Finite-time blowup for a complex Ginzburg-Landau equation

We prove that negative energy solutions of the complex Ginzburg-Landau equation $e^{-i\theta} u_t = \Delta u+ |u|^{\alpha} u$ blow up in finite time, where \alpha >0 and \pi /2<\theta <\pi /2. For a fixed initial value $u(0)$, we obtain estimates of the blow-up time $T_{max}^\theta$ as $\theta \to \pm \pi /2$. It turns out that $T_{max}^\theta$ stays bounded (respectively, goes to infinity) as $\theta \to \pm \pi /2$ in the case where the solution of the limiting nonlinear Schr\"odinger equation blows up in finite time (respectively, is global).Comment: 22 page

Linear vs. nonlinear effects for nonlinear Schrodinger equations with potential

We review some recent results on nonlinear Schrodinger equations with potential, with emphasis on the case where the potential is a second order polynomial, for which the interaction between the linear dynamics caused by the potential, and the nonlinear effects, can be described quite precisely. This includes semi-classical regimes, as well as finite time blow-up and scattering issues. We present the tools used for these problems, as well as their limitations, and outline the arguments of the proofs.Comment: 20 pages; survey of previous result

Parametric Analysis of Electrodeposited Nano-composite Coatings for Abrasive Wear Resistance

Nano-composite coatings have become the focus of widespread research in recent years due in part to their superior properties when compared to purely metallic films. The benefits of using these types of coatings include high-specific heat, optical non-linearity, novel magnetic properties, enhanced mechanical behavior (large hardness and wear resistance), and good corrosion resistance. This chapter presents a parametric study of electrodeposited nano-composite coatings for improved abrasive wear resistance. The following physical parameters were investigated using a Taguchi L18 fractional factorial design of experiments (DOEs): current density, pH, bath temperature, nano-particle concentration, and electrolyte agitation (stir rate). The results were evaluated using the signal-to-noise (S/N) ratio to develop a non-dimensional relationship between the physical parameters and the abrasive wear resistance of the coating. The relationship showed that the abrasive wear resistance of the coating increases as the quantity of nano-particle in the solution and the agitation frequency increase. The analysis of variance (ANOVA) indicated that the particle concentration had the greatest significance to the wear resistance of the coating

Asymptotic expansions of the solutions of the Cauchy problem for nonlinear parabolic equations

Let $u$ be a solution of the Cauchy problem for the nonlinear parabolic equation $$\partial_t u=\Delta u+F(x,t,u,\nabla u) \quad in \quad{\bf R}^N\times(0,\infty), \quad u(x,0)=\varphi(x)\quad in \quad{\bf R}^N,$$ and assume that the solution $u$ behaves like the Gauss kernel as $t\to\infty$. In this paper, under suitable assumptions of the reaction term $F$ and the initial function $\varphi$, we establish the method of obtaining higher order asymptotic expansions of the solution $u$ as $t\to\infty$. This paper is a generalization of our previous paper, and our arguments are applicable to the large class of nonlinear parabolic equations

Dissimilar Welding and Joining of Magnesium Alloys: Principles and Application

The growing concerns regarding fuel consumption within the aerospace and transportation industries make the development of fuel-efficient systems a significant engineering challenge. Currently, materials are selected because of their abilities to satisfy engineering demands for good thermal conductivity, strength-to-weight ratio, and tensile strength. These properties make magnesium an excellent option for various industrial or biomedical applications, given that is the lightest structural metal available. The utilization of magnesium alloys, however, requires suitable welding and joining processes that minimizes microstructural changes while maintaining good joint/bond strength. Currently, magnesium are joined using; mechanical fastening, adhesive bonding, brazing, fusion welding processes or diffusion bonding process. Fusion welding is the conventional process used for joining similar metals. However, the application of any welding technique to join dissimilar metals presents additional difficulties, the principal one being; the reaction of the two metals at the joint interface can create intermetallic compounds that may have unfavorable properties and metallurgical disruptions which deteriorates the joint performance. This chapter investigates the welding and joining technologies that are currently used to join magnesium alloys with emphasis on the development of multi-material structures for applications in the biomedical industries. Multi-material structures often provide the most efficient design solution to engineering challenges

Microstructural response and wear behaviour of Ti-6Al-4V impregnated with Ni/Al2O3 + TiO2 nanostructured coating using an electric arc

YesTitanium alloys are known for their excellent corrosion resistance; however, low surface hardness results in poor wear resistance, which limits its potential application. This study employs a novel two-step process to embed a hard Ni coating containing a mixture of nanosized particles (Al2O3 and TiO2) into the surface of the Ti-6Al-4V alloy using an electric arc produced during the inert tungsten gas welding process. The surface of the sample was evaluated using Vickers Microhardness, Scanning electron microscopy, Energy dispersive spectroscopy and pin-on-plate wear testing. Microstructural analysis showed that impregnating the titanium surface with Ni/(Al2O3 and TiO2) nanomaterials resulted in the formation of a hard martensitic structure to a depth of approximately 2 mm below the surface. The changes observed are driven by modification of the surface chemistry and the presence of nickel, causing grain size reduction, solid solution strengthening and dispersion strengthening of the treated layer by the nanoparticles. The hardness of the treated layer increased by more than 180% when 40 nm Al2O3 and 30 nm TiO2 particles were embedded into the surface. Similarly, the wear resistance of the treated surface improved by 100%

Nanoparticle enhanced eutectic reaction during diffusion brazing of aluminium to magnesium

YesDiffusion brazing has gained much popularity as a technique capable of joining dissimilar lightweight metal alloys and has the potential for a wide range of applications in aerospace and transportation industries, where microstructural changes that will determine the mechanical and chemical properties of the final joint must be controlled. This study explores the effect of Al2O3 nanoparticles on the mechanical and microstructural properties of diffusion brazed magnesium (AZ31) and aluminium (Al-1100) joints. The results showed that the addition of Al2O3 nanoparticle to the electrodeposited Cu coating increased the volume of eutectic liquid formed at the interface which caused a change to the bonding mechanism and accelerated the bonding process. When the Cu/Al2O3 nanocomposite coatings were used as the interlayer, a maximum bond strength of 46 MPa was achieved after 2 min bonding time while samples bonded using pure-Cu interlayers achieved maximum strength after 10 min bonding time. Chemical analysis of the bond region confirmed that when short bonding times are used, the intermetallic compounds formed at the interface are limited to the compounds consumed in the eutectic reaction

Aluminium surface impregnated with nano constituents for enhanced mechanical performance

YesAluminium alloys are widely used structural materials in automotive, aerospace, and transportation, among several other notable industries. However, aluminium alloys' low hardness and poor tribological performance prevent potential use in applications requiring high contact pressures and wear resistance. This paper presents a novel two-step technique for enhancing the mechanical properties of the aluminium alloy by impregnating the surface with Ni-coating containing hard TiO2 nanoparticles using a high-intensity electric arc generated during tungsten inert gas welding. The results show that the process significantly changes the Microstructure and mechanical properties. The surface hardness increased from 0.48 GPa to 0.65 GPa with a corresponding change of Young's modulus from 15 GPa to 24 GPa of the treated surface