ICEMS study of isothermal oxidation of Fe–Mn–Al–C–Cr–Si–Mo, Fe–Mn–Al–C–Cr–Si and Fe–9Cr–1Mo alloys

The purpose of this paper is to investigate the isothermal behavior of Fe–27.3Mn–7.6Al–C–6.5Cr–0.25Si–0.88Mo (Mo(0)) and Fe–27.3Mn–7.6Al–1.0C–6.5Cr–0.25Si (Mo(1)) alloys and compare it against Fe–9Cr–1Mo (FCR) commercial alloy. The experiments were carried out at 600°C, 700°C, 750°C and 850°C, each one during 72 h in static air. The oxidation kinetics was measured as a function of time using a Thermogravimetry analyzer (TGA). The structure and composition of the oxide scale were characterized by X-ray diffraction (XRD) and Integral Conversion Electron Mössbauer Spectroscopy (CEMS). The TGA results show that at all oxidation temperatures the sample FCR exhibit the lowest kinetic corrosion and the lowest weight gain, whereas Mo(0) the highest. By CEMS technique it were found a broad magnetic sextet, which has been fit by one hyperfine field distribution with mean hyperfine field characteristic to ferritic/martensite phase, one Fe^3?+? doublet and one singlet for the Mo(0) and Mo(1) alloys. Samples oxidized at highest temperatures exhibit a strong paramagnetic line, probably due that the Cr or Mn oxides may be enriched on the surface. Then, the magnetic phase can be converted partially into austenite phase at highest temperatures.     

Electro-optic metal–insulator–semiconductor–insulator–metal Mach-Zehnder plasmonic modulator

The performance of a CMOS-compatible electro-optic Mach-Zehnder plasmonic modulator is investigated using electromagnetic and carrier transport simulations. Each arm of the Mach-Zehnder device comprises a metal–insulator–semiconductor–insulator–metal (MISIM) structure on a buried oxide substrate. Quantum mechanical effects at the oxide/semiconductor interfaces were considered in the calculation of electron density profiles across the structure, in order to determine the refractive index distribution and its dependence on applied bias. This information was used in finite element simulations of the electromagnetic modes within the MISIM structure in order to determine the Mach-Zehnder arm lengths required to achieve destructive interference and the corresponding propagation loss incurred by the device. Both inversion and accumulation mode devices were investigated, and the layer thicknesses and height were adjusted to optimise the device performance. A device loss of <8 dB is predicted for a MISIM structure with a 25 nm thick silicon layer, for which the device length is <3 μm, and <5 dB loss is predicted for the limiting case of a 5 nm thick silicon layer in a 1.2 μm long device: in both cases, the maximum operating voltage is 7.5 V.     

Characterization of bismuth–tin–lead and bismuth–tin–lead–cadmium fusible alloys

Microstructure, electrical, mechanical and thermal properties of quenched bismuth–tin eutectic, Rose (Bi₅₀Sn_22.9Pb_27.1) and Wood’s (Bi₅₀Sn_12.5Pb₂₅Cd_12.5) alloys have been investigated using scanning electron microscopy, X-ray diffraction analysis, the double bridge method, the dynamic resonance method, Vickers hardness measurement and thermal analysis. Wood’s alloy (Bi–Pb–Sn–Cd) has low electrical resistivity and melting point but a high elastic modulus and internal friction when compared with the Rose (Bi–Pb–Sn) alloy. The presence of cadmium in Wood’s alloy decreases its melting point and electrical resistivity with an increase in its elastic modulus, which improves the mechanical properties. Wood’s alloy (Bi–Pb–Sn–Cd) has better properties, which make it useful in various applications such as in protection shields for radiotherapy, locking of mechanical devices and welding at low temperature.     

