On Spectral Decomposition of States and Gramians of Bilinear Dynamical Systems

The article proves that the state of a bilinear control system can be split uniquely into generalized modes corresponding to the eigenvalues of the dynamics matrix. It is also shown that the Gramians of controllability and observability of a bilinear system can be divided into parts (sub-Gramians) that characterize the measure of these generalized modes and their interactions. Furthermore, the properties of sub-Gramians were investigated in relation to modal controllability and observability. We also propose an algorithm for computing the Gramians and sub-Gramians based on the element-wise computation of the solution matrix. Based on the proposed algorithm, a novel criterion for the existence of solutions to the generalized Lyapunov equation is proposed, which allows, in some cases, to expand the domain of guaranteed existence of a solution of bilinear equations. Examples are provided that illustrate the application and practical use of the considered spectral decompositions.

Effect of multiple forging on the microstructure and properties of an as-cast Cu–Ni–Si alloy with high Ni and Si contents

A Cu–Ni–Si alloy with high Ni and Si contents was prepared by the traditional melting and casting method, and then multiple forging and ageing were conducted to investigate their effect on the microstructure and properties. The results show that reticular Ni31Si12 phases are located on the grain boundaries of the dendritic α-Cu(Ni,Si) solution matrix in the as-cast Cu–Ni–Si alloy because of the high Ni and Si contents, and some rice-like Ni2Si phases precipitate in the interior of α-Cu(Ni,Si) grains during cooling. With increasing number of forging passes, the morphology of the α-Cu(Ni,Si) matrix changes from dendrites to elongated dendrites and then equiaxed grains, the Ni31Si12 phase changes from reticular to irregular and then particle-like, while the Ni2Si phase gradually disappears. As a result, the hardness increases continuously up to 18 forging passes, while the electrical conductivity first increases and then decreases significantly. The hardness and electrical conductivity achieve the highest values with 18 forging passes and a subsequent ageing treatment at 450 °C for 4 h, and the corresponding microstructure comprises an equiaxed α-Cu(Ni,Si) matrix with microscale Ni31Si12 particles and sub-microscale Ni2Si precipitates.

Fundamental solution matrix and Cauchy properties of quaternion combined impulsive matrix dynamic equation on time scales

In this paper, we establish some basic results for quaternion combined impulsive matrix dynamic equation on time scales for the first time. Quaternion matrix combined-exponential function is introduced and some basic properties are obtained. Based on this, the fundamental solution matrix and corresponding Cauchy matrix for a class of quaternion matrix dynamic equation with combined derivatives and bi-directional impulses are derived.

Microstructural Characteristics in Babbitt Coatings Deposited by LPCS

Studies have already established that the mechanical properties of Babbitt coatings significantly depend on the microstructural characteristics, such as the amount and distribution of intermetallic compounds dispersed in a soft solid solution matrix. For Sn–Sb–Cu-based Babbitt coatings, the formation of SbSn- and CuSn-based precipitates has a substantial influence on the resulting microhardness and thus determines the maximum load carrying capacity. Thermal spraying of Sn-based Babbitt coatings results in a relatively more refined structure of these precipitates than in common manufacturing processes, such as casting, due to the thermal processing conditions. This study aims to evaluate the effect of the temperature of the propellant gas and substrate temperature on the microstructural characteristics of Sn–Sb–Cu-based Babbitt coatings deposited by low pressure cold spraying (LPCS). The deposits were examined for their phase composition, microhardness and mesoscopic structure. It was found that the coatings were mainly composed of Sb2Sn23, Sb0.49Sn0.51 and Sorosite (CuSn or CuSb0.115Sn0.835), regardless of the substrate temperature or temperature of the propellant gas to be investigated. For a gas temperature above 300 °C, an increased microhardness was observed, which correlates with the appearance of a more homogenous distribution of Sb0.49Sn0.51 dispersed in a soft Sn-rich solid solution matrix.

The Microstructural Peculiarities of Beryllium Bronze after Heat Treatment

In this article, the microstructural peculiarities and properties of dispersion-hardened beryllium bronze with Ni and Ti are studied after quenching (780 °C) in a supersaturated solid solution and aging (320 °C, 3h). Decomposition of the α-solid solution matrix is implemented by means of an intermittent reaction with a primary allocation intermetallic χ-phase (type Be12Ti) with a VCT-lattice. It is shown that the strength properties (yield strength, micro-hardness) of the alloy more than double after aging.

