Matrix Formulation Research Articles

Morphological and physicochemical behaviors of borneol precipitates

Since borneol is a water-insoluble bicyclic monoterpene alcohol which could be soluble in some organic solvents, it is possible for using as matrix former of solvent removal-based in situ forming matrix (ISM) formulation. In this study, borneol was dissolved in organic solvents of ISM including N-methyl pyrrolidone (NMP), dimethyl sulfoxide (DMSO), 2-pyrrolidone (PYR), and using ethanol as a controlled solvent. Borneol precipitates (B precipitate) and intact borneol (intact B) were characterized by infrared spectroscopy (IR), powder X-ray diffractometry (PXRD), differential scanning calorimetry (DSC), and thermogravimetric analysis (TGA). Moreover, the behavior of borneol solutions after injection into phosphate buffer pH 6.8 was also investigated which borneol in DMSO and NMP exhibited faster matrix formation. All B precipitates showed similar peaks of function groups in IR spectra as intact B. They exhibited a degradation temperature less than intact B whereas the melting temperature of all B precipitates was rather higher than intact B. The crystallinity of B precipitates was decreased as compared with intact B in which B precipitate from DMSO exhibited the lowest crystallinity change. Thus, DMSO was considered as the most suitable solvent for borneol-ISM whereas NMP and PYR also showed the potential. These obtained data of physicochemical characteristics are useful for developing borneol-based ISM formulation using a solvent-removal technique.

Inverse dynamics in rigid body mechanics

Inverse Dynamics is used to calculate the forces and moments in the joints of multibody systems investigated in fields such as Biomechanics or Robotics. In a didactic spirit, this paper begins with an overview of the derivations of the kinematical and dynamical equations of rigid bodies from the point of view of modern Continuum Mechanics. Then, it introduces a matrix formulation for the solution of Inverse Dynamics problems and, finally, reports a simple two-dimensional example of application to a problem in Biomechanics.

Change Detection in Dual Polarization Sentinel-1 Data With Wilks’ Lambda

When the covariance matrix formulation is used for multilook polarimetric synthetic aperture radar (SAR) data, Wilks' Lambda can be used for change detection between acquisitions at two time points. We briefly describe the theory for dual polarization, diagonal only data. A case study illustrates the technique on Sentinel-1 C-band data covering the international Frankfurt Airport. We successfully detect change including direction of change in the sense that Wilks' Lambda shows whether radar signal increases or decreases over time.

Bioactive Nanofiber Matrix Formulations for the Delivery of Exendin-4 for Tendon Regeneration: In Vitro and in Vivo Assessment

Bioactive Nanofiber Matrix Formulations for the Delivery of Exendin-4 for Tendon Regeneration: In Vitro and in Vivo Assessment

Robust Mixed Performance Control of Uncertain T-S Fuzzy Systems With Interval Time-Varying Delay by Sampled-Data Input

In this paper, a sampled-data parallel distributed compensator (PDC) is proposed to guarantee mixed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{2}/H_{\infty }$ </tex-math></inline-formula> performance of uncertain T-S fuzzy systems with interval time-varying delay and linear fractional perturbations. A full matrix formulation approach is developed to present our main results in LMI conditions. To achieve better results, new inequality and Lyapunov-Krasovskii functional are developed to improve the conservativeness of the proposed results. Finally, some numerical examples are illustrated to show the use of our main results. In this paper, interval time-varying delay and interval sampling are considered instead of constant delay and periodic sampling in published literatures.

An optimum design of one dimensional photonic crystal for solar cell applications

Efficient anti reflection (AR) coatings and back reflectors are crucial components for the better performance of a solar cell. Hence perfect designing of the same is very important. We propose the design of both these structures based on a multilayer dielectric system, a one dimensional photonic crystal, with maximum efficiency on the basis of optical interference transfer matrix theory. Optical parameters were optimized and transmission and reflection spectra were obtained using transfer matrix formulation via a personal computer using MATLAB program. Theoretical analysis has shown that a triple layer AR coating and a DBR based back reflector effectively enhance the efficiency of a solar cell.

Rapid Prediction of Effect of Ferrous Iron on the Stability of Emulsion Explosives Matrix

Designing an emulsified matrix formulation in the laboratory, the ratios of the emulsifier span-80 and T-152 were 1:0, 2:1, 1:2, 0:1 respectively. Then the preparation was added by 0.04% Fe2+ impurities emulsion matrix. Based on the water-soluble test method, we used ultrasonic instrument to focus on emulsion matrix containing Fe2+ impurities. The results show that the crystallization amount of emulsion matrix by adding Fe2+ is more than that of not adding Fe2+ .Impurities Fe2+ has damaging effects on the stability of its interface membrane. At the same time, ultrasound can accelerate the speed of demulsification of emulsion matrix. As composite emulsifiers span-80: T-152=1:2, the stability of emulsion matrix is the best.