Chern–Simons–Rozansky–Witten topological field theory

We construct and study a new topological field theory in three dimensions. It is a hybrid between Chern–Simons and Rozansky–Witten theory and can be regarded as a topologically-twisted version of the N=4$N=4$d=3$d=3$ supersymmetric gauge theory recently discovered by Gaiotto and Witten. The model depends on a gauge group G and a hyper-Kähler manifold X with a tri-holomorphic action of G. In the case when X is an affine space, we show that the model is equivalent to Chern–Simons theory whose gauge group is a supergroup. This explains the role of Lie superalgebras in the construction of Gaiotto and Witten. For general X, our model appears to be new. We describe some of its properties, focusing on the case when G is simple and X is the cotangent bundle of the flag variety of G. In particular, we show that Wilson loops are labeled by objects of a certain category which is a quantum deformation of the equivariant derived category of coherent sheaves on X.     

Hardness and microstructural variation of Al–Mg–Mn–Sc–Zr alloy

Variations of Vickers hardness were observed in Al–Mg–Mn alloy and Al–Mg–Mn–Sc–Zr alloy at different ageing times, ranging from a peak value of 81.2 HV at 54 ks down to 67.4 HV at 360 ks, below the initial hardness value, 71.8 HV at 0 ks for the case of Al–Mg–Mn–Sc–Zr alloy. Microstructures of samples at each ageing stage were examined carefully by transmission electron microscopes (TEMs) both in two-dimensions and three-dimensions. The presence of different types, densities, and sizes of particles were observed dispersed spherical Al₃Sc_1−xZr_x and also block-shaped Al₃Sc precipitates growing along <1 0 0>_Al with facets {1 0 0} and {1 1 0} of the precipitates. TEM analysis both in two-dimensions and three-dimensions, performed on various samples, confirmed the direct correlation between the hardness and the density of Al₃Sc.     

The Hintermann–Merlini–Baxter–Wu and the infinite-coupling-limit Ashkin–Teller models

We show how the Hintermann–Merlini–Baxter–Wu model (which is a generalization of the well-known Baxter–Wu model to a general Eulerian triangulation) can be mapped onto a particular infinite-coupling-limit of the Ashkin–Teller model. We work out some mappings among these models, also including the standard and mixed Ashkin–Teller models. Finally, we compute the phase diagram of the infinite-coupling-limit Ashkin–Teller model on the square, triangular, hexagonal, and kagome lattices.     

A golden point rule in rock–paper–scissors–lizard–spock game

We study a novel five-species system on two-dimensional lattices when each species have two superior and two inferior partners. Here we simplify the huge parameter space of predation probability to only two parameters. Both of Monte Carlo simulation and Mean Field Theory reveal that two of strategies may die out when the ratio of the two parameters is close to the golden point 0.618, and the remaining three strategies are provided a cyclic dominance system.     

Plastic deformation properties of Zr–Nb–Ti–Ta–Hf high-entropy alloys

We have investigated the plastic deformation properties of single-phase Zr–Nb–Ti–Ta–Hf high-entropy alloys from room temperature (RT) up to 300 °C. Uniaxial deformation tests at a constant strain rate of 10^?4?s^?1 were performed, including incremental tests such as stress relaxations, strain-rate changes, and temperature changes in order to determine the thermodynamic activation parameters of the deformation process. The microstructure of deformed samples was characterized by transmission electron microscopy. The strength of the investigated Zr–Nb–Ti–Ta–Hf phase is not as high as the values frequently reported for high-entropy alloys in other systems. At RT we measure a flow stress of about 850 °C. We find an activation enthalpy of about 1 eV and a stress dependent activation volume between 0.5 and 2 nm³. The measurement of the activation parameters at higher temperatures is affected by structural changes evolving in the material during plastic deformation.     

On the development of a high-order compact scheme for exhibiting the switching and dissipative solution natures in the Camassa–Holm equation

