Hexagons and spiral defect chaos in non-Boussinesq convection at low Prandtl numbers

We study the stability and dynamics of non-Boussinesq convection in pure gases ?CO2 and SF6? with Prandtl numbers near Pr? 1 and in a H2-Xe mixture with Pr= 0.17. Focusing on the strongly nonlinear regime we employ Galerkin stability analyses and direct numerical simulations of the Navier-Stokes equations. For Pr ? 1 and intermediate non-Boussinesq effects we find reentrance of stable hexagons as the Rayleigh number is increased. For stronger non-Boussinesq effects the usual, transverse side-band instability is superseded by a longitudinal side-band instability. Moreover, the hexagons do not exhibit any amplitude instability to rolls. Seemingly, this result contradicts the experimentally observed transition from hexagons to rolls. We resolve this discrepancy by including the effect of the lateral walls. Non-Boussinesq effects modify the spiral defect chaos observed for larger Rayleigh numbers. For convection in SF6 we find that non-Boussinesq effects strongly increase the number of small, compact convection cells and with it enhance the cellular character of the patterns. In H2-Xe, closer to threshold, we find instead an enhanced tendency toward roll-like structures. In both cases the number of spirals and of targetlike components is reduced. We quantify these effects using recently developed diagnostics of the geometric properties of the patterns.

Reentrant hexagons in non-Boussinesq convection.

While non-Boussinesq hexagonal convection patterns are known to be stable close to threshold (i.e. for Rayleigh numbers R ? Rc ), it has often been assumed that they are always unstable to rolls for slightly higher Rayleigh numbers. Using the incompressible Navier?Stokes equations for parameters corresponding to water as the working fluid, we perform full numerical stability analyses of hexagons in the strongly nonlinear regime ( ? (R ? Rc )/Rc = O(1)). We find ?re-entrant? behaviour of the hexagons, i.e. as is increased they can lose and regain stability. This can occur for values of as low as = 0.2. We identify two factors contributing to the re-entrance: (i) far above threshold there exists a hexagon attractor even in Boussinesq convection as has been shown recently and (ii) the non-Boussinesq effects increase with . Using direct simulations for circular containers we show that the re-entrant hexagons can prevail even for sidewall conditions that favour convection in the form of competing stable rolls. For sufficiently strong non-Boussinesq effects hexagons even become stable over the whole -range considered, 0 6 6 1.5.

Variable structure control with chattering elimination and guaranteed stability for a generalized T-S model

In this paper, a fuzzy based Variable Structure Control (VSC) with guaranteed stability is presented. The main objective is to obtain an improved performance of highly non-linear unstable systems. The main contribution of this work is that, firstly, new functions for chattering reduction and error convergence without sacrificing invariant properties are proposed, which is considered the main drawback of the VSC control. Secondly, the global stability of the controlled system is guaranteed.The well known weighting parameters approach, is used in this paper to optimize local and global approximation and modeling capability of T-S fuzzy model.A one link robot is chosen as a nonlinear unstable system to evaluate the robustness, effectiveness and remarkable performance of optimization approach and the high accuracy obtained in approximating nonlinear systems in comparison with the original T-S model. Simulation results indicate the potential and generality of the algorithm. The application of the proposed FLC-VSC shows that both alleviation of chattering and robust performance are achieved with the proposed FLC-VSC controller. The effectiveness of the proposed controller is proven in front of disturbances and noise effects.

Stability and mechanical evaluation of bovine pericardium cross-linked with polyurethane prepolymer in aqueous medium

The present study investigates the potential use of non-catalyzed water-soluble blocked polyurethane prepolymer (PUP) as a bifunctional cross-linker for collagenous scaffolds. The effect of concentration (5, 10, 15 and 20%), time (4, 6, 12 and 24 h), medium volume (50, 100, 200 and 300%) and pH (7.4, 8.2, 9 and 10) over stability, microstructure and tensile mechanical behavior of acellular pericardial matrix was studied. The cross-linking index increased up to 81% while the denaturation temperature increased up to 12 °C after PUP crosslinking. PUP-treated scaffold resisted the collagenase degradation (0.167 ± 0.14 mmol/g of liberated amine groups vs. 598 ± 60 mmol/g for non-cross-linked matrix). The collagen fiber network was coated with PUP while viscoelastic properties were altered after cross-linking. The treatment of the pericardial scaffold with PUP allows (i) different densities of cross-linking depending of the process parameters and (ii) tensile properties similar to glutaraldehyde method.