The Effects of Formulation on Imidacloprid Dissipation in Grapes and Vine Leaves and on Required Pre-Harvest Intervals under Lebanese Climatic Conditions.

In this study, imidacloprid, a systemic insecticide, currently having a specified European Commission MRL value for vine leaves (2 mg kg−1), was applied on a Lebanese vineyard under different commercial formulations: as a soluble liquid (SL) and water dispersible granules (WDG). In Lebanon, many commercial formulations of imidacloprid are subject to the same critical good agricultural practice (cGAP). It was, therefore, important to verify the variability in dissipation patterns according to matrix nature and formulation type. Random samplings of grapes and vine leaves were performed starting at 2 days until 18 days after treatment. Residue extractions were performed according to the QuEChERS method and the analytical determination using liquid chromatography coupled to tandem mass spectrometry (LC-MS-MS). The SL formulation yielded significantly higher initial deposit than the WDG formulation on grapes and vine leaves. The formulation type did not significantly affect the dissipation rates; the estimated half-lives in grapes and vine leaves were 0.5 days for all imidacloprid formulations. No pre-harvest intervals were necessary on grapes. PHIs of 3.7 days for the SL formulation and 2.8 days for the WDG formulation were estimated on vine leaves. The results showed that the type of formulation and the morphological and physiological characteristics of the matrix had an effect on the initial deposits, and thus residue levels, but not on the dissipation patterns.

Design and finite element study of Kevlar based combat helmet for protection against high-velocity impacts

High-velocity impact-resistant helmets are used by police forces, law enforcement and military personnel, firefighters, as well as civilians working in construction, manufacturing, mining and material handling industries among other sectors as protection against impact damage caused by projectiles of various shapes and sizes. In this study, an attempt was made to investigate the impact-resistance of fiber-reinforced polymer composite based helmets through finite element analysis. The composite helmets were modelled in different sacking sequences using bi-directional woven fabrics such as Kevlar-129 (K), 3 K-Carbon (C) and EC9-Glass (G) fabrics as reinforcements and an epoxy matrix formulation. Investigation was focused to study the high-velocity impact resistance and energy absorption performance of composite helmets in hybrid and non-hybrid stacking sequences such as KKK, KGK, KCK, KCG and GCK subjected to high-velocity impact simulations at 398 m.s−1. It was observed that neat Kevlar and Kevlar-glass sandwich hybrid composite helmets withstood the projectile, while all other hybrid helmets were completely perforated during impact. It was also found that Kevlar-glass sandwich helmets offered cost savings of about 21% compared to neat Kevlar-epoxy composite. Hence Kevlar-glass sandwich composite can be used to develop protective helmets due to their attractive impact resistance properties and lower cost. The variation in helmet weight among all the considered composite material combinations was only about 5%.

Temperature-dependence of riboflavin phosphorescence in cryosolvents

The molecular mobility of amorphous excipients is important for the stability of biomaterials during preservation, facilitating matrix formulation and product design. Phosphorescence spectroscopy is a sensitive optical method to study molecular mobility. However, there is a need to expand the pool of probes available for analysis since molecules differ in sensitivity. This research explored the feasibility and limitations of using riboflavin as a phosphorescent probe for monitoring matrix molecular mobility. Phosphorescence decays of riboflavin in four amorphous cryosolvents (aqueous solutions of glycerol, ethanol, sucrose, and dextran) were collected at 77 K to capture its natural phosphorescence lifetime (estimated at 170 ms). Decays were also collected during ballistic heating to assess the sensitivity of riboflavin towards changes in matrix molecular mobility. Riboflavin exhibited good sensitivity towards matrix secondary relaxations in the glass, indicating that riboflavin has excellent potential as an edible phosphorescent probe for molecular mobility in food and pharmaceutical products.

