Finite Boundary Research Articles

Benchmark between N-body, PIC, and semi-Lagrangian simulations of Landau-damped Langmuir wave

This work presents a benchmark study comparing three distinct numerical methods—Particle-In-Cell (PIC), semi-Lagrangian, and N-body simulations—for analyzing the damping of Langmuir waves in a one-dimensional Vlasov–Poisson plasma system. Each approach has unique advantages in terms of accuracy, resolution, and computational cost. The comparison aims to discriminate between numerical artifacts and physical phenomena, identifying the contribution of finite particle numbers and boundary conditions in both linear and nonlinear regimes. The study demonstrates strong agreement between the PIC and semi-Lagrangian methods in both regimes. N-body simulations, while requiring a specific method to overcome statistical noise, agree in the limit of many bodies (>500). Crucial subtleties regarding initial and boundary conditions are discussed throughout.

Restrictions by object under Article 101(1) TFEU: From dark art to administrable framework

Abstract This article presents the principles underpinning the approach followed by the Court of Justice (ECJ) when evaluating whether a practice has, as its object, the restriction of competition. It discusses, inter alia, what an authority (or claimant) needs to prove and explains what the evaluation of the economic and legal context involves in concrete terms. The analysis shows that the ECJ’s overall approach is both predictable (in the sense that the notion has clear and finite boundaries) and administrable (in the sense that the said approach places adequate and workable demands on authorities and claimants). It appears, on the other hand, that there are ways in which some principles underpinning the case law could be streamlined and made more explicit so as to guarantee the uniform application of Article 101(1) TFEU across the European Union at a time when private enforcement is on the rise.

On undevelopment and de‐development: A geographical critique on perpetual growth and resource‐based accumulation

AbstractEconomic development is often defined as a cycle of sustained growth adding to ever‐increasing living standards of the general population. However, in human and economic geography such an orthodox definition of development is increasingly considered problematic. Not only have cycles of lower growth, rising debt, inequality and environmental degradation challenged the foundations of post‐war prosperity. Economic development in advanced nations must also be associated with the development of underdevelopment in peripheral countries. In this essay, I therefore contend that what is otherwise defined as ‘development’ has increasingly taken the form of ‘undevelopment’, i.e., a regressive cycle of falling productivity, financialisation, rising inequality, global imbalance and irreversible climate change. Although it is difficult to change the global course of undevelopment, I argue that de‐development can develop into its logical successor. Indeed, by progressively transcending the capitalist world‐system, I conclude that a more durable global economic system can emerge where global wealth redistribution and economic activity within the planet's finite boundaries are central.

Using RBF-FD for calculation of hydroelastic vibrations of axisymmetric orthotropic shells of rotation

Geometrically nonlinear differential equations describing the dynamic deformation of axisymmetric shells of rotation are derived on the basis of general equations for solving functions in the global coordinate system. The equations take into account thinning/thickening at large longitudinal strains as well as transverse shear for thick shells. The motion and pressure of an ideal incompressible fluid is described by a displacement potential. To obtain the numerical solution, the finite difference method based on spline interpolation by polyharmonic radial basis functions is applied. The calculation method is implemented in software package. Good agreement of the calculated displacements with the results of modeling by different finite elements in ANSYS is obtained. The frequencies of the hydroelastic vibrations of the tanks are compared with those obtained by the finite element and boundary element method, as well as with results from published articles by other researchers.

Numerical analysis of circular hollow section bar with stiffened flattened ends

Circular hollow sections are usually used in long-span roof truss systems due to the advantages they offer. One of the typology for connecting elements in such structures involves the flattening of bar ends, in order to provide a simpler and more economical connection. A new flattening typology called stiffened flattening is proposed, characterized by a non-flat geometry, with the creation of stiffeners in the lateral edges of the bar flattened ends. A theoretical, numerical and experimental study was carried out on the behavior of a plane truss composed of circular hollow sections, in which diagonal bars have stiffened flattening ends. The diagonal connecting system with the chord members uses connecting plates. The plates are welded to the chords and the diagonals are connected to latter through a single bolt. This work presents the numerical analysis of a circular hollow section bar with stiffened flattening ends subjected to compression. This is a study of the behavior of an isolated bar compressed from the truss, which corresponds to the most requested diagonal composed by circular hollow sections with stiffened flattening ends. The numerical analysis using finite elements method was developed through ANSYS software with the Parametric Design Language (APDL), in which parameters such as geometry, material, element type, definition of the finite element mesh, boundary conditions and application of compression loads are specified. A non-linear analysis was performed using shell element on the bar with stiffened flattened ends. The numerical analysis result satisfactorily represented the structural behavior of the isolated circular hollow section bar with stiffened flattening ends. It was possible to observe the buckling effect of the compressed circular hollow section bar and the effect of the axial load eccentricity due to the stiffened flattening of bar ends.

