On simultaneous arithmetic progressions on elliptic curves

In this paper we study elliptic curves which have a number of points whose coordinates are in arithmetic progression. We first motivate this diophantine problem, prove some results, provide a number of interesting examples and, finally point out open questions which focus on the most interesting aspects of the problem for us.Comment: 22 page

Matrix Product State Representations

This work gives a detailed investigation of matrix product state (MPS) representations for pure multipartite quantum states. We determine the freedom in representations with and without translation symmetry, derive respective canonical forms and provide efficient methods for obtaining them. Results on frustration free Hamiltonians and the generation of MPS are extended, and the use of the MPS-representation for classical simulations of quantum systems is discussed.Comment: Minor changes. To appear in QI

Rheological effects in the linear response and spontaneous fluctuations of a sheared granular gas

The decay of a small homogeneous perturbation of the temperature of a dilute granular gas in the steady uniform shear flow state is investigated. Using kinetic theory based on the inelastic Boltzmann equation, a closed equation for the decay of the perturbation is derived. The equation involves the generalized shear viscosity of the gas in the time-dependent shear flow state, and therefore it predicts relevant rheological effects beyond the quasi-elastic limit. A good agreement is found when comparing the theory with molecular dynamics simulation results. Moreover, the Onsager postulate on the regression of fluctuations is fulfilled

Dependence of the drag over super hydrophobic and liquid infused surfaces on the textured surface and Weber number

Direct Numerical Simulations of a turbulent channel flow have been performed. The lower wall of the channel is made of staggered cubes with a second fluid locked in the cavities. Two viscosity ratios have been considered, m=μ1/μ2=0.02 and 0.4 (the subscript 1 indicates the fluid in the cavities and 2 the overlying fluid) mimicking the viscosity ratio in super–hydrophobic surfaces (SHS) and liquid infused surfaces (LIS) respectively. A first set of simulations with a slippery interface has been performed and results agree well with those in literature for perfect slip conditions and Stokes approximations. To assess how the dynamics of the interface affects the drag, a second set of DNS has been carried out at We=40 and 400 corresponding to We+≃10−3 and 10−2. The deformation of the interface is fully coupled to the Navier-Stokes equation and tracked in time using a Level Set Method. Two gas fractions, GF=0.5 and 0.875, have been considered to assess how the spacing between the cubes affects the deformation of the interface and therefore the drag. For the dimensions of the substrate here considered, under the ideal assumption of flat interface, staggered cubes with GF=0.875 provide about 20% drag reduction for We=0. However, a rapid degradation of the performances is observed when the dynamics of the interface is considered, and the same geometry increases the drag of about 40% with respect to a smooth wall. On the other hand, the detrimental effect of the dynamics of the interface is much weaker for GF=0.5 because of the reduced pitch between the cubes

Internal energy fluctuations of a granular gas under steady uniform shear flow

The stochastic properties of the total internal energy of a dilute granular gas in the steady uniform shear flow state are investigated. A recent theory formulated for fluctuations about the homogeneous cooling state is extended by analogy with molecular systems. The theoretical predictions are compared with molecular dynamics simulation results. Good agreement is found in the limit of weak inelasticity, while systematic and relevant discrepancies are observed when the inelasticity increases. The origin of this behavior is discussed

Production and propagation of heavy hadrons in air-shower simulators

Very energetic charm and bottom hadrons may be produced in the upper atmosphere when a primary cosmic ray or the leading hadron in an extensive air shower collide with a nucleon. At $E\approx 10^8$ GeV their decay length becomes of the order of 10 km, implying that they tend to interact in the air instead of decaying. Since the inelasticity in these collisions is much smaller than the one in proton and pion collisions, there could be rare events where a heavy-hadron component transports a significant amount of energy deep into the atmosphere. We have developed a module for the detailed simulation of these processes and have included it in a new version of the air shower simulator AIRES. We study the frequency, the energy distribution and the depth of charm and bottom production, as well as the depth and the energy distribution of these quarks when they decay. As an illustration, we consider the production and decay of tau leptons (from $D_s$ decays) and the lepton flux at PeV energies from a 30 EeV proton primary. The proper inclusion of charm and bottom hadrons in AIRES opens the possibility to search for air-shower observables that are sensitive to heavy quark effects.Comment: Accepted for publication in Astroparticle Physic

Electronic Raman Scattering in Twistronic Few-Layer Graphene

We study electronic contribution to the Raman scattering signals of two-, three- and four-layer graphene with layers at one of the interfaces twisted by a small angle with respect to each other. We find that the Raman spectra of these systems feature two peaks produced by van Hove singularities in moir\'{e} minibands of twistronic graphene, one related to direct hybridization of Dirac states, and the other resulting from band folding caused by moir\'{e} superlattice. The positions of both peaks strongly depend on the twist angle, so that their detection can be used for non-invasive characterization of the twist, even in hBN-encapsulated structures.Comment: 7 pages (including 4 figures) + 10 pages (3 figures) supplemen

Nonsingular electrovacuum solutions with dynamically generated cosmological constant

We consider static spherically symmetric configurations in a Palatini extension of General Relativity including $R^2$ and Ricci-squared terms, which is known to replace the central singularity by a wormhole in the electrovacuum case. We modify the matter sector of the theory by adding to the usual Maxwell term a nonlinear electromagnetic extension which is known to implement a confinement mechanism in flat space. One feature of the resulting theory is that the non-linear electric field leads to a dynamically generated cosmological constant. We show that with this matter source the solutions of the model are asymptotically de Sitter and possess a wormhole topology. We discuss in some detail the conditions that guarantee the absence of singularities and of traversable wormholes.Comment: 7 double-column pages; v2: several changes in abstract and introductio

Mesoscopic Theory of Critical Fluctuations in Isolated Granular Gases

Fluctuating hydrodynamics is used to describe the total energy fluctuations of a freely evolving gas of inelastic hard spheres near the threshold of the clustering instability. They are shown to be governed by vorticity fluctuations only, that also lead to a renormalization of the average total energy. The theory predicts a power-law divergent behavior of the scaled second moment of the fluctuations, and a scaling property of their probability distribution, both in agreement with simulations results. A more quantitative comparison between theory and simulation for the critical amplitudes and the form of the scaling function is also carried out