Specific Boundary Conditions Research Articles

Analysis of stress and deformation of an exponentially graded viscoelastic coated half plane under indentation by a rigid flat punch indenter tip

This paper solves the dynamic contact problem when a rigid flat punch indents into an exponentially graded (FG) viscoelastic coated homogeneous half-plane. A harmonic vertical force is applied to the FG coating, and the solution is obtained for the stress and displacement for both the FG viscoelastic coating and the half-plane using the Helmholtz functions and the Fourier integral transform technique. By applying specific boundary conditions, the contact mechanics problem is converted into a singular integral equation of the first kind. This equation is then solved numerically using the Gauss-Chebyshev integration formulas. The analysis provides detailed insights into how various parameters—such as external excitation frequency, loss factor ratio, Young’s modulus ratio, density ratio, Poisson’s ratio, indentation load, and punch length—affect the dynamic contact stress and dynamic in-plane stress.

Multi-species kinetic-fluid coupling for high-energy density simulations

Many physics problems are subject to a mix of continuum and non-equilibrium flows or conditions where one transition into the other, as a function of time and/or space. Numerically, such flows could be described with a purely kinetic method which, in the limit of small particle mean free paths, reproduces a continuum regime. However, from a computational perspective, such approaches are usually very expensive or simply not feasible, even on modern computational architectures. A solution is the construction of hybrid methods which connect the kinetic and hydrodynamic system of evolution equations. Such coupling usually requires specific boundary conditions between non-equilibrium and continuum regimes which come with their own numerical challenges and can introduce unphysical effects. Here, we present a hybrid model which uses a buffer region to transition from a kinetic into a fluid description following the original work of Degond et al. [1]. In the buffer region, both, the kinetic and hydrodynamic equations are solved simultaneously while being coupled via a so-called transition function. The latter also ensures a smooth conversion from the coupled model to either the kinetic or continuum approach at the interfaces of the buffer region. With that, the method avoids the need to find direct interface boundary conditions and allows one to localize the use of a high dimensional kinetic model only where it is needed. In our work, we extend the original method of Degond to flows with multiple particle species in 3D. We derive the coupled equations for the multispecies Vlasov-Bhatnagar-Gross-Krook (VBGK) model and its limiting Euler or Navier-Stokes hydrodynamic equations. To validate our model numerically, we simulate a Sod shock problem and study the effect of kinetic multi-species mixing in the preheat phase of a high energy-density plasma physics experiment.

Response of frequency domain in generalized thermoelastic medium under modified Green‐Lindsay with non‐local and two temperature

AbstractThis paper introduces a novel model for a generalized thermoelastic medium with homogeneity and isotropy, by applying the Modified Green‐Lindsay (MG‐L) theory of thermoelasticity. The focus is on analysing the deformation due to time‐harmonic by considering the impact of non‐local and two‐temperature (TT) parameters. The governing equations are solved using dimensionless quantities and a potential function. To address the boundary value problem in the frequency domain, the Hankel transform is employed. Specific boundary conditions, such as a normal force or thermal source, are applied. Analytical expressions for components of displacement, stresses, conductive temperature, and temperature distribution are derived in the transformed domain A numerical inversion technique is utilised to translate the solution into the physical domain. The study delves into exploring the influence of non‐local and two‐temperature parameters, as well as different theories of thermoelasticity on stresses, temperature distribution and conductive temperature. These effects are visually represented through graphical illustrations. Additionally, special cases of interest are examined and discussed.

Evaluation of data-driven neural operators in ocean acoustic propagation modeling

Various types of neural networks have been employed to tackle a wide range of complex partial differential equations (PDEs) and ordinary differential equations (ODEs). Notably, neural operators such as DeepONet and FNO show promise in handling these problems, offering potential real-time prediction capabilities. In contrast to physics-informed neural network (PINN) methods, neural operators primarily derive insight from extensive, well-prepared datasets. In the context of ocean acoustic propagation modeling, where the challenge involves solving the wave or Helmholtz equation given specific boundary conditions, this study focuses on assessing the performance of data-driven neural operators in predicting sound pressure. Unlike conventional approaches that map between finite-dimensional Euclidean spaces, neural operators excel in learning mappings between infinite-dimensional function spaces—a particularly advantageous feature in sound propagation modeling tasks. This research specifically delves into evaluating the generalization capabilities of neural operators when applied to sound propagation modeling in a range-independent shallow water environment. By exploring the neural operators' effectiveness in this domain, the study aims to contribute valuable insights into their potential applications for real-world ocean acoustics simulations.

