Anisotropic power-law inflation of the five dimensional scalar–vector and scalar-Kalb–Ramond model

We will study the cosmological implications of the five dimensional scalar–vector and scalar-Kalb–Ramond model. In particular, a new set of Bianchi type I power-law analytic solution will be obtained for this model. The cosmic no-hair conjecture can be shown to break down in the presence of the scalar–vector and scalar-Kalb–Ramond couplings. The effect of the Kalb–Ramond field in the presence of the power-law solution will be shown explicitly. We will also show that the presence of a phantom field does, however, destabilize the corresponding Bianchi type I power-law inflationary solutions.     

Analytical and numerical solutions to the Davey–Stewartson equation with power-law nonlinearity

This paper studies the Davey–Stewartson equation. The traveling wave solution of this equation is obtained for the case of power-law nonlinearity. Subsequently, this equation is solved by the exponential function method. The mapping method is then used to retrieve more solutions to the equation. Finally, the equation is studied with the aid of the variational iteration method. The numerical simulations are also given to complete the analysis.     

Geometrical thermodynamics and P–V criticality of the black holes with power-law Maxwell field

We study the thermodynamical structure of Einstein black holes in the presence of power Maxwell invariant nonlinear electrodynamics for two different cases. The behavior of temperature and conditions regarding the stability of these black holes are investigated. Since the language of geometry is an effective method in general relativity, we concentrate on the geometrical thermodynamics to build a phase space for studying thermodynamical properties of these black holes. In addition, taking into account the denominator of the heat capacity, we use the proportionality between cosmological constant and thermodynamical pressure to extract the critical values for these black holes. Besides, the effects of the variation of different parameters on the thermodynamical structure of these black holes are investigated. Furthermore, some thermodynamical properties such as the volume expansion coefficient, speed of sound, and isothermal compressibility coefficient are calculated and some remarks regarding these quantities are given.     

Local probes strongly favor ΛCDM against power-law and R_h=ct universe

We constrain three cosmological models – the concordance cold dark matter plus cosmological constant(ΛCDM) model, the power-law(PL) model, and the Rh =ct model – using the available local probes, which include the JLA compilation of type-Ia supernovae(SNe Ia), the direct measurement of the Hubble constant(H_(z)), and the baryon acoustic oscillations(BAO). For the ΛCDM model, we consider two different cases, i.e. zero and non-zero spatial curvature. We find that by using the JLA alone, the ΛCDM and PL models are indistinguishable, but the Rh =ct model is strongly disfavored. If we combine JLA+H_(z), the ΛCDM model is strongly favored over the other two models. The combination of all three datasets supports ΛCDM as the best model. We also use the low-redshift(z 0.2) data to constrain the deceleration parameter using the cosmography method, and find that only the ΛCDM model is consistent with cosmography. However, there is no strong evidence to distinguish between flat and non-flatΛCDM models by using the local data alone.     

Modulational instability and localized breather in discrete Schrödinger equation with helicoidal hopping and a power-law nonlinearity

We investigate the discrete nonlinear Schrödinger model with helicoidal hopping and a power-law nonlinearity, motivated by the tunable nonlinearity in the model of DNA chain and ultra-cold atoms trapped in a helix-shaped optical trap. In the study of modulational instability, we find a successive destabilization along with increasing nonlinear-power. In particular, the critical amplitudes of second-stage instability decrease as nonlinear-power increases. Furthermore, it is shown that information on the stability properties of weakly localized solutions can be inferred from the plane-wave modulational instability results. This link enable us to analytically estimate the critical parameters at which the breather solutions turn unstable, and find these parameters are dramatically influenced by the nonlinear-power. The stability properties of localized breathers perform an obvious change when the nonlinear power crosses a critical value ${\gamma }_{cr}$. It is reflected that at weak nonlinearity the breathers exhibit monostability, while exceeding ${\gamma }_{cr}$ the bistability and instability will set in. The interplay between nonlinear-power and long-range hopping on the stability properties of breathers is also discussed in detail.     

Schrödinger vs. dirac bound state spectra of Q\bar Q-systems and a plausible lorentz structure of the effective power-law potential-systems and a plausible lorentz structure of the effective power-law potential

It is shown that a non-relativistic power-law potential model for the heavy quarks in the form V(r)=Ar ^v+V ₀, (A, ν>0) acquires relativistic consistency in generating Dirac bound states of \(Q\bar Q\) -system in agreement with the Schrödinger spectroscopy if the interaction is modelled by equally mixed scalar and vector parts as suggested by the phenomenology of fine-hyperfine splittings of heavy quarkonium systems in a non-relativistic perturbative approach.     

Structure and Magnetoresistance of Co–Gd and Al–Co–Gd Alloy Films

Technical Physics - Structural data and dependences of the film resistance on magnetic field strength R(H) are presented for Co–Gd and Al–Co–Gd alloy films obtained by vacuum...     

Interdiffusion and solid solution strengthening in Ni–Co–Pt and Ni–Co–Fe ternary systems

Diffusion couple experiments are conducted in Co–Ni–Pt system at 1200?°C and in Co–Ni–Fe system at 1150?°C, by coupling binary alloys with the third element. Uphill diffusion is observed for both Co and Ni in Pt rich corner of the Co–Ni–Pt system, whereas in the Co–Ni–Fe system, it is observed for Co. Main and cross interdiffusion coefficients are calculated at the composition of intersection of two independent diffusion profiles. In both the systems, the main interdiffusion coefficients are positive over the whole composition range and the cross interdiffusion coefficients show both positive and negative values at different regions. Hardness measured by performing the nanoindentations on diffusion couples of both the systems shows the higher values at intermediate compositions.     

