A Numerical Study of Two-Phase Flow Models with Dynamic Capillary Pressure and Hysteresis

Saturation overshoot and pressure overshoot are studied by incorporating dynamic capillary pressure, capillary pressure hysteresis and hysteretic dynamic coefficient with a traditional fractional flow equation in one-dimensional space. Using the method of lines, the discretizations are constructed by applying the Castillo–Grone’s mimetic operators in the space direction and a semi-implicit integrator in the time direction. Convergence tests and conservation properties of the schemes are presented. Computed profiles capture both the saturation overshoot and pressure overshoot phenomena. Comparisons between numerical results and experiments illustrate the effectiveness and different features of the models.     

Error-Correcting Codes over an Alphabet of Four Elements

The problem of finding the values of A_q(n,d)—the maximum size of a code of length n and minimum distance d over an alphabet of q elements—is considered. Upper and lower bounds on A₄(n,d) are presented and some values of this function are settled. A table of best known bounds on A₄(n,d) is given for n 12. When q M < 2q, all parameters for which A_q(n,d) = M are determined.     

Local-field effects on the spontaneous emission rate of CdTe and CdSe quantum dots in dielectric media

The refractive index dependence of the spontaneous emission rate is determined using organically capped CdSe and CdTe quantum dots as probes. The radiative lifetime of the exciton emission is measured in a variety of apolar solvents with refractive indices n between 1.37 and 1.50. It is demonstrated that quantum dots provide a model system for testing theories on the influence of local-field effects on the spontaneous emission rate. The experimentally observed influence of n on the radiative lifetime is smaller than predicted by well-known models for local-field corrections but is in good agreement with a recently developed fully microscopic model for the local-field enhancement of the spontaneous emission rate.     

Synthesis and luminescence of CdS quantum dots capped with a silica precursor

A novel synthesis method for efficiently luminescing CdS nanocrystals is reported using (3-mercaptopropyl)-trimethoxysilane (MPS) as a capping agent in THF or MeOH. The synthesis yields particles capped with a precursor for coating the particle with a silica shell and offers control over a wide range of particle sizes (2-) by varying the MPS concentration. The temperature dependence of the luminescence and the luminescence life time was studied and explained in terms of a donor-acceptor recombination process in which both electron and hole are trapped at low temperature. In addition to varying the emission color by controlling the particle size, nanocrystals were doped with Zn or Cu resulting in a blue shift or a red shift of the emission.     

Dipole moment changes in the singlet and triplet excited states of 4-dimethylamino-4′-nitrostilbene detected by nanosecond time-resolved microwave conductivity

Dipole moment changes accompanying the formantion of singlet and triplet excited states of 4-dimethylamino-4′-nitro- stilbene on laser flash photolysis of solutions in n-hexane and benzene have been observed by measuring changes in the microwave conductivity of the medium with nanosecond time resolution.     

Sum of ranking differences (SRD) to ensemble multivariate calibration model merits for tuning parameter selection and comparing calibration methods

Most multivariate calibration methods require selection of tuning parameters, such as partial least squares (PLS) or the Tikhonov regularization variant ridge regression (RR). Tuning parameter values determine the direction and magnitude of respective model vectors thereby setting the resultant predication abilities of the model vectors. Simultaneously, tuning parameter values establish the corresponding bias/variance and the underlying selectivity/sensitivity tradeoffs. Selection of the final tuning parameter is often accomplished through some form of cross-validation and the resultant root mean square error of cross-validation (RMSECV) values are evaluated. However, selection of a “good” tuning parameter with this one model evaluation merit is almost impossible. Including additional model merits assists tuning parameter selection to provide better balanced models as well as allowing for a reasonable comparison between calibration methods. Using multiple merits requires decisions to be made on how to combine and weight the merits into an information criterion. An abundance of options are possible. Presented in this paper is the sum of ranking differences (SRD) to ensemble a collection of model evaluation merits varying across tuning parameters. It is shown that the SRD consensus ranking of model tuning parameters allows automatic selection of the final model, or a collection of models if so desired. Essentially, the user’s preference for the degree of balance between bias and variance ultimately decides the merits used in SRD and hence, the tuning parameter values ranked lowest by SRD for automatic selection. The SRD process is also shown to allow simultaneous comparison of different calibration methods for a particular data set in conjunction with tuning parameter selection. Because SRD evaluates consistency across multiple merits, decisions on how to combine and weight merits are avoided. To demonstrate the utility of SRD, a near infrared spectral data set and a quantitative structure activity relationship (QSAR) data set are evaluated using PLS and RR.     

Novel synthesis of 3,4-diaminobutanenitriles and 4-amino-2-butenenitriles from 2-(cyanomethyl)aziridines through intermediate aziridinium salts: an experimental and theoretical approach

1-Arylmethyl-2-(cyanomethyl)aziridines were transformed into 4-(N,N-bis(arylmethyl)amino)-3-(pyrrolidin-1-yl)butanenitriles and 4-(N,N-bis(arylmethyl)amino)-2-butenenitriles via 4-(N,N-bis(arylmethyl)amino)-3-bromobutanenitriles in high yields and purity. The key steps involve the unprecedented regiospecific ring opening of intermediate 2-(cyanomethyl)aziridinium salts by bromide and pyrrolidine in acetonitrile, exclusively at the substituted aziridine carbon atom. The results were rationalized on the basis of ab initio calculations.     

Borate Hydrides as a New Material Class: Structure,Computational Studies,and Spectroscopic Investigations on Sr5(BO3)3H and Sr5(11BO3)3D

The unprecedented borate hydride Sr₅(BO₃)₃H and deuteride Sr₅(¹¹BO₃)₃D crystallizing in an apatite-related structure are reported. Despite the presence of hydride anions, the compound decomposes only slowly in air. Doped with Eu²⁺, it shows broad-band orange-red emission under violet excitation owing to the 4f⁶5d–4f⁷ transition of Eu²⁺. The observed ¹H NMR chemical shift is in good agreement with previously reported ¹H chemical shifts of ionic metal hydrides as well as with quantum chemical calculations and very different from ¹H chemical shifts usually found for hydroxide ions in similar materials. FTIR and Raman spectroscopy of different samples containing ¹H, ²H, ^natB, and ¹¹B combined with calculations unambiguously prove the absence of hydroxide ions and the sole incorporation of hydride ions into the borate. The orange-red emission obtained by doping with Eu²⁺ shows that the new compound class might be a promising host material for optical applications.     

Counterexamples to Conjectures About Subset Takeaway and Counting Linear Extensions of a Boolean Lattice

We develop an algorithm for efficiently computing recursively defined functions on posets. We illustrate this algorithm by disproving conjectures about the game Subset Takeaway (Chomp on a hypercube) and computing the number of linear extensions of the lattice of a 7-cube and related lattices.