A parabolic approach to the control of opinion spreading

We analyze the problem of controlling to consensus a nonlinear system modeling opinion spreading. We derive explicit exponential estimates on the cost of approximately controlling these systems to consensus, as a function of the number of agents N and the control time-horizon T. Our strategy makes use of known results on the controllability of spatially discretized semilinear parabolic equations. Both systems can be linked through time-rescalin

Solutions to Maxwell's Equations using Spheroidal Coordinates

Analytical solutions to the wave equation in spheroidal coordinates in the short wavelength limit are considered. The asymptotic solutions for the radial function are significantly simplified, allowing scalar spheroidal wave functions to be defined in a form which is directly reminiscent of the Laguerre-Gaussian solutions to the paraxial wave equation in optics. Expressions for the Cartesian derivatives of the scalar spheroidal wave functions are derived, leading to a new set of vector solutions to Maxwell's equations. The results are an ideal starting point for calculations of corrections to the paraxial approximation

Measurement of the lifetime of Pb52+^{52+}, Pb53+^{53+} and Pb54+^{54+} beams at 4.2 MeV per nucleon subject to electron cooling

By measuring the lifetime of stored beams, the recombination of the ions with cooling electrons was investigated. Rates found are larger than expected for radiative electron capture and significantly higher for Pb53+ than for Pb54+ and Pb52+. These results are important for the design of the lead ion injection system for the Large Hadron Collider and for recombination theories

Assignment of resonances in dissociative recombination of HD+ ions: high-resolution measurements compared with accurate computations

The collision-energy resolved rate coefficient for dissociative recombination of HD+ ions in the vibrational ground state is measured using the photocathode electron target at the heavy-ion storage ring TSR. Rydberg resonances associated with ro-vibrational excitation of the HD+ core are scanned as a function of the electron collision energy with an instrumental broadening below 1 meV in the low-energy limit. The measurement is compared to calculations using multichannel quantum defect theory, accounting for rotational structure and interactions and considering the six lowest rotational energy levels as initial ionic states. Using thermal equilibrium level populations at 300 K to approximate the experimental conditions, close correspondence between calculated and measured structures is found up to the first vibrational excitation threshold of the cations near 0.24 eV. Detailed assignments, including naturally broadened and overlapping Rydberg resonances, are performed for all structures up to 0.024 eV. Resonances from purely rotational excitation of the ion core are found to have similar strengths as those involving vibrational excitation. A dominant low-energy resonance is assigned to contributions from excited rotational states only. The results indicate strong modifications in the energy dependence of the dissociative recombination rate coefficient through the rotational excitation of the parent ions, and underline the need for studies with rotationally cold species to obtain results reflecting low-temperature ionized media.Comment: 15 pages, 10 figures. Paper to appear in Phys. Rev. A (version as accepted

Singular Cucker-Smale Dynamics

The existing state of the art for singular models of flocking is overviewed, starting from microscopic model of Cucker and Smale with singular communication weight, through its mesoscopic mean-filed limit, up to the corresponding macroscopic regime. For the microscopic Cucker-Smale (CS) model, the collision-avoidance phenomenon is discussed, also in the presence of bonding forces and the decentralized control. For the kinetic mean-field model, the existence of global-in-time measure-valued solutions, with a special emphasis on a weak atomic uniqueness of solutions is sketched. Ultimately, for the macroscopic singular model, the summary of the existence results for the Euler-type alignment system is provided, including existence of strong solutions on one-dimensional torus, and the extension of this result to higher dimensions upon restriction on the smallness of initial data. Additionally, the pressureless Navier-Stokes-type system corresponding to particular choice of alignment kernel is presented, and compared - analytically and numerically - to the porous medium equation

Search for supersymmetry with a dominant R-parity violating LQDbar couplings in e+e- collisions at centre-of-mass energies of 130GeV to 172 GeV

A search for pair-production of supersymmetric particles under the assumption that R-parity is violated via a dominant LQDbar coupling has been performed using the data collected by ALEPH at centre-of-mass energies of 130-172 GeV. The observed candidate events in the data are in agreement with the Standard Model expectation. This result is translated into lower limits on the masses of charginos, neutralinos, sleptons, sneutrinos and squarks. For instance, for m_0=500 GeV/c^2 and tan(beta)=sqrt(2) charginos with masses smaller than 81 GeV/c^2 and neutralinos with masses smaller than 29 GeV/c^2 are excluded at the 95% confidence level for any generation structure of the LQDbar coupling.Comment: 32 pages, 30 figure