Linear Approximation Research Articles

Thermal Test Apparatus for Mini Heat Sinks

Abstract Demands for more powerful and smaller electronic devices have increased the energy dissipation requirements. Accurate determination of the thermal performance of small sized heat sinks is necessary for innovation within the heat dissipation sector. This study designed, developed, and tested an apparatus for determining the thermal performance of mini heat sinks (MHS). The test apparatus consisted of a wind tunnel, fan, heater, heater block, five temperature sensors, air velocity sensor, and a data acquisition system. A robust dataset was created by testing the heater without a MHS and testing two different MHS materials of polycarbonate (PC) and aluminum (AL) and having 16 to 21 repeat tests. Linear and polynomial approximations for the temperature profile were explored. For the steady state tests, the mean and 90% confidence interval were calculated to determine statistically significant differences. The temperature gradient at the interface, rate of heat transfer, and the thermal resistances from the polynomial fit had higher variation than the linear fit. The experimentally determined heater surface temperature had a 90% confidence interval of ±0.3 to ±0.7°C. The 90% confidence intervals for the thermal resistances were 1.0 to 1.5 K/W for linear and 2.3 to 6.0 K/W for polynomial. Statistically significant differences for the temperature gradient at the interface, rate of heat transfer, and thermal resistances between the bare, PC, and AL were found. Due to heat losses, the linear fit had greater precision, but the polynomial fit had greater accuracy.

Understanding of Lithium-ion battery degradation using multisine-based nonlinear characterization method

The nonlinearity of lithium-ion battery voltage response has been recently gained high attention in battery characterization and health diagnosis. The multisine-based nonlinear characterization method has the potential for development as an expedient on-board technique for analyzing nonlinear responses. Despite this, it remains challenging to analyze the effect of aging degradation on LIB nonlinearity. In this study, the odd random-phase multisine method is performed on fresh and aged three-electrode experimental cells. This allowed for the separation of impedance-related linear approximation and odd or even order nonlinearity toward the full-cell voltage into their respective electrodes. The results demonstrate that, as the LIB degrades, the increase of impedance-related linear approximation estimated by the multisine-based method agrees well with the results of conventional EIS. The variation of nonlinearities is demonstrated in relation to the effect of degradation modes. The multisine-based method presents the advantage of simultaneously capturing impedance-related and nonlinearity information. This makes it become a fast diagnostic method that can be implemented in a BMS to quantify the causes of battery degradation, thereby supporting battery utilization optimization and future battery designs.

Identification of the Bandwidth of a Magneto-Inertial Navigation Filter

We address the analysis of a nonlinear navigation filter used in Magneto-Inertial Dead-Reckoning (MIDR) whose input data are provided by a home-made device. This filter takes the measurements given by the magnetic sensors as inputs and returns the velocity of the body. Therefore, any unmodeled time-varying disturbance in the measurements impacts the estimation of the velocity and yields errors that distort the estimation. For dimensioning purpose, we aim to identify the bandwidth of the linearized part of this filter. To derive a model of this bandwidth, we first simplify our filter as a time-invariant Single-Input Single-Ouput (SISO) system in the situation where the steady-state regime is reached. The Best Linear Approximation (BLA) of this nonlinear system can hence be described by a conventional transfer function. We justify the validity of such a linear approximation for Extended Kalman Filters (EKF) and identify it with different methods, yielding a model for the bandwidth depending on the experimental conditions of navigation. We show that our filter is actually suitable for pedestrian navigation. Finally, simulations in realistic physical situations are used for validation.

Electroosmotic flow and heat transfer characteristics of a class of biofluids in microchannels at high Zeta potential