A multiverse model in T2 dS wedge holography

We construct a multiverse model where empty AdSd+1 space is cut off by a pair of accelerated dSd space universes, at a finite AdS boundary cutoff which we treat as a T2 deformation in the holographic dual, and one in the AdS interior, the IR brane; and denote the construction as T2 dS wedge holography. We glue together several copies of this configuration along the UV cutoff and the IR branes in a periodic matter. To provide the model with dynamics similar to those of near Nariai black holes used in other multiverse toy models, we specialize to d = 2 and add dS JT gravity as an intrinsic gravity theory on the IR branes. We then study the entanglement entropy with respect to a finite cutoff observer, who finds a Page curve transition due to an entanglement island connecting the UV cutoff and IR brane. This process involves the coarse-graining of information outside the causally accessible region to the observer. Our model provides an explicit realization of entanglement between IR and UV degrees of freedom encoded in the multiverse.

Numerical Simulation of Electromagnetic Nondestructive Testing Technology for Elasto-Plastic Deformation of Ferromagnetic Materials Based on Magneto-Mechanical Coupling Effect.

A numerical tool for simulating the detection signals of electromagnetic nondestructive testing technology (ENDT) is of great significance for studying detection mechanisms and improving detection efficiency. However, the quantitative analysis methods for ENDT have not yet been sufficiently studied due to the absence of an effective constitutive model. This paper proposed a new magneto-mechanical model that can reflect the dependence of relative permeability on elasto-plastic deformation and proposed a finite element-infinite element coupling method that can replace the traditional finite element truncation boundary. The validity of the finite element-infinite element coupling method is verified by the experimental result of testing electromagnetic analysis methods using TEAM Problem 7. Then, the reliability and accuracy of the proposed model are verified by comparing the simulation results under elasto-plastic deformation with experimental results. This paper also investigates the effect of elasto-plastic deformation on the transient magnetic flux signal, a quantitative hyperbolic tangent model between Bzpp (peak-peak value of the normal component of magnetic flux signal) and elastic stress, and the exponential function relationship between Bzpp and plastic deformation is established. In addition, the difference and mechanism of a magnetic flux signal under elasto-plastic deformations are analyzed. The results reveal that the variation of the transient magnetic flux signal is mainly due to domain wall pinning, which is significantly affected by elasto-plastic deformation. The results of this paper are important for improving the accuracy of quantitative ENDT for elasto-plastic deformation.

Metaharvesting: emergent energy harvesting by piezoelectric metamaterials

Vibration energy harvesting is a technology that enables electric power generation by augmenting vibrating materials or structures with piezoelectric elements. In a recent work, we quantified the intrinsic energy-harvesting availability (EHA) of a piezoelectric phononic crystal (Piezo-PnC) by calculating its damping ratio across the Brillouin zone and subtracting off the damping ratio of the corresponding non-piezoelectric version of the phononic crystal. It was highlighted that the resulting quantity indicates the amount of useful energy available for harvesting and is independent of the finite structure size and boundary conditions and of any forcing conditions. Here, we investigate the intrinsic EHA of two other material systems chosen to be statically equivalent to a given Piezo-PnC: a piezoelectric locally resonant metamaterial (Piezo-LRM) and a piezoelectric inertially amplified metamaterial (Piezo-IAM). Upon comparing with the intrinsic EHA of the Piezo-PnC, we observe an emergence of energy-harvesting capacity, a phenomenon we refer to as metaharvesting. This is analogous to the concept of metadamping, except the quantity evaluated is associated with piezoelectric energy harvesting rather than raw dissipation. Our results show that the intrinsic EHA is enhanced by local resonances and enhanced further by inertial amplification. These findings offer a new paradigm for the design—at the fundamental level—of architectured piezoelectric materials with superior energy-harvesting capacity.

