5,157 research outputs found
On the Typical Structure of Graphs in a Monotone Property
Given a graph property , it is interesting to determine the
typical structure of graphs that satisfy . In this paper, we
consider monotone properties, that is, properties that are closed under taking
subgraphs. Using results from the theory of graph limits, we show that if
is a monotone property and is the largest integer for which
every -colorable graph satisfies , then almost every graph with
is close to being a balanced -partite graph.Comment: 5 page
On String Graph Limits and the Structure of a Typical String Graph
We study limits of convergent sequences of string graphs, that is, graphs
with an intersection representation consisting of curves in the plane. We use
these results to study the limiting behavior of a sequence of random string
graphs. We also prove similar results for several related graph classes.Comment: 18 page
Modified kagome physics in the natural spin-1/2 kagome lattice systems - kapellasite Cu3Zn(OH)6Cl2 and haydeeite Cu3Mg(OH)6Cl2
The recently discovered natural minerals Cu3Zn(OH)6Cl2 and Cu3Mg(OH)6Cl2 are
spin 1/2 systems with an ideal kagome geometry. Based on electronic structure
calculations, we develop a realistic model which includes couplings across the
kagome hexagons beyond the original kagome model that are intrinsic in real
kagome materials. Exact diagonalization studies for the derived model reveal a
strong impact of these couplings on the magnetic ground state. Our predictions
could be compared to and supplied with neutron scattering, thermodynamic and
NMR data.Comment: 5 pages, 5 figures, 1 tabl
Creation and Growth of Components in a Random Hypergraph Process
Denote by an -component a connected -uniform hypergraph with
edges and vertices. We prove that the expected number of
creations of -component during a random hypergraph process tends to 1 as
and tend to with the total number of vertices such that
. Under the same conditions, we also show that
the expected number of vertices that ever belong to an -component is
approximately . As an immediate
consequence, it follows that with high probability the largest -component
during the process is of size . Our results
give insight about the size of giant components inside the phase transition of
random hypergraphs.Comment: R\'{e}sum\'{e} \'{e}tend
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
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
Preliminary investigation on temperature, chemistry and isotopes of mine water pumped in Bytom geological basin (USCB,Southern Poland) as a potential geothermal energy source
Mine water from both operating and abandoned mines can be used for individual space heating projects, district heating/cooling systems or for preheating air for mine ventilation. Examples of such applications are already known from Canada, US, Netherlands, UK, and Spain. The Upper Silesian Coal Basin (USCB) in Poland, where 34 of 65 hard coal mines have been abandoned since 1989, represents a potentially large opportunity for mine water heating schemes. This paper describes the mines from Bytom (northern USCB) as a potential location for ground source heat extraction projects. Hydrogeological and hydrogeochemical studies of pumped waters have been carried out in order to better understand the potential of the Bytom heat resource. The monitoring program is still ongoing, but initial results compare favorably with existing mine water geothermal source systems where water temperatures are comparable or lower than those found at Bytom. Initial hydrochemical and isotope data demonstrate stability in water composition at most of the monitoring points. These data elucidate the hydrogeological cycle during active dewatering and provide a baseline for understanding the geothermal behavior of the system, which is crucial for optimizing heat extraction. Preliminary results also reveal very stable mine water temperatures in the pumped, and hydrologically connected, Szombierki system and suggest remarkable stability in the characteristics of the main hydrothermal reservoirs
Weak limits for quantum random walks
We formulate and prove a general weak limit theorem for quantum random walks
in one and more dimensions. With denoting position at time , we show
that converges weakly as to a certain distribution which
is absolutely continuous and of bounded support. The proof is rigorous and
makes use of Fourier transform methods. This approach simplifies and extends
certain preceding derivations valid in one dimension that make use of
combinatorial and path integral methods
Stringhalt in a Horse
On Oct. 5, 1943, a 9-year-old, brown, riding horse was brought to the veterinary clinic with history and symptoms of stringhalt. When the patient moved at any natural gait, the left hind leg was flexed so that the hoof closely approximated the body. This condition may be defined as an involuntary flexing, affecting one or both posterior limbs. The limb is lifted with excessive suddenness and beyond normal flexion. Numerous investigators in their study of this myoclonic condition have advanced various theories in regard to the possible etiology
Maximum relative height of one-dimensional interfaces : from Rayleigh to Airy distribution
We introduce an alternative definition of the relative height h^\kappa(x) of
a one-dimensional fluctuating interface indexed by a continuously varying real
paramater 0 \leq \kappa \leq 1. It interpolates between the height relative to
the initial value (i.e. in x=0) when \kappa = 0 and the height relative to the
spatially averaged height for \kappa = 1. We compute exactly the distribution
P^\kappa(h_m,L) of the maximum h_m of these relative heights for systems of
finite size L and periodic boundary conditions. One finds that it takes the
scaling form P^\kappa(h_m,L) = L^{-1/2} f^\kappa (h_m L^{-1/2}) where the
scaling function f^\kappa(x) interpolates between the Rayleigh distribution for
\kappa=0 and the Airy distribution for \kappa=1, the latter being the
probability distribution of the area under a Brownian excursion over the unit
interval. For arbitrary \kappa, one finds that it is related to, albeit
different from, the distribution of the area restricted to the interval [0,
\kappa] under a Brownian excursion over the unit interval.Comment: 25 pages, 4 figure
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