Добірка наукової літератури з теми "Multiparametric Solution"

Inspired by Reshetikhin's twisting procedure to obtain multiparametric extensions of a Hopf algebra, a general "symmetry transformation" of the "particle conserving" R-matrix is found such that the resulting multiparametric R-matrix, with a spectral parameter as well as a color parameter, is also a solution of the Yang–Baxter equation (YBE). The corresponding transformation of the quantum YBE reveals a new relation between the associated quantized algebra and its multiparametric deformation. As applications of this general relation to some particular cases, multiparametric and colored extensions of the quantum group GL q(N) and the Yangian algebra Y(glN) are investigated and their explicit realizations are also discussed. Possible interesting physical applications of such extended Yangian algebras are indicated.

Free vibration analysis of the porous functionally graded circular plates has been presented on the basis of classical plate theory. The three defined coupled equations of motion of the porous functionally graded circular/annular plate were decoupled to one differential equation of free transverse vibrations of plate. The one universal general solution was obtained as a linear combination of the multiparametric special functions for the functionally graded circular and annular plates with even and uneven porosity distributions. The multiparametric frequency equations of functionally graded porous circular plate with diverse boundary conditions were obtained in the exact closed-form. The influences of the even and uneven distributions of porosity, power-law index, diverse boundary conditions and the neglected effect of the coupling in-plane and transverse displacements on the dimensionless frequencies of the circular plate were comprehensively studied for the first time. The formulated boundary value problem, the exact method of solution and the numerical results for the perfect and imperfect functionally graded circular plates have not yet been reported.

Abstract This work proposes an approach to estimate the parameters of capacitance and inductance in a boost converter using an explicit solution. A multiparametric programming (MPP) algorithm is fundamental to the suggested methodology, which aims to develop parameters as explicit functions of measurements. In this method, the generalised mathematical model of the boost converter is discretised into an algebraic equation. The parameter estimation problem is then formulated and solved using Karush-Kuhn-Tucker. Finally, an explicit solution of estimate parameters such as capacitor and inductor is formulated as an explicit function of the inductor currents and capacitor voltage. Finally, the state variables of the boost converter are numerically obtained and used to test the capability of the proposed work. The results presented in this work prove the MPP algorithm can estimate the boost converter’s parameters, which can be extended to other power converters and filters.

Abstract Technology is advancing ever faster in all areas of human activity, making the objects around us ever more complicated. Notably, complex objects have multiple parameters that define their condition, whether normal, near-critical, critical, over-critical, etc. If critical infrastructures are in critical condition, their collapse jeopardizes not only the infrastructures, but also their environment. This is why timely maintenance and control of condition is imperative for complex objects. This paper dwells upon a method for monitoring and controlling the condition of a complex multiparametric object; the method uses a minimum number of monitored parameters to retain full data on the condition of a complex object, to optimize the periodicity of taking readings depending on the functional phase of the object, and to determine how object parameters relate to each other and how they affect the quality of its functioning; such minimization reduces computational complexity and the bandwidth requirement. Russian Invention Patents granted to the authors certify the novelty and practical significance of the proposed solution.

The design of a gravity retaining wall should be simple to construct, quick to build and the best economic solution to a problem. This can be achieved by using advanced optimization methods. Since geotechnical engineers are not always able to determine the exact soil properties and other project data, an optimal design of a gravity retaining wall should also be determined for a wide range of input parameters. Therefore, a multiparametric analysis of an optimal designed gravity retaining wall was carried out. Optimum designs of gravity retaining walls were obtained for 567 combinations of different design parameters. Diagrams were developed to help engineers determine the optimum section of the wall, based on construction costs. An exhaustive search was carried out within the available parameters (project data). The parameters were ranked according to which had the most influence on the optimum cost of the gravity retaining wall and the utilization of multiple constraints. The most important parameter for the optimal cost of a gravity retaining wall is the height of the retained ground, followed by the shear angle of the soil, the soil–wall interaction coefficient, the slope angle and the variable surcharge load. The shear angle of the soil is most relevant to the bearing capacity and eccentricity condition, while the soil–wall interaction coefficient is most relevant to the sliding condition. Since European countries apply different load, material and resistance safety factors, the optimization model was developed in a general form, where different design approaches and unit prices could be applied. The case study provides an improved optimization model for selecting the optimal design of gravity walls, for engineers.