Long wave theory for experimental devices with compressed/expanded surfactant monolayers

Surfactant monolayers are of interest in a variety of phenomena, including thin film dynamics and the formation and dynamics of foams. Measurement of surface properties has received a continuous attention and requires good theoretical models to extract the relevant physico- chemical information from experimental data. A common experimental set up consists in a shallow liquid layer whose free surface is slowly com- pressed/expanded in periodic fashion by moving two slightly immersed solid barriers, which varies the free surface area and thus the surfactant concentration. The simplest theory ignores the fluid dynamics in the bulk fluid, assuming spatially uniform surfactant concentration, which requires quite small forcing frequencies and provides reversible dynamics in the compression/expansion cycles. Sometimes, it is not clear whether depar- ture from reversibility is due to non-equilibrium effects or to the ignored fluid dynamics. Here we present a long wave theory that takes the fluid dynamics and the symmetries of the problem into account. In particular, the validity of the spatially-uniform-surfactant-concentration assumption is established and a nonlinear diffusion equation is derived. This allows for calculating spatially nonuniform monolayer dynamics and uncovering the physical mechanisms involved in the surfactant behavior. Also, this analysis can be considered a good means for extracting more relevant information from each experimental run.

Discontinuous solutions and boundary value problems for non-linearly elastic fibre-reinforced materials

En este trabajo se han analizado varios problemas en el contexto de la elasticidad no lineal basándose en modelos constitutivos representativos. En particular, se han analizado problemas relacionados con el fenómeno de perdida de estabilidad asociada con condiciones de contorno en el caso de material reforzados con fibras. Cada problema se ha formulado y se ha analizado por separado en diferentes capítulos. En primer lugar se ha mostrado el análisis del gradiente de deformación discontinuo para un material transversalmente isótropo, en particular, el modelo del material considerado consiste de una base neo-Hookeana isótropa incrustada con fibras de refuerzo direccional caracterizadas con un solo parámetro. La solución de este problema se vincula con instabilidades que dan lugar al mecanismo de fallo conocido como banda de cortante. La perdida de elipticidad de las ecuaciones diferenciales de equilibrio es una condición necesaria para que aparezca este tipo de soluciones y por tanto las inestabilidades asociadas. En segundo lugar se ha analizado una deformación combinada de extensión, inación y torsión de un tubo cilíndrico grueso donde se ha encontrado que la deformación citada anteriormente puede ser controlada solo para determinadas direcciones de las fibras refuerzo. Para entender el comportamiento elástico del tubo considerado se ha ilustrado numéricamente los resultados obtenidos para las direcciones admisibles de las fibras de refuerzo bajo la deformación considerada. En tercer lugar se ha estudiado el caso de un tubo cilíndrico grueso reforzado con dos familias de fibras sometido a cortante en la dirección azimutal para un modelo de refuerzo especial. En este problema se ha encontrado que las inestabilidades que aparecen en el material considerado están asociadas con lo que se llama soluciones múltiples de la ecuación diferencial de equilibrio. Se ha encontrado que el fenómeno de instabilidad ocurre en un estado de deformación previo al estado de deformación donde se pierde la elipticidad de la ecuación diferencial de equilibrio. También se ha demostrado que la condición de perdida de elipticidad y ^W=2 = 0 (la segunda derivada de la función de energía con respecto a la deformación) son dos condiciones necesarias para la existencia de soluciones múltiples. Finalmente, se ha analizado detalladamente en el contexto de elipticidad un problema de un tubo cilíndrico grueso sometido a una deformación combinada en las direcciones helicoidal, axial y radial para distintas geotermias de las fibras de refuerzo . In the present work four main problems have been addressed within the framework of non-linear elasticity based on representative constitutive models. Namely, problems related to the loss of stability phenomena associated with boundary value problems for fibre-reinforced materials. Each of the considered problems is formulated and analysed separately in different chapters. We first start with the analysis of discontinuous deformation gradients for a transversely isotropic material under plane deformation. In particular, the material model is an augmented neo-Hookean base with a simple unidirectional reinforcement characterised by a single parameter. The solution of this problem is related to material instabilities and it is associated with a shear band-type failure mode. The loss of ellipticity of the governing differential equations is a necessary condition for the existence of these material instabilities. The second problem involves a detailed analysis of the combined non-linear extension, inflation and torsion of a thick-walled circular cylindrical tube where it has been found that the aforementioned deformation is controllable only for certain preferred directions of transverse isotropy. Numerical results have been illustrated to understand the elastic behaviour of the tube for the admissible preferred directions under the considered deformation. The third problem deals with the analysis of a doubly fibre-reinforced thickwalled circular cylindrical tube undergoing pure azimuthal shear for a special class of the reinforcing model where multiple non-smooth solutions emerge. The associated instability phenomena are found to occur prior to the point where the nominal stress tensor changes monotonicity in a particular direction. It has been also shown that the loss of ellipticity condition that arises from the equilibrium equation and ^W=2 = 0 (the second derivative of the strain-energy function with respect to the deformation) are equivalent necessary conditions for the emergence of multiple solutions for the considered material. Finally, a detailed analysis in the basis of the loss of ellipticity of the governing differential equations for a combined helical, axial and radial elastic deformations of a fibre-reinforced circular cylindrical tube is carried out.

