Theory for structure and bulk-modulus determination

A new method for direct evaluation of both crystalline structure, bulk modulus B_0, and bulk-modulus pressure derivative B'_0 of solid materials with complex crystal structures is presented. The explicit and exact results presented here permit a multidimensional polynomial fit of the total energy as a function of all relevant structure parameters to simultaneously determine the equilibrium configuration and the elastic properties. The method allows for inclusion of general (internal) structure parameters, e.g., bond lengths and angles within the unit cell, on an equal footing with the unit-cell lattice parameters. The method is illustrated by the calculation of B_0 and B'_0 for a few selected materials with multiple structure parameters for which data is obtained by using first-principles density functional theory.Comment: 7 pages, 2 figures, submitted to Phys. Rev.

Adsorption of Methanol on Aluminum Oxide: A Density Functional Study

Theoretical calculations based on density functional theory have made significant contributions to our understanding of metal oxides, their surfaces, and the binding of molecules at these surfaces. In this paper we investigate the binding of methanol at the alpha-Al2O3(0001) surface using first-principles density functional theory. We calculate the molecular adsorption energy of methanol to be E^g_ads=1.03 eV/molecule. Taking the methanol-methanol interaction into account, we obtain the adsorption energy E_ads=1.01 eV/molecule. Our calculations indicate that methanol adsorbs chemically by donating electron charge from the methanol oxygen to the surface aluminum. We find that the surface atomic structure changes upon adsorption, most notably the spacing between the outermost Al and O layers changes from 0.11 Angstrom to 0.33 Angstrom.Comment: 11 pages, 3 figures, 1 tabl

A Harris-type van der Waals density functional scheme

Large biomolecular systems, whose function may involve thousands of atoms, cannot easily be addressed with parameter-free density functional theory (DFT) calculations. Until recently a central problem was that such systems possess an inherent sparseness, that is, they are formed from components that are mutually separated by low-electron-density regions where dispersive forces contribute significantly to the cohesion and behavior. The introduction of, for example, the van der Waals density functional (vdW-DF) method [PRL 92, 246401 (2004)] has addressed part of this sparse-matter system challenge. However, while a vdW-DF study is often as computationally efficient as a study performed in the generalized gradient approximation, the scope of large-sparse-matter DFT is still limited by computer time and memory. It is costly to self-consistently determine the electron wavefunctions and hence the kinetic-energy repulsion. In this paper we propose and evaluate an adaption of the Harris scheme [PRB 31, 1770 (1985)]. This is done to speed up non-selfconsistent vdW-DF studies of molecular-system interaction energies. Also, the Harris-type analysis establishes a formal link between dispersion-interaction effects on the effective potential for electron dynamics and the impact of including selfconsistency in vdW-DF calculations [PRB 76, 125112 (2007)].Comment: 15 page

Diffusion and Weak Turbulence

Contents Introduction 3 1 Diffusion in Surface Waves 6 1.1 The Faraday Experiment . . . . . . . . . . . . . . . . . . . . . . . 6 1.2 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3 Notation and Tools . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.4 Surface Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2 Relative Particle Motion 15 2.1 Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2 Relative Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.3 Moments of the Relative Diffusivity . . . . . . . . . . . . . . . . . 19 3 Theory of Weak Turbulence 32 3.1 Hamiltonian Formalism . . . . . . . . . . . . . . . . . . . . . . . . 33 3.2 Kinetic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.2.1 Derivation of Three-Wave Kinetic Equation . . . . . . . . 36 3.2.2 The Four-Wave Kinetic Equation . . . . . . . . . . . . . . 40 3.3 Application to Surface Waves . . . . .

Physica A 239 (1997) 314

On the surface of a vertically oscillated fluid, capillary waves with a clearly discernible wavelength are formed if the amplitude of the oscillations exceeds a critical value. Particles sprinkled on the fluid surface are experimentally found to move in an almost Brownian motion when measured over distances larger than . We extend earlier studies of the diffusivity to length scales ranging from 0:1 to 10. We observe a cross-over in the diffusive motion from a strongly anomalous diffusion below , to a motion that is closer to being Brownian above . Our observations show that the particle motion is well described by an amplitude-independent fractional Brownian motion, effective at sizes less than , convoluted with an amplitude-dependent fractional Brownian motion, effective on all length scales smaller than the system size