We investigate the switching dynamics of multistable nematic liquid crystal devices. In particular, we identify a remarkably simple two-dimensional device which exploits hybrid alignment at the surfaces to yield a bistable response. We also consider a three-dimensional tristable nematic device with patterned anchoring, recently implemented in practice, and discuss how the director and disclination patterns change during switching.

We consider the Dirichlet eigenvalue problem, (the eigenfunction) and ? > 0 (the eigen value), ? is an arbitrary domain in RN with finite measure, 1 < p < ?, 1 < q < p*, p* = Np/(N - p) if 1 < p < N and p* = ? if p >= N. We study several existence and uniqueness results as well as some properties of the solutions. Moreover, we indicate how to extend to the general case some proofs known in the classical case p = q. © 2010 Texas State University - San Marcos.

It is observed in vitro and in vivo that when two populations of different types of cells come near to each other, the rate of proliferation of most cells decreases. This phenomenon is often called contact inhibition of growth between two cells. In this paper, we consider a simplified 1-dimensional PDE-model for normal and abnormal cells, motivated by a paper of Chaplain, Graziano and Preziosi. We show that if the two populations are initially segregated, then they remain segregated due to the contact inhibition mechanism. In this case the system of PDE's can be formulated as a free boundary problem.

Many real life problems can he reduced to the solution of a complex exponentials approximation problem which is usually ill-posed. Recently a new transform for solving this problem, formulated as a specific moments problem in the plane, has been proposed in a theoretical framework. In this work some computational issues are addressed to make this new tool useful in practice. An algorithm is developed and used to solve a Nuclear Magnetic Resonance spectrometry problem, two time series interpolation and extrapolation problems and a shape from moments problem.

A spinning particle in the Schwarzschild spacetime deviates from geodesic behavior because of its spin. A spinless particle also deviates from geodesic behavior when a test radiation field is superimposed on the Schwarzschild background: in fact the interaction with the radiation field, i.e., the absorption and re-emission of radiation, leads to a friction-like drag force responsible for the well known effect which exists already in Newtonian gravity, the Poynting-Robertson effect. Here the Poynting-Robertson effect is extended to the case of spinning particles by modifying the Mathisson-Papapetrou model describing the motion of spinning test particles to account for the contribution of the radiation force. The resulting equations are numerically integrated and some typical orbits are shown in comparison with the spinless case. Furthermore, the interplay between spin and radiation forces is discussed by analyzing the deviation from circular geodesic motion on the equatorial plane when the contribution due to the radiation can also be treated as a small perturbation. Finally the estimate of the amount of radial variation from the geodesic radius is shown to be measurable in principle.

Most physical phenomena are described by time-dependent Hamiltonian systems with qualitative features that should be preserved by numerical integrators used for approximating their dynamics. The initial energy of the system together with the energy added or subtracted by the outside forces, represent a conserved quantity of the motion. For a class of time-dependent Hamiltonian systems [8] this invariant can be defined by means of an auxiliary function whose dynamics has to be integrated simultaneously with the system's equations. We propose splitting procedures featured by a SB3A property that allows to construct composition methods with a reduced number of determining order equations and to provide the same high accuracy for both the dynamics and the preservation of the invariant quantity.

Over the past decade there have been many investigations aimed at defining the role of scientists and research groups in their coauthorship networks. Starting from the assumptions of network analysis, in this work we propose an analytical definition of a collaboration potential between authors of scientific papers based on both coauthorships and content sharing. The collaboration potential can also be considered a useful tool to investigate the relationships between a single scientist and research groups, thus allowing for the identification of characteristic "types" of scientists (integrated, independent, etc.). We computed the collaboration potential for a set of authors belonging to research groups of an institute specialized in the field of Medical Genetics. The methods presented in the paper are rather general as they can be applied to compute a collaboration potential for a network of cooperating actors in every situation in which one can qualify the content of some activities and which of them are in common among the actors of the network.

We provide an asymptotic analysis of the optimal cost in a planar network model

We study the inverse problem of determining the conformational freedom of two protein domains from residual dipolar coupling (RDC) measurements. For each paramagnetic ion attached to one of the domains we obtain a magnetic susceptibility tensor ? from the RDC of couples of atoms of that domain, and a mean paramagnetic susceptibility tensor ? ̄ from the RDC of couples of atoms of the other domain. The latter is an integral average of rotations of ? which depends on the conformational freedom of the two domains. In this paper we consider the case when we have data from paramagnetic ions attached separately to each of the domains. We prove that in this case not all the elements of ? and ? ̄ are independent. We derive the mathematical equations for the compatibility of the measurements and show how these relations can be used in the presence of noisy data to determine a compatible set of ? and ? ̄ with an unconstrained minimization. If available, information about the shape of the noise can be included in the target function. We show that in this case the compatible set obtained has a reduced error with respect to the noisy data.

Magnetic tomography is an ill-posed and ill-conditioned inverse problem since, in general, the solution is non-unique and the measured magnetic field is affected by high noise. We use a joint sparsity constraint to regularize the magnetic inverse problem. This leads to a minimization problem whose solution can be approximated by an iterative thresholded Landweber algorithm. The algorithm is proved to be convergent and an error estimate is also given. Numerical tests on a bidimensional problem show that our algorithm outperforms Tikhonov regularization when the measurements are distorted by high noise.

This paper presents a novel approach for the extraction of the transients content of audio signals, usually represented as superposition of stationary, transient, and stochastic components. The proposed model exploits the predictable and peculiar time-scale behavior of transients by modeling them as superposition of suitable wavelet atoms. These latter allow to predict transients information even at scales where the tonal component is dominant. In this way it is possible to avoid, if required, the pre-analysis of the tonal component. Extensive experimental results show that the proposed model achieves good performances with a moderate computational effort and without any user's dependence.

This special issue collects papers which develop and update methodologies and results illustrated at the International Workshop MASCOT01--1st Meeting on Applied Scientific Computing and Tools-- Grid Generation, Approximated Solutions and Visualization, held in Rome, October 22-24, 2001 at the Istituto per le Applicazioni del Calcolo (IAC). The meeting was supported by IMACS, the International Association for Mathematics and Computers in Simulation and ISGG, the International Society of Grid Generation and co-sponsored by the Italian National Group of Scientific Computing (GNCS-- Gruppo Nazionale di Calcolo Scientifico) and the Italian Society for Applied and Industrial Mathematics (SIMAI--Societa' Italiana per la Matematica Applicata e Industriale). Publication of the MASCOT01 Proceedings followed the Workshop, and in this issue, extensions and new results are presented. MASCOT meetings are intended to become a forum to discuss a wide spectrum of topics concerning scientific computing as applied to the effective solution of complex application problems. Thus topics range from theoretical to application inquiries and results, and include investigation in approximation and interpolation, advances in numerical grid generation, development of effective solvers of partial differential equations (PDEs) and the design of user-friendly and effective software tools. Modern and innovative modeling and simulation environments combine a large amount of expertise to handle complex and multidisciplinary application problems.