Woven reinforced composites are often hindered by challenges in accurately predicting their mechanical behavior. This obstacle primarily stems from the heterogeneous nature of these materials. Consequently, employing multi-scale approaches becomes imperative to ascertain their overall responses under complex loading conditions, incorporating detailed descriptions of microstructure and the constitutive laws governing their components. However, effectively incorporating these methodologies into real-scale applications, particularly within FE² analyses, remains challenging due to the significant computational requirements. This challenge intensifies when numerous direct calculations are necessary for testing various configurations, a critical aspect in optimization, inverse analysis, or real-time simulations. The need for such calculations adds to the computational demands, posing a significant obstacle to integrated into practical applications. To address these issues, while considering the scale effects, this thesis aims to develop efficient numerical tools to achieve accurate and fast predictions of woven composite response. First, we develop virtual twins (multiparametric solution) for real-time prediction of composite response, using non-intrusive Proper Generalized Decomposition (PGD) based methods. This aims at providing an accurate approximation of these high-dimensional problems, that involved several microstructural parameters, with limited dataset. These multiparametric solutions are constructed for both linear and nonlinear behavior including history- and rate-dependent behaviors. Second, we develop an approach based on Artificial Neural Networks (ANNs) to perform a macroscopic surrogate model of composites. This model, referred to as Multiscale Thermodynamics Informed Neural Networks (MuTINN), is founded on thermodynamic principles and introduces specific quantities of interest that serve as internal state variables at the macroscopic level. This captures efficiently the state and evolution laws governing the history-dependent behavior of these composites while retaining the thermodynamic admissibility and the physical interpretability of their overall responses. This approach has successfully associated with FE code, streamlining the application of multiscale FE-MuTINN approach for composite structure computations. The prediction capabilities of the proposed approach are demonstrated across the material scales, exemplified through diverse instances of woven composite structures. These applications account for anisotropic yarn damage and an elastoplastic polymer matrix behavior. This promises a potential solution to alleviate the computational challenges associated with multiscale simulations of large composite structures and paving the way for the development of a hybrid twin solution
Although woven reinforced composites are experiencing rapid growth across various engineering and industrial domains, their widespread adoption is often hindered by challenges in accurately predicting their mechanical behavior. This obstacle primarily stems from the heterogeneous nature of these materials. Consequently, employing multi-scale approaches becomes imperative to predict their overall response under complex loading conditions, incorporating detailed descriptions of microstructure and the constitutive laws governing their components. However, effectively incorporating these methodologies into real-scale applications, particularly within FE² analyses, remains challenging due to the significant computational requirements they entail. This challenge intensifies when numerous direct calculations are necessary for testing various configurations, a critical aspect in optimization, inverse analysis, or real-time simulations. The need for such calculations adds to the computational demands, posing a significant obstacle to integrated into practical applications. To address these issues, while considering the scale effects, this thesis aims to develop efficient numerical tools to achieve accurate and fast predictions of woven composite response. First, we develop virtual twins (multiparametric solution) for real-time prediction of composite response, using non-intrusive Proper Generalized Decomposition (PGD) based methods. This aims at providing an accurate approximation of high-dimensional problems, that involved several microstructural parameters, with limited dataset. These multiparametric solutions are constructed for both linear and nonlinear behavior including history- and rate-dependent behaviors. Second, we develop an approach based on ANN to perform a macroscopic surrogate model of composites. This model, referred to as Multiscale Thermodynamics Informed Neural Networks (MuTINN), is founded on thermodynamic principles and introduces specific quantities of interest that serve as internal state variables at the macroscopic level. This captures efficiently the state and evolution laws governing the history-dependent behavior of these composites while retaining the thermodynamic admissibility and the physical interpretability of their overall responses. This approach has successfully associated with FE code, streamlining the application of multiscale FE-MuTINN approach for composite structure computations. The prediction capabilities of the proposed approach are demonstrated across the material scales, exemplified through diverse instances of woven composite structures. These applications account for anisotropic yarn damage and an elastoplastic polymer matrix behavior. This promises a potential solution to alleviate the computational challenges associated with multiscale simulations of large composite structures and paving the way for the development of a hybrid twin solution

This paper presents the design, fabrication and characterization of a novel multiparametric microelectromechanical (MEMS) biosensor based on live mammalian cells with capabilities of sensing the toxicity of field water with minimized false-positive rate. This biosensor combines two biosensing techniques, resonant frequency measurements and electric cell-substrate impedance sensing (ECIS) on a single chip. The sensor is based on the innovative placement of the working microelectrode for ECIS technique as the upper electrode of a quartz crystal microbalance (QCM) resonator. This multiparametric biosensor was characterized with bovine aortic endothelial cells (BAECs). Toxicity tests to study BAECs responsiveness to health-threatening concentrations of ammonia in de-ionized water as a toxicant model will also be presented. The increase of the resonant frequency and decrease of impedance of the biosensor indicated the detachment of cells as a result of toxicant stimulation of ammonia solution. These gravimetric and impedimetric measurements on the same cell monolayer demonstrate that the multiparametric biosensor is able to perform two types of measurements simultaneously and this sensor can successfully be tested with drinking water containing toxicants.

This paper proposes a new methodology for a multi parameter approach using the p-median. The optimized solution must fulfill the following criteria: It must minimize distances between cities without a university to a city that has a university; It must prioritize cities with a higher population; It must prioritize cities with a lower United Nation Human Development Index. The use of a multiparametric approach was only possible by introducing the concept of a generalized distance. The results compare the existing distribution of campuses of the Federal system with the best location resulting from the multi parameter method proposed here. Locations for expansion of the current established university in Amazonas State, Brazil, are proposed.

A method for parametric analysis of the stability loss boundary has been developed for periodic regimes of nonlinear forced vibrations for a first time. The method allows parametric frequency-domain calculations of the stability loss together with the vibration amplitudes and design parameter values corresponding to the stability boundaries. The tracing algorithm is applied to obtain the trajectories of stability loss points as functions of design parameters. The parametric stability loss is formulated for cases when: (i) the design parameters characterise the properties of nonlinear contact interfaces (e.g. gap, contact stiffness, friction coefficient, etc.) and (ii) the design parameters describe linear components of the analysed structure (e.g. parameters of geometric shape, material, natural frequencies, modal damping etc.) and (iii) these parameters describe the excitation loads (e.g. their level, distribution or frequency). An approach allowing the multiparametric analysis of stability boundaries is proposed. The method uses the multiharmonic representation of the periodic forced response and aimed at the analysis of realistic gas-turbine structures comprising thousands and millions degrees of freedom. The method can be used for the effective search of isolated branches of the nonlinear solutions and examples of detection and search of the isolated branches are given: for relatively small and for large-scale finite element models. The efficiency of the method for calculation of the stability boundaries and for the search of isolated branches is demonstrated on simple systems and on a large-scale model of a turbine blade.