Solid–state diffusion–controlled growth of the phases in the Au–Sn system

The solid state diffusion-controlled growth of the phases is studied for the Au–Sn system in the range of room temperature to 200 °C using bulk and electroplated diffusion couples. The number of product phases in the interdiffusion zone decreases with the decrease in annealing temperature. These phases grow with significantly high rates even at the room temperature. The growth rate of the AuSn₄ phase is observed to be higher in the case of electroplated diffusion couple because of the relatively small grains and hence high contribution of the grain boundary diffusion when compared to the bulk diffusion couple. The diffraction pattern analysis indicates the same equilibrium crystal structure of the phases in these two types of diffusion couples. The analysis in the AuSn₄ phase relating the estimated tracer diffusion coefficients with grain size, crystal structure, the homologous temperature of experiments and the concept of the sublattice diffusion mechanism in the intermetallic compounds indicate that Au diffuses mainly via the grain boundaries, whereas Sn diffuses via both the grain boundaries and the lattice.     

Extension of the Arrowsmith–Essam Formula to the Domany–Kinzel Model

Arrowsmith and Essam gave an expansion formula for point-to-point connectedness functions of the mixed site-bond percolation model on oriented lattices, in which each term is characterized by a graph. We extend this formula to general k-point correlation functions, which are point-to-set (with k points) connectivities in the context of percolation, of the two-neighbor discrete-time Markov process (stochastic cellular automata with two parameters) in one dimension called the Domany–Kinzel model, which includes the mixed site-bond oriented percolation model on a square lattice as a special case. Our proof of the formula is elementary and based on induction with respect to time-step, which is different from the original graph-theoretical one given by Arrowsmith and Essam. We introduce a system of m interacting random walkers called m friendly walkers (m FW) with two parameters. Following the argument of Cardy and Colaiori, it is shown that our formula is useful to derive a theorem that the correlation functions of the Domany–Kinzel model are obtained as an m0 limit of the generating functions of the m FW.     

On the Coupling Time of the Heat-Bath Process for the Fortuin–Kasteleyn Random–Cluster Model

We consider the coupling from the past implementation of the random–cluster heat-bath process, and study its random running time, or coupling time. We focus on hypercubic lattices embedded on tori, in dimensions one to three, with cluster fugacity at least one. We make a number of conjectures regarding the asymptotic behaviour of the coupling time, motivated by rigorous results in one dimension and Monte Carlo simulations in dimensions two and three. Amongst our findings, we observe that, for generic parameter values, the distribution of the appropriately standardized coupling time converges to a Gumbel distribution, and that the standard deviation of the coupling time is asymptotic to an explicit universal constant multiple of the relaxation time. Perhaps surprisingly, we observe these results to hold both off criticality, where the coupling time closely mimics the coupon collector’s problem, and also at the critical point, provided the cluster fugacity is below the value at which the transition becomes discontinuous. Finally, we consider analogous questions for the single-spin Ising heat-bath process.     

Fredholm–Lagrangian–Grassmannian and the Maslov index

This is a review article on the topology of the space, so called, Fredholm–Lagrangian–Grassmannian and the quantity “Maslov index” for paths in this space based on the standard theory of functional analysis. Our standing point is to define the Maslov index for arbitrary paths in terms of the fundamental spectral property of the Fredholm operators as an intersection number with the “Maslov cycle”. This argument was first recognized by J. Phillips and was used to define the “Spectral flow” not only for loops but also for arbitrary paths of selfadjoint Fredholm operators. We make the arguments as elementary as possible.     

Peakon–antipeakon interaction in the Dullin–Gottwald–Holm equation

In this Letter, we obtain a two-peakon solution to a special Dullin–Gottwald–Holm equation explicitly by direct computation, and then discuss the peakon–antipeakon interaction in this equation. Our results show that, like the Camassa–Holm equation, during the soliton absorption time, the peakon–antipeakon in this equation is essentially a single-peaked, double-cornered wave. However, the two corners may travel in opposite direction for some ω, which is different from that in the Camassa–Holm equation.     

Nonlinear properties of multiphase high-temperature superconductors of the Bi–Sr–Ca–Cu–O system in the temperature range of the superconducting transition

The nonlinear characteristics of high-temperature superconductors of the Bi–Sr–Ca–Cu–O system have been experimentally investigated in the temperature range of the superconducting transition under the influence of a harmonic alternating magnetic field. The effect of the generation of odd harmonics in the signal of response to a harmonic alternating magnetic field for multiphase high-temperature superconductors containing regions with different values of the critical temperature in their bulk has been observed for the first time. The mechanism of harmonic generation in a superconductor in the resistive state, which is associated with the switch effect, i.e., with the redistribution of eddy current density between the local regions of the superconductor, has been considered.     

