Numerical Method Research Articles

Experimental and numerical investigation on the hydroelastic response of barge and KVLCC2 ship

In this paper, the hydroelasticity of two segmented ship models (Barge and KVLCC2) is investigated by experimental and numerical methods. A two-way Computational Fluid Dynamics (CFD) and Finite Element Analysis (FEA) coupled method is adopted and further validated its accuracy against experimental results. The current approach emphasizes the overall convergence between two solvers, maintaining a strongly coupled manner to comprehensively address the fluid-structure interaction phenomenon, including the added mass effect. A series of experiments of a segmented Barge and KVLCC2 under various wave conditions were firstly conducted. The motions of the models are measured and the displacement Response Amplitude Operators (RAOs) are calculated. The CFD-FEA coupled method is demonstrated in agreement with experimental results by comparing the numerical prediction with the tank test results in terms of motion, affirming the validity and robustness. Finally, the hydroelastic response is discussed and investigated.

Thermal modal analysis of hypersonic composite wing on transient aerodynamic heating

Considering the influence of thermal stress and material property variations, this study employs the Navier–Stokes equations and Fourier heat conduction law to establish a semi-implicit time-domain numerical analysis method for hypersonic aerothermal-structural coupling. Study the temporal variation pattern of different regions of the composite material wing under aerodynamic heating. Using the obtained transient temperature field of the wing, the thermal modal of the wing at different time points is calculated using the finite element method. Additionally, it conducts an analysis and discussion on the factors influencing the thermal modal. Composites can be effectively utilized as thermal protection materials for aircraft. During the aerodynamic heating process, the leading edge temperature reaches thermal equilibrium first, followed by the trailing edge, and the belly plate experiences a slower thermal response. Temperature rise significantly affects higher-order modes, with the change in material properties during the early stages of heating being the dominant factor. This leads to a faster decrease in natural frequency. As heat conduction progresses, the influencing factors of thermal stresses gradually increase, and the natural frequency decreases slowly or even rises.

Box integrals with fermion bubbles for low-energy measurements of the weak mixing angle

The Moller experiment and the P2 experiment aim at measuring the weak mixing angle at low scales. The Moller experiment uses e-e-→e-e-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$e^- e^- \\rightarrow e^- e^-$$\\end{document}-scattering, the P2 experiment uses e-N→e-N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$e^- N \\rightarrow e^- N$$\\end{document}-scattering. In both cases, two-loop electroweak corrections have to be taken into account, and here in particular diagrams which give rise to large logarithms. In this paper we compute a set of two-loop electroweak Feynman integrals for point-like particles, which are obtained from a box integral by the insertion of a light fermion loop. By rationalising all occurring square roots we show that these Feynman integrals can be expressed in terms of multiple polylogarithms. We present the results in a form, which makes the large logarithms manifest. We provide highly efficient numerical evaluation routines for these integrals.

A Hybrid Continuation Framework for Analyzing Nonlinear Normal Modes of Systems With Contact Nonlinearity

Abstract The prediction of the modal properties of structural systems with contact clearances and prestress presents a computational challenge, as the nonlinearity induced by piecewise-linear stiffness eliminates the use of efficient linear modal analysis techniques. The most common approach to obtaining the nonlinear normal modes (NNMs) of these structural systems is a numerical framework that integrates numerical integration, the shooting method, and the pseudo-arc-length continuation scheme. This numerical continuation framework (NCF) computes NNMs through iterative numerical calculations; thus, the computational cost of the nonlinear modal analysis of complex nonlinear systems, particularly piecewise-linear systems, becomes prohibitively expensive as the model size increases. In this study, a hybrid continuation framework (HCF) combining analytic and numerical methods is proposed to enable efficient computations of NNMs for systems with contact boundaries. This new hybrid framework utilizes a semi-analytic method to conduct the iterative shooting procedure; thus, the computational burden of the numerical continuation can be significantly reduced. The proposed method is demonstrated on spring-mass oscillators with contact elements, and the NNMs obtained using the proposed method are validated by those computed using the traditional numerical continuation framework. The modal properties of the systems can be computed using the proposed framework with significant speed-up. Furthermore, the modal properties, including internal resonance and sharp turning in NNM curves, of the piecewise-linear systems are identified and discussed.

