Problem of oscillating cone in supersonic flow is solved by small perturbation techniques

Small perturbation technique solves the problem of an oscillating cone in supersonic flow. The logic of the program is straightforward, as reflected in the actual instructions for solving the problem

Superconducting instability in the Holstein-Hubbard model: A numerical renormalization group study

We have studied the d-wave pairing-instability in the two-dimensional Holstein-Hubbard model at the level of a full fluctuation exchange approximation which treats both Coulomb and electron-phonon (EP) interaction diagrammatically on an equal footing. A generalized numerical renormalization group technique has been developed to solve the resulting self-consistent field equations. The $d$-wave superconducting phase diagram shows an optimal T_c at electron concentration ~ 0.9 for the purely electronic Hubbard system. The EP interaction suppresses the d-wave T_c which drops to zero when the phonon-mediated on-site attraction $U_p$ becomes comparable to the on-site Coulomb repulsion $U$. The isotope exponent $\alpha$ is negative in this model and small compared to the classical BCS value $\alpha_{BCS} = 1/2$ or compared to typical observed values in non-optimally doped cuprate superconductors.Comment: 4 pages RevTeX + 3 PS figures include

Effect of a Normal-State Pseudogap on Optical Conductivity in Underdoped Cuprate Superconductors

We calculate the c-axis infrared conductivity $\sigma_c(\omega)$ in underdoped cuprate superconductors for spinfluctuation exchange scattering within the CuO$_2$-planes including a phenomenological d-wave pseudogap of amplitude $E_g$. For temperatures decreasing below a temperature $T^* \sim E_g/2$, a gap for $\omega < 2E_g$ develops in $\sigma_c(\omega)$ in the incoherent (diffuse) transmission limit. The resistivity shows 'semiconducting' behavior, i.e. it increases for low temperatures above the constant behavior for $E_g=0$. We find that the pseudogap structure in the in-plane optical conductivity is about twice as big as in the interplane conductivity $\sigma_c(\omega)$, in qualitative agreement with experiment. This is a consequence of the fact that the spinfluctuation exchange interaction is suppressed at low frequencies as a result of the opening of the pseudogap. While the c-axis conductivity in the underdoped regime is described best by incoherent transmission, in the overdoped regime coherent conductance gives a better description.Comment: to be published in Phys. Rev. B (November 1, 1999

Superconductivity and Pseudogap in Quasi-Two-Dimensional Metals around the Antiferromagnetic Quantum Critical Point

Spin fluctuations (SF) and SF-mediated superconductivity (SC) in quasi-two-dimensional metals around the antiferrromagnetic (AF) quantum critical point (QCP) are investigated by using the self-consistent renormalization theory for SF and the strong coupling theory for SC. We introduce a parameter y0 as a measure for the distance from the AFQCP which is approximately proportional to (x-xc), x being the electron (e) or hole (h) doping concentration to the half-filled band and xc being the value at the AFQCP. We present phase diagrams in the T-y0 plane including contour maps of the AF correlation length and AF and SC transition temperatures TN and Tc, respectively. The Tc curve is dome-shaped with a maximum at around the AFQCP. The calculated one-electron spectral density shows a pseudogap in the high-density-of-states region near (pi,0) below around a certain temperature T* and gives a contour map at the Fermi energy reminiscent of the Fermi arc. These results are discussed in comparison with e- and h-doped high-Tc cuprates.Comment: 5 pages, 3 figure

Spin Fluctuation-Induced Superconductivity in Organic Compounds

Spin fluctuation-induced superconductivity in two-dimensional organic compounds such as \kappa-(ET)_2-X is investigated by using a simplified dimer Hubbard model with right-angled isosceles triangular lattice (transfer matrices -\tau, -\tau^\prime). The dynamical susceptiblity and the self-energy are calculated self-consistently within the fluctuation exchange approximation and the value for T_c as obtained by solving the linearized Eliashberg-type equations is in good agreement with experiment. The pairing symmetry is of d_{x^2-y^2} type. The calculated (U/\tau)-dependence of T_c compares qualitatively well with the observed pressure dependence of T_c. Varying the value for \tau^\prime/\tau from 0 to 1 we interpolate between the square lattice and the regular triangular lattice and find firstly that values of T_c for \kappa-(ET)_2-X and cuprates scale well and secondly that T_c tends to decrease with increasing \tau^\prime/\tau and no superconductivity is found for \tau^\prime/\tau=1, the regular triangular lattice.Comment: 4 pages, 6 eps figures, uses jpsj.st

Application of Deep Learning Long Short-Term Memory in Energy Demand Forecasting

The smart metering infrastructure has changed how electricity is measured in both residential and industrial application. The large amount of data collected by smart meter per day provides a huge potential for analytics to support the operation of a smart grid, an example of which is energy demand forecasting. Short term energy forecasting can be used by utilities to assess if any forecasted peak energy demand would have an adverse effect on the power system transmission and distribution infrastructure. It can also help in load scheduling and demand side management. Many techniques have been proposed to forecast time series including Support Vector Machine, Artificial Neural Network and Deep Learning. In this work we use Long Short Term Memory architecture to forecast 3-day ahead energy demand across each month in the year. The results show that 3-day ahead demand can be accurately forecasted with a Mean Absolute Percentage Error of 3.15%. In addition to that, the paper proposes way to quantify the time as a feature to be used in the training phase which is shown to affect the network performance

Asymmetric Fermi superfluid with different atomic species in a harmonic trap

We study the dilute fermion gas with pairing between two species and unequal concentrations in a harmonic trap using the mean field theory and the local density approximation. We found that the system can exhibit a superfluid shell structure sandwiched by the normal fermions. This superfluid shell structure occurs if the mass ratio is larger then certain critical value which increases from the weak-coupling BCS region to the strong-coupling BEC side. In the strong coupling BEC regime, the radii of superfluid phase are less sensitive to the mass ratios and are similar to the case of pairing with equal masses. However, the lighter leftover fermions are easier to mix with the superfluid core than the heavier ones. A partially polarized superfluid can be found if the majority fermions are lighter, whereas phase separation is still found if they are heavier.Comment: 12 pages, 7 figure

Superconductivity in the quasi-two-dimensional Hubbard model

On the basis of spin and pairing fluctuation-exchange approximation, we study the superconductivity in quasi-two-dimensional Hubbard model. The integral equations for the Green's function are self-consistently solved by numerical calculation. Solutions for the order parameter, London penetration depth, density of states, and transition temperature are obtained. Some of the results are compared with the experiments for the cuprate high-temperature superconductors. Numerical techniques are presented in details. With these techniques, the amount of numerical computation can be greatly reduced.Comment: 17 pages, 13 figure

Reduction of Tc due to Impurities in Cuprate Superconductors

In order to explain how impurities affect the unconventional superconductivity, we study non-magnetic impurity effect on the transition temperature using on-site U Hubbard model within a fluctuation exchange (FLEX) approximation. We find that in appearance, the reduction of Tc roughly coincides with the well-known Abrikosov-Gor'kov formula. This coincidence results from the cancellation between two effects; one is the reduction of attractive force due to randomness, and another is the reduction of the damping rate of quasi-particle arising from electron interaction. As another problem, we also study impurity effect on underdoped cuprate as the system showing pseudogap phenomena. To the aim, we adopt the pairing scenario for the pseudogap and discuss how pseudogap phenomena affect the reduction of Tc by impurities. We find that 'pseudogap breaking' by impurities plays the essential role in underdoped cuprate and suppresses the Tc reduction due to the superconducting (SC) fluctuation.Comment: 14 pages, 28 figures To be published in JPS