Using optimal control theory to identify network structures that foster synchrony

Network structures are known to influence a population’s propensity to synchronize. Previous attempts to identify synchrony promoting structures have focused on homogeneous populations. We use optimal control theory to construct networks that allow heterogeneous populations to maintain high levels of synchrony, explore the relationship between population heterogeneity and the structure of the optimal networks, and identify salient optimal network features that may enhance synchrony. In particular, we identify a new parameter, the average strength of neighbors, that may foster synchrony and observe that repulsion, in addition to attraction, can foster synchrony.     

Optimal control of a reflection boundary coefficient in an acoustic wave equation

We seek to optimally control a reflection boundary coefficient for an acoustic wave equation. The goal-quantified by an objective functional- is to drive the solution close to a target by adjusting this coefficient, which acts as a control. The problem is solved by finding the optimal control, which minimizes the objective functional. Then the optimal control is used as a an approximation for an inverse “ identification” problem.     

Machine failure forewarning via phase-space dissimilarity measures

We present a model-independent, data-driven approach to quantify dynamical changes in nonlinear, possibly chaotic, processes with application to machine failure forewarning. From time-windowed data sets, we use time-delay phase-space reconstruction to obtain a discrete form of the invariant distribution function on the attractor. Condition change in the system's dynamic is quantified by dissimilarity measures of the difference between the test case and baseline distribution functions. We analyze time-serial mechanical (vibration) power data from several large motor-driven systems with accelerated failures and seeded faults. The phase-space dissimilarity measures show a higher consistency and discriminating power than traditional statistical and nonlinear measures, which warrants their use for timely forewarning of equipment failure.     

Bayesian analysis of pentaquark signals from CLAS data

We examine the results of two measurements by the CLAS collaboration, one of which claimed evidence for a Theta(+) pentaquark, while the other found no such evidence. The unique feature of these two experiments was that they were performed with the same experimental setup. Using a Bayesian analysis, we find that the results of the two experiments are in fact compatible with each other, but that the first measurement did not contain sufficient information to determine unambiguously the existence of a Theta(+). Further, we suggest a means by which the existence of a new candidate particle can be tested in a rigorous manner.     

On the spectral decompositions of the linear transport operator with periodic boundary conditions

It is shown that the linear transport operator for a slab with periodic boundary conditions, or for infinite medium, can be analyzed within the Friedrichs' model of perturbation for non-selfadjoint operators. This leads to rephrasing Case's generalized eigenfunction expansion in terms of Hilbert space operators only.     

On the singular limit of a model transport semigroup

We consider the diffusion limit of a model transport equation on the torus or the whole space, as a scaling parameter ε (the mean free path), tends to zero. We show that, for arbitrary initial data $u_0(x,v)$\nopagenumbers\end , the solution converges in norm topology for each $t>0$\nopagenumbers\end , to the solution of a diffusion equation with initial data \def\d{{\rm d}}$u_D^0(x)=\int u_0(x,v)\,\d v$\nopagenumbers\end . The proof relies on Fourier analysis which diagonalizes the transport operator, a Dunford functional calculus and the analysis of the behaviour of the transport spectrum as ε tends to zero. Copyright © 2000 John Wiley & Sons, Ltd.