A structural systematic study of three isomers of difluoro-N-(4-pyridyl)benzamide

The isomers 2,3-, (I), 2,4-, (II), and 2,5-difluoro-N-(4-pyridyl)benzamide, (III), all with formula C₁₂H₈F₂N₂O, all exhibit intramolecular C-H...O=C and N-H...F contacts [both with S(6) motifs]. In (I), intermolecular N-H...O=C interactions form one-dimensional chains along [010] [N...O = 3.0181 (16) Å], with weaker C-H...N interactions linking the chains into sheets parallel to the [001] plane, further linked into pairs via C-H...F contacts about inversion centres; a three-dimensional herring-bone network forms via C-H...π(py) (py is pyridyl) interactions. In (II), weak aromatic C-H...N(py) interactions form one-dimensional zigzag chains along [001]; no other interactions with H...N/O/F < 2.50 Å are present, apart from long N/C-H...O=C and C-H...F contacts. In (III), N-H...N(py) interactions form one-dimensional zigzag chains [as C(6) chains] along [010] augmented by a myriad of weak C-H...π(arene) and O=C...O=C interactions and C-H...O/N/F contacts. Compound (III) is isomorphous with the parent N-(4-pyridyl)benzamide [Noveron, Lah, Del Sesto, Arif, Miller & Stang (2002). J. Am. Chem. Soc. 124, 6613-6625] and the three 2/3/4-fluoro-N-(4-pyridyl)benzamides [Donnelly, Gallagher & Lough (2008). Acta Cryst. C64, o335-o340]. The study expands our series of fluoro(pyridyl)benzamides and augments our understanding of the competition between strong hydrogen-bond formation and weaker influences on crystal packing

A structural systematic study of four isomers of difluoro-N-(3-pyridyl)benzamide

The four isomers 2,4-, (I), 2,5-, (II), 3,4-, (III), and 3,5-difluoro-N-(3-pyridyl)benzamide, (IV), all with formula C12H8F2N2O, display molecular similarity, with interplanar angles between the C6/C5N rings ranging from 2.94 (11)° in (IV) to 4.48 (18)° in (I), although the amide group is twisted from either plane by 18.0 (2)-27.3 (3)°. Compounds (I) and (II) are isostructural but are not isomorphous. Intermolecular N-H...O=C interactions form one-dimensional C(4) chains along [010]. The only other significant interaction is C-H...F. The pyridyl (py) N atom does not participate in hydrogen bonding; the closest H...Npy contact is 2.71 Å in (I) and 2.69 Å in (II). Packing of pairs of one-dimensional chains in a herring-bone fashion occurs via [pi]-stacking interactions. Compounds (III) and (IV) are essentially isomorphous (their a and b unit-cell lengths differ by 9%, due mainly to 3,4-F2 and 3,5-F2 substitution patterns in the arene ring) and are quasi-isostructural. In (III), benzene rotational disorder is present, with the meta F atom occupying both 3- and 5-F positions with site occupancies of 0.809 (4) and 0.191 (4), respectively. The N-H...Npy intermolecular interactions dominate as C(5) chains in tandem with C-H...Npy interactions. C-H...O=C interactions form R22(8) rings about inversion centres, and there are [pi]-[pi] stacks about inversion centres, all combining to form a three-dimensional network. By contrast, (IV) has no strong hydrogen bonds; the N-H...Npy interaction is 0.3 Å longer than in (III). The carbonyl O atom participates only in weak interactions and is surrounded in a square-pyramidal contact geometry with two intramolecular and three intermolecular C-H...O=C interactions. Compounds (III) and (IV) are interesting examples of two isomers with similar unit-cell parameters and gross packing but which display quite different intermolecular interactions at the primary level due to subtle packing differences at the atom/group/ring level arising from differences in the peripheral ring-substitution patterns

Fractal Cosmology in an Open Universe

The clustering of galaxies is well characterized by fractal properties, with the presence of an eventual cross-over to homogeneity still a matter of considerable debate. In this letter we discuss the cosmological implications of a fractal distribution of matter, with a possible cross-over to homogeneity at an undetermined scale R_{homo}. Contrary to what is generally assumed, we show that, even when R_{homo} -> \infty, this possibility can be treated consistently within the framework of the expanding universe solutions of Friedmann. The fractal is a perturbation to an open cosmology in which the leading homogeneous component is the cosmic background radiation (CBR). This cosmology, inspired by the observed galaxy distributions, provides a simple explanation for the recent data which indicate the absence of deceleration in the expansion (q_o \approx 0). Correspondingly the `age problem' is also resolved. Further we show that the model can be extended back from the curvature dominated arbitrarily deep into the radiation dominated era, and we discuss qualitatively the modifications to the physics of the anisotropy of the CBR, nucleosynthesis and structure formation.Comment: 7 pages, no figures, to appear in Europhysics Letter

Integrating Dynamics and Wear Modelling to Predict Railway Wheel Profile Evolution

