On the nuclear density distribution for nucleus-nucleus scattering. II

We investigate the effect of the antisymmetrization on the density distribution for nucleus-nucleus scattering. In contrast to an earlier paper¹ the motion of the nuclei is now taken into account. For experimentally available energies we find no pronounced density compression in the overlap region. For very high energies a superposition of the densities is justified.     

Parallel Calculation of Accurate Path Lines in Virtual Environments through Exploitation of Multi-Block CFD Data Set Topology

The use of Virtual Reality (VR) techniques for the investigation of complex flow phenomena offers distinct advantages in comparison to conventional visualization techniques. Especially for unsteady flows, VR methodology provides an intuitive approach for the exploration of simulated fluid flows. However, the visualization of Computational Fluid Dynamics (CFD) data is often too time-consuming to be carried out in real-time, and thus violates essential constraints concerning real-time interaction and visualization. To overcome this obstacle, we make use of the fact that typically a multi-block approach is employed for domain decomposition, and we use the corresponding data structures for the computation of path lines and for parallelization. In this paper, we present the synthesis of fragmented multi-block data sets and our implementation of an accurate path line integration scheme in order to speed up path line computations. We report on the results of our efforts and describe a combination of this algorithm with a highly efficient visualization approach of large amounts of particle traces, thus considerably improving interactivity when exploring large scale CFD data sets.Mathematics Subject Classifications (2000) 76Mxx, 76M27, 76M28, 65M55, 65L05, 65L06, 65D05, 65Y05, 68U05.     

Invertibility theory for Toeplitz plus Hankel operators and singular integral operators with flip

It is well known that a Toeplitz operator is invertible if and only if its symbols admits a canonical Wiener-Hopf factorization, where the factors satisfy certain conditions. A similar result holds also for singular integral operators. More generally, the dimension of the kernel and cokernel of Toeplitz or singular integral operators which and Fredholm operators can be expressed in terms of the partial indices of an associated Wiener-Hopf factorization problem.In this paper we establish corresponding results for Toeplitz plus Hankel operators and singular integral operators with flip under the assumption that the generating functions are sufficiently smooth (e.g., Hölder continuous). We are led to a slightly different factorization problem, in which pairs , instead of the partial indices appear. These pairs provide the relevant information about the dimension of the kernel and cokernel and thus answer the invertibility problem.     

Stochastic gain in population dynamics

We introduce an extension of the usual replicator dynamics to adaptive learning rates. We show that a population with a dynamic learning rate can gain an increased average payoff in transient phases and can also exploit external noise, leading the system away from the Nash equilibrium, in a resonancelike fashion. The payoff versus noise curve resembles the signal to noise ratio curve in stochastic resonance. Seen in this broad context, we introduce another mechanism that exploits fluctuations in order to improve properties of the system. Such a mechanism could be of particular interest in economic systems.     

Hierarchical porous silica materials with a trimodal pore system using surfactant templates

Porous silica exhibiting a hierarchically ordered trimodal pore system with a well-defined reverse opal microstructure and bimodal mesoporosity in the walls has been prepared by using polystyrene latex spheres, a novel block copolymer and an ionic liquid surfactant as templates. The resulting materials exhibit hierarchical order at three length scales (small mesopores: 2-3 nm; large mesopores: 11-12 nm; macropores: 360 nm).     

Functional MRI using intravascular contrast agents: detrending of the relative cerebrovascular (rCBV) time course

In pharmacological fMRI experiments in animal models, blood pool contrast agents may be used to map cerebral blood volume change as a surrogate for neural activation. When the background signal drift due to contrast agent washout is non-negligible over the duration of the signal changes of interest, time-course detrending is essential for accurate interpretation of the experiment. Detrending approaches based on estimation of the background signal from a baseline period of the time course prior to pharmacological (or functional) challenge were evaluated with the aim of identifying a robust method of estimating the contrast agent washout contribution to the background signal drift. For fMRI studies in the rat, it was found that a constrained fit of a mono-exponential washout model was more accurate than a constant background approximation and unconstrained fits for experiments investigating the functional response to rapid pharmacological challenges such as cocaine and amphetamine. Moreover, the constrained fitting approach allows shorter baseline periods than unconstrained extrapolation, reducing the required duration of the experiment.     

Asymptotics of Determinants of Bessel Operators

 For aL ^∞ (ℝ₊)∩L ¹ (ℝ₊) the truncated Bessel operator B _τ (a) is the integral operator acting on L ² [0,τ] with the kernel

Activation parameters for the reactive intermediates relevant to carbonylation catalysts based on cobalt carbonyls

Time-resolved spectroscopic techniques have been used to prepare and to interrogate transient species that are models for reactive intermediates in cobalt-catalyzed hydroformylation. Flash photolysis of acetylcobalt carbonyl complexes of the type RC(O)Co(CO)3(PR'3) (A; R = CH3, CD3, or C2H5; R' = Ph or nBu) leads to CO photodissociation to give the "unsaturated" intermediate [RC(O)Co(CO)2(PR'3)] (I), which decays by two competitive pathways, alkyl migration to the cobalt to give RCo(CO)3PR'3 (M) and reaction with CO to re-form A. With the perdeuterioacetyl complex (R = CD3, R' = Ph), rate constants both of CO trapping (kco) and of methyl migration (kM) were just slightly smaller than those of the perprotio analogue (kh/kd = 1.04 +/- 0.01 and 1.07 +/- 0.09, respectively). Thus, any stabilization of the "vacant" coordination site of I by agostic interactions with the acetyl methyl group appears to be kinetically insignificant, consistent with the previous conclusion (Inorg. Chem. 2000, 39, 3098-3106) that this site is stabilized by an eta 2-coordinated carbonyl. Changing the phosphine ligand has a greater influence on the kinetics of I. The species generated by the flash photolysis of the trialkyl phosphine complex CH3C(O)Co-(CO)3(P(nBu3)) exhibited a much larger kM than was the case for the PPh3 analogue, although there was little difference in the kco values. Similarly, kM proved to be sensitive to the nature of R as demonstrated by the slower alkyl migration (at 298 K) for the intermediate formed by CO photodissociation from the propionyl complex C2H5C(O)Co(CO)3PPh3 relative to the acetyl analogue. Nonetheless, all these intermediates displayed analogous time-resolved infrared spectra and general kinetics behavior in benzene solution (implying common mechanisms for decay), so it is concluded that all are present as the eta 2-chelated acyl structure under these conditions.