Numerical Behavior Research Articles

Simulations and analysis of underwater acoustic wave propagation model based on Helmholtz equation

In this study, we explore the effectiveness of elliptic partial differential equations (PDEs) in two and three dimensional space based on Helmholtz equation for simulations of acoustic sound in a very complex environment of propagation. For this purpose, we use an advance and robust numerical technique by utilizing the properties of shifted Chebyshev spectral collocation method. This technique is an extension of the traditional Chebyshev polynomials, incorporating a shift in their argument to enhance flexibility across a wider domain, while retaining an extraordinary numerical characteristic such as orthogonality and spectral convergence making them exceptionally effective in finding the approximate solutions. The exponential order of convergence of the proposed approach is shown both through theoretical and numerical approaches. We provide a number of numerical experiments to verify the theoretical results. The spectral convergence has been substantially enhanced by these numerical examples. The exponential order is further validated by numerical error behaviour in both L 2 and L ∞ norms.

Microalgae bio-reactive façade: A radiative-convective model powered by hourly illumination computation and historical weather data

This article presents a numerical model predicting the performance of a microalgae biofaçade. The core of the model is the association of radiative, convective, and conductive heat transfers. These key physical phenomena are modulated by actual weather data and coupled to a biological model of the microalga Chlorella vulgaris. Based on the conjunction of temperature and illumination predictions, the biofaçade performances are categorized between low, adequate, high temperature × light-deficient, light-sufficient conditions. The capabilities of the model (dissection of acute events to year-round performance prediction) are illustrated using the city of Marseille, France, over the year 2020. The numerical behavior of the model itself is then analyzed. The influence of the Urban Heat Island submodel is discussed, and a global sensitivity analysis (Sobol’s indices) is led to assess the impact of uncertain physical parameters. The model accuracy is evaluated at 7.4% of the total daytime (under conservative assumptions) . The most influential parameters are the microalgae culture emissivity and the building indoor emissivity. All in all, the confidence in this model is high enough so that it can be used to design a biofaçade numerically.

Numerical and experimental 3-point bending quasi-static flexural behavior of single-strap joints joined using AF163-2K adhesive films

ABSTRACT This paper evaluated the mechanical characteristics of adhesive-single-bonded strap joints with varied numbers of adhesive layers subjected to flexural loads. Six samples were submitted to a 3-point bending test, three with the strap facing up and three with the strap facing down, and the failure behavior was analyzed. A 3-D finite element (FE) model was created in ABAQUS/Explicit. The adhesive layer (AF163-2K) failure was represented by cohesive zone components. It was discovered that the samples with the thickest adhesive layer obtained the highest load values. Furthermore, compared to samples with the strap facing down, those with the strap facing up demonstrated greater strength. Experiments were conducted to validate the constructed numerical model. Given that this type of configuration is one of the most commonly employed, especially in the repair of aeronautical structures, studying single-strap joints is deemed beneficial for designers.

Slow dissipation and spreading in disordered classical systems: A direct comparison between numerics and mathematical bounds.

We study the breakdown of Anderson localization in the one-dimensional nonlinear Klein-Gordon chain, a prototypical example of a disordered classical many-body system. A series of numerical works indicate that an initially localized wave packet spreads polynomially in time, while analytical studies rather suggest a much slower spreading. Here, we focus on the decorrelation time in equilibrium. On the one hand, we provide a mathematical theorem establishing that this time is larger than any inverse power law in the effective anharmonicity parameter λ, and on the other hand our numerics show that it follows a power law for a broad range of values of λ. This numerical behavior is fully consistent with the power law observed numerically in spreading experiments, and we conclude that the state-of-the-art numerics may well be unable to capture the long-time behavior of such classical disordered systems.

Analysis of the alternative air ductwork by Numerical airflow behavior combined with the New Economic index and standard

