On global Hessenberg based methods for solving Sylvester matrix equations

In the first part of this paper, we investigate the use of Hessenberg-based methods for solving the Sylvester matrix equation $AX+XB=C$. To achieve this goal, the Sylvester form of the global generalized Hessenberg process is presented. Using this process, different methods based on a Petrov–Galerkin or on a minimal norm condition are derived. In the second part, we focus on the SGl-CMRH method which is based on the Sylvester form of the Hessenberg process with pivoting strategy combined with a minimal norm condition. In order to accelerate the SGl-CMRH method, a preconditioned framework of this method is also considered. It includes both fixed and flexible variants of the SGl-CMRH method. Moreover, the connection between the flexible preconditioned SGl-CMRH method and the fixed one is studied and some upper bounds for the residual norm are obtained. In particular, application of the obtained theoretical results is investigated for the special case of solving linear systems of equations with several right-hand sides. Finally, some numerical experiments are given in order to evaluate the effectiveness of the proposed methods.     

Spreading and Curing Behaviors of a Thermosetting Droplet-Silicone on a Heated Surface

Thermosetting materials are widely used as encapsulation in the electrical packaging to protect the core electronic components from external force, moisture, dust, and other factors. However, the spreading and curing behaviors of such kind of fluid on a heated surface have been rarely explored. In this study, we experimentally and numerically investigated the spreading and curing behaviors of the silicone(OE6550 A/B, which is widely used in the light-emitting diode packaging) droplet with diameter of ～2.2 mm on a heated surface with temperature ranging from 25 ℃ to 250 ℃. For the experiments, we established a setup with high-speed camera and heating unit to capture the fast spreading process of the silicone droplet on the heated surface. For the numerical simulation, we built a viscosity model of the silicone by using the Kiuna's model and combined the viscosity model with the Volume of Fluid(VOF) model by the User Defined Function(UDF) method. The results show that the surface temperature significantly affected the spreading behaviors of the silicone droplet since it determines the temperature and viscosity distribution inside the droplet. For surface temperature varied from 25 ℃ to 250 ℃, the final contact radius changed from ～2.95 mm to ～1.78 mm and the total spreading time changed from ～511 s to ～0.15 s. By further analyzing the viscosity evolution of the droplet, we found that the decreasing of the total spreading time was caused by the decrease of the viscosity under high surface temperature at initial spreading stage, while the reduction of the final contact radius was caused by the curing of the precursor film. This study supplies a strategy to tuning the spreading and curing behavior of silicone by imposing high surface temperature, which is of great importance to the electronic packaging.     

Simultaneously enhancing mechanical and microwave absorption properties of Cf/SiC composites via SiC nanowires additions

C_f/SiC composite is an excellent structural and functional material, silicon carbide nanowires (SiCnws) are not only a toughening material but also a great application in the field of microwave absorption. In this study, SiCnws are grown on the surface of carbon fiber (C_f) by polymer impregnation and pyrolysis, and the SiC matrix was prepared by chemical vapor osmosis method. The SiCnws are introduced to enhance the mechanical and microwave absorption properties simultaneously. After 3 impregnations, the flexural strength of the composite was 107.35 ± 10 MPa. When the thickness is 1.86 mm, the minimum reflection loss value is ?41.08 dB, and the effective absorption bandwidth (RL ≤ ?10 dB) is 3.86 GHz. Furthermore, the microwave absorption mechanism of the material is discussed. This work provides a new method to prepare lightweight, stable and high-performance microwave absorption materials, and these materials are expected to be used in high temperature environments.     

Hydroxyapatite cages with aligned pores for bone grafting – Seeding of human osteoblast-like cells in vitro and their response in dynamic culture mode

Hydroxyapatite (HA) is a highly regarded synthetic bone graft material. Porous HA ceramics blocks are used to substitute harvested natural bone grafts. Being similar to bone mineral, HA material integrates with the host bone through surface osteointegration and slowly resorb along with the natural bone remodeling process. The blocks in use currently have random and tortuous pore structures. The present work explores the usefulness of cage-like HA ceramic design with end-to-end open pores, with the help of in vitro cell culture methods. Such a structure, on implantation, will take up the blood factors and cells and host the bone remodeling process inside the bulk of the cage, leading to early healing. In the study, HA samples with aligned through-pores were prepared and explored in vitro, with a focus on how the pores host the cells inside and to what level the cells maintain their activity. Human osteoblast-like cells (HOS) were used, at different seeding and culturing approaches. Cell seeding was done through (i) conventional large volume cell suspension, (ii) a confined mini chamber with a limited volume of cell suspension, and (iii) placing a concentrated drop of cell suspension directly on top of the scaffold. The third approach gave the best cell adhesion and proliferation, and hence used for further explorations. A dynamic culture system was designed in-house by bifurcating the cell culture wells using vertical inserts, holding the samples horizontally with their ends open to both sides, and making the media flow across using a rocker platform. The HOS cell adhesion, viability and proliferation were tested in the HA cages, in static and dynamic culture conditions, with conventional porous ceramics as the control. The cell infiltration was deeper and the cell viability over a period of 7 days was significantly higher in dynamic culture conditions in the test samples.     

Torsional statics of two-dimensionally functionally graded microtubes

A size-dependent governing equation is derived to investigate the torsional static behaviors of two-dimensionally functionally graded microtubes based on the modified couple stress theory. The shear modulus is assumed to vary along the tube’s length direction according to an exponential distribute function, and varies along the tube’s radius direction according to a power-law function. A generalized differential quadrature method is developed to determine the rotational angle and shear stresses. Some illustrative examples are given to investigate the effects of applied torques, the length scale parameter and various material compositions on the torsional angle and shear stresses.     

