Minimum fuel coplanar aeroassisted orbital transfer using collocation and nonlinear programming

The fuel optimal control problem arising in coplanar orbital transfer employing aeroassisted technology is addressed. The mission involves the transfer from high energy orbit (HEO) to low energy orbit (LEO) without plane change. The basic approach here is to employ a combination of propulsive maneuvers in space and aerodynamic maneuvers in the atmosphere. The basic sequence of events for the coplanar aeroassisted HEO to LEO orbit transfer consists of three phases. In the first phase, the transfer begins with a deorbit impulse at HEO which injects the vehicle into a elliptic transfer orbit with perigee inside the atmosphere. In the second phase, the vehicle is optimally controlled by lift and drag modulation to satisfy heating constraints and to exit the atmosphere with the desired flight path angle and velocity so that the apogee of the exit orbit is the altitude of the desired LEO. Finally, the second impulse is required to circularize the orbit at LEO. The performance index is maximum final mass. Simulation results show that the coplanar aerocapture is quite different from the case where orbital plane changes are made inside the atmosphere. In the latter case, the vehicle has to penetrate deeper into the atmosphere to perform the desired orbital plane change. For the coplanar case, the vehicle needs only to penetrate the atmosphere deep enough to reduce the exit velocity so the vehicle can be captured at the desired LEO. The peak heating rates are lower and the entry corridor is wider. From the thermal protection point of view, the coplanar transfer may be desirable. Parametric studies also show the maximum peak heating rates and the entry corridor width are functions of maximum lift coefficient. The problem is solved using a direct optimization technique which uses piecewise polynomial representation for the states and controls and collocation to represent the differential equations. This converts the optimal control problem into a nonlinear programming problem which is solved numerically by using a modified version of NPSOL. Solutions were obtained for the described problem for cases with and without heating constraints. The method appears to be more robust than other optimization methods. In addition, the method can handle complex dynamical constraints

On Primordial Perturbations of Test Scalar Fields

The primordial perturbations of test scalar fields not affecting the evolution of background may be very interesting since they can be transferred to the curvature perturbations by some mechanisms, and thus under certain condition can be responsible for the structure formation of observable universe. In this brief report we study the primordial perturbations of test scalar fields in various (super)accelerated expanding backgrounds.Comment: 4 pages, no figures, clarifications and refs. added, typos corrected, to publish in PR

A Microscopic Simulation Laboratory for Evaluation of Off-street Parking Systems

The parking industry produces an enormous amount of data every day that, properly analyzed, will change the way the industry operates. The collected data form patterns that, in most cases, would allow parking operators and property owners to better understand how to maximize revenue and decrease operating expenses and support the decisions such as how to set specific parking policies (e.g. electrical charging only parking space) to achieve the sustainable and eco-friendly parking. However, there lacks an intelligent tool to assess the layout design and operational performance of parking lots to reduce the externalities and increase the revenue. To address this issue, this research presents a comprehensive agent-based framework for microscopic off-street parking system simulation. A rule-based parking simulation logic programming model is formulated. The proposed simulation model can effectively capture the behaviors of drivers and pedestrians as well as spatial and temporal interactions of traffic dynamics in the parking system. A methodology for data collection, processing, and extraction of user behaviors in the parking system is also developed. A Long-Short Term Memory (LSTM) neural network is used to predict the arrival and departure of the vehicles. The proposed simulator is implemented in Java and a Software as a Service (SaaS) graphic user interface is designed to analyze and visualize the simulation results. This study finds the active capacity of the parking system, which is defined as the largest number of actively moving vehicles in the parking system under the facility layout. In the system application of the real world testbed, the numerical tests show (a) the smart check-in device has marginal benefits in vehicle waiting time; (b) the flexible pricing policy may increase the average daily revenue if the elasticity of the price is not involved; (c) the number of electrical charging only spots has a negative impact on the performance of the parking facility; and (d) the rear-in only policy may increase the duration of parking maneuvers and reduce the efficiency during the arrival rush hour. Application of the developed simulation system using a real-world case demonstrates its capability of providing informative quantitative measures to support decisions in designing, maintaining, and operating smart parking facilities

Decomposing and valuing callable convertible bonds: a new method based on exotic options

In the framework of Black-Scholes-Merton option pricing models, by employing exotic options instead of plain options or warrants, this paper presents an equivalent decomposition method for usual Callable Convertible Bonds (CCB). Furthermore, the analytic valuation formulae for CCB are worked out by using the analytic formulae for those simpler securities decomposed from CCB. Moreover, this method is validated by comparing with Monte Carlo simulation. Besides, the effects of call clauses, coupon clauses and soft call condition clauses are analyzed respectively. These give lots of new insights into the valuation and analysis of CCB and much help to hedge their risks.Callable convertible bonds; Equivalent decomposition; Up-and-out calls; American binary calls; Derivative pricing