An ODE Model of the Motion of Pelagic Fish

A system of ordinary differential equations (ODEs) is derived from a discrete system of Vicsek, Czirók et al. [Phys. Rev. Lett. 75(6):1226–1229, 1995], describing the motion of a school of fish. Classes of linear and stationary solutions of the ODEs are found and their stability explored using equivariant bifurcation theory. The existence of periodic and toroidal solutions is also proven under deterministic perturbations and structurally stable heteroclinic connections are found. Applications of the model to the migration of the capelin, a pelagic fish that undertakes an extensive migration in the North Atlantic, are discussed and simulation of the ODEs presented.     

Collision hamiltonian for non-linear molecules

A model hamiltonian which describes the non-reactive collision of two non-linear molecules has been constructed. This hamiltonian gives insight into the character of the complex translational, vibrational and rotational motions. The main features of the isolated molecule case are essentially disturbed by the non-adiabatic interaction between the macroscopic molecular motions and the vibrations. The usual angular momentum expressions are found to be the asymptotic limits of the true angular momenta in the case when these non-adiabaticities are switched off.     

Anomalous temperature dependence of elastic constant c44 in V, Nb, Ta, Pd, and Pt

The anomalous temperature dependence of elastic constant c₄₄ for elements V, Nb, Ta, Pd, and Pt, has been calculated using first-principles theory. It is shown that the variation of elastic constant for simple elements can be approximated as the sum of thermal expansion and electronic components. The thermal expansion contributes the normal linearly decreasing effect to the elastic constant with temperature, while electronic contribution is determined by the unique character of electronic structure of elements and leads to the anomalous effect to the elastic constant with temperature.     

The Aharonov–Bohm effect in graphene rings

This is a review of electronic quantum interference in mesoscopic ring structures based on graphene, with a focus on the interplay between the Aharonov–Bohm effect and the peculiar electronic and transport properties of this material. We first present an overview on recent developments of this topic, both from the experimental as well as the theoretical side. We then review our recent work on signatures of two prominent graphene-specific features in the Aharonov–Bohm conductance oscillations, namely Klein tunneling and specular Andreev reflection. We close with an assessment of experimental and theoretical development in the field and highlight open questions as well as potential directions of the developments in future work.     

High order finite difference methods with subcell resolution for advection equations with stiff source terms

A new high order finite-difference method utilizing the idea of Harten ENO subcell resolution method is proposed for chemical reactive flows and combustion. In reaction problems, when the reaction time scale is very small, e.g., orders of magnitude smaller than the fluid dynamics time scales, the governing equations will become very stiff. Wrong propagation speed of discontinuity may occur due to the underresolved numerical solution in both space and time. The present proposed method is a modified fractional step method which solves the convection step and reaction step separately. In the convection step, any high order shock-capturing method can be used. In the reaction step, an ODE solver is applied but with the computed flow variables in the shock region modified by the Harten subcell resolution idea. For numerical experiments, a fifth-order finite-difference WENO scheme and its anti-diffusion WENO variant are considered. A wide range of 1D and 2D scalar and Euler system test cases are investigated. Studies indicate that for the considered test cases, the new method maintains high order accuracy in space for smooth flows, and for stiff source terms with discontinuities, it can capture the correct propagation speed of discontinuities in very coarse meshes with reasonable CFL numbers.     

Hydrogen adsorption on palladium and palladium hydride at 1 bar

The dissociative sticking probability for H₂ on Pd films supported on sputtered Highly Ordered Pyrolytic Graphite (HOPG) has been derived from measurements of the rate of the H–D exchange reaction at 1 bar. The sticking probability for H₂, S, is higher on Pd hydride than on Pd (a factor of 1.4 at 140 °C), but the apparent desorption energy derived from S is the same on Pd and Pd hydride within the uncertainty of the experiment. Density Functional Theory (DFT) calculations for the (1 1 1) surfaces of Pd and Pd hydride show that, at a surface H coverage of a full mono layer, H binds less strongly to Pd hydride than to Pd. The activation barrier for desorption at a H coverage of one mono layer is slightly lower on Pd hydride, whereas the activation energy for adsorption is similar on Pd and Pd hydride. It is concluded that the higher sticking probability on Pd hydride is most likely caused by a slightly lower equilibrium coverage of H, which is a consequence of the lower heat of adsorption for H on Pd hydride.     

Angle-resolved photoemission study of a vacancy-induced state in substoichiometric VC

A vacancy induced state has been identified at about 1.8eV binding energy on the (100) face of VC_0.80 using angle-resolved photoelectron spectroscopy. The recorded spectra are compared with calculated spectra for VC_1.0 and the results show that the origin of the observed state cannot be accounted for by the energy band structure of VC_1.0. Photoemission spectra recorded after exposing the clean surface to O₂ and CO are also presented and used in a discussion of the sensitivity of the vacancy induced state to surface contamination.     

Application of the Monte Carlo method to the problem of surface segregation simulation

A generalization of the Monte Carlo method to the case of grand canonical ensemble allowing the elimination of the problem of determination of the chemical potential of alloy components was proposed. The method is particularly convenient for the calculations of surface segregations because it excludes time-consuming calculation of the temperature-dependent bulk chemical potential μ(T). The new method was used for calculating segregations at the (100), (110), and (111) surfaces of the Ni₅₀Pd₅₀ alloy using the Ising model with ab initio effective interatomic interaction potentials.