Oscillation of forced impulsive differential equations with pp-Laplacian and nonlinearities given by Riemann-Stieltjes integrals

In this article, we study the oscillation of second order forced impulsive differential equation with $p$-Laplacian and nonlinearities given by Riemann-Stieltjes integrals of the form \begin{equation*} \left( p(t)\phi _{\gamma }\left( x^{\prime }(t)\right) \right) ^{\prime}+q_{0}\left( t\right) \phi _{\gamma }\left( x(t)\right)+\int_{0}^{b}q\left( t,s\right) \phi _{\alpha \left( s\right) }\left(x(t)\right) d\zeta \left(s\right) =e(t), t\neq \tau _{k}, \end{equation*} with impulsive conditions \begin{equation*} x\left( \tau _{k}^{+}\right) =\lambda _{k}~x\left( t_{k}\right), x^{\prime }\left( \tau _{k}^{+}\right) =\eta _{k}~x^{\prime }\left( \tau_{k}\right), \end{equation*} where \phi _{\gamma }\left( u\right) :=\left\vert u\right\vert ^{\gamma } \mbox{{\rm sgn}\,}u, $\gamma, b\in \left( 0,\infty \right),$ $\alpha \in C\left[ 0,b\right)$ is strictly increasing such that $0\leq \alpha \left( 0\right) <\gamma <\alpha \left( b-\right)$, and $\left\{ \tau_{k}\right\}_{k\in {\mathbb{N}}}$ is the the impulsive moments sequence. Using the Riccati transformation technique, we obtain sufficient conditions for this equation to be oscillatory

Interval oscillation criteria for nonlinear impulsive differential equations with variable delay

In this paper, the interval qualitative properties of a class of second order nonlinear differential equations are studied. For the hypothesis of delay being variable $\tau(t)$, an "interval delay function" is introduced to estimate the ratio of functions $x(t-\tau(t))$ and $x(t)$ on each considered interval, then Riccati transformation and $H$ functions are applied to obtain interval oscillation criteria. The known results gained by Huang and Feng [Comput. Math. Appl. 59(2010), 18–30] under the assumption of constant delay $\tau$ are developed. Moreover, examples are also given to illustrate the effectiveness and non-emptiness of our results

Forced oscillation of conformable fractional partial delay differential equations with impulses

In this paper, we establish some interval oscillation criteria for impulsive conformable fractional partial delay differential equations with a forced term. The main results will be obtained by employing Riccati technique. Our results extend and improve some results reported in the literature for the classical differential equations without impulses. An example is provided to illustrate the relevance of the new theorems

Nonlinear Modeling and Identification of Unsteady Aerodynamics at Stall

For an aircraft with delta wing shape, aerodynamics in stall angles-of-attack at both low and high-subsonic Mach conditions is known to be unsteady and nonlinear in nature. In these conditions, the longitudinal aerodynamic loads depend on the history of angle-ofattack and side-slip. The classical method of using damping or acceleration aerodynamic derivatives for modeling the unsteady variation of coefficients is unsuitable. Hence, two novel approaches for modeling aerodynamic loads in these conditions are proposed in this thesis. The unsteady effect in stall conditions at low Mach number is reflected in forced oscillation wind tunnel tests as dependence of longitudinal loads on amplitude and frequency of sinusoidal angle-of-attack input. The variations in longitudinal loads are nonlinear as their power spectrum contains super-harmonics of input frequency. The approaches presented in literature are equivalent when these are reduced to equivalent linear transfer function formulation, while their nonlinear adaptations are semi-empirical or adhoc. Hence, Volterra Variational Modeling (VVM) is proposed as a systematic approach to capture the nonlinear nature of unsteady variations. The VVM is derived from Volterra series as a set of parametric differential equations of the so-called kernel states. The kernel-states have special harmonic input response properties which are leveraged to develop a systematic methodology to capture the nonlinear unsteady variations in pitching moment coefficient. VVM is shown to inherently reproduce the nonlinear features of unsteady aerodynamic loads like amplitude dependence of nonlinear variations, different effective time-scale for pitch-up and pitchdown motions and same number of super-harmonics as seen in the experimental data. Hence, it offers several advantages compared to all the modeling approaches in literature. The VVM is a powerful approach due to following features: (i) Mathematically rigorous structure, (ii) Physical interpretations of parameters, (iii) it facilitates linear analysis of the flight modes (iv) simple identification methodology using forced oscillation wind tunnel test data (v) open to innovations in model structure and estimation technique. These concepts are demonstrated for the Generic Tailless Aircraft and F16XL aircraft using comprehensive sets of wind tunnel test data . The unsteady phenomena at high sub-sonic Mach number is called AbruptWing Stall, and novel model called ”Bifurcational Model of Aerodynamic Asymmetry” is proposed for modeling it. It shown to be a topologically rich structure which can model the static hysteresis and unsteady variations in rolling moment coefficient versus the side-slip angle, in order to reproduce the effects of Abrupt Wing Stall on flight dynamics