Peristalsis is an important dynamic phenomenon in the field of biomedical research, and has great application prospects in microscale fluids. In recent years, this biomimetic (peristaltic) phenomenon has gained widespread attention due to its large-scale applications in various medical and industrial fields, such as radiation therapy, peristaltic blood pumps, and drug delivery systems. In this study, the electroosmotic flow and heat transfer characteristics are investigated under high wall Zeta potential and slip boundary conditions for a certain type of biological fluid that satisfies the Newtonian fluid model. Fluid flows under the joint action of external electric field, magnetic field, and Joule heating. Firstly, without using the Debye-Hückel linear approximation, the numerical solutions are given by using the Chebyshev spectral method for the nonlinear Poisson-Boltzmann equation, the fourth-order differential equation satisfied by the stream function, and the thermal energy equation. The results are compared with those obtained by using the Debye-Hückel linear approximation to demonstrate the effectiveness of the numerical method used in this study. Secondly, the effects of wall Zeta potential, Hartmann number <inline-formula><tex-math id="M11">\begin{document}$H$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231685_M11.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231685_M11.png"/></alternatives></inline-formula>, electroosmotic parameter <inline-formula><tex-math id="M12">\begin{document}$m$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231685_M12.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231685_M12.png"/></alternatives></inline-formula>, slip parameter <inline-formula><tex-math id="M13">\begin{document}$\beta $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231685_M13.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231685_M13.png"/></alternatives></inline-formula> are discussed on the flow characteristics, peristaltic pumping, and trapping phenomena under electromagnetic environments, and the influence of Joule heating parameter <inline-formula><tex-math id="M14">\begin{document}$\gamma $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231685_M14.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231685_M14.png"/></alternatives></inline-formula> and Brinkman number <inline-formula><tex-math id="M15">\begin{document}$Br$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231685_M15.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231685_M15.png"/></alternatives></inline-formula> is explored on heat transfer characteristics. The results show that 1) wall Zeta potential plays an important role in controlling the velocity of fluid peristaltic flow; 2) the increase of electroosmotic parameter <inline-formula><tex-math id="M16">\begin{document}$m$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231685_M16.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231685_M16.png"/></alternatives></inline-formula> and slip parameter <inline-formula><tex-math id="M17">\begin{document}$\beta $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231685_M17.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231685_M17.png"/></alternatives></inline-formula> increases the flow velocity in the central region of the channel, while the increase of Hartmann number <inline-formula><tex-math id="M18">\begin{document}$H$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231685_M18.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231685_M18.png"/></alternatives></inline-formula> hinders the flow of fluid; 3) these flow behaviors exhibit opposite trends near the channel walls; 4) the number of streamlines captured by peristaltic transport decreases with Hartmann number <inline-formula><tex-math id="M19">\begin{document}$H$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231685_M19.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231685_M19.png"/></alternatives></inline-formula> and electroosmotic parameter <inline-formula><tex-math id="M20">\begin{document}$m$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231685_M20.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231685_M20.png"/></alternatives></inline-formula> increasing; 5) the increase of Joule heating parameter <inline-formula><tex-math id="M21">\begin{document}$\gamma $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231685_M21.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231685_M21.png"/></alternatives></inline-formula> and Brinkman number <inline-formula><tex-math id="M22">\begin{document}$Br$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231685_M22.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231685_M22.png"/></alternatives></inline-formula> leads temperature to rise.

Effects of nonlinear thermal radiation on the efficiency of building integrated photovoltaic systems with nanofluid cooling.

The nonlinear effects of thermal radiation on the free convection flow of certain nanofluids along a heated wall are studied numerically using an original finite-difference method. Nanofluids are used to improve the performance of flat and curved integrated photovoltaic modules. The partial differential equations governing the flow are difficult to solve due to the strong non-linearity of the radiative term. In contrast to previous studies, the problem is solved directly without linearization by Rosseland's nonlinear approximation. The proposed numerical method is validated with results from the literature. The effects of nonlinearity and various physical parameters such as time, volume fraction and radiation parameter on the velocity, temperature, Nusselt number and skin friction coefficient of the CuO-water nanofluid are analyzed and presented graphically. A comparative study between the solutions given by the linear and non-linear problems reveals that Rosseland's linear approximation is no longer valid when the effect of thermal radiation is significant. On the other hand, the non-linear model better reflects the physical phenomena involved in the cooling process. Finally, a comparison of the performance of five nanofluids (CuO, Ag, Al2O3, Cu and TiO2 in water) shows that the Cu-water nanofluid performs best, with a high heat transfer rate and low shear stresses.

