Smooth and non-smooth traveling wave solutions of some generalized Camassa-Holm equations

In this paper we employ two recent analytical approaches to investigate the possible classes of traveling wave solutions of some members of a recently-derived integrable family of generalized Camassa-Holm (GCH) equations. A recent, novel application of phase-plane analysis is employed to analyze the singular traveling wave equations of three of the GCH NLPDEs, i.e. the possible non-smooth peakon and cuspon solutions. One of the considered GCH equations supports both solitary (peakon) and periodic (cuspon) cusp waves in different parameter regimes. The second equation does not support singular traveling waves and the last one supports four-segmented, non-smooth $M$-wave solutions. Moreover, smooth traveling waves of the three GCH equations are considered. Here, we use a recent technique to derive convergent multi-infinite series solutions for the homoclinic orbits of their traveling-wave equations, corresponding to pulse (kink or shock) solutions respectively of the original PDEs. We perform many numerical tests in different parameter regime to pinpoint real saddle equilibrium points of the corresponding GCH equations, as well as ensure simultaneous convergence and continuity of the multi-infinite series solutions for the homoclinic orbits anchored by these saddle points. Unlike the majority of unaccelerated convergent series, high accuracy is attained with relatively few terms. We also show the traveling wave nature of these pulse and front solutions to the GCH NLPDEs

Monopoly power and distribution in fragmented markets : the case of groundwater

Using data from Pakistan's Punjab, the authors examine monopoly power in the market for groundwater - irrigation water extracted using private tubewells - a market characterized by barriers to entry and spatial fragmentation. Simple theory predicts that tubewell owners should price-discriminate in favor of their own share tenants. And this analysis of individual groundwater transactions over an 18-month period confirms such price discrimination. And among those studied, tubewell owners and their tenants use considerably more groundwater on their plots than do other farmers. The authors also provide evidence that monopoly pricing of groundwater leads to compensating - albeit small - reallocations of canal water, which farmers exchange in a separate informal market. Despite the substantial misallocation of groundwater, a welfare analysis show that monopoly pricing has limited effects on equity and efficiency. In the long run, a policy aimed at eliminating monopoly pricing would do little to help the poorest farmers.Water and Industry,Water Resources Law,Water Conservation,Environmental Economics&Policies,Water Supply and Systems,Water and Industry,Water Conservation,Water Supply and Sanitation Governance and Institutions,Drought Management,Water Use

An unusual cause of gynaecomastia in a male

Summary: Beta-human chorionic gonadotropin (βhCG) is normally produced by syncytiotrophoblasts of the placenta during pregnancy and aids embryo implantation. However, it is also secreted in varying amounts in non-pregnant conditions commonly heralding a neoplastic process. We present a case of 50-year-old man, who presented with bilateral gynaecomastia with elevated testosterone, oestradiol, suppressed gonadotropins with progressively increasing levels of human chorionic gonadotropin (hCG). Biochemical and radiological investigations including ultrasonography of testes, breast tissue, MRI pituitary and CT scan full body did not identify the source of hCG. FDG PET scan revealed a large mediastinal mass with lung metastasis. Immunostaining and histological analysis confirmed the diagnosis of primary choriocarcinoma of the mediastinum. It is highly aggressive and malignant tumor with poor prognosis. Early diagnosis and management are essential for the best outcome. Learning Points: High βhCG in a male patient or a non-pregnant female suggests a paraneoplastic syndrome. In the case of persistently positive serum hCG, exclude immunoassay interference by doing the urine hCG as heterophilic antibodies are not present in the urine. Non-gestational choriocarcinoma is an extremely rare trophoblastic tumor and should be considered in young men presenting with gynaecomastia and high concentration of hCG with normal gonads. A high index of suspicion and extensive investigations are required to establish an early diagnosis of extra-gonadal choriocarcinoma. Early diagnosis is crucial to formulate optimal management strategy and to minimize widespread metastasis for best clinical outcome

CFD-based process optimization of a dissolved air flotation system for drinking water production

