Stability of zonal regimes in a truncated model of forced atmospheric flow

Summary The stability properties of zonal circulations induced by external forcing in a rotating atmosphere are investigated making use of a truncated model of the barotropic vorticity equation for forced, dissipative non-divergent flow in spherical geometry. Sufficient conditions for global and local asymptotic stability are found as a function of the dissipation time-scale, the coefficients of non-linear interaction between zonal flow and wave components, and the absolute rotation speed of the atmosphere. For weak, axisymmetric forcing fields the corresponding forced zonal circulation is a global attractor for states belonging to the configuration space of the model, while for larger forcing intensities it is only locally attracting, the extension of the basin of attraction being an increasing function of the absolute angular velocity of the atmosphere.

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Sommario Si analizzano le proprietà di stabilità di circolazioni zonali forzate in una atmosfera rotante facendo uso di un modello troncato a pochi modi dell'equazione di vorticità barotropica per flussi dissipativi in geometria sferica. Si determinano condizioni sufficienti per la stabilità asintotica sia locale che globale in funzione delle scale di tempo dissipative e di interazione nonlineare.

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This research was partly supported by C.N.R. through G.N.F.M.     

Over-reflection of travelling internal waves in a rotating stratified fluid

Summary It has been known for many years that waves of different kind propagating in a fluid and incident on a mean flow localized shear layer can exhibit, in the linear theory, a reflection coefficient larger than unity. When this phenomenon takes place the wave is said to be over-reflected at the shear layer. In this paper the over-reflection of inertial-gravity waves in a stratified rotating fluid in horizontal sheared motion is studied by making use of the constancy of the net vertical energy flux associated with the wave field. It is found that over-reflection can take place if some physical conditions, explicitly evaluated, are locally satisfied in the fluid. Such conditions are discussed and a comparison is carried out with the same phenomenon in a nonrotating system.

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Riassunto Si sa da molti anni che la teoria lineare di onde di diversa natura, propagantesi in un fluido ed interagenti con uno strato localizzato di shear, prevede, in alcuni casi, un coefficiente di riflessione maggiore dell'unità. Questo fenomeno prende il nome di super riflessione. In questo articolo si studia la super riflessione delle onde gravito-inerziali in un fluido stratificato in moto orizzontale con la velocità dipendente dalla sola coordinata verticale. Lo studio è portato a termine servendosi della condizione di continuità e costanza del flusso netto verticale di energia associata al campo d'onda. Si trova che la super riflessione avviene se sono soddisfatte alcune condizioni fisiche che sono esplicitamente determinate: tali condizioni sono inoltre discusse in dettaglio ed i risultati sono confrontati con quelli, classici, relativi alla propagazione di onde interne nei fluidi stratificati in assenza di rotazione.

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Резюме В течение многих лет известно, что линейная теория волн различной природы, которые распространяются в жидкости и взаимодействуют с локализованным пограничным слоем, предсказывает, что в некоторых случаях коэффициенты отражения могут превьщать единицу. Зто явление носит название супер-отражения (сверх-отражение) на пограничном слое. В этой статье исследуется супер-отражение инерциальной гравитационной волны в стратифицированной вращающейся жидкости в случаэ горизонтального движения со скоростью, зависящей только от вертикальной координаты. При рассмотрении учитывается постоянство результирующей вертикальной энергии, связанной с полем волны. Получено, что сверх-отражение может иметь место, если локально в жидкости выполняются некоторые физические условия. Проводится обсуждение этих условий и полученные результаты сравниваются с классическими результатами по распространению внутренних волн в стратифицированной жидкости в отсутствии вращения.

     

Atomic-resolution electron energy loss spectroscopy imaging in aberration corrected scanning transmission electron microscopy

The "delocalization" of inelastic scattering is an important issue for the ultimate spatial resolution of innershell spectroscopy in the electron microscope. It is demonstrated in a nonlocal model for electron energy loss spectroscopy (EELS) that delocalization of scanning transmission electron microscopy (STEM) images for single, isolated atoms is primarily determined by the width of the probe, even for light atoms. We present experimental data and theoretical simulations for Ti L-shell EELS in a [100] SrTiO3 crystal showing that, in this case, delocalization is not significantly increased by dynamical propagation. Issues relating to the use of aberration correctors in the STEM geometry are discussed.     

Steering in computational science: Mesoscale modelling and simulation

This paper outlines the benefits of computational steering for high performance computing applications. Lattice-Boltzmann mesoscale fluid simulations of binary and ternary amphiphilic fluids in two and three dimensions are used to illustrate the substantial improvements which computational steering offers in terms of resource efficiency and time to discover new physics. We discuss details of our current steering implementations and describe their future outlook with the advent of computational grids.     

