We analyze the superconducting state properties for the case of a two-band self-consistent BCS model that considers an electron band structure suitable for iron based superconducting materials. The superconducting gap parameters corresponding to each component electron band, |Δ _11(T)| and |Δ _22(T)| , are investigated as function of temperature, T, inter-orbital hopping parameter, t_4 , and electron doping, N. The values of the two ratios 2|Δ ^0_11|/T_c and 2|Δ ^0_22|/T_c are not universal, and they are strongly dependent on the value of the hopping parameter, t_4 . In the case of s^± -wave symmetry, the superconducting state in the system exists only at certain electron doping concentrations, leading to a complex superconducting phase diagram for iron based superconducting materials.

In the current work a seven-equation model of two-dimensional two-phase flow problems is analyzed by a parallel formulation of a WENO multiresolution scheme. The scheme adaptivity is obtained by a third order interpolating wavelet transform associated to a threshold operator. In this way, a sparse representation of the vector solution is obtained at each time step. The evolution in time is performed by a third order TVD Runge-Kutta scheme. For the spatial integration on the sparse grid, the Lax-Friedrich flux splitting scheme is considered in which the flux derivatives are approximated by the standard fifth-order WENO scheme. The parallel formulation of the code is based on OpenMP, which is crucial for the computation of long term simulations with shorter computational times. The considered adaptive parallel WENO scheme has the capability of accurately capturing the formation of shocks and the evolution of rarefaction waves, as evinced by the presented numerical simulations.

We present a possible phase diagram for the superconductivity state in a two-band scenario that includes contributions from the inter-orbital off-diagonal hopping term. Our model accounts for intra-band attractive electron–electron interactions that leads to the formation of superconducting Cooper pairs in each component band and for an inter-band attractive electron–electron interaction responsible for a single superconductive transition temperature T_c in the model. Using a mean field approximation, we obtained an analytical equation for the superconducting critical temperature that includes contributions from a hybridization term due to the mixing of the two electron bands. For a numerical solution of this equation, we considered a band structure that reproduced as much as possible the situation in the Ba _1-x K _x Fe _2 As _2 pnictide superconductor material. Our possible phase diagram T_c vs. N is obtained assuming that Cooper pairs in both electron bands have either s-wave or s^± -wave symmetry. The main result of our calculation is the existence of a complex phase diagram that at different inter-orbital hopping strengths can have one or two local maxima for the transition critical temperature T_c . The electron concentration at which these maxima occur in the phase diagram can be tuned using the inter-orbital off-diagonal hopping term.

In the current work a WENO multiresolution scheme is considered for solving a seven-equation model of two- dimensional two-phase flow problems. A third order interpolating wavelet transform associated to a threshold operator is the main tool for obtaining the sparse representation of the solution at each time step. The spatial operator is solved on the sparse grid by the Lax-Friedrich flux splitting scheme in which the flux derivatives are approximated by the standard WENO scheme. A parallel formulation of the code based on OpenMP allows long term simulations to be obtained with shorter computational times. This type of adaptive parallel scheme can accurately capture the formation of shocks and the evolution of rarefaction waves. As a consequence, more detailed structures of the solution are identified, enriching the understanding of the analyzed two-phase flow phenomena.

The current work addresses a multiresolution scheme for solving two-phase volcanic flow problems. The multiresolution is obtained by a third order interpolating wavelet transform associated to a threshold operator, which allows a sparse representation of the solution in each time step. The spatial operator is solved by the Lax-Friedrich flux splitting approach in which the flux derivatives are approximated by the standard WENO scheme. Two-phase volcanic flows benefit from this type of adaptive schemes since they can accurately capture the formation of shocks and the evolution of rarefaction waves. Substantial computational gains are obtained through the grid reduction feature while maintaining the quality of the solutions.