Introduction of Local Resonators to a Nonlinear Metamaterial With Topological Features

Abstract Recent work in nonlinear topological metamaterials has revealed many useful properties such as amplitude dependent localized vibration modes and nonreciprocal wave propagation. However, thus far, there have not been any studies to include the use of local resonators in these systems. This work seeks to fill that gap through investigating a nonlinear quasi-periodic metamaterial with periodic local resonator attachments. We model a one-dimensional metamaterial lattice as a spring-mass chain with coupled local resonators. Quasi-periodic modulation in the nonlinear connecting springs is utilized to achieve topological features. For comparison, a similar system without local resonators is also modeled. Both analytical and numerical methods are used to study this system. The dispersion relation of the infinite chain of the proposed system is determined analytically through the perturbation method of multiple scales. This analytical solution is compared to the finite chain response, estimated using the method of harmonic balance and solved numerically. The resulting band structures and mode shapes are used to study the effects of quasi-periodic parameters and excitation amplitude on the system behavior both with and without the presence of local resonators. Specifically, the impact of local resonators on topological features such as edge modes is established, demonstrating the appearance of a trivial bandgap and multiple localized edge states for both main cells and local resonators. These results highlight the interplay between local resonance and nonlinearity in a topological metamaterial demonstrating for the first time the presence of an amplitude invariant bandgap alongside amplitude dependent topological bandgaps.

Biased versus unbiased numerical methods for stochastic simulations

Approximate numerical methods are one of the most used strategies to extract information from many-interacting-agents systems. In particular, numerical approximations are of extended use to deal with epidemic, ecological and biological models, since unbiased methods like the Gillespie algorithm can become unpractical due to high CPU time usage required. However, the use of approximations has been debated and there is no clear consensus about whether unbiased methods or biased approach is the best option. In this work, we derive scaling relations for the errors in approximations based on binomial extractions. This finding allows us to build rules to compute the optimal values of both the discretization time and number of realizations needed to compute averages with the biased method with a target precision and minimum CPU-time usage. Furthermore, we also present another rule to discern whether the unbiased method or biased approach is more efficient. Ultimately, we will show that the choice of the method should depend on the desired precision for the estimation of averages.

Topological nano-switches in higher-order topological insulators

Abstract We consider multi-terminal transport through a flake of rectangular shape of a two-dimensional topological insulator in the presence of an in-plane magnetic field. This system has been shown to be a second-order topological insulator, thus exhibiting corner states at its boundaries. The position of the corner states and their decay length can be controlled by the direction of the magnetic field. In the leads we assume that the magnetic field is absent and therefore we have helical one-dimensional propagating states characteristic of the spin-Hall effect. Using a low-energy effective Hamiltonian we show analytically that, in a two-terminal setup, transport can be turned on and off by a rotation of the in-plane magnetic field. Similarly, in a three terminal configuration, the in-plane magnetic field can be used to turn on and off the transmission between neighbouring contacts, thus realising a directional switch. Analytical calculations are supplemented by a numerical finite-difference method. For small values of the Fermi energy and field strength, the analytical results agree exceptionally well with the numerics. The effect of disorder is also addressed in the numerical approach. We find that the switching functionality is remarkably robust to the presence of strong disorder stemming from the topological nature of the states contributing to the electron transport.

Double-virtual NNLO QCD corrections for five-parton scattering. II. The quark channels

We complete the computation of two-loop helicity amplitudes required to obtain next-to-next-to-leading order QCD corrections for three-jet production at hadron colliders, including all contributions beyond the leading-color approximation. The analytic expressions are reconstructed from finite-field samples obtained with the numerical unitarity method. We find that the reconstruction is significantly facilitated by exploiting the overlaps between rational coefficient functions of quark and gluon processes, and we display their compact generating sets. We implement our results in a public code, and demonstrate its suitability for phenomenological applications. Published by the American Physical Society 2024

Double-virtual NNLO QCD corrections for five-parton scattering. I. The gluon channel

