Discrete Approach Research Articles

Numerical simulation of high-frequency induction welding in longitudinal welded tubes

In the present paper the high-frequency induction welding process is studied numerically. The mathematical model comprises a harmonic vector potential formulation of the Maxwell equations and a quasi-static, convection dominated heat equation coupled through the Joule heat term and nonlinear constitutive relations. Its main novelties are a new analytic approach which permits to compute a spatially varying feed velocity depending on the angle of the Vee-opening and additional spring-back effects. Moreover, a numerical stabilization approach for the finite element discretization allows to consider realistic weld-line speeds and thus a fairly comprehensive three-dimensional simulation of the tube welding process.

Compressed sensing: a discrete optimization approach

We study the Compressed Sensing (CS) problem, which is the problem of finding the most sparse vector that satisfies a set of linear measurements up to some numerical tolerance. CS is a central problem in Statistics, Operations Research and Machine Learning which arises in applications such as signal processing, data compression, image reconstruction, and multi-label learning. We introduce an ℓ2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell _2$$\\end{document} regularized formulation of CS which we reformulate as a mixed integer second order cone program. We derive a second order cone relaxation of this problem and show that under mild conditions on the regularization parameter, the resulting relaxation is equivalent to the well studied basis pursuit denoising problem. We present a semidefinite relaxation that strengthens the second order cone relaxation and develop a custom branch-and-bound algorithm that leverages our second order cone relaxation to solve small-scale instances of CS to certifiable optimality. When compared against solutions produced by three state of the art benchmark methods on synthetic data, our numerical results show that our approach produces solutions that are on average 6.22%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$6.22\\%$$\\end{document} more sparse. When compared only against the experiment-wise best performing benchmark method on synthetic data, our approach produces solutions that are on average 3.10%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$3.10\\%$$\\end{document} more sparse. On real world ECG data, for a given ℓ2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell _2$$\\end{document} reconstruction error our approach produces solutions that are on average 9.95%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$9.95\\%$$\\end{document} more sparse than benchmark methods (3.88%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$3.88\\%$$\\end{document} more sparse if only compared against the best performing benchmark), while for a given sparsity level our approach produces solutions that have on average 10.77%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10.77\\%$$\\end{document} lower reconstruction error than benchmark methods (1.42%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1.42\\%$$\\end{document} lower error if only compared against the best performing benchmark). When used as a component of a multi-label classification algorithm, our approach achieves greater classification accuracy than benchmark compressed sensing methods. This improved accuracy comes at the cost of an increase in computation time by several orders of magnitude. Thus, for applications where runtime is not of critical importance, leveraging integer optimization can yield sparser and lower error solutions to CS than existing benchmarks.

Semi-analytical method for calculating ground vibrations from a tunnel in a homogeneous half-space with an irregular surface

This paper proposes a novel two-dimensional (2D) semi-analytical method for calculating ground vibrations from a tunnel situated in a homogeneous half-space with an irregular surface. The circular tunnel is conceptualized as an elastic solid, while the soil is modelled as an elastic, isotropic, and homogeneous half-space with an irregular surface. A virtual horizontal interface is introduced to divide the soil domain into an irregular region with an arbitrary-shaped surface and a half-space with a circular hollow. The wavefield scattered by the irregular surface is simulated by the boundary integral equation. Through the application of the discrete wavenumber approach and expansion of wavefield on the irregular surface, the boundary integral equation is transformed into a set of simultaneous matrix equations containing unknown expansion coefficients. By utilizing the transformation between cylindrical and plane waves, the boundary conditions on soil-tunnel interface are satisfied, yielding a solution for a harmonic point load acting on the tunnel in a half-space with an irregular surface. The proposed method can simulate topographies with arbitrary shapes and only requires the discretization of the irregular part of the ground surface, which provides a highly efficient tool to investigate the propagation characteristics of train-induced vibrations in complex topographies. The proposed method is verified through comparisons with the existing analytical methods and the finite element method. The dynamic responses of a tunnel embedded in a half-space with a Gaussian-shaped surface are meticulously investigated. A case study involving a site for the Shenzhen metro line 5 is performed. The numerical results demonstrate that the presence of irregular topography alters the distribution of ground vibrations, leading to significant differences in responses within the irregular region and certain disparities in the regular region. The effect of the location, size, and undulating direction of the irregular topography on ground vibrations is frequency-dependent.