Two-phase bubbly flow is widely associated with the nuclear thermal-hydraulics for future reactors design. In many cases within such reactors, the relative velocity between the two-phases is crucial in operational and safety analysis. More insights from either mathematical or numerical investigations are desired to better understand and predict the relative velocity behavior. The relative velocity prediction has been getting more interest as a tool towards accurate modeling of two-phase bubbly flows. For this purpose, a non-equilibrium two-phase flow model based on mixture formulations is considered in this paper. We present our recent effort in simulation two-phase flows using a third order interpolating wavelet transform based on a threshold operator. This allows a sparse representation of the complete numerical solution in every time step where the flux derivatives are approximated by the standard WENO scheme. The model equations and numerical computations are tested and verified through gas-liquid two-phase mixtures by means of thermal-hydraulics tests. These simulations examine the effect of high and low relative velocities at different gas void fractions. The computations demonstrated good mesh convergence simulations adapting mixture formulations for two-phase bubbly flows. Quantitative performance of simulations are also presented to further investigate the model equations by comparing the results with different Riemann solvers based numerical methods. The same trend is also displayed for two-dimensional test cases demonstrating the capabilities of multi-resolution techniques to resolve non-equilibrium two-phase flow equations within nuclear reactors.

PurposeThe purpose of this work is to present the implementation of weighted essentially non-oscillatory (WENO) wavelet methods for solving multiphase flow problems. The particular interest is gas–liquid two-phase mixture with velocity non-equilibrium. Numerical simulations are carried out on different scenarios of one-dimensional Riemann problems for gas–liquid flows. Results are validated and qualitatively compared with solutions provided by other standard numerical methods.Design/methodology/approachThis paper extends the framework of WENO wavelet adaptive method to a fully hyperbolic two-phase flow model in a conservative form. The grid adaptivity in each time step is provided by the application of a thresholded interpolating wavelet transform. This facilitates the construction of a small yet effective sparse point representation of the solution. The method of Lax–Friedrich flux splitting is used to resolve the spatial operator in which the flux derivatives are approximated by the WENO scheme.FindingsHyperbolic models of two-phase flow in conservative form are efficiently solved, as shocks and rarefaction waves are precisely captured by the chosen methodology. Substantial computational gains are obtained through the grid reduction feature while maintaining the quality of the solutions. The results indicate that WENO wavelet methods are robust and sufficient to accurately simulate gas–liquid mixtures.Originality/valueResolution of two-phase flows is rarely studied using WENO wavelet methods. It is the first time such a study on the relative velocity is reported in two-phase flows using such methods.

Purpose The current work aims to present a parallel code using the open multi-processing (OpenMP) programming model for an adaptive multi-resolution high-order finite difference scheme for solving 2D conservation laws, comparing efficiencies obtained with a previous message passing interface formulation for the same serial scheme and considering the same type of 2D formulations laws. Design/methodology/approach The serial version of the code is naturally suitable for parallelization because the spatial operator formulation is based on a splitting scheme per direction for which the flux components are numerically computed by a Lax–Friedrichs factorization independently for each row or column. High-order approximations for numerical fluxes are computed by the third-order essentially non-oscillatory (ENO) and fifth-order weighted essentially non-oscillatory (WENO) interpolation schemes, assuming sparse grids in each direction. The grid adaptivity is obtained by a cubic interpolating wavelet transform applied in each space dimension, associated to a threshold operator. Time is evolved by a third order TVD Runge–Kutta method. Findings The parallel formulation is implemented automatically at compiling time by the OpenMP library routines, being virtually transparent to the programmer. This over simplifies any concerns about managing and/or updating the adaptive grid when compared to what is necessary to be done when other parallel approaches are considered. Numerical simulations results and the large speedups obtained for the Euler equations in gas dynamics highlight the efficiency of the OpenMP approach. Research limitations/implications The resulting speedups reflect the effectiveness of the OpenMP approach but are, to a large extension, limited by the hardware used (2 E5-2620 Intel Xeon processors, 6 cores, 2 threads/core, hyper-threading enabled). As the demand for OpenMP threads increases, the code starts to make explicit use of the second logical thread available in each E5-2620 processor core and efficiency drops. The speedup peak is reached near the possible maximum (24) at about 22, 23 threads. This peak reflects the hardware configuration and the true software limit should be located way beyond this value. Practical implications So far no attempts have been made to parallelize other possible code segments (for instance, the ENO|-WENO-TVD code lines that process the different data components which could potentially push the speed up limit to higher values even further. The fact that the speedup peak is located close to the present hardware limit reflects the scalability properties of the OpenMP programming and of the splitting scheme as well. Consequently, it is likely that the speedup peak with the OpenMP approach for this kind of problem formulation will be close to the physical (and/or logical) limit of the hardware used. Social implications This work is the result of a successful collaboration among researchers from two different institutions, one internationally well-known and with a long-term experience in applied mathematics for industrial applications and the other in a starting process of international academic insertion. In this way, this scientific partnership has the potential of promoting further knowledge exchange, involving students and other collaborators. Originality/value The proposed methodology (use of OpenMP programming model for the wavelet adaptive splitting scheme) is original and contributes to a very active research area in the past years, namely, adaptive methods for conservation laws and their parallel formulations, which is of great interest for the entire scientific community.

