Atom Scattering from Disordered Surfaces in the Sudden Approximation: Double Collisions Effects and Quantum Liquids

The Sudden Approximation (SA) for scattering of atoms from surfaces is generalized to allow for double collision events and scattering from time-dependent quantum liquid surfaces. The resulting new schemes retain the simplicity of the original SA, while requiring little extra computational effort. The results suggest that inert atom (and in particular He) scattering can be used profitably to study hitherto unexplored forms of complex surface disorder.Comment: 15 pages, 1 figure. Related papers available at http://neon.cchem.berkeley.edu/~dan

Limited Range Fractality of Randomly Adsorbed Rods

Multiple resolution analysis of two dimensional structures composed of randomly adsorbed penetrable rods, for densities below the percolation threshold, has been carried out using box-counting functions. It is found that at relevant resolutions, for box-sizes, $r$, between cutoffs given by the average rod length and the average inter-rod distance $r_1$, these systems exhibit apparent fractal behavior. It is shown that unlike the case of randomly distributed isotropic objects, the upper cutoff $r_1$ is not only a function of the coverage but also depends on the excluded volume, averaged over the orientational distribution. Moreover, the apparent fractal dimension also depends on the orientational distributions of the rods and decreases as it becomes more anisotropic. For box sizes smaller than the box counting function is determined by the internal structure of the rods, whether simple or itself fractal. Two examples are considered - one of regular rods of one dimensional structure and rods which are trimmed into a Cantor set structure which are fractals themselves. The models examined are relevant to adsorption of linear molecules and fibers, liquid crystals, stress induced fractures and edge imperfections in metal catalysts. We thus obtain a distinction between two ranges of length scales: $r$ where the internal structure of the adsorbed objects is probed, and $< r < r_1$ where their distribution is probed, both of which may exhibit fractal behavior. This distinction is relevant to the large class of systems which exhibit aggregation of a finite density of fractal-like clusters, which includes surface growth in molecular beam epitaxy and diffusion-limited-cluster-cluster-aggregation models.Comment: 10 pages, 7 figures. More info available at http://www.fh.huji.ac.il/~dani/ or http://www.fiz.huji.ac.il/staff/acc/faculty/biham or http://chem.ch.huji.ac.il/employee/avnir/iavnir.htm . Accepted for publication in J. Chem. Phy

Elastic Scattering by Deterministic and Random Fractals: Self-Affinity of the Diffraction Spectrum

The diffraction spectrum of coherent waves scattered from fractal supports is calculated exactly. The fractals considered are of the class generated iteratively by successive dilations and translations, and include generalizations of the Cantor set and Sierpinski carpet as special cases. Also randomized versions of these fractals are treated. The general result is that the diffraction intensities obey a strict recursion relation, and become self-affine in the limit of large iteration number, with a self-affinity exponent related directly to the fractal dimension of the scattering object. Applications include neutron scattering, x-rays, optical diffraction, magnetic resonance imaging, electron diffraction, and He scattering, which all display the same universal scaling.Comment: 20 pages, 11 figures. Phys. Rev. E, in press. More info available at http://www.fh.huji.ac.il/~dani

Inversion of Randomly Corrugated Surfaces Structure from Atom Scattering Data

The Sudden Approximation is applied to invert structural data on randomly corrugated surfaces from inert atom scattering intensities. Several expressions relating experimental observables to surface statistical features are derived. The results suggest that atom (and in particular He) scattering can be used profitably to study hitherto unexplored forms of complex surface disorder.Comment: 10 pages, no figures. Related papers available at http://neon.cchem.berkeley.edu/~dan

Counting flags in triangle-free digraphs

Motivated by the Caccetta-Haggkvist Conjecture, we prove that every digraph on n vertices with minimum outdegree 0.3465n contains an oriented triangle. This improves the bound of 0.3532n of Hamburger, Haxell and Kostochka. The main new tool we use in our proof is the theory of flag algebras developed recently by Razborov.Comment: 19 pages, 7 figures; this is the final version to appear in Combinatoric