A comprehensive review on the modeling of tropical cyclone boundary layer wind field

Tropical cyclone (TC) wind field models are becoming increasingly sophisticated and complex. This review systematically discusses a range of models capable of simulating TCs in terms of modifications or simplifications of the governing equation, the Navier–Stokes equations, as a starting point. The discussion focuses on linear models, which include slab models, height-resolving models, and numerical simulation methods, respectively. The linear model offers quick calculations and insights into physical mechanisms, while slab models have limitations in capturing important processes and site conditions. The height-resolving model is widely used for Monte Carlo simulations, providing realistic three-dimensional wind structures. Nonlinear simulations yield reliable results for typhoon trajectory prediction, although they require specific boundary and initial conditions. Integration of nonlinear simulation with artificial intelligence and machine learning shows promise for faster typhoon prediction. However, challenges remain in terms of data training for machine learning models. Future advancements in these areas have the potential to enhance hazard assessment and weather forecasting.

Aerodynamic means of reducing the influence of warning accessories on drag and emissions, for intervention vehicles

Aerodynamic performance of passenger vehicles is one of the most efficient methods to further reduce the CO2 emissions and comply with the increasing constraints in the legislation. Previously performed studies on exterior warning accessories (systems with visual alerting signals that may be found on intervention vehicles e.g. ambulances), indicate a significant degradation of aerodynamic coefficient (Cd). Even if this category of vehicles does not have to comply with the standard emission rules, it is important to study and discover the means to reduce aerodynamic drag for this type of vehicles considering the general aim to reduce air pollution. The target would be to have a Cd level equal to that found in the base vehicles, before transformation (i.e. often, intervention vehicles are obtained by converting a vehicle available to general customers - multistage vehicle transformation).The current paper’s purpose is to continue the investigation on methods to improve the aerodynamic performance of intervention vehicles. This will be done by compensating the shape and dimensions of the warning devices with the addition of supplementary body elements or by adapting existing parts. The Cd value of the different configurations is assessed using computational fluid dynamics (CFD) software based on Lattice Boltzmann mathematical model. 3D models of different generic body type vehicles (sedan, hatch back, SUV) were created and immersed in a virtual wind tunnel. To simulate the real-world measurement method specific boundary conditions on walls, inlets, outlets were set while the fluid environment was defined with a network from fine (2mm length, near the studied model), to coarse (20mm length, near exterior walls).The results indicate that there is great potential in reducing the aerodynamic drag and, by extension, fuel consumption and CO2 emissions for all body types studied. Deviations could exist due to different make designs, or diversity of warning devices for example so the results obtained have a general nature. Nevertheless, the conclusion remains the same: if one’s aim is to improve air quality or prepare for new legislation (that will also apply to intervention vehicles), the aerodynamic optimization should be further scrutinized as it can prove to be a robust method to obtain the targeted results.

Dual-functional perforated metamaterial plate for amplified energy harvesting of both acoustic and flexural waves

