The Three Body Problem and the Runge-Lenz Equivalent Constant of the Motion

The Runge-Lenz equivalent for the Hydrogen Molecular Cation (and the Earth, Moon and Sun) problem is obtained

Integrals of motion for one-dimensional Anderson localized systems

Anderson localization is known to be inevitable in one-dimension for generic disordered models. Since localization leads to Poissonian energy level statistics, we ask if localized systems possess `additional' integrals of motion as well, so as to enhance the analogy with quantum integrable systems. We answer this in the affirmative in the present work. We construct a set of nontrivial integrals of motion for Anderson localized models, in terms of the original creation and annihilation operators. These are found as a power series in the hopping parameter. The recently found Type-1 Hamiltonians, which are known to be quantum integrable in a precise sense, motivate our construction. We note that these models can be viewed as disordered electron models with infinite-range hopping, where a similar series truncates at the linear order. We show that despite the infinite range hopping, all states but one are localized. We also study the conservation laws for the disorder free Aubry-Andre model, where the states are either localized or extended, depending on the strength of a coupling constant. We formulate a specific procedure for averaging over disorder, in order to examine the convergence of the power series. Using this procedure in the Aubry-Andre model, we show that integrals of motion given by our construction are well-defined in localized phase, but not so in the extended phase. Finally, we also obtain the integrals of motion for a model with interactions to lowest order in the interaction.

Calibration of the spring constant of cantilevers of arbitrary shape using the phase signal in an atomic force microscope.

The measurement of cantilever parameters is an essential part of performing a calibrated measurement with an atomic force microscope (AFM). The thermal motion method is a widely used technique for calibrating the spring constant of an AFM cantilever, which can be applied to non-rectangular cantilevers. Given the trend towards high frequency scanning, calibration of non-rectangular cantilevers is of increasing importance. This paper presents two results relevant to cantilever calibration via the thermal motion method. We demonstrate the possibility of using the AFM's phase signal to acquire the thermal motion. This avoids the challenges associated with connecting the raw photodiode signal to a separate spectrum analyser. We also describe how numerical calculations may be used to calculate the parameters needed in a thermal motion calibration of a non-rectangular cantilever. Only accurate knowledge of the relative size of the in-plane dimensions of the cantilever is needed in this computation. We use this pair of results in the calibration of a variety of rectangular and non-rectangular cantilevers. We observe an average difference between the Sader and thermal motion values of cantilever stiffness of 10%.

Extraction and Clustering of Motion Trajectories in Video

A system is described that tracks moving objects in a video dataset so as to extract a representation of the objects' 3D trajectories. The system then finds hierarchical clusters of similar trajectories in the video dataset. Objects' motion trajectories are extracted via an EKF formulation that provides each object's 3D trajectory up to a constant factor. To increase accuracy when occlusions occur, multiple tracking hypotheses are followed. For trajectory-based clustering and retrieval, a modified version of edit distance, called longest common subsequence (LCSS) is employed. Similarities are computed between projections of trajectories on coordinate axes. Trajectories are grouped based, using an agglomerative clustering algorithm. To check the validity of the approach, experiments using real data were performed.

Improved simultaneous computation of motion detection and optical flow for object tracking

Object tracking systems require accurate segmentation of the objects from the background for effective tracking. Motion segmentation or optical flow can be used to segment incoming images. Whilst optical flow allows multiple moving targets to be separated based on their individual velocities, optical flow techniques are prone to errors caused by changing lighting and occlusions, both common in a surveillance environment. Motion segmentation techniques are more robust to fluctuating lighting and occlusions, but don't provide information on the direction of the motion. In this paper we propose a combined motion segmentation/optical flow algorithm for use in object tracking. The proposed algorithm uses the motion segmentation results to inform the optical flow calculations and ensure that optical flow is only calculated in regions of motion, and improve the performance of the optical flow around the edge of moving objects. Optical flow is calculated at pixel resolution and tracking of flow vectors is employed to improve performance and detect discontinuities, which can indicate the location of overlaps between objects. The algorithm is evaluated by attempting to extract a moving target within the flow images, given expected horizontal and vertical movement (i.e. the algorithms intended use for object tracking). Results show that the proposed algorithm outperforms other widely used optical flow techniques for this surveillance application.

