Terms Of Absolute Coordinates Research Articles

Molecular dynamics simulation of simple polymer chain formation using divide and conquer algorithm based on the augmented Lagrangian method

This paper presents an efficient multibody methodology for the simulation of molecular dynamics of simple polymer chains. The algorithm is formulated in terms of absolute coordinates. The augmented Lagrangian method is incorporated into the divide and conquer framework giving new parallel, logarithmic order algorithm suitable for the simulation of general multibody system topologies. The approach is robust in case of potential rank deficiencies of the Jacobian matrices that embrace the group of systems involving redundant constraints, and which may repeatedly enter singular configurations. Series of nanosecond-long molecular dynamics simulations of simplified polymer chain models are performed to demonstrate the correctness of the methodology and investigate the structure formation of the system subjected to non-bonded (Lennard–Jones) and bonded (torsional) interactions. Conformational changes and dynamic properties of the polymer chains are studied under gradual cooling of the system. The simulation results show that some of the homopolymers collapse into well-formed helices. The fraction of the succeeded runs, in which defect-free helices are found, is a function of initial conditions, chain length, and cooling rate. The employed computational multibody approach appeared to be useful in molecular dynamics simulations implying potential for future research and further development in this field.

Virtual lifeline: Multimodal sensor data fusion for robust navigation in unknown environments

We present a novel, multimodal indoor navigation technique that combines pedestrian dead reckoning (PDR) with relative position information from wireless sensor nodes. It is motivated by emergency response scenarios where no fixed or pre-deployed global positioning infrastructure is available and where typical motion patterns defeat standard PDR systems. We use RF and ultrasound beacons to periodically re-align the PDR system and reduce the impact of incremental error accumulation. Unlike previous work on multimodal positioning, we allow the beacons to be dynamically deployed (dropped by the user) at previously unknown locations. A key contribution of this paper is to show that despite the fact that the beacon locations are not known (in terms of absolute coordinates), they significantly improve the performance of the system. This effect is especially relevant when a user re-traces (parts of) the path he or she had previously travelled or lingers and moves around in an irregular pattern at single locations for extended periods of time. Both situations are common and relevant for emergency response scenarios. We describe the system architecture, the fusion algorithms and provide an in depth evaluation in a large scale, realistic experiment.

Symbolic Formulation of Large-scale Open-loop Multibody Systems for Vibration Analysis Using Absolute Joint Coordinates

A novel symbolic formulation is presented to model dynamics of large-scale open-loop holonomic multibody systems, by using absolute joint coordinates and via matrix transformation, instead of solving constraint equations. The resulting minimal set of second-order linear ordinary differential equations (ODEs) can be used for linear vibration analysis and control directly. The ODEs are generated in three steps. Firstly, a set of linearized ODEs are formulated in terms of absolute coordinates without considering any constraint. Secondly, an overall transform matrix representing constraint topology for the entire constrained system is generated. Finally, matrices for a minimal set of ODEs for the open-loop holonomic multibody system are obtained via matrix transformation. The correctness and efficiency of the presented algorithm are verified by numerical experiments on various cases of holonomic multibody systems with different open-loop topologies, including chain topology and tree topology. It is indicated that the proposed method can significantly improve efficiency without losing computational accuracy.

Orbit determination and European Station Positioning from satellite laser ranging

Within the 1979–1982 time frame, at Delft University's Department of Aerospace Engineering some numerical experiments were performed by processing a limited number of multiday global tracking data arcs. Each arc consisted of laser ranging data acquired in the 1978–1980 period. These arcs were selected especially for their relative abundance of European observations of the satellites LAGEOS, Starlette, and GEOS 3. An evaluation of the orbit errors due to errors in the gravity models was performed both in terms of apparent range and timing biases of each pass over a tracking station and of orbit differences between solutions in which different gravity models were applied. In addition, from LAGEOS and Starlette tracking data, separate solutions were obtained for the positions of the European laser ranging stations at Kootwijk, Wettzell, Grasse, and Metsähovi. In spite of the use of the most accurate tailored gravity models available at the time, the results, both in terms of absolute coordinates and in baselines, often differ considerably from more recent solutions by other authors. It is hypothesized that intermittent data‐taking problems at some of the European stations are responsible for these differences. Their distorting effects are relatively strong because of the limited number of passes on which our solutions are based.