Bulk-local dS3 holography: the matter with TT¯ + Λ2

We propose an algorithm which builds a concrete dual for large-radius 3d de Sitter with a timelike York boundary for both gravity and bulk effective fields. This generalizes the solvable TT¯ + Λ2 deformation, whose finite real spectrum accounts for the refined Gibbons-Hawking entropy as a microstate count while reproducing the radial static patch geometry. The required generalization to produce approximately local boundary conditions for bulk quantum fields requires a scheme for defining double-trace operators dual to deformed boundary conditions to realize the finite timelike boundary, valid at finite N. By starting with a small stint of a pure TT¯ trajectory, the theory becomes finite, enabling well-defined subtractions to define the double-trace deformation so as to match the large-N prescription of Hartman, Kruthoff, Shaghoulian, and Tajdini to good approximation. We incorporate the matter effecting an uplift from negative to positive cosmological constant, and analyze the effect of matter on the energy spectrum of the theory arising from time-dependent bulk excitations. This validates the cosmic horizon dS3 microstate count for large-radius dS3 holography, embedding TT¯ + Λ2 concretely into a larger theory consistent with bulk locality for matter fields. We comment briefly on potential upgrades to four dimensions and other future directions.

Using wave based SEA methods to model noise and vibration in underwater structures across a broad frequency range

Modelling noise and vibration transmission in underwater structures is often challenging due to the large size of the structures and the need for analysis across a broad frequency range. Finite Element and Boundary Element methods are useful at lower frequencies but are typically not computationally tractable for system level models at mid and high frequencies. Statistical Energy Analysis (SEA) methods are widely used for modeling structures in air at mid and high frequencies. However, traditional SEA methods often do not contain enough detail to describe wave propagation in heavy fluid loaded structures in underwater applications. This paper discusses the use of a more general 'wave based' SEA method that uses periodic structure theory to accurately calculate the wavetypes of typical underwater structures. The paper illustrates the method by initially considering simple structural sections and showing the effects of: curvature, heavy fluid-loading, panel stiffeners/ribs. The method is then applied to a simplified full scale submarine model and comparisons are made with a nodal finite element model. The domain of validity and the hypotheses of the method are then discussed.

Aspect ratio-dependent volume resistivity in unidirectional composites: Insights from electrical conduction behavior

The electrical properties of carbon fibers serve as the foundation for the multifunctional applications of carbon fiber-reinforced composite structures. In scenarios that exploit the electrical characteristics of materials, accurate estimation of electrical resistivity stands as a critical factor. This study endeavors to elucidate the electrical conduction behaviors in unidirectional composites with different fiber orientation angles (0°, 15°, 30°, 45°, 60°, 75°, and 90°) and aspect ratios, thereby deriving the volume resistivity within an arbitrary Cartesian coordinate system. Employing thermal infrared imaging technology and finite element analysis, we identified distinctive electrical conduction behaviors associated with aspect ratios in carbon fiber composite plates. Notably, a critical aspect ratio exists wherein the diagonal yarn is the only conductive path between two electrodes. Below this critical threshold, no direct conductive path exists, and current flows through the shortest distance between parallel yarns. Conversely, beyond the critical aspect ratio value, multiple yarns form conductive paths between the two electrodes. Based on the electrical conduction behavior of unidirectional composites under different angles and aspect ratios, the volume resistivity with finite boundaries was derived and examined under an arbitrary Cartesian coordinate basis.

Computational Mathematics for Electromagnetic Field Simulation

Computational science could be a key portion of making reenactments and investigations of electromagnetic areas superior, which is critical for numerous ranges, from restorative imaging to broadcast communications. This theoretical talks around the essential thoughts, computer methods, and fundamental issues that come up when utilizing scientific models to form precise considers of electromagnetic areas. Maxwell's conditions portray how electric and attractive areas carry on in space and time and are utilized to recreate electromagnetic areas. Since real-life circumstances are so complicated and distinctive, these conditions, which are made up of differential conditions with fractional subordinates, got to be fathomed numerically. Utilizing procedures like finite difference, limited component, and boundary component strategies, computational science breaks these issues down into shapes that can be fathomed. Limited contrast strategies utilize a framework to induce near to subordinates, whereas finite element strategies break the space up into littler pieces to accurately illuminate complicated geometries. Boundary component strategies center on fundamentally details along the domain's edges, giving fast answers for problems within the exterior world. Each strategy strikes a adjust between exactness, the speed of calculations, and the capacity to work with distinctive electromagnetic occasions. Overseeing the complexity of the coding system, accurately speaking to the highlights of the fabric, and dealing with nonlinearities within the conditions are a few of the issues that come up in computational electromagnetic field reenactment. To create simulations more exact and productive, analysts are continuously looking into unused math calculations, concurrent computer methods, and optimization methodologies.

