On the modeling of some triodes-based nonlinear oscillators with complex dynamics: case of the Van der Pol oscillator

In this work, the dynamic of the triode-based Van der Pol oscillator coupled to a linear circuit is investigated (Triode-based VDPCL oscillator). Towards this end, we present a mathematical model of the triode, chosen from among the many different ones present in literature. The dynamical behavior of the system is investigated using classical tools such as two-parameter Lyapunov exponent, one-parameter bifurcation diagram associated with the graph of largest Lyapunov exponent, phase portraits, and time series. Numerical simulations reveal rather rich and complex phenomena including chaos, transient chaos, the coexistence of solutions, crisis, period-doubling followed by reverse period-doubling sequences (bubbles), and bursting oscillation. The coexistence of attractors is illustrated by the phase portraits and the cross-section of the basin of attraction. Such triode-based nonlinear oscillators can find their applications in many areas where ultra-high frequencies and high powers are demanded (radio, radar detection, satellites communication, etc.) since triode can work with these performances and are often used in the aforementioned areas. In contrast to some recent work on triode-based oscillators, LTSPICE simulations, based on real physical consideration of the triode, are carried out in order to validate the theoretical results obtained in this paper as well as the mathematical model adopted for the triode.

The Role of Mineral Deficiencies in Insulin Resistance and Obesity

: Minerals are critical for maintaining overall health. These tiny chemical compounds are responsible for enzymatic activation, maintaining healthy teeth and bones, regulating energy metabolism, enhancing immunity and aiding muscle and brain function. However, mineral deficiency in the form of inadequate or under nourished intake affects millions of people throughout the world, with well-documented adverse health consequences of malnutrition. Conversely, mineral deficiency may also be a risk factor for insulin resistance (IR) and obesity. This review focuses on another, more “less discussed” form of malnutrition, namely mineral deficiency and its contribution to metabolic disorders. At the cellular level, minerals maintain not only molecular communication but also trigger several key biochemical pathways. Disturbances in these processes due to mineral insufficiency may gradually lead to metabolic disorders such as insulin resistance, pre-diabetes and central obesity which might lead to renal failure, cardiac arrest, hepatic carcinoma and various neurodegenerative diseases. Here we discuss the burden of disease promoted by mineral deficiencies and the medical, social and economic consequences. Mineral deficiency-mediated IR and obesity have a considerable negative impact on individual well-being and physical consideration and economic productivity. We discuss possible molecular mechanisms of mineral deficiency that may lead to IR and obesity and suggest strategies to counter these metabolic disorders. To protect mankind from mineral nutrient deficiencies, the key is to take a variety of foods in reasonable quantities, such as organic and pasture-raised eggs, low fat dairy, and grass-fed and finished meats, insecticide and pesticide-free vegetables and fruits.

Magnetic Dipole and Thermal Radiation Impacts on Stagnation Point Flow of Micropolar Based Nanofluids over a Vertically Stretching Sheet: Finite Element Approach

An analysis for magnetic dipole with stagnation point flow of micropolar nanofluids is modeled for numerical computation subject to thermophoresis, multi buoyancy, injection/suction, and thermal radiation. The partial derivative is involved in physical consideration, which is transformed to format of ordinary differential form with the aid of similarity functions. The variational finite element procedure is harnessed and coded in Matlab script to obtain the numerical solution of the coupled non-linear ordinary differential problem. The fluid temperature, velocity, tiny particles concentration, and vector of micromotion are studied for two case of buoyancy (assisting 0<λ, and opposing 0>λ) through finite-element scheme. The velocity shows decline against the rising of ferromagnetic interaction parameter (β) (assisting 0<λ and opposing 0>λ), while the inverse behaviour is noted in micro rotation profile. Growing the thermo-phoresis and microrotation parameters receded the rate of heat transfer remarkable, and micromotion and fluid velocity enhance directly against buoyancy ratio. Additionally, the rate of couple stress increased against rising of thermal buoyancy (λ) and boundary concentration (m) in assisting case, but opposing case shows inverse behavior. The finite element scheme convergency was tested by changing the mesh size, and also test the validity with available literature.

Epistemic Chances, or “Almost-Objective” Probabilities

In this chapter is introduced the key concept of this book, a concept that I call epistemic chance. The definition of an epistemic chance invokes two kinds of considerations. One is limitations of knowledge on the part of an agent assigning probabilities to events. The other is a physical consideration, involving the dynamics of the system under consideration. Epistemic chances, therefore, do not fall neatly into the familiar dichotomy of chance and credence. They are hybrid probabilities.

