Cross-section and polarization of neutrino-produced τ\tau's made simple

Practical formulae are derived for the cross-section and polarization of the $\tau$ lepton produced in deep-inelastic neutrino-nucleon scattering in the frame of the simple quark-parton model.Comment: 10 pages, no figure

Estimating the number of change-points in a two-dimensional segmentation model without penalization

In computational biology, numerous recent studies have been dedicated to the analysis of the chromatin structure within the cell by two-dimensional segmentation methods. Motivated by this application, we consider the problem of retrieving the diagonal blocks in a matrix of observations. The theoretical properties of the least-squares estimators of both the boundaries and the number of blocks proposed by L\'evy-Leduc et al. [2014] are investigated. More precisely, the contribution of the paper is to establish the consistency of these estimators. A surprising consequence of our results is that, contrary to the onedimensional case, a penalty is not needed for retrieving the true number of diagonal blocks. Finally, the results are illustrated on synthetic data.Comment: 30 pages, 8 figure

Extremely Large and Anisotropic Upper Critical Field and the Ferromagnetic Instability in UCoGe

Magnetoresistivity measurements with fine tuning of the field direction on high quality single crystals of the ferromagnetic superconductor UCoGe show anomalous anisotropy of the upper critical field H_c2. H_c2 for H // b-axis (H_c2^b) in the orthorhombic crystal structure is strongly enhanced with decreasing temperature with an S-shape and reaches nearly 20 T at 0 K. The temperature dependence of H_c2^a shows upward curvature with a low temperature value exceeding 30 T, while H_c2^c at 0 K is very small (~ 0.6 T). Contrary to conventional ferromagnets, the decrease of the Curie temperature with increasing field for H // b-axis marked by an enhancement of the effective mass of the conduction electrons appears to be the origin of the S-shaped H_c2^b curve. These results indicate that the field-induced ferromagnetic instability or magnetic quantum criticality reinforces superconductivity.Comment: 5 pages, 4 figures, accepted for publication in J. Phys. Soc. Jp

Pressure Evolution of the Ferromagnetic and Field Re-entrant Superconductivity in URhGe

Fine pressure ($P$) and magnetic field ($H$) tuning on the ferromagnetic superconductor URhGe are reported in order to clarify the interplay between the mass enhancement, low field superconductivity (SC) and field reentrant superconductivity (RSC) by electrical resistivity measurements. With increasing $P$, the transition temperature and the upper critical field of the low field SC decrease slightly, while the RSC dome drastically shifts to higher fields and shrinks. The spin reorientation field $H_{\rm R}$ also increases. At a pressure $P\sim 1.8$ GPa, the RSC has collapsed while the low field SC persists and may disappear only above 4 GPa. Via careful $(P, H)$ studies of the inelastic $T^2$ resistivity term, it is demonstrated that this drastic change is directly related with the $P$ dependence of the effective mass which determines the critical field of the low field SC and RSC on the basis of triplet SC without Pauli limiting field.Comment: 5 pages, 6 figures, to appear in Journal of the Physical Society of Japa

Quantum Free Yang-Mills on the Plane

We construct a free-probability quantum Yang-Mills theory on the two dimensional plane, determine the Wilson loop expectation values, and show that this theory is the $N=\infty$ limit of U(N) quantum Yang-Mills theory on the plane.Comment: 24 pages, tikz figure

Charge-monopole versus Gravitational Scattering at Planckian Energies

The amplitude for the scattering of a point magnetic monopole and a point charge, at centre-of-mass energies much larger than the masses of the particles, and in the limit of low momentum transfer, is shown to be proportional to the (integer-valued) monopole strength, assuming the Dirac quantization condition for the monopole-charge system. It is demonstrated that, for small momentum transfer, charge-monopole electromagnetic effects remain comparable to those due to the gravitational interaction between the particles even at Planckian centre-of-mass energies.Comment: 9 pages, revtex, IMSc/93-4

Stress transmission in granular matter

The transmission of forces through a disordered granular system is studied by means of a geometrical-topological approach that reduces the granular packing into a set of layers. This layered structure constitutes the skeleton through which the force chains set up. Given the granular packing, and the region where the force is applied, such a skeleton is uniquely defined. Within this framework, we write an equation for the transmission of the vertical forces that can be solved recursively layer by layer. We find that a special class of analytical solutions for this equation are L\'evi-stable distributions. We discuss the link between criticality and fragility and we show how the disordered packing naturally induces the formation of force-chains and arches. We point out that critical regimes, with power law distributions, are associated with the roughness of the topological layers. Whereas, fragility is associated with local changes in the force network induced by local granular rearrangements or by changes in the applied force. The results are compared with recent experimental observations in particulate matter and with computer simulations.Comment: 14 pages, Latex, 5 EPS figure

The Length of an SLE - Monte Carlo Studies

The scaling limits of a variety of critical two-dimensional lattice models are equal to the Schramm-Loewner evolution (SLE) for a suitable value of the parameter kappa. These lattice models have a natural parametrization of their random curves given by the length of the curve. This parametrization (with suitable scaling) should provide a natural parametrization for the curves in the scaling limit. We conjecture that this parametrization is also given by a type of fractal variation along the curve, and present Monte Carlo simulations to support this conjecture. Then we show by simulations that if this fractal variation is used to parametrize the SLE, then the parametrized curves have the same distribution as the curves in the scaling limit of the lattice models with their natural parametrization.Comment: 18 pages, 10 figures. Version 2 replaced the use of "nu" for the "growth exponent" by 1/d_H, where d_H is the Hausdorff dimension. Various minor errors were also correcte

Phase transitions driven by L\'evy stable noise: exact solutions and stability analysis of nonlinear fractional Fokker-Planck equations

Phase transitions and effects of external noise on many body systems are one of the main topics in physics. In mean field coupled nonlinear dynamical stochastic systems driven by Brownian noise, various types of phase transitions including nonequilibrium ones may appear. A Brownian motion is a special case of L\'evy motion and the stochastic process based on the latter is an alternative choice for studying cooperative phenomena in various fields. Recently, fractional Fokker-Planck equations associated with L\'evy noise have attracted much attention and behaviors of systems with double-well potential subjected to L\'evy noise have been studied intensively. However, most of such studies have resorted to numerical computation. We construct an {\it analytically solvable model} to study the occurrence of phase transitions driven by L\'evy stable noise.Comment: submitted to EP

Sign-time distribution for a random walker with a drifting boundary

We present a derivation of the exact sign-time distribution for a random walker in the presence of a boundary moving with constant velocity.Comment: 5 page