Time delay of light signals in an energy-dependent spacetime metric

In this note we review the problem of time delay of photons propagating in a spacetime with a metric that explicitly depends on the energy of the particles (Gravity-Rainbow approach). We show that corrections due to this approach -- which is closely related to DSR proposal -- produce for small redshifts ($z<<1$) smaller time delays than in the generic Lorentz Invariance Violating case.Comment: 5 pages. This version contains two new references with respect to the published versio

Approaching Space Time Through Velocity in Doubly Special Relativity

We discuss the definition of velocity as dE/dp, where E,p are the energy and momentum of a particle, in Doubly Special Relativity (DSR). If this definition matches dx/dt appropriate for the space-time sector, then space-time can in principle be built consistently with the existence of an invariant length scale. We show that, within different possible velocity definitions, a space-time compatible with momentum-space DSR principles can not be derived.Comment: 11 pages, no figures, minor changes, references added, final version to appear in PR

Numerical simulations challenged on the prediction of massive subhalo abundance in galaxy clusters: the case of Abell 2142

In this Letter we compare the abundance of member galaxies of a rich, nearby ($z=0.09$) galaxy cluster, Abell 2142, with that of halos of comparable virial mass extracted from sets of state-of-the-art numerical simulations, both collisionless at different resolutions and with the inclusion of baryonic physics in the form of cooling, star formation, and feedback by active galactic nuclei. We also use two semi-analytical models to account for the presence of orphan galaxies. The photometric and spectroscopic information, taken from the Sloan Digital Sky Survey Data Release 12 (SDSS DR12) database, allows us to estimate the stellar velocity dispersion of member galaxies of Abell 2142. This quantity is used as proxy for the total mass of secure cluster members and is properly compared with that of subhalos in simulations. We find that simulated halos have a statistically significant ($\gtrsim 7$ sigma confidence level) smaller amount of massive (circular velocity above $200\,{\rm km\, s^{-1}}$) subhalos, even before accounting for the possible incompleteness of observations. These results corroborate the findings from a recent strong lensing study of the Hubble Frontier Fields galaxy cluster MACS J0416 \citep{grillo2015} and suggest that the observed difference is already present at the level of dark matter (DM) subhalos and is not solved by introducing baryonic physics. A deeper understanding of this discrepancy between observations and simulations will provide valuable insights into the impact of the physical properties of DM particles and the effect of baryons on the formation and evolution of cosmological structures.Comment: 8 pages, 2 figures. Modified to match the version published in ApJ

A Neutron Scattering Study of the Structure of Poly(dimethylsiloxane)-Stabilized Poly(methyl methacrylate) (PDMS–PMMA) Latexes in Dodecane

Hard-sphere particles in nonpolar solvents are an essential tool for colloid scientists. Sterically stabilized poly(methyl methacrylate) (PMMA) particles have long been used as the exemplary hard-sphere system. However, neither the particles themselves nor the poly(12-hydroxystearic acid) (PHSA) stabilizer necessary to prevent aggregation in nonpolar solvents are commercially available. To counter this, several alternatives have been proposed. In recent years, there has been an increased interest in poly(dimethylsiloxane) (PDMS) stabilizers as a commercially available alternative to PHSA, yet the structure of particles made in this way is not as well understood as those produced using PHSA. In this work, we employ small-angle neutron scattering to determine the internal structure of PDMS-stabilized PMMA particles, synthesized with and without an additional crosslinking agent. We report data consistent with a homogeneous PMMA core with a linearly decaying PDMS shell. The thickness of the shell was in excess of 50 nm, thicker than the PHSA layer typically used to stabilize PMMA but consistent with reports of the layer thickness for similar molecular weight PDMS at planar surfaces. We also show that the amount of the hydrogenous material in the particle core of the crosslinked particles notably exceeds the amount of added ethylene glycol dimethacrylate crosslinker, suggesting some entrapment of the PDMS stabilizer in the PMMA matrix

The fractional porous medium equation on the hyperbolic space

We consider a nonlinear degenerate parabolic equation of porous medium type, whose diffusion is driven by the (spectral) fractional Laplacian on the hyperbolic space. We provide existence results for solutions, in an appropriate weak sense, for data belonging either to the usual Lp spaces or to larger (weighted) spaces determined either in terms of a ground state of the laplacian, or of the (fractional) Green’s function. For such solutions, we also prove different kind of smoothing effects, in the form of quantitative L1- L∞ estimates. To the best of our knowledge, this seems the first time in which the fractional porous medium equation has been treated on non-compact, geometrically non-trivial examples

Nondestructive Measurement of Orbital Angular Momentum for an Electron Beam

Free electrons with a helical phase front, referred to as "twisted" electrons, possess an orbital angular momentum (OAM) and, hence, a quantized magnetic dipole moment along their propagation direction. This intrinsic magnetic moment can be used to probe material properties. Twisted electrons thus have numerous potential applications in materials science. Measuring this quantity often relies on a series of projective measurements that subsequently change the OAM carried by the electrons. In this Letter, we propose a nondestructive way of measuring an electron beam's OAM through the interaction of this associated magnetic dipole with a conductive loop. Such an interaction results in the generation of induced currents within the loop, which are found to be directly proportional to the electron's OAM value. Moreover, the electron experiences no OAM variations and only minimal energy losses upon the measurement, and, hence, the nondestructive nature of the proposed technique.Comment: 5 pages, 3 figures, and supplemental material that is comprised of text and 4 figure