Interplay between structure and size in a critical crystal nucleus

We study the kinetics of crystal nucleation of an undercooled Lennard-Jones liquid using various path-sampling methods. We obtain the rate constant and elucidate the pathways for crystal nucleation. Analysis of the path ensemble reveals that crystal nucleation occurs along many different pathways, in which critical solid nuclei can be small, compact, and face centered cubic, but also large, less ordered, and more body centered cubic. The reaction coordinate thus includes, besides the cluster size, also the quality of the crystal structure.     

Multivariate Polynomial Minimization and Its Application in Signal Processing

We make a conjecture that the number of isolated local minimum points of a 2n-degree or (2n+1)-degree r-variable polynomial is not greater than n ^r when n 2. We show that this conjecture is the minimal estimate, and is true in several cases. In particular, we show that a cubic polynomial of r variables may have at most one local minimum point though it may have 2^r critical points. We then study the global minimization problem of an even-degree multivariate polynomial whose leading order coefficient tensor is positive definite. We call such a multivariate polynomial a normal multivariate polynomial. By giving a one-variable polynomial majored below a normal multivariate polynomial, we show the existence of a global minimum of a normal multivariate polynomial, and give an upper bound of the norm of the global minimum and a lower bound of the global minimization value. We show that the quartic multivariate polynomial arising from broad-band antenna array signal processing, is a normal polynomial, and give a computable upper bound of the norm of the global minimum and a computable lower bound of the global minimization value of this normal quartic multivariate polynomial. We give some sufficient and necessary conditions for an even order tensor to be positive definite. Several challenging questions remain open.     

Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit

Classical optical lithography is diffraction limited to writing features of a size lambda/2 or greater, where lambda is the optical wavelength. Using nonclassical photon-number states, entangled N at a time, we show that it is possible to write features of minimum size lambda/(2N) in an N-photon absorbing substrate. This result allows one to write a factor of N2 more elements on a semiconductor chip. A factor of N = 2 can be achieved easily with entangled photon pairs generated from optical parametric down-conversion. It is shown how to write arbitrary 2D patterns by using this method.     

Investigation of excited states of11B and7Li by means of thermal neutron capture on10B nuclei

Theγ-radiation from the¹⁰B(n,γ) reaction is studied using an unpolarized target. More accurate values for energies of transitions in¹¹B could be determined. No new levels have been found. TheQ value of this reaction: 11,454.1 (2)keV, is in agreement with earlier experiments. Also a new value for the cross section could be derived: 0.29 (4) barn, which is a factor 5 more accurate than earlier experiments. The¹⁰B(n, α)⁷ Li reaction, leading to the 478 keV state in⁷Li, is studied by means of polarized¹⁰B nuclei and polarized neutrons. The resulting anisotropy in the directional distribution of the⁷Li particles manifests itself in the Doppler broadening of the 478 keV line. Analysis of the line shape directly yields the conclusion, that the reaction proceeds for more than 96% through theJ=7/2 channel of¹¹B in case of destructive channel interference of theJ=5/2 channel. Constructive channel interference is only possible if the reaction proceeds for more than 99.5% through theJ=7/2 channel. It appeared that the outcomingα and⁷Li particles are emitted predominantly in directions perpendicular to the nuclear orientation axis.     

Numerical study of the flow in a three-dimensional thermally driven cavity

Solutions for the fully compressible Navier–Stokes equations are presented for the flow and temperature fields in a cubic cavity with large horizontal temperature differences. The ideal-gas approximation for air is assumed and viscosity is computed using Sutherland's law. The three-dimensional case forms an extension of previous studies performed on a two-dimensional square cavity. The influence of imposed boundary conditions in the third dimension is investigated as a numerical experiment. Comparison is made between convergence rates in case of periodic and free-slip boundary conditions. Results with no-slip boundary conditions are presented as well. The effect of the Rayleigh number is studied.     

Conformational analysis of 1,2-difluoroethane, an ab-initio investigation

Contrary to expectation, the gauche conformer of 1,2-difluoroethane is more stable than the trans conformer in the gas phase. In order to understand the underlying causes of the “gauche effect”, a complete geometry relaxation was performed for the gauche and trans conformers of 1,2-difluoroethane with the 4-21G, 4-31G and 4-31G** basis sets. The 4-31G** optimized geometry of the gauche conformer compares well with the experimental values obtained from a number of electron-diffraction studies. A correction for the correlation energy, calculated by means of second-order Møller—Plesset perturbation theory with the 6-31G** basis set, proves to be essential to obtain a correct estimate of the energy difference between the gauche and trans conformers 1,2-difluoroethane.     

Photostabilizing of bisphenol A polycarbonate by using UV-absorbers and self protective block copolymers based on resorcinol polyarylate blocks

Bisphenol A polycarbonate degrades due to sunlight, humidity and oxygen. In this study two possible techniques to stabilize the polymer were compared, i.e. blending of UV-absorbers (UVAs) into the polymer or using block copolymers based on resorcinol polyarylates. Combination of different analysis techniques shows that the protection by UVAs is not as good as by the resorcinol polyarylate block copolymers. The block copolymer rearranges itself through a photo-Fries rearrangement within hours into a UV-absorbing top layer. Two different block compositions were studied, and the copolymer with the highest concentration of resorcinol polyarylate groups shows the best protection.     

Growth rate determination of heterogeneous microbial population in swine manure

The effect of manure concentration on the growth of the heterogeneous microbial population under batch condition was studied. Four manure concentrations were used in the study. The dehydrogenase activity was used as a measure of the active biomass in the manure. The chemical oxygen demand test was used to measure the change in organic material caused by biological activities. The growth curve of the heterogeneous microbial population in swine manure was essentially similar to that of a pure culture grown batchwise in that it had the four principle phases: lag, exponential growth, stationary, and death. The exponential growth phase followed a diauxic growth pattern. High concentration of manure had an inhibitory effect on the microbial growth. Manure diluted less than 1:3 (manure:water) depressed the specific growth rate of the microbial population.