yet a larger national sex difference in mathematics anxiety relative to less developed countries. Further, although relatively more mothers work in STEM fields in more developed countries, these parents valued, on average, mathematical competence more in their sons than their daughters. The proportion of mothers working in STEM was unrelated to sex differences in mathematics anxiety or performance. We propose that the gender stratification model fails to account for these national patterns and that an alternative model is needed. In the discussion, we suggest how an interaction between socio-cultural values and sex-specific psychological traits can better explain these patterns. We also discuss implications for policies aiming to increase girls' STEM participation