Fitting multiple bell curves stably and accurately to a time series as applied to Hubbert cycles or other phenomena

Bell curves are applicable to understating many observations and measurements across the sciences. Relating Gaussian curves to data is a common because of its relation to both the Central Limit Theorem and to random error. Similarly, fitting logistic derivatives to oil or other nonrenewable resource production is common practice. Fitting bell curves to a time series is an inherently non-linear problem requiring initial estimates of the parameters describing the bellcurves. Poor estimates lead to instability and divergent solutions. Fitting to a cumulative curve improves stability, but at the expense of accuracy of the final solution. Jointly fitting multiple bell curves is superior to extraction of curves one at a time, but further exacerbates the non-linearity. Including both the cumulative data and the bell-curve data within the inversion, can exploit the greater stability of the cumulative fit and the greater accuracy of a direct fit. The algorithm presented here inverts for multiple bells by combining cumulative and direct fits to exploit the best features of both. The versatility and accuracy of the algorithm are demonstrated using two different Earth Science examples: a seismo-volcanic sequence recorded by a hydrophone array moored to the seafloor and U.S. coal production. The MatLab function used here for joint curve determination is included in the online manuscript complementary material

^25Mg NMR study of the MgB_2 superconductor

^25Mg NMR spectra and nuclear spin-lattice relaxation time, T_1, have been measured in polycrystalline ^25MgB_2 with a superconducting transition temperature T_c = 39.0 K in zero magnetic field. From the first order and second order quadrupole perturbed NMR spectrum a quadrupole coupling frequency nu_Q = 222(1.5) kHz is obtained. T_1T = 1090(50) sK and Knight shift K_c = 242(4) ppm are temperature independent in the normal conducting phase. The ^25Mg Korringa ratio equals to 0.95 which is very close to the ideal value of unity for s-electrons. The comparison of the experimental nu_Q, T_1T, and K_c with the corresponding values obtained by LDA calculations shows an excellent agreement for all three quantities.Comment: 4 pages including 4 eps-figures, revtex

Effect of light Sr doping on the spin-state transition in LaCoO_3

We present an inelastic neutron scattering study of the low energy crystal-field excitations in the lightly doped cobalt perovskite La_0.998Sr_0.002CoO_3. In contrast to the parent compound LaCoO_3 an inelastic peak at energy transfer ~0.75 meV was found at temperatures below 30 K. This excitation apparently corresponds to a transition between a ground state orbital singlet and a higher excited orbital doublet, originating from a high-spin triplet split by a small trigonal crystal field. Another inelastic peak at an energy transfer ~0.6 meV was found at intermediate temperatures starting from T > 30 K. This confirms the presence of a thermally induced spin-state transition from the low-spin Co^3+ to a magnetic high-spin state in the non-disturbed LaCoO_3 matrix. We suggest that hole doping of LaCoO_3 leads to the creation of a magnetic polaron and hence to the low-to-high spin state transition on the relevant Co sites.Comment: 4 pages, 2 figures; based on a talk given at ICM'06, Kyoto; to appear in JMM

Magnetic excitations in the spin-trimer compounds Ca3Cu3-xNix(PO4)4 (x=0,1,2)

Inelastic neutron scattering experiments were performed for the spin-trimer compounds Ca3Cu3-xNix(PO4)4 (x=0,1,2) in order to study the dynamic magnetic properties. The observed excitations can be associated with transitions between the low-lying electronic states of linear Cu-Cu-Cu, Cu-Cu-Ni, and Ni-Cu-Ni trimers which are the basic constituents of the title compounds. The exchange interactions within the trimers are well described by the Heisenberg model with dominant antiferromagnetic nearest-neighbor interactions J. For x=0 we find JCu-Cu=-4.74(2) meV which is enhanced for x=1 to JCu-Cu=-4.92(6) meV. For x=1 and x=2 we find JCu-Ni=-0.85(10) meV and an axial single-ion anisotropy parameter DNi=-0.7(1) meV. While the x=0 and x=1 compounds do not exhibit long-range magnetic ordering down to 1 K, the x=2 compound shows antiferromagnetic ordering below TN=20 K, which is compatible with the molecular-field parameter 0.63(12) meV derived by neutron spectroscopy.Comment: 22 pages (double spacing), 1 table, 9 figures, Submitted to Phys. Rev. B (2007

Correlation between oxygen isotope effects on the transition temperature and the magnetic penetration depth in high-temperature superconductors close to optimal doping

The oxygen-isotope (^{16}O/^{18}O) effect (OIE) on the in-plane magnetic penetration depth \lambda_{ab}(0) in optimally-doped YBa_2Cu_3O_{7-\delta} and La_{1.85}Sr_{0.15}CuO_4, and in slightly underdoped YBa_2Cu_4O_8 and Y_{0.8}Pr_{0.2}Ba_2Cu_3O_{7-\delta} was studied by means of muon-spin rotation. A substantial OIE on \lambda_{ab}(0) with an OIE exponent \beta_O=-d\ln\lambda_{ab}(0)/d\ln M_O\approx - 0.2 (M_O is the mass of the oxygen isotope), and a small OIE on the transition temperature T_c with an OIE exponent \alpha_O=-d\ln T_{c}/d \ln M_O\simeq0.02 to 0.1 were observed. The observation of a substantial isotope effect on \lambda_{ab}(0), even in cuprates where the OIE on T_c is small, indicates that lattice effects play an important role in cuprate HTS.Comment: 6 pages, 4 figure

Asterism decoding for layered space-time systems using 8PSK

The area of layered space-time (LST) systems has received enormous attention recently as they can provide a roughly linear increase in data rate by using multiple transmit and receive antennas. The optimal detection strategy for a LST receiver is to perform a maximum-likelihood (ML) search over all possible transmitted symbol combinations has an exponential complexity when the constellation size of number of transmit antennas increases. While sub-optimal decoders, such as VBLAST, provide linear decoding only where the number of receive antennas is at least equal to the number of transmit antennas. The decoding scheme proposed in this paper, called Asterism decoding, looks for a more efficient way of finding the ML solution by first considering the case of multiple transmit antennas and a single receive antenna. The decoder is then extended to achieve ML like performance for any number of receive antennas. It further shows that Asterism decoding has at least an approximate order of magnitude reduction in computational complexity when compared to ML decoding. Asterism decoding is the first lower complexity decoder that achieves ML-like performance for systems where the number of receive antennas is less than the number of transmit antennas without the additional use of error coding