2,745 research outputs found
Fully Analyzing an Algebraic Polya Urn Model
This paper introduces and analyzes a particular class of Polya urns: balls
are of two colors, can only be added (the urns are said to be additive) and at
every step the same constant number of balls is added, thus only the color
compositions varies (the urns are said to be balanced). These properties make
this class of urns ideally suited for analysis from an "analytic combinatorics"
point-of-view, following in the footsteps of Flajolet-Dumas-Puyhaubert, 2006.
Through an algebraic generating function to which we apply a multiple
coalescing saddle-point method, we are able to give precise asymptotic results
for the probability distribution of the composition of the urn, as well as
local limit law and large deviation bounds.Comment: LATIN 2012, Arequipa : Peru (2012
Intrinsic peculiarities of real material realizations of a spin-1/2 kagome lattice
Spin-1/2 magnets with kagome geometry, being for years a generic object of
theoretical investigations, have few real material realizations. Recently, a
DFT-based microscopic model for two such materials, kapellasite Cu3Zn(OH)6Cl2
and haydeeite Cu3Mg(OH)6Cl2, was presented [O. Janson, J. Richter and H.
Rosner, arXiv:0806.1592]. Here, we focus on the intrinsic properties of real
spin-1/2 kagome materials having influence on the magnetic ground state and the
low-temperature excitations. We find that the values of exchange integrals are
strongly dependent on O--H distance inside the hydroxyl groups, present in most
spin-1/2 kagome compounds up to date. Besides the original kagome model,
considering only the nearest neighbour exchange, we emphasize the crucial role
of the exchange along the diagonals of the kagome lattice.Comment: 4 pages, 4 figures. A paper for the proceedings of the HFM 2008
conferenc
The first order convergence law fails for random perfect graphs
We consider first order expressible properties of random perfect graphs. That
is, we pick a graph uniformly at random from all (labelled) perfect
graphs on vertices and consider the probability that it satisfies some
graph property that can be expressed in the first order language of graphs. We
show that there exists such a first order expressible property for which the
probability that satisfies it does not converge as .Comment: 11 pages. Minor corrections since last versio
Critical behaviour of combinatorial search algorithms, and the unitary-propagation universality class
The probability P(alpha, N) that search algorithms for random Satisfiability
problems successfully find a solution is studied as a function of the ratio
alpha of constraints per variable and the number N of variables. P is shown to
be finite if alpha lies below an algorithm--dependent threshold alpha\_A, and
exponentially small in N above. The critical behaviour is universal for all
algorithms based on the widely-used unitary propagation rule: P[ (1 + epsilon)
alpha\_A, N] ~ exp[-N^(1/6) Phi(epsilon N^(1/3)) ]. Exponents are related to
the critical behaviour of random graphs, and the scaling function Phi is
exactly calculated through a mapping onto a diffusion-and-death problem.Comment: 7 pages; 3 figure
Cutting edges at random in large recursive trees
We comment on old and new results related to the destruction of a random
recursive tree (RRT), in which its edges are cut one after the other in a
uniform random order. In particular, we study the number of steps needed to
isolate or disconnect certain distinguished vertices when the size of the tree
tends to infinity. New probabilistic explanations are given in terms of the
so-called cut-tree and the tree of component sizes, which both encode different
aspects of the destruction process. Finally, we establish the connection to
Bernoulli bond percolation on large RRT's and present recent results on the
cluster sizes in the supercritical regime.Comment: 29 pages, 3 figure
Boundary layer concentrations and landscape scale emissions of volatile organic compounds in early spring
International audienceBoundary layer concentrations of several volatile organic compounds (VOC) were measured during two campaigns in springs of 2003 and 2006. The measurements were conducted over boreal landscapes near SMEAR II measurement station in Hyytiälä, Southern Finland. In 2003 the measuremens were performed using a light aircraft and in 2006 using a hot air balloon. Isoprene concentrations were low, usually below detection limit. This can be explained by low biogenic production due to cold weather, phenological stage of the isoprene emitting plants, and snow cover. Monoterpenes were observed frequently. The average total monoterpene concentration in the boundary layer was 33 pptv. Many anthropogenic compounds such as benzene, xylene and toluene, were observed in high amounts. Ecosystem scale surface emissions were estimated using a simple mixed box budget methodology. Total monoterpene emissions varied up to 80 ?g m?2 h?1, ?-pinene contributing typically more than two thirds of that. These emissions were somewhat higher that those calculated using emission algorithm. The highest emissions of anthropogenic compounds were those of p/m xylene
Magnetic properties of the low-dimensional spin-1/2 magnet \alpha-Cu_2As_2O_7
In this work we study the interplay between the crystal structure and
magnetism of the pyroarsenate \alpha-Cu_2As_2O_7 by means of magnetization,
heat capacity, electron spin resonance and nuclear magnetic resonance
measurements as well as density functional theory (DFT) calculations and
quantum Monte Carlo (QMC) simulations. The data reveal that the magnetic Cu-O
chains in the crystal structure represent a realization of a quasi-one
dimensional (1D) coupled alternating spin-1/2 Heisenberg chain model with
relevant pathways through non-magnetic AsO_4 tetrahedra. Owing to residual 3D
interactions antiferromagnetic long range ordering at T_N\simeq10K takes place.
Application of external magnetic field B along the magnetically easy axis
induces the transition to a spin-flop phase at B_{SF}~1.7T (2K). The
experimental data suggest that substantial quantum spin fluctuations take place
at low magnetic fields in the ordered state. DFT calculations confirm the
quasi-one-dimensional nature of the spin lattice, with the leading coupling J_1
within the structural dimers. QMC fits to the magnetic susceptibility evaluate
J_1=164K, the weaker intrachain coupling J'_1/J_1 = 0.55, and the effective
interchain coupling J_{ic1}/J_1 = 0.20.Comment: Accepted for publication in Physical Review
Orbital dynamics of "smart dust" devices with solar radiation pressure and drag
This paper investigates how perturbations due to asymmetric solar radiation pressure, in the presence of Earth shadow, and atmospheric drag can be balanced to obtain long-lived Earth centred orbits for swarms of micro-scale 'smart dust' devices, without the use of active control. The secular variation of Keplerian elements is expressed analytically through an averaging technique. Families of solutions are then identified where Sun-synchronous apse-line precession is achieved passively to maintain asymmetric solar radiation pressure. The long-term orbit evolution is characterized by librational motion, progressively decaying due to the non-conservative effect of atmospheric drag. Long-lived orbits can then be designed through the interaction of energy gain from asymmetric solar radiation pressure and energy dissipation due to drag. In this way, the usual short drag lifetime of such high area-to-mass spacecraft can be greatly extended (and indeed selected). In addition, the effect of atmospheric drag can be exploited to ensure the rapid end-of-life decay of such devices, thus preventing long-lived orbit debris
Staircase polygons: moments of diagonal lengths and column heights
We consider staircase polygons, counted by perimeter and sums of k-th powers
of their diagonal lengths, k being a positive integer. We derive limit
distributions for these parameters in the limit of large perimeter and compare
the results to Monte-Carlo simulations of self-avoiding polygons. We also
analyse staircase polygons, counted by width and sums of powers of their column
heights, and we apply our methods to related models of directed walks.Comment: 24 pages, 7 figures; to appear in proceedings of Counting Complexity:
An International Workshop On Statistical Mechanics And Combinatorics, 10-15
July 2005, Queensland, Australi
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