Metamaterials with defect states are commonly utilized in energy harvesting from acoustic and elastic waves due to their remarkable ability to localize waves. In this study, a novel piezoelectric energy harvester based on a perforated double-pillars metamaterial plate with a point defect, which offers the advantage of efficiently harvesting both ambient acoustic and flexural wave energy, is proposed. The proposed structure incorporates a locally resonant mechanism that enhances the concentration of vibration energy at the defect band frequency. Then, the amplified wave energy is efficiently converted into electrical energy by attaching a piezoelectric patch at the defect position. To initiate this investigation, the differential quadrature method is employed to theoretically estimate the boundary frequencies of the first band gap. Subsequently, this study investigates how holes size, electrical boundary conditions, and electrical circuit connections affect the energy harvesting of both acoustic and flexural waves. Correspondingly, the mechanisms behind their effects are thoroughly explained. Numerical results demonstrate that the wave energy localization performance can be remarkably amplified with an increasing holes radius, and the harvesters with the 1mm holes radius generate voltages that are approximately 2.12 and 1.44 times higher than those with the 0mm holes radius from acoustic and flexural waves, respectively. Furthermore, variations in the defect band frequency and corresponding wave localization behavior depend on the specific electrical boundary conditions and circuit connection approaches, ultimately leading to distinct results in the output electrical energy. These findings present valuable insights and guidelines for the development of high-performance electronic applications in the context of acoustic and elastic wave energy harvesting.

Fossilized autogenic responses of grain‐size transition to sediment supply and water discharge: Alluvial fan experiments

ABSTRACTAutogenic feedbacks can produce large‐scale, organized stratigraphic patterns in alluvial fans, but autogenic depositional signatures of specific upstream boundary conditions remain challenging to interpret. Here, a combination of theory, experiment and field application is used to explore how autogenic lithofacies changes can be interpreted as stratigraphic indicators of upstream boundary conditions. Six experiments were conducted to test the effects of sediment supply and water discharge rates on autogenic advance and retreat of the lithofacies boundary (grain‐size transition) in an alluvial fan with two dominant grain sizes. Migration of the grain‐size transition caused a short‐term zigzag pattern in the grain‐size transition position in the dip‐directional deposit section. For each experiment, time‐lapse images and laser topographic scans of the fan surface and stratigraphic cross‐sections of the final deposits were used to quantify characteristic timescales of autogenic processes. Timescales for fan‐margin migration, surface wet‐fraction change and grain‐size transition migration generally shorten as sediment supply rate increases and water discharge rate decreases. Increasing the sediment supply rate shortens the duration of the fluvial sediment storage and release cycle, producing higher frequency zigzags in the grain‐size transition trajectory. Increasing the water discharge tends to widen channels and lengthens the duration of the fluvial sediment storage and release cycle, constructing lower frequency zigzags in the grain‐size transition trajectory. Increasing the water discharge also enables more sediment to transport further downstream during release events, leading to higher magnitude zigzags in the grain‐size transition trajectory. These relationships between upstream boundary conditions and the grain‐size transition trajectory demonstrate how autogenic stratigraphic signals could be used as a tool to infer relative changes in boundary conditions.

Imposing different boundary conditions for thermal computational homogenization problems with FFT‐ and tensor‐train‐based Green's operator methods

AbstractTo compute the effective properties of random heterogeneous materials, a number of different boundary conditions are used to define the apparent properties on cells of finite size. Typically, depending on the specific boundary condition, different numerical methods are used. The article at hand provides a unified framework for Lippmann–Schwinger solvers in thermal conductivity and Dirichlet (prescribed temperature), Neumann (prescribed normal heat flux) as well as periodic boundary conditions. We focus on the explicit jump finite‐difference discretization and discuss different techniques for computing the discrete Green's operator. These include Fourier‐type methods, that is, based on discrete sine, cosine and Fourier transformations, as well as low‐rank tensor methods, that is, the tensor‐train approximation, whose computational prowess was demonstrated recently. We use the developed computational technology to investigate a number of interesting random materials and assess different microstructure‐generation techniques in terms of their compatibility with the prescribed boundary conditions.

A Finite Difference Technique for Numerical Solution of the Boundary Value Problem in ODEs of Order Three

In the article, we study the approximate numerical solution to the boundary value problem in ordinary differential equations. In the present article, a third-order two-point boundary value problem is considered for discussion. We developed a second order accurate finite difference method for the approximate numerical solution of the considered problem. We took a special boundary condition; we did not find this boundary condition in the literature. We have discussed the standard convergence analysis of the proposed method. Numerical experiments on linear, nonlinear, and obstacle problems approve the order of accuracy and efficiency of the method.

