A nonlinear model for marble sulphation including surface rugosity and mechanical damage

Here we propose and analyze a mathematical model that aims to describe the marble sulphation process occurring in a given material. The model accounts for rugosity as well as for damaging effects. This model is characterized by some technical difficulties that seem hard to overcome from a theoretical viewpoint. Therefore, we introduce some physically reasonable modifications in order to establish the existence of a suitable notion of solution on a given time interval. Numerical simulations are presented and discussed, also in view of further research.     

Convergence to a terrace solution in multistable reaction–diffusion equation with discontinuities

In this paper we address the large-time behavior of solutions of bistable and multistable reaction–diffusion equation with discontinuities around the stable steady states. We show that the solution always converges to a special solution, which may either be a traveling wave in the bistable case, or more generally a terrace (i.e. a collection of stacked traveling waves with ordered speeds) in the multistable case.     

Preparation of Zirconia Nanocrystals from Concentrated Zirconium Aqueous Solutions

A high concentration (0.8 M) zirconium solution turned into a stable aqueous colloid of about 60 nm in size upon low temperature (96^°C) incubation. Changing the acid concentration did not affect the colloidal growth rate nor the final colloid size much. However, the induction time before the rapid growth of colloidal particle could be altered. By limiting the incubation to just before the rapid growth of colloidal zirconia, and the addition of organic acids as surface modifiers, non-agglomerated primary crystallites (10 nm) of m-ZrO₂ could be recovered. These modified primary crystallites could then be repeatedly flocculated and redispersed in water by adjusting the pH.     

Exact Solution in Chaotic Inflation Model with Potential Minima

Taking the cosmological expansion rate directly as a function of field φ, H=H(φ), we present a new exact solution to Einstein's equations that describe the evolution of cosmological chaotic inflation model. The inflation is driven by the evolution of scalar field with inflation potential V(φ)=(λ/8)(φ²-υ²)². The spectral indices of the scalar density n_s and gravitational wave fluctuations n_g are computed. The value of n_s lies well inside the limits set by the cosmic background explorer satellite.     

Observations on the role of MgCl2 in the Weissler reaction

Aqueous solutions of Nal containing CCl₄ and MgCl₂ at various concentrations were irradiated under air with 1 MHz ultrasound and the yield of I₃⁻ was determined. The yield was not affected by MgCl₂ at concentrations up to 0.1 M. This contrasts with the finding of Lepoint and co-workers, who reported a sharp minimum in the yield at a MgCl₂ concentration of 2.5 × 10⁻³M, the yield decreased to 60% at 1 M MgCl₂, the reason being the lower solubility of CCl₄ at high MgCl₂ concentrations. In the absence of CCl₄, another dependence on the MgCl₂ concentration was observed: the yield was not affected up to 1 M, and at higher MgCl₂ concentrations the yield rapidly decreased owing to the increased viscosity of the solution. On the basis of these observations, there is no strong reason to postulate an electrical mechanism for the initiation of chemical reactions in the cavitation bubbles.     

Thermophysical effects of carbon nanotubes on MHD flow over a stretching surface

This article is intended for investigating the effects of magnetohydrodynamics (MHD) and volume fraction of carbon nanotubes (CNTs) on the flow and heat transfer in two lateral directions over a stretching sheet. For this purpose, three types of base fluids specifically water, ethylene glycol and engine oil with single and multi-walled carbon nanotubes are used in the analysis. The convective boundary condition in the presence of CNTs is presented first time and not been explored so far. The transformed nonlinear differential equations are solved by the Runge–Kutta–Fehlberg method with a shooting technique. The dimensionless velocity and shear stress are obtained in both directions. The dimensionless heat transfer is determined on the surface. Three different models of thermal conductivity are comparable for both CNTs and it is found that the Xue [1] model gives the best approach to guess the superb thermal conductivity in comparison with the Maxwell [2] and Hamilton and Crosser [3] models. And finally, another finding suggests the engine oil provides the highest skin friction and heat transfer rates.     

Wronskian Form Solutions for a Variable Coefficient Kadomtsev–Petviashvili Equation

Starting from a simple transformation, and with the aid of symbolic computation, we establish the relation- ship between the solution of a generalized variable coefficient Kadomtsev-Petviashvili （vKP） equation and the solution of a system of linear partial differential equations. According to this relation, we obtain Wronskian form solutions of the vKP equation, and further present N-soliton-like solutions for some degenerated forms of the vKP equation. Moreover, we also discuss the influences of arbitrary constants on the soliton and N-soliton solutions of the KPII equation.     

含相变微粒流体热对流启动的Galerkin解

采用Bubnov-Galerkin方法对有恒壁温条件下,两平板间夹有含相变颗粒流体的自然对流热启动瑞利数进行了近似解析求解,求出了临界瑞利数Racr和波频数kcr随相变物质浓度,以及在相变温度范围内随加热表面温度的解析关系表达式.从而,为实现该类功能性潜热流体的自然对流传热强化,及其优化控制蓄热过程有理论指导意义.     

Double-Alekseev inverse scattering method in the stationary axi-symmetric vacuum gravitation field equations

We present a new improvement to the Alekseev inverse scattering method. This improved inverse scattering method is extended to a double form, followed by the generation of some new solutions of the double-complex Kinnersley equations. As the double-complex function method contains the Kramer-Neugebauer substitution and analytic continuation, a pair of real gravitation soliton solutions of the Einstein’s field equations can be obtained from a double N-soliton solution. In the case of the flat Minkowski space background solution, the general formulas of the new solutions are presented.