Black Holes and Galactic Density Cusps Spherically Symmetric Anisotropic Cusps

Aims: In this paper we study density cusps that may contain central black holes. The actual co-eval self-similar growth would not distinguish between the central object and the surroundings. Methods: To study the environment of a growing black hole we seek descriptions of steady `cusps' that may contain a black hole and that retain at least a memory of self-similarity. We refer to the environment in brief as the `bulge' and on smaller scales, the `halo'. Results: We find simple descriptions of the simulations of collisionless matter by comparing predicted densities, velocity dispersions and distribution functions with the simulations. In some cases central point masses may be included by iteration. We emphasize that the co-eval self-similar growth allows an explanation of the black hole bulge mass correlation between approximately similar collisionless systems. Conclusions: We have derived our results from first principles assuming adiabatic self-similarity and either self-similar virialisation or normal steady virialisation. We conclude that distribution functions that retain a memory of self-similar evolution provide an understanding of collisionless systems. The implied energy relaxation of the collisionless matter is due to the time dependence. Phase mixing relaxation may be enhanced by clump-clump interactions.Comment: 9 pp, 3 figs, accepted by A\&

Ring Expansion Of Alkylidenecarbenes Derived From Lactams, Lactones, And Thiolactones Into Strained Heterocyclic Alkynes: A Theoretical Study

Strained cycloalkynes are of considerable interest to theoreticians and experimentalists, and possess much synthetic value as well. Herein, a series of cyclic alkylidenecarbenes—formally obtained by replacing the carbonyl oxygen of four-, five-, and six-membered lactams, lactones, and thiolactones with a divalent carbon—were modeled at the CCSD(T)/cc-pVTZ//B3LYP/6-311+G** and CCSD(T)/cc-pVTZ//CCSD/6-311+G** levels of theory. The singlet carbenes were found to be more stable than the triplets. The strained heterocyclic alkynes formed by ring expansion of these singlet carbenes were also modeled. Interestingly, the C≡C bonds in the five-membered heterocycles, obtained from the rearrangement of β-lactam- and β-lactone-derived alkylidenecarbenes, displayed lengths intermediate between formal double and triple bonds. Furthermore, 2-(1-azacyclobutylidene)carbene was found to be nearly isoenergetic with its ring-expanded isomer, and 1-oxacyclopent-2-yne was notably higher in energy than its precursor carbene. In all other cases, the cycloalkynes were lower in energy than the corresponding carbenes. The transition states for ring-expansion were always lower for the 1,2-carbon shifts than for 1,2-nitrogen or oxygen shifts, but higher than for the 1,2-sulfur shifts. These predictions should be verifiable using carbenes bearing appropriate isotopic labels. Computed vibrational spectra for the carbenes, and their ring-expanded isomers, are presented and could be of value to matrix isolation experiments

Micromechanics of sea urchin spines

The endoskeletal structure of the Sea Urchin, Centrostephanus rodgersii, has numerous long spines whose known functions include locomotion, sensing, and protection against predators. These spines have a remarkable internal microstructure and are made of single-crystal calcite. A finite-element model of the spine's unique porous structure, based on micro-computed tomography (microCT) and incorporating anisotropic material properties, was developed to study its response to mechanical loading. Simulations show that high stress concentrations occur at certain points in the spine's architecture; brittle cracking would likely initiate in these regions. These analyses demonstrate that the organization of single-crystal calcite in the unique, intricate morphology of the sea urchin spine results in a strong, stiff and lightweight structure that enhances its strength despite the brittleness of its constituent material

A continuum-microscopic method based on IRBFs and control volume scheme for viscoelastic fluid flows

A numerical computation of continuum-microscopic model for visco-elastic flows based on the Integrated Radial Basis Function (IRBF) Control Volume and the Stochastic Simulation Techniques (SST) is reported in this paper. The macroscopic flow equations are closed by a stochastic equation for the extra stress at the microscopic level. The former are discretised by a 1D-IRBF-CV method while the latter is integrated with Euler explicit or Predictor-Corrector schemes. Modelling is very efficient as it is based on Cartesian grid, while the integrated RBF approach enhances both the stability of the procedure and the accuracy of the solution. The proposed method is demonstrated with the solution of the start-up Couette flow of the Hookean and FENE dumbbell model fluids

A TQFT associated to the LMO invariant of three-dimensional manifolds

We construct a Topological Quantum Field Theory (in the sense of Atiyah) associated to the universal finite-type invariant of 3-dimensional manifolds, as a functor from the category of 3-dimensional manifolds with parametrized boundary, satisfying some additional conditions, to an algebraic-combinatorial category. It is built together with its truncations with respect to a natural grading, and we prove that these TQFTs are non-degenerate and anomaly-free. The TQFT(s) induce(s) a (series of) representation(s) of a subgroup ${\cal L}_g$ of the Mapping Class Group that contains the Torelli group. The N=1 truncation produces a TQFT for the Casson-Walker-Lescop invariant.Comment: 28 pages, 13 postscript figures. Version 2 (Section 1 has been considerably shorten, and section 3 has been slightly shorten, since they will constitute a separate paper. Section 4, which contained only announce of results, has been suprimated; it will appear in detail elsewhere. Consequently some statements have been re-numbered. No mathematical changes have been made.

Competing interactions in artificial spin chains

The low-energy magnetic configurations of artificial frustrated spin chains are investigated using magnetic force microscopy and micromagnetic simulations. Contrary to most studies on two-dimensional artificial spin systems where frustration arises from the lattice geometry, here magnetic frustration originates from competing interactions between neighboring spins. By tuning continuously the strength and sign of these interactions, we show that different magnetic phases can be stabilized. Comparison between our experimental findings and predictions from the one-dimensional Anisotropic Next-Nearest-Neighbor Ising (ANNNI) model reveals that artificial frustrated spin chains have a richer phase diagram than initially expected. Besides the observation of several magnetic orders and the potential extension of this work to highly-degenerated artificial spin chains, our results suggest that the micromagnetic nature of the individual magnetic elements allows observation of metastable spin configurations.Comment: 5 pages, 4 figure

Bessel processes, the Brownian snake and super-Brownian motion

We prove that, both for the Brownian snake and for super-Brownian motion in dimension one, the historical path corresponding to the minimal spatial position is a Bessel process of dimension -5. We also discuss a spine decomposition for the Brownian snake conditioned on the minimizing path.Comment: Submitted to the special volume of S\'eminaire de Probabilit\'es in memory of Marc Yo

Creativity and the measurement subclinical psychopathology in the general population: schizotypy, psychoticism, and hypomania

The aims of the study were to investigate the roles of well-known psychopathology measures in predicting creativity, to assess the concepts of a multitrait and single trait understanding, and to evaluate the role of latent measures of hypomania predicting creativity. Following the completion of a battery of questionnaires 203 participants completed 2 creative cognition tasks. Multivariate multiple regression analyses revealed significant effects for both schizotypy and the latent hypomania scales. Critically, these showed that some negatively (introvertive anhedonia, excitement, and social vitality) and others positively (impulsive nonconformity and mood volatility) predicted creativity. These findings suggest future avenues should evaluate the roles of mood, autonomy, and asociality in mediating the link between subclinical psychopathology and creativity. Further, research should both manipulate state and control trait mood when evaluating psychopathology and creativity