A multigroup diffusion solver using pseudo transient continuation for a radiation-hydrodynamic code with patch-based AMR

We present a scheme to solve the nonlinear multigroup radiation diffusion (MGD) equations. The method is incorporated into a massively parallel, multidimensional, Eulerian radiation-hydrodynamic code with Adaptive Mesh Refinement (AMR). The patch-based AMR algorithm refines in both space and time creating a hierarchy of levels, coarsest to finest. The physics modules are time-advanced using operator splitting. On each level, separate “level-solve” packages advance the modules. Our multigroup level-solve adapts an implicit procedure which leads to a two-step iterative scheme that alternates between elliptic solves for each group with intra-cell group coupling. For robustness, we introduce pseudo transient continuation (Ψtc). We analyze the magnitude of the Ψtc parameter to ensure positivity of the resulting linear system, diagonal dominance and convergence of the two-step scheme. For AMR, a level defines a subdomain for refinement. For diffusive processes such as MGD, the refined level uses Dirichlet boundary data at the coarse–fine interface and the data is derived from the coarse level solution. After advancing on the fine level, an additional procedure, the sync-solve (SS), is required in order to enforce conservation. The MGD SS reduces to an elliptic solve on a combined grid for a system of G equations, where G is the number of groups. We adapt the “partial temperature” scheme for the SS; hence, we reuse the infrastructure developed for scalar equations. Results are presented. We consider a multigroup test problem with a known analytic solution. We demonstrate utility of Ψtc by running with increasingly larger timesteps. Lastly, we simulate the sudden release of energy Y inside an Al sphere (r = 15 cm) suspended in air at STP. For Y = 11 kT, we find that gray radiation diffusion and MGD produce similar results. However, if Y = 1 MT, the two packages yield different results. Our large Y simulation contradicts a long-standing theory and demonstrates the inadequacy of gray diffusion.     

Kinetic length and step permeability on the Si(1 1 1) (1 × 1) surface

Information on the kinetic regime of step motion and step permeability on the Si(1 1 1) (1 × 1) surface has been obtained from observations of island decay that were made with low energy electron microscopy. Island area during decay exhibits the expected power law dependence on time, with exponent, α, that is a qualitative indicator of the kinetic regime. A new method is presented for determining the kinetic length quantitatively from measurements of the decay exponent in the symmetric island decay geometry on top of a larger concentric circular island. Using this approach, we determine the kinetic length on the Si(1 1 1) (1 × 1) surface at 1163 K to be d ∼ 75a, where a is the lattice constant. It is shown that this result locates step motion firmly in the diffusion limited regime. Mass conservation of decaying island stacks is also observed at this temperature, which indicates that steps are effectively impermeable in the context of diffusion limited step kinetics.     

Measurements of scintillation efficiency and pulse shape for low energy recoils in liquid xenon

Results of observations of low energy nuclear and electron recoil events in liquid xenon scintillator detectors are given. The relative scintillation efficiency for nuclear recoils is 0.22±0.01 in the recoil energy range 40–70 keV. Under the assumption of a single dominant decay component to the scintillation pulse shape the log-normal mean parameter T₀ of the maximum likelihood estimator of the decay time constant for 6 keV <E_ee<30 keV nuclear recoil events is equal to 21.0±0.5 ns. It is observed that for electron recoils T₀ rises slowly with energy, having a value ∼30 ns at E_ee∼15 keV. Electron and nuclear recoil pulse shapes are found to be well fitted by single exponential functions although some evidence is found for a double exponential form for the nuclear recoil pulse shape.     

Time decay of excitations in the one-dimensional trapping problem

An exact solution is obtained for the survival fraction in the one-dimensional diffusion problem with randomly distributed deep traps. The time decay is studied both with and without a bias field. The small concentration (x) long time (t) decay behaves as exp[-(x ² t/t ₀)^1/3]. The exact results are compared with the coherent potential approximation (CPA) and the first passage time approach (FPT). We find that in most cases of practical interest the FPT is superior to the CPA.     

Energy transfer dynamics in B-phycoerythrin from the red alga Porphyridium purpureum

The B-phycoerythrin hexamer (αβ)₆γ of Porphyridium purpureum was isolated and purified. The absorption, circular dichroism, fluorescence and ultrafast time-resolved spectra were obtained. The results showed a double absorption peak at 545 nm and 565 nm and a shoulder peak at 498 nm, and fluorescence emission maxima at 580 nm and 620 nm were observed. The circular dichroism spectra in the near-ultraviolet region were obtained and resolved for the first time, which showed that the two peaks at 260 nm and 305 nm were considered to be correlated to phenylalanine (Phe) and tryptophan (Trp) in a conservative hydrophobic microenvironment, respectively. The circular dichroism spectra in the visible region showed that PEB139α/PEB158β and PEB82α/PEB82β existed as two exciton-coupled bilin pairs. Energy transfer within the exciton-coupled pairs was by exciton splitting, while between the exciton-coupled pairs was by Förster resonance. From the studies of the energy transfer dynamics by ultrafast time-resolved fluorescence spectroscopy, it was confirmed that the energy transfer of the B-PE hexamer had three time components of 8 ps, 60 ps, and 1200 ps. In addition, the internal energy transfer pathways of B-phycoerythrin hexamer were identified by deconvoluting the fluorescence decay curve at different detection wavelengths.     