First integrals and analytical solutions of the nonlinear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient

Fin materials can be observed in a variety of engineering applications. They are used to ease the dissipation of heat from a heated wall to the surrounding environment. In this work, we consider a nonlinear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient. The equation(s) under study are highly nonlinear. Both the thermal conductivity and the heat transfer coefficient are given as arbitrary functions of temperature. Firstly, we consider the Lie group analysis for different cases of thermal conductivity and the heat transfer coefficients. These classifications are obtained from the Lie group analysis. Then, the first integrals of the nonlinear straight fin problem are constructed by three methods, namely, Noether’s classical method, partial Noether approach and Ibragimov’s nonlocal conservation method. Some exact analytical solutions are also constructed. The obtained result is also compared with the result obtained by other methods.     

Stability of axisymmetric motions in a rotating inviscid atmosphere

Summary We study the set of ordinary differential equations representing the truncation of the spectral vorticity equation in spherical geometry for two-dimensional, non divergent motions in a homogeneous, inviscid rotating atmosphere. The set of included spectral components represent an arbitrary axisymmetric field of motion (zonal flow) interacting with a couple of non zonal, wave-like perturbations. We analize the stability of the equilibrium configuration described by purely zonal flow, by an esplicit representation of the linear and non-linear parameters which characterize the unstable oscillations induced by perturbations of the equilibrium.

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Sommario Si studiano le soluzioni di un sistema di equazioni differenziali ordinarie che rappresentano il troncamento a poche componenti di Fourier dell'equazione di conservazione della vorticità per moti bidimensionali, non divergenti in una atmosfera rotante, inviscida e omogenea. Tale troncamento include tutte le componenti spettrali che rappresentano flussi a simmetria assiale (moti zonali) in interazione non lineare con una coppia di componenti asimmetriche che rappresentano flussi ondulatori. Si studia la stabilità della configurazione di equilibrio caratterizzata da moto zonale stazionario, analizzando i parametri lineari e non lineari che descrivono le oscillazioni instabili di ampiezza finita del campo di flusso che nascono da condizioni iniziali nell'intorno dell'equilibrio.

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This work was supported by the C.N.R. through the Gruppo Nazionale per la Fisica Matematica.     

Spatial resolution and information transfer in scanning transmission electron microscopy

The relation between image resolution and information transfer is explored. It is shown that the existence of higher frequency transfer in the image is just a necessary but not sufficient condition for the achievement of higher resolution. Adopting a two-point resolution criterion, we suggest that a 10% contrast level between two features in an image should be used as a practical definition of resolution. In the context of scanning transmission electron microscopy, it is shown that the channeling effect does not have a direct connection with image resolution because sharp channeling peaks do not move with the scanning probe. Through a quantitative comparison between experimental image and simulation, a Fourier-space approach is proposed to estimate defocus and sample thickness. The effective atom size in Z-contrast imaging depends on the annular detector's inner angle. Therefore, an optimum angle exists for the highest resolution as a trade-off between reduced atom size and reduced signal with limited information transfer due to noise.     

On regularity of block triangular fuzzy matrices

Necessary and sufficient conditions are given for the regularity of block triangular fuzzy matrices. This leads to characterization of idempotency of a class of triangular Toeplitz matrices. As an application, the existence of group inverse of a block triangular fuzzy matrix is discussed. Equivalent conditions for a regular block triangular fuzzy matrix to be expressed as a sum of regular block fuzzy matrices is derived. Further, fuzzy relational equations consistency is studied.     

Probabilistic Inductive Classes of Graphs

A unifying framework—probabilistic inductive classes of graphs (PICGs)—is defined by imposing a probability space on the rules and their left elements from the standard notion of inductive class of graphs. The rules can model the processes creating real-world social networks, such as spread of knowledge, dynamics of acquaintanceships or sexual contacts, and emergence of clusters. We demonstrate the characteristics of PICGs by casting some well-known models of growing networks in this framework. Results regarding expected size and order are derived. For PICG models of connected and 2-connected graphs order, size and asymptotic degree distribution are presented. The approaches used represent analytic alternative to computer simulation, which is mostly used to obtain the properties of evolving graphs.     

Spectroscopic imaging of single atoms within a bulk solid

The ability to localize, identify, and measure the electronic environment of individual atoms will provide fundamental insights into many issues in materials science, physics, and nanotechnology. We demonstrate, using an aberration-corrected scanning transmission electron microscope, the spectroscopic imaging of single La atoms inside CaTiO3. Dynamical simulations confirm that the spectroscopic information is spatially confined around the scattering atom. Furthermore, we show how the depth of the atom within the crystal may be estimated.