Apparent Fractality Emerging from Models of Random Distributions

The fractal properties of models of randomly placed $n$-dimensional spheres ($n$=1,2,3) are studied using standard techniques for calculating fractal dimensions in empirical data (the box counting and Minkowski-sausage techniques). Using analytical and numerical calculations it is shown that in the regime of low volume fraction occupied by the spheres, apparent fractal behavior is observed for a range of scales between physically relevant cut-offs. The width of this range, typically spanning between one and two orders of magnitude, is in very good agreement with the typical range observed in experimental measurements of fractals. The dimensions are not universal and depend on density. These observations are applicable to spatial, temporal and spectral random structures. Polydispersivity in sphere radii and impenetrability of the spheres (resulting in short range correlations) are also introduced and are found to have little effect on the scaling properties. We thus propose that apparent fractal behavior observed experimentally over a limited range may often have its origin in underlying randomness.Comment: 19 pages, 12 figures. More info available at http://www.fh.huji.ac.il/~dani

Interspecific Germline Transmission of Cultured Primordial Germ Cells

In birds, the primordial germ cell (PGC) lineage separates from the soma within 24 h following fertilization. Here we show that the endogenous population of about 200 PGCs from a single chicken embryo can be expanded one million fold in culture. When cultured PGCs are injected into a xenogeneic embryo at an equivalent stage of development, they colonize the testis. At sexual maturity, these donor PGCs undergo spermatogenesis in the xenogeneic host and become functional sperm. Insemination of semen from the xenogeneic host into females from the donor species produces normal offspring from the donor species. In our model system, the donor species is chicken (Gallus domesticus) and the recipient species is guinea fowl (Numida meleagris), a member of a different avian family, suggesting that the mechanisms controlling proliferation of the germline are highly conserved within birds. From a pragmatic perspective, these data are the basis of a novel strategy to produce endangered species of birds using domesticated hosts that are both tractable and fecund

Intrinsically determined cell death of developing cortical interneurons

Cortical inhibitory circuits are formed by GABAergic interneurons, a cell population that originates far from the cerebral cortex in the embryonic ventral forebrain. Given their distant developmental origins, it is intriguing how the number of cortical interneurons is ultimately determined. One possibility, suggested by the neurotrophic hypothesis1-5, is that cortical interneurons are overproduced, and then following their migration into cortex, excess interneurons are eliminated through a competition for extrinsically derived trophic signals. Here we have characterized the developmental cell death of mouse cortical interneurons in vivo, in vitro, and following transplantation. We found that 40% of developing cortical interneurons were eliminated through Bax- (Bcl-2 associated X-) dependent apoptosis during postnatal life. When cultured in vitro or transplanted into the cortex, interneuron precursors died at a cellular age similar to that at which endogenous interneurons died during normal development. Remarkably, over transplant sizes that varied 200-fold, a constant fraction of the transplanted population underwent cell death. The death of transplanted neurons was not affected by the cell-autonomous disruption of TrkB (tropomyosin kinase receptor B), the main neurotrophin receptor expressed by central nervous system (CNS) neurons6-8. Transplantation expanded the cortical interneuron population by up to 35%, but the frequency of inhibitory synaptic events did not scale with the number of transplanted interneurons. Together, our findings indicate that interneuron cell death is intrinsically determined, either cell-autonomously, or through a population-autonomous competition for survival signals derived from other interneurons

A FE parametric study of RWS beam-to-column bolted connections with cellular beams

In recent years, researchers study alternative connection designs for steel seismic-resistant frames by reducing the beam section in different ways including that of creating an opening in its web (RWS connections). A similar design is applied in the fabrication of perforated (i.e. cellular and castellated) beams mostly used to support the service integration, as well as the significant mass reduction in steel frames. This paper presents a comprehensive finite element (FE) analysis of extended end-plate beam-to-column connections, with both single and multiple circular web openings introduced along the length of the beam while subjected to the cyclic loading proposed by the SAC protocol from FEMA 350 (2000). The three-dimensional (3D) FE solid model was validated against FE and experimental results and the chosen configuration was capable of representing the structural behaviour of a partially restrained connection, without the necessity to be idealised as fully fixed. The study focuses in the interaction of such connections and the mobilisation of stresses from the column to the perforated beam. The parameters introduced were the distance from the face of the column, S, and the web opening spacing, So, with closely and widely spaced web openings. It is found that RWS connections with cellular beams behave in a satisfactory manner and provide enhanced performance in terms of the stress distribution when subjected to cyclic loading. The design of partially restrained RWS connections should be primarily based on the distance of the first opening from the face of the column