Analysis and simulation methods for free-running, injection-locked and super-regenerative oscillators

RESUMEN: En los últimos años, muchos esfuerzos han sido dedicados al desarrollo de técnicas complementarias para el análisis de circuitos autónomos de microondas. Estas técnicas están pensadas para su uso en combinación con balance armónico, ampliamente usado para el análisis a frecuencias de microondas. De hecho, balance armónico sufre de restricciones cuando se utiliza para el análisis de circuitos autónomos, en su mayoría debidos a su falta de sensibilidad a las propiedades de estabilidad de la solución que se genera o se extingue mediante bifurcaciones. En esta tesis doctoral se presentan nuevos métodos de simulación y análisis para la caracterización y modelado de osciladores libres, sincronizados y superregenerativos. Todos los resultados obtenidos mediante los nuevos métodos de simulación y análisis han sido comparados satisfactoriamente con otras técnicas de simulación y con medidas.ABSTRACT: In the last years, numerous efforts have been devoted to the development of complementary analysis tools for autonomous microwave circuits. They are intended to be applied in combination with the harmonic-balance (HB) method, widely used at microwave frequencies. In fact, HB suffers from a number of shortcomings when dealing with autonomous circuits, mostly due the fact that it is insensitive to the stability properties of the solution, generated and extinguished through bifurcation phenomena. Here, new simulation and analysis methodologies for the characterization and modeling of free-running, injection-locked and super-regenerative oscillators have been proposed to overcome these problems when using commercial software. Results from the different new analysis methodologies have been successfully compared with independent simulations and with measurements

An Investigation of Stochastic Cooling in the Framework of Control Theory

This report provides a description of unbunched beam stochastic cooling in the framework of control theory. The main interest in the investigation is concentrated on the beam stability in an active cooling system. A stochastic cooling system must be considered as a closed-loop, similar to the feedback systems used to damp collective instabilities. These systems, which are able to act upon themselves, are potentially unstable. The self-consistent solution for the beam motion is derived by means of a mode analysis of the collective beam motion. This solution yields a criterion for the stability of each collective mode. The expressions also allow for overlapping frequency bands in the beam spectrum and thus are valid over the entire frequency range. Having established the boundaries of stability in this way, the Fokker-Planck equation is used to describe the cooling process. This description does not include collective effects and thus a stable beam must be assumed. Hence the predictions about the cooling process following from the Fokker-Planck equation only make physical sense within the boundaries of beam stability. Finally it is verified that the parameters of the cooling system which give the best cooling results are compatible with the stability of the beam.Comment: 64 pages, latex, 11 eps-figures appended as uuencoded file, german hyphenation corrected I

