Dynamic portrait of the planetary 2/1 mean-motion resonance - II. Systems with a more massive inner planet

This paper presents the second part in our study of the global structure of the planar phase space of the planetary three-body problem, when both planets lie in the vicinity of a 2/1 mean-motion resonance. While Paper I was devoted to cases where the outer planet is the more massive body, the present work is devoted to the cases where the more massive body is the inner planet. As before, outside the well-known Apsidal Corotation Resonances (ACR), the phase space shows a complex picture marked by the presence of several distinct regimes of resonant and non-resonant motion, crossed by families of periodic orbits and separated by chaotic zones. When the chosen values of the integrals of motion lead to symmetric ACR, the global dynamics are generally similar to the structure presented in Paper I. However, for asymmetric ACR the resonant phase space is strikingly different and shows a galore of distinct dynamical states. This structure is shown with the help of dynamical maps constructed on two different representative planes, one centred on the unstable symmetric ACR and the other on the stable asymmetric equilibrium solution. Although the study described in the work may be applied to any mass ratio, we present a detailed analysis for mass values similar to the Jupiter-Saturn case. Results give a global view of the different dynamical states available to resonant planets with these characteristics. Some of these dynamical paths could have marked the evolution of the giant planets of our Solar system, assuming they suffered a temporary capture in the 2/1 resonance during the latest stages of the formation of our Solar system.

Lorentz violation and the proper-time method

In this Letter, we apply the proper-time method to generate the Lorentz-violating Chern-Simons terms in the four-dimensional Yang-Mills and non-linearized gravity theories. It is shown that the coefficient of the induced Chern-Simons term is finite but regularization dependent. (C) 2008 Elsevier B.V. All rights reserved.

Mean Motion in Stochastic Plasmas With a Space-Dependent Diffusion Coefficient

Radial transport in the tokamap, which has been proposed as a simple model for the motion in a stochastic plasma, is investigated. A theory for previous numerical findings is presented. The new results are stimulated by the fact that the radial diffusion coefficients is space-dependent. The space-dependence of the transport coefficient has several interesting effects which have not been elucidated so far. Among the new findings are the analytical predictions for the scaling of the mean radial displacement with time and the relation between the Fokker-Planck diffusion coefficient and the diffusion coefficient from the mean square displacement. The applicability to other systems is also discussed. (c) 2009 WILEY-VCH GmbH & Co. KGaA, Weinheim

On the motion under focal attraction in a rotating medium

New results are established here on the phase portraits and bifurcations of the kinematic model in system (1), first presented by H.K. Wilson in [3], and by him attributed to L. Markus (unpublished). A new, self-sufficient, study which extends that of [3] and allows an essential conclusion for the applicability of the model is reported here.

Motion Detection for Video Surveillance

This thesis is related to the broad subject of automatic motion detection and analysis in videosurveillance image sequence. Besides, proposing the new unique solution, some of the previousalgorithms are evaluated, where some of the approaches are noticeably complementary sometimes.In real time surveillance, detecting and tracking multiple objects and monitoring their activities inboth outdoor and indoor environment are challenging task for the video surveillance system. Inpresence of a good number of real time problems limits scope for this work since the beginning. Theproblems are namely, illumination changes, moving background and shadow detection.An improved background subtraction method has been followed by foreground segmentation, dataevaluation, shadow detection in the scene and finally the motion detection method. The algorithm isapplied on to a number of practical problems to observe whether it leads us to the expected solution.Several experiments are done under different challenging problem environment. Test result showsthat under most of the problematic environment, the proposed algorithm shows the better qualityresult.

Motion Cues Analysis for Parkinson Gait Recognition

Background: Previous assessment methods for PG recognition used sensor mechanisms for PG that may cause discomfort. In order to avoid stress of applying wearable sensors, computer vision (CV) based diagnostic systems for PG recognition have been proposed. Main constraints in these methods are the laboratory setup procedures: Novel colored dresses for the patients were specifically designed to segment the test body from a specific colored background. Objective: To develop an image processing tool for home-assessment of Parkinson Gait(PG) by analyzing motion cues extracted during the gait cycles. Methods: The system is based on the idea that a normal body attains equilibrium during the gait by aligning the body posture with the axis of gravity. Due to the rigidity in muscular tone, persons with PD fail to align their bodies with the axis of gravity. The leaned posture of PD patients appears to fall forward. Whereas a normal posture exhibits a constant erect posture throughout the gait. Patients with PD walk with shortened stride angle (less than 15 degrees on average) with high variability in the stride frequency. Whereas a normal gait exhibits a constant stride frequency with an average stride angle of 45 degrees. In order to analyze PG, levodopa-responsive patients and normal controls were videotaped with several gait cycles. First, the test body is segmented in each frame of the gait video based on the pixel contrast from the background to form a silhouette. Next, the center of gravity of this silhouette is calculated. This silhouette is further skeletonized from the video frames to extract the motion cues. Two motion cues were stride frequency based on the cyclic leg motion and the lean frequency based on the angle between the leaned torso tangent and the axis of gravity. The differences in the peaks in stride and lean frequencies between PG and normal gait are calculated using Cosine Similarity measurements. Results: High cosine dissimilarity was observed in the stride and lean frequencies between PG and normal gait. High variations are found in the stride intervals of PG whereas constant stride intervals are found in the normal gait. Conclusions: We propose an algorithm as a source to eliminate laboratory constraints and discomfort during PG analysis. Installing this tool in a home computer with a webcam allows assessment of gait in the home environment.

Motion cue analysis for parkinsonian gait recognition

This paper presents a computer-vision based marker-free method for gait-impairment detection in Patients with Parkinson's disease (PWP). The system is based upon the idea that a normal human body attains equilibrium during the gait by aligning the body posture with Axis-of-Gravity (AOG) using feet as the base of support. In contrast, PWP appear to be falling forward as they are less-able to align their body with AOG due to rigid muscular tone. A normal gait exhibits periodic stride-cycles with stride-angle around 45o between the legs, whereas PWP walk with shortened stride-angle with high variability between the stride-cycles. In order to analyze Parkinsonian-gait (PG), subjects were videotaped with several gait-cycles. The subject's body was segmented using a color-segmentation method to form a silhouette. The silhouette was skeletonized for motion cues extraction. The motion cues analyzed were stride-cycles (based on the cyclic leg motion of skeleton) and posture lean (based on the angle between leaned torso of skeleton and AOG). Cosine similarity between an imaginary perfect gait pattern and the subject gait patterns produced 100% recognition rate of PG for 4 normal-controls and 3 PWP. Results suggested that the method is a promising tool to be used for PG assessment in home-environment.

Avoiding the Fog of Crisis: A Protocol for the Proper Domestic Use of the Military

Failure to contemplate and define an appropriate role for the armed forces of the national government in domestic crises of this sort is a serious problem. It is all the more serious now as these potential crises seem to multiply in character and scope. This thesis will explore the history of this problem and its recent implications. It will argue the need for a comprehensive, operational framework, codified in law, which defines the various alternative uses of all emergency services, both civilian and military, and is applicable to “all hazards.” I will attempt to provide a blue-print for what such a framework should look like.