Integrability and exact spectrum of a pairing model for nucleons

A pairing model for nucleons, introduced by Richardson in 1966, which describes proton-neutron pairing as well as proton-proton and neutron-neutron pairing, is re-examined in the context of the quantum inverse scattering method. Specifically, this shows that the model is integrable by enabling the explicit construction of the conserved operators. We determine the eigenvalues of these operators in terms of the Bethe ansatz, which in turn leads to an expression for the energy eigenvalues of the Hamiltonian.

Exact solution at integrable coupling of a model for the Josephson effect between small metallic grains

A model is introduced for two reduced BCS systems which are coupled through the transfer of Cooper pairs between the systems. The model may thus be used in the analysis of the Josephson effect arising from pair tunneling between two strongly coupled small metallic grains. At a particular coupling strength the model is integrable and explicit results are derived for the energy spectrum, conserved operators, integrals of motion, and wave function scalar products. It is also shown that form factors can be obtained for the calculation of correlation functions. Furthermore, a connection with perturbed conformal field theory is made.

Integrable coupling in a model for Josephson tunneling between non-identical BCS systems

We extend a recent construction for an integrable model describing Josephson tunneling between identical BCS systems to the case where the BCS systems have different single particle energy levels. The exact solution of this generalized model is obtained through the Bethe ansatz.

Integrable variant of the one-dimensional Hubbard model

A new integrable model which is a variant of the one-dimensional Hubbard model is proposed. The integrability of the model is verified by presenting the associated quantum R-matrix which satisfies the Yang-Baxter equation. We argue that the new model possesses the SO(4) algebra symmetry, which contains a representation of the eta-pairing SU(2) algebra and a spin SU(2) algebra. Additionally, the algebraic Bethe ansatz is studied by means of the quantum inverse scattering method. The spectrum of the Hamiltonian, eigenvectors, as well as the Bethe ansatz equations, are discussed. (C) 2002 American Institute of Physics.

Long-run growth effects of taxation in a non-scale growth model with innovation

In previous studies, taxing income or consumption hinders long-run growth. Incorporating saving and leisure into the non-scale Schumpeterian model of [Journal of Political Economy 107 (1999) 715-730], we show that the usual growth effects of taxing consumption and labor income do not exist. (C) 2002 Elsevier Science B.V. All rights reserved.

A model of factors affecting an information system's change in state

Management are keen to maximize the life span of an information system because of the high cost, organizational disruption, and risk of failure associated with the re-development or replacement of an information system. This research investigates the effects that various factors have on an information system's life span by understanding how the factors affect an information system's stability. The research builds on a previously developed two-stage model of information system change whereby an information system is either in a stable state of evolution in which the information system's functionality is evolving, or in a state of revolution, in which the information system is being replaced because it is not providing the functionality expected by its users. A case study surveyed a number of systems within one organization. The aim was to test whether a relationship existed between the base value of the volatility index (a measure of the stability of an information system) and certain system characteristics. Data relating to some 3000 user change requests covering 40 systems over a 10-year period were obtained. The following factors were hypothesized to have significant associations with the base value of the volatility index: language level (generation of language of construction), system size, system age, and the timing of changes applied to a system. Significant associations were found in the hypothesized directions except that the timing of user changes was not associated with any change in the value of the volatility index. Copyright (C) 2002 John Wiley Sons, Ltd.

A general model for host plant selection in phytophagous insects

We develop a general theoretical framework for exploring the host plant selection behaviour of herbivorous insects. This model can be used to address a number of questions, including the evolution of specialists, generalists, preference hierarchies, and learning. We use our model to: (i) demonstrate the consequences of the extent to which the reproductive success of a foraging female is limited by the rate at which they find host plants (host limitation) or the number of eggs they carry (egg limitation); (ii) emphasize the different consequences of variation in behaviour before and after landing on (locating) a host (termed pre- and post-alighting, respectively); (iii) show that, in contrast to previous predictions, learning can be favoured in post-alighting behaviour-in particular, individuals can be selected to concentrate oviposition on an abundant low-quality host, whilst ignoring a rare higher-quality host; (iv) emphasize the importance of interactions between mechanisms in favouring specialization or learning. (C) 2002 Elsevier Science Ltd.

Field quantization, photons and non-Hermitean modes

Field quantization in unstable optical systems is treated by expanding the vector potential in terms of non-Hermitean (Fox-Li) modes. We define non-Hermitean modes and their adjoints in both the cavity and external regions and make use of the important bi-orthogonality relationships that exist within each mode set. We employ a standard canonical quantization procedure involving the introduction of generalized coordinates and momenta for the electromagnetic (EM) field. Three-dimensional systems are treated, making use of the paraxial and monochromaticity approximations for the cavity non-Hermitean modes. We show that the quantum EM field is equivalent to a set of quantum harmonic oscillators (QHOs), associated with either the cavity or the external region non-Hermitean modes, and thus confirming the validity of the photon model in unstable optical systems. Unlike in the conventional (Hermitean mode) case, the annihilation and creation operators we define for each QHO are not Hermitean adjoints. It is shown that the quantum Hamiltonian for the EM field is the sum of non-commuting cavity and external region contributions, each of which can be expressed as a sum of independent QHO Hamiltonians for each non-Hermitean mode, except that the external field Hamiltonian also includes a coupling term responsible for external non-Hermitean mode photon exchange processes. The non-commutativity of certain cavity and external region annihilation and creation operators is associated with cavity energy gain and loss processes, and may be described in terms of surface integrals involving cavity and external region non-Hermitean mode functions on the cavity-external region boundary. Using the essential states approach and the rotating wave approximation, our results are applied to the spontaneous decay of a two-level atom inside an unstable cavity. We find that atomic transitions leading to cavity non-Hermitean mode photon absorption are associated with a different coupling constant to that for transitions leading to photon emission, a feature consequent on the use of non-Hermitean mode functions. We show that under certain conditions the spontaneous decay rate is enhanced by the Petermann factor.

