Optimal resource allocation in conflicts with the Lanchester linear law (2,1) model

This paper presents a detailed analysis of a model for military conflicts where the defending forces have to determine an optimal partitioning of available resources to counter attacks from an adversary in two different fronts in an area fire situation. Lanchester linear law attrition model is used to develop the dynamical equations governing the variation in force strength. Here we address a static resource allocation problem namely, Time-Zero-Allocation (TZA) where the resource allocation is done only at the initial time. Numerical examples are given to support the analytical results.

Law student lifestyle pressures

One significant factor influencing student wellbeing is the degree to which their studies are subject to external lifestyle pressures. These pressures are relieved or exacerbated by choices students make around their approaches to study, and the amount of time they devote to work and leisure. This Chapter considers results from a 2012 survey of law students at the University of New South Wales (UNSW), Sydney, Australia. Those results are compared to results from a similar US law student survey, and comparable data from the UK and Australia more broadly. In addition, the UNSW study compares key lifestyle choices of undergraduate (LLB) and graduate (JD) law students. The significance of the analysis in this Chapter for understanding law students’ wellbeing is that comparing American and Australian law students’ lifestyle patterns provides insights into contextual variation between both groups, which is important to bear in mind when comparing American and Australian research on law students’ wellbeing, and appreciating the limits of such comparisons. In particular, much of the wellbeing literature to date has focused on course-based stressors, but in light of recent research indicating that improvements in students’ course-based experiences may not have a direct effect on law students’ elevated levels of psychological distress, it is important to understand the broader life pressures and stressors that may be impacting law students’ wellbeing.

The relationship between class participation and law students' learning, engagement and stress: Do demographics matter?

Student participation in the classroom has long been regarded as an important means of increasing student engagement and enhancing learning outcomes by promoting active learning. However, the approach to class participation common in U.S. law schools, commonly referred to as the Socratic method, has been criticised for its negative impacts on student wellbeing. A multiplicity of American studies have identified that participating in law class discussions can be alienating, intimidating and stressful for some law students, and may be especially so for women, and students from minority backgrounds. Using data from the Law School Student Assessment Survey (LSSAS), conducted at UNSW Law School in 2012, this Chapter provides preliminary insights into whether assessable class participation (ACP) at an Australian law school is similarly alienating and stressful for students, including the groups identified in the American literature. In addition, we compare the responses of undergraduate Bachelor of Laws (LLB) and graduate Juris Doctor (JD) students. The LSSAS findings indicate that most respondents recognise the potential learning and social benefits associated with class participation in legal education, but remain divided over their willingness to participate. Further, in alignment with general trends identified in American studies, LLB students, women, international students, and non-native English speakers perceive they contribute less frequently to class discussions than JD students, males, domestic students, and native English speakers, respectively. Importantly, the LSSAS indicates students are more likely to be anxious about contributing to class discussions if they are LLB students (compared to their JD counterparts), and if English is not their first language (compared to native English speakers). There were no significant differences in students’ self-reported anxiety levels based on gender, which diverges from the findings of American research.

Observation of a power-law memory kernel for fluctuations within a single protein molecule

The fluctuation of the distance between a fluorescein-tyrosine pair within a single protein complex was directly monitored in real time by photoinduced electron transfer and found to be a stationary, time-reversible, and non-Markovian Gaussian process. Within the generalized Langevin equation formalism, we experimentally determine the memory kernel K(t), which is proportional to the autocorrelation function of the random fluctuating force. K(t) is a power-law decay, t(-0.51 +/- 0.07) in a broad range of time scales (10(-3)-10 s). Such a long-time memory effect could have implications for protein functions.

Retro-Proportional-Navigation: A New Guidance Law for Interception of High-Speed Targets

In this paper, a new proportional-navigation guidance law, called retro-proportional-navigation, is proposed. The guidance law is designed to intercept targets that are of higher speeds than the interceptor. This is a typical scenario in a ballistic target interception. The capture region analysis for both proportional-navigation and retro-proportional-navigation guidance laws are presented. The study shows that, at the cost of a higher intercept time, the retro-proportional-navigation guidance law demands lower terminal lateral acceleration than proportional navigation and can intercept high-velocity targets from many initial conditions that the classical proportional navigation cannot. Also, the capture region with the retro-proportional-navigation guidance law is shown to be larger compared with the classical proportional-navigation guidance law.

Use of Fick's law and Maxwell–Stefan equations in computation of multicomponent diffusion

This article does not have an abstract.

Sliding mode control based guidance law with impact time constraints

In this paper, the sliding mode control based guidance laws to intercept stationary targets at a desired impact time are proposed. Then, it is extended to constant velocity targets using the notion of predicted interception. The desired impact time is achieved by selecting the interceptor's lateral acceleration to enforce a sliding mode on a switching surface designed using non-linear engagement dynamics. Numerical simulation results are presented to validate the proposed guidance law for different initial engagement geometries, impact times and salvo attack scenarios

Impact angle constraint guidance law using cubic splines for intercepting stationary targets

In this paper the cubic spline guidance law is presented for intercepting a stationary target at a desired impact angle. The guidance law is obtained from cubic spline curve based trajectory using an inverse method. The cubic spline t rajectory curve expresses the altitude as a cubic polynomial of the downrange. The guidance law is modified to achieve interception in the cases where impact angle is greater that or equal to 90◦. The guidance law is implemented in a feedback mode to maintain the desired impact angle and to reduce miss distance in the presence of lateral acceleration saturation and atmospheric distur- bances. The simulation results show that the guidance law fulfills all the requirements.

Three Dimensional Impact Angle Constrained Guidance Law using Sliding Mode Control

In this paper, three dimensional impact angle control guidance laws are proposed for stationary targets. Unlike the usual approach of decoupling the engagement dynamics into two mutually orthogonal 2-dimensional planes, the guidance laws are derived using the coupled dynamics. These guidance laws are designed using principles of conventional as well as nonsingular terminal sliding mode control theory. The guidance law based on nonsingular terminal sliding mode guarantees finite time convergence of interceptor to the desired impact angle. In order to derive the guidance laws, multi-dimension switching surfaces are used. The stability of the system, with selected switching surfaces, is demonstrated using Lyapunov stability theory. Numerical simulation results are presented to validate the proposed guidance law.

A Nonlinear Guidance Law for Impact Time Control

This paper discusses the problem of impact time control of an interceptor against a stationary target. A nonlinear guidance law is proposed with the interceptor heading angle variation as a function of the range to target. Closed-form expressions for the design parameters are derived for an exact analysis of the impact time. A feedback form of the guidance law is presented for addressing realistic implementation in the presence of autopilot lag. Using the closed-form expressions of the impact time, a cooperative guidance scheme is presented for simultaneous impact in a salvo attack. Extensive simulation studies are presented validating the analytic findings.