Nung Kwan Yip

On Optimal Information Capture by Energy-Constrained Mobile Sensors

A mobile sensor is used to cover a number of points of interest (PoIs), where dynamic events appear and disappear according to the given random processes. The sensor, which is of sensing range r, visits the PoIs in a cyclic schedule and gains information about any event that falls within its range. We consider the temporal dimension of the sensing as given by a utility function, which specifies how much information is gained about an event as a function of the cumulative sensing or observation time. The quality of monitoring (QoM), i.e., the fraction of information captured about all events, depends on the speed of the sensor and has been analyzed in an earlier paper for different utility functions. The prior work, however, does not consider the energy of motion, which is an important constraint for mobile sensor coverage. In this paper, we analyze the expected Information captured Per unit of Energy consumption (IPE) as a function of the event type (in terms of the utility function), the event dynamics, and the speed of the mobile sensor. Our analysis uses a realistic energy model of motion, and it allows the sensor speed to be optimized for information capture. The case of multiple sensors will also be discussed. Extensive simulation results verify and illustrate the analytical results.

Optically Modulated Electrokinetic Manipulation and Concentration of Colloidal Particles near an Electrode Surface

We study a recently demonstrated AC electrokinetic technique for manipulation and concentration of colloidal particles on an electrode surface. The technique uses indium tin oxide (ITO)-based parallel-plate electrodes on which highly localized infrared (1064 nm) laser illumination is shone. We show that the highly localized laser illumination leads to a highly nonuniform heating of the electrode substrate, which in turn drives an electrothermal microvortex resulting in a rapid transport of particles toward the illuminated site. Hundreds of polystyrene particles, with diameters ranging from 2.0 to 0.1 microm, suspended in a low conductivity solution (2.0 mS/m) could be aggregated at selected locations on the electrode by activating the laser illumination at suitable AC frequencies. Subsequent deactivation of the laser illumination causes the particles to scatter, and we explore this dynamical behavior for 1.0 microm particles using Delaunay tessellations and high-speed videography. We establish that drag from the electrothermal microvortex acts against a repulsive force, which decreases with increasing AC frequency, to create stable particle clusters. Moreover, experimentally we show that this particle capturing technique can be characterized by a critical frequency: a frequency at which the captured colloidal particle cluster becomes unstable and particles are carried away into the bulk by the electrothermal microvortex. This critical frequency increases with decreasing particle diameter for similar particles. For 0.1 microm particles, comparison of aggregation at different AC frequencies is achieved by the comparison of fluorescent intensity profiles of the aggregations.

Pinning and De-Pinning Phenomena in Front Propagation in Heterogeneous Media

This paper investigates the pinning and de-pinning phenomena of some evolutionary partial differential equations which arise in the modelling of the propagation of phase boundaries in materials under the combined effects of an external driving force F and an underlying heterogeneous environment. The phenomenology is the existence of pinning states—stationary solutions—for small values of F, and the appearance of genuine motion whenF is above some threshold value. In the case of a periodic medium, we characterise quantitatively, near the transition regime, the scaling behaviour of the interface velocity as a function of F . The results are proved for a class of semilinear and reaction-diffusion equations.

Continuum Theory of Epitaxial Crystal Growth. I

We present various continuum limits to describe epitaxial thin film growth. We consider a hierarchy of models which can take into account the diffusion of terrace adatoms, attachment and detachment of edge adatoms, vapor phase diffusion and the effect of multiple species. The starting point is the Burton–Cabrera–Frank type step flow model. We have obtained partial differential equations in the form of a coupled system of diffusion equation for the adatom density and a Hamilton–Jacobi equation for the film height function. This is supplemented with appropriate boundary conditions at the continuum level to describe the growth at the peaks and valleys on the film. The results here can be used in a macroscopic description of thin film growth.

