Analysis of a particle method for the one‐dimensional Vlasov‐Maxwell system

In this article we present a particle method for solving numerically the one‐dimensional Vlasov‐Maxwell equations. This method is based on the formulation by characteristics. We perform the error analysis and we investigate the properties of this scheme. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009     

Regularity Properties of the Degenerate Monge-Amp`ere Equations on Compact K¨ahler Manifolds

The author establishes a result concerning the regularity properties of the degenerate complex Monge-Ampère equations on compact Kǎhler manifolds.     

Riemannian manifolds carrying a pair of skew symmetric conformal vector fields

We deal with a Riemannian manifoldM carrying a pair of skew symmetric conformal vector fields (X, Y). The existence of such a pairing is determined by an exterior differential system in involution (in the sense of Cartan). In this case,M is foliated by 3-dimensional totally geodesic submanifolds. Additional geometric properties are proved.     

The effect of silica–alumina catalysts on degradation of polyolefins by a continuous flow reactor

Catalytic degradation of polyolefins was performed in a continuous flow reactor that allows the study of the degradation processes at steady state, characterized by constant values of reaction parameters and properties of the products. The continuous flow reactor was operated at atmospheric pressure and at feed rate of 0–1.5 kg h^?1 polyolefins over two silica–alumina catalysts having different SiO₂/Al₂O₃ mole ratio. Polyethylene (PE), polypropylene (PP) and polystyrene (PS) were degraded at 420, 380 and 360 °C respectively. The cracking effect of silica–alumina was proved by the increased amount of gaseous products and by the decreased molecular weight of liquid products. The differences in surface area and in concentration and acidic strength of active centers of the two catalysts affected the distribution of degradation products. Molar rate of degradation was increased in the presence of catalysts, however the mass rate of degradation was decreased leading to higher values of the calculated activation energies. These interesting results might open new perspectives in understanding the macroscopic mechanism for catalytic degradation of polyolefins.     

A Variational Characterization of the Effective Yield Set for Ionic Polycrystals

The effective yield set of ionic polycrystals is characterized by means of variational principles in $L^\infty $ associated to supremal functionals acting on matrix-valued divergence-free fields.     

Fixed point results on a metric space endowed with a finite number of graphs and applications

In this paper, we consider self-mappings defined on a metric space endowed with a finite number of graphs. Under certain conditions imposed on the graphs, we establish a new fixed point theorem for such mappings. The obtained result extends, generalizes and improves many existing contributions in the literature including standard fixed point theorems, fixed point theorems on a metric space endowed with a partial order and fixed point theorems for cyclic mappings.     

Investigation of clay modifier effects on the structure and rheology of supercritical carbon dioxide‐processed polymer nanocomposites

Superior property enhancements in polymer–clay nanocomposites can be achieved if one can significantly enhance the nanoclay dispersion and polymer–clay interactions. Recent studies have shown that nanoclays can be dispersed in polymers using supercritical carbon dioxide (scCO₂). However, there is need for a better understanding of how changing the clay modifier affects the clay dispersability by scCO₂ and the resultant nanocomposite rheology. To address this, the polystyrene (PS)/clay nanocomposites with “weak” interaction (Cloisite 93A clay) and “strong” interaction (Cloisite 15A clay) have been prepared using the supercritical CO₂ method in the presence of a co‐solvent. Transmission electron microscopy images and small‐angle X‐ray diffraction illustrate that composites using 15A and 93A clays show similar magnitude of reduction in the average tactoid size, and dispersion upon processing with scCO₂. When PS and the clays are coprocessed in scCO₂, the “dispersion” of clays appears to be independent of modifier or polymer–clay interaction. However, the low‐frequency storage modulus in the scCO₂‐processed 15A nanocomposites is two orders of magnitude higher than that of 93A nanocomposites. It is postulated that below percolation (solution blended composites), the strength of polymer–clay interaction is not a significant contributor to rheological enhancement. In the scCO₂‐processed nanocomposites the enhanced dispersion passes the percolation threshold and the interactions dictate the reinforcement potential of the clay–polymer–clay network. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 823–831, 2010     

Multiple solutions for a nonlinear and non-homogeneous problem in Orlicz-Sobolev spaces

We study a non-homogeneous boundary value problem in a smooth bounded domain in R^N. We prove the existence of at least two non-negative and non-trivial weak solutions. Our approach relies on Orlicz-Sobolev spaces theory combined with adequate variational methods and a variant of Mountain Pass Lemma.     

Perfect Matchings and Perfect Powers

In the last decade there have been many results about special families of graphs whose number of perfect matchings is given by perfect or near perfect powers (N. Elkies et al., J. Algebraic Combin. 1 (1992), 111–132; B.-Y. Yang, Ph.D. thesis, Department of Mathematics, MIT, Cambridge, MA, 1991; J. Propp, New Perspectives in Geometric Combinatorics, Cambridge University Press, 1999). In this paper we present an approach that allows proving them in a unified way. We use this approach to prove a conjecture of James Propp stating that the number of tilings of the so-called Aztec dungeon regions is a power (or twice a power) of 13. We also prove a conjecture of Matt Blum stating that the number of perfect matchings of a certain family of subgraphs of the square lattice is a power of 3 or twice a power of 3. In addition we obtain multi-parameter generalizations of previously known results, and new multi-parameter exact enumeration results. We obtain in particular a simple combinatorial proof of Bo-Yin Yang's multivariate generalization of fortresses, a result whose previously known proof was quite complicated, amounting to evaluation of the Kasteleyn matrix by explicit row reduction. We also include a new multivariate exact enumeration of Aztec diamonds, in the spirit of Stanley's multivariate version.