More examples of structure formation in the Lemaitre-Tolman model

In continuing our earlier research, we find the formulae needed to determine the arbitrary functions in the Lemaitre-Tolman model when the evolution proceeds from a given initial velocity distribution to a final state that is determined either by a density distribution or by a velocity distribution. In each case the initial and final distributions uniquely determine the L-T model that evolves between them, and the sign of the energy-function is determined by a simple inequality. We also show how the final density profile can be more accurately fitted to observational data than was done in our previous paper. We work out new numerical examples of the evolution: the creation of a galaxy cluster out of different velocity distributions, reflecting the current data on temperature anisotropies of CMB, the creation of the same out of different density distributions, and the creation of a void. The void in its present state is surrounded by a nonsingular wall of high density.Comment: LaTeX 2e with eps figures. 30 pages, 11 figures, 30 figure files. Revision matches published versio

Atomic Binding Energies From a Modified Thomas-Fermi-Dirac Theory

A quantum correction of the statistical model of the atom was obtained by modifying March and Plaskett's region of integration in the (n/sub r/,l), or quantum-number, plane. Integrations over the plane lead, in the unmodified case, to the Thomas-Fermi density expression and energy equation. Integrations over the modified region are here shown to produce a modified Thomas-Fermi expression for the electron density, and a correction to the kinetic energy. The latter correction shows a similarity to the Weizsacker correction, but is smaller by a slowly changing factor of the order of 10. A modified Thomas-Fermi-Dirac equation was derived by the standard variational procedure. Numerical solutions of the equation were obtained, yielding atomic binding energies in much better agreement with experimental values than those of the unmodified theory. (auth

Oxidation and fragmentation of plastics in a changing environment; from UV-radiation to biological degradation

Understanding the fate of plastics in the environment is of critical importance for the quantitative assessment of the biological impacts of plastic waste. Specially, there is a need to analyze in more detail the reputed longevity of plastics in the context of plastic degradation through oxidation and fragmentation reactions. Photo-oxidation of plastic debris by solar UV radiation (UVR) makes material prone to subsequent fragmentation. The fragments generated following oxidation and subsequent exposure to mechanical stresses include secondary micro- or nanoparticles, an emerging class of pollutants. The paper discusses the UV-driven photo-oxidation process, identifying relevant knowledge gaps and uncertainties. Serious gaps in knowledge exist concerning the wavelength sensitivity and the dose-response of the photo-fragmentation process. Given the heterogeneity of natural UV irradiance varying from no exposure in sediments to full UV exposure of floating, beach litter or air-borne plastics, it is argued that the rates of UV-driven degradation/fragmentation will also vary dramatically between different locations and environmental niches. Biological phenomena such as biofouling will further modulate the exposure of plastics to UV radiation, while potentially also contributing to degradation and/or fragmentation of plastics independent of solar UVR. Reductions in solar UVR in many regions, consequent to the implementation of the Montreal Protocol and its Amendments for protecting stratospheric ozone, will have consequences for global UV-driven plastic degradation in a heterogeneous manner across different geographic and environmental zones. The interacting effects of global warming, stratospheric ozone and UV radiation are projected to increase UV irradiance at the surface in localized areas, mainly because of decreased cloud cover. Given the complexity and uncertainty of future environmental conditions, this currently precludes reliable quantitative predictions of plastic persistence on a global scale

Unit circle elliptic beta integrals

We present some elliptic beta integrals with a base parameter on the unit circle, together with their basic degenerations.Comment: 15 pages; minor corrections, references updated, to appear in Ramanujan

Quark exchange model for charmonium dissociation in hot hadronic matter

A diagrammatic approach to quark exchange processes in meson-meson scattering is applied to the case of inelastic reactions of the type (Q\barQ)+(q\barq)\rightarrow (Q\barq) + (q\barQ), where $Q$ and $q$ refer to heavy and light quarks, respectively. This string-flip process is discussed as a microscopic mechanism for charmonium dissociation (absorption) in hadronic matter. The cross section for the reaction $J/\psi + \pi \to D+ \bar D$ is calculated using a potential model, which is fitted to the meson mass spectrum. The temperature dependence of the relaxation time for the \J/Psi distribution in a homogeneous thermal pion gas is obtained. The use of charmonium for the diagnostics of the state of hot hadronic matter produced in ultrarelativistic nucleus-nucleus collisions is discussed.Comment: 24 pages, 3 tables, 7 figure

Kaon-Nucleon Scattering Amplitudes and Z∗^*-Enhancements from Quark Born Diagrams

We derive closed form kaon-nucleon scattering amplitudes using the ``quark Born diagram" formalism, which describes the scattering as a single interaction (here the OGE spin-spin term) followed by quark line rearrangement. The low energy I=0 and I=1 S-wave KN phase shifts are in reasonably good agreement with experiment given conventional quark model parameters. For $k_{lab}> 0.7$ Gev however the I=1 elastic phase shift is larger than predicted by Gaussian wavefunctions, and we suggest possible reasons for this discrepancy. Equivalent low energy KN potentials for S-wave scattering are also derived. Finally we consider OGE forces in the related channels K$\Delta$, K$^*$N and K$^*\Delta$, and determine which have attractive interactions and might therefore exhibit strong threshold enhancements or ``Z$^*$-molecule" meson-baryon bound states. We find that the minimum-spin, minimum-isospin channels and two additional K$^*\Delta$ channels are most conducive to the formation of bound states. Related interesting topics for future experimental and theoretical studies of KN interactions are also discussed.Comment: 34 pages, figures available from the authors, revte