Gramian-constrained optimization process for the stiffness model identification of industrial manipulators

AbstractThis work deals with the elastostatic identification of industrial manipulators. By reviewing the basics of the physical elastic properties of both links and joints in the framework of the lumped stiffness modeling techniques, the Gramian nature of the stiffness matrices has been found out adequate to do so. Then, a novel optimization method has been developed, which incorporates the Gramian matrix formulation along a non-linear optimization process, acting as an intrinsic constraint for the conservativeness of the elastostatic modeling. Numerical and experimental analyses evince the effectiveness of the proposed method, as the elastostatic models obtained by means of the proposed technique predict more than 93.7% of the compliance deviations of a real industrial robot. The proposed method is simple enough to be jointly applicable to the most recent elastostatic model reduction techniques.

Zero-order achromatic variable-wave retarder in standard single-mode optical fiber

In this work, we present numerically and experimentally a zero-order achromatic variable-wave retarder (AVWR) in a standard optical fiber. The model is based on Pancharatnam’s model including three concatenated variable wave retarders (VWR). The results show high degree of achromaticity over 100 nm from 1500 to 1600 nm covering the Erbium band. In order to explain the AVWR ellipticity and azimuth behavior, we carry out a numerical simulation based on the Jones matrix formulation and compared it directly with a single VWR.

Single‐layer tri‐state switching as an economical method to address linear light‐emitting diode arrays

This paper reports on new schemes based on the concept of tri-state switching for routing linear arrays of light-emitting diodes (LEDs) on slim substrates. The schemes use a minimal number of wires in single-metal planar technologies, where wires are not allowed to cross. They have in common that the number of LEDs, NL, addressable by NW wires is given by NL = 4NW − 6. The designs are built on a family of hierarchically interconnected structures with (2n+1 − 2) LEDs and (2n−1 + 1) wires, for positive integers n. A process termed linear expansion straightforwardly extends them to arbitrary values of NW and adds 4 LEDs with each additional wire. Expressions for series resistances and the average wire length normalized to the array length are derived. In hierarchical designs, the average normalized wire length asymptotically approaches 7/12 for large n. A matrix formulation graphically elucidates the new interconnection schemes.

A matrix approach to get the variance of the square of the fluctuation function of the DFA

The fluctuation analysis (FA) and the detrended fluctuation analysis (DFA) make it possible to estimate the Hurst exponent H, which characterizes the self-similarity of a signal. Both are based on the fact that the so-called fluctuation function, which can be seen as an approximation of the standard deviation of the process scaled in time by multiplying the time variable by a positive constant, depends on H. The main novelty of the paper is to provide the expression of the variance of the square of the fluctuation function, by using a matrix formulation. We show that it depends on the correlation function of the signal under study when it is zero-mean and Gaussian. Illustrations are given when dealing with a zero-mean white Gaussian noise. Moving average processes and first-order autoregressive processes are also addressed.

A spectral element approach to computing normal modes

SUMMARYWe introduce a new approach to the computation of gravito-elastic free oscillations or normal modes of spherically symmetric bodies based on a spectral element discretization of the radial ordinary differential equations. Our method avoids numerical instabilities often encountered in the classical method of radial integration and root finding of the characteristic function. To this end, the code is built around a sparse matrix formulation of the eigenvalue problem taking advantage of state-of-the-art parallel iterative solvers. We apply the method to toroidal, spheroidal and radial modes and we demonstrate its versatility in the presence of attenuation, fluid layers and gravity (including the purely elastic case, the Cowling approximation, and full gravity). We demonstrate higher-order convergence and verify the software by computing seismograms and comparing these to existing numerical solutions. Finally, to emphasize the general applicability of our code, we show spectra and eigenfunctions of Earth, Mars and Jupiter’s icy moon Europa and discuss the different types of modes that emerge.

Microstructure-based analysis of residual stress concentration and plastic strain localization followed by fracture in metal-matrix composites

A numerical study is performed to investigate the deformation and fracture in metal matrix – ceramic particle composites using Al6061T6 and ZrC as an example of the compound materials. The step-by-step packing method is adopted for generating three-dimensional model microstructures of metal-matrix composites, with the irregular shape of particles and polycrystalline structure of the matrix being taken into account. The dynamic boundary-value problems are solved by the finite-element method. Constitutive models describing the mechanical behavior of the composite compounds include anisotropic elasticity, crystal plasticity with the strain hardening and strain fracture criterion for the matrix and isotropic elastic-brittle formulation with the stress fracture criterion for particles. A user-defined subroutine is developed to combine the anisotropic matrix and isotropic particle responses and implemented in the finite element calculations of the composite thermomechanical behavior. The interrelated plastic strain localization in the aluminum matrix and crack origination and growth in the matrix and ceramic particle are investigated under compression and tension, including the influence of the cooling-induced residual stresses. A detailed analysis is performed to evaluate the residual stress concentration in local regions of bulk tension formed under all-round and uniaxial compression of the composite due to the concave and convex interfacial asperities.