Mixed convection analysis in a dual-driven cavity with a stable vertical temperature gradient using the lattice Boltzmann method

The complex dynamics of mixed convection circumstances, concentrating on two examples. In the first case, mixed convection was investigated in a single-sided lid-driven cavity with a top and bottom walls arrangement and the second scenario explores parallel and anti-parallel topologies, focusing on mixed convection in a double-sided lid-driven cavity. The main parameters in this study are the Reynolds, Rayleigh, Prandtl, Grashof, and Richardson numbers. Calculation of numerical solutions to the Navier-Stokes equations over wide ranges in parameters, 0 ? Gr ? 106, 0 ? Re ? 3000, Pr~O(1), and an aspect ratio approximately O(1). The study analyzes these results systematically to understand the relative importance of natural convection and forced convection. As a result of this study, a two-dimensional cavity with specific boundary conditions was created. In a square domain with adiabatic side walls, a top wall is maintained at a higher temperature than the bottom wall. The flow characteristics approach those of a typical driven-cavity of a non-stratified fluid when Gr/Re2 ? 1. There are low fluctuations in temperature and well-mixed fluids throughout the majority of the interior. Much of the inner cavity?s middle and bottom are stationary when Gr/Re2?1. Temperature patterns in these areas are vertically linear and isotherms are nearly horizontal. Lattice Boltzmann method considers the effect of gravity on mixed convection by adjusting the y-velocity using a temperature-dependent forcing factor. The calculation of the Nusselt number at the top wall reveals enhanced heat transfer, with the results suggesting increased intensity when Gr/Re2?1.

Archimedes Screw Pump Efficiency Based on Three Design Parameters using Computational Fluid Dynamics Software – Ansys CFX

Utilization of Archimedes screw pumps as water lifting pumps has become widespread in past decade due to frequent occurrences of floods in Malaysia. The problem of insufficient drainage in various urban areas exacerbates the impact of heavy rainfall, prompting efforts to mitigate this issue with minimal maintenance cost and low impact to the environment. Thus, this study is aiming to study the design parameters of screw pump to obtain the optimal efficiency of the Archimedes screw pump specifically for flood mitigation in Malaysia. The main design parameters affecting pump’s efficiency are rotor profile, pitch length, length of the pump, rotational speed, inclination angle, and material selection. However, only three design parameters were considered in the study, that are the angle of inclination, the number of blades, and the angular velocity of the rotating pump. These three design parameters are selected as many previous findings focusing on varying angle of inclination with number of blades with constant rotational speed. Thus, this study will find the highest efficiency when these three design parameters are integrated with variation of rotational speeds at 25, 30 and 40 RPM. Basically, screw pump is designed using SOLIDWORKS and simulations with specific boundary conditions are conducted using the ANSYS-CFX software, which utilizes computational fluid dynamics (CFD) techniques. These boundary conditions are based on previous study by Rosly et al in 2016. The inlet flow rate of 0.002 m3/s and diameter of the screw pump are constant while the other three main parameters are varying within the acceptable ranges which are reported from prior studies. The outcomes found that the highest torque is generated by a single rotating blade at 5.65 Nm which rotates at 30 RPM at 30° angle of inclination. Meanwhile, the highest efficiency of 24.04% is obtained with a single rotating blade at 40 RPM with 20° angle of inclination. Based on the findings, it is concluded that these three main design parameters of screw pump may not be sufficient to obtain the optimal efficiency for the specific boundary conditions used in the simulation study. Thus, several combinations of design parameters should be considered in the future to increase the screw pump’s efficiency.

