Intrinsic volumes of inscribed random polytopes in smooth convex bodies

Let $K$ be a $d$ dimensional convex body with a twice continuously differentiable boundary and everywhere positive Gauss-Kronecker curvature. Denote by $K_n$ the convex hull of $n$ points chosen randomly and independently from $K$ according to the uniform distribution. Matching lower and upper bounds are obtained for the orders of magnitude of the variances of the $s$-th intrinsic volumes $V_s(K_n)$ of $K_n$ for $s\in\{1, ..., d\}$. Furthermore, strong laws of large numbers are proved for the intrinsic volumes of $K_n$. The essential tools are the Economic Cap Covering Theorem of B\'ar\'any and Larman, and the Efron-Stein jackknife inequality

Compact Stars in Hadron and Quark-Hadron Models

We investigate strongly interacting dense matter and neutron stars using a flavor-SU(3) approach based on a non-linear realization of chiral symmetry as well as a hadronic flavor-SU(2) parity-doublet model. We study chiral symmetry restoration and the equation of state of stellar matter and determine neutron star properties using different sets of degrees of freedom. Finally, we include quarks in the model approach. We show the resulting phase diagram as well as hybrid star solutions for this model.Comment: conference proceedings Iwara 200

On the multiplicity of arrangements of congruent zones on the sphere

Consider an arrangement of $n$ congruent zones on the $d$-dimensional unit sphere $S^{d-1}$, where a zone is the intersection of an origin symmetric Euclidean plank with $S^{d-1}$. We prove that, for sufficiently large $n$, it is possible to arrange $n$ congruent zones of suitable width on $S^{d-1}$ such that no point belongs to more than a constant number of zones, where the constant depends only on the dimension and the width of the zones. Furthermore, we also show that it is possible to cover $S^{d-1}$ by $n$ congruent zones such that each point of $S^{d-1}$ belongs to at most $A_d\ln n$ zones, where the $A_d$ is a constant that depends only on $d$. This extends the corresponding $3$-dimensional result of Frankl, Nagy and Nasz\'odi (2016). Moreover, we also examine coverings of $S^{d-1}$ with congruent zones under the condition that each point of the sphere belongs to the interior of at most $d-1$ zones

Comparison of lunar rocks and meteorites: Implications to histories of the moon and parent meteorite bodies

A number of similarities between lunar and meteoritic rocks are reported and suggest that the comparison is essential for a clear understanding of meteorites as probes of the early history of the solar systems: (1) Monomict and polymict breccias occur in lunar rocks, as well as in achondritic and chondritic meteorites, having resulted from complex and repeated impact processes. (2) Chondrules are present in lunar, as well as in a few achondritic and most chondritic meteorites. It is pointed out that because chondrules may form in several different ways and in different environments, a distinction between the different modes of origin and an estimate of their relative abundance is important if their significance as sources of information on the early history of the solar system is to be clearly understood. (3) Lithic fragments are very useful in attempts to understand the pre- and post-impact history of lunar and meteoritic breccias. They vary from little modified (relative to the apparent original texture), to partly or completely melted and recrystallized lithic fragments

Fixed point merger in the SU(N) gauge beta functions

We discuss qualitative behavior of the SU(N) gauge beta functions in QCD with many massless flavors. Non-perturbative beta functions can be obtained by extracting the renormalized trajectories in the exact renormalization group framework. We examine the renormalization group equations for the general four-fermi couplings as well as the gauge coupling obtained in a simple approximation scheme. It is shown that the gauge beta function possesses not only an IR but also a UV fixed point in the conformal window. These fixed points merge with each other and disappear at the edge of the conformal window. The scaling dimensions of the quark mass operator at the fixed points are also shown.Comment: 33 pages, 18 figure

SU(3) sextet model with Wilson fermions

We investigate the spectrum and IR properties of the SU(3) "sextet" model with two Dirac fermions in the two-index symmetric representation via lattice simulations. This model is a prime candidate for a realization of Walking Technicolor, which features a minimal matter content and it is expected to be inside or very close to the lower boundary of the conformal window. We use the Wilson discretization for the fermions and map the phase structure of the lattice model. We study several spectral and gradient flow observables both in the bulk and the weak coupling phases. While in the bulk phase we find clear signs of chiral symmetry breaking, in the weak coupling phase there is no clear indication for it, and instead the chiral limit of the model seems compatible with an IR-conformal behavior.Comment: 32 pages, many figure

Finite Density QCD: a New Approach

We introduce a new approach to analyze the phase diagram of QCD at finite chemical potential and temperature, test it in the Gross-Neveu model at finite baryon density, and apply it to the study of the chemical potential-temperature phase diagram of QCD with four degenerate flavors of Kogut-Susskind type.Comment: 21 pages, 9 figures. Some comments and references adde

Results from Lattice QCD

I present our recent results on the critical end point in the \mu_B-T phase diagram of QCD with two flavours of light dynamical quarks and compare them with similar results from other groups. Implications for a possible energy scan at the RHIC are discussed. I also comment briefly on the new results of great relevance to heavy ion collisions from finite temperature lattice QCD simulations on speed of sound, specific heat and on the fate of J/\psi.Comment: Invited Plenary Talk given at 5th International Conference on Physics and Astrophysics of Quark Gluon Plasma, Kolkata, India, February 8-12, 2005; LaTeX in Journal of Physics G style; 9 pages including figure