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

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

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

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

La Curva en S como Herramienta para la Medición de los Ciclos de Vida de Productos

The aim of this article was to carry out a study of the life cycles of three products of Colombian companies; based on a logistic model of population growth as a life cycles measurement tool. We found that the products life cycles have a similar behavior to the population growth, according to an S curve. The inflection points of the curves were obtained by a nonlinear regression. These points might be used as a tool for strategic decision making in products, in terms of identifying key instants for launching technological innovations, investments and execute marketing strategies

Analysis of al-2 Mutations in Neurospora

The orange pigmentation of the fungus Neurospora crassa is due to the accumulation of the xanthophyll neurosporaxanthin and precursor carotenoids. Two key reactions in the synthesis of these pigments, the formation of phytoene from geranylgeranyl pyrophosphate and the introduction of β cycles in desaturated carotenoid products, are catalyzed by two domains of a bifunctional protein, encoded by the gene al-2. We have determined the sequence of nine al-2 mutant alleles and analyzed the carotenoid content in the corresponding strains. One of the mutants is reddish and it is mutated in the cyclase domain of the protein, and the remaining eight mutants are albino and harbor different mutations on the phytoene synthase (PS) domain. Some of the mutations are expected to produce truncated polypeptides. A strain lacking most of the PS domain contained trace amounts of a carotenoid-like pigment, tentatively identified as the squalene desaturation product diapolycopene. In support, trace amounts of this compound were also found in a knock-out mutant for gene al-2, but not in that for gene al-1, coding for the carotene desaturase. The cyclase activity of the AL-2 enzyme from two albino mutants was investigated by heterologous expression in an appropriately engineered E. coli strain. One of the AL-2 enzymes, predictably with only 20% of the PS domain, showed full cyclase activity, suggesting functional independence of both domains. However, the second mutant showed no cyclase activity, indicating that some alterations in the phytoene synthase segment affect the cyclase domain. Expression experiments showed a diminished photoinduction of al-2 transcripts in the al-2 mutants compared to the wild type strain, suggesting a synergic effect between reduced expression and impaired enzymatic activities in the generation of their albino phenotypes