Comments on ‘‘Modeling fractional stochastic systems as non-random fractional dynamics driven Brownian motions

Applied Mathematical Modelling, Vol.33

HSU-Robbins and Spitzer's theorems for the variations of fractional Brownian motion

Using recent results on the behavior of multiple Wiener-Itô integrals based on Stein's method, we prove Hsu-Robbins and Spitzer's theorems for sequences of correlated random variables related to the increments of the fractional Brownian motion.

Brownian motion of spiral waves driven by spatiotemporal structured noise

Spiral chemical waves subjected to a spatiotemporal random excitability are experimentally and numerically investigated in relation to the light-sensitive Belousov-Zhabotinsky reaction. Brownian motion is identified and characterized by an effective diffusion coefficient which shows a rather complex dependence on the time and length scales of the noise relative to those of the spiral. A kinematically based model is proposed whose results are in good qualitative agreement with experiments and numerics.

An analytical approach to sorting in periodic and random potentials

There has been a recent revolution in the ability to manipulate micrometer-sized objects on surfaces patterned by traps or obstacles of controllable configurations and shapes. One application of this technology is to separate particles driven across such a surface by an external force according to some particle characteristic such as size or index of refraction. The surface features cause the trajectories of particles driven across the surface to deviate from the direction of the force by an amount that depends on the particular characteristic, thus leading to sorting. While models of this behavior have provided a good understanding of these observations, the solutions have so far been primarily numerical. In this paper we provide analytic predictions for the dependence of the angle between the direction of motion and the external force on a number of model parameters for periodic as well as random surfaces. We test these predictions against exact numerical simulations.

Coarsening of solid-liquid mixtures in a random acceleration field

The effects of flow induced by a random acceleration field (g-jitter) are considered in two related situations that are of interest for microgravity fluid experiments: the random motion of isolated buoyant particles, and diffusion driven coarsening of a solid-liquid mixture. We start by analyzing in detail actual accelerometer data gathered during a recent microgravity mission, and obtain the values of the parameters defining a previously introduced stochastic model of this acceleration field. The diffusive motion of a single solid particle suspended in an incompressible fluid that is subjected to such random accelerations is considered, and mean squared velocities and effective diffusion coefficients are explicitly given. We next study the flow induced by an ensemble of such particles, and show the existence of a hydrodynamically induced attraction between pairs of particles at distances large compared with their radii, and repulsion at short distances. Finally, a mean field analysis is used to estimate the effect of g-jitter on diffusion controlled coarsening of a solid-liquid mixture. Corrections to classical coarsening rates due to the induced fluid motion are calculated, and estimates are given for coarsening of Sn-rich particles in a Sn-Pb eutectic fluid, an experiment to be conducted in microgravity in the near future.

Generalization of the persistent random walk to dimensions greater than 1

We propose a generalization of the persistent random walk for dimensions greater than 1. Based on a cubic lattice, the model is suitable for an arbitrary dimension d. We study the continuum limit and obtain the equation satisfied by the probability density function for the position of the random walker. An exact solution is obtained for the projected motion along an axis. This solution, which is written in terms of the free-space solution of the one-dimensional telegraphers equation, may open a new way to address the problem of light propagation through thin slabs.

Iowa in Motion, Planning Ahead State Transportation Plan, May 8, 2012

According to 23 CFR § 450.214(a), “The State shall develop a long-range statewide transportation plan, with a minimum 20-year forecast period at the time of adoption, that provides for the development and implementation of the multimodal transportation system for the State.” The state transportation plan (Plan) is a document that will address this requirement and serve as a transportation investment guide between now and 2040. Iowa’s most recent plan was developed by the Iowa Department of Transportation and adopted in 1997 through a planning process called Iowa in Motion. Much of Iowa in Motion has been implemented and this Plan, "Iowa in Motion – Planning Ahead," will build on the success of its predecessor. The Plan projects the demand for transportation infrastructure and services to 2040 based on consideration of social and economic changes likely to occur during this time. Iowa’s economy and the need to meet the challenges of the future will continue to place pressure on the transportation system. With this in mind, the Plan will provide direction for each transportation mode, and will support a renewed emphasis on efficient investment and prudent, responsible management of our existing transportation system. In recent years, the Iowa DOT has branded this philosophy as stewardship. As Iowa changes and the transportation system evolves, one constant will be that the safe and efficient movement of Iowans and our products is essential for stable growth in Iowa’s economy. Iowa’s extensive multimodal and multijurisdictional transportation system is a critical component of economic development and job creation throughout the state.

