Linear and Second-Order Evolution of Cosmic Baryon Perturbations below 10^6 Solar Masses

Studies of the growth of cosmic perturbations are typically focused on galactic scales and above. In this paper we investigate the evolution of perturbations in baryons, photons, and dark matter for masses below 10^6 M_\odot (or wavenumbers above 100 Mpc^-1). Fluctuations on these scales are of interest and importance because they grow to become the earliest collapsed objects and provide the first light sources in the so called dark ages. We investigate both the linear evolution and the second-order nonlinear effects arising from the coupling of large-scale velocity fields to small-scale perturbations in the baryon density and the electron ionization fraction. We find that this second order nonlinear coupling dominates the growth of perturbations with masses \la 10^3 M_\odot immediately after recombination, enhancing the baryon fluctuation amplitudes by a factor of ~ 5, but the nonlinear effect does not persist at late times.Comment: 21 pages, 8 figures. Accepted for publication in Ap

Pair-Interactions of Self-Propelled SiO2-Pt Janus Colloids

Driven by the necessity to achieve a thorough comprehension of the bottom-up fabrication process of functional materials, this experimental study investigates the pair-wise interactions or collisions between chemically active SiO2-Pt Janus Colloids. These collisions are categorized based on the Janus colloids' orientations before and after they make physical contact. In addition to the hydrodynamic interactions, the Janus colloids are also known to affect each other's chemical field, resulting in chemophoretic interactions, which depend on the reactive nature of the metal site. These interactions lead to a noticeable decrease in particle speed and changes in orientation, which depends on the duration of contact, yielding different collision types. Our findings reveal distinct configurations of contact during collisions, whose mechanisms and likelihood is found to be dependent primarily on the chemical interactions. Such estimates of collision and their characterization in dilute suspensions shall have key impact in determining the arrangement and time scales of dynamical structures and assemblies of denser suspensions, and potentially the functional materials of the future.Comment: 15 pages, 11 figures

Cosmological Models with Shear and Rotation

Cosmological models involving shear and rotation are considered, first in the General Relat ivistic and then in the Newtonian framework with the aim of investigating singularities in them by using numerical and analytical techniques. The dynamics of these rotating models ar e studied. It is shown that singularities are unavoidable in such models and that the centr ifugal force arising due to rotation can never overcome the gravitational and shearing forc e over a length of time.Comment: 17 pages, 6 figures Journal Ref: J. Astrophys. Astr. (1999) 20, 79-8

Gamma-Ray Bursts and Magnetars as Possible Sources of Ultra High Energy Cosmic Rays: Correlation of Cosmic Ray Event Positions with IRAS Galaxies

We use the two-dimensional Kolmogorov-Smirnov (KS) test to study the correlation between the 60 cosmic ray events above 4x10^19 eV from the AGASA experiment and the positions of infrared luminous galaxies from the IRAS PSCz catalog. These galaxies are expected to be hosts to gamma ray bursts (GRB) and magnetars, both of which are associated with core collapse supernovae and have been proposed as possible acceleration sites for ultra high energy cosmic rays. We find consistency between the models and the AGASA events to have been drawn from the same underlying distribution of positions on the sky with KS probabilities ~50%. Application of the same test to the 11 highest AGASA events above 10^20 eV, however, yields a KS probability of < 0.5%, rejecting the models at >99.5% significance level. Taken at face value, these highest energy results suggest that the existing cosmic ray events above 10^20 eV do not owe their origin to long burst GRBs, rapidly rotating magnetars, or any other events associated with core collapse supernovae. The larger data set expected from the AUGER experiment will test whether this conclusion is real or is a statistical fluke that we estimate to be at the 2 sigma level.Comment: 15 pages, 4 figures. Final Version to be published in Phys. Rev.

Incidental Gall Bladder Malignancy after Elective Cholecystectomy- A hospital-based study

Objectives: This study was to evaluate the clinical incidental of gall bladder malignancy and its risk factors in various age group patients after elective cholecystectomy. Methods: Stages of malignancy was diagnosed according to the Eight Edition of AJCC TNM Manual. A total of 954 patients of gall bladder stone were enrolled in this study, among them 18(1.88%) patients were diagnosed with gall bladder malignancy on histopathological examinations. Results: Most of the patients 14(77.78%) were in age group of greater than 50 years and duration of symptoms was &gt;40 weeks. Intraoperative findings in majorities of patients had 9(50%) shrunken fibrosed gall bladder with stones (chronic cholecystitis), 5(27.78%) polyploid mass, 3(16.67%) difficult cholecystectomy and 1(5.56%) thickened wall. on histopathological examination of specimens confirms that the majority of the patients 7(38.88%) had (Tis) carcinoma in situ, 4(22.22%) T1a, and 3(16.67%) T 2a and T2b. Conclusions: Gall bladder malignancy was commonly seen in lower middle socioeconomic class old age female patients. Due to nonspecific clinical and sonographic features,diagnosis of incidental gall bladder malignancies are usually missed. Chronic inflammation, cholelithiasis and adenomyomatosis are the major risk factors. Histopathological examination of the specimen is ensured so as to diagnose and treat life threatening incidental gall bladder malignancy. Performing cholecystectomy should never be the only treatment of gall stones or any other pathology unless and until histopathological examinations of specimens ensures to diagnose gall bladder malignancies

Recurrence relations for a family of iterations assuming Holder continuous second order Frechet derivative

[EN] The semilocal convergence using recurrence relations of a family of iterations for solving nonlinear equations in Banach spaces is established. It is done under the assumption that the second order Frechet derivative satisfies the Holder continuity condition. This condition is more general than the usual Lipschitz continuity condition used for this purpose. Examples can be given forwhich the Lipschitz continuity condition fails but the Holder continuity condition works on the second order Frechet derivative. Recurrence relations based on three parameters are derived. A theorem for existence and uniqueness along with the error bounds for the solution is provided. The R-order of convergence is shown to be equal to 3 + q when theta = +/- 1; otherwise it is 2 + q, where q epsilon (0, 1]. Numerical examples involving nonlinear integral equations and boundary value problems are solved and improved convergence balls are found for them. Finally, the dynamical study of the family of iterations is also carried out.Gupta, DK.; Martínez Molada, E.; Singh, S.; Hueso, JL.; Srivastava, S.; Kumar, A. (2021). Recurrence relations for a family of iterations assuming Holder continuous second order Frechet derivative. International Journal of Nonlinear Sciences and Numerical Simulation. 22(3-4):267-285. https://doi.org/10.1515/ijnsns-2016-0151S267285223-