Universal Jamming Phase Diagram in the Hard-Sphere Limit

We present a new formulation of the jamming phase diagram for a class of glass-forming fluids consisting of spheres interacting via finite-ranged repulsions at temperature $T$, packing fraction $\phi$ or pressure $p$, and applied shear stress $\Sigma$. We argue that the natural choice of axes for the phase diagram are the dimensionless quantities $T/p\sigma^3$, $p\sigma^3/\epsilon$, and $\Sigma/p$, where $T$ is the temperature, $p$ is the pressure, $\Sigma$ is the stress, $\sigma$ is the sphere diameter, $\epsilon$ is the interaction energy scale, and $m$ is the sphere mass. We demonstrate that the phase diagram is universal at low $p\sigma^3/\epsilon$; at low pressure, observables such as the relaxation time are insensitive to details of the interaction potential and collapse onto the values for hard spheres, provided the observables are non-dimensionalized by the pressure. We determine the shape of the jamming surface in the jamming phase diagram, organize previous results in relation to the jamming phase diagram, and discuss the significance of various limits.Comment: 8 pages, 5 figure

Numerical and experimental study of the effects of noise on the permutation entropy

We analyze the effects of noise on the permutation entropy of dynamical systems. We take as numerical examples the logistic map and the R\"ossler system. Upon varying the noise strengthfaster, we find a transition from an almost-deterministic regime, where the permutation entropy grows slower than linearly with the pattern dimension, to a noise-dominated regime, where the permutation entropy grows faster than linearly with the pattern dimension. We perform the same analysis on experimental time-series by considering the stochastic spiking output of a semiconductor laser with optical feedback. Because of the experimental conditions, the dynamics is found to be always in the noise-dominated regime. Nevertheless, the analysis allows to detect regularities of the underlying dynamics. By comparing the results of these three different examples, we discuss the possibility of determining from a time series whether the underlying dynamics is dominated by noise or not

A to Z of the Muon anomalous magnetic moment in the MSSM with Pati-Salam at the GUT scale

We analyse the low energy predictions of the minimal supersymmetric standard model (MSSM) arising from a GUT scale Pati-Salam gauge group further constrained by an A4 × Z5 family symmetry, resulting in four soft scalar masses at the GUT scale: one left-handed soft mass m0 and three right-handed soft masses m1, m2, m3, one for each generation. We demonstrate that this model, which was initially developed to describe the neutrino sector, can explain collider and non-collider measurements such as the dark matter relic density, the Higgs boson mass and, in particular, the anomalous magnetic moment of the muon (g − 2)μ. Since about two decades, (g − 2)μ suffers a puzzling about 3σ excessoftheexperimentallymeasuredvalueoverthetheoreticalprediction,whichour model is able to fully resolve. As the consequence of this resolution, our model predicts specific regions of the parameter space with the specific properties including light smuons and neutralinos, which could also potentially explain di-lepton excesses observed by CMS and ATLAS

The nucleus of the Sagittarius dSph galaxy and M54: a window on the process of galaxy nucleation

We present the results of a thorough study of the nucleus of the Sgr dwarf spheroidal galaxy and of the bright globular cluster M54 that resides within the same nucleus (Sgr,N). We have obtained accurate radial velocities and metallicity estimates for 1152 candidate Red Giant Branch stars of Sgr and M54 lying within ~ 9 arcmin from the center of the galaxy, from Keck/DEIMOS and VLT/FLAMES spectra of the infrared Calcium II triplet. Using both velocity and metallicity information we selected two samples of 425 and 321 very-likely members of M54 and of Sgr,N, respectively. The two considered systems display significantly different velocity dispersion profiles: M54 has a steeply decreasing profile from r=0, where sigma= 14.2 km/s, to r=3.5 arcmin where it reaches sigma=5.3 km/s, then it appears to rise again to sigma= 10 km/s at r=7 arcmin. In contrast Sgr,N has a uniformly flat profile at sigma=9.6 km/s over the whole 0 < r < 9 arcmin range. Using data from the literature we show that the velocity dispersion of Sgr remains constant at least out to r ~ 100 arcmin and there is no sign of the transition between the outer flat-luminosity-profile core and the inner nucleus in the velocity profile. These results - together with a re-analysis of the surface brightness profile of Sgr,N and a suite of dedicated N-body simulations - provide very strong support for the hypothesis that the nucleus of Sgr formed independently of M54, which probably plunged to its present position, coincident with Sgr,N, because of significant decay of the original orbit due to dynamical friction.Comment: Accepted for publication by the Astronomical Journal. emulateapj.cls, 26 pag., 21 low resolution figures. A full-resolution color version of the paper can be retrieved from http://www.bo.astro.it/SGR/Sgr_nucleus.ps.g

Accurate Results from Perturbation Theory for Strongly Frustrated S=1/2S=1/2 Heisenberg Spin Clusters

We investigate the use of perturbation theory in finite sized frustrated spin systems by calculating the effect of quantum fluctuations on coherent states derived from the classical ground state. We first calculate the ground and first excited state wavefunctions as a function of applied field for a 12-site system and compare with the results of exact diagonalization. We then apply the technique to a 20-site system with the same three fold site coordination as the 12-site system. Frustration results in asymptotically convergent series for both systems which are summed with Pad\'e approximants. We find that at zero magnetic field the different connectivity of the two systems leads to a triplet first excited state in the 12-site system and a singlet first excited state in the 20-site system, while the ground state is a singlet for both. We also show how the analytic structure of the Pad\'e approximants at $|\lambda| \simeq 1$ evolves in the complex $\lambda$ plane at the values of the applied field where the ground state switches between spin sectors and how this is connected with the non-trivial dependence of the $$ number on the strength of quantum fluctuations. We discuss the origin of this difference in the energy spectra and in the analytic structures. We also characterize the ground and first excited states according to the values of the various spin correlation functions.Comment: Final version, accepted for publication in Physical review