Characteristics of Ni- Cr Binary Alloys Produced by Conventional Powder Metallurgy

The characteristics of Ni-Cr porous alloys containing 0.5 wt%Cr up to 12 wt%Cr were determined. The alloys were prepared from a mix of Ni-particles with filamentary shape and Cr-particles with irregular shape which then mixed with 0.5 wt% paraffin wax as a binder. The samples were formed by compaction and then sintered at 1200 °C for 1 h. The microstructure of samples was found to consist of a Ni-Cr solid solution matrix with X-ray energy dispersive analysis of Cr% less than 0.33 wt%. The matrix microstructure which composed of equiaxed grains (20-60 μm) surrounded high Cr content islands which also contained γ phase (Ni2.88 Cr1.22). The apparent density of the alloys was found to decrease with Cr content from 8.32 g/cm3 for samples containing 0.5 wt%Cr to 7.26 g/cm3 for samples containing 12 wt%Cr. Therefore, the estimated porosity was found to increase from 6.4% to 16.6% with increasing Cr content from 0.5 wt% to 12 wt%. The microhardness of the samples varied from 153.6 to 284.2 VHN for the equiaxed grains and from 119.6 to 240.6 VHN for the island areas.

A Study of Normalized Population Diversity in Particle Swarm Optimization

The values and velocities of a Particle swarm optimization (PSO) algorithm can be recorded as a series of matrix and its population diversity can be considered as an observation of the distribution of matrix elements. Each dimension is measured separately in the dimension-wise diversity. On the contrary, the element-wise diversity measures all dimensions together. In this chapter, the PSO algorithm is first represented in the matrix format. Then, based on the analysis of the relationship between pairs of vectors in the PSO solution matrix, different normalization strategies are utilized for dimension-wise and element-wise population diversity, respectively. Experiments on benchmark functions are conducted. Based on the simulation results of 10 benchmark functions (including unimodal/multimodal function, separable/non-separable function), the properties of normalized population diversities are analyzed and discussed.

Interfacial Dilational Viscoelasticity of Adsorption Layers at the Hydrocarbon/Water Interface: The Fractional Maxwell Model

In this communication, the single element version of the fractional Maxwell model (single-FMM or Scott–Blair model) is adopted to quantify the observed behavior of the linear interfacial dilational viscoelasticity. This mathematical tool is applied to the results obtained by capillary pressure experiments under low-gravity conditions aboard the International Space Station, for adsorption layers at the hydrocarbon/water interface. Two specific experimental sets of steady-state harmonic oscillations of interfacial area are reported, respectively: a drop of pure water into a Span-80 surfactant/paraffin-oil matrix and a pure n-hexane drop into a C13DMPO/TTAB mixed surfactants/aqueous-solution matrix. The fractional constitutive single-FMM is demonstrated to embrace the standard Maxwell model (MM) and the Lucassen–van-den-Tempel model (L–vdT), as particular cases. The single-FMM adequately fits the Span-80/paraffin-oil observed results, correctly predicting the frequency dependence of the complex viscoelastic modulus and the inherent phase-shift angle. In contrast, the single-FMM appears as a scarcely adequate tool to fit the observed behavior of the mixed-adsorption surfactants for the C13DMPO/TTAB/aqueous solution matrix (despite the single-FMM satisfactorily comparing to the phenomenology of the sole complex viscoelastic modulus). Further speculations are envisaged in order to devise combined FMM as rational guidance to interpret the properties and the interfacial structure of complex mixed surfactant adsorption systems.

MULTICOMPONENT Al-BRONZE COATINGS THERMALLY SPRAYED ONTO TIN BRONZE SUBSTRATE: MICROSTRUCTURAL, MECHANICAL AND CORROSION CHARACTERIZATION IN A 3.5% NaCl SOLUTION

In this work, multicomponent Al-bronze alloys coated Tin-Bronze substrates, fabricated by thermal flame spraying, are characterized by X-ray diffraction and scanning electron microscopy coupled with energy dispersive spectroscopy. Mechanical characterizations are also presented: microhardness measurement and friction coefficient. The electrochemical behavior of tin-bronze samples uncoated and coated with multicomponent Al-Bronze coatings is studied in NaCl 3.5% solutions using potentiodynamic polarization curves and polarization resistance measurements. The microstructure of the coatings has a lamellar morphology. Each lamella is constituted of a mixture of Cu3Al globular micro precipitates ([Formula: see text]-phase) uniformly distributed over the solid solution matrix ([Formula: see text]-Cu). An oxide based on Cu, Al and Fe is also present in very low concentration. [Formula: see text]-phase is unexpected because it is present only above 570∘C in the Cu-Al phase diagram. Compared with the tin-bronze substrate, multicomponent Al-bronze coatings show a friction coefficient three times lower and have a better electrochemical behavior in 3.5% NaCl solution.