ДЕЯКІ АСИМПТОТИЧНІ ВЛАСТИВОСТІ РОЗВ’ЯЗКІВ ТРИГАРМОНІЙНИХ РІВНЯНЬ

The author considers the optimization problem for the triharmonic equation in the presence of specific boundary conditions. As a result, the triharmonic Poisson integral was constructed in Cartesian coordinates for the upper half-plane. The asymptotic properties of this operator on Lipschitz classes in a uniform metric were studied. An exact equality was found for the upper bound of the deviation of the Lipschitz class functions from the triharmonic Poisson integral defined in Cartesian coordinates for the upper half-plane in the metric space. The results obtained in the article demonstrate the connection between the methods of approximation theory and the principles of optimal decision theory. Keywords: optimization problem, class of Lipschitz functions, uniform metric, triharmonic Poisson integral.

On the well posedness of a mathematical model for a singular nonlinear fractional pseudo-hyperbolic system with nonlocal boundary conditions and frictional damping terms

<abstract><p>This paper is devoted to the study of the well-posedness of a singular nonlinear fractional pseudo-hyperbolic system with frictional damping terms. The fractional derivative is described in Caputo sense. The equations are supplemented by classical and nonlocal boundary conditions. Upon some a priori estimates and density arguments, we establish the existence and uniqueness of the strongly generalized solution for the associated linear fractional system in some Sobolev fractional spaces. On the basis of the obtained results for the linear fractional system, we apply an iterative process in order to establish the well-posedness of the nonlinear fractional system. This mathematical model of pseudo-hyperbolic systems arises mainly in the theory of longitudinal and lateral vibrations of elastic bars (beams), and in some special case it is propounded in unsteady helical flows between two infinite coaxial circular cylinders for some specific boundary conditions.</p></abstract>

Homogenisation method based on energy conservation and independent of boundary conditions

The foundation of homogenisation methods rests on the postulate of Hill–Mandel, describing energy consistency throughout the transition of scales. The consideration of this principle is therefore crucial in the discipline of Digital Rock Physics which focuses on the upscaling of rock properties. For this reason, numerous studies have developed numerical schemes for porous media to enforce the Hill–Mandel condition to be respected. The most common method is to impose specific boundary conditions, such as periodic ones. However, these boundary conditions influence both the effective property and the size of the REV. The recent study of Thovert and Mourzenko (2020) has shown that most boundary conditions still result in the same intrinsic effective physical property if the averaging is applied outside the range of the boundary layer. From this discovery, it becomes logical to question the status of Hill–Mandel postulate in porous media when homogenising away from the boundary. In this contribution, we simulate Stokes flow through random packings of spheres and a range of rock microstructures. For each, we plot the evolution of the ratio micro- vs macro-scale of the energy of the fluid transport outside the boundary layer, for a growing subsample size of porous media. Here, we prove that we naturally find energy consistency across scales when reaching the size of the Representative Elementary Volume (REV), which is a known condition for rigorous upscaling. Furthermore, we show that this index for the energy consistency is a more accurate indicator of REV convergence since the mean value is already known to be unitary.

Moral Considerations and Layoffs Dilemma: Analysis of Empathetic Ability in Decision-making

Empathy, the perceptive grasp and comprehension of someone else's emotional state, holds immense significance in social interactions. Its manifestation, nonetheless, undergoes fluctuations across diverse scenarios, making it a fascinating and complex aspect of human behaviour. To delve into this captivating phenomenon, this dissertation explores the ethical quandary faced by company managers when deciding whether to lay off employees during financial crises. In this scenario, empathy's role becomes even more critical. Employing the sensitive topic of employee layoffs as a prime example, the study unravels the intricacies of empathy disparity among individuals, delving into the psychological, cultural, and personal factors contributing to varying levels of empathetic responses. While universally recognised as essential, this meticulous analysis highlights how empathy can sometimes be elusive or inconsistent. Furthermore, the research sheds light on the cascading impact of leadership empathy on employee empathy and the subsequent influence of individual employee empathy on group empathy. Understanding the interconnected nature of empathy within an organizational context becomes pivotal for nurturing a compassionate and supportive work environment. Moreover, this study delves into the far-reaching implications of empathy within organizations. The intricate interplay between empathy, decision-making, conflict resolution, and team dynamics is examined. The research identifies specific boundary conditions that may affect the effectiveness of empathy, shedding light on when empathy might be less impactful and when it can genuinely foster positive outcomes.

