Numerical Study of the Lowest Energy Configurations for Global String-Antistring Pairs

We investigate the lowest energy configurations for string - antistring pairs at fixed separations by numerically minimizing the energy. We show that for separations smaller than a critical value, a region of false vacuum develops in the middle due to large gradient energy density. Consequently, well defined string - antistring pairs do not exist for such separations. We present an example of vortex - antivortex production by vacuum bubbles where this effect seems to play a dynamical role in the annihilation of the pair. We also study the dependence of the energy of an string-antistring pair on their separation and find deviations from a simple logarithmic dependence for small separations.Comment: 14 pages, in LATEX, 7 figures (not included

Third order differential subordination and superordination results for analytic functions involving the Srivastava-Attiya operator

In this article, by making use of the linear operator introduced and studied by Srivastava and Attiya \cite{srivastava1}, suitable classes of admissible functions are investigated and the dual properties of the third-order differential subordinations are presented. As a consequence, various sandwich-type theorems are established for a class of univalent analytic functions involving the celebrated Srivastava-Attiya transform. Relevant connections of the new results are pointed out.Comment: 16. arXiv admin note: substantial text overlap with arXiv:1809.0651

The Cosmological Kibble Mechanism in the Laboratory: String Formation in Liquid Crystals

We have observed the production of strings (disclination lines and loops) via the Kibble mechanism of domain (bubble) formation in the isotropic to nematic phase transition of a sample of uniaxial nematic liquid crystal. The probablity of string formation per bubble is measured to be $0.33 \pm 0.01$. This is in good agreement with the theoretical value $1/ \pi$ expected in two dimensions for the order parameter space $S^2/{\bf Z}_2$ of a simple uniaxial nematic liquid crystal.Comment: 17 pages, in TEX, 2 figures (not included, available on request

Curvature Inspired Cosmological Scenario

Using modified gravity with non-linear terms of curvature, $R^2$ and $R^{(r +2)}$ (with $r$ being the positive real number and $R$ being the scalar curvature), cosmological scenario,beginning at the Planck scale, is obtained. Here, a unified picture of cosmology is obtained from $f(R)-$ gravity. In this scenario, universe begins with power-law inflation, followed by deceleration and acceleration in the late universe as well as possible collapse of the universe in future. It is different from $f(R)-$ dark energy models with non-linear curvature terms assumed as dark energy. Here, dark energy terms are induced by linear as well as non-linear terms of curvature in Friedmann equation being derived from modified gravity.It is also interesting to see that, in this model, dark radiation and dark matter terms emerge spontaneously from the gravitational sector. It is found that dark energy, obtained here, behaves as quintessence in the early universe and phantom in the late universe. Moreover, analogous to brane-tension in brane-gravity inspired Friedmann equation, a tension term $\lambda$ arises here being called as cosmic tension. It is found that, in the late universe, Friedmann equation (obtained here) contains a term $- \rho^2/2\lambda$ ($\rho$ being the phantom energy density) analogous to a similar term in Friedmann equation with loop quantum effects, if $\lambda > 0$ and brane-gravity correction when $\lambda < 0.$Comment: 19 Pages. To appear in Int. J. Thro. Phy

Total Cross Sections

A unified approach to total cross-sections, based on the QCD contribution to the rise with energy, is presented for the processes $pp$, $p{\bar p}$, $\gamma p, \gamma \gamma, e^+e^- \to hadrons$. For proton processes, a discussion of the role played by soft gluon summation in taming the fast rise due to mini-jets is presented. For photon-photon processes, a comparison with other models indicates the need for precision measurements in both the low and high energy region, likely only with measurements at future Linear Colliders.Comment: 15 pages, 9 figures, LaTeX, uses hsproc.sty and art10.sty. Talk given by G. Pancheri at 'International Hadron Structure-2000', October 1-6, Staralesn

Zero momentum gluons and the total pp and pbarp cross-sections

We describe a QCD motivated model for total cross-sections which uses the eikonal representation and incorporates QCD mini-jets to drive the rise with energy of the cross-section, while the impact parameter distribution is obtained through the Fourier transform of the transverse momentum distribution of soft gluons emitted in the parton-parton interactions giving rise to mini-jets in the final state. A singular but integral expression for the running coupling constant in the infrared region is part of this model.Comment: 4 pages, 1 figure, uses slac_one.rtx, 34th ICHEP Conference, Philadelphia 200

Total cross-section at LHC from minijets and soft gluon resummation in the infrared region

A model for total cross-sections incorporating QCD jet cross-sections and soft gluon resummation is described and compared with present data on $pp$ and ${\bar p}p$ cross-sections. Predictions for LHC are presented for different parameter sets. It is shown that they differ according to the small x-behaviour of available parton density functions.Comment: 10 pages, 3 figures, uses appolb.cls, LaTeX. Talk presented by G. Pancheri at the EURIDICE Final Meeting, August 24-27th, 2006, Kazimierz, Polan

Total cross sections and soft gluon resummation

We discuss a model for total hadronic and photonic cross-sections which includes hard parton-parton scattering to drive the rise and soft gluon resummation to tame it. Unitarity is ensured by embedding the cross-section in the eikonal formalism. Predictions for LHC and ILC are presented.Comment: 9 pages, 2 figures, Presented at PLC2005, Kazimierz, September 2005, requires appolb.cl