Dissolved air flotation (DAF) has received more attention recently as a separation technique in both drinking water as well as wastewater treatment. However, the process as well as the preceding flocculation step is complex and not completely understood. Given the multiphase nature of the process, fluid dynamics studies are important to understand and optimize the DAF system in terms of operation and design. The present study is intended towards a comprehensive computational analysis for design optimization of the treatment plant in Kluizen, Belgium. Setting up the modelling framework involving the multiphase flow problem is briefly discussed. 3D numerical simulations on a scaled down model of the DAF design were analysed. The flow features give better confidence, but the flocs escape through the outlet still prevails which is averse to the system performance. In order to improve the performance and ease of maintenance, design modifications have been proposed by using a perforated tube for water extraction and are found to be satisfactory. The discussion is further reinforced through validating the numerical model against the experimental findings for stratified flow conditions

Supersymmetric And Smooth Hybrid Inflation In The Light Of WMAP3

In their minimal form both supersymmetric and smooth hybrid inflation yield a scalar spectral index n_s close to 0.98, to be contrasted with the result n_s=0.951+0.015-0.019 from WMAP3. To realize better agreement, following hep-ph/0604198, we extend the parameter space of these models by employing a non-minimal Kaehler potential. We also discuss non-thermal leptogenesis by inflaton decay and obtain new bounds in these models on the reheat temperature to explain the observed baryon asymmetry.Comment: 21 pages, 12 figures, revtex4. v2: minor revisions, additional references, to appear in PR

Centralized Control System Design for Underwater Transportation using two Hovering Autonomous Underwater Vehicles (HAUVs)

In this paper, a centralized control system is designed for the two HAUVs undertaking underwater transportation of a spherical payload via cylindrical manipulators. First, the nonlinear coupled dynamic model is developed considering the rigid body connection method for transportation. The effect of the hydrodynamic, hydrostatic and thrust parameters are taken about the centre of the combined body i.e. the centre of payload. Path trajectory is generated using the minimum snap trajectory algorithm. The trajectory is divided into segments for each directional motion which is further divided into the waypoints based on the time step of the duration. The path between two waypoints is represented by a 7th order polynomial. The centralized control system is designed to follow the desired trajectory. The control system is designed using PID controllers for the motion control in each direction. The main technical requirements are the stability of the payload, accurate trajectory tracking and robustness to overcome uncertainties. Stability cannot be compromised because of the rigid connection between the vehicles and the payload, whereas, tracking is given a tolerance of ±5%. Transportation task is observed for the desired motion in the horizontal plane. The time domain motion simulation results show that the desired trajectory has been accurately followed by the combined system while meeting the technical requirements

Leader-Follower Formation Control for Underwater Transportation using Multiple Autonomous Underwater Vehicles

The successful ability to conduct underwater transportation using multiple autonomous underwater vehicles (AUVs) is important for the commercial sector to undertake precise underwater installations on large modules, whilst for the military sector it has the added advantage of improved secrecy for clandestine operations. The technical requirements are the stability of the payload and internal collision avoidance while keeping track of the desired trajectory considering the underwater effects. Here, a leader-follower formation control strategy was developed and implemented on the transportation system of AUVs. PID controllers were used for the vehicles and a linear feedback controller for maintaining the formation. A Kalman Filter (KF) was designed to estimate the full state of the leader under disturbance, noise and limited sensor readings. The results demonstrate that though the technical requirements are met, the thrust oscillations under disturbance and noise produce the undesired heading angles

Assessment of Collision Avoidance Strategies for an Underwater Transportation System

Transportation using multiple autonomous vehicles with detection avoidance capability is useful for military applications. It is important for such systems to avoid collisions with underwater obstacles in an effective way, while keeping track of the target location. In this paper, sensor-based and path-planning methods of external collision avoidance were investigated for an underwater transportation system. In particular, sensor-based wall-following and hard-switching collision avoidance strategies and an offline RRT* path-planning method was implemented on the simulation model of the transportation system of four Hovering Autonomous Underwater Vehicles (HAUVs). Time-domain motion simulations were performed with each method and their ability to avoid obstacles was compared. The hard-switching method resulted in high yaw moments which caused the vehicle to travel towards the goal by a longer distance. Conversely, in the wall-following method, the yaw moment was kept to zero. Moreover, the wall-following method was found to be better than the hard-switching method in terms of time and power efficiency. The comparison between the offline RRT* path-planning and wall-following methods showed that the fuel efficiency of the former is higher whilst its time efficiency is poorer. The major drawback of RRT* is that it can only avoid the previously known obstacles. In future, offline RRT* and wall following can be blended for a better solution. The outcome of this paper provides guidance for the selection of the most appropriate method for collision avoidance for an underwater transportation system