Laplace transform wave functions

The wave function defining a quantum-mechanical system is considered as the Laplace transform of some distribution and the consequent form of the Variational Principle derived; an integral equation defines the eigenfunctions of a certain subclass. The model of the hydrogen-like atom is used to test the theory; the eigenfunctions and associated energy levels of the ground and excited states are obtained for arbitrary values of the orbital quantum number.     

Molecular dynamics simulations of a poly(p-phenylene) oligomer

We have studied the conformation and coefficient of thermal expansion in the poly(p-phenylene) oligomer p-sexiphenyl (C₃₆H₂₆) by molecular dynamics simulations. Studies of the backbone phenyl–phenyl torsion angle in a simulated p-sexiphenyl crystal at room temperature indicate the presence of torsional librations of approximately ±20°. Further analysis of the phenyl–phenyl backbone torsion angle in less closely packed regions of the simulated crystal (crystal ends) indicate the presence of 180° phenyl ring flips, in agreement with solid-state deuterium NMR data on poly(p-phenylene oligomers). The linear coefficient of thermal expansion was also calculated and found to be negative, in qualitative agreement with experimental data on rigid-rod compounds. © 1993 John Wiley & Sons, Inc.     

Segmentation algorithm for non-stationary compound Poisson processes

We introduce an algorithm for the segmentation of a class of regime switching processes. The segmentation algorithm is a non parametric statistical method able to identify the regimes (patches) of a time series. The process is composed of consecutive patches of variable length. In each patch the process is described by a stationary compound Poisson process, i.e. a Poisson process where each count is associated with a fluctuating signal. The parameters of the process are different in each patch and therefore the time series is non-stationary. Our method is a generalization of the algorithm introduced by Bernaola-Galván, et al. [Phys. Rev. Lett. 87, 168105 (2001)]. We show that the new algorithm outperforms the original one for regime switching models of compound Poisson processes. As an application we use the algorithm to segment the time series of the inventory of market members of the London Stock Exchange and we observe that our method finds almost three times more patches than the original one.     

Ring contracting sulfur extrusion from oxidized phenothiazine ring systems

Lithium, used in conjunction with sodium metal, produces a high yield of carbazole when reacted with phenothiazine-5-oxide or phenothiazine-5,5-dioxide. A high yield of 9-ethylcarbazole is also produced when these reagents react with 10-ethylphenothiazine, 10-ethylphenothiazine-5-oxide, and 10-ethylphenothiazine-5,5-dioxide. Degassed Raney nickel produces carbazole in high yield when reacted with phenothiazine and phenothiazine-5-oxide. A moderate yield of 9-ethylcarbazole is produced when n-butyllithium is reacted with 10-ethylphenothiazine-5-oxide.     

Syntheses,structure, and reactivity of acyclic enetriyne and enetetrayne derivatives

Sonogashira coupling of buta-1,3-diynylbenzene with ((2-iodophenyl)ethynyl)trimethylsilane and 1,2-diiodobenzene led to the novel enetriyne, 1-ethynyl-2-(phenylbuta-1,3-diynyl)benzene, and enetetrayne, 1,2-bis(phenylbuta-1,3-diynyl)benzene, respectively. Solid state structural and thermal analyses are also described. In solution, 1-ethynyl-2-(phenylbuta-1,3-diynyl)benzene was found to undergo thermal Bergman cyclization to afford 2-(phenylethynyl)naphthalene.     

Structural analysis of tris(tetra-n-butylammonium) hexakisisothiocyanatoyttrate(III)

The structural analysis of [(n-C₄H₉)₄N]₃[Y(NCS)₆] (I) using single-crystal diffraction data and full-matrix least squares refinement has been carried out. The hexaisothiocyanate complex crystallizes in the centrosymmetric triclinic space group P (No. 2) with unit cell constants of a = 12.431(1), b = 12.866(1), c = 22.750(2) Å, = 90.78(1), = 92.05(1), = 96.67(1)°, and Z = 2. The molecular unit consists of three separate cationic tetra-n-butylammonium groups and an independent hexakisisothiocyanatoyttrate anionic group in which the six thiocyanate ligands are octahedrally coordinated through the N atom to the Y central ion. Selected bond distances and angles are presented as well as the synthesis and peripheral studies of (I).     

