Professor A. J. H. van der Walt- 'n Waardering

My kennismaking met prof. Andries van der Walt dateer vanaf Februarie1925, nou een-en-dertig jaar gelede

Ons erfenis van driehonderd jaar

Waar ons tans die stigting van die blanke volksplanting aan die Kaap driehonderd jaar gelede herdenk, gaan dit nie om bloot in die herinnering terug te roep ’n eenmalige gebeurtenis van April 1652 nie, maar veel meer die uitwerking en gevolge daarvan, soos sigbaar in die Unie van Suid-Afrika vandag

Inertia and chiral edge modes of a skyrmion magnetic bubble

The dynamics of a vortex in a thin-film ferromagnet resembles the motion of a charged massless particle in a uniform magnetic field. Similar dynamics is expected for other magnetic textures with a nonzero skyrmion number. However, recent numerical simulations revealed that skyrmion magnetic bubbles show significant deviations from this model. We show that a skyrmion bubble possesses inertia and derive its mass from the standard theory of a thin-film ferromagnet. Besides center-of-mass motion, other low energy modes are waves on the edge of the bubble traveling with different speeds in opposite directions.Comment: updated simulation detail

The exclusive \bar{B} --> \pi e^+ e^- and \bar{B} --> \rho e^+ e^- decays in the two Higgs doublet model with flavor changing neutral currents

We calculate the leading logarithmic QCD corrections to the matrix element of the decay b --> d e^+ e^- in the two Higgs doublet model with tree level flavor changing currents (model III). We continue studying the differential branching ratio and the CP violating asymmetry for the exclusive decays B --> \pi e^+ e^- and B --> \rho e^+ e^- and analysing the dependencies of these quantities on the selected model III parameters, \xi^{U,D}, including the leading logarithmic QCD corrections. Further, we present the forward-backward asymmetry of dileptons for the decay B --> \rho e^+ e^- and discuss the dependencies to the model III parameters. We observe that there is a possibility to enhance the branching ratios and suppress the CP violating effects for both decays in the framework of the model III. Therefore, the measurements of these quantities will be an efficient tool to search the new physics beyond the SM.Comment: 27 pages, 14 Figure

A dynamic density functional theory for particles in a flowing solvent

We present a dynamic density functional theory (dDFT) which takes into accou nt the advection of the particles by a flowing solvent. For potential flows we can use the same closure as in the absence of solvent flow. The structure of the resulting advected dDFT suggests that it could be used for non-potential flows as well. We apply this dDFT to Brownian particles (e.g., polymer coils) in a solvent flowing around a spherical obstacle (e.g., a colloid) and compare the results with direct simulations of the underlying Brownian dynamics. Although numerical limitations do not allow for an accurate quantitative check of the advected dDFT both show the same qualitative features. In contrast to previous works which neglected the deformation of the flow by the obstacle, we find that the bow-wave in the density distribution of particles in front of the obstacle as well as the wake behind it are reduced dramatically. As a consequence the friction force exerted by the (polymer) particles on the colloid can be reduced drastically.Comment: 7 pages, 5 figures, 2 tables, submitte

Self Consistent Random Phase Approximation and the restoration of symmetries within the three-level Lipkin model

We show that it is possible to restore the symmetry associated with the Goldstone mode within the Self Consistent Random Phase Approximation (SCRPA) applied to the three-level Lipkin model. We determine one and two-body densities as very convergent expansions in terms of the generators of the RPA basis. We show that SCRPA excitations correspond to the heads of some rotational bands in the exact spectrum. It turns out that the SCRPA eigenmodes for N=2 coincide with exact solutions, given by the diagonalisation procedure