Proposed modifications to metabolic model for glycogen-accumulating organisms under anaerobic conditions

Filipe et al. (2001) proposed an anaerobic metabolic model for glycogen-accumulating organisms (GAO) in which the succinate-propionate pathway was used to describe the production of propionyl-CoA. However, propionyl-CoA is only an intermediate product in the above pathway. Stopping at propionyl-CoA instead of propionate (the end product of the pathway) results in the consumption of one ATP from succinate to succinyl-CoA, which was not accounted for in the model of Filipe et al. (2001). This resulted in significant errors in the stoichiometric coefficients in the final metabolic model. A modified model is presented in this communication and is shown to fit the experimental data significantly better than the original model. (C) 2002 Wiley Periodicals, Inc.

Maintaining muscle mass during extended disuse: Aestivating frogs as a model species

Prolonged muscle disuse in vertebrates can lead to a pathological change resulting in muscle wasting and a loss of muscle strength. In this paper, we review muscle disuse atrophy in the vertebrates and examine the factors that influence the magnitude of the atrophic response during extended periods of inactivity, both artificially imposed (e.g. limb immobilisation) and naturally occurring, such as the quiescence associated with dormancy (e.g. hibernation and aestivation). The severity of muscle atrophy is positively correlated with mass-specific metabolic rate, and the metabolic depression that occurs during dormancy would appear to have a protective role, reducing or preventing muscle atrophy despite periods of inactivity lasting 6-9 months. In the light of these findings, the role of reactive oxygen species and antioxidants during muscle disuse is emphasised.

Ellipsoidal harmonic (Lame) MRI shims

Ellipsoidal harmonics are presented as a basis function set for the design of shim coils for magnetic resonance imaging (MRI) or spectroscopy. MR shim coils may be either superconductive or resistive. Ellipsoidal harmonics form an orthogonal set over an ellipsoid and hence are appropriate in circumstances where the imaging or spectroscopic region of a magnet more closely conforms to an ellipsoid rather than a sphere. This is often the case in practice. The Cartesian form of ellipsoidal harmonics is discussed. A method for the design of streamline coil designs is detailed and patterns for third-order ellipsoidal (Lame) shims wound on a cylindrical surface are presented.

The damped and coherently-driven Jaynes-Cummings model

We investigate the influence of a single-mode cavity on the Autler-Townes doublet that arises when a three-level atom is strongly driven by a laser field tuned to one of the atomic transitions and probed by a tunable, weak field coupled to the other transition. We assume that the cavity mode is coupled to the driven transition and the cavity and laser frequencies are equal to the atomic transition frequency. We find that the Autler-Townes spectrum can have one, two or three peaks depending on the relative magnitudes of the Rabi frequencies of the cavity and driving fields. We show that, in order to understand the three-peaked spectrum, it is necessary to go beyond the secular approximation, leading to interesting quantum interference effects. We find that the positions and relative intensities of the three spectral components are affected strongly by the atom-cavity coupling strength g and the cavity damping K. For an increasing g and/or decreasing K the triplet evolves into a single peak. This results in 'undressing' of the system such that the atom collapses into its ground state. We interpret the spectral features in terms of the semiclassical dressed-atom model, and also provide complementary views of the cavity effects in terms of quantum Langevin equations and the fully quantized, 'double -dressing' model.

Metal-insulator transition and charge ordering in the extended Hubbard model at one-quarter filling

We study, with exact diagonalization, the zero temperature properties of the quarter-filled extended Hubbard model on a square lattice. We find that increasing the ratio of the intersite Coulomb repulsion, V, to the bandwidth drives the system from a metal to a charge ordered insulator. The evolution of the optical conductivity spectrum with increasing V is in agreement with the observed optical conductivity of several layered molecular crystals with the theta and beta crystal structures.

Assessment of the ability to model proteins with leucine-rich repeats in light of the latest structural information

The three-dimensional structures of leucine-rich repeat (LRR) -containing proteins from five different families were previously predicted based on the crystal structure of the ribonuclease inhibitor. using an approach that combined homology-based modeling, structure-based sequence alignment of LRRs, and several rational assumptions. The structural models have been produced based on very limited sequence similarity, which, in general. cannot yield trustworthy predictions. Recently, the protein structures from three of these five families have been determined. In this report we estimate the quality of the modeling approach by comparing the models with the experimentally determined structures. The comparison suggests that the general architecture, curvature, interior/exterior orientations of side chains. and backbone conformation of the LRR structures can be predicted correctly. On the other hand. the analysis revealed that, in some cases. it is difficult to predict correctly the twist of the overall super-helical structure. Taking into consideration the conclusions from these comparisons, we identified a new family of bacterial LRR proteins and present its structural model. The reliability of the LRR protein modeling suggests that it would be informative to apply similar modeling approaches to other classes of solenoid proteins.