A Singular Perturbation Analysis for the Transient Semiconductor Device Equations in One Space Dimension

A singular perturbation analysis for the basic semiconductorequations is presented. Asymptotic expansions are derived andthe existence of solutions is investigated. Effects of velocitysaturation are included in the model.     

Theory and simulations of rigid polyelectrolytes

Theoretical and numerical studies are reported on stiff, linear polyelectrolytes within the framework of the cell model, first reviewing analytical results obtained on a mean-field Poisson—Boltzmann level, and then using molecular dynamics simulations to show the circumstances under which these fail quantitatively and qualitatively. For the hexagonally packed nematic phase of the polyelectrolytes the osmotic coefficient is computed as a function of density. In the presence of multivalent counterions it can become negative, leading to effective attractions. This is shown to result from a reduced contribution of the virial part to the pressure. The osmotic coefficient and ionic distribution functions are computed from Poisson—Boltzmann theory with and without a recently proposed correlation correction. Simulation results for the case of poly(p-phenylene) are presented and compared with recently obtained experimental data on this stiff polyelectrolyte. Ion—ion correlations in the strong coupling regime are studied and compared with the predictions of the recently advocated Wigner crystal theories.     

Uniform Asymptotic Representation of Solutions of the Basic Semiconductor-Device Equations

In this paper we analyse the basic semiconductor-device equationsmodelling a symmetric one-dimensional voltage-controlled diodeunder the assumptions of zero recombination-generation and constantmobilities. Employing the singular-perturbation formulationwith the normed Debye length as perturbation parameter we derivethe zeroth-order terms of the matched asymptotic expansion ofthe solutions, which are sums of uniformly smooth outer terms(reduced solutions) and exponentially varying inner terms (layersolutions). The main result of the paper is that, if the perturbationparameter is sufficiently small, then there exists a solutionof the semiconductor-device problem which is approximated uniformlyby the zeroth-order term of the expansion, even for large appliedvoltages. This result shows the validity of the asymptotic expansionsof the solutions of the semiconductor-device problem in physicallyrelevant high-injection situations.     

Analytical representations for the radial distribution functions of mixtures of adhesive spheres

A study has been made of the pole topology of the Laplace transforms of the pair distribution functions (PDFs) of a binary mixture of adhesive hard spheres (AHS) both for the Percus-Yevick equation and the mean spherical model (MSM). Expressions are given that describe how the distribution of the poles in the left half of the complex plane varies with the system parameters for the special case of the MSM for symmetric binary AHS mixtures. The locations of the poles closest to the imaginary axis are known to determine the asymptotic form of the PDFs, i.e. either exponentially monotonic or exponentially oscillatory decaying. As a byproduct of this inquiry analytical r space representations of the PDFs are derived that allow their accurate and efficient determination over the entire r range.     

Finite Deformations of Thin Beams, Asymptotic Analysis by Singular Perturbation Methods

Boundary-value problems for a system of singularly perturbednon-linear ordinary differential equations modelling large deflectionsof thin beams are examined. Using the theory of singularly perturbedboundary value problems we establish the existence of locallyunique solutions and derive asymptotic expansions.     

VIABILITY MODEL OF TROPHIC INTERACTIONS IN MARINE ECOSYSTEMS

ABSTRACT. An attempt to use viability models for studying marine ecosystems is proposed as a possible alternative to classical ecosystem modeling. Viability models do not consider optimal solutions but instead define all possible evolutions of a dynamical system under given constraints. Applied to marine ecosystems, a viability model is formulated based on the trophic coefficients of a mass‐balanced model. This requires relatively few assumptions about the processes involved and can integrate uncertainty associated with the required estimates of input parameters. An iterative algorithm is proposed to calculate the viability kernel, i.e., the envelope of all viable trajectories of the ecosystem. An application to the Benguela ecosystem is presented, considering interactions between detritus, phytoplankton, zooplankton, pelagic fish, demersal fish and fisheries. Results show how a viability kernel could be used to better define the healthy states of a marine ecosystem, by defining what states should be avoided. The paper discusses how viability models of trophic interactions could help to define a new ecosystem‐based indicator for fisheries management. It then discusses how this approach can potentially contribute to a paradigm shift that is emerging in the management of renewable resources.     

Weak solutions of interior boundary-value problems for plates with transverse shear deformation

Corresponding author; email: c.constanda{at}strath.ac.uk The existence, uniqueness, and continuous dependence on thedata are investigated for the solutions of the equations ofbending of plates with transverse shear deformation in a Sobolevspace setting.     

Computation of Current-Voltage Characteristics in a Semiconductor Device using Arc-length Continuation

This paper is concerned with the computation of semiconductordevice current—voltage characteristics. We describe analgorithm which allows the computation of characteristics bycontinuation in a parameter which approximates the arc lengthof the characteristic. The use of this parameterization allowsthe characteristic to continue beyond snap-back voltages, whilecontinuation in the voltage fails past snap-back voltages. Wediscuss the implementation of the parameterization and givea numerical example.     

Corroding the chromium cation

Two [Cr,O₂]⁺ isomers have been selectively produced and studied by FT-ICR mass spectrometry. The Cr(O₂)⁺ complex was formed by supersonically expanding a plasma produced by laser vaporization of chromium metal with the helium carrier gas, which was seeded with traces of oxygen, while the chromyl cation is formed in an expansion with N₂O. The complex is stable against thermal collisions, but in a bimolecular reaction with water it is rapidly converted to the chromyl cation, with ligand exchange being only a minor side reaction. Isotopic studies suggest a side-on geometry for Cr(O₂)⁺, in accordance with density functional (B3LYP) calculations. The present work indicates that an investigation of the selected isomers can indeed be carried out, if appropriate chemical methods for the ion generation are applied.