Search results for " Mathematical"
showing 10 items of 686 documents
Crystallization in suspensions of hard spheres: a Monte Carlo and molecular dynamics simulation study
2011
The crystallization of a metastable melt is one of the most important non-equilibrium phenomena in condensed matter physics, and hard sphere colloidal model systems have been used for several decades to investigate this process by experimental observation and computer simulation. Nevertheless, there is still an unexplained discrepancy between the simulation data and experimental nucleation rate densities. In this paper we examine the nucleation process in hard spheres using molecular dynamics and Monte Carlo simulation. We show that the crystallization process is mediated by precursors of low orientational bond-order and that our simulation data fairly match the experimental data sets.
Exciton-Phonon Coupling in the Ultraviolet Absorption and Emission Spectra of Bulk Hexagonal Boron Nitride
2018
We present an \textit{ab initio} method to calculate phonon-assisted absorption and emission spectra in the presence of strong excitonic effects. We apply the method to bulk hexagonal BN which has an indirect band gap and is known for its strong luminescence in the UV range. We first analyse the excitons at the wave vector $\overline{q}$ of the indirect gap. The coupling of these excitons with the various phonon modes at $\overline{q}$ is expressed in terms of a product of the mean square displacement of the atoms and the second derivative of the optical response function with respect to atomic displacement along the phonon eigenvectors. The derivatives are calculated numerically with a fin…
Limits on the release of Rb isotopes from a zeolite based 83mKr calibration source for the XENON project
2011
The isomer 83mKr with its half-life of 1.83 h is an ideal calibration source for a liquid noble gas dark matter experiment like the XENON project. However, the risk of contamination of the detector with traces of the much longer lived mother isotop 83Rb (86.2 d half-life) has to be ruled out. In this work the release of 83Rb atoms from a 1.8 MBq 83Rb source embedded in zeolite beads has been investigated. To do so, a cryogenic trap has been connected to the source for about 10 days, after which it was removed and probed for the strongest 83Rb gamma-rays with an ultra-sensitive Germanium detector. No signal has been found. The corresponding upper limit on the released 83Rb activity means tha…
Solvent hydrodynamics speed up crystal nucleation in suspensions of hard spheres
2014
We present a computer simulation study on the crystal nucleation process in suspensions of hard spheres, fully taking into account the solvent hydrodynamics. If the dynamics of collodial crystallization were purely diffusive, the crystal nucleation rate densities would drop as the inverse of the solvent viscosity. However, we observe that the nucleation rate densities do not scale in this way, but are enhanced at high viscosities. This effect might explain the large discrepancy between the nuclation rate densities obtained by simulation and experiment that have reported in the literature so far.
The effect of wear on the tetragonal-to-monoclinic transformation and the residual stress distribution in zirconia-toughened alumina cutting tools
1998
Abstract Zirconia-toughened alumina cutting tools have been examined after machining an AISI 1040 steel. The Raman spectrum of zirconia and the fluorescence spectrum from alumina have been used to determine the extent of the tetragonal-to-monoclinic (t-m) transformation and the residual stresses in and around the worn-out crater, respectively. Although about 15% vol. m-zirconia is present even in a brand new cutting tool, it was shown that the crater region undergoes the t-m transformation up to 40% vol. In both cases, the transformed zone is concentrated near the surface. The residual stresses in alumina are slightly compressive in the new cutting tool and away from the crater region, but …
Depletion-induced percolation in networks of nanorods.
2006
Above a certain density threshold, suspensions of rod-like colloidal particles form system-spanning networks. Using Monte Carlo simulations, we investigate how the depletion forces caused by spherical particles affect these networks in isotropic suspensions of rods. Although the depletion forces are strongly anisotropic and favor alignment of the rods, the percolation threshold of the rods decreases significantly. The relative size of the effect increases with the aspect ratio of the rods. The structural changes induced in the suspension by the depletant are characterized in detail and the system is compared to an ideal fluid of freely interpenetrable rods.
Depletion induced isotropic-isotropic phase separation in suspensions of rod-like colloids
2007
When non-adsorbing polymers are added to an isotropic suspension of rod-like colloids, the colloids effectively attract each other via depletion forces. We performed Monte Carlo simulations to study the phase diagram of such rod-polymer mixture. The colloidal rods were modeled as hard spherocylinders; the polymers were described as spheres of the same diameter as the rods. The polymers may overlap with no energy cost, while the overlap of polymers and rods is forbidden. Large amounts of depletant cause phase separation of the mixture. We estimated the phase boundaries of isotropic-isotropic coexistence both in the bulk and in confinement. To determine the phase boundaries we applied the gra…
Periodic unmixing of a binary metallic vapor
2005
We report on a type of surface structuring after short pulse laser ablation of a binary alloy. We observe the emergence of a concentric ring structure with changing elemental composition. The composition changes are interpreted by condensation of the ambient ablation vapor due to stress wave excitations in the ablation spot.
Portfolios with fuzzy returns: Selection strategies based on semi-infinite programming
2008
AbstractThis paper provides new models for portfolio selection in which the returns on securities are considered fuzzy numbers rather than random variables. The investor's problem is to find the portfolio that minimizes the risk of achieving a return that is not less than the return of a riskless asset. The corresponding optimal portfolio is derived using semi-infinite programming in a soft framework. The return on each asset and their membership functions are described using historical data. The investment risk is approximated by mean intervals which evaluate the downside risk for a given fuzzy portfolio. This approach is illustrated with a numerical example.
Cross-Efficiency in Fuzzy Data Envelopment Analysis (FDEA): Some Proposals
2013
Different techniques have been proposed in the literature to rank decision making units (DMUs) in the context of Fuzzy Data Envelopment Analysis. In our opinion, those that result from using a ranking method to order the fuzzy efficiencies obtained are susceptible to a serious criticism: they are not based on objective criteria. Cross-efficiency evaluation was introduced as an extension of DEA aimed at ranking the DMUs. This methodology has found a significant number of applications and has been extensively investigated. In this chapter, we discuss some difficulties that arise with the definition of fuzzy cross-efficiencies and we propose a fuzzy cross-efficiency evaluation based on the FDE…