Fast particle-mesh code for Milgromian dynamics

Modified Newtonian dynamics (MOND) is a promising alternative to dark matter. To further test the theory, there is a need for fluid- and particle-dynamics simulations. The force in MOND is not a direct particle-particle interaction, but derives from a potential for which a nonlinear partial differential equation (PDE) needs to be solved. Normally, this makes the problem of simulating dynamical evolution computationally expensive. We intend to develop a fast particle-mesh (PM) code for MOND (the AQUAL formalism). We transformed the nonlinear equation for MOND into a system of linear PDEs plus one algebraic equation. An iterative scheme with the fast Fourier transform (FFT) produces successively better numerical approximations. The algorithm was tested for dynamical systems in MOND where analytical solutions are known: the two-body problem, a body with a circular ring, and a spherical distribution of particles in thermal equilibrium in the self-consistent potential. The PM code can accurately calculate the forces at subpixel scale and reproduces the analytical solutions. Four iterations are required for the potential, but when the spatial steps are small compared to the kernel width, one iteration is suffices. The use of a smoothing kernel for the accelerations is inevitable in order to eliminate the self-gravity of the point particles. Our PDE solver is $15$ to $42$ times as slow as a standard Poisson solver. However, the smoothing and particle propagation takes up most of the time above one particle per $10^3$ pixels. The FFTs, the smoothing, and the propagation part in the code can all be parallelized.Comment: 13 pages, 13 figure

Bulk Fermi surface and momentum density in heavily doped La2−x_{2-x}Srx_xCuO4_4 using high resolution Compton scattering and positron annihilation spectroscopies

We have observed the bulk Fermi surface (FS) in an overdoped ($x$=0.3) single crystal of La$_{2-x}$Sr$_x$CuO$_4$ by using Compton scattering. A two-dimensional (2D) momentum density reconstruction from measured Compton profiles yields a clear FS signature in the third Brillouin zone along [100]. The quantitative agreement between density functional theory (DFT) calculations and momentum density experiment suggests that Fermi-liquid physics is restored in the overdoped regime. In particular the predicted FS topology is found to be in good accord with the corresponding experimental data. We find similar quantitative agreement between the measured 2D angular correlation of positron annihilation radiation (2D-ACAR) spectra and the DFT based computations. However, 2D-ACAR does not give such a clear signature of the FS in the extended momentum space in either the theory or the experiment.Comment: 9 pages, 8 figure

Lattice models and Landau theory for type II incommensurate crystals

Ground state properties and phonon dispersion curves of a classical linear chain model describing a crystal with an incommensurate phase are studied. This model is the DIFFOUR (discrete frustrated phi4) model with an extra fourth-order term added to it. The incommensurability in these models may arise if there is frustration between nearest-neighbor and next-nearest-neighbor interactions. We discuss the effect of the additional term on the phonon branches and phase diagram of the DIFFOUR model. We find some features not present in the DIFFOUR model such as the renormalization of the nearest-neighbor coupling. Furthermore the ratio between the slopes of the soft phonon mode in the ferroelectric and paraelectric phase can take on values different from -2. Temperature dependences of the parameters in the model are different above and below the paraelectric transition, in contrast with the assumptions made in Landau theory. In the continuum limit this model reduces to the Landau free energy expansion for type II incommensurate crystals and it can be seen as the lowest-order generalization of the simplest Lifshitz-point model. Part of the numerical calculations have been done by an adaption of the Effective Potential Method, orginally used for models with nearest-neighbor interaction, to models with also next-nearest-neighbor interactions.Comment: 33 pages, 7 figures, RevTex, submitted to Phys. Rev.

Electronic coupling of colloidal CdSe nanocrystals monitored by thin-film positron-electron momentum density methods

The effect of temperature controlled annealing on the confined valence electron states in CdSe nanocrystal arrays, deposited as thin films, was studied using two-dimensional angular correlation of annihilation radiation (2D-ACAR). A reduction in the intensity by ~35% was observed in a feature of the positron annihilation spectrum upon removal of the pyridine capping molecules above 200 degrees Celsius in a vacuum. This reduction is explained by an increased electronic interaction of the valence orbitals of neighboring nanocrystals, induced by the formation of inorganic interfaces. Partial evaporation of the nanoporous CdSe layer and additional sintering into a polycrystalline thin film was observed at a relatively low temperature of ~486 degrees Celsius.Comment: The article has been accepted by Applied Physics Letters. After it is published, it will be found at http://apl.aip.or

Positron depth profiling of the structural and electronic structure transformations of hydrogenated Mg-based thin films

We report positron depth-profiling studies on the hydrogen sorption behavior and phase evolution of Mg-based thin films. We show that the main changes in the depth profiles resulting from the hydrogenation to the respective metal hydrides are related to a clear broadening in the observed electron momentum densities in both Mg and Mg2Ni films. This shows that positron annihilation methods are capable of monitoring these metal-to-insulator transitions, which form the basis for important applications of these types of films in switchable mirror devices and hydrogen sensors in a depth-sensitive manner. Besides, some of the positrons trap at the boundaries of columnar grains in the otherwise nearly vacancy-free Mg films. The combination of positron annihilation and x-ray diffraction further shows that hydrogen loading at elevated temperatures, in the range of 480–600 K, leads to a clear Pd–Mg alloy formation of the Pd catalyst cap layer. At the highest temperatures, the hydrogenation induces a partial delamination of the ? 5?nm thin capping layer, as sensitively monitored by positron depth profiling of the fraction of ortho-positronium formed at interface with the cap layer. The delamination effectively blocks the hydrogen cycling. In Mg–Si bilayers, we investigated the reactivity upon hydrogen loading and heat treatments near 480 K, which shows that Mg2Si formation is fast relative to MgH2. The combination of positron depth profiling and transmission electron microscopy shows that hydrogenation promotes a complete conversion to Mg2Si for this destabilized metal hydride system, while a partially unreacted, Mg-rich amorphous prelayer remains on top of Mg2Si after a single heat treatment in an inert gas environment. Thin film studies indicate that the difficulty of rehydrogenation of Mg2Si is not primarily the result from slow hydrogen dissociation at surfaces, but is likely hindered by the presence of a barrier for removal of Mg from the readily formed Mg2Si.Radiation, Radionuclides and ReactorsApplied Science