On the existence and stability of periodic orbits in non ideal problems: General results

In this work, motivated by non-ideal mechanical systems, we investigate the following O.D.E. ẋ = f (x) + εg (x, t) + ε2g (x, t, ε), where x ∈ Ω ⊂ ℝn, g, g are T periodic functions of t and there is a 0 ∈ Ω such that f (a 0) = 0 and f′ (a0) is a nilpotent matrix. When n = 3 and f (x) = (0, q (x 3) , 0) we get results on existence and stability of periodic orbits. We apply these results in a non ideal mechanical system: the Centrifugal Vibrator. We make a stability analysis of this dynamical system and get a characterization of the Sommerfeld Effect as a bifurcation of periodic orbits. © 2007 Birkhäuser Verlag, Basel.

Analysis of electric torque in single machine-infinite bus system using phase shifters

ResumoThe main idea of this work is based on the analysis of the electric torque through the acting of the PS in the power system, provided of a control for the compensation degree (PSC). A linear model of the single machine-infinite bus system is used with a PS installed (SMIB/PS system). The variable that represents the presence of PS in the net is associated to the phase displacement introduced in the terminal voltage of the synchronous machine by PS. For the input signals of the PSC are evaluated variations of the angular speed of the rotor, the current magnitude and the active power through the line where the PS is located. The simulations are accomplished to analyze the influence of the PS in the torque formation (synchronizing and damping), of the SMIB/PS system. The analysis are developed in the time and frequency domain.

Improving the stability conditions of TS fuzzy systems with fuzzy Lyapunov functions

In this paper, the fuzzy Lyapunov function approach is considered for stabilizing continuous-time Takagi-Sugeno fuzzy systems. Previous linear matrix inequality (LMI) stability conditions are relaxed by exploring further the properties of the time derivatives of premise membership functions and by introducing a slack LMI variable into the problem formulation. The stability results are thus used in the state feedback design which is also solved in terms of LMIs. Numerical examples illustrate the efficiency of the new stabilizing conditions presented. © 2011 IFAC.

Robust control applied to power flow control in single-phase inverter with LCL filter, using droop control and D-stability

This paper proposes a new methodology to control the power flow between a distributed generator (DG) and the electrical power distribution grid. It is used the droop voltage control to manage the active and reactive power. Through this control a sinusoidal voltage reference is generated to be tracked by voltage loop and this loop generates the current reference for the current loop. The proposed control introduces feed-forward states improving the control performance in order to obtain high quality for the current injected to the grid. The controllers were obtained through the linear matrix inequalities (LMI) using the D-stability analysis to allocate the closed-loop controller poles. Therefore, the results show quick transient response with low oscillations. Thus, this paper presents the proposed control technique, the main simulation results and a prototype with 1000VA was developed in the laboratory in order to demonstrate the feasibility of the proposed control. © 2012 IEEE.

Stability of nonlinear system using takagi-sugeno fuzzy models and hyper-rectangle of LMIs

This paper presents a theorem based on the hyper-rectangle defined by the closed set of the time derivatives of the membership functions of Takagi-Sugeno fuzzy systems. This result is also based on Linear Matrix Inequalities and allows the reduction of the conservatism of the stability analysis in the sense of Lyapunov. The theorem generalizes previous results available in the literature. © 2013 Brazilian Society for Automatics - SBA.

Semi-analytical study of the rotational motion stability of artificial satellites using quaternions

This study at aims performing the stability analysis of the rotational motion to artificial satellites using quaternions to describe the satellite attitude (orientation on the space). In the system of rotational motion equations, which is composed by four kinematic equations of the quaternions and by the three Euler equations in terms of the rotational spin components. The influence of the gravity gradient and the direct solar radiation pressure torques have been considered. Equilibrium points were obtained through numerical simulations using the softwares Matlab and Octave, which are then analyzed by the Routh-Hurwitz Stability Criterion.

Stability, viscous dissipation and local thermal non-equilibrium in fluid saturated porous media

In this thesis, the field of study related to the stability analysis of fluid saturated porous media is investigated. In particular the contribution of the viscous heating to the onset of convective instability in the flow through ducts is analysed. In order to evaluate the contribution of the viscous dissipation, different geometries, different models describing the balance equations and different boundary conditions are used. Moreover, the local thermal non-equilibrium model is used to study the evolution of the temperature differences between the fluid and the solid matrix in a thermal boundary layer problem. On studying the onset of instability, different techniques for eigenvalue problems has been used. Analytical solutions, asymptotic analyses and numerical solutions by means of original and commercial codes are carried out.

