Dynamic properties in a family of competitive growing models

The properties of a wide variety of growing models, generically called $X/RD$, are studied by means of numerical simulations and analytic developments. The study comprises the following $X$ models: Ballistic Deposition, Random Deposition with Surface Relaxation, Das Sarma-Tamboronea, Kim-Kosterlitz, Lai-Das Sarma, Wolf-Villain, Large Curvature, and three additional models that are variants of the Ballistic Deposition model. It is shown that after a growing regime, the interface width becomes saturated at a crossover time ($t_{x2}$) that, by fixing the sample size, scales with $p$ according to $t_{x2}(p)\propto p^{-y}, \qquad (p > 0)$, where $y$ is an exponent. Also, the interface width at saturation ($W_{sat}$) scales as $W_{sat}(p)\propto p^{-\delta}, \qquad (p > 0)$, where $\delta$ is another exponent. It is proved that, in any dimension, the exponents $\delta$ and $y$ obey the following relationship: $\delta = y \beta_{RD}$, where $\beta_{RD} = 1/2$ is the growing exponent for $RD$. Furthermore, both exponents exhibit universality in the $p \to 0$ limit. By mapping the behaviour of the average height difference of two neighbouring sites in discrete models of type $X/RD$ and two kinds of random walks, we have determined the exact value of the exponent $\delta$. Finally, by linking four well-established universality classes (namely Edwards-Wilkinson, Kardar-Parisi-Zhang, Linear-MBE and Non-linear-MBE) with the properties of both random walks, eight different stochastic equations for all the competitive models studied are derived.Comment: 23 pages, 6 figures, Submitted to Phys. Rev.

Fold-Saddle Bifurcation in Non-Smooth Vector Fields on the Plane

This paper presents results concerning bifurcations of 2D piecewise-smooth dynamical systems governed by vector fields. Generic three parameter families of a class of Non-Smooth Vector Fields are studied and its bifurcation diagrams are exhibited. Our main result describes the unfolding of the so called Fold-Saddle singularity

Commuting multiparty quantum observables and local compatibility

A formula for the commutator of tensor product matrices is used to shows that, for qubits, compatibility of quantum multiparty observables almost never implies local compatibility at each site and to predict when this happens/does not happen in a concise manner. In particular, it is shown that two ``fully nontrivial'' $n$-qubit observables are compatible locally and globally if and only if they are equal up to sign. In addition, the formula gives insight into the construction of new paradoxes of the type of the Kochen-Specker Theorem, which can then be easily rephrased into proposals for new no hidden variable experiments of the type of the ``Bell Theorem without inequalities''.Comment: 6 page

Spanning trees for the geometry and dynamics of compact polymers

Using a mapping of compact polymers on the Manhattan lattice to spanning trees, we calculate exactly the average number of bends at infinite temperature. We then find, in a high temperature approximation, the energy of the system as a function of bending rigidity and polymer elasticity. We identify the universal mechanism for the relaxation of compact polymers and then endow the model with physically motivated dynamics in the convenient framework of the trees. We find aging and domain coarsening after quenches in temperature. We explain the slow dynamics in terms of the geometrical interconnections between the energy and the dynamics.Comment: 10 pages, 8 figure

Brans-Dicke cylindrical wormholes

Static axisymmetric thin-shell wormholes are constructed within the framework of the Brans-Dicke scalar-tensor theory of gravity. Examples of wormholes associated with vacuum and electromagnetic fields are studied. All constructions must be threaded by exotic matter, except in the case of geometries with a singularity of finite radius, associated with an electric field, which can have a throat supported by ordinary matter. These results are achieved with any of the two definitions of the flare-out condition considered.Comment: 11 pages, 3 figures; v3: corrected version, conclusions unchange

Matter X waves

We predict that an ultra-cold Bose gas in an optical lattice can give rise to a new form of condensation, namely matter X waves. These are non-spreading 3D wave-packets which reflect the symmetry of the Laplacian with a negative effective mass along the lattice direction, and are allowed to exist in the absence of any trapping potential even in the limit of non-interacting atoms. This result has also strong implications for optical propagation in periodic structuresComment: 5 pages, 2 figure

