A Fast Algorithm for Solving the Poisson Equation on a Nested Grid

We present a numerical method for solving the Poisson equation on a nested grid. The nested grid consists of uniform grids having different grid spacing and is designed to cover the space closer to the center with a finer grid. Thus our numerical method is suitable for computing the gravity of a centrally condensed object. It consists of two parts: the difference scheme for the Poisson equation on the nested grid and the multi-grid iteration algorithm. It has three advantages: accuracy, fast convergence, and scalability. First it computes the gravitational potential of a close binary accurately up to the quadraple moment, even when the binary is resolved only in the fine grids. Second residual decreases by a factor of 300 or more by each iteration. We confirmed experimentally that the iteration converges always to the exact solution of the difference equation. Third the computation load of the iteration is proportional to the total number of the cells in the nested grid. Thus our method gives a good solution at the minimum expense when the nested grid is large. The difference scheme is applicable also to the adaptive mesh refinement in which cells of different sizes are used to cover a domain of computation.Comment: 22 pages 21 figures. To appear in Ap

Molecular probing of low-temperature incommensurate phases

Two-dimensional (2D) excitation-emission spectra of biphenyl doped with free-base chlorin were measured at 5 K under various pressures up to 350 MPa. Besides the features related to zero-phonon lines and their phonon sidebands, a broad spectral band amounting to 80% of the total intensity at 5 K was revealed in the 2D spectra. The obtained inhomogeneous distribution function shows drastic changes with increasing pressure — the triplet structure observable at normal pressure in the incommensurate phase ICIII of biphenyl converges to a singlet in the high-pressure commensurate phase CI. These observations are assumed to reflect specific for incommensurate phases relaxation after an optical excitation of probe molecules and interaction of them with the incommensurate modulation wave

Demonstrating Discreteness and Collision Error in Cosmological N-body Simulations of Dark Matter Gravitational Clustering

Two-body scattering and other discreteness effects are unimportant in cosmological gravitational clustering in most scenarios, since the dark matter has a small particle mass. The collective field should determine evolution: Two-body scattering in simulations violates the Poisson-Vlasov equations. We test this in PM, P$^3$M, Tree, and NGPM codes, noting that a collisionless code will preserve the one-dimensional character of plane wave collapse. We find collisionality vanishing as the softening parameter approaches the mean interparticle separation. Solutions for the problem are suggested, involving greater computer power, PM-based nested grid codes, and a more conservative approach to resolution claims.Comment: Final version accepted for ApJ Letters. Minor revisions, including due to bug fix in tree code. Uses aasms4.sty. 15 pages. Higher resolution figures available at ftp://kusmos.phsx.ukans.edu/preprints/discret

Morphology and photoluminescence study of titania nanoparticles

Titania nanoparticles are prepared by sol–gel chemistry with a poly(ethylene oxide) methyl ether methacrylate-block-poly(dimethylsiloxane)-block-poly(ethylene oxide) methyl ether methacrylate triblock copolymer acting as the templating agent. The sol–gel components—hydrochloric acid, titanium tetraisopropoxide, and triblock copolymer—are varied to investigate their effect on the resulting titania morphology. An increased titania precursor or polymer content yields smaller primary titania structures. Microbeam grazing incidence small-angle X-ray scattering measurements, which are analyzed with a unified fit model, reveal information about the titania structure sizes. These small structures could not be observed via the used microscopy techniques. The interplay among the sol–gel components via our triblock copolymer results in different sized titania nanoparticles with higher packing densities. Smaller sized titania particles, (∼13–20 nm in diameter) in the range of exciton diffusion length, are formed by 2% by weight polymer and show good crystallinity with less surface defects and high oxygen vacancies

Molecular probing of low-temperature incommensurate phases

Two-dimensional (2D) excitation-emission spectra of biphenyl doped with free-base chlorin were measured at 5 K under various pressures up to 350 MPa. Besides the features related to zero-phonon lines and their phonon sidebands, a broad spectral band amounting to 80% of the total intensity at 5 K was revealed in the 2D spectra. The obtained inhomogeneous distribution function shows drastic changes with increasing pressure — the triplet structure observable at normal pressure in the incommensurate phase ICIII of biphenyl converges to a singlet in the high-pressure commensurate phase CI. These observations are assumed to reflect specific for incommensurate phases relaxation after an optical excitation of probe molecules and interaction of them with the incommensurate modulation wave

Low-temperature dynamics of incommensurate biphenyl as probed by spectral hole burning

We have measured the temperature dependence of the homogeneous width of spectral holes in the incommensurate phase III of chlorin-doped biphenyl from 60 mK to 10 K. Below 2 K a power law ($\sim T^\alpha$, $\alpha= 1.36, 1.74$ for different spectral peaks) prevails. Above 2 K a strong coupling to low-energy (5 and $\rm 9\; cm^{-1}$) vibrational modes dominates. No indication of a low-temperature lock-in transition was found

Energy transfer in ethane-bisporphyrins studied by fluorescence line narrowing and spectral hole burning

The quasi-line fluorescence excitation spectrum of 1,2-bis (2,3,7,8,12,13,17,18-octaethyl-21H,23 H-porphino) ethane at 4.8 K consists of two subbands with the splitting mean value of 51cm⁻¹, that are ascribed to the donor and the acceptor half of the homodimer. The donor's fluorescence is quenched by an efficient energy transfer to the acceptor. The energy transfer rate of 10¹¹ s⁻¹, determined by spectral hole burning, has been compared with the calculated value and a conclusion of nonconsistency with the Forster energy transfer mechanism has been drawn

Energy transfer in ethane-bisporphyrins studied by fluorescence line narrowing and spectral hole burning

The quasi-line fluorescence excitation spectrum of 1,2-bis (2,3,7,8,12,13,17,18-octaethyl-21H,23 H-porphino) ethane at 4.8 K consists of two subbands with the splitting mean value of 51cm⁻¹, that are ascribed to the donor and the acceptor half of the homodimer. The donor's fluorescence is quenched by an efficient energy transfer to the acceptor. The energy transfer rate of 10¹¹ s⁻¹, determined by spectral hole burning, has been compared with the calculated value and a conclusion of nonconsistency with the Forster energy transfer mechanism has been drawn