Methods for the Quantification of Motor Stability for the Assessment of Fall Risk

The research field of the Thesis is the evaluation of motor variability and the analysis of motor stability for the assessment of fall risk. Since many falls occur during walking, a better understanding of motor stability could lead to the definition of a reliable fall risk index aiming at measuring and assessing the risk of fall in the elderly, in the attempt to prevent traumatic events. Several motor variability and stability measures are proposed in the literature, but still a proper methodological characterization is lacking. Moreover, the relationship between many of these measures and fall history or fall risk is still unknown, or not completely clear. The aim of this thesis is hence to: i) analyze the influence of experimental implementation parameters on variability/stability measures and understand how variations in these parameters affect the outputs; ii) assess the relationship between variability/stability measures and long- short-term fall history. Several implementation issues have been addressed. Following the need for a methodological standardization of gait variability/stability measures, highlighted in particular for orbital stability analysis through a systematic review, general indications about implementation of orbital stability analysis have been showed, together with an analysis of the number of strides and the test-retest reliability of several variability/stability numbers. Indications about the influence of directional changes on measures have been provided. The association between measures and long/short-term fall history has also been assessed. Of all the analyzed variability/stability measures, Multiscale entropy and Recurrence quantification analysis demonstrated particularly good results in terms of reliability, applicability and association with fall history. Therefore, these measures should be taken in consideration for the definition of a fall risk index.

Morphological instability analysis of a misfit strained core-shell nanowire for the growth of quantum dots

Nell'ambito delle nanostrutture, un ruolo primario è svolto dai punti quantici. In questo lavoro siamo interessati all'analisi teorica del processo di creazione dei punti quantici: esso può avvenire per eteroepitassia, in particolare secondo il metodo studiato da Stranski-Krastanov. Un film di Germanio viene depositato su un substrato di Silicio in modo coerente, cioè senza dislocazioni, e, a causa del misfit tra le maglie dei due materiali, c'è un accumulo di energia elastica nel film. A una certa altezza critica questa energia del film può essere ridotta se il film si organizza in isole (punti quantici), dove la tensione può essere rilassata lateralmente. L'altezza critica dipende dai moduli di Young (E, υ), dal misfit tra le maglie (m) e dalla tensione superficiali (γ). Il trasporto di materiale nel film è portato avanti per diffusione superficiale. Il punto focale nell'analisi delle instabilità indotte dal misfit tra le maglie dei materiali è la ricerca delle caratteristiche che individuano il modo di crescita più rapido dei punti quantici. In questo lavoro siamo interessati ad un caso particolare: la crescita di punti quantici non su una superficie piana ma sulla superficie di un nanofilo quantico a geometria cilindrica. L'analisi delle instabilità viene condotta risolvendo le equazioni all'equilibrio: a tal fine sono state calcolate le distribuzioni del tensore delle deformazioni e degli sforzo di un nanofilo core-shell con una superficie perturbata al primo ordine rispetto all'ampiezza della perturbazione. L'analisi è stata condotta con particolari condizioni al contorno ed ipotesi geometriche, e diverse scelte dello stato di riferimento del campo degli spostamenti. Risolto il problema elastico, è stata studiata l'equazione dinamica di evoluzione descrivente la diffusione di superficie. Il risultato dell'analisi di instabilità è il tasso di crescita in funzione del numero d'onda q, con diversi valori del raggio del core, spessore dello shell e modo normale n, al fine di trovare il più veloce modo di crescita della perturbazione.