Charge and/or spin limits for black holes at a non-commutative scale

We study the cosmological dynamics for R ^p exp(λ R) gravity theory in the metric formalism, using dynamical systems approach. Considering higher-dimensional FRW geometries in case of an imperfect fluid which has two different scale factors in the normal and extra dimensions, we find the exact solutions, and study its behaviour and stability for both vacuum and matter cases. It is found that stable solutions corresponding to accelerated expansion at late times exist, which can describe the inflationary era of the Universe. We also study the evolution of scale factors both in the normal and extra dimensions for different values of anisotropy parameter and the number of extra dimensions for such a scenario.     

Dynamics of anisotropic power-law <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) cosmology

Modified theories of gravity have attracted much attention of the researchers in the recent years. In particular, the f(R) theory has been investigated extensively due to important f(R) gravity models in cosmological contexts. This paper is devoted to exploring an anisotropic universe in metric f(R) gravity. A locally rotationally symmetric Bianchi type I cosmological model is considered for this purpose. Exact solutions of modified field equations are obtained for a well-known f(R) gravity model. The energy conditions are also discussed for the model under consideration. The viability of the model is investigated via graphical analysis using the present-day values of cosmological parameters. The model satisfies null energy, weak energy, and dominant energy conditions for a particular range of the anisotropy parameter while the strong energy condition is violated, which shows that the anisotropic universe in f(R) gravity supports the crucial issue of accelerated expansion of the universe.     

Noether symmetry of <Emphasis Type="Italic">F</Emphasis>(<Emphasis Type="Italic">T</Emphasis>) cosmology with quintessence and phantom scalar fields

In this paper, we investigate the Noether symmetries of F(T) cosmology involving matter and dark energy. In this model, the dark energy is represented by a canonical scalar field with a potential. Two special cases for dark energy are considered, including phantom energy and quintessence. We obtain F(T)～T ^3/4, and the scalar potential V(?)～? ² for both models of dark energy and discuss quantum picture of this model. Some astrophysical implications are also discussed.     

A fragment-based approach towards <Emphasis Type="Italic">ab-initio</Emphasis> treatment of polymeric materials

The present study deals with hypersurface-homogeneous cosmological models with anisotropic dark energy in Saez–Ballester theory of gravitation. Exact solutions of field equations are obtained by applying a special law of variation of Hubble’s parameter that yields a constant negative value of the deceleration parameter. Three physically viable cosmological models of the Universe are presented for the values of parameter K occurring in the metric of the space–time. The model for K = 0 corresponds to an accelerating Universe with isotropic dark energy. The other two models for K = 1 and ?1 represent accelerating Universe with anisotropic dark energy, which isotropize for large time. The physical and geometric behaviours of the models are also discussed.     

The zero active mass condition in Friedmann–Robertson–Walker cosmologies

Many cosmological measurements today suggest that the Universe is expanding at a constant rate. This is inferred from the observed age versus redshift relationship and various distance indicators, all of which point to a cosmic equation of state (EoS) p = -ρ/3, where ρ and p are, respectively, the total energy density and pressure of the cosmic fluid. It has recently been shown that this result is not a coincidence and simply confirms the fact that the symmetries in the Friedmann–Robertson–Walker (FRW) metric appear to be viable only for a medium with zero active mass, i.e., ρ + 3p = 0. In their latest paper, however, Kim, Lasenby and Hobson (2016) have provided what they believe to be a counter argument to this conclusion. Here, we show that these authors are merely repeating the conventional mistake of incorrectly placing the observer simultaneously in a comoving frame, where the lapse function gtt is coordinate dependent when ρ + 3p ≠ 0, and a supposedly different, freefalling frame, in which g_tt = 1, implying no time dilation. We demonstrate that the Hubble flow is not inertial when ρ + 3p ≠ 0, so the comoving frame is generally not in free fall, even though in FRW, the comoving and free-falling frames are supposed to be identical at every spacetime point. So this confusion of frames not only constitutes an inconsistency with the fundamental tenets of general relativity but, additionally, there is no possibility of using a gauge transformation to select a set of coordinates for which g_tt = 1 when ρ + 3p ≠ 0.     