This research studies the numerical modelling using computational fluid dynamics with a k-Epsilon turbulence model to analyze airflow behaviors inside the alternative compared with conventional air ductwork combined with a comprehensive analysis of the economic parameter created by the author called Reveal Comparative Advantage Cost index. All alternative air ductwork has lower pressure drop and a higher ability to maintain the temperature inside, showing that alternative air duct systems have a significant advantage over conventional air ductwork. The fabric ductwork has a lower pressure drop than galvanized steel perforated ductwork, which is 69.15 %. The pre-insulated ductwork can keep the best temperature inside, with a different temperature value between the air inlet and air outlet of 0.06°C. The Reveal Comparative Advantage Cost of construction costs of the galvanized steel ductwork and the galvanized steel perforated ductwork are 1.02 and 1.06, which means the conventional air ductwork is initially cost-effective in terms of investment and operating costs. However, alternative air ductwork is the better option for long-term use. They have cost-effective electrical energy and maintenance costs with a high Reveal Comparative Advantage Cost index. Significantly, the pre-insulated ductwork has the Reveal Comparative Advantage Cost index of maintenance, electrical energy, and construction costs of 1.38, 1.09, and 0.95, respectively. The results of the airflow behaviors study combined with the Reveal Comparative Advantage Cost index study show that the galvanized steel perforated ductwork is not a selectivity that qualifies either for airflow behaviors or is unsuitable for investment. Pre-insulated ductwork is the appropriate option due to the high airflow behaviors and cost, which makes it suitable for investment. However, the Thailand Authority should develop alternative air ductwork Thai standards for engineering design and safety building.

Nonlinear electro-elastic finite element analysis with neural network constitutive models

In the present work, the applicability of physics-augmented neural network (PANN) constitutive models for complex electro-elastic finite element analysis is demonstrated. For the investigations, PANN models for electro-elastic material behavior at finite deformations are calibrated to different synthetically generated datasets describing the constitutive response of dielectric elastomers. These include an analytical isotropic potential, a homogenised rank-one laminate, and a homogenised metamaterial with a spherical inclusion. Subsequently, boundary value problems inspired by engineering applications of composite electro-elastic materials are considered. Scenarios with large electrically induced deformations and instabilities are particularly challenging and thus necessitate extensive investigations of the PANN constitutive models in the context of finite element analyses. First of all, an excellent prediction quality of the model is required for very general load cases occurring in the simulation. Furthermore, simulation of large deformations and instabilities poses challenges on the stability of the numerical solver, which is closely related to the constitutive model. In all cases studied, the PANN models yield excellent prediction qualities and a stable numerical behavior even in highly nonlinear scenarios. This can be traced back to the PANN models excellent performance in learning both the first and second derivatives of the ground truth electro-elastic potentials, even though it is only calibrated on the first derivatives. Overall, this work demonstrates the applicability of PANN constitutive models for the efficient and robust simulation of engineering applications of composite electro-elastic materials.

Personality and cognition: shoal size discrimination performance is related to boldness and sociability among ten freshwater fish species

Several studies have reported that animals’ personalities are often correlated with individual differences in cognition. Here, we tested whether personality is related to cognition across species, focusing on 10 freshwater fishes and a task relevant for fitness, the ability to discriminate shoal size. Bolder species exhibited more ‘shuttle’ behavior for information sampling during shoal selection and showed high performance (HP) in the numerical discrimination than shyer species, i.e., low performance (LP) species. Species at both the high and low ends of sociability showed LP, possibly due to loosened selection pressure because of either no need to perform shoal size discrimination tasks frequently in nature for very high sociability species or decreased willingness and motivation to join and stay within shoals for very low sociability species. Notably, the numerical discrimination was sensitive to the numerical contrast ratio in LP species but not in HP species, suggesting that the numerical system used for size discrimination also varied between species. Overall, we demonstrated the interspecies relationship between personality and shoal size discrimination across fish species, suggesting an evolutionary link between numerical abilities and behavior.

Connecting continuum poroelasticity with discrete synthetic vascular trees for modelling liver tissue

The modelling of liver tissue across multiple length scales constitutes a significant challenge, primarily due to the multiphysics coupling of mechanical response and perfusion within the complex multiscale vascularization of the organ. In this paper, we present a modelling framework that connects continuum poroelasticity and discrete vascular tree structures to model liver tissue across disparate levels of the perfusion hierarchy. The connection is achieved through a series of modelling decisions, which include source terms in the pressure equation to model inflow from the supplying tree, pressure boundary conditions to model outflow into the draining tree, and contact conditions to model surrounding tissue. We investigate the numerical behaviour of our framework and apply it to a patient-specific full-scale liver problem that demonstrates its potential to help assess surgical liver resection procedures.