A projection‐based quaternion discretization of the geometrically exact beam model

AbstractIn the present work the geometrically exact beam model is formulated in terms of unit quaternions. A projection‐based discretization approach is proposed which is based on a normalization of the quaternion approximation. The discretization relies on NURBS shape functions and, alternatively, on Lagrangian interpolation. The redundancy of the quaternions is resolved by applying the method of Lagrange multipliers. In a second step the Lagrange multipliers are eliminated circumventing the need to solve saddle point systems. The resulting finite elements retain the objectivity of the underlying beam formulation. Optimal rates of convergence are observed in representative numerical examples.

IAVRS-International Affective Virtual Reality System: Psychometric Assessment of 360° Images by Using Psychophysiological Data.

Virtual Reality is an effective technique for eliciting emotions. It provides immersive and ecologically valid emotional experiences while maintaining experimental control. Recently, novel VR forms like 360° videos have been used successfully for emotion elicitation. Some preliminary databases of 360° videos for emotion elicitation have been proposed, but they tapped mainly into an emotional dimensional approach and did not include a concurrent physiological assessment of an emotional profile. This study expands on these databases by combining dimensional and discrete approaches to validate a new set of 360° emotion-inducing images. Twenty-six participants viewed 46 immersive images, and their emotional reactions were measured using self-reporting, psychophysiological signals, and eye tracking. The IAVRS database can successfully elicit a wide range of emotional responses, including both positive and negative valence, as well as different levels of arousal. Results reveal an important correspondence between the discrete and dimensional models of emotions. Furthermore, the images that exhibit convergence between the dimensional and discrete emotional models are particularly impactful regarding arousal and valence values. The IAVRS database provides insights into potential relationships between physiological parameters and emotional responses. This preliminary investigation highlights the complexity of emotional elicitation processes and their physiological correlates, suggesting the need for further research to deepen our understanding.

How can hotels Co-create value through the localized mini bar in the room: discrete choice modeling approach with CSR strategies with local products

ABSTRACT Even though Hotel mini bars is an excellent service and product delivery channel during the guest stay, typical selections of varieties and displays have been used without innovative ideas. This study argues that Mini Bars in the hotel can be capitalized to share the Hotel’s Corporate Social Responsibility vision and enhance customer perception toward the hotel brands with revenue increase. The current study adopts Discrete Choice Modeling to investigate the best choice attributes and levels of hotel mini bar. The results address how the hotel and local industry can co-create value for the hotel, local businesses, and guests.

Stabilizing regions of dominant pole placement for second order lead processes with time delay using filtered PID controllers.

In order to handle second order lead processes with time delay, this paper provides a unique dominant pole placement based filtered PID controller design approach. This method does not require any finite term approximation like Pade to obtain the quasi-polynomial characteristic polynomial, arising due to the presence of the time delay term. The continuous time second order plus time delay systems with zero (SOPTDZ) are discretized using a pole-zero matching method with specified sampling time, where the transcendental exponential delay terms are converted into a finite number of poles. The pole-zero matching discretization approach with a predetermined sampling period is also used to discretize the continuous time filtered PID controller. As a result, it is not necessary to use any approximate discretization technique, such as Euler or Tustin, to derive the corresponding discrete time PID controller from its continuous time counterpart. The analytical expressions for discrete time dominant pole placement based filtered PID controllers are obtained using the coefficient matching approach, while two distinct kinds of non-dominant poles, namely all real and all complex conjugate, have been taken into consideration. The stabilizable region in the controller and design parameter space for the chosen class of linear second order time delay systems with lead is numerically approximated using the particle swarm optimization (PSO) based random search technique. The efficacy of the proposed method has been validated on a class of SOPTDZ systems including stable, integrating, unstable processes with minimum as well as non-minimum phase zeros.