We compute the two-loop helicity amplitudes for the scattering of five gluons, including all contributions beyond the leading-color approximation. The analytic expressions are represented as linear combinations of transcendental functions with rational coefficients, which we reconstruct from finite-field samples obtained with the numerical unitarity method. Guided by the requirement of removing unphysical singularities, we find a remarkably compact generating set of rational coefficients, which we display entirely in the manuscript. We implement our results in a public code, which provides efficient and reliable numerical evaluations for phenomenological applications. Published by the American Physical Society 2024

Hydrogeological characterization of low permeability medium for conceptualization of a mine site in Eastern Turkey

The mining site in Eastern Anatolia of Turkey were encounter a significant risk of slope instability within the operational area. One of the processes that govern slope stability is the pore water pressure distribution. The conceptualization and characterization of porous media serve as fundamental prerequisites for the implementation of numerical methods aimed at predicting pore water distribution. This study aims to characterize the hydrogeological properties of water bearing rocks in the active mining site in Eastern Anatolia of Turkey. A total of 21 wells and drill holes were drilled in the study area to conduct in-situ tests, monitoring, and sampling. The large diameter wells drilled in surrounding the carbonate rocks were to determine the groundwater flow and boundary conditions and also wells tapped metasediments and diorite unit for hydraulic testing. The lugeon tests and installation of vibrating wire piezometers were carried out at small diameter drill holes to obtain localized hydraulic conductivity of metasediments and diorite at different depths and monitoring pore water pressure distribution along some critical cross-sections. The results obtained from these tests are used for developing hydrogeological conceptual model for groundwater flow. The results of in-situ tests show that the metasediment and diorite units act as a single hydrostratigraphic unit. The metasediments and diorite have high total porosity and low specific yield indicating that the pore water is retained by electrostatic forces in the medium and it resists flow due to low hydraulic conductivity. The vertical variation in hydraulic conductivity values indicates that the medium is highly heterogeneous.

Numerical evaluation of impact resistance of reinforced concrete walls

Reinforced concrete(RC) structures are occasionally subjected to accidental impact during service, which can cause economic losses and casualties. Most previous research on the impact resistance of RC structures has focused on beams, columns, and slabs except walls. Thus, it is necessary to study the impact response and resistance performance of essential RC walls with high resistance requirements, such as critical shear walls, important structures, and vital protective structures of high-rise buildings in earthquake and mountainous areas under low-speed impact. This research verified the finite element model (FEM) through pendulum impact experiments on RC walls (with an impact mass of 2 tons) firstly, then proposed the damage assessment parameters of the RC wall, and analysed the impact response mechanism and resistance performance of RC walls with several reinforcement ratios under different impact loads. The research results indicate that the impact effect on the wall must consider the different value (D-value) between local and global deformation. The impact load significantly influences the peak impact force and the displacement of the RC wall. The mass affects the RC wall’s global residual deflection. At the same time, the velocity significantly influences local displacement, and correspondingly, the RC wall is more prone to local damage with high velocity. Thickness, the concrete fc, and the reinforcement ratio affect the impact resistance of the RC wall. The thicker wall can cause a shorter impact duration, and milder concrete damage, but the smaller rebar stress. The larger fc will bring greater rebar stress and milder concrete damage. A high reinforcement ratio will increase the impact force platform value and the RC wall’s concrete damaged ratio but will reduce the plastic strain of the rebars.

Layered construction process with the material point method

This paper presents a novel procedure to simulate layered construction processes with the material point method (MPM), a method suitable for modelling large deformations. For the first time, the paper provides the MPM with the capability of modelling the behaviour of earth structures from their construction until the eventual post-failure behaviour in an integrated manner without requiring, as currently done, the use of other numerical tools for the construction simulation. In addition, the proposed methodology includes the option of simulating the engineering practice of compensating settlements that occurred during construction, to match the designed geometry. This option, typically neglected in alternative numerical methods, is implemented by filling the computational elements of the layers that become empty by adding new material points.The construction process proposed and its numerical implementation into an open-source code are described in detail. The validation is carried out by modelling an elastic oedometric column with varying number of layers and by comparing it with analytical solutions and finite element-based results. The construction of a soil embankment in dry, saturated, and partially saturated conditions is also simulated. It shows the capability of the method to capture the excess pore water pressures that may develop.