Quality of monitoring of stochastic events by periodic & proportional-share scheduling of sensor coverage

We analyze the quality of monitoring (QoM) of stochastic events by a periodic sensor which monitors a point of interest (PoI) for q time every p time. We show how the amount of information captured at a PoI is affected by the proportion q/p, the time interval p over which the proportion is achieved, the event type, and the stochastic event arrival dynamics and staying times. The periodic PoI sensor schedule happens in two broad contexts. In the case of static sensors, a sensor monitoring a PoI may be periodically turned off to conserve energy, thereby extending the lifetime of the monitoring until the sensor can be recharged or replaced. In the case of mobile sensors, a sensor may move between the PoIs in a repeating visit schedule. In this case, the PoIs may vary in importance, and the scheduling objective is to distribute the sensors coverage time in proportion to the importance levels of the PoIs. Based on our QoM analysis, we optimize a class of periodic mobile coverage schedules that can achieve such proportional sharing while maximizing the QoM of the total system.

Quality of monitoring of stochastic events by periodic and proportional-share scheduling of sensor coverage

We analyze the quality of monitoring (QoM) of stochastic events by a periodic sensor which monitors a point of interest (PoI) for q time every p time. We show how the amount of information captured at a PoI is affected by the proportion q/p, the time interval p over which the proportion is achieved, the event type in terms of its stochastic arrival dynamics and staying times and the utility function. The periodic PoI sensor schedule happens in two broad contexts. In the case of static sensors, a sensor monitoring a PoI may be periodically turned off to conserve energy, thereby extending the lifetime of the monitoring until the sensor can be recharged or replaced. In the case of mobile sensors, a sensor may move between the PoIs in a repeating visit schedule. In this case, the PoIs may vary in importance, and the scheduling objective is to distribute the sensors coverage time in proportion to the importance levels of the PoIs. Based on our QoM analysis, we optimize a class of periodic mobile coverage schedules that can achieve such proportional sharing while maximizing the QoM of the total system.

Pulsating Wave for Mean Curvature Flow in Inhomogeneous Medium

We prove the existence and uniqueness of pulsating waves for the motion by mean curvature of an n-dimensional hypersurface in an inhomogeneous medium, represented by a periodic forcing. The main difficulty is caused by the degeneracy of the equation and the fact the forcing is allowed to change sign. Under the assumption of weak inhomogeneity, we obtain uniform oscillation and gradient bounds so that the evolving surface can be written as a graph over a reference hyperplane. The existence of an effective speed of propagation is established for any normal direction. We further prove the Lipschitz continuity of the speed with respect to the normal and various stability properties of the pulsating wave. The results are related to the homogenisation of mean curvature flow with forcing.

Stochastic Steepest Descent Optimization of Multiple-Objective Mobile Sensor Coverage

We propose a steepest descent method to compute optimal control parameters for balancing between multiple performance objectives in stateless stochastic scheduling, wherein the scheduling decision is effected by a simple constant-time coin toss operation only. We apply our method to the scheduling of a mobile sensors coverage time among a set of points of interest (PoIs). The coverage algorithm is guided by a Markov chain, wherein the sensor at PoI i decides to go to the next PoI j with transition probability pij. We use steepest descent to compute the transition probabilities for optimal tradeoff among different performance goals with regard to the distributions of per-PoI coverage times and exposure times and the entropy and energy efficiency of sensor movement. For computational efficiency, we show how we can optimally adapt the step size in steepest descent to achieve fast convergence. However, we found that the structure of our problem is complex, because there may exist surprisingly many local optima in the solution space, causing basic steepest descent to easily get stuck at a local optimum. To solve the problem, we show how proper incorporation of noise in the search process can get us out of the local optima with high probability. We provide simulation results to verify the accuracy of our analysis and show that our method can converge to the globally optimal control parameters under different assigned weights to the performance goals and different initial parameters.

A Quantitative Description of Mesh Dependence for the Discretization of Singularly Perturbed Nonconvex Problems

We investigate the limiting description for a finite-difference approximation of a singularly perturbed Allen--Cahn type energy functional. The key issue is to understand the interaction between two small length-scales: the interfacial thickness

Optical Diffusometry Techniques and Applications in Biological Agent Detection

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