Regret-based budgeted decision rules under severe uncertainty

One way to make decisions under uncertainty is to select an optimal option from a possible range of options, by maximizing the expected utilities derived from a probability model. However, under severe uncertainty, identifying precise probabilities is hard. For this reason, imprecise probability models uncertainty through convex sets of probabilities, and considers decision rules that can return multiple options to reflect insufficient information. Many well-founded decision rules have been studied in the past, but none of those standard rules are able to control the number of returned alternatives. This can be a problem for large decision problems, due to the cognitive burden decision makers have to face when presented with a large number of alternatives. Our contribution proposes regret-based ideas to construct new decision rules which return a bounded number of options, where the limit on the number of options is set in advance by the decision maker as an expression of their cognitive limitation. We also study their consistency and numerical behaviour.

Singularly perturbative behaviour of nonlinear advection–diffusion-reaction processes

The purpose of this paper is to use a wavelet technique to generate accurate responses for models characterized by the singularly perturbed generalized Burgers-Huxley equation (SPGBHE) while taking multi-resolution features into account. The SPGBHE’s behaviours have been captured correctly depending on the dominance of advection and diffusion processes. It should be noted that the required response was attained through integration and by marching on time. The wavelet method is seen to be very capable of solving a singularly perturbed nonlinear process without linearization by utilizing multi-resolution features. Haar wavelet method results are compared with corresponding results in the literature and are found in agreement in determining the numerical behaviour of singularly perturbed advection–diffusion processes. The most outstanding aspects of this research are to utilize the multi-resolution properties of wavelets by applying them to a singularly perturbed nonlinear partial differential equation and that no linearization is needed for this purpose.

Adaptation of nanofluids with magnetohydrodynamic Williamson fluid to enhance the thermal and solutal flow analysis with viscous dissipation: A numerical study

The Williamson nanofluid flow along with the thermal and solutal transport effects like enthalpy and viscous dissipation, has lots of applications in numerous engineering fields such as heat exchangers, automotive engineering, cooling systems, aerospace, and biomedical applications. The temperature-dependent viscosity has implications in the polymer processing, chemical processing, microfluidic devices, environmental fluid dynamics, and oil and gas industries. The current research deals with the numerical study of the magnetohydrodynamic flow of 2-dimensional Williamson nanofluid flowing on a stretched cylinder. The thermophysical property (viscosity) is assumed to depend on temperature for this flow system. The transmission analysis of solutal and heat processes, along with enthalpy and viscous dissipation, is also considered here. The boundary layer approach is used to address the main leading equations, and ODEs are generated from the main equations by assuming similarity transformations. The main novelty of this problem is the use of a multistep technique, which is the Adams-Bashforth Predictor and Corrector method, along with the RK-4 scheme and the secant method. The key parameters are used to illustrate the graphical and numerical behavior of the velocity, temperature, and concentration regions. The variations in the Williamson fluid coefficient cause the fluid velocity to increase, whereas alterations in the curvature parameter cause the velocity region to decrease. The temperature in a given area declines due to the impact of the Prandtl number. The fluids temperature shows augmented values in the occurrence of variation in the thermopherosis coefficient, Brownian motion coefficient, curvature parameter, and heat generation parameter. The curvature parameter, thermopherosis coefficient, and activation energy lead to an increase in the fluid concentration region, whereas a decrease in concentration is noted due to the Brownian motion coefficient, Damkholer number and Schmidt number.

Numerical Simulation of Droplet Dispersion and Passenger Infection Risk Assessment in a Subway Carriage

Droplet transmission is a critical pathway for the spread of respiratory infectious viruses. A thorough understanding of the mechanisms of droplet dispersion within subway carriages is crucial to curb the widespread transmission of the virus. This study utilizes computational fluid dynamics (CFD) to establish a full-scale numerical model of a subway carriage. The numerical model and droplet evaporation behavior are validated using experimental data and literature. The impact of primary parameters such as the initial droplet size, release velocity, release position, relative humidity, and passenger density on the droplet diffusion and probability of infection for passengers is investigated. The results indicate that large droplets (100 μm) are deposited on the carriage floor before complete evaporation, while tiny droplets (10 μm) evaporate rapidly, leading to a longer suspension time in the air within the carriage. The infected passenger’s position influences the ventilation system’s efficiency in removing the droplets; removal takes significantly longer when the infected passenger is closer to the carriage end. Additionally, a low relative humidity (35%) and high passenger density (4 p/m2) result in more droplets being trapped by passengers’ bodies. The infection probability for passengers depends on the initial size and quantity of droplets trapped by their bodies. Maintaining higher relative humidity levels and limiting the passenger numbers within the subway carriage can reduce the number of droplets captured by passengers’ bodies, thus helping to reduce the infection probability of fellow passengers.

