A generalized family of anisotropic compact object in general relativity

We present model for anisotropic compact star under the general theory of relativity of Einstein. In the study a 4-dimensional spacetime has been considered which is embedded into the 5-dimensional flat metric so that the spherically symmetric metric has class 1 when the condition $e^{\lambda}=\left(\,1+C\,e^{\nu} \,{\nu'}^2\,\right)$ is satisfied ($\lambda$ and $\nu$ being the metric potentials along with a constant $C$). A set of solutions for the field equations are found depending on the index $n$ involved in the physical parameters. The interior solutions have been matched smoothly at the boundary of the spherical distribution to the exterior Schwarzschild solution which necessarily provides values of the unknown constants. We have chosen the values of $n$ as $n=2$ and $n$=10 to 20000 for which interesting and physically viable results can be found out. The numerical values of the parameters and arbitrary constants for different compact stars are assumed in the graphical plots and tables as follows: (i) LMC X-4 : $a=0.0075$, $b=0.000821$ for $n=2$ and $a=0.0075$, $nb=0.00164$ for $n\ge 10$, (ii) SMC X-1: $a=0.00681$, $b=0.00078$ for $n=2$, and $a=0.00681$, $nb=0.00159$ for $n \ge 10$. The investigations on the physical features of the model include several astrophysical issues, like (i) regularity behavior of stars at the centre, (ii) well behaved condition for velocity of sound, (iii) energy conditions, (iv) stabilty of the system via the following three techniques - adiabatic index, Herrera cracking concept and TOV equation, (v) total mass, effective mass and compactification factor and (vi) surface redshift. Specific numerical values of the compact star candidates LMC X-4 and SMC X-1 are calculated for central and surface densities as well as central pressure to compare the model value with actual observational data.Comment: 20 pages, 9 figures, 2 Table

Derivation of an integral of Boros and Moll via convolution of Student t-densities

We show that the evaluation of an integral considered by Boros and Moll is a special case of a convolution result about Student t-densities obtained by the authors in 2008

Phosphoinositides, kinases and adaptors coordinating endocytosis in Trypanosoma brucei

In the kinetoplastid parasite Trypanosoma brucei clathrin-mediated endocytosis is essential for survival and aids immune evasion in the mammalian host. The formation of endocytic clathrin coated vesicles in T. brucei is via a unique mechanism owing to an evolutionarily recent loss of the adaptor protein (AP)2 complex, a central hub in endocytic vesicle assembly. Despite this loss, recent studies examining endocytic clathrin coat assembly have highlighted a high degree of conservation between trypanosomes and their mammalian hosts. In particular phosphatidylinositol 4,5-bisphosphate (PI(4,5)P(2)) and its putative effectors, TbCALM and TbEpsinR, are central to clathrin-mediated endocytosis in the trypanosome, just as they are in animal cells. In addition to providing insights into the cell biology of T. brucei, these studies also suggest an ancient, possibly pan-eukaryotic connection between PtdIns(4,5)P(2) and endocytosis

Enhanced grain surface effect on magnetic properties of nanometric La0.7Ca0.3MnO3 manganite : Evidence of surface spin freezing of manganite nanoparticles

We have investigated the effect of nanometric grain size on magnetic properties of single phase, nanocrystalline, granular La0.7Ca0.3MnO3 (LCMO) sample. We have considered core-shell structure of our LCMO nanoparticles, which can explain its magnetic properties. From the temperature dependence of field cooled (FC) and zero-field cooled (ZFC) dc magnetization (DCM), the magnetic properties could be distinguished into two regimes: a relatively high temperature regime T > 40 K where the broad maximum of ZFC curve (at T = Tmax) is associated with the blocking of core particle moments, whereas the sharp maximum (at T = TS) is related to the freezing of surface (shell) spins. The unusual shape of M (H) loop at T = 1.5 K, temperature dependent feature of coercive field and remanent magnetization give a strong support of surface spin freezing that are occurring at lower temperature regime (T < 40 K) in this LCMO nanoparticles. Additionally, waiting time (tw) dependence of ZFC relaxation measurements at T = 50 K show weak dependence of relaxation rate [S(t)] on tw and dM/dln(t) following a logarithmic variation on time. Both of these features strongly support the high temperature regime to be associated with the blocking of core moments. At T = 20 K, ZFC relaxation measurements indicates the existence of two different types of relaxation processes in the sample with S(t) attaining a maximum at the elapsed time very close to the wait time tw = 1000 sec, which is an unequivocal sign of glassy behavior. This age-dependent effect convincingly establish the surface spin freezing of our LCMO nanoparticles associated with a background of superparamagnetic (SPM) phase of core moments.Comment: 41 pages, 10 figure

Critical States in a Dissipative Sandpile Model

A directed dissipative sandpile model is studied in the two-dimension. Numerical results indicate that the long time steady states of this model are critical when grains are dropped only at the top or, everywhere. The critical behaviour is mean-field like. We discuss the role of infinite avalanches of dissipative models in periodic systems in determining the critical behaviour of same models in open systems.Comment: 4 pages (Revtex), 5 ps figures (included