The Hagedorn spectrum and large NcN_c QCD in 2+1 and 3+1 dimensions

We show that a Hagedorn spectrum (i.e., spectrum where the number of hadrons grows exponentially with the mass) emerges automatically in large $N_c$ QCD in 2+1 and 3+1 dimensions. The approach is based on the study of Euclidean space correlation functions for composite operators constructed from quark and gluon fields and exploits the fact that the short time behavior of the correlators is known in QCD. The demonstration relies on one critical assumption: that perturbation theory accurately describes the trace of the logarithm of a matrix of point-to-point correlation functions in the regime where the perturbative corrections to the asymptotically free value are small.Comment: 18 pages, 5 figure

Confining Flux Tubes in a Current Algebra Approach

We describe flux tubes and their interactions in a low energy sigma model induced by $SU({N_f}) \rightarrow SO({N_f})$ flavor symmetry breaking in $SO(N_c)$ QCD. Unlike standard QCD, this model allows gauge confinement to manifest itself in the low energy theory, which has unscreened spinor color sources and global $Z_2$ flux tubes. We construct the flux tubes and show how they mediate the confinement of spinor sources. We further examine the flux tubes' quantum stability, spectrum and interactions. We find that flux tubes are Alice strings, despite ambiguities in defining parallel transport. Furthermore, twisted loops of flux tube support skyrmion number, just as gauged Alice strings form loops that support monopole charge. This model, while phenomenologically nonviable, thus affords a perspective on both the dynamics of confinement and on subtleties which arise for global Alice strings.Comment: 29 pages (REVTEX) plus 6 figures, two corrections in the final section and added reference

On construction and (non)existence of cc-(almost) perfect nonlinear functions

Functions with low differential uniformity have relevant applications in cryptography. Recently, functions with low $c$-differential uniformity attracted lots of attention. In particular, so-called APcN and PcN functions (generalization of APN and PN functions) have been investigated. Here, we provide a characterization of such functions via quadratic polynomials as well as non-existence results

Effects of Overload and Underload on Internal Strains/Stresses and Crack Closure during Fatigue-Crack Propagation

The overload and/or underload occurring during constant-amplitude fatiguecrack growth result in the retardation and/or acceleration in the crack-growth rate, making it difficult to predict the crack-propagation behavior and fatigue lifetime. Although there have been numerous investigations to account for these transient crackgrowth behavior, the phenomena are still not completely understood. Neutron and X-ray diffraction, and electric-potential measurements were employed to investigate these transient crack-growth micromechanisms; gain a thorough understanding of the crack-tip deformation and fracture behaviors under applied loads; and establish a quantitative relationship between the crack-tip-driving force and crack-growth behavior. Five different fatigue-crack-growth experiments (i.e., fatigued, tensile overloaded, compressive underloaded, tensile overloaded-compressive underloaded, and compressive underloaded-tensile overloaded) were performed to observe these transient crack-growth behaviors. The development of internal-strain distributions during variable-amplitude loadings, and the resultant residual-stress distributions around a crack tip were examined using neutron diffraction. The effects of a single tensile overload on fatigue-crack growth were focused on probing the crack-growth-retardation micromechanisms. Neutron diffraction and polychromatic X-ray microdiffraction showed high dislocation densities and considerable crystallographic tilts near the crack tip immediately after the overload. The interactions between the overload-induced plastic zone and newly-developed fatigue plastic zone, and their influences on the evolution of residual-strain profiles are discussed. Neutron-diffraction and electric-potential measurements provide in-situ observation of the crack-opening/closing processes and internal-stress distributions in the vicinity of the crack tip during real-time fatigue-crack propagation following a tensile overload. Immediately after applying a tensile overload, the crack-tip became blunt and the large compressive residual stresses were developed around the crack tip. In the retardation period after the tensile overloading, the combined effects of the cracktip blunting at an overload point and compressive-residual stresses accompanying the crack closure induced the stress concentration at a blunting region until a maximum crack-arrest load was reached. Then, the stress concentration was transferred from the blunting region to actual crack-tip position with gradual crack opening, requiring a higher applied load. This observation of the stress-transfer phenomenon significantly promotes the fundamental understanding of overload-retardation phenomena. The postoverload crack-growth rates were normalized with the effective-stress-intensity-factor range, which suggests that it can be considered as the fatigue-crack-tip-driving force