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Reduction of solution of game of pursuit for survival payoff to solution of Cauchy problem for first order partial differential equation
Darken-Alcock-Richardson equation for dilute solid solutions of interstitial solutes in binary alloy solvents
Partial configurational thermodynamic functions of interstitial species in ternary solid solutions containing substitutional and interstitial solute atoms
Ternary solid solutions with substitutional and interstitial solute atoms, developing statistical mechanical interaction model
Numerical solutions for radiative transport in a class of anisotropically scattering materials are presented. Conditions for convergence and divergence of the iterative method are given and supported by computed results. The relation of two flux theories to the equation of radiative transfer for isotropic scattering is discussed. The adequacy of the two flux approach for the reflectance, radiative flux and radiative flux divergence of highly scattering media is evaluated with respect to solutions of the radiative transfer equation.
In this overview paper, we review the basic principles of the method of space-time conservation element and solution element for solving the conservation laws in one and two spatial dimensions. The present method is developed on the basis of local and global flux conservation in a space-time domain, in which space and time are treated in a unified manner. In contrast to the modern upwind schemes, the approach here does not use the Riemann solver and the reconstruction procedure as the building blocks. The drawbacks of the upwind approach, such as the difficulty of rationally extending the 1D scalar approach to systems of equations and particularly to multiple dimensions is here contrasted with the uniformity and ease of generalization of the Conservation Element and Solution Element (CE/SE) 1D scalar schemes to systems of equations and to multiple spatial dimensions. The assured compatibility with the simplest type of unstructured meshes, and the uniquely simple nonreflecting boundary conditions of the present method are also discussed. The present approach has yielded high-resolution shocks, rarefaction waves, acoustic waves, vortices, ZND detonation waves, and shock/acoustic waves/vortices interactions. Moreover, since no directional splitting is employed, numerical resolution of two-dimensional calculations is comparable to that of the one-dimensional calculations. Some sample applications displaying the strengths and broad applicability of the CE/SE method are reviewed.
An organic crystal according to one embodiment includes an organic crystal comprising diphenylacetylene and stilbene or a stilbene derivative, the crystal having physical characteristics of formation from solution, the organic crystal exhibiting a signal response signature for neutrons from a radioactive source. A system according to one embodiment includes an organic crystal comprising diphenylacetylene and stilbene or a stilbene derivative, the crystal having physical characteristics of formation from solution, the organic crystal exhibiting a signal response signature for neutrons from a radioactive source; and a photodetector for detecting the signal response of the organic crystal. Methods of making such crystals are also provided.
We develop an approach, by calculating the autocorrelation function of spins, to derive the magnetic field gradient-induced transverse (T{sub 2}) relaxation of spins undergoing restricted diffusion. This approach is an extension to the method adopted by McGregor. McGregor's approach solves the problem only in the fast diffusion limit; however, our approach yields a single analytical solution suitable in all diffusion regimes, including the intermediate regime. This establishes a direct connection between the well-known slow diffusion result of Torrey and the fast diffusion result. We also perform free induction decay measurements on spin-exchange optically polarized {sup 3}He gas with different diffusion constants. The measured transverse relaxation profiles are compared with the theory and satisfactory agreement has been found throughout all diffusion regimes. In addition to the transverse relaxation, this approach is also applicable to solving the longitudinal relaxation (T{sub 1}) regardless of the diffusion limits. It turns out that the longitudinal relaxation in the slow diffusion limit differs by a factor of 2 from that in the fast diffusion limit.
Adsorption of n-nonane/1-hexanol (C9/C6OH) mixtures into the lamellar phase formed by a 50/50 w/w triethylene glycol mono-n-decyl ether (C10E3)/water system was studied using configurational-bias Monte Carlo simulations in the osmotic Gibbs ensemble. The interactions were described by the Shinoda–Devane–Klein coarse-grained force field. Prior simulations probing single-component adsorption indicated that C9 molecules preferentially load near the center of the bilayer increasing the bilayer thickness, whereas C6OH molecules are more likely to be found near the interface of the polar and non-polar moieties swelling the bilayer in the lateral dimension. Here, we extend this work to binary C9/C6OH adsorption to probe whether the difference in the spatial preferences may lead to a synergistic effect and enhanced loadings for the mixture. Comparing loading trends and the thermodynamics of binary adsorption to unary adsorption reveals that C9–C9 interactions lead to the largest enhancement, whereas C9–C6OH and C6OH–C6OH interactions are less favorable for this bilayer system. As a result, ideal adsorbed solution theory yields satisfactory predictions of the binary loading.
