On certain new integrable second order nonlinear differential equations and their connection with two dimensional Lotka-Volterra system

In this paper, we consider a second order nonlinear ordinary differential equation of the form $\ddot{x}+k_1\frac{\dot{x}^2}{x}+(k_2+k_3x)\dot{x}+k_4x^3+k_5x^2+k_6x=0$, where $k_i$'s, $i=1,2,...,6,$ are arbitrary parameters. By using the modified Prelle-Singer procedure, we identify five new integrable cases in this equation besides two known integrable cases, namely (i) $k_2=0, k_3=0$ and (ii) $k_1=0, k_2=0, k_5=0$. Among these five, four equations admit time dependent first integrals and the remaining one admits time independent first integral. From the time independent first integral, nonstandard Hamiltonian structure is deduced thereby proving the Liouville sense of integrability. In the case of time dependent integrals, we either explicitly integrate the system or transform to a time-independent case and deduce the underlying Hamiltonian structure. We also demonstrate that the above second order ordinary differential equation is intimately related to the two-dimensional Lotka-Volterra (LV) system. From the integrable parameters of above nonlinear equation and all the known integrable cases of the latter can be deduced thereby.Comment: Accepted for publication in J. Math. Phy

A Multiobjective G.A./Fuzzy Logic augmented flight controller for an F16 aircraft.

An investigation is made in this paper of the pos- sibility of enhancing the performance of controllers of unstable systems while retaining safety critical function. In this case, a General Dynamics F16 fighter is considered in simulation. A fuzzy logic controller is designed and its membership functions tuned by Multiobjective Genetic Algorithms in order to design an augmented flight controller with enhanced manouverability which still retains safety critical operation. The controller is assessed in terms of pilot effort and thus reduction of pilot fatigue. The controller is incorporated into a six degree of freedom real-time flight simulator, and flight tested by a qualified pilot instructor

Measurement and characterisation technique for real-time die temperature prediction of MOSFET-based power electronics

This paper presents a technique to predict the die temperature of a MOSFET based on an empirical model derived following an offline thermal characterization. First, a method for the near-simultaneous measurement of die temperature during controlled power dissipation is presented. The method uses a linear arbitrary waveform power controller which is momentarily disconnected at regular intervals to allow the forward voltage drop of the MOSFET's antiparallel diode to be measured. Careful timing ensures the power dissipation is not significantly affected by the repeated disconnection of the power controller. Second, a pseudorandom binary sequence-based system identification approach is used to determine the thermal transfer impedance, or cross coupling between the dice of two devices on shared cooling using the near-simultaneous measurement and control method. A set of infinite impulse response digital filters are fitted to the cross-coupling characteristics and used to form a temperature predictor. Experimental verification shows excellent agreement between measured and predicted temperature responses to power dissipation. Results confirm the usefulness of the technique for predicting die temperatures in real time without the need for on-die sensors

A nonlocal connection between certain linear and nonlinear ordinary differential equations: extension to coupled equations

Identifying integrable coupled nonlinear ordinary differential equations (ODEs) of dissipative type and deducing their general solutions are some of the challenging tasks in nonlinear dynamics. In this paper we undertake these problems and unearth two classes of integrable coupled nonlinear ODEs of arbitrary order. To achieve these goals we introduce suitable nonlocal transformations in certain linear ODEs and generate the coupled nonlinear ODEs. In particular, we show that the problem of solving these classes of coupled nonlinear ODEs of any order effectively reduces to solving a single first order nonlinear ODE. We then describe a procedure to derive explicit general solutions for the identified integrable coupled ODEs, when the above mentioned first order nonlinear ODE reduces to a Bernoulli equation. The equations which we generate and solve include the two coupled versions of modified Emden equations (in second order), coupled versions of Chazy equations (in third order), and their variants, higher dimensional coupled Ricatti and Abel's chains, as well as a new integrable chain and higher order equations

Non-standard conserved Hamiltonian structures in dissipative/damped systems : Nonlinear generalizations of damped harmonic oscillator

In this paper we point out the existence of a remarkable nonlocal transformation between the damped harmonic oscillator and a modified Emden type nonlinear oscillator equation with linear forcing, $\ddot{x}+\alpha x\dot{x}+\beta x^3+\gamma x=0,$ which preserves the form of the time independent integral, conservative Hamiltonian and the equation of motion. Generalizing this transformation we prove the existence of non-standard conservative Hamiltonian structure for a general class of damped nonlinear oscillators including Li\'enard type systems. Further, using the above Hamiltonian structure for a specific example namely the generalized modified Emden equation $\ddot{x}+\alpha x^q\dot{x}+\beta x^{2q+1}=0$, where $\alpha$, $\beta$ and $q$ are arbitrary parameters, the general solution is obtained through appropriate canonical transformations. We also present the conservative Hamiltonian structure of the damped Mathews-Lakshmanan oscillator equation. The associated Lagrangian description for all the above systems is also briefly discussed.Comment: Accepted for publication in J. Math. Phy