The silk road project : dance and embodiment in the age of motion capture

The Silk Road Project was a practice-based research project investigating the potential of motion capture technology to inform perceptions of embodiment in dance performance. The project created a multi-disciplinary collaborative performance event using dance performance and real-time motion capture at Deakin University’s Deakin Motion Lab. Several new technological advances in producing real-time motion capture performance were produced, along with a performance event that examined the aesthetic interplay between a dancer’s movement and the precise mappings of its trajectories created by motion capture and real-time motion graphic visualisations.

A radiological method to determine the accuracy of motion capture marker placement on palpable anatomical landmarks through a shoe

The accuracy of marker placement on palpable surface anatomical landmarks is an important consideration in biomechanics. Although marker placement reliability has been studied in some depth, it remains unclear whether or not the markers are accurately positioned over the intended landmark in order to define the static position and orientation of the segment. A novel method using commonly available X-ray imaging was developed to identify the accuracy of markers placed on the shoe surface by palpating landmarks through the shoe. An anterior–posterior and lateral–medial X-ray was taken on 24 participants with a newly developed marker set applied to both the skin and shoe. The vector magnitude of both skin- and shoe-mounted markers from the anatomical landmark was calculated, as well as the mean marker offset between skin- and shoe-mounted markers. The accuracy of placing markers on the shoe relative to the skin-mounted markers, accounting for shoe thickness, was less than 5mm for all markers studied. Further, when using the developed guidelines provided in this study, the method was deemed reliable (Intra-rater ICCs¼0.50–0.92). In conclusion, the method proposed here can reliably assess marker placement accuracy on the shoe surface relative to chosen anatomical landmarks beneath the skin.

Understanding the relationships between the calf muscle pump, ankle range of motion and healing for adults with venous leg ulcers: a review of the literature

Exercise offers the potential to improve circulation, wound healing outcomes, and functional and emotional wellbeing for adults experiencing venous leg ulceration. Individuals with chronic leg ulcers typically have multiple comorbidities such as arthritis, asthma, chronic obstructive airways disease, cardiac disease or neuromuscular disorders, which would also benefit from regular exercise. The aim of this review is to highlight the relationships between the calf muscle pump and venous return and range of ankle motion for adults with venous leg ulcers. The effect of exercise will also be considered in relation to the healing rates for adults experiencing venous leg ulceration. The findings suggest there is evidence that exercises which engage the calf muscle pump improve venous return. Ankle range of motion, which is crucial for complete activation of the calf muscle pump, can also be improved with simple, home-based exercise programs. However, observational studies still report that venous leg ulcer patients are less physically active than age-matched controls. Therefore, the behavioural reasons for not exercising must be considered. Only two studies, both underpowered, have assessed the effect of exercise on the healing rates of venous leg ulcers. In conclusion, exercise is feasible with this patient population. However, future studies with larger sample sizes are needed to provide stronger evidence to support the therapeutic benefit of exercise as an adjunct therapy in wound care.

The effect of warm-up intensity on range of motion and anaerobic performance

Although there is a paucity of scientific support for the benefits of warm-up, athletes commonly warm up prior to activity with the intention of improving performance and reducing the incidence of injuries. The purpose of this study was to examine the role of warm-up intensity on both range of motion (ROM) and anaerobic performance. Nine males (age = 21.7 +/- 1.6 years, height = 1.77 +/- 0.04 m, weight = 80.2 +/- 6.8 kg, and VO2max = 60.4 +/- 5.4 ml/kg/min) completed four trials. Each trial consisted of hip, knee, and ankle ROM evaluation using an electronic inclinometer and an anaerobic capacity test on the treadmill (time to fatigue at 13 km/hr and 20% grade). Subjects underwent no warm-up or a warm-up of 15 minutes running at 60, 70 or 80% VO2max followed by a series of lower limb stretches. Intensity of warm-up had little effect on ROM, since ankle dorsiflexion and hip extension significantly increased in all warm-up conditions, hip flexion significantly increased only after the 80% VO2max warm-up, and knee flexion did not change after any warm-up. Heart rate and body temperature were significantly increased (p < 0.05) prior to anaerobic performance for each of the warm-up conditions, but anaerobic performance improved significantly only after warm-up at 60% VO2max (10%) and 70% VO2max (13%). A 15-minute warm-up at an intensity of 60-70% VO2max is therefore recommended to improve ROM and enhance subsequent anaerobic performance.

