Heat kernel expansion in the covariant perturbation theory

Working within the framework of the covariant perturbation theory, we obtain the coincidence limit of the heat kernel of an elliptic second order differential operator that is applicable to a large class of quantum field theories. The basis of tensor invariants of the curvatures of a gravity and gauge field background, to the second order, is derived, and the form factors acting on them are obtained in two integral representations. The results are verified by the functional trace operation, by the short proper time (Schwinger–DeWitt) expansions, as well as by the computation of the Green function for the two-dimensional scalar field model.     

Modeling multiphase latex particle equilibrium morphology

Multiphase waterborne polymer particles provide advantages in more demanding applications and their performance depends on particle morphology. Currently, no general approach to predict the morphology of multiphase latex particles is available. In this work, a model based on Monte Carlo methods was developed for the prediction of equilibrium morphologies of multiphase waterborne systems, such as polymer‐polymer and polymer‐polymer‐inorganic hybrids. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 2579–2583, 2010     

Hybrid approach to the rational management of machine replacement

The paper analyzes a nonlinear integer-valued optimization problem that describes the optimal machine replacement under improving technology. The problem is extended into the classes of real-valued discrete-time optimization problems and continuous-time optimal control. The results include some qualitative properties of optimal management policies and the construction of an efficient numeric algorithm.     

Large Deviations for Random Trees

We consider large random trees under Gibbs distributions and prove a Large Deviation Principle (LDP) for the distribution of degrees of vertices of the tree. The LDP rate function is given explicitly. An immediate consequence is a Law of Large Numbers for the distribution of vertex degrees in a large random tree. Our motivation for this study comes from the analysis of RNA secondary structures.     

Oscillation criteria for second-order nonlinear differential equations with damping

For a second-order nonlinear differential equation with a damping term, we obtain new oscillation criteria without an assumption that has been required for related results reported in the literature over the last two decades. Two approaches refining the standard integral averaging technique suggested in the paper can be used to derive a variety of simpler oscillation theorems for different classes of nonlinear differential equations, and both sets of oscillation criteria established in the paper are of independent interest. Several examples are provided to illustrate the relevance of the new theorems.     

Decision Making Times in Mean-Field Dynamic Ising Model

We consider a dynamic mean-field ferromagnetic model in the low-temperature regime in the neighborhood of the zero magnetization state. We study the random time it takes for the system to make a decision, i.e., to exit the neighborhood of the unstable equilibrium and approach one of the two stable equilibrium points. We prove a limit theorem for the distribution of this random time in the thermodynamic limit.     

Multifrequency tapered plasmonic nanoantennas

We suggest a multifrequency Yagi–Uda-type nanoantenna loaded with an array of tapered plasmonic nanorods. The arrays of director nanorods can be used for the excitation of the nanoantenna by emitters matched spectrally with their resonant frequency and placed in their near-field region. An overlap of multifrequency operating bands of the nanoantenna provides novel opportunities for broadband operation, and the same nanoantenna architecture can be employed both as a transmitter and/or as a receiver, thus being useful for broadband wireless communication.