106,700 research outputs found

    General calculation of 4f−5d4f-5d transition rates for rare-earth ions using many-body perturbation theory

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    The 4f−5d4f-5d transition rates for rare-earth ions in crystals can be calculated with an effective transition operator acting between model 4fN4f^N and 4fN−15d4f^{N-1}5d states calculated with effective Hamiltonian, such as semi-empirical crystal Hamiltonian. The difference of the effective transition operator from the original transition operator is the corrections due to mixing in transition initial and final states of excited configurations from both the center ion and the ligand ions. These corrections are calculated using many-body perturbation theory. For free ions, there are important one-body and two-body corrections. The one-body correction is proportional to the original electric dipole operator with magnitude of approximately 40% of the uncorrected electric dipole moment. Its effect is equivalent to scaling down the radial integral \ME {5d} r {4f}, to about 60% of the uncorrected HF value. The two-body correction has magnitude of approximately 25% relative to the uncorrected electric dipole moment. For ions in crystals, there is an additional one-body correction due to ligand polarization, whose magnitude is shown to be about 10% of the uncorrected electric dipole moment.Comment: 10 pages, 1 figur

    Acyclic orientations on the Sierpinski gasket

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    We study the number of acyclic orientations on the generalized two-dimensional Sierpinski gasket SG2,b(n)SG_{2,b}(n) at stage nn with bb equal to two and three, and determine the asymptotic behaviors. We also derive upper bounds for the asymptotic growth constants for SG2,bSG_{2,b} and dd-dimensional Sierpinski gasket SGdSG_d.Comment: 20 pages, 8 figures and 6 table

    An integrated theory of language production and comprehension

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    Currently, production and comprehension are regarded as quite distinct in accounts of language processing. In rejecting this dichotomy, we instead assert that producing and understanding are interwoven, and that this interweaving is what enables people to predict themselves and each other. We start by noting that production and comprehension are forms of action and action perception. We then consider the evidence for interweaving in action, action perception, and joint action, and explain such evidence in terms of prediction. Specifically, we assume that actors construct forward models of their actions before they execute those actions, and that perceivers of others' actions covertly imitate those actions, then construct forward models of those actions. We use these accounts of action, action perception, and joint action to develop accounts of production, comprehension, and interactive language. Importantly, they incorporate well-defined levels of linguistic representation (such as semantics, syntax, and phonology). We show (a) how speakers and comprehenders use covert imitation and forward modeling to make predictions at these levels of representation, (b) how they interweave production and comprehension processes, and (c) how they use these predictions to monitor the upcoming utterances. We show how these accounts explain a range of behavioral and neuroscientific data on language processing and discuss some of the implications of our proposal

    The influence of gyroscopic forces on the dynamic behavior and flutter of rotating blades

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    The structural dynamics of a cantilever turbomachine blade mounted on a spinning and precessing rotor are investigated. Both stability and forced vibration are considered with a blade model that increases in complexity (and verisimilitude) from a spring-restrained point mass, to a uniform cantilever, to a twisted uniform cantilever turbomachine blade mounted on a spinning and precessing rotor are investigated. Both stability and forced vibration are considered with a blade model that increases in complexity (and verisimilitude) from a spring-restrained point mass, to a uniform cantilever, to a twisted uniform cantilever, to a tapered twisted cantilever of arbitrary cross-section. In every instance the formulation is from first principles using a finite element based on beam theory. Both ramp-type and periodic-type precessional angular displacements are considered. In concluding, forced vibrating and flutter are studied using the final and most sophisticated structural model. The analysis of stability is presented and a number of numerical examples are worked out

    Impure Thoughts on Inelastic Dark Matter

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    The inelastic dark matter scenario was proposed to reconcile the DAMA annual modulation with null results from other experiments. In this scenario, WIMPs scatter into an excited state, split from the ground state by an energy delta comparable to the available kinetic energy of a Galactic WIMP. We note that for large splittings delta, the dominant scattering at DAMA can occur off of thallium nuclei, with A~205, which are present as a dopant at the 10^-3 level in NaI(Tl) crystals. For a WIMP mass m~100GeV and delta~200keV, we find a region in delta-m-parameter space which is consistent with all experiments. These parameters in particular can be probed in experiments with thallium in their targets, such as KIMS, but are inaccessible to lighter target experiments. Depending on the tail of the WIMP velocity distribution, a highly modulated signal may or may not appear at CRESST-II.Comment: 3 pages, 1 figure, accepted for publication in Physical Review Letter

    Unitary Fermi Gas in a Harmonic Trap

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    We present an {\it ab initio} calculation of small numbers of trapped, strongly interacting fermions using the Green's Function Monte Carlo method (GFMC). The ground state energy, density profile and pairing gap are calculated for particle numbers N=2∼22N = 2 \sim 22 using the parameter-free "unitary" interaction. Trial wave functions are taken of the form of correlated pairs in a harmonic oscillator basis. We find that the lowest energies are obtained with a minimum explicit pair correlation beyond that needed to exploit the degeneracy of oscillator states. We find that energies can be well fitted by the expression aTFETF+Δmod(N,2)a_{TF} E_{TF} + \Delta {\rm mod}(N,2) where ETFE_{TF} is the Thomas-Fermi energy of a noninteracting gas in the trap and Δ\Delta is a pairing gap. There is no evidence of a shell correction energy in the systematics, but the density distributions show pronounced shell effects. We find the value Δ=0.7±0.2ω\Delta= 0.7\pm 0.2\omega for the pairing gap. This is smaller than the value found for the uniform gas at a density corresponding to the central density of the trapped gas.Comment: 2 figures, 2 table
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