This work extends the calculations performed by G. Litak, T. Ord, K. Rage, and A. Vargunin, Physica C 483, 30 (2012), by including second nearest neighbors in an attractive two-orbital Hubbard model. We assumed that both the intra-orbital (U-i,U-j with i = 1, 2) and the inter-orbital Hubbard correlations (U-i,U- j with i not equal j) are negative; namely, U-i,U-j <= 0, for all(i, j). We calculated the T - n phase diagram in the mean-field approximation. For a finite chemical potential xi(0)(1) and a certain second nearest-neighbor parameter t(2) superconductivity develops in two dome-like regions, each of which has its own energy gap. Notoriously, for t(2)/vertical bar t1 vertical bar = 0.70 and xi 0(1)/vertical bar t1 vertical bar = 3 where t(1) is the nearest-neighbor parameter, T-c becomes zero around n = 2.5. (C) 2017 Elsevier B.V. All rights reserved.

We describe the interaction between small transition metal clusters and graphene using first principles calculations. The coupling is analyzed in terms of different features of the system: binding energy, decomposition into atomic orbitals, the presence of defects on the graphene layer, and both the band and geometrical structures. The binding strength is found to follow the d-band model, which anticipates the binding energies of clusters on graphene layers from the position of the cluster's d-band centers relative to the their highest-occupied and lowest-unoccupied molecular orbital levels. These findings are verified for 6-atom and 13-atom transition metal clusters (Ti, Pd, Pt, and Au) and considering different types of defects. The adhesion of the TM clusters is substantially larger on defective graphene layers than on pristine ones. Buckling of the graphene layer may arise from the presence of defects but it does not necessarily imply strong binding. However, buckling can sometimes offer configurational paths through which the adsorbed cluster is stabilized changing its original shape. Insights into this work offer mechanisms to tailor the electronic properties of the combined nanoparticle-graphene system by changing the size and composition of transition metal clusters.

The current work presents a parallel formulation using the MPI protocol for an adaptive high order finite difference scheme to solve 2D conservation laws. Adaptivity is achieved at each time iteration by the application of an interpolating wavelet transform in each space dimension. High order approximations for the numerical fluxes are computed by ENO and WENO schemes. Since time evolution is made by a TVD Runge-Kutta space splitting scheme, the problem is naturally suitable for parallelization. Numerical simulations and speedup results are presented for Euler equations in gas dynamics problems.

The current work presents a WENO wavelet adaptive method for solving multiphase flow problems. The grid adaptivity in each time step is obtained by the application of a thresholded interpolating wavelet transform, which allows the construction of a small yet effective sparse point representation of the solution. The spatial operator is solved by the Lax-Friedrich flux splitting approach in which the flux derivatives are approximated by the WENO scheme. Hyperbolic models of two-phase flow in conservative form are efficiently solved since shocks and rarefaction waves are precisely captured by the chosen methodology. Substantial computational gains are obtained through the grid reduction feature while maintaining the quality of the solutions.