Interaction energy and surface reconstruction between sheets of layered silicates

Interactions between two layered silicate sheets, as found in various nanoscale materials, are investigated as a function of sheet separation using molecular dynamics simulation. The model systems are periodic in the xy plane, open in the z direction, and subjected to stepwise separation of the two silicate sheets starting at equilibrium. Computed cleavage energies are 383 mJ /m(2) for K-mica, 133 mJ /m(2) for K-montmorillonite (cation exchange capacity=91), 45 mJ /m(2) for octadecylammonium (C(18))-mica, and 40 mJ /m(2) for C(18)-montmorillonite. These values are in quantitative agreement with experimental data and aid in the molecular-level interpretation. When alkali ions are present at the interface between the silicate sheets, partitioning of the cations between the surfaces is observed at 0.25 nm separation (mica) and 0.30 nm separation (montmorillonite). Originally strong electrostatic attraction between the two silicate sheets is then reduced to 5% (mica) and 15% (montmorillonite). Weaker van der Waals interactions decay within 1.0 nm separation. The total interaction energy between sheets of alkali clay is less than 1 mJ /m(2) after 1.5 nm separation. When C(18) surfactants are present on the surfaces, the organic layer (>0.8 nm) acts as a spacer between the silicate sheets so that positively charged ammonium head groups remain essentially in the same position on the surfaces of the two sheets at any separation. As a result, electrostatic interactions are efficiently shielded and dispersive interactions account for the interfacial energy. The flexibility of the hydrocarbon chains leads to stretching, disorder, and occasional rearrangements of ammonium head groups to neighbor cavities on the silicate surface at medium separation (1.0-2.0 nm). The total interaction energy amounts to less than 1 mJ /m(2) after 3 nm separation.     

ColliderBit: a GAMBIT module for the calculation of high-energy collider observables and likelihoods

We describe ColliderBit, a new code for the calculation of high energy collider observables in theories of physics beyond the Standard Model (BSM). ColliderBit features a generic interface to BSM models, a unique parallelised Monte Carlo event generation scheme suitable for large-scale supercomputer applications, and a number of LHC analyses, covering a reasonable range of the BSM signatures currently sought by ATLAS and CMS. ColliderBit also calculates likelihoods for Higgs sector observables, and LEP searches for BSM particles. These features are provided by a combination of new code unique to ColliderBit, and interfaces to existing state-of-the-art public codes. ColliderBit is both an important part of the GAMBIT framework for BSM inference, and a standalone tool for efficiently applying collider constraints to theories of new physics.     

Mass selective separation applied to radioisotopes of cesium

A technique that uses the intrinsic mass‐based separation capability of a quadrupole mass spectrometer has been used to resolve spectral radiometric interference of two isotopes of the same element. In this work the starting sample was a mixture of ¹³⁷Cs and ¹³⁴Cs and was (activity) dominated by ¹³⁷Cs. This methodology separated and ‘implanted’ ¹³⁴Cs that was later quantified for spectral features and activity with traditional radiometric techniques. This work demonstrated a ¹³⁴Cs/¹³⁷Cs activity ratio enhancement of >4 orders of magnitude and complete removal of ¹³⁷Cs spectral features from the implanted target mass (i.e. 134). Copyright © 2016 John Wiley & Sons, Ltd.     

Isotactic poly(p-fluorostyrene): Conformation and molecular packing analysis

The chain conformation and molecular packing of isotactic poly(p-fluorostyrene) have been examined using calculations made with semiempirical potential energy functions. Isolated chain conformational energies indicate no difference in conformation for the fluoropolymer from the conformation for isotactic polystyrene. The energy for packing poly(p-fluorostyrene) chains into a crystalline array as 3₁ or 4₁ helices was also compared with the energies for packing polystyrene in both of these helical forms. While not being the lowest energy mode of packing for poly(p-fluorostyrene), the packing of 4₁-helices does yield a local energy minimum. Such packing of 4₁ helical polystrene chains is considerably less energetically feasible. The results indicate the causes for the experimentally observed difference in the crystalline conformations of the two isotactic polymers as being due to intermolecular influences.