Heterocyclic reactive mesogens: synthesis,characterisation and mesomorphic behaviour

Novel heterocyclic and photopolymerizable liquid crystalline materials (reactive mesogens) with smectic phases have been synthesized and characterized. A selection of heterocyclic rings, such as benzothiazole, benzothiadiazole and pyrimidine, has been incorporated into the aromatic core to control the electrochemical/luminescence properties and the structural geometry. Particular emphasis is focused on structure–property relationships, in which the variation of molecular structure and its subsequent effect on the liquid crystalline transition temperatures have been investigated.     

Parallel computing in nonconvex programming

In this paper, we are concerned with the development of parallel algorithms for solving some classes of nonconvex optimization problems. We present an introductory survey of parallel algorithms that have been used to solve structured problems (partially separable, and large-scale block structured problems), and algorithms based on parallel local searches for solving general nonconvex problems. Indefinite quadratic programming posynomial optimization, and the general global concave minimization problem can be solved using these approaches. In addition, for the minimum concave cost network flow problem, we are going to present new parallel search algorithms for large-scale problems. Computational results of an efficient implementation on a multi-transputer system will be presented.     

Integer programming models for the multidimensional assignment problem with star costs

We consider a variant of the multidimensional assignment problem (MAP) with decomposable costs in which the resulting optimal assignment is described as a set of disjoint stars. This problem arises in the context of multi-sensor multi-target tracking problems, where a set of measurements, obtained from a collection of sensors, must be associated to a set of different targets. To solve this problem we study two different formulations. First, we introduce a continuous nonlinear program and its linearization, along with additional valid inequalities that improve the lower bounds. Second, we state the standard MAP formulation as a set partitioning problem, and solve it via branch and price. These approaches were put to test by solving instances ranging from tripartite to 20-partite graphs of 4 to 30 nodes per partition. Computational results show that our approaches are a viable option to solve this problem. A comparative study is presented.     

A stochastic multiscale model for electricity generation capacity expansion

Long-term planning for electric power systems, or capacity expansion, has traditionally been modeled using simplified models or heuristics to approximate the short-term dynamics. However, current trends such as increasing penetration of intermittent renewable generation and increased demand response requires a coupling of both the long and short term dynamics. We present an efficient method for coupling multiple temporal scales using the framework of singular perturbation theory for the control of Markov processes in continuous time. We show that the uncertainties that exist in many energy planning problems, in particular load demand uncertainty and uncertainties in generation availability, can be captured with a multiscale model. We then use a dimensionality reduction technique, which is valid if the scale separation present in the model is large enough, to derive a computationally tractable model. We show that both wind data and electricity demand data do exhibit sufficient scale separation. A numerical example using real data and a finite difference approximation of the Hamilton–Jacobi–Bellman equation is used to illustrate the proposed method. We compare the results of our approximate model with those of the exact model. We also show that the proposed approximation outperforms a commonly used heuristic used in capacity expansion models.     

Maximum lifetime connected coverage with two active-phase sensors

A sensor with two active phrases means that active mode has two phases, the full-active phase and the semi-active phase, which require different energy consumptions. A full-active sensor can sense data packets, transmit, receive, and relay the data packets. A semi-active sensor cannot sense data packets, but it can transmit, receive, and relay data packets. Given a set of targets and a set of sensors with two active phrases, find a sleep/active schedule of sensors to maximize the time period during which active sensors form a connected coverage set. In this paper, this problem is showed to have polynomial-time ${(7.875+\varepsilon)}$ -approximations for any ${\varepsilon >0 }$ when all targets and sensors lie in the Euclidean plane and all sensors have the same sensing radius R _s and the same communication radius R _c with R _c ≥ 2R _s .     

Iterative roots of multidimensional operators and applications to dynamical systems

Solutions φ(x) of the functional equation φ(φ(x)) = f (x) are called iterative roots of the given function f (x). They are of interest in dynamical systems, chaos and complexity theory and also in the modeling of certain industrial and financial processes. The problem of computing this “square root” of a function or operator remains a hard task. While the theory of functional equations provides some insight for real and complex valued functions, iterative roots of nonlinear mappings from \({\mathbb{R}^n}\) to \({\mathbb{R}^n}\) are less studied from a theoretical and computational point of view. Here we prove existence of iterative roots of a certain class of monotone mappings in \({\mathbb{R}^n}\) spaces and demonstrate how a method based on neural networks can find solutions to some examples that arise from simple physical dynamical systems.