Search results for " function"
showing 10 items of 9395 documents
Magic numbers, excitation levels, and other properties of small neutral 4He clusters (Nor = 50).
2006
The ground-state energies and the radial and pair distribution functions of neutral 4He clusters are systematically calculated by the diffusion Monte Carlo method in steps of one 4He atom from 3 to 50 atoms. In addition the chemical potential and the low-lying excitation levels of each cluster are determined with high precision. These calculations reveal that the "magic numbers" observed in experimental 4He cluster size distributions, measured for free jet gas expansions by nondestructive matter-wave diffraction, are not caused by enhanced stabilities. Instead they are explained in terms of an enhanced growth due to sharp peaks in the equilibrium concentrations in the early part of the expa…
Scaling theory for radial distributions of star polymers in dilute solution in the bulk and at a surface, and scaling of polymer networks near the ad…
1991
Monomer density profiles ρ(r) and center–end distribution functions g(rCE) of star polymers are analyzed by using a scaling theory in arbitrary dimensions d, considering dilute solutions and the good solvent limit. Both the case of a free star in the bulk and of a center‐adsorbed star at a free surface are considered. In the latter case of a semi‐infinite problem, a distinction is made between repulsive walls, attractive walls—where for large arm length l the configuration of the star is quasi‐(d−1) dimensional—, and ‘‘marginal walls’’ where for l→∞ the transition from d‐dimensional structure occurs. For free stars, ρ(r) behaves as r−d+1/ν for small r, where ν is the exponent describing the…
Monte Carlo simulation of many-arm star polymers in two-dimensional good solvents in the bulk and at a surface
1991
A Monte Carlo technique is proposed for the simulation of statistical properties of many-arm star polymers on lattices. In this vectorizing algorithm, the length of each arml is increased by one, step by step, from a starting configuration withl=1 orl=2 which is generated directly. This procedure is carried out for a large sample (e.g., 100,000 configurations). As an application, we have studied self-avoiding stars on the square lattice with arm lengths up tol max=125 and up tof=20 arms, both in the bulk and in the geometry where the center of the star is adsorbed on a repulsive surface. The total number of configurations, which behaves asN∼l γ G–1μ fl , whereμ=2.6386 is the usual effective…
A family of weakest link models for fiber strength distribution
2007
It is well known that the most widely used distribution function for fiber tensile strength, the two-parameter Weibull distribution, does not always adequately describe the experimentally observed fiber strength scatter and the strength dependence on fiber length. To remedy this discrepancy, modifications of the Weibull distribution have been proposed that, while providing a good empirical fit to the strength data, sometimes lack the theoretical appeal of the weakest link models. We derive a family of weakest link models based on the assumption of a two-stage failure process incorporating explicitly the probabilities of flaw initiation and the fiber fracture due to the largest flaw (i.e. th…
Decoupled solution of radial and weakly meshed distribution networks through a backward method
2008
A methodology for the analysis of radial or weakly meshed distribution systems supplying voltage dependent loads is developed. The solution process is iterative and, at each step, the loads are simulated by means of impedances. The network is divided into two sub-networks which must be solved separately and sequentially; in the first, named RP-net, only the lines resistances and the loads shunt equivalent resistances are considered; in the second, named XQ-net, only the lines reactances and the shunt equivalent reactances are taken into account. After a brief presentation of the b/f method, which is currently the most commonly used technique to solve distribution networks, the proposed meth…
Optimal Shape Design in Contact Problems
1989
From the mathematical point of view, optimal shape design (or optimum design, optimization of the domain, structural optimization) is a branch of the calculus of variations and especially of optimal control where study is devoted to the problem of finding the optimal shape for an object. In an optimal shape design process the objective is to optimize certain criteria involving the solution of a partial differential equation with respect to its domain of definition, [2, 3, 5].
Algorithmic approaches to Siegel's fundamental domain
2017
Siegel determined a fundamental domain using the Minkowski reduction of quadratic forms. He gave all the details concerning this domain for genus 1. It is the determination of the Minkowski fundamental domain presented as the second condition and the maximal height condition, presented as the third condition, which prevents the exact determination of this domain for the general case. The latest results were obtained by Gottschling for the genus 2 in 1959. It has since remained unexplored and poorly understood, in particular the different regions of Minkowski reduction. In order to identify Siegel's fundamental domain for genus 3, we present some results concerning the third condition of thi…
On the integration of Riemann-measurable vector-valued functions
2016
We confine our attention to convergence theorems and descriptive relationships within some subclasses of Riemann-measurable vector-valued functions that are based on the various generalizations of the Riemann definition of an integral.
From the Golgi-Cajal mapping to the transmitter-based characterization of the neuronal networks leading to two modes of brain communication: Wiring a…
2007
After Golgi-Cajal mapped neural circuits, the discovery and mapping of the central monoamine neurons opened up for a new understanding of interneuronal communication by indicating that another form of communication exists. For instance, it was found that dopamine may be released as a prolactin inhibitory factor from the median eminence, indicating an alternative mode of dopamine communication in the brain. Subsequently, the analysis of the locus coeruleus noradrenaline neurons demonstrated a novel type of lower brainstem neuron that monosynaptically and globally innervated the entire CNS. Furthermore, the ascending raphe serotonin neuron systems were found to globally innervate the forebrai…
Evidence of superatom electronic shells in ligand-stabilized aluminum clusters
2011
Ligand-stabilized aluminum clusters are investigated by density functional theory calculations. Analysis of Kohn-Sham molecular orbitals and projected density of states uncovers an electronic shell structure that adheres to the superatom complex model for ligand-stabilized aluminum clusters. In this current study, we explain how the superatom complex electron-counting rule is influenced by the electron-withdrawing ligand and a dopant atom in the metallic core. The results may guide the prediction of new stable ligand-stabilized (superatom) complexes, regardless of core and electron-withdrawing ligand composition.