Modelling the interior sound field of a railway vehicle using statistical energy analysis

The sound field in train compartments, treated as a series of connected air cavities, is modelled using statistical energy analysis, SEA. For the case under study, with five cavities in series and the source in the second cavity, a closed-form solution is obtained. An adjusted SEA model is used to predict the rate of spatial decay within a cavity. The SEA model is validated using results from a ray tracing method and from scale model measurements. For the octave bands 500–4000 Hz, good agreement is shown between the results from measurements, the ray tracing and the SEA model, for the two saloons closest to the source cavity (a vestibule). The SEA model was shown to slightly underestimate the rate of spatial decay within a cavity. It is concluded that a reasonable cause is the additional diffusion due to the seating.     

Chaotic motion at the emergence of the time averaged energy decay

A system plus environment conservative model is used to characterize the nonlinear dynamics when the time averaged energy for the system particle starts to decay. The system particle dynamics is regular for low values of the N environment oscillators and becomes chaotic in the interval 13≤N≤15, where the system time averaged energy starts to decay. To characterize the nonlinear motion we estimate the Lyapunov exponent (LE), determine the power spectrum and the Kaplan-Yorke dimension. For much larger values of N the energy of the system particle is completely transferred to the environment and the corresponding LEs decrease. Numerical evidence shows the connection between the variations of the amplitude of the particles energy time oscillation with the time averaged energy decay and trapped trajectories.     

Volume and surface effects in the luminescence decay of electron-hole drops in Ge

Measurements of the luminescence time decay of electron-hole drops (EHD) in Ge are interpreted by taking into account the EHD volume recombination and the evaporation of free excitons (FE) at the EHD surface. From this study we get the EHD binding energy at T = 0 which is φ(0) = 15 ± 2 K. This result is consistent with the spectroscopic value of φ(0) if one takes into account the exchange splitting of FE.     

Decay of kaonium in a chiral approach

The decay of the K⁺K⁻ hadronic atom kaonium is investigated non-perturbatively using meson-meson interaction amplitudes taken from leading order chiral perturbation theory in an approach adapted from that proposed by Oller and Oset (1997) [18]. The Kudryavtsev-Popov eigenvalue equation is solved numerically for the energy shift and decay width due to strong interactions in the 1s state. These calculations introduce a cutoff ∼1.4 GeV in O(4) momentum space that is necessary to regulate divergent loop contributions to the meson-meson scattering amplitudes in the strong-interaction sector. One finds lifetimes of (2.2±0.9)×¹⁰−18 s for the ground state of kaonium.     

Modeling quantum mechanical double slit interference via anomalous diffusion: Independently variable slit widths

Based on a re-formulation of the classical explanation of quantum mechanical Gaussian dispersion (Grössing et al. (2010) [1]) as well as interference of two Gaussians (Grössing et al. (2012) [6]), we present a new and more practical way of their simulation. The quantum mechanical “decay of the wave packet” can be described by anomalous sub-quantum diffusion with a specific diffusivity varying in time due to a particle’s changing thermal environment. In a simulation of the double-slit experiment with different slit widths, the phase with this new approach can be implemented as a local quantity. We describe the conditions of the diffusivity and, by connecting to wave mechanics, we compute the exact quantum mechanical intensity distributions, as well as the corresponding trajectory distributions according to the velocity field of two Gaussian wave packets emerging from a double-slit. We also calculate probability density current distributions, including situations where phase shifters affect a single slit’s current, and provide computer simulations thereof.     

First principle study of structural,phase stabilization and oxygen-ion diffusion properties of β-La2 − xLxMo2O9 (L = Gd,Sm, Nd and Bi) and β-La2Mo2 − yMyO9 (M = Cr,W)

We have performed a first principle study of structural and phase stabilization of β-La_2 ? xL_xMo₂O₉ (L = Gd, Sm, Nd and Bi) and β-La₂Mo_2 ? yM_yO₉ (M = Cr, W). The substitutional-site properties were discussed in terms of the empirical parameter, bond valence sums (BVS), which characterizes the interactions between atoms and its nearest-neighbor atoms and correlates well with the stability of the structure. We found that Gd, Sm and Nd atoms prefer the crystallographic sites with largest BVS values. The nonlinear dependence of cell parameter on W content in W-doped systems results from the nonlinear change in Mo/W–O bond length with W content. The decrease of cohesive energy and the deviation of BVS values from the expected values upon the Gd, Sm, Nd and W-doped concentration help us understand the experimentally observed stabilization of the β phase to lower temperatures in these doped system. The O ion diffusion properties in W-doped systems have been studied using the nudged elastic band method and the dimer method. We found that, W-doping leads to the obvious increase in the energy barriers of O ion concerted diffusion. In addition, there is a remarkable decrease in the difference of energy barriers between two diffusion channels involving O(1) ion, which sheds light on only one relaxation peak in the mechanical relaxation measurement in W-doped system, compared to undoped system.     