Dynamics of a Completely Integrable NN-Coupled Li\'enard Type Nonlinear Oscillator

We present a system of $N$-coupled Li\'enard type nonlinear oscillators which is completely integrable and possesses explicit $N$ time-independent and $N$ time-dependent integrals. In a special case, it becomes maximally superintegrable and admits $(2N-1)$ time-independent integrals. The results are illustrated for the N=2 and arbitrary number cases. General explicit periodic (with frequency independent of amplitude) and quasiperiodic solutions as well as decaying type/frontlike solutions are presented, depending on the signs and magnitudes of the system parameters. Though the system is of a nonlinear damped type, our investigations show that it possesses a Hamiltonian structure and that under a contact transformation it is transformable to a system of uncoupled harmonic oscillators.Comment: One new section adde

Effects of Threat and Sleep Deprivation on Action Tendencies and Response Inhibition

The ability to control action is crucial for adaptive responding, but may be compromised in situations involving strong emotions (e.g., threat) or when people are deprived of resources (e.g., sleep). As compromised action control can have large consequences in threatening situations, for example when police officers face a potentially armed suspect, we experimentally investigated how acute threat and partial sleep deprivation affect the ability to control impulsive responses, in 52 healthy young adults performing a simulated shooting task. The results showed that acute threat increased the tendency to act quickly (i.e., reduced response times; Coef = 9.46, 95% CI [3.49, 15.29], p = .001) and impaired response inhibition (i.e., increased stop signal reaction times; Coef = -4.91, 95% CI [-9.47, -0.44], p = .035). In addition, three nights of partial sleep deprivation (five hours [n = 28] vs. eight hours [n = 24] of sleep), led to a significant decrease in overall response accuracy (Coef = -0.22, 95% CI [- 0.40, -0.05], p = .025). Contrary to expectations, our results did not show increased threat sensitivity in sleep-deprived individuals (all p > .13). Nevertheless, they may have important implications for professionals who are required to maintain behavioral control under high levels of threat and who experience disturbed sleep due to e.g. shift work, as both factors negatively affected performanc

Erythrocytes and Vascular Function: Oxygen and Nitric Oxide

Erythrocytes regulate vascular function through the modulation of oxygen delivery and the scavenging and generation of nitric oxide (NO). First, hemoglobin inside the red blood cell binds oxygen in the lungs and delivers it to tissues throughout the body in an allosterically regulated process, modulated by oxygen, carbon dioxide and proton concentrations. The vasculature responds to low oxygen tensions through vasodilation, further recruiting blood flow and oxygen carrying erythrocytes. Research has shown multiple mechanisms are at play in this classical hypoxic vasodilatory response, with a potential role of red cell derived vasodilatory molecules, such as nitrite derived nitric oxide and red blood cell ATP, considered in the last 20 years. According to these hypotheses, red blood cells release vasodilatory molecules under low oxygen pressures. Candidate molecules released by erythrocytes and responsible for hypoxic vasodilation are nitric oxide, adenosine triphosphate and S-nitrosothiols. Our research group has characterized the biochemistry and physiological effects of the electron and proton transfer reactions from hemoglobin and other ferrous heme globins with nitrite to form NO. In addition to NO generation from nitrite during deoxygenation, hemoglobin has a high affinity for NO. Scavenging of NO by hemoglobin can cause vasoconstriction, which is greatly enhanced by cell free hemoglobin outside of the red cell. Therefore, compartmentalization of hemoglobin inside red blood cells and localization of red blood cells in the blood stream are important for healthy vascular function. Conditions where erythrocyte lysis leads to cell free hemoglobin or where erythrocytes adhere to the endothelium can result in hypertension and vaso constriction. These studies support a model where hemoglobin serves as an oxido-reductase, inhibiting NO and promoting higher vessel tone when oxygenated and reducing nitrite to form NO and vasodilate when deoxygenated. How erythrocytes modulate vascular tone has been widely studied over the last two decades. The vasodilation of the vasculature under hypoxic conditions has inspired much research ranging from the effect of oxygen partial pressure on smooth muscle cell contractility and endothelial nitric oxide synthase (eNOS) activity to nitrite reduction by hemoglobin (Hb) inside erythrocytes and subsequent production of nitric oxide. Here we review how red blood cells (RBCs) and hemoglobin regulate vascular function and blood flow