The high-order exponential semi-implicit scalar auxiliary variable approach for the general nonlocal Cahn-Hilliard equation

The nonlocal Cahn-Hilliard equation with nonlocal diffusion operator is more suitable for the simulation of microstructure phase transition than the local Cahn-Hilliard equation. In this paper, based on the exponential semi-implicit scalar auxiliary variable method, the highly efficient and accurate schemes (in time) with unconditional energy stability for solving the nonlocal Cahn-Hilliard equation are proposed. On the one hand, we have demonstrated the unconditional energy stability and mass conservation for the nonlocal Cahn-Hilliard equation with its high-order numerical schemes in the continuous and discrete level carefully and rigorously. On the other hand, in order to reduce the calculation and storage cost in numerical simulation, we use the fast solver based on fast Fourier transform and conjugate gradient approach for spatial discretization. Some numerical simulations involving the Gaussian kernel are presented and show the stability, accuracy, efficiency and unconditional energy stability of the proposed schemes.

Tunable Emissive CsPbBr3/Cs4PbBr6 Quantum Dots Engineered by Discrete Phase Transformation for Enhanced Photogating in Field-Effect Phototransistors.

Precise control of quantum structures in hybrid nanocrystals requires advancements in scientific methodologies. Here, on the design of tunable CsPbBr3/Cs4PbBr6 quantum dots are reported by developing a unique discrete phase transformation approach in Cs4PbBr6 nanocrystals. Unlike conventional hybrid systems that emit solely in the green region, this current strategy produces adjustable luminescence in the blue (450nm), cyan (480nm), and green (510nm) regions with high photoluminescence quantum yields up to 45%, 60%, and 85%, respectively. Concentration-dependent studies reveal that phase transformation mechanisms and the factors that drive CsBr removal occur at lower dilutions while the dissolution-recrystallization process dominates at higher dilutions. When the polymer-CsPbBr3/Cs4PbBr6 integrated into a field-effected transistor the resulting phototransistors featured enhanced photosensitivity exceeding 105, being the highest reported for an n-type phototransistor, while maintaining good transistor performances as compared to devices consisting of polymer-CsPbBr3 NCs.

Rope–sheave contact transient analysis in hoisting operations with a bristle model and an arbitrary Lagrangian–Eulerian approach

AbstractThis paper describes the development of a computational model for the rope–sheave contact interaction in reeving systems when the ropes are modeled with an arbitrary Lagrangian–Eulerian approach. This discretization approach has been developed in previous publications as a general and systematic method for the modeling and simulation of reeving systems. However, the rope–sheave contact model was avoided assuming the no-slip contact condition. The contact model developed in this paper introduces specialized ALE-ANCF-cubic rope contact elements that are used to discretize the rope segment winded at the sheave. The contact is modeled using a set of virtual discrete bristles attached to material points in the mid-line of the rope in one end and in contact with the sheave in the other end. Therefore, a second Lagrangian mesh, apart of the ALE mesh used to discretize the rope, is used to define the fixed ends of the bristles. The kinematics and dynamics used to calculate the normal and tangential contact forces are described in detail. The contact model is 3D and can be used to analyze the contact with a sheave groove with arbitrary shape. The tangential contact force model can be used to describe stick and slip contact conditions and, to improve the simulation performance of the model, an LuGre regularization tangential contact force model is used. The rope-sheave contact model is used to analyze the behavior of a simple elevator system. The numerical results show that the static rope-sheave contact interaction agrees well with an analytical solution of the problem. Finally, the same elevator system is analyzed dynamically for a cabin ride of 8 meters with a steady velocity of 1 m/s. Results show that the normal and tangential contact forces during the steady velocity period are not so different from the static solution, but very different from the classical Creep Theory and Firbank’s Theory.

An optimization strategy for anchor point placement for underground coal mine area positioning

Coal mine underground positioning technology plays an important role in safe mining, personnel monitoring and dispatching, and post-disaster rescue. Recently, there has been an increasing interest in indoor localization due to the demand for location-based services. Diverse techniques have been described in the literature to improve indoor localization services, but their accuracy is significantly affected by the number and location of the anchors, which act as a reference point for localizing tags in a given space. This work describes APOTSA, a novel approach for discovering a high-quality placement of anchors to improve the accuracy of area-based indoor localization systems while requiring a shorter execution time than existing approaches. The proposed algorithm is based on Tabu search and optimizes the localization accuracy by minimizing the expected residence area, which indicates a geographical area containing the tag. APOTSA's effectiveness with respect to solution quality and time of execution is shown by evaluating different scenarios involving up to five anchors. Moreover, a simple yet effective discretization approach is introduced to speed up the calculations, and the trade-off between the running time and solution quality of our algorithm can be controlled by a parameter. Our results indicate that the expected residence area and the time of execution can be reduced by up to 9.5 % and 99 %compared to the state-of-the-art local search anchors placement (LSAP) algorithm, respectively.