The interface instability development induced by the bulk density perturbations in accelerated media

The development of hydrodynamic instabilities has a significant impact on the operation of laser fusion systems. During radiation compression, the shells of a target are accelerated, resulting in the growth of perturbations at their interfaces. In this paper, we study the influence of density perturbations on the stability of the contact boundary during accelerated motion. The analysis is performed in a two-dimensional planar formulation using the linear approximation and assuming a weak spatial dependence on the temperature near the contact boundary. Due to the consideration of small time intervals, the phenomenon of heat conduction is not taken into account. The cases of acceleration of a medium described by the Mie–Grüneisen equation of state (EoS) into a vacuum and of acceleration of two contacting media, each described by the ideal plasma EoS, are considered. The time dependence of the amplitude of the boundary perturbation on time is obtained. The obtained values are in agreement with the results of numerical analysis. It is shown that the boundary curvature occurs independently of the acceleration direction. The theoretical results are compared with numerical results for laser fusion systems.

Economic Model Predictive Control in Buildings Based on Piecewise Linear Approximation of Predicted Mean Vote Index

Energy shortage is a challenge for many countries, and building energy consumption accounts for a considerable proportion of global energy consumption. The main work of this paper is to optimize the energy consumption of heating, ventilating, and air conditioning (HVAC) systems in buildings based on economic model predictive control (EMPC). The cost in EMPC design includes energy consumption and predicted mean vote (PMV), which is an index that evaluates the thermal comfort of indoor occupants. In order to model the nonlinearity of the PMV index, we propose a lattice piecewise linear (PWL) approximation, which has high approximation precision and facilitates the resulting optimization problem, which is basically a piecewise quadratic programming problem. For the piecewise quadratic programming, we propose a descent algorithm that converges quickly and scales well with the length of the prediction horizon in the EMPC problem. The experimental results demonstrate that the proposed method saves 19.78% of the electricity cost compared to the conventional control strategy and significantly increases indoor comfort. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> — The motivation of this article is to provide a control strategy to reduce building energy consumption and ensure indoor thermal comfort. In most of the existing methods for air conditioning temperature control, the occupants’ comfort hasn’t been considered. In this paper, thermal comfort is described by the PMV index, which is basically nonlinear. In order to model the thermal comfort more accurately, in this paper, the PMV index is approximated piecewise linearly in order to meet the requirements of accuracy and computational efficiency. The resulting optimization problem is not hard to solve, and we provide an efficient algorithm for solving this optimization problem. Preliminary simulation experiments demonstrate that this approach is practical, i.e., it achieves energy reduction and ensures thermal comfort. Our strategy, however, has not yet been deployed in real buildings. In future research, we will propose similar techniques for large-scale systems in order to solve energy optimization problems containing multiple thermal zones and realize the proposed technique in real buildings.

Scattering of gravity-capillary waves on a bottom step

Under the linear approximation, we study the scattering of gravity-capillary waves on a bottom step. The boundary conditions can be satisfied by considering a countable number of evanescent modes that are localized near the bottom step. Such modes have certain specific features compared to similar modes for pure gravity waves. In particular, there exists an extra mode. When a numerical solution is calculated, this extra mode allows us to match in the fluid region and impose the additional condition at the surface, which arises for capillary gravity waves (and not for pure gravity waves). The approximate formulas are suggested for the transformation coefficients. By means of numerical calculations, we find the reflection and transmission coefficients of traveling waves and compare the results with the predictions of the approximate formulas. The approximate formulas are shown to agree well with the numerical data. Both numerical and approximate results agree with the energy flux conservation. We also study the wave transformation on the rectangular underwater bump and trench, which are straightforward extensions of our step calculations. We calculate the transformation coefficients numerically and illustrate the transformation by time-dependent results, which are also shown as animations in the supplementary material.