Computational study of internal and external condensing flows and experimental synthesis to investigate their attainability and stability in ground-based and space-based environments

This doctoral thesis presents the computational work and synthesis with experiments for internal (tube and channel geometries) as well as external (flow of a pure vapor over a horizontal plate) condensing flows. The computational work obtains accurate numerical simulations of the full two dimensional governing equations for steady and unsteady condensing flows in gravity/0g environments. This doctoral work investigates flow features, flow regimes, attainability issues, stability issues, and responses to boundary fluctuations for condensing flows in different flow situations. This research finds new features of unsteady solutions of condensing flows; reveals interesting differences in gravity and shear driven situations; and discovers novel boundary condition sensitivities of shear driven internal condensing flows. Synthesis of computational and experimental results presented here for gravity driven in-tube flows lays framework for the future two-phase component analysis in any thermal system. It is shown for both gravity and shear driven internal condensing flows that steady governing equations have unique solutions for given inlet pressure, given inlet vapor mass flow rate, and fixed cooling method for condensing surface. But unsteady equations of shear driven internal condensing flows can yield different “quasi-steady” solutions based on different specifications of exit pressure (equivalently exit mass flow rate) concurrent to the inlet pressure specification. This thesis presents a novel categorization of internal condensing flows based on their sensitivity to concurrently applied boundary (inlet and exit) conditions. The computational investigations of an external shear driven flow of vapor condensing over a horizontal plate show limits of applicability of the analytical solution. Simulations for this external condensing flow discuss its stability issues and throw light on flow regime transitions because of ever-present bottom wall vibrations. It is identified that laminar to turbulent transition for these flows can get affected by ever present bottom wall vibrations. Detailed investigations of dynamic stability analysis of this shear driven external condensing flow result in the introduction of a new variable, which characterizes the ratio of strength of the underlying stabilizing attractor to that of destabilizing vibrations. Besides development of CFD tools and computational algorithms, direct application of research done for this thesis is in effective prediction and design of two-phase components in thermal systems used in different applications. Some of the important internal condensing flow results about sensitivities to boundary fluctuations are also expected to be applicable to flow boiling phenomenon. Novel flow sensitivities discovered through this research, if employed effectively after system level analysis, will result in the development of better control strategies in ground and space based two-phase thermal systems.

A class of exact Navier-Stokes solutions for homogeneous flat-plate boundary layers and their linear stability

We introduce a new boundary layer formalism on the basis of which a class of exact solutions to the Navier–Stokes equations is derived. These solutions describe laminar boundary layer flows past a flat plate under the assumption of one homogeneous direction, such as the classical swept Hiemenz boundary layer (SHBL), the asymptotic suction boundary layer (ASBL) and the oblique impingement boundary layer. The linear stability of these new solutions is investigated, uncovering new results for the SHBL and the ASBL. Previously, each of these flows had been described with its own formalism and coordinate system, such that the solutions could not be transformed into each other. Using a new compound formalism, we are able to show that the ASBL is the physical limit of the SHBL with wall suction when the chordwise velocity component vanishes while the homogeneous sweep velocity is maintained. A corresponding non-dimensionalization is proposed, which allows conversion of the new Reynolds number definition to the classical ones. Linear stability analysis for the new class of solutions reveals a compound neutral surface which contains the classical neutral curves of the SHBL and the ASBL. It is shown that the linearly most unstable Görtler–Hämmerlin modes of the SHBL smoothly transform into Tollmien–Schlichting modes as the chordwise velocity vanishes. These results are useful for transition prediction of the attachment-line instability, especially concerning the use of suction to stabilize boundary layers of swept-wing aircraft.

