Assembling hydrodynamic cloaks to conceal complex objects from drag

Transformation hydrodynamics and the corresponding metamaterials have been proposed as a means to exclude the drag force acting on an object. Here, we report a strategy to deploy the hydrodynamic cloaks in a more practical manner by assembling different-shaped cloaking parts. Our strategy is to first model a square-shaped cloak and a carpet cloak and then combine them to conceal a more complex-shaped space in the three-dimensional hydrodynamic flow. With the derivation of transformation hydrodynamics, the coordinate transformations for each hydrodynamic cloaking are demonstrated with the calculated viscosity tensors. The pressure and velocity fields of the square, triangular (carpet), and exemplary three-dimensional house-shaped cloaks are numerically simulated, thus showing a cloaking effect and reduced drag. This study suggests an efficient way of cloaking complex architectures from fluid-dynamic forces.     

Tensile behaviour of corroded and hydrogen embrittled 2024 T351 aluminum alloy specimen

The synergetic effect of corrosion and corrosion induced hydrogen embrittlement damage processes which occur at local scale has been found to result in a dramatic macroscopic tensile ductility loss of the 2024 aluminum alloy. In the present work, the tensile behaviour of corroded 2024 T351 specimens has been estimated on the basis of FE analysis by taking into account the local material properties in the damaged areas. A parametric study is involved to account for the effect of thickness in the results. Calculated tensile properties obtained with the analysis agree well with experimental data.     

Vibrational control of crystal growth from liquid phase

Modeling and numerical simulations of the convective flows induced by the vibration of the monocrystal during crystal growth have been performed for two configurations simulating the Cz and FZ methods. This permitted to emphasize the role of different vibrational mechanisms in the formation of the average flows. It is shown that an appropriate combination of these mechanisms can be used to counteract the usual convective flows (buoyancy- and/or thermocapillary-driven) inherent to crystal growth processes from the liquid phase. While vibrational convection is rather complex due to these identified mechanisms, the new modeling used in the present paper opens up very promising perspectives to efficiently control heat and mass transfer during real industrial applications of crystal growth from the liquid phase.     

Two-dimensional numerical calculation of the flow field about a scoop inlet by the piecewise linear method

The piecewise linear method (PLM) based on time operator splitting is used to solve the unsteady compressible Euler equations describing the two-dimensional flow around and through a straight wall inlet placed stationary in a rapidly rotating supersonic flow. The PLM scheme is formulated as a Lagrangian step followed by an Eulerian remap. The inhomogeneous terms in the Euler equations written in cylindrical coordinates are first removed by Sod's method and the resulting set of equations is further reduced to two sets of one-dimensional Lagrangian equations, using time operator splitting. The numerically generated flow fields are presented for different values of the back pressure imposed at the downstream exit of the inlet nozzle. An oblique shock wave is formed in front of the almost whole portion of the inlet entrance, the incoming streamlines being deflected towards the higher pressure side after passing through the oblique shock wave and then bending down to the lower pressure side. A reverse flow appears inside the inlet nozzle owing to the recovery pressure of the incoming streams being lower than the back pressure of the inlet nozzle.     

Optimal design of a convergent-barrel cold spray nozzle by numerical method

A convergent-barrel (CB) cold spray nozzle was designed through numerical simulation. It was found that the main factors influencing significantly particle velocity and temperature include the length and diameter of the barrel section, the nature of the accelerating gas and its pressure and temperature, and the particle size. Particles can achieve a relatively low velocity but a high temperature under the same gas pressure using a CB nozzle compared to a convergent-divergent (CD) nozzle. The experiment results with Cu powder using the designed CB nozzle confirmed that particle deposition can be realized under a lower gas pressure with a CB nozzle.     

基于二次插值的非饱和土壤水流问题的特征差分方法及数值模拟

本文针对一类非饱和土壤水流问题,提出了基于二次插值的特征差分格式,得到了严谨的L2模误差估计.并作了数值试验,指明方法的有效性.     

Numerical simulation of the spatiotemporal evolution of a nanoparticle–plasma system

A one-dimensional nanodusty plasma was modeled by self-consistently coupling a plasma model with nanoparticle growth, charging, and transport models. As nanoparticles grow from subnanometer to tens of nm in diameter, the numerical results predict a rich spatiotemporal structure, including four distinct temporal phases: a charge-limited phase, a charge accumulation phase, an early ion drag phase, and a sheath interaction phase.     

On numerical ranges and roots

Existence of the fractional powers is established in Banach algebra setting, in terms of the numerical ranges of elements involved. The behavior of the spectra and (for Hermitian ∗-algebras satisfying some additional hypotheses) the ∗-numerical range under taking these powers also is investigated.     

Constraint incorporation in optimization

Numerical methods for solving constrained optimization problems need to incorporate the constraints in a manner that satisfies essentially competing interests; the incorporation needs to be simple enough that the solution method is tractable, yet complex enough to ensure the validity of the ultimate solution. We introduce a framework for constraint incorporation that identifies a minimal acceptable level of complexity and defines two basic types of constraint incorporation which (with combinations) cover nearly all popular numerical methods for constrained optimization, including trust region methods, penalty methods, barrier methods, penalty-multiplier methods, and sequential quadratic programming methods. The broad application of our framework relies on addition and chain rules for constraint incorporation which we develop here.     

New efficient numerical procedures for solving stochastic variational problems with a priori maximum pointwise error estimates

In a previous paper we gave a new formulation and derived the Euler equations and other necessary conditions to solve strong, pathwise, stochastic variational problems with trajectories driven by Brownian motion. Thus, unlike current methods which minimize the control over deterministic functionals (the expected value), we find the control which gives the critical point solution of random functionals of a Brownian path and then, if we choose, find the expected value.This increase in information is balanced by the fact that our methods are anticipative while current methods are not. However, our methods are more directly connected to the theory and meaningful examples of deterministic variational theory and provide better means of solution for free and constrained problems. In addition, examples indicate that there are methods to obtain nonanticipative solutions from our equations although the anticipative optimal cost function has smaller expected value.In this paper we give new, efficient numerical methods to find the solution of these problems in the quadratic case. Of interest is that our numerical solution has a maximal, a priori, pointwise error of O(h3/2) where h is the node size. We believe our results are unique for any theory of stochastic control and that our methods of proof involve new and sophisticated ideas for strong solutions which extend previous deterministic results by the first author where the error was O(h²).We note that, although our solutions are given in terms of stochastic differential equations, we are not using the now standard numerical methods for stochastic differential equations. Instead we find an approximation to the critical point solution of the variational problem using relations derived from setting to zero the directional derivative of the cost functional in the direction of simple test functions.Our results are even more significant than they first appear because we can reformulate stochastic control problems or constrained calculus of variations problems in the unconstrained, stochastic calculus of variations formulation of this paper. This will allow us to find efficient and accurate numerical solutions for general constrained, stochastic optimization problems. This is not yet being done, even in the deterministic case, except by the first author.