Coupled frustrated quantum spin-1/2 chains with orbital order in volborthite Cu3V2O7(OH)2(H2O)2

We present a microscopic magnetic model for the spin-liquid candidate volborthite Cu3V2O7(OH)2(H2O)2. The essentials of this DFT-based model are (i) the orbital ordering of Cu(1) 3d 3z2-r2 and Cu(2) 3d 3x2-y2, (ii) three relevant couplings J_ic, J_1 and J_2, (iii) the ferromagnetic nature of J_1 and (iv) frustration governed by the next-nearest-neighbor exchange interaction J_2. Our model implies magnetism of frustrated coupled chains in contrast to the previously proposed anisotropic kagome model. Exact diagonalization studies reveal agreement with experiments.Comment: 5 pages, 4 figures + supplementar

The isolated perfused mouse uterus as a model for the study of implantation in vitro. Methodology and morphology

In order to facilitate investigations of mammalian blastocyst implantation in the endometrium, an in-vitro organ perfusion technique was developed. This technique was designed to avoid the drawbacks of inVivo and cell culture investigations, while retaining physiological resolution of the endo- and paracrinology and specifically a normal epithelium to stroma relationship. The ovary, oviduct and uterine horn from 21 mice were perfused in-vitro for 10 hours. The surgical techniques for isolation of the organs as well as the perfusion procedure are described. The resultant morphology of the perfused tissue, including implantations is described and illustrated by light and transmission electron microscopy. The model seems to be useful for studying the mammalian implantation as implantation takes place and decidua is formed during perfusion

On Connected Diagrams and Cumulants of Erdos-Renyi Matrix Models

Regarding the adjacency matrices of n-vertex graphs and related graph Laplacian, we introduce two families of discrete matrix models constructed both with the help of the Erdos-Renyi ensemble of random graphs. Corresponding matrix sums represent the characteristic functions of the average number of walks and closed walks over the random graph. These sums can be considered as discrete analogs of the matrix integrals of random matrix theory. We study the diagram structure of the cumulant expansions of logarithms of these matrix sums and analyze the limiting expressions in the cases of constant and vanishing edge probabilities as n tends to infinity.Comment: 34 pages, 8 figure

Parameterized complexity of DPLL search procedures

We study the performance of DPLL algorithms on parameterized problems. In particular, we investigate how difficult it is to decide whether small solutions exist for satisfiability and other combinatorial problems. For this purpose we develop a Prover-Delayer game which models the running time of DPLL procedures and we establish an information-theoretic method to obtain lower bounds to the running time of parameterized DPLL procedures. We illustrate this technique by showing lower bounds to the parameterized pigeonhole principle and to the ordering principle. As our main application we study the DPLL procedure for the problem of deciding whether a graph has a small clique. We show that proving the absence of a k-clique requires n steps for a non-trivial distribution of graphs close to the critical threshold. For the restricted case of tree-like Parameterized Resolution, this result answers a question asked in [11] of understanding the Resolution complexity of this family of formulas

The topological structure of scaling limits of large planar maps

We discuss scaling limits of large bipartite planar maps. If p is a fixed integer strictly greater than 1, we consider a random planar map M(n) which is uniformly distributed over the set of all 2p-angulations with n faces. Then, at least along a suitable subsequence, the metric space M(n) equipped with the graph distance rescaled by the factor n to the power -1/4 converges in distribution as n tends to infinity towards a limiting random compact metric space, in the sense of the Gromov-Hausdorff distance. We prove that the topology of the limiting space is uniquely determined independently of p, and that this space can be obtained as the quotient of the Continuum Random Tree for an equivalence relation which is defined from Brownian labels attached to the vertices. We also verify that the Hausdorff dimension of the limit is almost surely equal to 4.Comment: 45 pages Second version with minor modification

Creativity and Autonomy in Swarm Intelligence Systems

This work introduces two swarm intelligence algorithms -- one mimicking the behaviour of one species of ants (\emph{Leptothorax acervorum}) foraging (a `Stochastic Diffusion Search', SDS) and the other algorithm mimicking the behaviour of birds flocking (a `Particle Swarm Optimiser', PSO) -- and outlines a novel integration strategy exploiting the local search properties of the PSO with global SDS behaviour. The resulting hybrid algorithm is used to sketch novel drawings of an input image, exploliting an artistic tension between the local behaviour of the `birds flocking' - as they seek to follow the input sketch - and the global behaviour of the `ants foraging' - as they seek to encourage the flock to explore novel regions of the canvas. The paper concludes by exploring the putative `creativity' of this hybrid swarm system in the philosophical light of the `rhizome' and Deleuze's well known `Orchid and Wasp' metaphor

