Gradient design of metal hollow sphere (MHS) foams with density gradients

This is the post-print version of the final paper published in Composites Part B: Engineering. The published article is available from the link below. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. Copyright @ 2011 Elsevier B.V.Metal hollow sphere (MHS) structures with a density gradient have attracted increasing attention in the effort to pursue improved energy absorption properties. In this paper, dynamic crushing of MHS structures of different gradients are discussed, with the gradients being received by stacks of hollow spheres of the same external diameter but different wall thicknesses in the crushing direction. Based on the dynamic performance of MHS structures with uniform density, a crude semi-empirical model is developed for the design of MHS structures in terms of gradient selections for energy absorption and protection against impact. Following this, dynamic responses of density graded MHS foams are comparatively analyzed using explicit finite element simulation and the proposed formula. Results show that the simple semi-empirical model can predict the response of density gradient MHS foams and is ready-to-use in the gradient design of MHS structures.The National Science Foundation of China and the State Key Laboratory of Explosion Science and Technology (Beijing Institute of Technology

Constricted channel flow with different cross-section shapes

Pressure driven steady flow through a uniform circular channel containing a constricted portion is a common problem considering physiological flows such as underlying human speech sound production. The influence of the constriction’s cross-section shape (circle, ellipse, circular sector) on the flow within and downstream from the constriction is experimentally quantified. An analytical boundary layer flow model is proposed which takes into account the hydraulic diameter of the cross-section shape. Comparison of the model outcome with experimental and three-dimensional numerically simulated flow data shows that the pressure distribution within the constriction can be modeled accurately so that the model is of interest for analytical models of fluid–structure interaction without the assumption of two-dimensional flow

Effects of uncertainties and errors on Lyapunov control

Lyapunov control (open-loop) is often confronted with uncertainties and errors in practical applications. In this paper, we analyze the robustness of Lyapunov control against the uncertainties and errors in quantum control systems. The analysis is carried out through examinations of uncertainties and errors, calculations of the control fidelity under influences of the certainties and errors, as well as discussions on the caused effects. Two examples, a closed control system and an open control system, are presented to illustrate the general formulism.Comment: 4 pages, 5 figure

Direct diffusion through interpenetrating networks: Oxygen in titanium

How impurity atoms move through a crystal is a fundamental and recurrent question in materials. The previous understanding of oxygen diffusion in titanium relied on interstitial lattice sites that were recently found to be unstable, making the diffusion pathways for oxygen unknown. Using first-principles quantum-mechanical methods, we find three oxygen interstitial sites in titanium, and quantify the multiple interpenetrating networks for oxygen diffusion. Surprisingly, no single transition dominates, but all contribute to diffusion.Comment: 10 pages, 3 figures; additional supporting materia

Intelligent design guidance

This paper presents results from an investigation regarding the use of the Design Structure Matrix (DSM) as a means to guide a designer through the calculation of numerical relationships within the early design system Designer. Characteristics, relationships and goals are used within Designer to enable the evaluation and approximation of the design model and are represented within the system as a digraph. Despite being a useful representation of the interactions within the design model, the digraph does not aid the designer in identifying a sequence of activities that need to be performed in order to evaluate the model. The DSM system was used to represent the characteristics and the dependencies obtained through the relationships. The sequence of characteristics within the DSM was optimised and used to produce a design process to guide the designer in model evaluation. The objective of the optimisation was to minimise the amount of iteration within the design process. The process enabled a designer who is unfamiliar with the model to evaluate it and satisfy the design goals and requirements. Both the DSM system and the Designer system are generic in nature andmay be applied to any design problem

On the duality relation for correlation functions of the Potts model

We prove a recent conjecture on the duality relation for correlation functions of the Potts model for boundary spins of a planar lattice. Specifically, we deduce the explicit expression for the duality of the n-site correlation functions, and establish sum rule identities in the form of the M\"obius inversion of a partially ordered set. The strategy of the proof is by first formulating the problem for the more general chiral Potts model. The extension of our consideration to the many-component Potts models is also given.Comment: 17 pages in RevTex, 5 figures, submitted to J. Phys.

Fixed subgroups are compressed in surface groups

For a compact surface $\Sigma$ (orientable or not, and with boundary or not) we show that the fixed subgroup, $\operatorname{Fix} B$, of any family $B$ of endomorphisms of $\pi_1(\Sigma)$ is compressed in $\pi_1(\Sigma)$ i.e., $\operatorname{rk}((\operatorname{Fix} B)\cap H)\leq \operatorname{rk}(H)$ for any subgroup $\operatorname{Fix} B \leq H \leq \pi_1(\Sigma)$. On the way, we give a partial positive solution to the inertia conjecture, both for free and for surface groups. We also investigate direct products, $G$, of finitely many free and surface groups, and give a characterization of when $G$ satisfies that $\operatorname{rk}(\operatorname{Fix} \phi) \leq \operatorname{rk}(G)$ for every $\phi \in Aut(G)$