Rossby waves and α\alpha-effect

Rossby waves drifting in the azimuthal direction are a common feature at the onset of thermal convective instability in a rapidly rotating spherical shell. They can also result from the destabilization of a Stewartson shear layer produced by differential rotation as expected in the liquid sodium experiment (DTS) working in Grenoble, France. A usual way to explain why Rossby waves can participate to the dynamo process goes back to Busse (1975). In his picture, the flow geometry is a cylindrical array of parallel rolls aligned with the rotation axis. The axial flow component (the component parallel to the rotation axis) is (i) maximum in the middle of each roll and changes its sign from one roll to the next. It is produced by the Ekman pumping at the fluid containing shell boundary. The corresponding dynamo mechanism can be explained in terms of an $\alpha$-tensor with non-zero coefficients on the diagonal. In rapidly rotating objects like the Earth's core (or in a fast rotating experiment), Rossby waves occur in the limit of small Ekman number ($\approx 10^{-15}$). In that case, the main source of the axial flow component is not the Ekman pumping but rather the ``geometrical slope effect'' due to the spherical shape of the fluid containing shell. This implies that the axial flow component is (ii) maximum at the borders of the rolls and not at the centers. If assumed to be stationary, such rolls would lead to zero coefficients on the diagonal of the $\alpha$-tensor, making the dynamo probably less efficient if possible at all. Actually, the rolls are drifting as a wave, and we show that this drift implies non--zero coefficients on the diagonal of the $\alpha$-tensor. These new coefficients are in essence very different from the ones obtained in case (i) and cannot be interpreted in terms of the heuristic picture of Busse (1975)

A theory of the infinite horizon LQ-problem for composite systems of PDEs with boundary control

We study the infinite horizon Linear-Quadratic problem and the associated algebraic Riccati equations for systems with unbounded control actions. The operator-theoretic context is motivated by composite systems of Partial Differential Equations (PDE) with boundary or point control. Specific focus is placed on systems of coupled hyperbolic/parabolic PDE with an overall `predominant' hyperbolic character, such as, e.g., some models for thermoelastic or fluid-structure interactions. While unbounded control actions lead to Riccati equations with unbounded (operator) coefficients, unlike the parabolic case solvability of these equations becomes a major issue, owing to the lack of sufficient regularity of the solutions to the composite dynamics. In the present case, even the more general theory appealing to estimates of the singularity displayed by the kernel which occurs in the integral representation of the solution to the control system fails. A novel framework which embodies possible hyperbolic components of the dynamics has been introduced by the authors in 2005, and a full theory of the LQ-problem on a finite time horizon has been developed. The present paper provides the infinite time horizon theory, culminating in well-posedness of the corresponding (algebraic) Riccati equations. New technical challenges are encountered and new tools are needed, especially in order to pinpoint the differentiability of the optimal solution. The theory is illustrated by means of a boundary control problem arising in thermoelasticity.Comment: 50 pages, submitte

Cylindrical anisotropic α2\alpha^{2} dynamos

We explore the influence of geometry variations on the structure and the time-dependence of the magnetic field that is induced by kinematic $\alpha^{2}$ dynamos in a finite cylinder. The dynamo action is due to an anisotropic $\alpha$ effect which can be derived from an underlying columnar flow. The investigated geometry variations concern, in particular, the aspect ratio of height to radius of the cylinder, and the thickness of the annular space to which the columnar flow is restricted. Motivated by the quest for laboratory dynamos which exhibit Earth-like features, we start with modifications of the Karlsruhe dynamo facility. Its dynamo action is reasonably described by an $\alpha^{2}$ mechanism with anisotropic $\alpha$ tensor. We find a critical aspect ratio below which the dominant magnetic field structure changes from an equatorial dipole to an axial dipole. Similar results are found for $\alpha^{2}$ dynamos working in an annular space when a radial dependence of $\alpha$ is assumed. Finally, we study the effect of varying aspect ratios of dynamos with an $\alpha$ tensor depending both on radial and axial coordinates. In this case only dominant equatorial dipoles are found and most of the solutions are oscillatory, contrary to all previous cases where the resulting fields are steady.Comment: 15 pages, 8 figure

El PACMUBIS de Tlajomulco y los derechos humanos: Valoración del diseño y análisis de los logros y límites de una política pública municipal para hacer frente al cambio climático