More Benefits of Semileptonic Rare B Decays at Low Recoil: CP Violation

We present a systematic analysis of the angular distribution of Bbar -> Kbar^\ast (-> Kbar pi) l^+ l^- decays with l = e, mu in the low recoil region (i.e. at high dilepton invariant masses of the order of the mass of the b-quark) to account model-independently for CP violation beyond the Standard Model, working to next-to-leading order QCD. From the employed heavy quark effective theory framework we identify the key CP observables with reduced hadronic uncertainties. Since some of the CP asymmetries are CP-odd they can be measured without B-flavour tagging. This is particularly beneficial for Bbar_s,B_s -> phi(-> K^+ K^-) l^+ l^- decays, which are not self-tagging, and we work out the corresponding time-integrated CP asymmetries. Presently available experimental constraints allow the proposed CP asymmetries to be sizeable, up to values of the order ~ 0.2, while the corresponding Standard Model values receive a strong parametric suppression at the level of O(10^-4). Furthermore, we work out the allowed ranges of the short-distance (Wilson) coefficients C_9,C_10 in the presence of CP violation beyond the Standard Model but no further Dirac structures. We find the Bbar_s -> mu^+ mu^- branching ratio to be below 9*10^-9 (at 95% CL). Possibilities to check the performance of the theoretical low recoil framework are pointed out.Comment: 18 pages, 3 fig.; 1 reference and comment on higher order effects added; EOS link fixed. Minor adjustments to Eqs 4.1-4.3 to match the (lower) q^2-cut as given in paper. Main results and conclusions unchanged; v3+v4: treatment of exp. uncert. in likelihood-function in EOS fixed and constraints from scan on C9,C10 updated (Fig 2,3 and Eqs 3.2,3.3). Main results and conclusions absolutely unchange

Nonequilibrium fluctuation dissipation relations of interacting Brownian particles driven by shear

We present a detailed analysis of the fluctuation dissipation theorem (FDT) close to the glass transition in colloidal suspensions under steady shear using mode coupling approximations. Starting point is the many-particle Smoluchowski equation. Under shear, detailed balance is broken and the response functions in the stationary state are smaller at long times than estimated from the equilibrium FDT. An asymptotically constant relation connects response and fluctuations during the shear driven decay, restoring the form of the FDT with, however, a ratio different from the equilibrium one. At short times, the equilibrium FDT holds. We follow two independent approaches whose results are in qualitative agreement. To discuss the derived fluctuation dissipation ratios, we show an exact reformulation of the susceptibility which contains not the full Smoluchowski operator as in equilibrium, but only its well defined Hermitian part. This Hermitian part can be interpreted as governing the dynamics in the frame comoving with the probability current. We present a simple toy model which illustrates the FDT violation in the sheared colloidal system.Comment: 21 pages, 13 figures, submitted to Phys. Rev.

Maximally-localized Wannier Functions in Antiferromagnetic MnO within the FLAPW Formalism

We have calculated the maximally-localized Wannier functions of MnO in its antiferromagnetic (AFM) rhombohedral unit cell, which contains two formula units. Electron Bloch functions are obtained with the linearized augmented plane-wave method within both the LSD and the LSD+U schemes. The thirteen uppermost occupied spin-up bands correspond in a pure ionic scheme to the five Mn 3d orbitals at the Mn_1 (spin-up) site, and the four O 2s/2p orbitals at each of the O_1 and O_2 sites. Maximal localization identifies uniquely four Wannier functions for each O, which are trigonally-distorted sp^3-like orbitals. They display a weak covalent bonding between O 2s/2p states and minority-spin d states of Mn_2, which is absent in a fully ionic picture. This bonding is the fingerprint of the interaction responsible for the AFM ordering, and its strength depends on the one-electron scheme being used. The five Mn Wannier functions are centered on the Mn_1 site, and are atomic orbitals modified by the crystal field. They are not uniquely defined by the criterion of maximal localization and we choose them as the linear combinations which diagonalize the r^2 operator, so that they display the D_3d symmetry of the Mn_1 site.Comment: 11 pages, 6 PostScript figures. Uses Revtex4. Hi-res figures available from the author

Fragility and compressibility at the glass transition

Isothermal compressibilities and Brillouin sound velocities from the literature allow to separate the compressibility at the glass transition into a high-frequency vibrational and a low-frequency relaxational part. Their ratio shows the linear fragility relation discovered by x-ray Brillouin scattering [1], though the data bend away from the line at higher fragilities. Using the concept of constrained degrees of freedom, one can show that the vibrational part follows the fragility-independent Lindemann criterion; the fragility dependence seems to stem from the relaxational part. The physical meaning of this finding is discussed. [1] T. Scopigno, G. Ruocco, F. Sette and G. Monaco, Science 302, 849 (2003)Comment: 4 pages, 2 figures, 2 tables, 33 references. Slightly changed after refereein