Numerical Evaluation of Pile Length, Lateral Bulging and Encasement Length: A Comparative Study on Ordinary and Encased Granular Piles

Numerical Evaluation of Pile Length, Lateral Bulging and Encasement Length: A Comparative Study on Ordinary and Encased Granular Piles

Axial Tensile Ultimate Strength of an Unbonded Flexible Riser Based on a Numerical Method

Unbonded flexible risers consist of several helical and cylindrical layers, which can undergo large bending deformation and can be installed to different configurations to adapt to harsh marine environments, and is a key equipment in transporting oil and gas resources from Ultra Deep Waters (UDWs) to offshore platforms. The helical interlayer of an unbonded flexible riser makes the structural behavior difficult to predict. In this paper, the axial tensile behavior and the axial tensile ultimate strength of an unbonded flexible riser are studied based on a typical 2.5-inch eight-layer unbonded flexible riser model, and verified through a theoretical method considering the contact between adjacent layers. First, the balance equation of separate layers is deduced by a functional principle, and then the overall theoretical model of an unbonded flexible riser is established considering the geometric relationship between adjacent layers. Then, the numerical model considering the detailed geometric properties of an unbonded flexible riser is established to simulate the axial tensile behavior. Finally, after being verified through the experimental results, the axial tensile stiffness and axial tensile strength of an unboned flexible riser considering the elasticity of the tensile armor layer are studied using the proposed two methods. Additionally, the effect of frictional coefficients is conducted. The numerical and theoretical results show good agreement with the test results, and the friction between adjacent layers would increase the axial tensile stiffness of an unbonded flexible riser.

Analysis of the Dynamical Properties of Discrete Predator-Prey Systems with Fear Effects and Refuges

This paper examines the dynamic behavior of a particular category of discrete predator-prey system that feature both fear effect and refuge, using both analytical and numerical methods. The critical coefficients and properties of bifurcating periodic solutions for Flip and Hopf bifurcations are computed using the center manifold theorem and bifurcation theory. Additionally, numerical simulations are employed to illustrate the bifurcation phenomenon and chaos characteristics. The results demonstrate that period-doubling and Hopf bifurcations are two typical routes to generate chaos, as evidenced by the calculation of the maximum Lyapunov exponents near the critical bifurcation points. Finally, a feedback control method is suggested, utilizing feedback of system states and perturbation of feedback parameters, to efficiently manage the bifurcations and chaotic attractors of the discrete predator-prey model.

Some specific wormhole solutions in extended f(R,G,T) gravity

This research work provides an exhaustive investigation of the viability of different coupled wormhole (WH) geometries with the relativistic matter configurations in the [Formula: see text] extended gravity framework. We consider a specific model in the context of [Formula: see text]-gravity for this purpose. Also, we assume a static spherically symmetric spacetime geometry and a unique distribution of matter with a set of shape functions ([Formula: see text]) for analyzing different energy conditions. In addition to this, we examined WH-models in the equilibrium scenario by employing anisotropic fluid. The corresponding results are obtained using numerical methods and then presented using different plots. In this case, [Formula: see text] gravity generates additional curvature quantities, which can be thought of as gravitational objects that maintain irregular WH-situations. Based on our findings, we conclude that in the absence of exotic matter, WH can exist in some specific regions of the parametric space using modified gravity model as [Formula: see text].