Water and ion dynamics in concentrated LiCl solutions were studied using ultrafast 2D IR spectroscopy with the methyl thiocyanate (MeSCN) CN stretch as the vibrational probe. The IR absorption spectrum of MeSCN has two peaks, one peak for water associated with the nitrogen lone pair of MeSCN (W) and the other peak corresponding to Li + associated with the lone pair (L). To extract the spectral diffusion (structural dynamics) of W and L species, we developed a method that isolates the peak of interest by subtracting the 2D Gaussian proxies of multiple interfering peaks. Center line slope data (normalized frequency–frequency correlation function) for 2D bands from the W and L are fit with triexponential functions. The fastest component (1.1–1.6 ps) is assigned to local hydrogen bond length fluctuations. The intermediate timescale (~4.0 ps) corresponds to the hydrogen bond network rearrangement. The slowest component decays in ~40 ps and corresponds to ion pair and ion cluster dynamics. The very similar W and L spectral diffusion indicates that the motions of the water and ions are strongly coupled. Orientational relaxations of the W and L species were extracted using a new method to eliminate the effects of overlapping peaks. The results show that MeSCN bound to water undergoes orientational relaxation significantly faster than MeSCN bound to Li + . The orientational and spectral diffusion results are compared. In conclusion, a Stark coupling model is used to extract the root mean square average electric field caused by the ion clouds along the CN moiety as a function of concentration.
A near-UV excited, oxyfluoride phosphor solid solution Sr{sub 1.975}Ce{sub 0.025}Ba(AlO{sub 4}F){sub 1-x}(SiO{sub 5}){sub x} has been developed for solid state white lighting applications. An examination of the host lattice, and the local structure around the Ce{sup 3+} activator ions through a combination of density functional theory, synchrotron X-ray and neutron powder diffraction and total scattering, and electron paramagnetic resonance, points to how chemical substitutions play a crucial role in tuning the optical properties of the phosphor. The maximum emission wavelength can be tuned from green ({lambda}{sub em} = 523 nm) to yellow ({lambda}{sub em} = 552 nm) by tuning the composition, x. Photoluminescent quantum yield is determined to be 70 {+-} 5% for some of the examples in the series. Excellent thermal properties were found for the x = 0.5 sample, with the photoluminescence intensity at 160 C only decreased to 82% of its room temperature value. Phosphor-converted LED devices fabricated using an InGaN LED ({lambda}{sub max} = 400 nm) exhibit high color rendering white light with R{sub a} = 70 and a correlated color temperature near 7000 K. The value of R{sub a} could be raised to 90 by the addition of a red component, and the correlated color temperature lowered to near 4000 K.
The streaming potentials of liquid beams of aqueous NaCl, NaBr, and NaI solutions are measured using soft X-ray, He(I), and laser multiphoton ionization photoelectron spectroscopy. Gaseous molecules are ionized in the vicinity of liquid beams and the photoelectron energy shifts are measured as a function of the distance between the ionization point and the liquid beam. The streaming potentials change their polarity with concentration of electrolytes, from which the singular points of concentration eliminating the streaming potentials are determined. The streaming currents measured in air also vanish at these concentrations. The electron binding energies of liquid water and I{sup −}, Br{sup −}, and Cl{sup −} anions are revisited and determined more accurately than in previous studies.
Using first-principles calculations, we reveal an unexpected structural softening in a recently proposed WB{sub 3+x} structural model that tries to explain the X-ray diffraction, high resolution TEM, pressure dependence of the normalized lattice c/a ratio, and hardness experimental results of the synthesized tungsten boride compounds with a nominal composition WB{sub 4}. We show that the interstitial boron in WB{sub 3+x}, which was proposed to strengthen the covalent bonding network, unexpectedly weakens the atomic bonding, resulting in a large reduction of its indentation strength to well below that of WB{sub 3}. This is in direct contradiction to the experimental results showing that synthesized WB{sub 4} is harder than WB{sub 3}. The unusual structural softening is attributed to the unique three-center covalent bonding formed by the interstitial boron atoms that can easily deform under indentation. Our results show that the proposed interstitial boron solid solution WB{sub 3+x} structure is incompatible with experimental results, which calls for further investigations to determine the crystal structure of the synthesized WB{sub 4}.
Your correspondents develop and apply fully nonorthogonal, local-reference perturbation theories describing non-covalent interactions. Our formulations are based on a Löwdin partitioning of the similarity-transformed Hamiltonian into a zeroth-order intramonomer piece (taking local CCSD solutions as its zeroth-order eigenfunction) plus a first-order piece coupling the fragments. If considerations are limited to a single molecule, the proposed intermolecular similarity-transformed perturbation theory represents a frozen-orbital variant of the “(2)”-type theories shown to be competitive with CCSD(T) and of similar cost if all terms are retained. Different restrictions on the zeroth- and first-order amplitudes are explored in the context of large-computation tractability and elucidation of non-local effects in the space of singles and doubles. To accurately approximate CCSD intermolecular interaction energies, a quadratically growing number of variables must be included at zeroth-order.
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