Noise-induced Brownian motion of spiral waves

We study the erratic displacement of spiral waves forced to move in a medium with random spatiotemporal excitability. Analytical work and numerical simulations are performed in relation to a kinematic scheme, assumed to describe the autowave dynamics for weakly excitable systems. Under such an approach, the Brownian character of this motion is proved and the corresponding dispersion coefficient is evaluated. This quantity shows a nontrivial dependence on the temporal and spatial correlation parameters of the external fluctuations. In particular, a resonantlike behavior is neatly evidenced in terms of the noise correlation time for the particular situation of spatially uniform fluctuations. Actually, this case turns out to be, to a large extent, exactly solvable, whereas a pair of dispersion mechanisms are discussed qualitatively and quantitatively to explain the results for the more general scenario of spatiotemporal disorder.

Stochastic differential equations with random coefficients

In this paper we establish the existence and uniqueness of a solution for different types of stochastic differential equation with random initial conditions and random coefficients. The stochastic integral is interpreted as a generalized Stratonovich integral, and the techniques used to derive these results are mainly based on the path properties of the Brownian motion, and the definition of the Stratonovich integral.

Autonomous Measurements of Bridge Pier and Abutment Scour using Motion-Sensing Radio Transmitters, TR-595, 2010

Two portable Radio Frequency IDentification (RFID) systems (made by Texas Instruments and HiTAG) were developed and tested for bridge scour monitoring by the Department of Civil and Environmental Engineering at the University of Iowa (UI). Both systems consist of three similar components: 1) a passive cylindrical transponder of 2.2 cm in length (derived from transmitter/responder); 2) a low frequency reader (~134.2 kHz frequency); and 3) an antenna (of rectangular or hexagonal loop). The Texas Instruments system can only read one smart particle per time, while the HiTAG system was successfully modified here at UI by adding the anti-collision feature. The HiTAG system was equipped with four antennas and could simultaneously detect 1,000s of smart particles located in a close proximity. A computer code was written in C++ at the UI for the HiTAG system to allow simultaneous, multiple readouts of smart particles under different flow conditions. The code is written for the Windows XP operational system which has a user-friendly windows interface that provides detailed information regarding the smart particle that includes: identification number, location (orientation in x,y,z), and the instance the particle was detected.. These systems were examined within the context of this innovative research in order to identify the best suited RFID system for performing autonomous bridge scour monitoring. A comprehensive laboratory study that included 142 experimental runs and limited field testing was performed to test the code and determine the performance of each system in terms of transponder orientation, transponder housing material, maximum antenna-transponder detection distance, minimum inter-particle distance and antenna sweep angle. The two RFID systems capabilities to predict scour depth were also examined using pier models. The findings can be summarized as follows: 1) The first system (Texas Instruments) read one smart particle per time, and its effective read range was about 3ft (~1m). The second system (HiTAG) had similar detection ranges but permitted the addition of an anti-collision system to facilitate the simultaneous identification of multiple smart particles (transponders placed into marbles). Therefore, it was sought that the HiTAG system, with the anti-collision feature (or a system with similar features), would be preferable when compared to a single-read-out system for bridge scour monitoring, as the former could provide repetitive readings at multiple locations, which could help in predicting the scour-hole bathymetry along with maximum scour depth. 2) The HiTAG system provided reliable measures of the scour depth (z-direction) and the locations of the smart particles on the x-y plane within a distance of about 3ft (~1m) from the 4 antennas. A Multiplexer HTM4-I allowed the simultaneous use of four antennas for the HiTAG system. The four Hexagonal Loop antennas permitted the complete identification of the smart particles in an x, y, z orthogonal system as function of time. The HiTAG system can be also used to measure the rate of sediment movement (in kg/s or tones/hr). 3) The maximum detection distance of the antenna did not change significantly for the buried particles compared to the particles tested in the air. Thus, the low frequency RFID systems (~134.2 kHz) are appropriate for monitoring bridge scour because their waves can penetrate water and sand bodies without significant loss of their signal strength. 4) The pier model experiments in a flume with first RFID system showed that the system was able to successfully predict the maximum scour depth when the system was used with a single particle in the vicinity of pier model where scour-hole was expected. The pier model experiments with the second RFID system, performed in a sandbox, showed that system was able to successfully predict the maximum scour depth when two scour balls were used in the vicinity of the pier model where scour-hole was developed. 5) The preliminary field experiments with the second RFID system, at the Raccoon River, IA near the Railroad Bridge (located upstream of 360th street Bridge, near Booneville), showed that the RFID technology is transferable to the field. A practical method would be developed for facilitating the placement of the smart particles within the river bed. This method needs to be straightforward for the Department of Transportation (DOT) and county road working crews so it can be easily implemented at different locations. 6) Since the inception of this project, further research showed that there is significant progress in RFID technology. This includes the availability of waterproof RFID systems with passive or active transponders of detection ranges up to 60 ft (~20 m) within the water–sediment column. These systems do have anti-collision and can facilitate up to 8 powerful antennas which can significantly increase the detection range. Such systems need to be further considered and modified for performing automatic bridge scour monitoring. The knowledge gained from the two systems, including the software, needs to be adapted to the new systems.