Cosmic acceleration in non-flat <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">T</Emphasis>) cosmology

We study f(T) cosmological models inserting a non-vanishing spatial curvature and discuss its consequences on cosmological dynamics. To figure this out, a polynomial f(T) model and a double torsion model are considered. We first analyze those models with cosmic data, employing the recent surveys of Union 2.1, baryonic acoustic oscillation and cosmic microwave background measurements. We then emphasize that the two popular f(T) models enable the crossing of the phantom divide line due to dark torsion. Afterwards, we compute numerical bounds up to 3-\(\sigma \) confidence level, emphasizing the fact that \(\Omega _{k0}\) turns out to be non-compatible with zero at least at 1\(\sigma \). Moreover, we underline that, even increasing the accuracy, one cannot remove the degeneracy between our models and the \(\Lambda \)CDM paradigm. So that, we show that our treatments contain the concordance paradigm and we analyze the equation of state behaviors at different redshift domains. We also take into account gamma ray bursts and we describe the evolution of both the f(T) models with high redshift data. We calibrate the gamma ray burst measurements through small redshift surveys of data and we thus compare the main differences between non-flat and flat f(T) cosmology at different redshift ranges. We finally match the corresponding outcomes with small redshift bounds provided by cosmography. To do so, we analyze the deceleration parameters and their variations, proportional to the jerk term. Even though the two models well fit late-time data, we notice that the polynomial f(T) approach provides an effective de-Sitter phase, whereas the second f(T) framework shows analogous results compared with the \(\Lambda \)CDM predictions.     

Global transformations preserving Sturm–Liouville spectral data

We show the existence of a real analytic isomorphism between the space of the impedance function ρ of the Sturm–Liouville problem ?ρ ^?2(ρ ² f′)′ +uf on (0, 1), where u is a function of ρ, ρ′, ρ″, and that of potential p of the Schrödinger equation ?y″ +py on (0, 1), keeping their boundary conditions and spectral data. This mapping is associated with the classical Liouville transformation f → ρf, and yields a global isomorphism between solutions of inverse problems for the Sturm–Liouville equations of the impedance form and those of the Schrödinger equations.     

A modification of Einstein–Schrödinger theory that contains both general relativity and electrodynamics

We modify the Einstein–Schrödinger theory to include a cosmological constant Λ _z which multiplies the symmetric metric, and we show how the theory can be easily coupled to additional fields. The cosmological constant Λ _z is assumed to be nearly cancelled by Schrödinger’s cosmological constant Λ _b which multiplies the nonsymmetric fundamental tensor, such that the total Λ =  Λ _z +  Λ _b matches measurement. The resulting theory becomes exactly Einstein–Maxwell theory in the limit as |Λ _z | → ∞. For |Λ _z | ~ 1/(Planck length)² the field equations match the ordinary Einstein and Maxwell equations except for extra terms which are < 10^?16 of the usual terms for worst-case field strengths and rates-of-change accessible to measurement. Additional fields can be included in the Lagrangian, and these fields may couple to the symmetric metric and the electromagnetic vector potential, just as in Einstein–Maxwell theory. The ordinary Lorentz force equation is obtained by taking the divergence of the Einstein equations when sources are included. The Einstein–Infeld–Hoffmann (EIH) equations of motion match the equations of motion for Einstein–Maxwell theory to Newtonian/Coulombian order, which proves the existence of a Lorentz force without requiring sources. This fixes a problem of the original Einstein–Schrödinger theory, which failed to predict a Lorentz force. An exact charged solution matches the Reissner–Nordström solution except for additional terms which are ~10^?66 of the usual terms for worst-case radii accessible to measurement. An exact electromagnetic plane-wave solution is identical to its counterpart in Einstein–Maxwell theory.     

A parametric reconstruction of the deceleration parameter

The present work is based on a parametric reconstruction of the deceleration parameter q(z) in a model for the spatially flat FRW universe filled with dark energy and non-relativistic matter. In cosmology, the parametric reconstruction technique deals with an attempt to build up a model by choosing some specific evolution scenario for a cosmological parameter and then estimate the values of the parameters with the help of different observational datasets. In this paper, we have proposed a logarithmic parametrization of q(z) to probe the evolution history of the universe. Using the type Ia supernova, baryon acoustic oscillation and the cosmic microwave background datasets, the constraints on the arbitrary model parameters \(q_{0}\) and \(q_{1}\) are obtained (within \(1\sigma \) and \(2\sigma \) confidence limits) by \(\chi ^{2}\)-minimization technique. We have then reconstructed the deceleration parameter, the total EoS parameter \(\omega _\mathrm{tot}\), the jerk parameter and have compared the reconstructed results of q(z) with other well-known parametrizations of q(z). We have also shown that two model selection criteria (namely, the Akaike information criterion and Bayesian information criterion) provide a clear indication that our reconstructed model is well consistent with other popular models.