Molecular phase space transport in water:non-stationary random walk model

Molecular transport in phase space is crucial for chemical reactions because it defines how pre-reactive molecular configurations are found during the time evolution of the system. Using Molecular Dynamics (MD) simulated atomistic trajectories we test the assumption of the normal diffusion in the phase space for bulk water at ambient conditions by checking the equivalence of the transport to the random walk model. Contrary to common expectations we have found that some statistical features of the transport in the phase space differ from those of the normal diffusion models. This implies a non-random character of the path search process by the reacting complexes in water solutions. Our further numerical experiments show that a significant long period of non-stationarity in the transition probabilities of the segments of molecular trajectories can account for the observed non-uniform filling of the phase space. Surprisingly, the characteristic periods in the model non-stationarity constitute hundreds of nanoseconds, that is much longer time scales compared to typical lifetime of known liquid water molecular structures (several picoseconds).

Application of the D-Fullness Technique for Breakdown Point Study of the Trimmed Likelihood Estimator to a Generalized Logistic Model

2000 Mathematics Subject Classification: 62J12, 62F35

Splitting monoidal stable model categories

If C is a stable model category with a monoidal product then the set of homotopy classes of self-maps of the unit forms a commutative ring, [S,S]C. An idempotent e of this ring will split the homotopy category: [X,Y]C≅e[X,Y]C⊕(1−e)[X,Y]C. We prove that provided the localised model structures exist, this splitting of the homotopy category comes from a splitting of the model category, that is, C is Quillen equivalent to LeSC×L(1−e)SC and [X,Y]LeSC≅e[X,Y]C. This Quillen equivalence is strong monoidal and is symmetric when the monoidal product of C is.

A monoidal algebraic model for rational SO(2)-spectra

The category of rational SO(2)--equivariant spectra admits an algebraic model. That is, there is an abelian category A(SO(2)) whose derived category is equivalent to the homotopy category of rational$SO(2)--equivariant spectra. An important question is: does this algebraic model capture the smash product of spectra? The category A(SO(2)) is known as Greenlees' standard model, it is an abelian category that has no projective objects and is constructed from modules over a non--Noetherian ring. As a consequence, the standard techniques for constructing a monoidal model structure cannot be applied. In this paper a monoidal model structure on A(SO(2)) is constructed and the derived tensor product on the homotopy category is shown to be compatible with the smash product of spectra. The method used is related to techniques developed by the author in earlier joint work with Roitzheim. That work constructed a monoidal model structure on Franke's exotic model for the K_(p)--local stable homotopy category. A monoidal Quillen equivalence to a simpler monoidal model category that has explicit generating sets is also given. Having monoidal model structures on the two categories removes a serious obstruction to constructing a series of monoidal Quillen equivalences between the algebraic model and rational SO(2)--equivariant spectra.

A Frequency-Dependent Equivalence Between Groove Gap Waveguide and Rectangular Waveguide

Recently gap waveguides have been shown as a potential alternative to conventional waveguides in the millimeter-wave band. Groove Gap Waveguide (GGW) has until now been studied though direct correspondence with rectangular waveguide with the same propagation channel dimensions. However there have been observed differences in the above cutoff propagation characteristics between these waveguide types. Furthermore, the behaviour of GGW below cutoff remains unknown. This work presents a discussion of below and above cutoff propagation characteristics, and introduces a simple model that explains observed GGW behavior and establishes its propagation characteristics.

Economic well-being and poverty among the elderly: an analysis based on a collective consumption model

We apply the collective consumption model of Browning, Chiappori and Lewbel (2006) to analyse economic well-being and poverty among the elderly. The model focuses on individual preferences, a consumption technology that captures the economies of scale of living in a couple, and a sharing rule that governs the intra-household allocation of resources. The model is applied to a time series of Dutch consumption expenditure surveys. Our empirical results indicate substantial economies of scale and a wifeís share that is increasing in total expenditures. We further calculated poverty rates by means of the collective consumption model. Collective poverty rates of widows and widowers turn out to be slightly lower than traditional ones based on a standard equivalence scale. Poverty among women (men) in elderly couples, however, seems to be heavily underestimated (overestimated) by the traditional approach. Finally, we analysed the impact of becoming a widow(er). Based on cross-sectional evidence, we find that the drop (increase) in material well-being following the husbandís death is substantial for women in high (low) expenditure couples. For men, the picture is reversed.

Generating Effective Test Suites for Model Transformations Using Classifying Terms

Generating sample models for testing a model transformation is no easy task. This paper explores the use of classifying terms and stratified sampling for developing richer test cases for model transformations. Classifying terms are used to define the equivalence classes that characterize the relevant subgroups for the test cases. From each equivalence class of object models, several representative models are chosen depending on the required sample size. We compare our results with test suites developed using random sampling, and conclude that by using an ordered and stratified approach the coverage and effectiveness of the test suite can be significantly improved.

The Traceless Oldroyd viscoelastic model

In the traceless Oldroyd viscoelastic model, the viscoelastic extra stress tensor is decomposed into its traceless (deviatoric) and spherical parts, leading to a reformulation of the classical Oldroyd model. The equivalence of the two models is established comparing model predictions for simple test cases. The new model is validated using several 2D benchmark problems. The structure and behavior of the new model are discussed and the future use of the new model in envisioned, both on the theoretical and numerical perspectives.

An approximate method for the solution of an influence function foil rolling model

Fleck and Johnson (Int. J. Mech. Sci. 29 (1987) 507) and Fleck et al. (Proc. Inst. Mech. Eng. 206 (1992) 119) have developed foil rolling models which allow for large deformations in the roll profile, including the possibility that the rolls flatten completely. However, these models require computationally expensive iterative solution techniques. A new approach to the approximate solution of the Fleck et al. (1992) Influence Function Model has been developed using both analytic and approximation techniques. The numerical difficulties arising from solving an integral equation in the flattened region have been reduced by applying an Inverse Hilbert Transform to get an analytic expression for the pressure. The method described in this paper is applicable to cases where there is or there is not a flat region.