Magnetization and spin dynamics of the spin S=1/2 hourglass nanomagnet Cu5(OH)2(NIPA)4*10H2O

We report a combined experimental and theoretical study of the spin S=1/2 nanomagnet Cu5(OH)2(NIPA)4*10H2O (Cu5-NIPA). Using thermodynamic, electron spin resonance and 1H nuclear magnetic resonance measurements on one hand, and ab initio density-functional band-structure calculations, exact diagonalizations and a strong coupling theory on the other, we derive a microscopic magnetic model of Cu5-NIPA and characterize the spin dynamics of this system. The elementary five-fold Cu2+ unit features an hourglass structure of two corner-sharing scalene triangles related by inversion symmetry. Our microscopic Heisenberg model comprises one ferromagnetic and two antiferromagnetic exchange couplings in each triangle, stabilizing a single spin S=1/2 doublet ground state (GS), with an exactly vanishing zero-field splitting (by Kramer's theorem), and a very large excitation gap of \Delta~68 K. Thus, Cu5-NIPA is a good candidate for achieving long electronic spin relaxation (T1) and coherence (T2) times at low temperatures, in analogy to other nanomagnets with low-spin GS's. Of particular interest is the strongly inhomogeneous distribution of the GS magnetic moment over the five Cu2+ spins. This is a purely quantum-mechanical effect since, despite the non-frustrated nature of the magnetic couplings, the GS is far from the classical collinear ferrimagnetic configuration. Finally, Cu5-NIPA is a rare example of a S=1/2 nanomagnet showing an enhancement in the nuclear spin-lattice relaxation rate 1/T1 at intermediate temperatures.Comment: 18 pages, 16 figures, 3 table

High-field Phase Diagram and Spin Structure of Volborthite Cu3V2O7(OH)2/2H2O

We report results of 51V NMR experiments on a high-quality powder sample of volborthite Cu3V2O7(OH)2/2H2O, a spin-1/2 Heisenberg antiferromagnet on a distorted kagome lattice. Following the previous experiments in magnetic fields $B$ below 12 T, the NMR measurements have been extended to higher fields up to 31 T. In addition to the two already known ordered phases (phases I and II), we found a new high-field phase (phase III) above 25 T, at which a second magnetization step has been observed. The transition from the paramagnetic phase to the antiferromagnetic phase III occurs at 26 K, which is much higher than the transition temperatures from the paramagnetic to the lower field phases I (B < 4.5 T) and II (4.5 < B < 25 T). At low temperatures, two types of the V sites are observed with different relaxation rates and line shapes in phase III as well as in phase II. Our results indicate that both phases II and III exhibit a heterogeneous spin state consisting of two spatially alternating Cu spin systems, one of which exhibits anomalous spin fluctuations contrasting with the other showing a conventional static order. The magnetization of the latter system exhibits a sudden increase upon entering into phase III, resulting in the second magnetization step at 26 T.We discuss the possible spin structure in phase III.Comment: 9 pages, 12 figure

Solubility limit and precipitate formation in Al-doped 4H-SiC epitaxial material

Heavily Al-doped 4H–SiC structures have been prepared by vapor phase epitaxy. Subsequent anneals have been carried out in an Ar atmosphere in a rf-heated furnace between 1500 °C and 2000 °C for 0.5 to 3 h. Secondary ion mass spectrometry has been utilized to obtain Al concentration versus depth as well as lateral distributions (ion images). Transmission electron microscopy(TEM) has been employed to study the crystallinity and determine phase composition after heat treatment. A solubility limit of ∼2×10²⁰ Al/cm³ (1900 °C) is extracted. Three-dimensional ion images show that the Al distribution does not remain homogeneous in layers heat treated at 1700 °C or above when the Al concentration exceeds 2×10²⁰ cm⁻³. Al-containing precipitates are identified by energy-filtered TEM.Financial support was partly received from the Swedish Foundation for Strategic Research (SSF) SiCEP program