Implementing the multistep adams-bashforth numerical approach on magnetohydrodynamic radiated casson fluid with darcy forchheimer, dissipation and activation energy

The main goal behind the conduction of this work is to use the Adams-Bashforth method in the field of fluid dynamics to solve the Navier–Stokes equations based on the boundary layer flow of magnetohydrodynamic Casson fluid passing on the upper horizontal parabolic surface with variable fluid characteristics and Darcy-Forchheimer effect. The temperature flow rate and mass rate are also investigated with the help of thermal radiation, viscous dissipation, heat generation and activation energy. The Adams-Bashforth technique is widely used in numerical analysis, scientific computing, fluid dynamics, chemical kinetics, astrophysics and is particularly useful in solving the stiff ODEs, where other methods may fail to converge. It is particularly useful for simulating the flow of fluids around complex geometries, such as aircraft wings or turbine blade. The equations of basic governing laws (Momentum, temperature and concentration) are achieved in the form of PDE’s. These PDEs are then transmuted into ODEs via similarity variables and the numerical behaviors of these ODEs are obtained with Adam-Bashforth (Predictor-Corrector) along with RK-4 technique on the Matlab software. The initial guesses are modified by using secant method. Graphical analyses are used to explain how different parameters affect the temperature, velocity and mass transport rate. The finding of results revealed that the inertia coefficient, Hartmann number and fluid parameter make the decrement in the velocity field. The amplification in temperature of fluid is noted for varying the radiation coefficient, dissipation and thermal generation coefficient. The solutal field drops due to activation energy and reaction coefficient. The findings are useful to observe the flow attributes, behaviors and helpful in the designing of thermal equipment in the thermal industries.

Experimental and numerical bond behavior of PBO FRCM tested using a pull-out set-up

Fabric-reinforced cementitious matrix (FRCM) composites have become increasingly popular in the field of externally bonded (EB) reinforcement of existing concrete and masonry structures. They are used as flexural, shear, and torsional strengthening of reinforced concrete (RC) members. They are comprised of high strength textiles embedded in an inorganic-based matrix. FRCM tensile mechanical properties are characterized by clamping-grip or clevis-grip tensile tests, whereas their bond behavior by indirect or single- and double-lap direct shear tests. The eccentricity between the applied load and the restraint in single-lap direct shear tests entails for the presence of normal stresses that can affect the bond stress-transfer mechanism. Furthermore, direct shear tests require relatively large and heavy specimens. To overcome these issues, a new pull-out test set-up was proposed in the literature to investigate the bond behavior of FRCM composites that fail at the textile-matrix interface. In this paper, nine pull-out tests are performed on PBO FRCM composites. Bonded lengths shorter and longer than the textile-matrix interface effective bond length are considered. Six specimens have a short bonded length (i.e., 150 mm), whereas three have a long bonded length (i.e., 450 mm). Applied stress – global slip curves of the specimens tested highlight the presence of friction at the textile-matrix interface. The results of the pull-out tests are compared with those of corresponding single-lap direct shear tests presented in a previous work with the same PBO FRCM composite and the same bonded length and width. The applied stress – global slip curves obtained from the two sets of test show good agreement. Finally, the pull-out test set-up is validated by means of a three-dimensional finite element model.

PACMAN: PAC-style bounds accounting for the Mismatch between Accuracy and Negative log-loss

Abstract The ultimate performance of machine learning algorithms for classification tasks is usually measured in terms of the empirical error probability (or accuracy) using a testing dataset, although these algorithms are optimized through the minimization of a typically different—more convenient—loss function using a training set. For classification tasks, this loss function is often the negative log-loss that yields the well-known cross-entropy risk that is typically better behaved (in terms of numerical behavior) than the 0-1 loss. Conventional studies on the generalization error do not usually take into account the underlying mismatch between losses at training and testing phases. In this work, we introduce a theoretical analysis based on a pointwise probably approximately correct (PAC) approach over the generalization gap considering the mismatch of testing on the accuracy metric and training on the negative log-loss, referred to as PACMAN. Building on the fact that the resulting mismatch can be written as a likelihood ratio, concentration inequalities can be used to obtain insights into the generalization gap in terms of PAC bounds, which depend on some meaningful information-theoretic quantities. An analysis of the obtained bounds and a comparison with available results in the literature is also provided.