Interlayer-exciton mediated three-hole-Auger-decay in the π⁎-band of highly oriented pyrolytic graphite

Resonant photoemission spectroscopy (resPES) is used to probe the occupied π- and unoccupied π^⁎-bands of carbon thin films with particular focus on the Auger decay. Highly Oriented Pyrolytic Graphite (HOPG) is studied at the C1s edge. We find strong resonant features at 285.5 eV and 292 eV in the resPES diagram. The normal two-hole Auger decay proceeds under constant kinetic energy (45°) only in the σ^⁎-region. In the π^⁎-region, however, it proceeds under 67.5° in terms of a E_bind(ħω) diagram. We attribute this to a multiple Auger decay with a net three hole final state. For this novel decay process we propose a model. We discuss the long lifetime of the first resonant excitation and conclude that it arises from the strong excitonic character of the first resonant state. We use HOPG as a reference system and suggest that this novel process is a tool to identify interlayer–substrate interaction of the carbon layers involved.     

New mechanism for non-trivial intra-molecular vibrational dynamics

We investigate the time evolution process of one selected (initially prepared by optical pumping) vibrational molecular state S, coupled to all other intra-molecular vibrational states R of the same molecule, and also to its environment Q. Molecular states forming the first reservoir R are characterized by a discrete dense spectrum, whereas the environment reservoir Q states form a continuous spectrum. Assuming the equidistant reservoir R states we find the exact analytical solution of the quantum dynamic equations. S-Q and R-Q couplings yield to spontaneous decay of the S and R states, whereas S-R exchange leads to recurrence cycles and Loschmidt echo at frequencies of S-R transitions and double resonances at the interlevel reservoir R transitions. Due to these couplings the system S time evolution is not reduced to a simple exponential relaxation. We predict various regimes of the system S dynamics, ranging from exponential decay to irregular damped oscillations. Namely, we show that there are possible four dynamic regimes of the evolution: (i) independent of the environment Q exponential decay suppressing backward R - S transitions, (ii) Loschmidt echo regime, (iii) incoherent dynamics with multicomponent Loschmidt echo, when the system state is exchanged its energy with many states of the reservoir, (iv) cycle mixing regime, when long time system dynamics looks as a random-like. We suggest applications of our results for interpretation of femtosecond vibration spectra of large molecules and nano-systems.     

Energy transfer as a random walk with long-range steps

We consider the incoherent energy transport in molecular crystals, where the transfer rates stem from Coulombic and exchange interactions. For substitutionally disordered lattices we present in a first passage model the excitation decay due to trapping by randomly distributed traps; the decay is related to the distribution of the number of distinct sites visited during the timet and is expressible through the cumulants of this distribution. The validity domains of approximate decay laws based on the first few cumulants are also discussed. We exemplify the findings for dipolar transfer rates between randomly distributed molecules on a square lattice, by comparing the random walk on the random system to its CTRW (continuous time random walk) counterpart.     

Simulation of the interface of (1 0 0) rutile with aqueous ionic solution

The interface of the rutile (1 0 0) surface with NaCl solutions has been simulated by classical molecular dynamics. In contrast to earlier simulations the protonation and hydroxylation equilibriums have been adjusted for different pH values (4, 7.4, and 9). The short range order close to the surface is described by two water layers with some orientational order and intermediate layers of positive or negative ions depending on the surface charge. A Stern model is confirmed with a dense layer of counterions on the charged TiO₂ surface and a diffuse layer, which only consists of few ions in our system. The increase of orientational order of the water molecules close to the surface is described by an exponential function with a decay parameter of 1.9 Å, superposed by a damped oscillation which is independent of the pH value. The diffusion is significantly slower than in the bulk within a range of 13 Å from the surface. We propose a common approach for describing the different z-dependences of orientational order and of the diffusion coefficients.     