The use of synchrotron edge topography to study polytype nearest neighbour relationships in SiC

A brief review of the phenomenon of polytypism is presented and its prolific abundance in Silicon Carbide discussed. An attempt has been made to emphasise modern developments in understanding this unique behaviour. The properties of Synchrotron Radiation are shown to be ideally suited to studies of polytypes in various materials and in particular the coalescence of polytypes in SiC. It is shown that with complex multipolytypic crystals the technique of edge topography allows the spatial extent of disorder to be determined and, from the superposition of Laue type reflections, neighbourhood relationships between polytypes can be deduced. Finer features have now been observed with the advent of second generation synchrotrons, the resolution available enabling the regions between adjoining polytypes to be examined more closely. It is shown that Long Period Polytypes and One Dimensionally Disordered layers often found in association with regions of high defect density are common features at polytype boundaries. An idealised configuration termed a "polytype sandwich" is presented as a model for the structure of SiC grown by the modified Lely technique. The frequency of common sandwich edge profiles are classified and some general trends of polytype neighbourism are summarised

Influence of constitution and charge on radical pairing interactions in tris-radical tricationic complexes

The results of a systematic investigation of trisradical tricationic complexes formed between cyclobis(paraquat-p-phenylene) bisradical dicationic (CBPQT2(•+)) rings and a series of 18 dumbbells, containing centrally located 4,4′-bipyridinium radical cationic (BIPY•+) units within oligomethylene chains terminated for the most part by charged 3,5-dimethylpyridinium (PY+) and/or neutral 3,5-dimethylphenyl (PH) groups, are reported. The complexes were obtained by treating equimolar amounts of the CBPQT4+ ring and the dumbbells containing BIPY2+ units with zinc dust in acetonitrile solutions. Whereas UV–Vis–NIR spectra revealed absorption bands centered on ca. 1100 nm with quite different intensities for the 1:1 complexes depending on the constitutions and charges on the dumbbells, titration experiments showed that the association constants (Ka) for complex formation vary over a wide range, from 800 M–1 for the weakest to 180 000 M–1 for the strongest. While Coulombic repulsions emanating from PY+ groups located at the ends of some of the dumbbells undoubtedly contribute to the destabilization of the trisradical tricationic complexes, solid-state superstructures support the contention that those dumbbells with neutral PH groups at the ends of flexible and appropriately constituted links to the BIPY•+ units stand to gain some additional stabilization from C–H···π interactions between the CBPQT2(•+) rings and the PH termini on the dumbbells. The findings reported in this Article demonstrate how structural changes implemented remotely from the BIPY•+ units influence their non-covalent bonding interactions with CBPQT2(•+) rings. Different secondary effects (Coulombic repulsions versus C–H···π interactions) are uncovered, and their contributions to both binding strengths associated with trisradical interactions and the kinetics of associations and dissociations are discussed at some length, supported by extensive DFT calculations at the M06-D3 level. A fundamental understanding of molecular recognition in radical complexes has relevance when it comes to the design and synthesis of non-equilibrium systems

NN Core Interactions and Differential Cross Sections from One Gluon Exchange

We derive nonstrange baryon-baryon scattering amplitudes in the nonrelativistic quark model using the ``quark Born diagram" formalism. This approach describes the scattering as a single interaction, here the one-gluon-exchange (OGE) spin-spin term followed by constituent interchange, with external nonrelativistic baryon wavefunctions attached to the scattering diagrams to incorporate higher-twist wavefunction effects. The short-range repulsive core in the NN interaction has previously been attributed to this spin-spin interaction in the literature; we find that these perturbative constituent-interchange diagrams do indeed predict repulsive interactions in all I,S channels of the nucleon-nucleon system, and we compare our results for the equivalent short-range potentials to the core potentials found by other authors using nonperturbative methods. We also apply our perturbative techniques to the N$\Delta$ and $\Delta\Delta$ systems: Some $\Delta\Delta$ channels are found to have attractive core potentials and may accommodate ``molecular" bound states near threshold. Finally we use our Born formalism to calculate the NN differential cross section, which we compare with experimental results for unpolarised proton-proton elastic scattering. We find that several familiar features of the experimental differential cross section are reproduced by our Born-order result.Comment: 27 pages, figures available from the authors, revtex, CEBAF-TH-93-04, MIT-CTP-2187, ORNL-CCIP-93-0

Critical Collapse of Cylindrically Symmetric Scalar Field in Four-Dimensional Einstein's Theory of Gravity

Four-dimensional cylindrically symmetric spacetimes with homothetic self-similarity are studied in the context of Einstein's Theory of Gravity, and a class of exact solutions to the Einstein-massless scalar field equations is found. Their local and global properties are investigated and found that they represent gravitational collapse of a massless scalar field. In some cases the collapse forms black holes with cylindrical symmetry, while in the other cases it does not. The linear perturbations of these solutions are also studied and given in closed form. From the spectra of the unstable eigen-modes, it is found that there exists one solution that has precisely one unstable mode, which may represent a critical solution, sitting on a boundary that separates two different basins of attraction in the phase space.Comment: Some typos are corrected. The final version to appear in Phys. Rev.