Eshelby problem in amorphous solids.

The Eshelby problem refers to the response of a two-dimensional elastic sheet to cutting away a circle, deforming it into an ellipse, and pushing it back. The resulting response is dominated by the so-called Eshelby kernel, which was derived for purely elastic (infinite) material, but has been employed extensively to model the redistribution of stress after plastic events in amorphous solids with finite boundaries. Here, we discuss and solve the Eshelby problem directly for amorphous solids, taking into account possible screening effects and realistic boundary conditions. We find major modifications compared to the classical Eshelby solution. These modifications are needed for modeling correctly the spatial responses to plastic events in amorphous solids.

Ground motion amplification by twin circular tunnels for obliquely incident seismic waves: Effects of saturated poroelastic soil parameters

Underground structures can significantly affect the ground motion and further influence the seismic design of aboveground structures around them. Although this issue has been well recognised and studied, it is not thoroughly addressed as a large number of factors are involved. This paper focuses on ground motion amplification induced by twin circular tunnels embedded in saturated poroelastic soil. The saturated poroelastic soil is modelled as a two-phase medium to consider parameters characterising the fluid phase. Three-dimensional scattering features of the twin tunnels for obliquely incident seismic waves are numerically investigated by a 2.5D finite element and boundary element hybrid model. It is shown that the presence of the twin tunnels can lead to significant modifications of the free-field motion, in terms of its magnitude and distribution. The three-dimensional oblique incidence scenario presents a more general perspective on the ground motion amplification. Moreover, the effects of saturated poroelastic soil parameters on the ground motion amplification, including soil permeability, groundwater levels, and the degree of saturation, are parametrically investigated. The differences in ground motion amplification patterns between the saturated poroelastic and dry poroelastic soil scenarios are notable, highlighting the effects of parameters characterising the fluid phase.

Fluid-structure interaction analysis of a healthy aortic valve and its surrounding haemodynamics.

The opening and closing dynamics of the aortic valve (AV) has a strong influence on haemodynamics in the aortic root, and both play a pivotal role in maintaining normal physiological functions of the valve. The aim of this study was to establish a subject-specific fluid-structure interaction (FSI) workflow capable of simulating the motion of a tricuspid healthy valve and the surrounding haemodynamics under physiologically realistic conditions. A subject-specific aortic root was reconstructed from magnetic resonance (MR) images acquired from a healthy volunteer, whilst the valve leaflets were built using a parametric model fitted to the subject-specific aortic root geometry. The material behaviour of the leaflets was described using the isotropic hyperelastic Ogden model, and subject-specific boundary conditions were derived from 4D-flow MR imaging (4D-MRI). Strongly coupled FSI simulations were performed using a finite volume-based boundary conforming method implemented in FlowVision. Our FSI model was able to simulate the opening and closing of the AV throughout the entire cardiac cycle. Comparisons of simulation results with 4D-MRI showed a good agreement in key haemodynamic parameters, with stroke volume differing by 7.5% and the maximum jet velocity differing by less than 1%. Detailed analysis of wall shear stress (WSS) on the leaflets revealed much higher WSS on the ventricular side than the aortic side and different spatial patterns amongst the three leaflets.

Not every finite CP is a phase

This paper proposes that phases are extended projections containing all the projections in the relevant functional sequence, and that extended projections lacking lower projections in the sequence are in turn not phases. The claim is motivated and supported by a detailed investigation of finite ECM in Korean, where embedded subjects are assigned accusative case across finite CP boundaries. I argue that finite ECM occurs in Korean when the embedded clause lacks a T projection in the verbal domain. A typology of clausal complementation emerges, distinguishing defective finite CPs as distinct entities from full CPs in terms of syntactic locality. The proposal also explains the puzzling individual-level restriction in Korean ECM: a GEN operator must occur in the structure to stopgap the semantic effects of missing T, namely to render the embedded finite clause a proposition of type t. The defective CP analysis extends to other languages exhibiting crossclausal finite A-dependency exclusively with defective CPs.