Radial nanotubes for nanoelectronics elements: structure and diffraction

Formulation of the problem. Nanotubes are promising objects for the development of nanoelectronic elements. The range of electronic properties of nanotubes can be significantly expanded by synthesizing structures on their surface. Such structures have a radial cylindrical lattice; a number of nanowires have a similar lattice. Radial crystals are a new group of cylindrical structures, the study of which is at an early stage. Therefore, it is necessary to develop both ideas about the structure of radial crystals and a method for their structural analysis. The aim. Consider the simplest radial structures and the features of diffraction by them. Results. A description of the close-packed structure of nanowires and atomic layers with bcc, fcc, and hcp radial lattices sorbed on the nanotube surfaces is proposed, taking into account the effect of radial relaxation. A linear approximation is proposed that makes it possible to quantitatively describe radial relaxation at the initial stage of block growth. The quantitative kinematic theory of Fraunhofer diffraction on achiral radial structures is considered as the basis for their structural analysis, and formulas relating the parameters of the direct and reciprocal lattices are obtained. The results of model calculations of scattering intensity distributions by layer planes of the reciprocal lattice of radial crystals and along the layer lines of their diffraction patterns are presented. Schemes of diffraction patterns of radial crystals with bcc, fcc, and hcp radial lattices are presented. The applicability of traditional selection rules and the significant dependence of the positions of pseudo-orthogonal reflections on the crystal size are shown. Practical significance. The proposed description of radial structures with bcc, fcc, and hcp radial lattices and the diffraction method of structural analysis of their achiral varieties will provide structural control of the products of their synthesis, which is necessary when carrying out a wide range of studies both at the stage of development work on the synthesis of nanoelectronic elements, and for technological control during their industrial production.

Logical analysis of data using linear approximation and heuristic algorithms for gene expression-based diagnostics

This research aims to develop a methodology that combines logical analysis of data with a white box model to predict the progression of chronic diseases. Such diseases represent a serious health problem, and accurate prediction and management are essential to improve patients’ quality of life. Current machine learning methods such as deep learning often have high accuracy, but their solutions are ‘black boxes’, making them difficult to understand. The research combines the best aspects of both methods to create more accurate and interpretable models for predicting the progression of chronic diseases. The methodology developed is expected to contribute to informative decision-making in medical practice, enrich knowledge in medical research and improve the quality of care for patients with chronic diseases.

Expected Policy Gradient for Network Aggregative Markov Games in Continuous Space.

In this article, we investigate the Nash-seeking problem of a set of agents, playing an infinite network aggregative Markov game. In particular, we focus on a noncooperative framework where each agent selfishly aims at maximizing its long-term average reward without having explicit information on the model of the environment dynamics and its own reward function. The main contribution of this article is to develop a continuous multiagent reinforcement learning (MARL) algorithm for the Nash-seeking problem in infinite dynamic games with convergence guarantee. To this end, we propose an actor-critic MARL algorithm based on expected policy gradient (EPG) with two general function approximators to estimate the value function and the Nash policy of the agents. We consider continuous state and action spaces and adopt a newly proposed EPG to alleviate the variance of the gradient approximation. Based on such formulation and under some conventional assumptions (e.g., using linear function approximators), we prove that the policies of the agents converge to the unique Nash equilibrium (NE) of the game. Furthermore, an estimation error analysis is conducted to investigate the effects of the error arising from function approximation. As a case study, the framework is applied on a cloud radio access network (C-RAN) by modeling the remote radio heads (RRHs) as the agents and the congestion of baseband units (BBUs) as the dynamics of the environment.

Mixture of hydrogen and methane under planetary interior conditions.

We employ first-principles molecular dynamics simulations to provide equation-of-state data, pair distribution functions (PDFs), diffusion coefficients, and band gaps of a mixture of hydrogen and methane under planetary interior conditions as relevant for Uranus, Neptune, and similar icy exoplanets. We test the linear mixing approximation, which is fulfilled within a few percent for the chosen P-T conditions. Evaluation of the PDFs reveals that methane molecules dissociate into carbon clusters and free hydrogen atoms at temperatures greater than 3000 K. At high temperatures, the clusters are found to be short-lived. Furthermore, we calculate the electrical conductivity from which we derive the non-metal-to-metal transition region of the mixture. We also calculate the electrical conductivity along the P-T profile of Uranus [N. Nettelmann et al., Planet. Space Sci., 2013, 77, 143-151] and observe the transition of the mixture from a molecular to an atomic fluid as a function of the radius of the planet. The density and temperature ranges chosen in our study can be achieved using dynamic shock compression experiments and seek to aid such future experiments. Our work also provides a relevant data set for a better understanding of the interior, evolution, luminosity, and magnetic field of the ice giants in our solar system and beyond.