Stability and potential application of spliced nuclear pre -mRNA introns

A major portion of this thesis work was dedicated to study the nature and significance of spliced introns. The initial work was focused on studying the IVS1$\sb{\rm C\beta 1}$ intron from a T-cell receptor (TCR)-$\beta$ gene. Compared to an intron lariat control from adenovirus pre-mRNA that was spliced in vitro, IVS1$\sb{\rm C\beta 1}$ was debranched less efficiently by HeLa S100 extracts, although IVS1$\sb{\rm C\beta 1}$ also used the consensus branchpoint in vivo. Subcellular-fractionation analysis showed that most IVS1$\sb{\rm C\beta 1}$ lariats cofractionated with pre-mRNA in the nucleus, consistent with the possibility that intron degradation releases splicing factors which will be available for further rounds of splicing. The half-life of IVS1$\sb{\rm C\beta 1}$ from the endogenous TCR-$\beta$ gene was measured using the general transcription inhibitor actinomycin D to be about $\sim$15 min, which was similar to that of unstable mRNAs such as c-myc mRNA.^ The general transcription inhibitor DRB was also used for intron stability analysis. Unexpectedly, DRB decreased intron and pre-mRNA levels only initially, it later increased the levels of intron-containing RNAs. Inhibition of transcription initiation appeared to be the major early effect (the reduction phase); whereas enhanced premature transcription termination was dominant later (the induction phase).^ Having established the procedures for studying in vivo spliced introns, this approach was applied to study the mechanism of nonsense-mediated downregulation (NMD), a phenomena in which premature termination codons (PTCs) decrease the levels of mRNAs. In this study, the novel intron-oriented approach was applied to study the mechanism of NMD. The levels of spliced introns immediately upstream and downstream of a PTC-bearing exon in a TCR-$\beta$ gene were identified and analyzed along with their pre-mRNA. Although PTC reduced the mRNA levels by 4 to 9 fold, the steady-state levels of spliced introns and the pre-mRNA-to-intron ratios were not significantly altered, indicating that the PTC did not significantly inhibit TCR-$\beta$ RNA splicing. Consistent with this conclusion, the half-lives of the PTC$\sp+$ and PTC$\sp-$ pre-mRNA were similar. The protein synthesis inhibitor cyclohexmide (CHX) upregulated the levels of the PTC$\sp+$ mRNA over 10 fold without affecting the levels of the spliced introns, suggesting that the reversal effect of CHX was through stabilization, not production. These results indicated that inhibition of splicing could not be the major mechanism for the NMD pathway of the TCR-$\beta$ gene, instead, suggesting that mRNA destabilization may be more important. (Abstract shortened by UMI.) ^

Slope stability analyses based on sediment cores of the Ligurian Margin, Southern France

Submarine slope failures of various types and sizes are common along the tectonic and seismically active Ligurian margin, northwestern Mediterranean Sea, primarily because of seismicity up to ~M6, rapid sediment deposition in the Var fluvial system, and steepness of the continental slope (average 11°). We present geophysical, sedimentological and geotechnical results of two distinct slides in water depth >1,500 m: one located on the flank of the Upper Var Valley called Western Slide (WS), another located at the base of continental slope called Eastern Slide (ES). WS is a superficial slide characterized by a slope angle of ~4.6° and shallow scar (~30 m) whereas ES is a deep-seated slide with a lower slope angle (~3°) and deep scar (~100 m). Both areas mainly comprise clayey silt with intermediate plasticity, low water content (30-75 %) and underconsolidation to strong overconsolidation. Upslope undeformed sediments have low undrained shear strength (0-20 kPa) increasing gradually with depth, whereas an abrupt increase in strength up to 200 kPa occurs at a depth of ~3.6 m in the headwall of WS and ~1.0 m in the headwall of ES. These boundaries are interpreted as earlier failure planes that have been covered by hemipelagite or talus from upslope after landslide emplacement. Infinite slope stability analyses indicate both sites are stable under static conditions; however, slope failure may occur in undrained earthquake condition. Peak earthquake acceleration from 0.09 g on WS and 0.12 g on ES, i.e. M5-5.3 earthquakes on the spot, would be required to induce slope instability. Different failure styles include rapid sedimentation on steep canyon flanks with undercutting causing superficial slides in the west and an earthquake on the adjacent Marcel fault to trigger a deep-seated slide in the east.

Effect of Aspect Ratio on the Three-Dimensional Global Instability Analysis of Incompressible Open Cavity Flows

The stability analysis of open cavity flows is a problem of great interest in the aeronautical industry. This type of flow can appear, for example, in landing gears or auxiliary power unit configurations. Open cavity flows is very sensitive to any change in the configuration, either physical (incoming boundary layer, Reynolds or Mach numbers) or geometrical (length to depth and length to width ratio). In this work, we have focused on the effect of geometry and of the Reynolds number on the stability properties of a threedimensional spanwise periodic cavity flow in the incompressible limit. To that end, BiGlobal analysis is used to investigate the instabilities in this configuration. The basic flow is obtained by the numerical integration of the Navier-Stokes equations with laminar boundary layers imposed upstream. The 3D perturbation, assumed to be periodic in the spanwise direction, is obtained as the solution of the global eigenvalue problem. A parametric study has been performed, analyzing the stability of the flow under variation of the Reynolds number, the L/D ratio of the cavity, and the spanwise wavenumber β. For consistency, multidomain high order numerical schemes have been used in all the computations, either basic flow or eigenvalue problems. The results allow to define the neutral curves in the range of L/D = 1 to L/D = 3. A scaling relating the frequency of the eigenmodes and the length to depth ratio is provided, based on the analysis results.