Event patterns extracted from anisotropic spectra of charged particles produced in Pb-Pb collisions at 2.76 TeV

Event patterns extracted from anisotropic spectra of charged particles produced in lead-lead collisions at 2.76 TeV are investigated. We use an inverse power-law resulted from the QCD calculus to describe the transverse momentum spectrum in the hard scattering process, and a revised Erlang distribution resulted from a multisource thermal model to describe the transverse momentum spectrum and anisotropic flow in the soft excitation process. The pseudorapidity distribution is described by a three-Gaussian function which is a revision of the Landau hydrodynamic model. Thus, the event patterns at the kinetic freeze-out are displayed by the scatter plots of the considered particles in the three-dimensional velocity, momentum, and rapidity spaces.Comment: 19 pages, 8 figures, The European Physical Journal A, accepte

The coset weight distributions of certain BCH codes and a family of curves

We study the distribution of the number of rational points in a family of curves over a finite field of characteristic 2. This distribution determines the coset weight distribution of a certain BCH code.Comment: Plain Tex, 15 pages; some numerical data adde

Isogeny-based post-quantum key exchange protocols

The goal of this project is to understand and analyze the supersingular isogeny Diffie Hellman (SIDH), a post-quantum key exchange protocol which security lies on the isogeny-finding problem between supersingular elliptic curves. In order to do so, we first introduce the reader to cryptography focusing on key agreement protocols and motivate the rise of post-quantum cryptography as a necessity with the existence of the model of quantum computation. We review some of the known attacks on the SIDH and finally study some algorithmic aspects to understand how the protocol can be implemented

Nematic Films and Radially Anisotropic Delaunay Surfaces

We develop a theory of axisymmetric surfaces minimizing a combination of surface tension and nematic elastic energies which may be suitable for describing simple film and bubble shapes. As a function of the elastic constant and the applied tension on the bubbles, we find the analogues of the unduloid, sphere, and nodoid in addition to other new surfaces.Comment: 15 pages, 18 figure

Extending pseudo-Anosov maps to compression bodies

We show that a pseudo-Anosov map on a boundary component of an irreducible 3-manifold has a power that partially extends to the interior if and only if its (un)stable lamination is a projective limit of meridians. The proof is through 3-dimensional hyperbolic geometry, and involves an investigation of algebraic limits of convex cocompact compression bodies.Comment: 29 page