Метод оценки времени нахождения дисперсных частиц в канале противоточной вихревой трубы

In this paper, the process of removing spherical particles from an incompressible fluid through the hot outlet of a vortex tube is investigated. The removal rate was estimated through computational simulations using OpenFOAM software. The numerical solution was carried out using denseParticleFoam solver of OpenFOAM, which implements the multiphase particle-in-cell (MP-PIC) method using the Eulerian approach for the continuous phase and the Lagrangian approach for the dispersed phase. Five series of numerical experiments were carried out, with variations in the initial particle position in the inlet stream and the density of the dispersed phase. Based on the results of the experiments, a relationship has been established between the density of particles and the time they remain in the vortex tube. The relationship between the particle density and the time it takes for the particles to reach the opposite end of the tube with a hot outlet diaphragm is demonstrated. The method of processing the obtained results is described. The possibility of using linear and quadratic approximations to estimate the residence time of particles in a tube channel is considered. For each set of experiments, confidence intervals and the mean absolute percentage error for the prepared approximation have been calculated.

A Simple Finite-Time Analysis of TD Learning with Linear Function Approximation

A Simple Finite-Time Analysis of TD Learning with Linear Function Approximation

Diffuse low-grade glioma: What is the optimal linear measure to assess tumor growth?

Radiological follow-up of diffuse low-grade gliomas (LGGs) growth is challenging. Approximative visual assessment still predominates over objective quantification due to the complexity of the pathology. The infiltrating character, diffuse borders and presence of surgical cavities demand LGG-based linear measurement rules to efficiently and precisely assess LGG evolution over time. We compared optimized 1D, 2D, and 3D linear measurements with manual volume segmentation as a reference to assess LGG tumor growth in 36 patients with LGG (340 magnetic resonance imaging scans), using the clinically important mean tumor diameter (MTD) and the velocity diameter expansion (VDE). LGG-specific progression thresholds were established using the high-grade gliomas-based RECIST, Macdonald, and RANO criteria, comparing the sensitivity to identify progression/non-progression for each linear method compared to the ground truth established by the manual segmentation. 3D linear volume approximation correlated strongly with manually segmented volume. It also showed the highest sensitivity for progression detection. The MTD showed a comparable result, whereas the VDE highlighted that caution is warranted in the case of small tumors with multiple residues. Novel LGG-specific progression thresholds, or the critical change in estimated tumor volume, were increased for the 3D (from 40% to 52%) and 2D methods (from 25% to 33%) and decreased for the 1D method (from 20% to 16%). Using the 3D method allowed a ~5-minute time gain. While manual volumetric assessment remains the gold standard for calculating growth rate, the 3D linear method is the best time-efficient standardized alternative for radiological evaluation of LGGs in routine use.

Off-Policy Prediction Learning: An Empirical Study of Online Algorithms.

Off-policy prediction-learning the value function for one policy from data generated while following another policy-is one of the most challenging problems in reinforcement learning. This article makes two main contributions: 1) it empirically studies 11 off-policy prediction learning algorithms with emphasis on their sensitivity to parameters, learning speed, and asymptotic error and 2) based on the empirical results, it proposes two step-size adaptation methods called and that help the algorithm with the lowest error from the experimental study learn faster. Many off-policy prediction learning algorithms have been proposed in the past decade, but it remains unclear which algorithms learn faster than others. In this article, we empirically compare 11 off-policy prediction learning algorithms with linear function approximation on three small tasks: the Collision task, the task, and the task. The Collision task is a small off-policy problem analogous to that of an autonomous car trying to predict whether it will collide with an obstacle. The and tasks are designed such that learning fast in them is challenging. In the Rooms task, the product of importance sampling ratios can be as large as 214 . To control the high variance caused by the product of the importance sampling ratios, step size should be set small, which, in turn, slows down learning. The task is more extreme in that the product of the ratios can become as large as 214 × 25 . The algorithms considered are Off-policy TD, five Gradient-TD algorithms, two Emphatic-TD algorithms, Vtrace, and variants of Tree Backup and ABQ that are applicable to the prediction setting. We found that the algorithms' performance is highly affected by the variance induced by the importance sampling ratios. Tree Backup, Vtrace, and ABTDare not affected by the high variance as much as other algorithms, but they restrict the effective bootstrapping parameter in a way that is too limiting for tasks where high variance is not present. We observed that Emphatic TDtends to have lower asymptotic error than other algorithms but might learn more slowly in some cases. Based on the empirical results, we propose two step-size adaptation algorithms, which we collectively refer to as the Ratchet algorithms, with the same underlying idea: keep the step-size parameter as large as possible and ratchet it down only when necessary to avoid overshoot. We show that the Ratchet algorithms are effective by comparing them with other popular step-size adaptation algorithms, such as the Adam optimizer.