Two-step method to deposit ZrO2 coating on carbon fiber: Preparation,characterization, and performance in SiC composites

Recently, ceramic matrix composites reinforced by short carbon fibers (CFs) attracted increasing attentions. To further improve mechanical properties and oxidation resistances, CFs were subjected to oxidation and acidification followed by sol-gel dip-coating to deposit ZrO₂ on their surfaces. ZrO₂-C_f/SiC composites were fabricated by joint hot compression molding and sintering, compared to C_f/SiC and SiC prepared by the same method. Microstructural analyses indicated that ZrO₂ coatings were successfully deposited on CF surfaces, formed strong bonding and interfaces between CF and the matrix. Meanwhile, CFs were found uniformly distributed in SiC matrix with random orientations. Flexural curves of ZrO₂-C_f/SiC and C_f/SiC revealed the presence of “false plasticity” regions after sharp drops, which were quite different from brittle flexural behavior of SiC ceramic. Compression strength of the three samples showed step-up growth. ZrO₂-C_f/SiC exhibited the highest value, indicating the introduction of CFs and ZrO₂ coatings do have great influence on mechanical performances. After heat treatment, ZrO₂-C_f/SiC exhibited better oxidation resistance than C_f/SiC, with weight loss ratios estimated to ??3.76% and ??6.43%, respectively. These improved properties indicated that ZrO₂-C_f/SiC would be excellent alternatives to other existence materials under ultra-high temperature environments.     

Homogenization with uncertainty in Poisson ratio for polymers with rubber particles

The main aim of this work is dual computer analysis of probabilistic coefficients for the homogenized tensor of the polymer filled with the rubber particles having randomized Poisson ratios of both constituents. The major issue is to verify an influence of a randomness in rubber Poisson ratio close to the compressibility limit on the uncertainty of the effective tensor probabilistic characteristics. Probabilistic analysis presented here is carried out using mainly the stochastic perturbation technique provided by the common application of the traditional FEM commercial code ABAQUS and the symbolic computations package MAPLE. This FEM-based technique employs polynomial response function of the optimum order recovered from the weighted least squares method and following a set of deterministic solutions obtained for various values of the randomized input parameter. Optimization procedure is released entirely into a symbolic environment, where maximization of the correlation factor together with minimization of the fitting variance and approximation error are applied. Homogenization technique consists in equating of deformation energies for the real composite and the artificial one characterized by the effective elasticity tensor with uncertainty.     

Covariance matrix adaptation evolution strategy based design of fixed structure robust H∞ loop shaping controller

This paper proposes the application of Covariance Matrix Adaptation Evolution Strategy (CMA-ES) in fixed structure H_∞ loop shaping controller design. Integral Time Absolute Error (ITAE) performance requirement is incorporated as a constraint with an objective of maximization of stability margin in the fixed structure H_∞ loop shaping controller design problem. Pneumatic servo system, separating tower process and F18 fighter aircraft system are considered as test systems. The CMA-ES designed fixed structure H_∞ loop-shaping controller is compared with the traditional H_∞ loop shaping controller, non-smooth optimization and Heuristic Kalman Algorithm (HKA) based fixed structure H_∞ loop shaping controllers in terms of stability margin. 20% perturbation in the nominal plant is used to validate the robustness of the CMA-ES designed H_∞ loop shaping controller. The effect of Finite Word Length (FWL) is considered to show the implementation difficulties of controller in digital processors. Simulation results demonstrated that CMA-ES based fixed structure H_∞ loop shaping controller is suitable for real time implementation with good robust stability and performance.     

Mechanophysical Cues in Extracellular Matrix Regulation of Cell Behavior

The extracellular matrix (ECM) is a macromolecular network that can provide biochemical and structural support for cell adhesion and formation. It regulates cell behavior by influencing biochemical and physical cues. It is a dynamic structure whose components are modified, degraded, or deposited during connective tissue development, giving tissues strength and structural integrity. The physical properties of the natural ECM environment control the design of naturally or synthetically derived biomaterials to guide cell function in tissue engineering. Tissue engineering is an important field that explores physical cues of the ECM to produce new viable tissue for medical applications, such as in organ transplant and organ recovery. Understanding how the ECM exerts physical effects on cell behavior, when cells are seeded in synthetic ECM scaffolds, is of utmost importance. Herein we review recent findings in this area that report on cell behaviors in a variety of ECMs with different physical properties, i.e., topology, geometry, dimensionality, stiffness, and tension.     

Effects of SiC content on the densification,microstructure, and mechanical properties of HfB2–SiC composites

To investigate the effects of SiC on microstructure, hardness, and fracture toughness, 0, 10, 20, and 30 vol% SiC were added to HfB₂ and sintered by SPS. Upon adding SiC to 30 vol%, relative density increased about 4%; but HfB₂ grain growth had a minimum at 20 vol% SiC. This may be due to grain boundary silicate glass, responsible for surface oxide wash out, enriched in SiO₂ with higher fraction of SiC. By SiO₂ enrichment, the glass viscosity increased and higher HfO₂ remained unsolved which subsequently lead to higher grain growth. Hardness has increased from about 13 to 15 GPa by SiC introduction with no sensible variation with SiC increase. Residual stress measurements by Rietveld method indicated high levels of tensile residual stresses in the HfB₂ Matrix. Despite the peak residual stress value at 20 vol% SiC, fracture toughness of this sample was the highest (6.43 MPa m^0.5) which implied that fracture toughness is mainly a grain size function. Tracking crack trajectory showed a mainly trans-granular fracture, but grain boundaries imposed a partial deflection on the crack pathway. SiC had a higher percentage in fracture surface images than the cross-section which implied a weak crack deflection.