Delay equations with fluctuating delay related to the regenerative chatter II: analysis of reduced bifurcation equation

In this article, we study the reduced bifurcation equations of the nonlinear delay differential equations with periodic delays, which models the machine tool chatter with continuously modulated spindle speed to determine the periodic solutions and analyze the tool motion. Analytical results show both modest increase of stability and existence of periodic solutions close to the new stability boundary.     

Transmission electron microscopy study of defects in AlN crystals with rough and smooth surface grains

Defects present in (0 0 0 1) textured polycrystalline AlN grown by the sublimation–recombination method were analyzed using transmission electron microscopy (TEM) methods. Grains in the polycrystalline boule had either a smooth or a rough surface. The rough surface grains had mainly edge dislocations, whereas the smooth surface grains had some sub-grain boundaries and were mostly free of dislocations. Dislocations at the grain boundaries were pinned and could not be annihilated.     

Wetting and conductivity of BiVO<Subscript>4</Subscript>-V<Subscript>2</Subscript>O<Subscript>5</Subscript> ceramic composites

The conductivity and transport number of oxygen ions of BiVO₄-(5, 7, 10, 12) wt % V₂O₅ ceramic composites are measured using the four-probe and coulomb-volumetric methods, respectively, in the temperature range from 500 to 660°C. The phase transition of wetting of grain boundaries with eutectic melt at 640°C is discovered. It is shown that the grain boundary wetting significantly raises the ionic conductivity of composites.     

Optimization problems for an energy functional with mass constraint revisited

In this paper we report on a variational problem under a constraint on the mass which is motivated by the torsional rigidity and torsional creep. Following a device by Alt, Caffarelli and Friedman we treat instead a problem without constraint but with a penalty term. We will complete some of the results of [C. Bandle, A. Wagner, Optimization problems for weighted Sobolev constants, Calc. Var. Partial Differential Equations 29 (2007) 481-507] where the existence of a Lipschitz continuous minimizer has been established. In particular we prove qualitative properties of the optimal shape.     

Domain decomposition methods for hyperbolic problems

In this paper a method is developed for solving hyperbolic initial boundary value problems in one space dimension using domain decomposition, which can be extended to problems in several space dimensions. We minimize a functional which is the sum of squares of the L ² norms of the residuals and a term which is the sum of the squares of the L ² norms of the jumps in the function across interdomain boundaries. To make the problem well posed the interdomain boundaries are made to move back and forth at alternate time steps with sufficiently high speed. We construct parallel preconditioners and obtain error estimates for the method. The Schwarz waveform relaxation method is often employed to solve hyperbolic problems using domain decomposition but this technique faces difficulties if the system becomes characteristic at the inter-element boundaries. By making the inter-element boundaries move faster than the fastest wave speed associated with the hyperbolic system we are able to overcome this problem.     

A coupled multivalued model for ice streams and its numerical simulation

^** Email: nati{at}dma.uvigo.es^*** Email: durany{at}dma.uvigo.es^**** Email: anaisabel.munoz{at}urjc.es^***** Email: emanuele.schiavi{at}urjc.es^****** Email: carlosv{at}udc.es This paper deals with the numerical solution of a non-linearmodel describing a free-boundary problem arising in modern glaciology.Considering a shallow, viscous ice sheet flow along a soft,deformable bed, a coupled non-linear system of differentialequations can be obtained. Particularly, an obstacle problemis then deduced and solved in the framework of its complementarityformulation. We present the numerical solution of the resultingmultivalued system modelling the ice sheet non-Newtonian dynamicsdriven by the underlying drainage system. Our numerical resultsshow the existence of fast ice streams when positive wave-likeinitial conditions are considered. The solutions are numericallycomputed with a decoupling iterative method and finite-elementtechnique. A duality algorithm and a projected Gauss–Seidelmethod are the alternatives used to cope with the resultingvariational inequality while the explicit treatment, Newtonmethod or a duality method are proposed to deal with the non-linearsource term. Finally, the numerical solutions are physicallyinterpreted and some comparisons among the numerical methodsare then discussed.     

Dynamics for a diffusive prey–predator model with different free boundaries

To understand the spreading and interaction of prey and predator, in this paper we study the dynamics of the diffusive Lotka–Volterra type prey–predator model with different free boundaries. These two free boundaries, which may intersect each other as time evolves, are used to describe the spreading of prey and predator. We investigate the existence and uniqueness, regularity and uniform estimates, and long time behaviors of global solution. Some sufficient conditions for spreading and vanishing are established. When spreading occurs, we provide the more accurate limits of $(u,v)$ as $t\to \infty$, and give some estimates of asymptotic spreading speeds of $u,v$ and asymptotic speeds of $g,h$. Some realistic and significant spreading phenomena are found.     

The Iterative-DRESOR method to solve radiative transfer in a plane-parallel, anisotropic scattering medium with specular-diffuse boundaries

Using the intensity with high directional resolution obtained by the Basic-DRESOR method as an initial guess, which is substituted into the integrated radiative transfer equation (IRTE), an iterative algorithm is proposed, called the Iterative-DRESOR method. This method can reduce the error levels of the intensity from several percent using the Basic-DRESOR method to a level of less than 1.0×10⁻⁶ with acceptable computation costs. The method is also validated against the exact heat flux in literature in some cases. It further clarifies some uncertain results for the reflectance in a pure, linearly anisotropic scattering medium with specular-diffuse boundaries. The directional distributions of intensity are obviously influenced by the reflecting modes of the boundary, especially in the zone near the boundary. The reflecting mode of an emitting boundary has little effect on the transmittance or reflectance. The reflecting mode of a non-emitting boundary also has little effect on the transmittance, but it obviously influences the reflectance. The difference between the reflectance for specular and diffuse boundaries increases at first, and then decreases, as the optical thickness of the medium increases. The difference will decrease as the scattering albedo of the medium increases, and it is negligible when the medium is pure scattering. The effect of the scattering phase function of the medium on the difference can also not be ignored. The Iterative-DRESOR method is expected to strengthen the capability of the Monte Carlo method to produce accurate results and to validate the results of other methods to solve RTE.     

Theory of Triple Junctions Mobility in Crystals with Impurities

We consider the steady state migration of the triple junction in the tricrystal with impurities which segregate strongly at the grain boundaries. If the mobility of impurities inside grain boundaries is much higher than the rate of impurity atoms jumps from the grain boundary into the bulk, the triple junction migration causes the divergence of the impurity content at the triple point. We show that this divergence can be relaxed either by the non-equilibrium segregation at the growing grain boundary or by the formation of the inclusion of the impurity-rich phase at the triple point. In the former case the dihedral angle at the triple point differs considerably from its equilibrium value and is strongly temperature-dependent. However, the triple junction cannot be described as an individual object with its own mobility. In the latter case of the cavity formation at the triple point the triple junction can be characterized by its own mobility. It is shown that the dependence of the triple junction migration rate on the driving force is approximately linear at the low migration rates and highly nonlinear at high migration rates. Moreover, there is the maximal allowable steady-state migration rate of the system triple junction-inclusion. For the higher migration rates the jerky motion of the triple junction occurs. Both models are in a good agreement with the experimental data.