TRANSFORMATIONAL MODEL OF A PLANE ROD DEFORMATION, RESTRAINED ON DOUBLE-SIDED SLIDING SUPPORTS

A linear transformational model of the dynamic deformation of a plane rod is constructed. The end sections of the plane rod are restrained on two-sided sliding supports of finite length, excluding the displacements of the surface points of end sections in the transverse direction. To describe the deformation process of restrained sections of the rod, the S.P. Timoshenko?s shear model is used. For unfixed part the classical Kirchhoff – Love model is used. The conditions for the kinematic coupling of the restrained and free sections of the rod are formulated. Based on the Hamilton – Ostrogradsky variational principle, the equations of motion, the corresponding boundary conditions, as well as the force conditions for the coupling of the sections are obtained in a geometrically linear approximation. Based on the obtained equations of motion, exact analytical solutions of free and forced harmonic oscillations problem of the plane rod were constructed. It is shown that within the framework of the deformation models used, the problems of longitudinal and bending vibrations of the rod are separated. Of these, bending vibrations occurring in a relatively low frequency range are of greatest practical interest. For them, numerical experiments were carried out to determine the three lower natural modes and frequencies of vibrations, as well as the dynamic response during resonant vibrations of a plane rod on the marked frequencies made of a unidirectional fiber composite based on ELUR-P carbon fiber and XT-118 epoxy. A significant transformation of transverse tangential stresses is shown during the transition through the boundaries from the free section of the rod to restrained one. Such transformation due to the difference in deformation models of the marked areas, as well as their pronounced localization in the areas of restrained areas located near the marked boundaries.

Method of calculation for dynamic strength of complex configuration frame structures of locomotives for transport engineering

The article presents a numerical and analytical method for studying the bending-longitudinal vibrations of the load-bearing frame of the locomotive frame of a complex configuration in the form of an elastic rod of variable cross-section with variable mass, bending and longitudinal stiffness, based on methods: piecemeal linear approximation, iterations and the Boundary Element Technology. Numerical studies are performed in C # and in MATHCAD 15.

Simultaneous topology design and optimization of PDE constrained processes based on mixed integer formulations

Simultaneous topological design and optimization of complex processes that are described by partial differential equations is a challenging but promising research area. Widely adopted nested and sequential approaches are mostly applicable based on heuristic solutions, hindering the theoretical improvement potential due to decentralized decision-making in subsequent stages with a significant number of trial-and-error procedures. This study introduces a mixed integer formulation addressing the governing equations and case-dependent topological constraints at each discretization point, enabling solutions through rigorous solvers under process-related constraints and objectives. Nonlinear expressions in the formulations are further tailored using piecewise linear approximations, still representing the major nonlinear trends through a mixed-integer linear nature to favor global optimality and benefit from computational advancements, when needed. Heat and Stokes flow problems are used as case studies to demonstrate the applicability of the methodology.

Геометрическая модель прогнозирования свойств систем с интервальными параметрами

We consider interval geometric modeling of complex multi parametric systems having a set of parameters of different character. Some of the parameters may have interval indefiniteness. System information basis is incomplete one. The processed information depends on continuous, discrete and conventional data. Geometric model has a form of matrix and each element of it corresponds to some state of the system. Each state is described by interval function of continuous input and output parameters. The set of interval functions generates some discrete set of multidimensional surfaces in discrete space. We use this approach and our modeling algorithm to find predictive model of drape coefficient. The algorithm is based on linear approximation of numerical factors in factor spaces. Interval functions make it possible for us to vary some numerical factors within the given intervals. As an example, the interval model of fabric drape coefficient is found. Fabric thickness and closeness of texture are considered as input parameters.