Coexistence of chaotic and non-chaotic states in the two-dimensional Gauss–Navier–Stokes dynamics

Recently, Gallavotti proposed an Equivalence Conjecture in hydrodynamics, which states that forced-damped fluids can be equally well represented by means of the Navier–Stokes equations (NS) and by means of time reversible modifications of NS called Gauss–Navier–Stokes equations (GNS). This Equivalence Conjecture received numerical support in several recent papers concerning two-dimensional fluid mechanics. The corresponding results rely on the fact that the NS and GNS systems only have one attracting set. Performing similar two-dimensional simulations, we find that there are conditions to be met by the GNS system for this to be the case. In particular, increasing the Reynolds number, while keeping fixed the number of Fourier modes, leads to the coexistence of different attractors. This makes difficult a test of the Equivalence Conjecture, but constitutes a spurious effect due to the insufficient spectral resolution. With sufficiently fine spectral resolution, the steady states are unique and the Equivalence Conjecture can be conveniently established.     

A study of morphological and compositional evolution of nanoprecipitates in the Zr–Nb system and their transformational behavior

The metastable transformational behavior (both martensitic and omega) along with compositional and morphological evolution of bcc β precipitates, dispersed in the hcp α matrix of a Zr–1 wt% Nb alloy, were studied as a function of temperature and time. The evolution of the chemical composition of the β phase suggested preference towards metastable compositions having Nb content higher than the equilibrium value. Thermodynamic analysis showed that the metastable chemical compositions are the driving force for the nucleation of such β precipitates. The β to martensite transformation was observed to be possible only if β precipitate size exceeded a critical value of 160?nm. Micromechanical modeling was performed to estimate the critical size of β precipitate required to induce martensite transformation and the model predictions were in close agreement with the experimental observations. The omega transformation, on the other hand, showed less size dependence.     

Current–current correlation function in the presence of chemical potential and magnetic field

A (2+1)-dimensional electronic system is considered, in which the relation between the Green functions and the conductivity is used. A current–current correlation function, Π_μν(B), of the fermion system was obtained in the presence of nonquantized fermion magnetic field B, chemical potential η and gap m. Using this function one can obtain an expression for polarization operator calculated without the magnetic field. The result obtained can be applied for graphene.     

Application of a parallel genetic algorithm to the global optimization of medium-sized Au–Pd sub-nanometre clusters

To contribute to the discussion of the high activity and reactivity of Au–Pd system, we have adopted the BPGA-DFT approach to study the structural and energetic properties of medium-sized Au–Pd sub-nanometre clusters with 11–18 atoms. We have examined the structural behaviour and stability as a function of cluster size and composition. The study suggests 2D–3D crossover points for pure Au clusters at 14 and 16 atoms, whereas pure Pd clusters are all found to be 3D. For Au–Pd nanoalloys, the role of cluster size and the influence of doping were found to be extensive and non-monotonic in altering cluster structures. Various stability criteria (e.g. binding energies, second differences in energy, and mixing energies) are used to evaluate the energetics, structures, and tendency of segregation in sub-nanometre Au–Pd clusters. HOMO–LUMO gaps were calculated to give additional information on cluster stability and a systematic homotop search was used to evaluate the energies of the generated global minima of mono-substituted clusters and the preferred doping sites, as well as confirming the validity of the BPGA-DFT approach.     

Gauss–Newton reconstruction method for optical tomography using the finite element solution of the radiative transfer equation

The radiative transfer equation can be utilized in optical tomography in situations in which the more commonly applied diffusion approximation is not valid. In this paper, an image reconstruction method based on a frequency domain radiative transfer equation is developed. The approach is based on a total variation output regularized least squares method which is solved with a Gauss–Newton algorithm. The radiative transfer equation is numerically solved with a finite element method in which both the spatial and angular discretizations are implemented in piecewise linear bases. Furthermore, the streamline diffusion modification is utilized to improve the numerical stability. The approach is tested with simulations. Reconstructions from different cases including domains with low-scattering regions are shown. The results show that the radiative transfer equation can be utilized in optical tomography and it can produce good quality images even in the presence of low-scattering regions.     

Anomalous properties of the Kronig–Penney model with compositional and structural disorder

We study the localisation properties of the eigenstates in the Kronig–Penney model with weak compositional and structural disorder. The main result is an expression for the localisation length that is valid for any kind of self- and inter-correlations of the two types of disorder. We show that the interplay between compositional and structural disorder can result in anomalous localisation.     