El cambio climático es un problema global que afecta a todos los países del mundo que pone en riesgo varios aspectos de la sociedad actual y que amenaza el disfrute de derechos humanos. La comunidad internacional ha firmado una serie de instrumentos donde se comprometen a colaborar en conjunto ante esta problemática. Si bien los esfuerzos internacionales son fundamentales, es importante que el cambio climático se aborde desde lo local, promoviendo políticas públicas que contribuyan a la mitigación y adaptación ante sus efectos. En esta investigación, se estudia el Plan de Acción Climática Municipal basada en el Bienestar y Sustentabilidad (PACMUBIS) de Tlajomulco de Zúñiga, Jalisco, como una estrategia municipal ante el cambio climático. El plan se analiza desde una perspectiva de derechos humanos con el objetivo de conocer los logros y límites de su diseño e implementación. La investigación se fundamenta en la siguiente estrategia: revisión documental de planes y estudios municipales para conocer sus aspectos básicos y vulnerabilidad ante el cambio climático, estudio a fondo del PACMUBIS desde su diseño hasta su implementación y entrevistas con actores clave para conocer su percepción y visión sobre el PACMUBIS y el papel de Tlajomulco ante el cambio climático. Los resultados indican que el PACMUBIS de Tlajomulco tiene planteamientos importantes sin embargo cuenta con áreas de mejora para poder consolidarse como política pública. Para finalizar, vale la pena indicar que el PACMUBIS solo llegó a la fase de diseño y elaboración el documento rector, pero no fue implementado debido a diversos obstáculos municipales.ITESO, A. C

Experimental evidence of solitary wave interaction in Hertzian chains

We study experimentally the interaction between two solitary waves that approach one to another in a linear chain of spheres interacting via the Hertz potential. When these counter propagating waves collide, they cross each other and a phase shift respect to the noninteracting waves is introduced, as a result of the nonlinear interaction potential. This observation is well reproduced by our numerical simulations and it is shown to be independent of viscoelastic dissipation at the beads contact. In addition, when the collision of equal amplitude and synchronized counter propagating waves takes place, we observe that two secondary solitary waves emerge from the interacting region. The amplitude of secondary solitary waves is proportional to the amplitude of incident waves. However, secondary solitary waves are stronger when the collision occurs at the middle contact in chains with even number of beads. Although numerical simulations correctly predict the existence of these waves, experiments show that their respective amplitude are significantly larger than predicted. We attribute this discrepancy to the rolling friction at the beads contacts during solitary wave propagation

Pyrolysis of polyethylene in the presence and absence of clay catalysts

La actividad catalítica en la pirólisis del PE de materiales arcillosos como bentonita y zeolita fue estudiada. Los resultados obtenidos muestran que estos catalizadores tienen propiedades catalíticas sufcientes para producir una disminución de la temperatura de descomposición del PE logrando mejores resultados con la zeolita. La cinética de la degradación térmica del PE fue determinada y se encontró que la energía de activación de la degradación térmica catalítica es menor que la energía de activación de la degradación térmica.Abstract: The catalytic efect of clay materials such as bentonite and zeolite in the pyrolysis of PE was studied. The results show that these catalysts have catalytic properties that produce a decrease in decomposition temperature of PE achieving beter results with the zeolite. The kinetics of thermal degradation of PE was determined and was found that the activation energy of catalytic thermal degradation is less than the activation energy for thermal degradation

Particle-Based Mesoscale Hydrodynamic Techniques

Dissipative particle dynamics (DPD) and multi-particle collision (MPC) dynamics are powerful tools to study mesoscale hydrodynamic phenomena accompanied by thermal fluctuations. To understand the advantages of these types of mesoscale simulation techniques in more detail, we propose new two methods, which are intermediate between DPD and MPC -- DPD with a multibody thermostat (DPD-MT), and MPC-Langevin dynamics (MPC-LD). The key features are applying a Langevin thermostat to the relative velocities of pairs of particles or multi-particle collisions, and whether or not to employ collision cells. The viscosity of MPC-LD is derived analytically, in very good agreement with the results of numerical simulations.Comment: 7 pages, 2 figures, 1 tabl

Coupled charge and spin dynamics in high-density ensembles of nitrogen-vacancy centers in diamond

We studied the spin depolarization of ensembles of nitrogen-vacancy (NV) centers in nitrogen-rich single crystal diamonds. We found a strong dependence of the evolution of the polarized state in the dark on the concentration of NV centers. At low excitation power, we observed a simple exponential decay profile in the low-density regime and a paradoxical inverted exponential profile in the high-density regime. At higher excitation power, we observed complex behavior, with an initial sharp rise in luminescence signal after the preparation pulse followed by a slower exponential decay. Magnetic field and excitation laser power-dependent measurements suggest that the rapid initial increase of the luminescence signal is related to recharging of the nitrogen-vacancy centers (from neutral to negatively charged) in the dark. The slow relaxing component corresponds to the longitudinal spin relaxation of the NV ensemble. The shape of the decay profile reflects the interplay between two mechanisms: the NV charge state conversion in the dark and the longitudinal spin relaxation. These mechanisms, in turn, are influenced by ionization, recharging and polarization dynamics during excitation. Interestingly, we found that charge dynamics are dominant in NV-dense samples even at very feeble excitation power. These observations may be important for the use of ensembles of NV centers in precession magnetometry and sensing applications.Comment: 7 pages, 6 figure