We study the two-component Ginzburg–Landau (GL) theory, in the presence of a self-consistent vortex line, to obtain the penetration depth (λ) and the effective healing length (ξ), in the asymptotic limit r → ∞. All these parameters versus T/Tc are analyzed for the materials MgB 2, V 3 Si and LiFeAs in the interval 0.88 ≤ T/Tc ≤ 1.0, where the GL theory is assumed to be valid. We find that κ ≡ λ/ξ, which is another parameter not related to the GL parameter, is T-independent for V 3 Si and LiFeAs , while is T-dependent for the compound MgB 2. This result suggests that even though all these three materials display two-gap superconductivity overall, near Tc superconductivity in V 3 Si and LiFeAs seems to be different from the one in MgB 2. The use of this parameter, κ, as a new way to "study" the superconducting materials, under the presence of a single vortex, is valid for 0.88Tc≲ T ≤ Tc, namely, in the GL formalism.

An extrapolation procedure based on the vanishing moments property of the orthonormal wavelet family is associated to the à trous discrete wavelet transform with filters taken from the biorthogonal spline wavelets. This coupling avoids the construction of wavelets in the interval, enabling the confidence region increase of the transform when analyzing data. Simulations corroborate the efficiency of the proposed scheme.

We studied the possible superconducting state in an electronic itinerant ferromagnetic system characterized by a density of states that presents a moderately strong peak that is controlled by a specific parameter a and is positioned near the band edge. Specifically, we investigated the superconducting critical temperature, T c , and the zero-temperature superconducting gap, Δ0. The analysis is done in a self-consistent way, the BCS mean-field equation being solved together with the electron density equation to trace possible changes in the system’s chemical potential due to the strong correlations between the component electrons. We discussed the density dependence of the superconducting critical temperature and zero-temperature superconducting gap for various values of the control parameter a and of the electron–electron attractive interaction. In the zero temperature limit we derive the system’s phase diagram and discuss the possible fermionic and bosonic regimes of the diagram as function of the strength of the attractive interaction.

We consider a model for superconductivity in a two-band superconductor, having an anisotropic electronic structure made of two partially overlapping bands with a first hole-like and a second electron-like Fermi surface. In this pairing scenario, driven by the interplay between interband V i,j and intraband V i,i pairing terms, we have solved the two gap equations at the critical temperature T=T c and calculate T c and the chemical potential μ as a function of the number of carriers n for various values of pairing interactions, V 1,1, V 2,2, and V 1,2. The results show the complexity of the physics of condensates with multiple order parameters with the chemical potential near band edges.

AbstractTo study the evolution of binary star clusters, we have imaged seven systems in the Small Magellanic Cloud with the SOAR 4m telescope using B and V filters. The sample contains pairs with well-separated components (d < 30 pc) as well as systems that apparently have merged, as evidenced by their unusual structures. By employing isochrone fitting to their color–magnitude diagrams, we have determined reddening values, ages and metallicities, and by fitting King models to their radial stellar-density profiles we estimated core radii. Disturbances of the density profiles are interpreted as evidence of interactions. Properties such as the distances between their components and their age differences are addressed in terms of the timescales involved, to assess the physical connection of the system. In two cases, the age difference is more than 50 Myr, which suggests a chance alignment, capture or sequential star formation.

A minimal two-band model to describe superconducting Fe-pnictide materials is considered. It is assumed that the electronic structure of these materials may be modeled in terms of two tight-binding bands, whereas the pairing mechanism is driven by an attractive interaction with intra-band and inter-band pairing. In the framework of a mean-field BCS-type approach, the two-gap equations at the critical temperature T c are solved, and T c and the chemical potential μ, as functions of the number of carriers n varying the pairing interaction V and cut-off energy ω D , are inferred. Furthermore, using a self-consistent approach, the isotope exponent α, as a function of the number carriers by considering an s-wave pairing symmetry, is calculated. The relevance of the present approach for the description of the recent experimental results of Fe-pnictide materials is finally discussed.