Multiple lie-poisson structures,reductions, and geometric phases for the Maxwell-Bloch travelling wave equations

Summary The real-valued Maxwell-Bloch equations on ℝ³ are investigated as a Hamiltonian dynamical system obtained by applying an S¹ reduction to an invariant subsystem of a dynamical system on ℂ³. These equations on ℝ³ are bi-Hamiltonian and possess several inequivalent Lie-Poisson structures parametrized by classes of orbits in the group SL(2, ℝ). Each Lie-Poisson structure possesses an associated Casimir function. When reduced to level sets of these functions, the motion takes various symplectic forms, from that of the pendulum to that of the Duffing oscillator. The values of the geometric (Hannay-Berry) phases obtained in reconstructing the solutions are found to depend upon the choice of Casimir function, that is, upon the parametrization of the reduced symplectic space.     

Dispersion effects in unreplicated factorial designs

Methods for estimation of dispersion effects in two‐level unreplicated factorial designs are studied. The consequences of non‐constant variance are discussed. A natural assumption concerning the form of the covariance of location effects leads to a particular normal model. Some linear combinations of the response variables are constructed in order to make a simple structure for inference. The precision of point estimators of dispersion effects, where one is based on experiments with replicates, are compared. A numerical example is given as an illustration of a test. Finally, estimations in fractional designs are described and discussed. Copyright © 2002 John Wiley & Sons, Ltd.     

Boundary Mobility and Energy Anisotropy Effects on Microstructural Evolution During Grain Growth

We have performed mesoscopic simulations of microstructural evolution during curvature driven grain growth in two-dimensions using anisotropic grain boundary properties obtained from atomistic simulations. Molecular dynamics simulations were employed to determine the energies and mobilities of grain boundaries as a function of boundary misorientation. The mesoscopic simulations were performed both with the Monte Carlo Potts model and the phase field model. The Monte Carlo Potts model and phase field model simulation predictions are in excellent agreement. While the atomistic simulations demonstrate strong anisotropies in both the boundary energy and mobility, both types of microstructural evolution simulations demonstrate that anisotropy in boundary mobility plays little role in the stochastic evolution of the microstructure (other than perhaps setting the overall rate of the evolution. On the other hand, anisotropy in the grain boundary energy strongly modifies both the topology of the polycrystalline microstructure the kinetic law that describes the temporal evolution of the mean grain size. The underlying reasons behind the strongly differing effects of the two types of anisotropy considered here can be understood based largely on geometric and topological arguments.     

Locked by Design: A Conformationally Constrained Transglutaminase Tag Enables Efficient Site‐Specific Conjugation

Based on the crystal structure of a natural protein substrate for microbial transglutaminase, an enzyme that catalyzes protein crosslinking, a recognition motif for site‐specific conjugation was rationally designed. Conformationally locked by an intramolecular disulfide bond, this structural mimic of a native conjugation site ensured efficient conjugation of a reporter cargo to the therapeutic monoclonal antibody cetuximab without erosion of its binding properties.     

Particle-particle particle-mesh method for dipolar interactions: on error estimates and efficiency of schemes with analytical differentiation and mesh interlacing

The interlaced and non-interlaced versions of the dipolar particle-particle particle-mesh (P(3)M) method implemented using the analytic differentiation scheme (AD-P(3)M) are presented together with their respective error estimates for the calculation of the forces, torques, and energies. Expressions for the optimized lattice Green functions, and for the Madelung self-forces, self-torques and self-energies are given. The applicability of the theoretical error estimates are thoroughly tested and confirmed in several numerical examples. Our results show that the accuracy of the calculations can be improved substantially when the approximate (mesh computed) Madelung self-interactions are subtracted. Furthermore, we show that the interlaced dipolar AD-P(3)M method delivers a significantly higher accuracy (which corresponds approximately to using a twice finer mesh) than the conventional method, allowing thereby to reduce the mesh size with respect to the non-interlaced version for a given accuracy. In addition, we present similar expressions for the dipolar ik-differentiation interlaced scheme, and we perform a comparison with the AD interlaced scheme. Rough tests for the relative speed of the dipolar P(3)M method using ik-differentiation and the interlaced/non-interlaced AD schemes show that when FFT computing time is the bottleneck, usually when working at high precisions, the interlaced AD-scheme can be several times faster than the other two schemes. For calculations with a low accuracy requirement, the interlaced version can perform worse than the ik and the non-interlaced AD schemes.     

A novel class of organo- (hydro-) gelators based on ascorbic acid

A library of novel, lipid-modified derivatives of ascorbic acid was shown to exhibit highly attractive properties as surfactants, emulsifiers, oil soluble antioxidants, and highly effective gelators in organic solvents and especially water. In these systems, intermolecular hydrogen bonding and van der Waals forces act synergistically to induce gelation as confirmed by spectroscopic studies. The morphology of the formed gel has been characterized by scanning electron microscopy.     

Complexation of tauro- and glyco-conjugated bile salts with α-cyclodextrin and hydroxypropyl-α-cyclodextrin studied by affinity capillary electrophoresis and molecular modelling

The interaction of the bile salts taurocholate, taurodeoxycholate, taurochenodeoxycholate, glycocholate, glycodeoxycholate, and glycochenodeoxycholate present in man, dog, and rat with α-cyclodextrin and 2-hydroxypropyl-α-cyclodextrin was investigated by mobility shift affinity capillary electrophoresis. The cyclodextrins are applied as excipients for solubilisation of drug substances with poor aqueous solubility. Accurate determination of stability constants is challenging for weak analyte-ligand interactions such as the conjugated bile salt α-cyclodextrin interactions. A new approach for correction of medium effects due to the high additive concentrations in the background electrolyte was introduced. The use of prostaglandin A(1) as an interacting marker molecule offered a more satisfactory approach for correction than the commonly employed methods based on viscosity or current ratios. The interacting marker was chosen over a non-interacting marker to avoid the difficult validation of the non-interacting properties. The investigated bile salts all interacted with α-cyclodextrin and 2-hydroxypropyl-α-cyclodextrin. Stability constants ranging from 14 to 95 M(-1) were obtained with slightly higher affinities toward the substituted cyclodextrin. Molecular modelling demonstrated that the interaction between the two species involves the side chain of the bile salt. All together, these results indicate minor bile salt-mediated displacement of substances from α-cyclodextrin complexes in the small intestine.     

The Momentum Map Representation of Images

This paper discusses the mathematical framework for designing methods of Large Deformation Diffeomorphic Matching (LDM) for image registration in computational anatomy. After reviewing the geometrical framework of LDM image registration methods, we prove a theorem showing that these methods may be designed by using the actions of diffeomorphisms on the image data structure to define their associated momentum representations as (cotangent-lift) momentum maps. To illustrate its use, the momentum map theorem is shown to recover the known algorithms for matching landmarks, scalar images, and vector fields. After briefly discussing the use of this approach for diffusion tensor (DT) images, we explain how to use momentum maps in the design of registration algorithms for more general data structures. For example, we extend our methods to determine the corresponding momentum map for registration using semidirect product groups, for the purpose of matching images at two different length scales. Finally, we discuss the use of momentum maps in the design of image registration algorithms when the image data is defined on manifolds instead of vector spaces.