Asymptotic stability of a mathematical model of cell population

We consider a simplified system of a growing colony of cells described as a free boundary problem. The system consists of two hyperbolic equations of first order coupled to an ODE to describe the behavior of the boundary. The system for cell populations includes non-local terms of integral type in the coefficients. By introducing a comparison with solutions of an ODE's system, we show that there exists a unique homogeneous steady state which is globally asymptotically stable for a range of parameters under the assumption of radially symmetric initial data.

On a parabolic-elliptic chemotactic system with non-constant chemotactic sensitivity

We study a parabolic–elliptic chemotactic system describing the evolution of a population’s density “u” and a chemoattractant’s concentration “v”. The system considers a non-constant chemotactic sensitivity given by “χ(N−u)”, for N≥0, and a source term of logistic type “λu(1−u)”. The existence of global bounded classical solutions is proved for any χ>0, N≥0 and λ≥0. By using a comparison argument we analyze the stability of the constant steady state u=1, v=1, for a range of parameters. – For N>1 and Nλ>2χ, any positive and bounded solution converges to the steady state. – For N≤1 the steady state is locally asymptotically stable and for χN<λ, the steady state is globally asymptotically stable.

Axisymmetric long liquid bridges stability and resonances

In this paper mathematical expressions for minimum-volume stability limits and resonance frequencies of axisymmetric long liquid bridges are presented. These expressions are valid for a wide range of liquid bridge configurations, accounting for ef-fects like unequal disks and axial microgravity in the case of minimum-volume stability limits,and unequal disks, axial microgravity,non-zero viscosity and liquid bridge volume different from the cylindrical one in the case of resonance frequencies.

Dynamic stability of long axisymmetric liquid bridges

This paper deals with the non-linear forced oscillations of axisymmetric long liquid bridges between equal disks. The dynamics of the liquid bridge has been analyzed by using a self-similar, one-dimensional model already used in similar problems. The influence of the dynamics on the static stability limits, as well as the main characteristics of the non-linear behaviour of long liquid bridges, have been studied with in the range of validity of the mathematical model used here.

Experimental and numerical assessment of the aeroelastic stability of blade pair packages

The stabilizing effect of grouping rotor blades in pairs has been assessed both, numerically and experimentally. The bending and torsion modes of a low aspect ratio high speed turbine cascade tested in the non-rotating test facility at EPFL (Ecole Polytechnique Fédérale de Lausanne) have been chosen as the case study. The controlled vibration of 20 blades in travelling wave form was performed by means of an electromagnetic excitation system, enabling the adjustement of the vibration amplitude and inter blade phase at a given frequency. Unsteady pressure transducers located along the blade mid-section were used to obtain the modulus and phase of the unsteady pressure caused by the airfoil motion. The stabilizing effect of the torsion mode was clearly observed both in the experiments and the simulations, however the effect of grouping the blades in pairs in the minimum damping at the tested frequency was marginal in the bending mode. A numerical tool was validated using the available experimental data and then used to extend the results at lower and more relevant reduced frequencies. It is shown that the stabilizing effect exists for the bending and torsion modes in the frequency range typical of low-pressure turbines. It is concluded that the stabilizing effect of this configuration is due to the shielding effect of the pressure side of the airfoil that defines the passage of the pair on the suction side of the same passage, since the relative motion between both is null. This effect is observed both in the experiments and simulations.

Stability of nonrelativistic quantum mechanical matter coupled to the (ultraviolet cutoff) radiation field

We announce a proof of H-stability for the quantized radiation field, with ultraviolet cutoff, coupled to arbitrarily many non-relativistic quantized electrons and static nuclei. Our result holds for arbitrary atomic numbers and fine structure constant. We also announce bounds for the energy of many electrons and nuclei in a classical vector potential and for the eigenvalue sum of a one-electron Pauli Hamiltonian with magnetic field.

Targeted disruption of the surfactant protein B gene disrupts surfactant homeostasis, causing respiratory failure in newborn mice.