Numerical Analysis on Performance Improvement of a Vertical Plate Indirect Evaporative Cooler with Baffles

The performance of the Plate Indirect Evaporative Cooler (PIEC) can be effectively improved by incorporating baffles in the dry channel. However, in the dimensional influence of the baffles on PIEC performance there remains a research gap. In order to investigate the impact of baffle dimensions on the wet bulb efficiency, namely the average heat transfer coefficient and the cooling capacity of the PIEC, this paper proposed and verified a three-dimensional numerical model and method based on the species transport model and the Euler wall film model. At the same time, in order to obtain the equilibrium point between the enhanced heat transfer performance and the additional resistance induced by baffles, a comprehensive performance evaluation index is introduced. The results indicate that, under the same conditions, (1) the baffle effect on PIEC performance is significant at a lower inlet air velocity, and the wet bulb efficiency of the PIEC with baffles can be improved by 22.8%; (2) the baffle effect on PIEC performance is negative if its relative length exceeds 60% or the primary air inlet velocity surpasses 4 m/s under the conditions specified in this paper; and (3) the baffle effect on PIEC performance is significant when its channel height is lower and its channel width is larger, and the wet bulb efficiency of the PIEC with baffles can be improved by 29.3%.

Simultaneous influence of contact angle, capillary number, and contraction ratio on droplet dynamics in hydrophobic microchannel

Abstract In droplet-based microfluidic systems, droplet motion and behavior largely depend on fluid properties, flow conditions, and microchannel geometry. This study presents a model to predict droplet dynamics within a contraction microchannel, considering various factors, such as contact angle (θ), capillary number (Ca), and contraction ratio (C), within defined ranges, through the employment of a three-dimensional numerical simulation method. Droplets may undergo trap, squeeze, or breakup as they traverse the contraction microchannel, contingent upon the aforementioned factors. The transition from trap to squeeze is determined by the critical value of Capillary number (〖Ca〗_I). Within the squeezed regime, the contact angle influences droplet deformation and velocity within the contraction microchannel. However, when capillary number (〖Ca〗_II) in contraction microchannel increases to a specific threshold corresponding to the contraction ratio, the droplet no longer in contact with the wall and becomes independent of the contact angle, a phenomenon referred to as detachment. Moreover, the contact angle's impact on the transition of droplets from squeeze to breakup is contingent upon the microchannel's contraction ratio. This study provides a comprehensive overview of droplet behavior within microfluidic systems, offering valuable insights for the optimization and design of microsystems.

Analysis of the Interaction Effects of Electromagnetic Fields with Major Living Tissues—One Health Concept Numerical Evaluation Strategy

The well-being and sociability of individuals have always been part of modernity. The development of new technologies that meet these aspirations is receiving increasing attention. Thus, strengthening the desired objectives of these technologies and minimizing their undesirable side effects is the subject of growing commitment. The present contribution aims, in this context, to evaluate and analyze the desired and undesirable effects of the interaction of electromagnetic fields with living tissues in general. These are routines based on mathematical modeling reinforcing the expected functions as well as those of control and protection against undesirable effects. These adverse effects correspond to the “One Health” concept, which encompasses the health of animals, plants and humans, as well as ecological disorders created by human activity. First, in this article, the interactions of electromagnetic fields with tissues are analyzed, involving their thermal biological effects of desired and undesired exposures. The roles of blood and sap fluids in bio-affected tissues are then analyzed. Secondly, the equations governing electromagnetics and bio-heat, as well as their coupled solution are studied. Third, the thermal behavior of tissues and the adverse effects of exposure are examined. Next, monitoring and defending the effects of exposures are discussed. This contribution, supported by a review of the literature, illustrates routines for mathematical modeling of the generalized interaction of electromagnetic fields with living tissues.

Load-end shortening curve of stiffener elements with beam-column buckling considering steel grades based on empirical formulae of critical stress

The existing load-end shortening formulae with beam-column buckling in CSR-H were derived from the theoretical buckling formulae of stiffener elements considering the effective width of attached plate. However, due to different yielding stress and plastic flow ability, the critical stress of stiffener elements for elastic-plastic beam-column buckling may be relevant to steel grades. The critical stress of beam-column buckling was analysed by numerical method and compression test under supply supported constraints. Separate seven steel column samples from slender to sturdy were designed to be studied for various grades of steel mainly including 921A, S355 and Q235. After comparison, the empirical formulae of critical stress considering different yield stress were proposed in power exponent expression, and then employed to replace the theoretical buckling formulae in the load-end shortening curves in incremental-iterative method. This new load-end shortening expression of stiffener elements with beam-column buckling mode could more accurately evaluate the progressive collapse behaviours under longitudinal compression.