Microstructure investigations and magnetic after-effect in amorphous and nanocrystalline Fe–Zr–Ti–B–Cu alloy

The microstructure evolution and low field magnetic properties i.e. initial magnetic susceptibility, stabilization field and magnetic after-effect as disaccommodation of the amorphous and nanocrystalline Fe₈₀Zr₄Ti₃B₁₂Cu₁ alloy were investigated. The heat treatment of the as-quenched Fe₈₀Zr₄Ti₃B₁₂Cu₁ alloy at 773 K for 1 h leads to its nanocrystallization. It was stated that initial magnetic susceptibility increases and intensity of disaccommodation decreases with increasing of annealing temperature. The magnetic after-effect of the investigated nanocrystalline samples is connected with relaxation processes that occur in the amorphous matrix.     

Chern–Simons,Wess–Zumino and other cocycles from Kashiwara–Vergne and associators

Descent equations play an important role in the theory of characteristic classes and find applications in theoretical physics, e.g., in the Chern–Simons field theory and in the theory of anomalies. The second Chern class (the first Pontrjagin class) is defined as \(p= \langle F, F\rangle \) where F is the curvature 2-form and \(\langle \cdot , \cdot \rangle \) is an invariant scalar product on the corresponding Lie algebra \(\mathfrak g\). The descent for p gives rise to an element \(\omega =\omega _3+\omega _2+\omega _1+\omega _0\) of mixed degree. The 3-form part \(\omega _3\) is the Chern–Simons form. The 2-form part \(\omega _2\) is known as the Wess–Zumino action in physics. The 1-form component \(\omega _1\) is related to the canonical central extension of the loop group LG. In this paper, we give a new interpretation of the low degree components \(\omega _1\) and \(\omega _0\). Our main tool is the universal differential calculus on free Lie algebras due to Kontsevich. We establish a correspondence between solutions of the first Kashiwara–Vergne equation in Lie theory and universal solutions of the descent equation for the second Chern class p. In more detail, we define a 1-cocycle C which maps automorphisms of the free Lie algebra to one forms. A solution of the Kashiwara–Vergne equation F is mapped to \(\omega _1=C(F)\). Furthermore, the component \(\omega _0\) is related to the associator \(\Phi \) corresponding to F. It is surprising that while F and \(\Phi \) satisfy the highly nonlinear twist and pentagon equations, the elements \(\omega _1\) and \(\omega _0\) solve the linear descent equation.     

Nonlinear dynamical symmetries of Smorodinsky–Winternitz and and Fokas–Lagerstorm systems

General solutions of the Smorodinsky–Winternitz system and the Fokas–Lagerstorm system, which are superintegrable in two-dimensional Euclidean space, are obtained using the algebraic method (structure function). Their dynamical symmetries, which are governed by deformed angular momentum algebras, are revealed.     

Grothendieck–Teichmüller and Batalin–Vilkovisky

It is proven that, for any affine supermanifold M equipped with a constant odd symplectic structure, there is a universal action (up to homotopy) of the Grothendieck–Teichmüller Lie algebra ${\mathfrak{grt}_1}$ on the set of quantum BV structures (i.e. solutions of the quantum master equation) on M.     

Surface tension and density of liquid Bi–Pb,Bi–Sn and Bi–Pb–Sn eutectic alloys

Surface tension and density measurement of liquid Bi₅₆Pb₄₄, Bi₄₃Sn₅₇ and Bi₄₆Pb₂₉Sn₂₅ eutectic alloys was carried out by using the large drop method over the temperature range of 380–750 K. The regular solution model has been used in conjunction with Butler's equation to calculate the surface tension of binary and ternary alloys of the Bi–Pb–Sn system, while the surface tension of ternary alloys has also been predicted by using geometric models. The new experimental results were compared with the calculated values of the surface tension as well as with the data available in the literature.     

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.     

Superconductivity of Y–Ba–Cu–O and substituted systems

Superconductivity of Y-Ba-Cu-O system is studied in the composition 2:2:3 and 1:2:3 of Y:Ba:Cu. The effect of replacement of Y or Ba by divalent Sr and Ca, trivalent Ce and tetravalent Zr is studied. X-ray diffraction, SEM and TEM techniques are used for materials characterization. Superconducting transition temperatures are measured resistively. Rapid resistance drop observed above 230 K in Y-Ba-Sr-Cu-O and Y-Ba-Ca-Cu-O systems indicate the possible existence of superconductivity above 230 K. Substitution of Ce in place of Y is found to reduce the onset Tc from 95 K to 80 K. For the first time, replacement of Cu by Zr in Y-Ba-Cu-O has yielded the onset Tc of about 105 K.     

Fermi–Pasta–Ulam recurrence and modulation instability

We give a qualitative conceptual explanation of the Fermi–Pasta–Ulam (FPU) like recurrence in the onedimensional focusing nonlinear Schrodinger equation (NLSE). The recurrence can be considered as a result of the nonlinear development of the modulation instability. All known exact localized solitary wave solutions describing propagation on the background of the modulationally unstable condensate show the recurrence to the condensate state after its interaction with solitons. The condensate state locally recovers its original form with the same amplitude but a different phase after soliton leave its initial region. Based on the integrability of the NLSE, we demonstrate that the FPU recurrence takes place not only for condensate, but also for a more general solution in the form of the cnoidal wave. This solution is periodic in space and can be represented as a solitonic lattice. That lattice reduces to isolated soliton solution in the limit of large distance between solitons. The lattice transforms into the condensate in the opposite limit of dense soliton packing. The cnoidal wave is also modulationally unstable due to soliton overlapping. The recurrence happens at the nonlinear stage of the modulation instability. Due to generic nature of the underlying mathematical model, the proposed concept can be applied across disciplines and nonlinear systems, ranging from optical communications to hydrodynamics.