Extended Brauer analysis of some Dynkin and Euclidean diagrams

<p>The analysis of algebraic invariants of algebras induced by appropriated multiset systems called Brauer configurations is a Brauer analysis of the data defining the multisets. Giving a complete description of such algebraic invariants (e.g., giving a closed formula for the dimensions of algebras induced by significant classes of Brauer configurations) is generally a tricky problem. Ringel previously proposed an analysis of this type in the case of Dynkin algebras, for which so-called Dynkin functions were used to study the numerical behavior of invariants associated with such algebras. This paper introduces two additional tools (the entropy and the covering graph of a Brauer configuration) for Brauer analysis, which is applied to Dynkin and Euclidean diagrams to define Dynkin functions associated with Brauer configuration algebras. Properties of graph entropies defined by the corresponding covering graphs are given to establish relationships between the theory of Dynkin functions, the Brauer configuration algebras theory, and the topological content information theory.</p>

Asymptotic behavior and numerical analysis for a Timoshenko beam with viscoelasticity and thermodiffusion effects

We study the qualitative and numerical behavior of a thermodiffusion Timoshenko beam with Kelvin–Voigt damping. The model, recently derived by Aouadi $ \rm et al. $ (2019), describes the behavior of a Timoshenko beam with thermodiffusion effects under the classical Fourier's and Fick's laws for heat and mass diffusion transmission, respectively. With the help of the semigroup theory of linear operators, we prove the well posedness of the considered problem. Without assuming the well-known condition of equal wave speeds, it is shown that the associated $ C_0 $-semigroup to the fully viscoelastic system is analytic. Exponential stability and impossibility of localization of the solutions in time are immediate consequences. Two partial viscoelastic systems are shown to be polynomially or exponentially stable. The approach based on the Gearhart–Herbst–Prüss–Huang theorem is used to show the lack of exponential stability, whereas the optimal polynomial decay rate can be shown using the Borichev & Tomilov's Theorem. Finally, we propose a spectral discretization method to prove that the associated discrete energy decays exponentially or polynomially otherwise.

Self-Organized States from Solutions of Active Ring Polymers in Bulk and under Confinement.

In the present work, we study, by means of numerical simulations, the structural and dynamical behavior of a suspension of active ring polymers in bulk and under lateral confinement. At high activity, when changing the distance between the confining planes and the polymers' density, we identify the emergence of a self-organized dynamical state, characterized by the coexistence of slowly diffusing clusters of rotating disks and faster rings moving in between them. We further assess that self-organization is robust in a range of polymer sizes, and we identify a critical value of the activity, necessary to trigger cluster formation. This system has distinctive features resembling at the same time polymers, liquid crystals, and active systems, where the interplay between activity, topology, and confinement leads to a spontaneous segregation in an initially one-component solution.

Probabilistic fatigue strength assessment of cross-ply laminates: Exploring effects of manufacturing defects through a two-scale modeling approach

The study presents a two-scale modeling approach allowing for an efficient fatigue strength evaluation on a macro scale considering a micro-mechanical defect characterization of a Carbon Fiber Reinforced Polymer (CFRP) material. The modeling approach integrates a macro model with the effective elastic properties from micro-mechanical simulations considering voids. This enables the analysis of defects’ influence on material fatigue strength using a probabilistic weakest link approach. A CFRP laminate with a cross-ply layup was investigated. Two simulation case studies demonstrate the effect of void content and size on the characteristic fatigue strength. An experimental investigation was conducted testing the laminates in tension–tension fatigue verifying the predicted numerical behavior. The numerical models identify a difference in the characteristic fatigue strength consistent with the fatigue test results. It is numerically concluded that the investigated CFRP material’s fatigue strength is affected by the presence of voids and even with only a slight difference in the global void volume fraction a scatter in fatigue strength is identified.

A Novel Numerical Approach for Solving the Newell-Whitehead Equation

Numerical solutions of Newell-Whitehead equation are investigated by collocation method in this study. Since higher order functions produce better approximations, septic B-spline basis functions is used for analysis and approximation. Error norms are calculated for the adequacy and effectiveness of the current method. Unconditional stability is proved using Von-Neumann theory. The numerical results are obtained and the comparisons are presented in the tables. Additionally, simulations of all numerical results are plotted to show the numerical behavior of the solution. Numerical results make the method more convenient and systematically handle the nonlinear solution process. The numerical solutions found make the method attractive and reliable for the solution of Fitzhugh-Nagumo type equations.