Bio-inertia resonates life into evolution

Life is an environmental signalcompromise d Le Châteliers system. The potential for it toissue Le Châteliers effect to discernable signals is de fin e d as bio inertia. To track the origin of such system recovering capability, we composite brachistochrone curves with experiments to provethat a path which can be projecting into three dimensional simple harmonic motion with internalcommutation is an efficient sustaining signal accumulat ing and transferring path. It is thereforedefined as bio quantum path (or bio perpetual motion path which composed of the fundamentalphysical structures of bio systems. The function of such a structure is to strengthen conservativeforces by splicing out non conservative forces f rom Le Châteliers process es . Experimentscalibrate horizontal gravitational loss as empirical bio inertia and reveal the cause for thediscrepancy between inertia l mass and gravitational mass in bio systems. By adapting C hu s constantinto Planck's law and the born of the S chrödinger Cat s bab ies , the fragile Copenhagensuperposition becomes converging super positio n which sustaining the lifespan of a non isolatedsystem . The Schrödinger wave function is therefore upgraded into repeatabilitysuperposition which equivalent s to the horizontal & vertical repeatability superposition definition ofthe binding Einstein gravitational wave s in bio systems and all rest on Newtonian turnover stationaryupgrading for inversion recovery . W ave particle duality is reinterpreted and a frequency notationwhich can be adapted to music , quantum mechanics till bio systems is established From the bindingand inversions of gravity on bio quantum pa th s , l ife is physically abiogenesis from a whirlpool withenough time commutation and continuously polarization by splicing. NKT cell clinical trial based onnew CSF stationary definition finally confirm s that ancient physical striking system s are stillun surpass able for dealing with cancer and other senility problems unless modern bio technologieswithout any physical consideration can touch eigen inversion converging patterns which enough toreplace above ancient interference in so me day

Vortex sheet roll-up revisited

The classical problem of roll-up of a two-dimensional free inviscid vortex sheet is reconsidered. The singular governing equation brings with it considerable difficulty in terms of actual calculation of the sheet dynamics. Here, the sheet is discretized into segments that maintain it as a continuous object with curvature. A model for the self-induced velocity of a finite segment is derived based on the physical consideration that the velocity remain bounded. This allows direct integration through the singularity of the Birkhoff–Rott equation. The self-induced velocity of the segments represents the explicit inclusion of stretching of the sheet and thus vorticity transport. The method is applied to two benchmark cases. The first is a finite vortex sheet with an elliptical circulation distribution. It is found that the self-induced velocity is most relevant in regions where the curvature and the sheet strength or its gradient are large. The second is the Kelvin–Helmholtz instability of an infinite vortex sheet. The critical time at which the sheet forms a singularity in curvature is accurately predicted. As observed by others, the vortex sheet strength forms a finite-valued cusp at this time. Here, it is shown that the cusp value rapidly increases after the critical time and is the impetus that initiates the roll-up process.

Micromechanical Boundary Element Modelling of Transgranular and Intergranular Cohesive Cracking in Polycrystalline Materials

In this paper a cohesive formulation is proposed for modelling intergranular and transgranular damage and microcracking evolution in brittle polycrystalline materials. The model uses a multi region boundary element approach combined with a dual boundary element formulation. Polycrystalline microstructures are created through a Voronoi tessellation algorithm. Each crystal has an elastic orthotropic behaviour and specific material orientation. Transgranular surfaces are inserted as the simulation evolves and only in those grains that experience stress levels high enough for the nucleation of a new potential crack. Damage evolution along (inter-or trans-granular) interfaces is then modelled using cohesive traction separation laws and, upon failure, frictional contact analysis is introduced to model separation, stick or slip. Moreover some physical consideration based on cohesive energies were made, in order to guarantee the cohesive model in consideration was appropriate for the purpose of this work. Finally numerical simulations have been performed to demonstrate the validity of the proposed formulation in comparison with experimental observations and literature results.

A Semi-Analytical Model for Fluid-Elastic Instability in Tube Arrays Including the Effects of Nonuniform Flow Velocity and Tube Displacement

A semi-analytical method to examine the influences of the axial variations in the tube vibration amplitude and flow velocity on the critical flow velocity is investigated. We illustrate that neglecting the axial variation in the tube vibration amplitude can result in an overestimation of the critical flow velocity (nonconservative estimate) when the flow velocity is nonuniform. A condition under which such overestimation arises is derived by the transformation of the eigenvalue problem that is made to take into account the axial variations in the tube vibration amplitude and flow velocity. This condition is the existence of a positive correlation between the deviations of two functions: one representing the axial variation in the flow velocity and the other square of the function representing the nonuniformity of the tube vibration amplitude. The case with marked partial admission is investigated through physical consideration for this flow-induced vibration problem. We also study cases where the difference between tube eigenfrequencies in the flow and transverse directions results in a transition in the instability direction, from the transverse direction to that of flow.