Duality in linearized gravity

We show that duality transformations of linearized gravity in four dimensions, i.e., rotations of the linearized Riemann tensor and its dual into each other, can be extended to the dynamical fields of the theory so as to be symmetries of the action and not just symmetries of the equations of motion. Our approach relies on the introduction of two "superpotentials", one for the spatial components of the spin-2 field and the other for their canonically conjugate momenta. These superpotentials are two-index, symmetric tensors. They can be taken to be the basic dynamical fields and appear locally in the action. They are simply rotated into each other under duality. In terms of the superpotentials, the canonical generator of duality rotations is found to have a Chern-Simons like structure, as in the Maxwell case.Comment: 10 pages; introduction rewritten and references adde

Recent variations of Ghiacciaio del Calderone, Abruzzi, Italy

AbstractResults of a detailed topographic survey of Ghiacciaio del Calderone, Italy, the southernmost in Europe, are described and compared with those of surveys made in earlier years. Recession and thinning, much affected by micro-climate, have been the predominant state of health during the 20th century. Between 1916 and 1990, volume is estimated to have been reduced by about 90% and area by about 68%

Petrology and geochemistry of mafic and ultramafic cumulate rocks from the eastern part of the Sabzevar ophiolite (NE Iran): Implications for their petrogenesis and tectonic setting

The Late Cretaceous Sabzevar ophiolite represents one of the largest and most complete fragments of Tethyan oceanic lithosphere in the NE Iran. It is mainly composed of serpentinized mantle peridotites slices; nonetheless, minor tectonic slices of all crustal sequence constituents are observed in this ophiolite. The crustal sequence contains a well-developed ultramafic and mafic cumulates section, comprising plagioclase-bearing wehrlite, olivine clinopyroxenite, olivine gabbronorite, gabbronorite, amphibole gabbronorite and quartz gabbronorite with adcumulate, mesocumulate, heteradcumulate and orthocumulate textures. The crystallization order for these rocks is olivine ​± ​chromian spinel → clinopyroxene → plagioclase → orthopyroxene → amphibole. The presence of primary magmatic amphiboles in the cumulate rocks shows that the parent magma evolved under hydrous conditions. Geochemically, the studied rock units are characterized by low TiO (0.18–0.57 ​wt.%), PO (<0.05 ​wt.%), KO (0.01–0.51 ​wt.%) and total alkali contents (0.12–3.04 ​wt.%). They indicate fractionated trends in the chondrite-normalized rare earth element (REE) plots and multi-element diagrams (spider diagrams). The general trend of the spider diagrams exhibit slight enrichment in large ion lithophile elements (LILEs) relative to high field strength elements (HFSEs) and positive anomalies in Sr, Pb and Eu and negative anomalies in Zr and Nb relative to the adjacent elements. The REE plots of these rocks display increasing trend from La to Sm, positive Eu anomaly (Eu/Eu∗ ​= ​1.06–1.54) and an almost flat pattern from medium REE (MREE) to heavy REE (HREE) region [(Gd/Yb) ​= ​1–1.17]. Moreover, clinopyroxenes from the cumulate rocks have low REE contents and show marked depletion in light REE (LREE) compared to MREE and HREE [(La/Sm) ​= ​0.10–0.27 and (La/Yb) ​= ​0.08–0.22]. The composition of calculated melts in equilibrium with the clinopyroxenes from less evolved cumulate samples are closely similar to island arc tholeiitic (IAT) magmas. Modal mineralogy, geochemical features and REE modeling indicate that Sabzevar cumulate rocks were formed by crystal accumulation from a hydrous depleted basaltic melt with IAT affinity. This melt has been produced by moderate to high degree (~15%) of partial melting a depleted mantle source, which partially underwent metasomatic enrichment from subducted slab components in an intra-oceanic arc setting.The authors thank the University of Isfahan (Isfahan, Iran) and the Instituto Andaluz de Ciencias de la Tierra (IACT, Granada, Spain) for their support in field work and sample preparation and for providing geochemical analyses facilities. We are grateful to Prof. Kristoffer Szilas, Prof. Tomo Morishita and two anonymous reviewers for their useful and constructive comments that improved the manuscript