Motion estimation using higher-order statistics

The objective of this paper is to introduce a fourth-order cost function of the displaced frame difference (DFD) capable of estimatingmotion even for small regions or blocks. Using higher than second-orderstatistics is appropriate in case the image sequence is severely corruptedby additive Gaussian noise. Some results are presented and compared to those obtained from the mean kurtosis and the mean square error of the DFD.

Vesicle motion during sustained exocytosis in chromaffin cells

Chromaffin cells release catecholamines by exocytosis, a process that includes vesicle docking, priming and fusion. Although all these steps have been intensively studied, some aspects of their mechanisms, particularly those regarding vesicle transport to the active sites situated at the membrane, are still unclear. In this work, we show that it is possible to extract information on vesicle motion in Chromaffin cells from the combination of Langevin simulations and amperometric measurements. We developed a numerical model based on Langevin simulations of vesicle motion towards the cell membrane and on the statistical analysis of vesicle arrival times. We also performed amperometric experiments in bovine-adrenal Chromaffin cells under Ba2+ stimulation to capture neurotransmitter releases during sustained exocytosis. In the sustained phase, each amperometric peak can be related to a single release from a new vesicle arriving at the active site. The amperometric signal can then be mapped into a spike-series of release events. We normalized the spike-series resulting from the current peaks using a time-rescaling transformation, thus making signals coming from different cells comparable. We discuss why the obtained spike-series may contain information about the motion of all vesicles leading to release of catecholamines. We show that the release statistics in our experiments considerably deviate from Poisson processes. Moreover, the interspike-time probability is reasonably well described by two-parameter gamma distributions. In order to interpret this result we computed the vesicles’ arrival statistics from our Langevin simulations. As expected, assuming purely diffusive vesicle motion we obtain Poisson statistics. However, if we assume that all vesicles are guided toward the membrane by an attractive harmonic potential, simulations also lead to gamma distributions of the interspike-time probability, in remarkably good agreement with experiment. We also show that including the fusion-time statistics in our model does not produce any significant changes on the results. These findings indicate that the motion of the whole ensemble of vesicles towards the membrane is directed and reflected in the amperometric signals. Our results confirm the conclusions of previous imaging studies performed on single vesicles that vesicles’ motion underneath plasma membranes is not purely random, but biased towards the membrane.

