On the continuum modelling of segregation of granular mixtures during hopper emptying in core flow mode

In this paper, the application of a continuum model is presented, which deals with the discharge of multi-component granular mixtures in core flow mode. The full model description is given (including the constitutive models for the segregation mechanism) and the interactions between particles at the microscopic level are parametrised in order to predict the development of stagnant zone boundaries during core flow discharges. Finally, the model is applied to a real industrial problem and predictions are made for the segregation patterns developed during mixture discharge in core flow mode.

Meiobenthos and macrobenthos are discrete entities and not artefacts of sampling a size continuum: Comment on Bett (2013)

Species size distributions for metazoan benthic invertebrates conform to the highly conservative bimodal pattern, regardless of the sieve mesh sizes or numbers of sieves used in their extraction. This pattern is not an artefact of sampling a size continuum as suggested by computer simulations using just 2 fixed mesh sizes in Bett (2013; Mar Ecol Prog Ser 487:1-6). Meiobenthos and macrobenthos are coherent entities, each with a distinct suite of functional attributes, and should not be regarded as a single unit for ecological modelling purposes.

Analytically continued generalized continuum distorted waves

The continuum distorted-wave eikonal-initial-state (CDW-EIS) theory of Crothers and McCann (Crothers DSF and McCann JF, 1983 J. Phys. B: At. Mol. Opt. Phys. 16 3229 ) used to describe ionization in ion-atom collisions is generalized (G) to GCDW-EIS, to incorporate the azimuthal ange dependence into the final-state wavefunction. This is accomplished by the analytic continuation of hydrogenic-like wavefunctions from below to above threshold, using parabolic coordinates and quantum numbers including magnetic quantum numbers, thus providing a more complete set of states. At impact energies lower than 25 ke V u^{-1}, the total CDW-EIS ionization cross section falls off, with decreasing energy, too quickly in comparison with experimental data by Crothers and McCann. The idea behind and motivation for the GCDW-EIS model is to improve the theory with respect to experiment, by including contributions from non-zero magnetic quantum numbers. We also therefore incidentally provide a new derivation of the theory of continuum distorted waves for zero magnetic quantum numbers while simultaneously generalizing it.

Total and single differential cross sections for simple resonant collisions using a fully orthonormal continuum-distorted-wave basis

Simple electron capture processes are studied using an orthonormal two state continuum-distorted-wave (CDW) basis. The suitability of the basis set is tested by comparing predictions for total and differential cross sections with available experimental data. Overall good agreement is obtained and the authors conclude that a relatively small CDW basis set may be suitable to model a wide variety of low-energy collisions if the members of this extended set are astutely chosen.

Magnetically quantized continuum distorted-wave theory in atomic and molecular collisions

The continuum distorted-wave eikonal initial-state (CDW-EIS) theory of Crothers and McCann (J Phys B 1983, 16, 3229) used to describe ionization in ion-atom collisions is generalized (G) to GCDW-EIS to incorporate the azimuthal angle dependence of each CDW in the final-state wave function. This is accomplished by the analytic continuation of hydrogenic-like wave functions from below to above threshold, using parabolic coordinates and quantum numbers including magnetic quantum numbers, thus providing a more complete set of states. At impact energies lower than 25 keVu(-1), the total ionization cross-section falls off, with decreasing energy, too quickly in comparison with experimental data. The idea behind and motivation for the GCDW-EIS model is to improve the theory with respect to experiment by including contributions from nonzero magnetic quantum numbers. We also therefore incidentally provide a new derivation of the theory of continuum distorted waves for zero magnetic quantum numbers while simultaneously generalizing it. (C) 2004 Wiley Periodicals, Inc.

Shifts in electron capture to the continuum at low collision energies: Enhanced role of target postcollision interactions

Measurements of electron velocity distributions emitted at 0degrees for collisions of 10- and 20-keV H+ incident ions on H-2 and He show that the electron capture to the continuum cusp formation, which is still possible at these low impact energies, is shifted to lower momenta than its standard position (centered on the projectile velocity), as recently predicted. Classical trajectory Monte Carlo calculations reproduce the observations remarkably well, and indicate that a long-range residual interaction of the electron with the target ion after ionization is responsible for the shifts, which is a general effect that is enhanced at low nuclear velocities.

Shifting of the electron-capture-to-the-continuum peak in proton-helium collisions at 10 and 20 keV

A refined theoretical approach has been developed to study the double-differential cross sections (DDCS's) in proton-helium collisions as a function of the ratio of ionized electron velocity to the incident proton velocity. The refinement is done in the present coupled-channel calculation by introducing a continuum distorted wave in the final state coupled with discrete states including direct as well as charge transfer channels. It is confirmed that the electron-capture-to-the-continuum (ECC) peak is slightly shifted to a lower electron velocity than the equivelocity position. Comparing measurements and classical trajectory Monte Carlo (CTMC) calculations at 10 and 20 keV proton energies, excellent agreement of the ECC peak heights is achieved at both energies. However, a minor disagreement in the peak positions between the present calculation and the CTMC results is noted. A smooth behavior of the DDCS is found in the present calculation on both sides of the peak whereas the CTMC results show some oscillatory behavior particularly to the left of the peak, associated with the statistical nature of CTMC calculations.

A dielectric continuum molecular dynamics method

We introduce a novel method to simulate hydrated macromolecules with a dielectric continuum representation of the surrounding solvent. In our approach, the interaction between the solvent and the molecular degrees of freedom is described by means of a polarization density free energy functional which is minimum at electrostatic equilibrium. After a pseudospectral expansion of the polarization and a discretization of the functional, we construct the equations of motion for the system based on a Car-Parrinello technique. In the limit of the adiabatic evolution of the polarization field variables, our method provides the solution of the dielectric continuum problem "on the fly," while the molecular coordinates are propagated. In this first study, we show how our dielectric continuum molecular dynamics method can be successfully applied to hydrated biomolecules, with low cost compared to free energy simulations with explicit solvent. To our knowledge, this is the first time that stable and conservative molecular dynamic simulations of solutes can be performed for a dielectric continuum model of the solvent. (C) 2001 American Institute of Physics.