Lattice models for granular-like velocity fields: Hydrodynamic limit

A recently introduced model describing -on a 1d lattice- the velocity field of a granular fluid is discussed in detail. The dynamics of the velocity field occurs through next-neighbours inelastic collisions which conserve momentum but dissipate energy. The dynamics can be described by a stochastic equation in full phase space, or through the corresponding Master Equation for the time evolution of the probability distribution. In the hydrodynamic limit, equations for the average velocity and temperature fields with fluctuating currents are derived, which are analogous to those of granular fluids when restricted to the shear modes. Therefore, the homogeneous cooling state, with its linear instability, and other relevant regimes such as the uniform shear flow and the Couette flow states are described. The evolution in time and space of the single particle probability distribution, in all those regimes, is also discussed, showing that the local equilibrium is not valid in general. The noise for the momentum and energy currents, which are correlated, are white and Gaussian. The same is true for the noise of the energy sink, which is usually negligible

Derivation of a Langevin equation in a system with multiple scales: the case of negative temperatures

We consider the problem of building a continuous stochastic model, i.e., a Langevin or Fokker-Planck equation, through a well-controlled coarse-graining procedure. Such a method usually involves the elimination of the fast degrees of freedom of the “bath” to which the particle is coupled. Specifically, we look into the general case where the bath may be at negative temperatures, as found, for instance, in models and experiments with bounded effective kinetic energy. Here, we generalize previous studies by considering the case in which the coarse graining leads to (i) a renormalization of the potential felt by the particle, and (ii) spatially dependent viscosity and diffusivity. In addition, a particular relevant example is provided, where the bath is a spin system and a sort of phase transition takes place when going from positive to negative temperatures. A Chapman-Enskog-like expansion allows us to rigorously derive the Fokker-Planck equation from the microscopic dynamics. Our theoretical predictions show excellent agreement with numerical simulation

Derivation of a Langevin equation in a system with multiple scales: the case of negative temperatures

We consider the problem of building a continuous stochastic model, i.e. a Langevin or Fokker-Planck equation, through a well-controlled coarse-graining procedure. Such a method usually involves the elimination of the fast degrees of freedom of the "bath" to which the particle is coupled. Specifically, we look into the general case where the bath may be at negative temperatures, as found - for instance - in models and experiments with bounded effective kinetic energy. Here, we generalise previous studies by considering the case in which the coarse-graining leads to (i) a renormalisation of the potential felt by the particle, and (ii) spatially dependent viscosity and diffusivity. In addition, a particular relevant example is provided, where the bath is a spin system and a sort of phase transition takes place when going from positive to negative temperatures. A Chapman-Enskog-like expansion allows us to rigorously derive the Fokker-Planck equation from the microscopic dynamics. Our theoretical predictions show an excellent agrement with numerical simulations

From Barcelona to Vancouver: the use of the green areas along space/time

El enfoque de esta reflexión es sobre el paisaje: en su relación con los jardines, la arquitectura y el medio ambiente, y el uso de las áreas a lo largo del espacio y el tiempo. A lo largo de la historia, las áreas verdes se conciben como resultado de una necesidad para las ciudades, un espacio añadido a las áreas construidas, volviéndose un impedimento para los Servicios del Eco Sistema Ecológico. Recientemente nos empezamos a dar cuenta de los nuevos factores que dan una nueva perspectiva a losPeer ReviewedPostprint (published version

From Barcelona to Vancouver: the use of the green areas along space/time

El enfoque de esta reflexión es sobre el paisaje: en su relación con los jardines, la arquitectura y el medio ambiente, y el uso de las áreas a lo largo del espacio y el tiempo. A lo largo de la historia, las áreas verdes se conciben como resultado de una necesidad para las ciudades, un espacio añadido a las áreas construidas, volviéndose un impedimento para los Servicios del Eco Sistema Ecológico. Recientemente nos empezamos a dar cuenta de los nuevos factores que dan una nueva perspectiva a losPeer ReviewedPostprint (published version

Orthogonally Additive and Orthogonality Preserving Holomorphic Mappings between C*-Algebras

We study holomorphic maps between C * -algebras A and B, when f: BA (0, ρ) → B is a holomorphic mapping whose Taylor series at zero is uniformly converging in some open unit ball U = BA (0, δ). If we assume that f is orthogonality preserving and orthogonally additive on A s a ∩ U and f (U) contains an invertible element in B, then there exist a sequence (hn) in B * * and Jordan * -homomorphisms Θ, Θ: M (A) → B * * such that f (x) = ∑ n = 1 ∞ h n Θ (an) = ∑n = 1 ∞ Θ (an) hn uniformly in a ∈ U. When B is abelian, the hypothesis of B being unital and f (U) ∩ i n v (B) ≠ ∅ can be relaxed to get the same statement.The authors are partially supported by the Spanish Ministry of Economy and Competitiveness, D.G.I. Project no. MTM2011-23843, and Junta de Andalucía Grant FQM3737

Clinical comparison of instrumentation systems for periodontal debridement: A randomized clinical trial.

AbstractObjectiveTo compare clinical efficacy, chairside time and post‐treatment hypersensitivity of four instruments used for subgingival periodontal debridement.Materials & MethodsSeventeen patients with stage II and III periodontitis were enrolled in this randomized clinical trial using a split‐mouth design. Quadrants were randomly divided into four treatment groups: Group A: Gracey curettes‐Hu‐Friedy®; Group B: piezoelectric ultrasonic (Satelec®) with No.1S insert; Group C: diamond burs 40 µm (Intensiv Perioset®); and Group D: piezosurgery ultrasonic (Mectron®) with PP1 insert. Clinical outcomes, chairside time and hypersensitivity were assessed at 1, 2, 4 and 8 weeks after treatment. The primary outcome variable was improvement in clinical attachment level.ResultsAt 8 weeks post‐treatment, Gracey curettes, piezoelectric ultrasonic (Satelec®) and piezosurgery ultrasonic (Mectron®) were statistically more effective than diamond burs in increasing attachment level and reducing probing pocket depth. Comparison of piezoelectric ultrasonic (Satelec®) and piezosurgery ultrasonic (Mectron®) with the other instruments showed a statistical difference (p < 0.001) in chairside time. Regarding post‐treatment hypersensitivity, no statistical differences were observed in any of the groups.ConclusionsGracey curettes, piezoelectric ultrasonic (Satelec®) and piezosurgery ultrasonic (Mectron®) were clinically more effective than diamond burs 40 µm. The ultrasonic instruments showed a significant reduction in chairside time