A deep learning-based surrogate model for trans-dimensional inversion of discrete fracture networks

Fractures and their geometrical patterns are usually required to analyze the mechanical and flow properties of porous media in the subsurface. Fracture characterization is therefore regarded of crucial importance for optimizing production management or achieving maximum storage capacity. In this research, we propose to invert the fracture networks under the Bayesian framework for the uncertainty quantification. In particular, the number of fractures in the modelling system is treated as unknown, leading to a trans-dimensional inverse problem, and the reversible jump Markov chain Monte Carlo algorithm is applied to sample the model space with possible model moves proposed in the sampling process. A deep learning network is further applied as a surrogate model in the sampling process for increasing the computational efficiency, instead of using the physical forward simulator. We apply the proposed methodology to estimate the spatial distribution of fracture networks based on the head measurements from the steady-state flow simulation. The prior distributions of fracture parameters such as position, orientation and length are described using the discrete fracture networks approach that is deeply rooted in stochastic modelling. Due to the high non-uniqueness, the correct spatial distribution of fracture patterns cannot be successfully recovered in this case study, even a good match between observed and simulated head data is reached. More analysis could be performed in the future with the production historical data or more informative priors.

EXPRESS: Constrained Assortment Optimization under the Cross-Nested Logit Model

We study the assortment optimization problem under general linear constraints, where the customer choice behavior is captured by the Cross-Nested Logit model. In this problem, there is a set of products organized into multiple subsets (or nests), where each product can belong to more than one nest. The aim is to find an assortment to offer to customers so that the expected revenue is maximized. We show that, under the Cross-Nested Logit model, the unconstrained assortment problem is NP-hard even when there are only two nests, and the problem is generally NP-hard to approximate to any constant factors. To tackle this challenging problem, we develop a new discretization mechanism to approximate the problem by a linear fractional program with a performance guarantee of [Formula: see text], for any accuracy level ε > 0. We then show that optimal solutions to the approximate problem can be obtained by solving mixed-integer linear programs. We further show that our discretization approach can also be applied to solve a joint assortment optimization and pricing problem, as well as an assortment problem under a mixture of Cross-Nested Logit models to account for multiple classes of customers. Our empirical results on a large number of randomly generated test instances demonstrate that, under a performance guarantee of 90% (i.e., expected revenues are guaranteed to be at least 90% of the optimal revenue), the percentage gaps between the objective values obtained from our approximation methods and the optimal expected revenues are no larger than 1.2%.

Markov Chains to Explore the Nanosystems for the Biophysical Studies of Cancers

The immune response is essential for the human body to function well and to survive against the sudden and chronic diseases such as viral & bacterial infections and cancers. In the immunosurveillance process, Natural Killer (NK) cells are one of the main elements in controlling the development of such infections and, for this reason, they have become the subject of “in-depth” studies especially for the application of new forms of immunotherapy. NK cells can rapidly destroy both autologous and tumor cells in vitro and for this reason the interest in their function is increasingly growing. Their presence in the tumor micro-environment (TME) also assumes prognostic value since the repertoire of NK cell receptors has been linked to anti-tumor function. In this work, a Markov chain modeling approach is proposed to analyze the network of interactions that NK cells carry out with other immune elements in the defense against cancer such as CD4+ cells and CD8+ cells and dendritic cells (DCs) that activate and enhance immune responses. The probabilistic approach used is promising since it helps to understand the balance and the communication in the micro-environment, in a realistic manner. The advantage of discrete time Markov chain approach is that, it can be further extended to complex networks using the state-of-the-art algorithms and can also be translated for the novel AI tools for the cytokines and protein databases.