In this paper a two-step iterative solution algorithm for solving the Camassa–Holm equation, which involves only the first-order derivative term, is presented. In each set of the u − P and u − m differential equations, one is governed by the inviscid nonlinear convection–reaction equation for the time-evolving fluid velocity component along the horizontal direction. The other equation is known as the inhomogeneous Helmholtz equation. The resulting reduction of differential order facilitates us to develop the flux discretization scheme in a stencil with comparatively fewer points. For accurately predicting the unidirectional propagation of the shallow water wave, the modified equation analysis for eliminating several leading discretization error terms and the Fourier analysis for minimizing a particular type of wave-like error are employed. In this study, the fifth-order spatially accurate combined compact upwind scheme is developed in a three-point stencil for approximating the first-order derivative term. For the purpose of retaining a long-term accurate Hamiltonian and multi-symplectic geometric structures in Camassa–Holm equation, the time integrator (or time-stepping scheme) chosen in this study should conserve symplecticity. Another main emphasis of conducting the present calculation of Camassa–Holm equation is to shed light on the conservation of Hamiltonians up to the time before wave breaking. We also intended to elucidate the switching scenario by virtue of the peakon–peakon interaction problem and the dissipative scenario after the time of head-on collision in the peakon–antipeakon interaction problem.     

Geometric Integrability of the Camassa–Holm Equation

It is observed that the Camassa–Holm equation describes pseudo-spherical surfaces and that therefore, its integrability properties can be studied by geometrical means. An sl(2, R)-valued linear problem whose integrability condition is the Camassa–Holm equation is presented, a Miura transform and a modified Camassa–Holm equation are introduced, and conservation laws for the Camassa–Holm equation are then directly constructed. Finally, it is pointed out that this equation possesses a nonlocal symmetry, and its flow is explicitly computed.     

Integrable generalization of the associated Camassa–Holm equation

In this paper, we study an integrable generalization of the associated Camassa–Holm equation. The generalized system is shown to be integrable in the sense of Lax pair and the bilinear Bäcklund transformations are presented through the Bell polynomial technique. Meanwhile, its infinite conservation laws are constructed, and conserved densities and fluxes are given in explicit recursion formulas. Furthermore, a Darboux transformation for the system is derived with the help of the gauge transformation between two Lax pairs. As an application, soliton and periodic wave solutions are given through the Darboux transformation.     

Estimates for the KdV-Limit of the Camassa–Holm Equation

In a number of scaling limits, we prove estimates relating the solutions of the Camassa–Holm equation to the solutions of the associated KdV equation. As a consequence, suitable solutions of the water wave problem and solutions of the Camassa–Holm equation stay close together for long times.     

Persistence Properties and Unique Continuation of Solutions to a Two-component Camassa–Holm Equation

We will consider a two-component Camassa–Holm system which arises in shallow water theory. The present work is mainly concerned with persistence properties and unique continuation to this new kind of system, in view of the classical Camassa–Holm equation. Firstly, it is shown that there are three results about these properties of the strong solutions. Then we also investigate the infinite propagation speed in the sense that the corresponding solution does not have compact spatial support for t > 0 though the initial data belongs to C₀^￥(\BbbR)C_{0}^{\infty}(\Bbb{R}).     

A class of blowup and global analytical solutions of the viscoelastic Burgersʼ equations

In this Letter, by employing the perturbational method, we obtain a class of analytical self-similar solutions of the viscoelastic Burgers? equations. These solutions are of polynomial-type whose forms, remarkably, coincide with that given by Yuen for the other physical models, such as the compressible Euler or Navier–Stokes equations and two-component Camassa–Holm equations. Furthermore, we classify the initial conditions into several groups and then discuss the properties on blowup and global existence of the corresponding solutions, which may be readily seen from the phase diagram.     

An energy-conserving Galerkin scheme for a class of nonlinear dispersive equations

A Galerkin scheme is presented for a class of conservative nonlinear dispersive equations, such as the Camassa–Holm equation and the regularized long wave equation. The scheme has two advantageous features: first, it is conservative in that it keeps the discrete analogue of the continuous energy conservation property in the original equations; second, it can be formulated only with cheap H¹$H^1$-elements even if the original equations include third derivative u_xxx$u_{\mathit{xxx}}$. Numerical experiments confirm the stability and effectiveness of the proposed scheme.     

A Three-component Extension of the Camassa–Holm Hierarchy

We introduce a bi-Hamiltonian hierarchy on the loop-algebra of endowed with a suitable Poisson pair. It gives rise to the usual Camassa–Holm (CH) hierarchy by means of a bi-Hamiltonian reduction, and its first nontrivial flow provides a three-component extension of the CH equation.