Derivation and solution of multifrequency radiation diffusion equations for homogeneous refractive lossy media

Starting from the radiation transport equation for homogeneous, refractive lossy media, we derive the corresponding time-dependent multifrequency diffusion equations. Zeroth and first moments of the transport equation couple the energy density, flux and pressure tensor. The system is closed by neglecting the temporal derivative of the flux and replacing the pressure tensor by its diagonal analogue. The radiation equations are coupled to a diffusion equation for the matter temperature. We are interested in modeling heating and cooling of silica (SiO₂), at possibly rapid rates. Hence, in contrast to related work, we retain the temporal derivative of the radiation field. We derive boundary conditions at a planar air–silica interface taking account of reflectivities obtained from the Fresnel relations that include absorption. The spectral dimension is discretized into a finite number of intervals leading to a system of multigroup diffusion equations. Three simulations are presented. One models cooling of a silica slab, initially at 2500 K, for 10 s. The other two are 1D and 2D simulations of irradiating silica with a CO₂ laser, λ = 10.59 μm. In 2D, a laser beam (Gaussian profile, r₀ = 0.5 mm for 1/e decay) shines on a disk (radius = 0.4, thickness = 0.4 cm).     

A comparative study of the energy migration and energy transfer in highly doped Nd:YAG single crystal

The donor-donor (D-D) energy migration interaction parameter C_DD in high-concentration Nd³⁺-doped YAG laser crystal is estimated, for the first time, by using the Yokota-Tanimoto (Y-T) model and the spectral overlap model (SOM) of Kushida. Firstly, the experimental luminescence decay curves of ⁴F_3/2 state of Nd³⁺ ions in YAG laser crystal at room temperature for 2.0 and 3.0 at% Nd³⁺ concentrations reported by Mao are fitted successfully by using the Y-T model and the parameter C_DD is obtained to be 1.50×10⁻³⁹ cm⁶/s. Secondly, the parameter C_DD is also directly calculated by using the SOM of Kushida: C_DD is calculated to be 2.73×10⁻³⁹ cm⁶/s. By comparing the energy migration interaction parameter C_DD and the donor-acceptor (D-A) energy transfer interaction parameter C_DA (1.794×10⁻⁴⁰ cm⁶/s), it is concluded that energy migration rate between Nd³⁺ ions in YAG laser crystal was about 11 times larger than energy transfer rate, and that energy migration would play a very important role in high-concentration Nd³⁺ -doped YAG laser crystal.     

Fluorescence Recovery Under Decaying Photobleaching Irradiation: Concept and Experiment

A novel modification of photobleaching method for measurement of lateral diffusion is developed. In this approach fluorescence recovery kinetics is measured under decaying photobleaching irradiation, termed as fluorescence recovery under decaying photobleaching (FRDP). The time evolution of fluorescence intensity normalized to input irradiation starts from the photobleaching kinetics and transforms into the kinetics of fluorescence recovery at a later stage resulting in appearance of minimum. The analytical solution for the kinetics of fluorescence for Gaussian lineshape of laser beam and hyperbolic decay of irradiation in the first order approximation on bleaching rate was obtained. The accuracy of the analytical function was evaluated with exact numerical solution computed with finite differentiates method. The FRDP method was successfully applied to fluorescein solution in the glycerol/water mixture (80%) under various experimental settings using home-made experimental set-up. The FRDP approach demonstrated 25–30 fold enhancement in signal intensity over classical fluorescence recovery after photobleaching (FRAP) method at 3–5 fold increase in total irradiation. Among other advantages of the FRDP is the opportunity to perform measurements on varying time scales under constant size of the bleaching spot, including “safe” long time measurements. The potential extra advantage of FRDP method for analysis of complex diffusion in the biological system is discussed.     

Orbital currents and charge density waves in a generalized Hubbard ladder

We study a generalized Hubbard model on the two-leg ladder at zero temperature, focusing on a parameter region with staggered flux (SF)/d-density wave (DDW) order. To guide our numerical calculations, we first investigate the location of a SF/DDW phase in the phase diagram of the half-filled weakly interacting ladder using a perturbative renormalization group (RG) and bosonization approach. For hole doping δ away from half-filling, finite-system density-matrix renormalization-group (DMRG) calculations are used to study ladders with up to 200 rungs for intermediate-strength interactions. In the doped SF/DDW phase, the staggered rung current and the rung electron density both show periodic spatial oscillations, with characteristic wavelengths 2/δ and 1/δ, respectively, corresponding to ordering wavevectors 2k_F and 4k_F for the currents and densities, where 2k_F = π (1 − δ). The density minima are located at the anti-phase domain walls of the staggered current. For sufficiently large dopings, SF/DDW order is suppressed. The rung density modulation also exists in neighboring phases where currents decay exponentially. We show that most of the DMRG results can be qualitatively understood from weak-coupling RG/bosonization arguments. However, while these arguments seem to suggest a crossover from non-decaying correlations to power-law decay at a length scale of order 1/δ, the DMRG results are consistent with a true long-range order scenario for the currents and densities.