Surfactant protein B (SP-B) is an 8.7-kDa, hydrophobic protein that enhances the spreading and stability of surfactant phospholipids in the alveolus. To further assess the role of SP-B in lung function, the SP-B gene was disrupted by homologous recombination in murine mouse embryonic stem cells. Mice with a single mutated SP-B allele (+/-) were unaffected, whereas homozygous SP-B -/- offspring died of respiratory failure immediately after birth. Lungs of SP-B -/- mice developed normally but remained atelectatic in spite of postnatal respiratory efforts. SP-B protein and mRNA were undetectable and tubular myelin figures were lacking in SP-B -/- mice. Type II cells of SP-B -/- mice contained no fully formed lamellar bodies. While the abundance of SP-A and SP-C mRNAs was not altered, an aberrant form of pro-SP-C, 8.5 kDa, was detected, and fully processed SP-C peptide was markedly decreased in lung homogenates of SP-B -/- mice. Ablation of the SP-B gene disrupts the routing, storage, and function of surfactant phospholipids and proteins, causing respiratory failure at birth.

Síntese, caracterização e modificação de superfícies de sílicas mesoporosas ordenadas para captura de CO2

Processos como a purificação do metano (CH4) e a produção de hidrogênio gasoso (H2) envolvem etapas de separação de CO2. Atualmente, etanolaminas como monoetanolamina (MEA), dietanolamina (DEA), metildietanolamina (MDEA) e trietanolamina (TEA) são as substâncias mais utilizadas no processo de separação/captura de CO2 em processos industriais. Entretanto, o uso destas substâncias apresenta alguns inconvenientes devido à alta volatilidade, dificuldade de se trabalhar com material líquido, também ao alto gasto energético envolvido das etapas de regeneração e à baixa estabilidade térmica e química. Com base nessa problemática, esse trabalho teve por objetivo a síntese de um tipo de sílica mesoporosa altamente ordenada (SBA-15) de modo a utilizá-la no processo de captura de CO2. O trabalho foi dividido em quatro etapas experimentais que envolveram a síntese da SBA-15, o estudo do comportamento térmico de algumas etanolaminas livres, síntese e caracterização de materiais adsorventes preparados a partir de incorporação de etanolaminas à SBA-15 e estudo da eficiência de captura de CO2 por esses materiais. Novas alternativas de síntese da SBA-15 foram estudadas neste trabalho, visando aperfeiçoar as propriedades texturais do material produzido. Tais alternativas são baseadas na remoção do surfatante, utilizado como molde na síntese da sílica mesoporosa, por meio da extração por Soxhlet, utilizando diferentes solventes. O processo contribuiu para melhorar as propriedades do material obtido, evitando o encolhimento da estrutura que pode ser ocasionado durante a etapa de calcinação. Por meio de técnicas como TG/DTG, DSC, FTIR e Análise Elementar de C, H e N foi realizada a caracterização físico-química e termoanalítica da MEA, DEA, MDEA e TEA, visando melhor conhecer as características destas substâncias. Estudos cinéticos baseados nos métodos termogravimétricos isotérmicos e não isotérmicos (Método de Ozawa) foram realizados, permitindo a determinação de parâmetros cinéticos envolvidos nas etapas de volatilização/decomposição térmica das etanolaminas. Além das técnicas acima mencionadas, MEV, MET, SAXS e Medidas de Adsorção de N2 foram utilizadas na caraterização da SBA-15 antes e após a incorporação das etanolaminas. Dentre as etanolaminas estudadas, a TEA apresentou maior estabilidade térmica, entretanto, devido ao seu maior impedimento estérico, é a etanolamina que apresenta menor afinidade com o CO2. Diferentemente das demais etanolaminas estudadas, a decomposição térmica da DEA envolve uma reação intramolecular, levando a formação de MEA e óxido de etileno. A incorporação destes materiais à SBA-15 aumentou a estabilidade térmica das etanolaminas, uma vez que parte do material permanece dentro dos poros da sílica. Os ensaios de adsorção de CO2 mostraram que a incorporação da MEA à SBA-15 catalisou o processo de decomposição térmica da mesma. A MDEA foi a etanolamina que apresentou maior poder de captura de CO2 e sua estabilidade térmica foi consideravelmente aumentada quando a mesma foi incorporada à SBA-15, aumentando também seu potencial de captura de CO2.

On the stability of Voronoi cells

Let T be a given subset of ℝ n , whose elements are called sites, and let s∈T. The Voronoi cell of s with respect to T consists of all points closer to s than to any other site. In many real applications, the position of some elements of T is uncertain due to either random external causes or to measurement errors. In this paper we analyze the effect on the Voronoi cell of small changes in s or in a given non-empty set P⊂T\{s}. Two types of perturbations of P are considered, one of them not increasing the cardinality of T. More in detail, the paper provides conditions for the corresponding Voronoi cell mappings to be closed, lower and upper semicontinuous. All the involved conditions are expressed in terms of the data.