A computational geometric approach for an ensemble-based topological entropy calculation in two and three dimensions

From the stirring of dye in viscous fluids to the availability of essential nutrients spreading over the surface of a pond, nature is rife with examples of mixing in two-dimensional fluids. The long-time exponential growth rate of a thin filament of dye stretched by the fluid is a well-known proxy for the quality of mixing in two dimensions. This growth rate in turn gives a lower bound on the flow's topological entropy, a measure quantifying the complexity of chaotic dynamics. In the real-world study of mixing, topological entropy may be hard to compute; the velocity field may not be known or may be expensive to recover or approximate, thus limiting our knowledge of the governing system and underlying mechanics driving the mixing. Central to this study are two questions: \emph{How can stretching rates in two-dimensional planar flows best be computed using only trajectory data?}, and \emph{Can a method for computing stretching rates in higher dimensions from only trajectory data be developed?}. In this spirit, we introduce the Ensemble-based Topological Entropy Calculation (E-tec), a method to derive a lower-bound on topological entropy that requires only finite number of system trajectories, like those obtained from ocean drifters, and no detailed knowledge of the velocity field. E-tec is demonstrated to be computationally more efficient than other competing methods in two dimensions that accommodate trajectory data. This is accomplished by considering the evolution of a ``rubber band" wrapped around the data points and evolving with their trajectories. E-tec records the growth of this band as the collective motion of trajectories strike, deform, and stretch it. This exponential growth rate acts as a lower bound on the topological entropy. In this manuscript, I demonstrate convergence of E-tec's approximation with respect to both the number of trajectories (ensemble size) and the duration of trajectories in time. Driving the efficiency of E-tec in two dimensions is the use of computational geometry tools. Not only this, by computing stretching rates in this new computational geometry framework, I extend E-tec to three dimensions using two methods. First, I consider a two-dimensional rubber sheet stretched around a collection of points in a three-dimensional flow. Similar to the band-stretching component of two-dimensional E-tec, a three-dimensional triangulation is used to record the growth of the sheet as it is stretched and deformed by points evolving in time. Second, I calculate the growth rates of one-dimensional rubber strings as they are stretched by the edges of this dynamic, moving triangulation

Ensemble-based Topological Entropy Calculation (E-tec)

Topological entropy measures the number of distinguishable orbits in a dynamical system, thereby quantifying the complexity of chaotic dynamics. One approach to computing topological entropy in a two-dimensional space is to analyze the collective motion of an ensemble of system trajectories taking into account how trajectories "braid" around one another. In this spirit, we introduce the Ensemble-based Topological Entropy Calculation, or E-tec, a method to derive a lower-bound on topological entropy of two-dimensional systems by considering the evolution of a "rubber band" (piece-wise linear curve) wrapped around the data points and evolving with their trajectories. The topological entropy is bounded below by the exponential growth rate of this band. We use tools from computational geometry to track the evolution of the rubber band as data points strike and deform it. Because we maintain information about the configuration of trajectories with respect to one another, updating the band configuration is performed locally, which allows E-tec to be more computationally efficient than some competing methods. In this work, we validate and illustrate many features of E-tec on a chaotic lid-driven cavity flow. In particular, we demonstrate convergence of E-tec's approximation with respect to both the number of trajectories (ensemble size) and the duration of trajectories in time.Comment: 13 pages, 15 figure

New data structures to handle speculative parallelization at runtime

Producción CientíficaSoftware-based, thread-level speculation (TLS) is a software technique that optimistically executes in parallel loops whose fully-parallel semantics can not be guaranteed at compile time. Modern TLS libraries allow to handle arbitrary data structures speculatively. This desired feature comes at the high cost of local store and/or remote recovery times: The easier the local store, the harder the remote recovery. Unfortunately, both times are on the critical path of any TLS system. In this paper we propose a solution that performs local store in constant time, while recover values in a time that is in the order of T, being T the number of threads. As we will see, this solution, together with some additional improvements, makes the difference between slowdowns and noticeable speedups in the speculative parallelization of non-synthetic, pointer-based applications on a real system. Our experimental results show a gain of 3.58× to 28× with respect to the baseline system, and a relative efficiency of up to, on average, 65 % with respect to a TLS implementation specifically tailored to the benchmarks used.Castilla-Leon Regional Government (VA172A12-2); Ministerio de Industria, Spain (CENIT OCEANLIDER); MICINN (Spain) and the European Union FEDER (MOGECOPP project TIN2011-25639, CAPAP-H3 net- work TIN2010-12011-E, CAPAP-H4 network TIN2011-15734-E)

Modeling of ground excavation with the particle finite element method

The present work introduces a new application of the Particle Finite Element Method (PFEM) for the modeling of excavation problems. PFEM is presented as a very suitable tool for the treatment of excavation problem. The method gives solution for the analysis of all processes that derive from it. The method has a high versatility and a reasonable computational cost. The obtained results are really promising.Postprint (published version

A new methods of mobile object measurement by using radio frequency identification

In this study, the mobile robot conducts tag of RFID and the antennas’ reader was scattered at the indoor-outdoor environment, which represents the novelty of the study, as this has not been done in the previous studies. This protects the mobile robot from weight increase reduces the consumption of the battery. Moreover, mobile object increase demands an increase in cheap passive Radio Frequency Identification tags in the system of navigation. Techniques of Signal processing utilize both accompanied by the theories of electromagnetics in locating the robot’s position. Numerous antennas usage provides a breadth of comparisons. In this work, have been provide a new RFID tracking approach that can also be used for interior positioning. This technique employs RSS to gather the signal intensity of reference tags before they are used. The next step is to send a signal. Setting up Power Level ranges via reference tags uses strength as a setting parameter. Then, based on the intensity of the signal, you can determine how far away you are. Reference tags are used to match the signal intensity of track tags. Finally, when track tags are installed in indoor locations, they can be used to monitor the movement of people. It will use the arithmetic mean of the positions of surrounding reference tags to determine the location. Values. According to preliminary results from an experiment, our approach is more precise than the antenna system. Approximately 10 to 20 lines