Study of the Deflection Angle and Shadow of Black Hole Solutions in Non-Plasma and Plasma Mediums Under the Effect of Einstein–Gauss–Bonnet Gravity

In this paper, the Gibbons and Werner technique is used to calculate the weak deflection angle for the black hole solution under the effects of Einstein–Gauss–Bonnet gravity. The Gauss–Bonnet theorem in the limits of weak field is used to evaluate the Gaussian optical curvature in order to obtain the results. The visual effects of the deflection angle on the impact parameter is also looked at and the smallest radius in the non-plasma/plasma medium. Moreover, in order to check the consistency of the results concerning the weak deflection angle, the Keeton and Petters approach is applied to study the deflection angle, which is the expansion of series with a single mass variable, which can be directly addressed by using the post–post Newtonian framework. Furthermore, the deflection angle and shadow under the influence of the plasma is examined by using the motion of particle in a non-magnetized plasma and pressure-free plasma medium as described by the new ray-tracing algorithm. It is shown that plasma as well as Einstein–Gauss-Bonnet gravity corrections are affected by shadows.     

On the computation of ground state and dynamics of Schrödinger–Poisson–Slater system

In this paper, we deal with the computation of ground state and dynamics of the Schrödinger–Poisson–Slater (SPS) system. To this end, backward Euler and time-splitting pseudospectral methods are proposed for the nonlinear Schrödinger equation with the nonlocal Hartree potential approximated by solving a Poisson equation. The approximation approaches for the Hartree potential include fast convolution algorithms, which are accelerated by using FFT in 1D and fast multipole method (FMM) in 2D and 3D, and sine/Fourier pseudospectral methods. The inconsistency in 0-mode in Fourier pseudospectral approach is pointed out, which results in a significant loss of high-order of accuracy as expected for spectral methods. Numerical comparisons show that in 1D the fast convolution and sine pseudospectral approaches are compatible. While, in 3D the fast convolution approach based on FMM is second-order accurate and the Fourier pseudospectral approach is better than it from both efficiency and accuracy point of view. Among all these approaches, the sine pseudospectral one is the best candidate in the numerics of the SPS system. Finally, we apply the backward Euler and time-splitting sine pseudospectral methods to study the ground state and dynamics of 3D SPS system in different setups.     

Einstein–Gauss–Bonnet black holes in de Sitter spacetime and the quasilocal formalism

We propose to compute the action and global charges of the asymptotically de Sitter solutions in Einstein–Gauss–Bonnet theory by using the counterterm method in conjunction with the quasilocal formalism. The general expression of the counterterms and the boundary stress tensor is presented for spacetimes of dimension d?7$d?7$. We apply this technique for several different solutions in Einstein–Gauss–Bonnet theory with a positive cosmological constant. Apart from known solutions, we consider also d=5$d=5$ vacuum rotating black holes with equal magnitude angular momenta. These solutions are constructed numerically within a nonperturbative approach, by directly solving the Einstein–Gauss–Bonnet equations with suitable boundary conditions.     

Effects of electron correlation on superconductivity in the Hatsugai–Kohmoto model

Understanding how electrons form pairs in the presence of strong electron correlations demands going beyond the BCS paradigm. We study a correlated superconducting model where the correlation effects are accounted for by a U term local in momentum space. The electron correlation is treated exactly while the electron pairing is treated approximately using the mean-field theory. The self-consistent equation for the pair potential is derived and solved. Somewhat contrary to expectation, a weak attractive U comparable to the pair potential can destroy the superconductivity, whereas for weak to intermediate repulsive U, the pair potential can be enhanced. The fidelity of the mean-field ground state is calculated to describe the strength of the elelectron correlation. We show that the pair potential is not equal to the single-electron superconducting gap for the strongly correlated superconductors, in contrast to the uncorrelated BCS limit.     

A theory of the inverse magnetoelectric effect in layered magnetostrictive–piezoelectric structures

A theory of the inverse magnetoelectric effect in layered structures has been presented. The theory is based on solving the equations of elastodynamics and electrostatics separately for the magnetostrictive and piezoelectric phases, taking into account the conditions at the interface between the phases. Expressions for the coefficient of inverse magnetoelectric conversion through the parameters characterizing the magnetostrictive and piezoelectric phases have been obtained. Theoretical dependences of the inverse magnetoelectric conversion coefficient on the frequency of the alternating-current electric field for the three-layer PZT–Ni–PZT structure and the two-layer terfenol-D–PZT structure have been calculated. The results of the calculations are in good agreement with the experimental data.     

Surface texture and density–density correlation in films of adamantane-containing polyimides and copolyimides

By means of electron microscopy, the spatial correlation of gold nanoparticles are studied, obtained by thermal vacuum sputtering of metal on a bromine-activated surface of films of adamantane-containing polyimides and copolyimides based on pyromellitic anhydride (PMDA), 4,4'-oxydianiline (ODA), and 1-aminoethyl-3-(4'-aminophenyl)adamantane (AEAPhA) or 3,4,3',4'-tetracarboxydiphenyloxide dianhydride (ODPA), ODA, and AEAPhA with varying ratio of ODA and AEAPhA fragments. It is shown that with increasing ratio of mole fractions [AEAPhA]/[ODA], the texture of the film surface, free volume, the correlation length, and the frequency of alternation of the particle distribution density change. The shortrange order decreases, while the long-range order increases in ensembles of particles. The supramolecular structure of the polymer is transformed similarly because of structural transitions in the amorphous state of ODPA–ODA–AEAPhA and the mesomorphic state of PMDA–ODA–AEAPhA.