Systematic solution for multi-model control approaches in nonlinear dynamic systems based on the s-gap metric

This paper proposes a systematic approach for optimizing the distribution of local models in multi-model control systems (MMCS) to enhance overall robustness. While existing literature discusses this method for linear parameter varying (LPV) and uncertain linear time-invariant (LTI) systems, significant limitations persist in addressing nonlinear dynamic systems. Robust control tools like the gap metric and generalized stability margin (GSM) have limited effectiveness in analyzing the robustness of nonlinear feedback systems. To address these challenges, novel concepts of the gap metric and GSM are introduced to determine central operating points (COPs) within local operating areas (LOAs) across the total operating area (TOA). These COPs guide the extraction of affine disturbance local models (ADLMs). Additionally, an optimization problem based on the s-gap metric and GSM is presented to optimize COPs placement and LOAs boundaries. Challenges such as non-monotonic behavior of the cost function and complexity arising from the s-gap metric formulation necessitate novel solution methods. To address these, constraints are applied to the cost function, and a novel discrete optimization approach is introduced. Finally, theoretical findings are applied to the Duffing system, pH neutralization process, and continuous stirred tank reactor (CSTR) plant to evaluate the proposed method's effectiveness. This comprehensive validation across different systems underscores the versatility and practical utility of the proposed approach.

Statistical analysis of infectious disease transmission risk based on exhaled respiratory droplet trajectory distribution

In the present work, the risk of infectious disease transmission is evaluated based on a statistical analysis of respiratory droplet trajectory distribution. An analytical model recently developed by the authors allows the prediction of the trajectory and evaporation rate of exhaled droplets. The model is used to collect data from a sampling set of more than twenty thousand droplets distributed over a range of diameters from 0.1 μm to 1 mm for different respiratory scenarios. The analytical tool implements the governing equations of droplet transport, evaporation, energy balance, and chemical composition. It also features a two-dimensional unsteady empirical model of respiratory cloud including momentum dissipation and buoyancy. A discrete random walk approach to simulate the droplet turbulent dispersion, and the randomization of the droplet release within the exhalation period and the mouth cross section area complete the model enabling statistical analyses to be rightly performed. With the due boundary conditions, different types of respiratory events can be modeled easily. With additional information on the exhaled droplet size distribution and viral content, spatial maps of virus concentration are derived and associated with the risk of infectious disease transmission being able to discriminate between various transmission routes such as fomite, airborne, or direct inhalation. Different scenarios are presented including mouth breathing, nose breathing, speaking, coughing, and sneezing. The fluid dynamic behavior of respiratory droplets is explored on a size basis, and the role of ventilation discussed. Risk evaluation provides useful information for a knowledgeable discussion on the prevention needs and means from case to case.

Gradient-based aerodynamic shape optimization using a discrete adjoint approach on a graphics processing unit

Gradient-based aerodynamic shape optimization using a discrete adjoint approach on a graphics processing unit

The effect of variations in experimental and computational fidelity on data assimilation approaches

AbstractWe conduct a comprehensive analysis of two data assimilation methods: the first utilizes the discrete adjoint approach with a correction applied to the production term of the turbulence transport equation, preserving the Boussinesq approximation. The second is a state observer method that implements a correction in the momentum equations alongside a turbulence model, both applied to fluid dynamics simulations. We investigate the impact of varying computational mesh resolutions and experimental data resolutions on the performance of these methods within the context of a periodic hill test case. Our findings reveal the distinct strengths and limitations of both methods, which successfully assimilate data to improve the accuracy of a RANS simulation. The performance of the variational model correction method is independent of input data and computational mesh resolutions. The state observer method, on the other hand, is sensitive to the resolution of the input data and CFD mesh.

Innovation Discrete Approach Based on Arabic Language Test Assessment

Innovation Discrete Approach Based on Arabic Language Test Assessment

On Discrete Frechet Distribution : Estimation and Application

A discrete two-parameter distribution corresponding to the continuous distribution is introduced and derived by using the approach of discretization of continuous distribution functions . The Survival and Hazard functions of the proposed distribution were also found and examined . Two methods were discussed to estimate the parameters , Maximum Likelihood and the Bayesian method , and then compare the performance using the simulation method . In addition, the compatibility of the proposed distribution was investigated through real data , and then the estimates of the survival and Hazard functions were reached . The superiority of the Bayesian method in data modelling was shown .