Direct current hybrid breakers : a design and its realization

The use of semiconductors for electric power circuit breakers instead of conventional breakers remains a utopia when designing fault current interrupters for high power networks. The major problems concerning power semiconductor circuit breakers are the excessive heat losses and their sensitivity to transients. However, conventional breakers are capable of dealing with such matters. A combination of the two methods, or so-called ‘hybrid breakers’, would appear to be a solution; however, hybrid breakers use separate parallel branches for conducting the main current and interrupting the short-circuit current. Such breakers are intended for protecting direct current (DC) traction systems. In this thesis hybrid switching techniques for current limitation and purely solidstate current interruption are investigated for DC breakers. This work analyzes the transient behavior of hybrid breakers and compares their operations with conventional breakers and similar solid-state devices in DC systems. Therefore a hybrid breaker was constructed and tested in a specially designed high power test circuit. A vacuum breaker was chosen as the main breaker in the main conducting path; then a commutation path was connected across the vacuum breaker where it provided current limitation and interruption. The commutation path operated only during any current interruption and the process required additional circuits. These included a certain energy storage, overvoltage suppressor and commutation switch. So that when discharging this energy, a controlled counter-current injection could be produced. That countercurrent opposed the main current in the breaker by superposition in order to create a forced currentzero. One-stage and two-stage commutation circuits have been treated extensively. This study project contains both theoretical and experimental investigations. A direct current shortcircuit source was constructed capable of delivering power equivalent to a fault. It supplied a direct voltage of 1kVDC which was rectified having been obtained from a 3-phase 10kV/380V supply. The source was successfully tested to deliver a fault current of 7kA with a time constant of 5ms. The hybrid breaker that was developed could provide protection for 750VDC traction systems. The breaker was equipped with a fault-recognizing circuit based on a current level triggering. An electronic circuit was built for this need and was included in the system. It monitored the system continuously and took action by generating trip signals when a fault was recognized. Interruption was followed by a suitable timing of the fast contact separation in the main breaker and the currentzero creation. An electrodynamically driven mechanism was successfully tested having a dead-time of 300:s to separate the main breaker contacts. Furthermore, a maximum peak current injection of kA at a frequency of 500Hz could be obtained in order to produce an artificial current-zero in the vacuum breaker. A successful current interruption with a prospective value of 5kA was achieved by the hybrid switching technique. In addition, measures were taken to prevent overvoltages. Experimentally, the concept of a hybrid breaker was compared with the functioning of all mechanical (air breaker) and all electronical (IGCT breaker) versions. Although a single stage interrupting method was verified experimentally, two two-stage interrupting methods were analyzed theoretically

Dynamics of biologically informed neural mass models of the brain

This book contributes to the development and analysis of computational models that help brain function to be understood. The mean activity of a brain area is mathematically modeled in such a way as to strike a balance between tractability and biological plausibility. Neural mass models (NMM) are used to describe switching between qualitatively different regimes (such as those due to pharmacological interventions, epilepsy, sleep, or context-induced state changes), and to explain resonance phenomena in a photic driving experiment. The description of varying states in an ordered sequence gives a principle scheme for the modeling of complex phenomena on multiple time scales. The NMM is matched to the photic driving experiment routinely applied in the diagnosis of such diseases as epilepsy, migraine, schizophrenia and depression. The model reproduces the clinically relevant entrainment effect and predictions are made for improving the experimental setting.Die vorliegende Arbeit stellt einen Beitrag zur Entwicklung und Analyse von Computermodellen zum Verständnis von Hirnfunktionen dar. Es wird die mittlere Aktivität eines Hirnareals analytisch einfach und dabei biologisch plausibel modelliert. Auf Grundlage eines Neuronalen Massenmodells (NMM) werden die Wechsel zwischen Oszillationsregimen (z.B. durch pharmakologisch, epilepsie-, schlaf- oder kontextbedingte Zustandsänderungen) als geordnete Folge beschrieben und Resonanzphänomene in einem Photic-Driving-Experiment erklärt. Dieses NMM kann sehr komplexe Dynamiken (z.B. Chaos) innerhalb biologisch plausibler Parameterbereiche hervorbringen. Um das Verhalten abzuschätzen, wird das NMM als Funktion konstanter Eingangsgrößen und charakteristischer Zeitenkonstanten vollständig auf Bifurkationen untersucht und klassifiziert. Dies ermöglicht die Beschreibung wechselnder Regime als geordnete Folge durch spezifische Eingangstrajektorien. Es wird ein Prinzip vorgestellt, um komplexe Phänomene durch Prozesse verschiedener Zeitskalen darzustellen. Da aufgrund rhythmischer Stimuli und der intrinsischen Rhythmen von Neuronenverbänden die Eingangsgrößen häufig periodisch sind, wird das Verhalten des NMM als Funktion der Intensität und Frequenz einer periodischen Stimulation mittels der zugehörigen Lyapunov-Spektren und der Zeitreihen charakterisiert. Auf der Basis der größten Lyapunov-Exponenten wird das NMM mit dem Photic-Driving-Experiment überein gebracht. Dieses Experiment findet routinemäßige Anwendung in der Diagnostik verschiedener Erkrankungen wie Epilepsie, Migräne, Schizophrenie und Depression. Durch die Anwendung des vorgestellten NMM wird der für die Diagnostik entscheidende Mitnahmeeffekt reproduziert und es werden Vorhersagen für eine Verbesserung der Indikation getroffen