     

Flat coordinates of topological conformal field theory and solutions of the Gauss–Manin system

A luminescent trace has been observed in a ruby crystal (Al₂O₃: Cr³⁺) that rotates at a frequency of 2 to 200 Hz and is irradiated by 532-nm coherent electromagnetic radiation. A method has been proposed to determine the lifetime of the excited electronic state of chromium ions from the measurement of the length of an arc of the trajectory of a light spot on the surface of a rotating ruby single crystal. A “comet trace” formed at the passage of radiation through the rotating crystal near the absorption band of the material has been detected inside the ruby crystal. It has been shown that the theory based on the analysis of the motion of polaritons in the rotating reference frame is in satisfactory agreement with experimental results.     

Acceleration of the Smith–Waterman algorithm using single and multiple graphics processors

Finding regions of similarity between two very long data streams is a computationally intensive problem referred to as sequence alignment. Alignment algorithms must allow for imperfect sequence matching with different starting locations and some gaps and errors between the two data sequences. Perhaps the most well known application of sequence matching is the testing of DNA or protein sequences against genome databases. The Smith–Waterman algorithm is a method for precisely characterizing how well two sequences can be aligned and for determining the optimal alignment of those two sequences. Like many applications in computational science, the Smith–Waterman algorithm is constrained by the memory access speed and can be accelerated significantly by using graphics processors (GPUs) as the compute engine. In this work we show that effective use of the GPU requires a novel reformulation of the Smith–Waterman algorithm. The performance of this new version of the algorithm is demonstrated using the SSCA#1 (Bioinformatics) benchmark running on one GPU and on up to four GPUs executing in parallel. The results indicate that for large problems a single GPU is up to 45 times faster than a CPU for this application, and the parallel implementation shows linear speed up on up to 4 GPUs.     

The geometry of the higher dimensional black hole thermodynamics in Einstein–Gauss–Bonnet theory

In this paper, we have studied the geometry of the five-dimensional black hole solutions in (a) Einstein–Yang–Mills–Gauss–Bonnet theory and (b) Einstein–Maxwell–Gauss–Bonnet theory with a cosmological constant for spherically symmetric space time. Formulating the Ruppeiner metric, we have examined the possible phase transition for both the metrics. It is found that depending on some restrictions phase transition is possible for the black holes. Also for Λ = 0 in Einstein–Gauss–Bonnet black hole, the Ruppeiner metric becomes flat and hence the black hole becomes a stable one.     

Changes in the state of polarization of apertured stochastic electromagnetic modified Bessel–Gauss beams in free-space propagation

By using the generalized Huygens–Fresnel diffraction integral, the analytical expressions for the cross-spectral density matrix, spectral degree of polarization, orientation angle and degree of ellipticity of polarization ellipse of apertured stochastic electromagnetic modified Bessel–Gauss beams (MBGBs) through a paraxial optical ABCD system are derived, and used to study the changes in the state of polarization of apertured stochastic electromagnetic MBGBs propagating in free space. The invariance of the on-axis state of polarization of unapertured stochastic electromagnetic MBGBs propagating through paraxial optical ABCD systems is illustrated analytically and numerically. For apertured stochastic electromagnetic MBGBs, the on-axis spectral degree of polarization, orientation angle and degree of ellipticity of polarization ellipse increase with increasing propagation distance, and approach asymptotic values when the propagation distance is large enough. There is a uniform distribution region of the state of polarization around the center of the beams whose range decreases with increasing truncation parameter. In addition, the state of polarization of apertured stochastic electromagnetic MBGBs upon propagation can be modulated by controlling the truncation parameter.     

Some solutions of the Gauss–Bonnet gravity with scalar field in four dimensions

We give all exact solutions of the Einstein–Gauss–Bonnet Field Equations coupled with a scalar field in four dimensions under certain assumptions. The main assumption we make in this work is to take the second covariant derivative of the coupling function proportional to the spacetime metric tensor. Although this assumption simplifies the field equations considerably, to obtain exact solutions we assume also that the spacetime metric is conformally flat. Then we obtain a class of exact solutions.     

Average intensity and spreading of super Lorentz–Gauss modes in turbulent atmosphere

The super Lorentz–Gaussian (SLG) modes has been introduced to describe the radiation emitted by the multi-mode diode lasers. Here the propagation properties of SLG modes in turbulent atmosphere are investigated. Based on the extended Huygens–Fresnel integral and the Hermite–Gaussian expansion of a Lorentzian function, analytical formulae for the average intensities and the effective beam sizes of SLG₀₁ and SLG₁₁ modes are derived in turbulent atmosphere. The average intensity distribution and the spreading properties of SLG₀₁ and SLG₁₁ modes in turbulent atmosphere are numerically demonstrated. The influences of the beam parameters and the structure constant of the atmospheric turbulence on the propagation of SLG₀₁ and SLG₁₁ modes in turbulent atmosphere are also discussed in detail.