Parametric Resonance in Adiabatic Oscillators

We use the averaging method and Levinson’s fundamental theorem to study phenomenon of parametric resonance in some new equations from the class of adiabatic oscillators.     

Discovering implied constraints in precedence graphs with alternatives

During automated problem solving it may happen that some knowledge that is known at the user level is lost in the formal model. As this knowledge might be important for efficient problem solving, it seems useful to re-discover it in order to improve the efficiency of the solving procedure. This paper compares three methods for discovering certain implied constraints in the constraint models describing manufacturing (and other) processes with serial, parallel, and alternative operations. In particular, we focus on identifying equivalent nodes in the precedence graph with parallel and alternative branches. Equivalent nodes correspond to operations that either must be all simultaneously present or none of them can be present in the schedule. Such information is frequently known at the user level, but it is lost in the formal model. The paper shows that identifying equivalent nodes is an NP-hard problem in general, but it is tractable if the graph has a nested structure. As the nested structure is typical for real-life processes and workflows, we use the nested graphs to experimentally compare the proposed methods.     

Diamond-related materials as potential new media in separation science

Recent progress in the development of various diamond-related materials (DRMs) has induced a strong interest in their use as a stationary phase in various separation techniques. DRMs meet many requirements for use as a stationary phase in chromatography, including excellent mechanical and chemical stability, high thermal stability, low chemical reactivity of the surface, and biocompatibility. The general physicochemical properties of diamond and the preparation of different types of DRMs are reviewed, and an overview is provided of current and possible future applications in solid-phase extraction and various separation technologies.     

Complete classification of local conservation laws for generalized Cahn–Hilliard–Kuramoto–Sivashinsky equation

In this paper, we consider nonlinear multidimensional Cahn–Hilliard and Kuramoto–Sivashinsky equations that have many important applications in physics and chemistry, and a certain natural generalization of these two equations to which we refer to as the generalized Cahn–Hilliard–Kuramoto–Sivashinsky equation. For an arbitrary number of spatial independent variables, we present a complete list of cases when the latter equation admits nontrivial local conservation laws of any order, and for each of those cases, we give an explicit form of all the local conservation laws of all orders modulo trivial ones admitted by the equation under study. In particular, we show that the original Kuramoto–Sivashinsky equation admits no nontrivial local conservation laws, and find all nontrivial local conservation laws for the Cahn–Hilliard equation.