A nondifferentiable extension of a theorem of Pucci and Serrin and applications

We study the multiplicity of critical points for functionals which are only differentiable along some directions. We extend to this class of functionals the three critical point theorem of Pucci and Serrin and we apply it to a one-parameter family of functionals Jλ, λ∈I⊂R. Under suitable assumptions, we locate an open subinterval of values λ in I for which Jλ possesses at least three critical points. Applications to quasilinear boundary value problems are also given.     

Physics, mind, society: Back and forth

The life course of the physicist and biologist George Feher may be seen as an epitome of science of the second half of the 20th century and the beginning of the 21st century. Feher, a native of Slovakia, barely escaped Nazism and communism and became a scientist in the USA. The Nazi concentration camps and the communist gulags have become a symbol of the 20th century. This symbol stands here to pose a question: How the two totalitarian systems, fraught with irrationality, may have arisen and thrived in parallel with an unprecedented expansion of science, the paragon of rationalism? The question has become even more urgent in the 21st century. The Ground Zero, an empty spot left after the collapse of the twin towers of the World Trade Center on 11 September 2001, has become the symbol of the entrance of humankind into the new millennium. We can do much, but we understand too little about who we are and what we are doing — this is a message that the two symbols convey about the precarious stage of our evolution. The second message concerns the role of artifacts, specifically scientific instruments, in the advancement of science. Human cultural evolution has been steadily progressing, in a form of a ratchet, only because artifacts have been continually evolving. Contrary to the common Popperian wisdom, the demarcation in science may not consist in the amenability to theoretical falsification, but rather in the amenability to instrumental grasping. Scientific instruments have empowered humans for impressive feats of manipulation with Nature and themselves. Knowledge arising in the course of autonomous evolution of artifacts may surpass the horizon of human understanding and grasping. New knowledge may still be power, but no longer the power of humans. We may need a revision of some fundamental ideas of European thought. Our understanding of the human mind may entirely reshape our comprehension of the nature of physical knowledge, and vice versa.     

New Plasmon Waveguides Composed of Twin Metal Wedges with a Nano Gap

We have numerically shown the existence of coupled wedge plasmons (CWPs) which propagates along a nano gap of a twin metal wedge. The CWPs are formed by wedge plasmons which can interact with each other. The dispersion relations of the wavenumber, propagation distance, and beam area of CWPs, are described and show that the characteristics of CWPs are similar to those of wedge plasmons and of gap plasmons. We also propose a new plasmon waveguide composed of twin metal wedges with a nano gap.     

A Simple Bi-directional Mode Expansion Propagation Algorithm Based on Modes of a Parallel-plate Waveguide

The bi-directional mode expansion propagation algorithm (BEP) is known to be an accurate and efficient method for modelling field distribution in high-index contrast waveguide structures with strong back-reflections like Bragg gratings and photonic crystals. The main difficulty of this method is that for lossy structures, the propagation constants of modes are to be searched in the complex plane. To speed-up this procedure, a two-step algorithm for eigenmode calculation based on the expansion into the modes of an empty metallic waveguide has recently been proposed. Proper truncation rules possessing good convergence of the expansion method for both TE and TM modes have also been recently published. In this contribution, both these approaches are combined in the development of an extremely simple version of the two-dimensional BEP method that makes use of the field expansion into the eigenmodes of a parallel-plate waveguide. The method is strictly reciprocal and appeared to be computationally reliable also for strongly lossy structures. High numerical stability is ensured using the scattering matrix formalism, and an efficient method of calculating Bloch modes for symmetric as well as asymmetric periodic waveguide structures is adopted. A wide range of applicability of the method is demonstrated by a few examples.     

Corn stover fractions and bioenergy

Information is presented on structure, composition, and response to enzymes of corn stover related to barriers for bioconversion to ethanol. Aromatic compounds occurred in most tissue cell walls. Ferulic acid esterase treatment before cellulase treatment significantly improved dry weight loss and release of phenolic acids and sugars in most fractions over cellulase alone. Leaf fractions were considerably higher in dry weight loss and released sugars with esterase treatment, but stem pith cells gave up the most phenolic acids. Results help identify plant fractions more appropriate for coproducts and bioconversion and those more suitable as residues for soil erosion control.     

Area,coarea, and approximation in <Emphasis Type="Italic">W</Emphasis><Superscript>1,1</Superscript>

Let Ω⊂ℝ ⁿ be an arbitrary open set. We characterize the space W ^1,1 _loc(Ω) using variants of the classical area and coarea formulas. We use these characterizations to obtain a norm approximation and trace theorems for functions in the space W ^1,1(ℝ ⁿ ).     

Working group report: Collider Physics

This is summary of the activities of the working group on collider physics in the IXth Workshop on High Energy Physics Phenomenology (WHEPP-9) held at the Institute of Physics, Bhubaneswar, India in January 2006. Some of the work subsequently done on these problems by the subgroups formed during the workshop is included in this report.     

Classical, phenomenological analysis of the kinetics of reactions at the gas-exposed surface of mixed ionic electronic conductors

The kinetics of reactions occurring at the gas-exposed surfaces of charged mixed ionic electronic conductors (MIECs) are examined from theoretical first principles. Analysis based on the classical electrochemical potential-transition state theory model reveals that the nature of the reactions is electrochemical in general. However, the influence of the surface potential on the reaction rate is opposite for adsorption and incorporation reactions. Two-dimensional finite volume models of an MIEC as working electrode in a half-cell configuration are presented. The results for a simple, two-step reduction process show that the effect of the surface potential on the rate of reactions is minimal for incorporation-limited reactions but more influential for adsorption-limited reactions. An erratum to this article is available at .