The aim of the work described was to predict wheel profile evolution by integrating multi-body dynamics simulations of a wheelset with a wear model. The wear modelling approach is based on a wear index commonly used in rail wear predictions. This assumes wear is proportional to Tγ, where T is tractive force and γ is slip at the wheel/rail interface. Twin disc testing of rail and wheel materials was carried out to generate wear coefficients for use in the model. The modelling code is interfaced with ADAMS/Rail, which produces multi-body dynamics simulations of a railway wheelset and contact conditions at the wheel/rail interface. Simplified theory of rolling contact is used to discretise the contact patches produced by ADAMS/Rail and calculate traction and slip within each. The wear model combines the simplified theory of rolling contact, ADAMS/Rail output and the wear coefficients to predict the wear and hence the change of wheel profile for given track layouts

On the geometry of closed G2-structure

We give an answer to a question posed recently by R.Bryant, namely we show that a compact 7-dimensional manifold equipped with a G2-structure with closed fundamental form is Einstein if and only if the Riemannian holonomy of the induced metric is contained in G2. This could be considered to be a G2 analogue of the Goldberg conjecture in almost Kahler geometry. The result was generalized by R.L.Bryant to closed G2-structures with too tightly pinched Ricci tensor. We extend it in another direction proving that a compact G2-manifold with closed fundamental form and divergence-free Weyl tensor is a G2-manifold with parallel fundamental form. We introduce a second symmetric Ricci-type tensor and show that Einstein conditions applied to the two Ricci tensors on a closed G2-structure again imply that the induced metric has holonomy group contained in G2.Comment: 14 pages, the Einstein condition in the assumptions of the Main theorem is generalized to the assumption that the Weyl tensor is divergence-free, clarity improved, typos correcte

The role of initial conditions in the ageing of the long-range spherical model

The kinetics of the long-range spherical model evolving from various initial states is studied. In particular, the large-time auto-correlation and -response functions are obtained, for classes of long-range correlated initial states, and for magnetized initial states. The ageing exponents can depend on certain qualitative features of initial states. We explicitly find the conditions for the system to cross over from ageing classes that depend on initial conditions to those that do not.Comment: 15 pages; corrected some typo

Discrete Matter, Far Fields, and Dark Matter

We show that in cosmology the gravitational action of the far away matter has quite relevant effects, if retardation of the forces and discreteness of matter (with its spatial correlation) are taken into account. The expansion rate is found to be determined by the density of the far away matter, i.e., by the density of matter at remote times. This leads to the introduction of an effective density, which has to be five times larger than the present one, if the present expansion rate is to be accounted for. The force per unit mass on a test particle is found to be of the order of 0.2cH_0. The corresponding contribution to the virial of the forces for a cluster of galaxies is also discussed, and it is shown that it fits the observations if a decorrelation property of the forces at two separated points is assumed. So it appears that the gravitational effects of the far away matter may have the same order of magnitude as the corresponding local effects of dark matter.Comment: 16 pages, 1 figure. LaTex documen

Universality of power law correlations in gravitational clustering

We present an analysis of different sets of gravitational N-body simulations, all describing the dynamics of discrete particles with a small initial velocity dispersion. They encompass very different initial particle configurations, different numerical algorithms for the computation of the force, with or without the space expansion of cosmological models. Despite these differences we find in all cases that the non-linear clustering which results is essentially the same, with a well-defined simple power-law behaviour in the two-point correlations in the range from a few times the lower cut-off in the gravitational force to the scale at which fluctuations are of order one. We argue, presenting quantitative evidence, that this apparently universal behaviour can be understood by the domination of the small scale contribution to the gravitational force, coming initially from nearest neighbor particles.Comment: 7 pages, latex, 3 postscript figures. Revised version to be published in Europhysics Letters. Contains additional analysis showing more directly the central role of nearest neighbour interactions in the development of power-law correlation

1-d gravity in infinite point distributions

The dynamics of infinite, asymptotically uniform, distributions of self-gravitating particles in one spatial dimension provides a simple toy model for the analogous three dimensional problem. We focus here on a limitation of such models as treated so far in the literature: the force, as it has been specified, is well defined in infinite point distributions only if there is a centre of symmetry (i.e. the definition requires explicitly the breaking of statistical translational invariance). The problem arises because naive background subtraction (due to expansion, or by "Jeans' swindle" for the static case), applied as in three dimensions, leaves an unregulated contribution to the force due to surface mass fluctuations. Following a discussion by Kiessling, we show that the problem may be resolved by defining the force in infinite point distributions as the limit of an exponentially screened pair interaction. We show that this prescription gives a well defined (finite) force acting on particles in a class of perturbed infinite lattices, which are the point processes relevant to cosmological N-body simulations. For identical particles the dynamics of the simplest toy model is equivalent to that of an infinite set of points with inverted harmonic oscillator potentials which bounce elastically when they collide. We discuss previous results in the literature, and present new results for the specific case of this simplest (static) model starting from "shuffled lattice" initial conditions. These show qualitative properties (notably its "self-similarity") of the evolution very similar to those in the analogous simulations in three dimensions, which in turn resemble those in the expanding universe.Comment: 20 pages, 8 figures, small changes (section II shortened, added discussion in section IV), matches final version to appear in PR