Frequency dependent exact trial functions in Galerkin boundary method for free vibration analysis of thin plate

Method of frequency dependent exact trial functions for thin plate vibration based on fundamental solutions of Voigt is suggested. Contrary to other methods, where one of the functions is chosen as the scale and specific boundary condition dependent, it employs only the frequency dependent functions for both space coordinates. Thus they are scale independent, so the same functions can be used for different boundary conditions and plate dimensions. General rule for the choice of exact trial functions is formulated. The boundary conditions are satisfied according to the Galerkin boundary method, which actually minimizes the energy residuals with respect to each weight function (fundamental solution).The verification of method is performed on examples of rectangular plate with various boundary conditions. Several arbitrarily chosen sets of trial functions were employed in calculation of the same tasks, and it is shown that accuracy of the method is almost independent from the choice of them. Even the small number of trial functions provides the very accurate results for natural frequencies.

Formulation and Numerical Solution of Plane Problems of the Theory of Elasticity in Strains

This article is devoted to the formulation and numerical solution of boundary-value problems in the theory of elasticity with respect to deformations. Similar to the well-known Beltrami–Michell stress equations, the Saint-Venant compatibility conditions are written in the form of differential equations for strains. A new version of plane boundary-value problems in strains is formulated. It is shown that for the correctness of plane boundary value problems, in addition to the usual conditions, one more special boundary condition is required using the equilibrium equation. To discretize additional boundary conditions and differential equations, it is convenient to use the finite difference method. By resolving grid equations and additional boundary conditions with respect to the desired quantities at the diagonal nodal points, we obtained convergent iterative relations for the internal and boundary nodes. To solve grid equations, the elimination method was also used. By comparing with the Timoshenko–Goodyear solution on the tension of a rectangular plate with a parabolic load, the validity of the formulated boundary value problems in strains and the reliability of the numerical results are shown. The accuracy of the results has been increased by an average of 15%.

Frequency sensitive dynamic stiffness of the soil base

This article describes a method for calculating the frequency sensitive dynamic stiffness of the soil base using the finite element method. The main advantage of the method is the ability to take into account the heterogeneity of the properties of the base when calculating dynamic stiffness. Requirements for creating a design model, special boundary conditions, size and type of finite elements, and processing of results are presented. Based on the calculation results, a comparison with standard dynamic stiffnesses was made. It is shown that due to the presence of layering in the base, the standard and numerical dynamic stiffness have significant discrepancies. A solution to the test problem of determining the dynamic stiffness for a rectangular stamp on a layered base is presented. A comparison of the calculation results with a known solution shows the acceptable accuracy and reliability of the solution and confirms the correctness of the proposed calculation method

Lumped model for a quasi-continuously operating open metal hydride heat pump system

Hydrogen as a potential future fuel for fuel cell vehicles is mostly stored in high-pressure tanks at 350 or 700 bar, which requires energy-intense compression of typically 15 % of the lower heating value. For the recovery of parts of the compression work, a promising possibility is the usage of an open metal hydride heat pump. Similarly to other sorption-based heat pump systems, in order to reach high specific thermal power, it is crucial to find a trade-off in the design and operation of the reactor between two main factors: enabling fast reaction dynamics and reducing losses due to temperature switches. The present work introduces a steady-state model with lumped metal hydride and reactor mass considering one-dimensional heat and mass transfer, which is able to quickly predict the corresponding specific thermal power and efficiency. A special focus is on the calculation of the non-complete conversion due to an operation at constant gas flow. The model is validated with existing experimental data over a broad range of operation conditions in terms of metal hydride specific hydrogen mass flow (1.6–7.6 gH2 min−1 kgMH-1) and temperature boundary conditions (cold side temperature: 13–25 °C, hot side temperature: 24–42 °C). It is capable of describing the specific thermal power and the efficiency as the two main performance indicators with a suitable accuracy. To give an example of the applicability of the developed tool, a generic discussion of the performance limitations of the selected reactor design is carried out, indicating that the reactor of the validation experiment is mainly mass transport limited.