Pentanacci and Pentanacci-Lucas hybrid numbers

The aim of this study is to introduce the Pentanacci and Pentanacci-Lucas hybrid numbers. Then, some properties with respect to these special numbers and relations between them are obtained. In addition, matrix formulations, generating functions, Binet- like formulas and some summation formulas of them are examined.

Optimal Control for Quantum Optimization of Closed and Open Systems

We provide a rigorous analysis of the quantum optimal control problem in the setting of a linear combination $s(t)B+(1-s(t))C$ of two noncommuting Hamiltonians $B$ and $C$. This includes both quantum annealing (QA) and the quantum approximate optimization algorithm (QAOA). The target is to minimize the energy of the final ``problem'' Hamiltonian $C$, for a time-dependent and bounded control schedule $s(t)\in [0,1]$ and $t\in \mc{I}:= [0,t_f]$. It was recently shown, in a purely closed system setting, that the optimal solution to this problem is a ``bang-anneal-bang'' schedule, with the bangs characterized by $s(t)= 0$ and $s(t)= 1$ in finite subintervals of $\mc{I}$, in particular $s(0)=0$ and $s(t_f)=1$, in contrast to the standard prescription $s(0)=1$ and $s(t_f)=0$ of quantum annealing. Here we extend this result to the open system setting, where the system is described by a density matrix rather than a pure state. This is the natural setting for experimental realizations of QA and QAOA. For finite-dimensional environments and without any approximations we identify sufficient conditions ensuring that either the bang-anneal, anneal-bang, or bang-anneal-bang schedules are optimal, and recover the optimality of $s(0)=0$ and $s(t_f)=1$. However, for infinite-dimensional environments and a system described by an adiabatic Redfield master equation we do not recover the bang-type optimal solution. In fact we can only identify conditions under which $s(t_f)=1$, and even this result is not recovered in the fully Markovian limit. The analysis, which we carry out entirely within the geometric framework of Pontryagin Maximum Principle, simplifies using the density matrix formulation compared to the state vector formulation.

Multi-Robot Routing Problem with Min–Max Objective

In this paper, we study the “Multi-Robot Routing problem” with min–max objective (MRR-MM) in detail. It involves the assignment of sequentially ordered tasks to robots such that the maximum cost of the slowest robot is minimized. The problem description, the different types of formulations, and the methods used across various research communities are discussed in this paper. We propose a new problem formulation by treating this problem as a permutation matrix. A comparative study is done between three methods: Stochastic simulated annealing, deterministic mean-field annealing, and a heuristic-based graph search method. Each method is investigated in detail with several data sets (simulation and real-world), and the results are analysed and compared with respect to scalability, computational complexity, optimality, and its application to real-world scenarios. The paper shows that the heuristic method produces results very quickly with good scalability. However, the solution quality is sub-optimal. On the other hand, when optimal or near-optimal results are required with considerable computational resources, the simulated annealing method proves to be more efficient. However, the results show that the optimal choice of algorithm depends on the dataset size and the available computational budget. The contribution of the paper is three-fold: We study the MRR-MM problem in detail across various research communities. This study also shows the lack of inter-research terminology that has led to different names for the same problem. Secondly, formulating the task allocation problem as a permutation matrix formulation has opened up new approaches to solve this problem. Thirdly, we applied our problem formulation to three different methods and conducted a detailed comparative study using real-world and simulation data.

Mathematical modeling of fully coupled reinforced Magneto-Electro-Thermo-Mechanical effective properties based on conditioned micromechanics

This paper deals with a mathematical modeling of fully coupled reinforced magneto-electro-thermo-mechanical behaviors. The modeling is based on micro–macro transition inclusion problem using the localization and concentration tensors. Various micromechanical modelings are elaborated mainly the Mori–Tanaka, self-consistent, incremental self consistent and the differential approaches. The higher dispersion between the magneto-electro-elastic properties leads to ill-conditioned concentration tensors. This drawback is point out here and a remedy based on block matrix formulations leading to well-conditioned tensors is proposed. The effective magneto-electro-thermo-elastic moduli are derived as a function of the resulting well-conditioned magneto-electro-thermo-mechanical concentration tensors. These properties are derived for different inclusion’s volume fraction, types, and shapes, and compared with the existing results.