Learning hierarchical prototypes of motion time series for interactive systems

Abstract. For interactive systems, recognition, reproduction, and generalization of observed motion data are crucial for successful interaction. In this paper, we present a novel method for analysis of motion data that we refer to as K-OMM-trees. K-OMM-trees combine Ordered Means Models (OMMs) a model-based machine learning approach for time series with an hierarchical analysis technique for very large data sets, the K-tree algorithm. The proposed K-OMM-trees enable unsupervised prototype extraction of motion time series data with hierarchical data representation. After introducing the algorithmic details, we apply the proposed method to a gesture data set that includes substantial inter-class variations. Results from our studies show that K-OMM-trees are able to substantially increase the recognition performance and to learn an inherent data hierarchy with meaningful gesture abstractions.

A retrospective cohort investigation of active range of motion within one week of open reduction and internal fixation of distal radius fractures

Distal radius fractures stabilized by open reduction internal fixation (ORIF) have become increasingly common. There is currently no consensus on the optimal time to commence range of motion (ROM) exercises post-ORIF. A retrospective cohort review was conducted over a five-year period to compare wrist and forearm range of motion outcomes and number of therapy sessions between patients who commenced active ROM exercises within the first seven days and from day eight onward following ORIF of distal radius fractures. One hundred and twenty-one patient cases were identified. Clinical data, active ROM at initial and discharge therapy assessments, fracture type, surgical approaches, and number of therapy sessions attended were recorded. One hundred and seven (88.4%) cases had complete datasets. The early active ROM group (n = 37) commenced ROM a mean (SD) of 4.27 (1.8) days post-ORIF. The comparator group (n = 70) commenced ROM exercises 24.3 (13.6) days post-ORIF. No significant differences were identified between groups in ROM at initial or discharge assessments, or therapy sessions attended. The results from this study indicate that patients who commenced active ROM exercises an average of 24 days after surgery achieved comparable ROM outcomes with similar number of therapy sessions to those who commenced ROM exercises within the first week.

Port-Hamiltonian theory of motion control for marine craft

Port-Hamiltonian Systems (PHS) have a particular form that incorporates explicitly a function of the total energy in the system (energy function) and also other functions that describe structure of the system in terms of energy distribution. For PHS, the product of the input and output variables gives the rate of energy change. This type of systems have the property that under certain conditions on the energy function, the system is passive; and thus, stable. Therefore, if one can design a controller such that the closed-loop system retains - or takes - a PHS form, such closed-loop system will inherit the properties of passivity and stability. In this paper, the classical model of marine craft is put into a PHS form. It is shown that models used for positioning control do not have a PHS form due to a kinematic transformation, but a control design can be done such that the closed-loop system takes a PHS form. It is further shown how integral action can be added and how the PHS-form can be exploited to provide a procedure for control design that ensures passivity and thus stability.

Numerical investigation of motion and deformation of a single red blood cell in a stenosed capillary

It is generally assumed that influence of the red blood cells (RBCs) is predominant in blood rheology. The healthy RBCs are highly deformable and can thus easily squeeze through the smallest capillaries having internal diameter less than their characteristic size. On the other hand, RBCs infected by malaria or other diseases are stiffer and so less deformable. Thus it is harder for them to flow through the smallest capillaries. Therefore, it is very important to critically and realistically investigate the mechanical behavior of both healthy and infected RBCs which is a current gap in knowledge. The motion and the steady state deformed shape of the RBCs depend on many factors, such as the geometrical parameters of the capillary through which blood flows, the membrane bending stiffness and the mean velocity of the blood flow. In this study, motion and deformation of a single two-dimensional RBC in a stenosed capillary is explored by using smoothed particle hydrodynamics (SPH) method. An elastic spring network is used to model the RBC membrane, while the RBC's inside fluid and outside fluid are treated as SPH particles. The effect of RBC's membrane stiffness (kb), inlet pressure (P) and geometrical parameters of the capillary on the motion and deformation of the RBC is studied. The deformation index, RBC's mean velocity and the cell membrane energy are analyzed when the cell passes through the stenosed capillary. The simulation results demonstrate that the kb, P and the geometrical parameters of the capillary have a significant impact on the RBCs' motion and deformation in the stenosed section.