2,322 research outputs found

    Resolvable Mendelsohn designs and finite Frobenius groups

    Full text link
    We prove the existence and give constructions of a (p(k)−1)(p(k)-1)-fold perfect resolvable (v,k,1)(v, k, 1)-Mendelsohn design for any integers v>k≄2v > k \ge 2 with v≡1mod  kv \equiv 1 \mod k such that there exists a finite Frobenius group whose kernel KK has order vv and whose complement contains an element ϕ\phi of order kk, where p(k)p(k) is the least prime factor of kk. Such a design admits K⋊⟚ϕ⟩K \rtimes \langle \phi \rangle as a group of automorphisms and is perfect when kk is a prime. As an application we prove that for any integer v=p1e1
ptet≄3v = p_{1}^{e_1} \ldots p_{t}^{e_t} \ge 3 in prime factorization, and any prime kk dividing piei−1p_{i}^{e_i} - 1 for 1≀i≀t1 \le i \le t, there exists a resolvable perfect (v,k,1)(v, k, 1)-Mendelsohn design that admits a Frobenius group as a group of automorphisms. We also prove that, if kk is even and divides pi−1p_{i} - 1 for 1≀i≀t1 \le i \le t, then there are at least φ(k)t\varphi(k)^t resolvable (v,k,1)(v, k, 1)-Mendelsohn designs that admit a Frobenius group as a group of automorphisms, where φ\varphi is Euler's totient function.Comment: Final versio

    Dynamics of the quantum dimer model on the triangular lattice: Soft modes and local resonating valence-bond correlations

    Full text link
    We report on an exhaustive investigation of the dynamical dimer-dimer correlations in imaginary time for the quantum dimer model on the triangular lattice using the Green's function Monte Carlo method. We show in particular that soft modes develop upon reducing the dimer-dimer repulsion, indicating the presence of a second-order phase transition into an ordered phase with broken translational symmetry. We further investigate the nature of this ordered phase, for which a 12-site unit cell has been previously proposed, with the surprising result that significant Bragg peaks are only present at two of the three high-symmetry points consistent with this unit cell. We attribute the absence of a detectable peak to its small magnitude due to the nearly uniform internal structure of the 12-site crystal cell.Comment: 6 pages, 8 figure

    Diagrammatic Monte Carlo algorithm for the resonant Fermi gas

    Get PDF
    We provide a description of a diagrammatic Monte Carlo algorithm for the resonant Fermi gas in the normal phase. Details are given on diagrammatic framework, Monte Carlo moves, and incorporation of ultraviolet asymptotics. Apart from the self-consistent bold scheme, we also describe a non-self-consistent scheme, for which the ultraviolet treatment is more involved.Comment: Revised and extended versio

    Ground-state phase diagram of the three-band Hubbard model from density matrix embedding theory

    Get PDF
    We determine the ground-state phase diagram of the three-band Hubbard model across a range of model parameters using density matrix embedding theory. We study the atomic-scale nature of the antiferromagnetic (AFM) and superconducting (SC) orders, explicitly including the oxygen degrees of freedom. All parametrizations of the model display AFM and SC phases, but the decay of AFM order with doping is too slow compared to the experimental phase diagram, and further, coexistence of AFM and SC orders occurs in all parameter sets. The local magnetic moment localizes entirely at the copper sites. The magnetic phase diagram is particularly sensitive to Δ_(pd) and t_(pp), and existing estimates of the charge transfer gap Δ_(pd) appear too large in so-called minimal model parametrizations. The electron-doped side of the phase diagram is qualitatively distinct from the hole-doped side and we find an unusual two-peak structure in the SC in the full model parametrization. Examining the SC order at the atomic scale, within the larger scale d_(xÂČ−yÂČ)-wave SC pairing order between Cu-Cu and O-O, we also observe a local p_(x(y)) [or d_(xz(yz))] symmetry modulation of the pair density on the Cu-O bonds. Our work highlights some of the features that arise in a three-band versus one-band picture, the role of the oxygen degrees of freedom in new kinds of atomic-scale SC orders, and the necessity of re-evaluating current parametrizations of the three-band Hubbard model

    Football goal scoring detection system

    Get PDF
    The project objective is to simulate Goal Line Technology (GLT) in a football goal. For this, an electronic system is designed and built which is able to detect when the ball has crossed the goal line. This system also can differentiate if the object which has crossed the goal line is the ball or the goalkeeper or whatever it may be. Infrared technology is used in order to develop the GLT, specifically a kind of infrared light curtain. To carry out this technology is necessary to define the basic operation of this. IR-Leds and IR-Photodiodes are used as emitters and receivers, respectively. They make a kind of infrared light curtain because unlike a proper curtain, in this case, all of the emitters are not switched on at the same time, only a pair of emitter-receiver are switched on, then they are switched off and then the following pair of emitter-receiver are switched on, doing a scan along of the emitters-receivers pairs columns. Another requirement of GLT is using an alarm device; a red-led is switched on in the case of detecting that the ball has crossed the goal line. On the other hand, if another thing crosses the goal line, no notification is showed. This system is designed and built for a goal, a ball and a player in scale; it can be applicable in real life and also shows another way of how the “ghost goals” can be solved. This system can help the referee to clarify controversial situations in football which means an improvement of this sport and a forward step in order to make this game fairer
    • 

    corecore