Development of a numerical and analytical methodology for analyzing hybrid laminates with multi-oriented piezoelectric and structural layers

Piezoelectric materials can generate an electrical response under mechanical stress, functioning as sensors. Conversely, applying an electrical field to these materials enables precise motion control, making them effective as actuators. Using a proposed methodology, this work focuses on evaluating the effective properties of hybrid multi-oriented composite laminates consisting of structural and piezoelectric layers driven by monoclinic constitutive equations. Square unit cell model was used to calculate all coefficients of the material tensor. The finite element (FE) homogenization method and periodic boundary conditions implemented by node-to-node constraint equations are used to study a representative volume element (RVE) modeled as three-layer unit cell in the mesoscale. The pre-processing, FE analysis, and post-processing are conducted in the FE package ABAQUSⓇ through Python scripts. The computational approach yields results that align closely with the analytical effective coefficients derived from the Asymptotic Homogenization Method (AHM), demonstrating the robustness and accuracy of the proposed methodology.

A new seismic wave input method for canyon sites based on the finite element method-indirect boundary integral equation method

The seismic input is the basis for the seismic safety analysis of dams, but current seismic input methods have not reasonably considered the influence of canyon scattering effects on the dynamic response of dams. In this paper, the total motion field of the canyon is deconstructed into the free field of a uniform half space and the scattering field of the canyon and they are obtained separately. The indirect boundary integral equation method (IBIEM) is used to determine the scattering field of the canyon, which is superimposed with the free field to obtain the seismic ground motion field (total motion field) of the canyon. The accuracy of the total motion field of the canyon is verified through reference solutions. In the finite element analysis of seismic ground motion field in the canyon, the total motion field at the truncation boundary of the canyon foundation is transformed into the equivalent seismic input loads and the interior of the canyon are simulated using the finite element method (FEM). Then, based on the wave input for the free field combined with the viscoelastic artificial boundary, a new wave input method for the total motion field combined with the viscoelastic artificial boundary is established. The seismic wave input method based on the finite element-indirect boundary integral equation method is applied to numerically determine the seismic response of a trapezoidal canyon. The differences in the seismic response of the canyon under free-field input and total motion field input are discussed. The results show that there is a certain deviation between the displacement and waveform obtained from the free-field input and the solutions obtained from the indirect boundary integral equation method. There is a large error for a large angle of incidence, and the errors increase with increasing seismic wave frequency. When the incident angle is 60°, the maximum error in the frequency domain reaches 92.3 %, and the maximum error in the time domain reaches 250 %. The displacement amplitude and waveform of the canyon obtained from the total motion field input showed agreement with the results of the indirect boundary integral equation method. The wave input method established in this paper has high calculation accuracy and reasonably considers the scattering effect of canyons, which provides a basis for more accurate predictions of the seismic response of dams on canyon foundations.

The cosmological switchback effect. Part II

Recent developments in static patch holography proposed that quantum gravity in de Sitter space admits a dual description in terms of a quantum mechanical theory living on a timelike surface near the cosmological horizon. In parallel, geometric observables associated with the Einstein-Rosen bridge of a black hole background were suggested to compute the computational complexity of the state dual to a gravitational theory. In this work, we pursue the study of the complexity=volume and complexity=action conjectures in a Schwarzschild-de Sitter geometry perturbed by the insertion of a shockwave at finite boundary times. This analysis extends previous studies that focused either on the complexity=volume 2.0 conjecture, or on the case of a shockwave inserted along the cosmological horizon. We show that the switchback effect, describing the delay in the evolution of complexity in reaction to a perturbation, is a universal feature of the complexity proposals in asymptotically de Sitter space. The geometric origin of this phenomenon is related to the causal connection between the static patches of de Sitter space when a positive pulse of null energy is inserted in the geometry.

Numerical Seakeeping Analysis for a Floating Helicopter After Ditching in Water

Abstract This paper investigates the seakeeping behavior of helicopters after an emergency landing in water, focusing on a Northern North Sea wave climate and considering a realistic helicopter geometry. Computational fluid dynamics techniques, including the cell-centered finite volume method and boundary element methods, were utilized to analyze motion responses and load distribution. The study ensures numerical result reliability through recommended simulation practices. Results indicate that the inviscid model produces similar outcomes to the viscous model in decay tests with roll, pitch, and heave motions. Natural periods for roll, pitch, and heave motions were obtained. Linearity between incident wave amplitude and pitch/heave response was noted for regular waves, while roll linearity was limited for small angles. In irregular wave conditions, helicopters tended to align perpendicular to waves over time, resulting in increased peak roll angles with higher significant wave heights. Exceedance rates of maximum roll peaks, useful for the assessment of capsizing probability, were quantified for different significant wave heights.