A Stress/Displacement Virtual Element Method for Plane Elasticity Problems

The numerical approximation of 2D elasticity problems is considered, in the framework of the small strain theory and in connection with the mixed Hellinger-Reissner variational formulation. A low-order Virtual Element Method (VEM) with a-priori symmetric stresses is proposed. Several numerical tests are provided, along with a rigorous stability and convergence analysis

Emergent SU(N) symmetry in disordered SO(N) spin chains

Strongly disordered spin chains invariant under the SO(N) group are shown to display random-singlet phases with emergent SU(N) symmetry without fine tuning. The phases with emergent SU(N) symmetry are of two kinds: one has a ground state formed of randomly distributed singlets of strongly bound pairs of SO(N) spins (a `mesonic' phase), while the other has a ground state composed of singlets made out of strongly bound integer multiples of N SO(N) spins (a `baryonic' phase). The established mechanism is general and we put forward the cases of $\mathrm{N}=2,3,4$ and $6$ as prime candidates for experimental realizations in material compounds and cold-atoms systems. We display universal temperature scaling and critical exponents for susceptibilities distinguishing these phases and characterizing the enlarging of the microscopic symmetries at low energies.Comment: 5 pages, 2 figures, Contribution to the Topical Issue "Recent Advances in the Theory of Disordered Systems", edited by Ferenc Igl\'oi and Heiko Riege

Highly-symmetric random one-dimensional spin models

The interplay of disorder and interactions is a challenging topic of condensed matter physics, where correlations are crucial and exotic phases develop. In one spatial dimension, a particularly successful method to analyze such problems is the strong-disorder renormalization group (SDRG). This method, which is asymptotically exact in the limit of large disorder, has been successfully employed in the study of several phases of random magnetic chains. Here we develop an SDRG scheme capable to provide in-depth information on a large class of strongly disordered one-dimensional magnetic chains with a global invariance under a generic continuous group. Our methodology can be applied to any Lie-algebra valued spin Hamiltonian, in any representation. As examples, we focus on the physically relevant cases of SO(N) and Sp(N) magnetism, showing the existence of different randomness-dominated phases. These phases display emergent SU(N) symmetry at low energies and fall in two distinct classes, with meson-like or baryon-like characteristics. Our methodology is here explained in detail and helps to shed light on a general mechanism for symmetry emergence in disordered systems.Comment: 26 pages, 12 figure

Massive Black Hole Binary Systems in Hierarchical Scenario of Structure Formation

The hierarchical scenario of structure formation describes how objects like galaxies and galaxy clusters are formed by mergers of small objects. In this scenario, mergers of galaxies can lead to the formation of massive black hole (MBH) binary systems. On the other hand, the merger of two MBH could produce a gravitational wave signal detectable, in principle, by the Laser Interferometer Space Antenna (LISA). In the present work, we use the Press-Schechter formalism, and its extension, to describe the merger rate of haloes which contain massive black holes. Here, we do not study the gravitational wave emission of these systems. However, we present an initial study to determine the number of systems formed via mergers that could permit, in a future extension of this work, the calculation of the signature in gravitational waves of these systems.Comment: to match the published version in International Journal of Modern Physics

Magnetically-controlled impurities in quantum wires with strong Rashba coupling

We investigate the effect of strong spin-orbit interaction on the electronic transport through non-magnetic impurities in one-dimensional systems. When a perpendicular magnetic field is applied, the electron spin polarization becomes momentum-dependent and spin-flip scattering appears, to first order in the applied field, in addition to the usual potential scattering. We analyze a situation in which, by tuning the Fermi level and the Rashba coupling, the magnetic field can suppress the potential scattering. This mechanism should give rise to a significant negative magnetoresistance in the limit of large barriers.Comment: 4 pages, 2 figure

On the probability distributions of the force and potential energy for a system with an infinite number of random point sources

In this work, we study the probability distribution for the force and potential energy of a test particle interacting with $N$ point random sources in the limit $N\rightarrow\infty$. The interaction is given by a central potential $V(R)=k/R^{\delta-1}$ in a $d$-dimensional euclidean space, where $R$ is the random relative distance between the source and the test particle, $\delta$ is the force exponent, and $k$ is the coupling parameter. In order to assure a well-defined limit for the probability distribution of the force and potential energy, we { must} renormalize the coupling parameter and/or the system size as a function of the number $N$ of sources. We show the existence of three non-singular limits, depending on the exponent $\delta$ and the spatial dimension $d$. (i) For $\delta<d$ the force and potential energy { converge} to their respective mean values. This limit is called Mean Field Limit. (ii) For $\delta>d+1$ the potential energy converges to a random variable and the force to a random vector. This limit is called Thermodynamic Limit. (iii) For $d<\delta<d+1$ the potential energy converges to its mean and the force to a random vector. This limit is called Mixed Limit Also, we show the existence of two singular limits: (iv) for $\delta=d$ the potential energy converges to its mean and the force to zero, and (v) for $\delta=d+1$ the energy converges to a finite value and the force to a random vector.Comment: 25 pages, 5 tables, Preprint Articl

Observational Study of the Multistructured Planetary Nebula NGC 7354

We present an observational study of the planetary nebula (PN) NGC 7354 consisting of narrowband Halpha and [NII]6584 imaging as well as low- and high-dispersion long-slit spectroscopy and VLA-D radio continuum. According to our imaging and spectroscopic data, NGC 7354 has four main structures: a quite round outer shell and an elliptical inner shell, a collection of low-excitation bright knots roughly concentrated on the equatorial region of the nebula, and two symmetrical jet-like features, not aligned either with the shells' axes, or with each other. We have obtained physical parameters like electron temperature and electron density as well as ionic and elemental abundances for these different structures. Electron temperature and electron density slightly vary throughout the nebula. The local extinction coefficient c_Hbeta shows an increasing gradient from south to north and a decreasing gradient from east to west consistent with the number of equatorial bright knots present in each direction. Abundance values show slight internal variations but most of them are within the estimated uncertainties. In general, abundance values are in good agreement with the ones expected for PNe. Radio continuum data are consistent with optically thin thermal emission. We have used the interactive three-dimensional modeling tool SHAPE to reproduce the observed morphokinematic structures in NGC 7354 with different geometrical components. Our SHAPE model is in very good agreement with our imaging and spectroscopic observations. Finally, after modeling NGC 7354 with SHAPE, we suggest a possible scenario for the formation of the nebula.Comment: Accepted for publication in AJ, 12 pages, 8 figure