Branching random motions, nonlinear hyperbolic systems and traveling waves

A branching random motion on a line, with abrupt changes of direction, is studied. The branching mechanism, being independient of random motion, and intensities of reverses are defined by a particle's current direction. A soluton of a certain hyperbolic system of coupled non-linear equations (Kolmogorov type backward equation) have a so-called McKean representation via such processes. Commonly this system possesses traveling-wave solutions. The convergence of solutions with Heaviside terminal data to the travelling waves is discussed.This Paper realizes the McKean programme for the Kolmogorov-Petrovskii-Piskunov equation in this case. The Feynman-Kac formula plays a key role.

Perceived spatial displacement of motion-defined contours in peripheral vision

The perceived displacement of motion-defined contours in peripheral vision was examined in four experiments. In Experiment 1, in line with Ramachandran and Anstis' finding [Ramachandran, V. S., & Anstis, S. M. (1990). Illusory displacement of equiluminous kinetic edges. Perception, 19, 611-616], the border between a field of drifting dots and a static dot pattern was apparently displaced in the same direction as the movement of the dots. When a uniform dark area was substituted for the static dots, a similar displacement was found, but this was smaller and statistically insignificant. In Experiment 2, the border between two fields of dots moving in opposite directions was displaced in the direction of motion of the dots in the more eccentric field, so that the location of a boundary defined by a diverging pattern is perceived as more eccentric, and that defined by a converging as less eccentric. Two explanations for this effect (that the displacement reflects a greater weight given to the more eccentric motion, or that the region containing stronger centripetal motion components expands perceptually into that containing centrifugal motion) were tested in Experiment 3, by varying the velocity of the more eccentric region. The results favoured the explanation based on the expansion of an area in centripetal motion. Experiment 4 showed that the difference in perceived location was unlikely to be due to differences in the discriminability of contours in diverging and converging pattems, and confirmed that this effect is due to a difference between centripetal and centrifugal motion rather than motion components in other directions. Our result provides new evidence for a bias towards centripetal motion in human vision, and suggests that the direction of motion-induced displacement of edges is not always in the direction of an adjacent moving pattern. (C) 2008 Elsevier Ltd. All rights reserved.

A search for invariant relative satellite motion

This report presents the canonical Hamiltonian formulation of relative satellite motion. The unperturbed Hamiltonian model is shown to be equivalent to the well known Hill-Clohessy-Wilshire (HCW) linear formulation. The in°uence of perturbations of the nonlinear Gravitational potential and the oblateness of the Earth; J2 perturbations are also modelled within the Hamiltonian formulation. The modelling incorporates eccentricity of the reference orbit. The corresponding Hamiltonian vector ¯elds are computed and implemented in Simulink. A numerical method is presented aimed at locating periodic or quasi-periodic relative satellite motion. The numerical method outlined in this paper is applied to the Hamiltonian system. Although the orbits considered here are weakly unstable at best, in the case of eccentricity only, the method ¯nds exact periodic orbits. When other perturbations such as nonlinear gravitational terms are added, drift is signicantly reduced and in the case of the J2 perturbation with and without the nonlinear gravitational potential term, bounded quasi-periodic solutions are found. Advantages of using Newton's method to search for periodic or quasi-periodic relative satellite motion include simplicity of implementation, repeatability of solutions due to its non-random nature, and fast convergence. Given that the use of bounded or drifting trajectories as control references carries practical di±culties over long-term missions, Principal Component Analysis (PCA) is applied to the quasi-periodic or slowly drifting trajectories to help provide a closed reference trajectory for the implementation of closed loop control. In order to evaluate the e®ect of the quality of the model used to generate the periodic reference trajectory, a study involving closed loop control of a simulated master/follower formation was performed. 2 The results of the closed loop control study indicate that the quality of the model employed for generating the reference trajectory used for control purposes has an important in°uence on the resulting amount of fuel required to track the reference trajectory. The model used to generate LQR controller gains also has an e®ect on the e±ciency of the controller.