An investigation of the stability in the large for an autonomous second-order two-degree-of-freedom system

An extension to an algorithm due to Simpson has been developed for the analysis of a second-order two-degree-of-freedom autonomous system. The form of equations considered arises from the study of mechanical systems with a single concentrated non-linearity and the method assumes a solution made up of harmonic terms whose amplitudes vary slowly in time. For a system possessing a stable equilibrium point and an unstable limit cycle arising from a subcritical Hopf bifurcation, the method has been applied to the problem of predicting the basin of attraction of the equilibrium point. The method reduces the problem from a search in four-dimensional phase space to a search for a boundary in a plane defined by amplitudes a₁ and a₂ in the assumed form of the solution. The method was applied to four weakly non-linear systems in which the non-linearity was due to either a linear spring with a small amount of cubic hardening or a linear spring with freeplay. Agreement was shown to be good in the cases considered. However, it would be expected that the method would not give such accurate results if the non-linear effect was more significant. This was illustrated for the case of the cubic hardening non-linearity.     

Exploring cold regions autonomous operations

The US Army must update its vehicle fleet to be better equipped for potential future military conflicts in northern climates (US Army, 2017). This process involves considering manned, optionally manned, and unmanned vehicles as viable options in the future. Optionally manned and unmanned vehicles in the armed forces have substantial benefits because they can operate without direct driver input or are able to perform missions deemed too dangerous for troops. Optionally manned vehicles allow the driver to shift some, or all, focus away from the task of driving the vehicle. In some cases, these autonomous vehicles may perform better than a human driver by rapidly sensing and reacting to terrain changes. Onboard sensing and decision making are equally applicable to both fully autonomous and teleoperated vehicles. This work will focus on the terrain sensing, waypoint navigation, and teleoperation potential of an optionally manned or unmanned vehicle. Results from a vehicle demonstration on two different terrain conditions will provide the basis for additional terrain sensing and autonomous vehicle development work in the coming year.     

平面自治系统极限环的存在性

本文研究一般自治系统的极限环存在性问题，在一定条件下，我们证明该系统极限环的存在性，所得结果推广和改进了文［５—７］的相应结论．     

高阶非线性微分方程的全局稳定性

本文通过将高阶非线性自治微分方程转化为Ｌｕｒｉｅ型控制系统的方法，借助于Ｐｏｐｏｖ的频率判据，得到了它们全局渐近稳定的判别准则，推广了文［１］的结果．     

Heuristic optimization methods for motion planning of autonomous agricultural vehicles

In this paper, two heuristic optimization techniques are tested and compared in the application of motion planning for autonomous agricultural vehicles: Simulated Annealing and Genetic Algorithms. Several preliminary experimentations are performed for both algorithms, so that the best neighborhood definitions and algorithm parameters are found. Then, the two tuned algorithms are run extensively, but for no more than 2000 cost function evaluations, as run-time is the critical factor for this application. The comparison of the two algorithms showed that the Simulated Annealing algorithm achieves the better performance and outperforms the Genetic Algorithm. The final optimum found by the Simulated Annealing algorithm is considered to be satisfactory for the specific motion planning application.     

Dynamical behaviors of a prey-predator system with impulsive control

In this paper, we study dynamics of a prey-predator system under the impulsive control. Sufficient conditions of the existence and the stability of semi-trivial periodic solutions are obtained by using the analogue of the Poincaré criterion. It is shown that the positive periodic solution bifurcates from the semi-trivial periodic solution through a transcritical bifurcation. A strategy of impulsive state feedback control is suggested to ensure the persistence of two species. Furthermore, a steady positive period-2 solution bifurcates from the positive periodic solution by the flip bifurcation, and the chaotic solution is generated via a cascade of flip bifurcations. Numerical simulations are also illustrated which agree well with our theoretical analysis.     

A mathematical model of the systemic circulatory system with logistically defined nervous system regulatory mechanisms

A mathematical model is developed that accurately describes the pressure, volume and flow dynamics of the systemic circulatory system over the full physiological range of human pressures and volumes. At the heart of this model are mathematical representations for the autonomic and central nervous system reflexes which maintain arterial pressure, cardiac output and cerebral blood flow. These representations involve functions in which a maximum effect and a minimum effect are smoothly connected by a logistic transition. A new approach to modelling the pressure – volume relationship in a vessel with smooth muscle contraction is also presented. To test the model, simulations of cardiac arrest and various haemorrhagic situations were conducted, and predicted results were compared with clinical observations. Near-perfect agreement was obtained between predicted and observed values of the mean circulatory filling pressure, cardiac output and arterial pressure decay in the face of significant haemorrhage, and the critical values delineating progressive from non-progressive hypovolaemic shock.     

Critically prime interval orders

We prove that a prime interval order, not necessarily finite, has no prime upper cover if and only if it has width two. On the other hand, we prove that every finite prime N-free order has at least one prime upper cover.     

Simultaneous spectrophotometric flow-through measurements of pH, carbon dioxide fugacity, and total inorganic carbon in seawater

An autonomous multi-parameter flow-through CO₂ system has been developed to simultaneously measure surface seawater pH, carbon dioxide fugacity (fCO₂), and total dissolved inorganic carbon (DIC). All three measurements are based on spectrophotometric determinations of solution pH at multiple wavelengths using sulfonephthalein indicators. The pH optical cell is machined from a PEEK polymer rod bearing a bore-hole with an optical pathlength of ∼15 cm. The fCO₂ optical cell consists of Teflon AF 2400 (DuPont) capillary tubing sealed within the bore-hole of a PEEK rod. This Teflon AF tubing is filled with a standard indicator solution with a fixed total alkalinity, and forms a liquid core waveguide (LCW). The LCW functions as both a long pathlength (∼15 cm) optical cell and a membrane that equilibrates the internal standard solution with external seawater. fCO₂ is then determined by measuring the pH of the internal solution. DIC is measured by determining the pH of standard internal solutions in equilibrium with seawater that has been acidified to convert all forms of DIC to CO₂. The system runs repetitive measurement cycles with a sampling frequency of ∼7 samples (21 measurements) per hour. The system was used for underway measurements of sea surface pH, fCO₂, and DIC during the CLIVAR/CO₂ A16S cruise in the South Atlantic Ocean in 2005. The field precisions were evaluated to be 0.0008 units for pH, 0.9 μatm for fCO₂, and 2.4 μmol kg⁻¹ for DIC. These field precisions are close to those obtained in the laboratory. Direct comparison of our measurements and measurements obtained using established standard methods revealed that the system achieved field agreements of 0.0012 ± 0.0042 units for pH, 1.0 ± 2.5 μatm for fCO₂, and 2.2 ± 6.0 μmol kg⁻¹ for DIC. This system integrates spectrophotometric measurements of multiple CO₂ parameters into a single package suitable for observations of both seawater and freshwater.     

Integral invariants for non-barotropic flows in a four dimensional space time manifold

Properties of non-barotropic flows are described using Lie derivatives of differential forms in a Euclidean four dimensional space-time manifold. Vanishing of the Lie derivative implies that the corresponding physical quantity remains invariant along the integral curves of the flow. Integral invariants of non-barotropic perfect and viscous flows are studied using the concepts of relative and absolute invariance of forms. The four dimensional expressions for the rate of change of the generalized circulation, generalized vorticity flux, generalized helicity and generalized parity in the case of ideal and viscous non-barotropic flows are thereby obtained.