Search Results (49)

We continue Riemann’s program of geometrizing physics, extending it to encompass gravitational and electromagnetic fields as well as media, all of which influence the geometry of spacetime. The motion of point-like objects—both massive and massless—follows geodesics in this modified geometry. To describe this geometry, we generalize the notion of a metric to local scaling functions which permit not only quadratic but also linear dependence on temporal and spatial separations. Our local scaling functions are defined on flat spacetime coordinates. We demonstrate how to construct various geometries directly from field sources, using symmetry and superposition, without relying on field equations. For each geometry, two key visualizations elucidate the connection between the geometry and the dynamics as follows: (1) the cross-sections of the ball of admissible velocities, and (2) the cross-sections of the local scaling function. Full article

The calcareous nannoplankton comprises haptophyte eukaryotes known as coccolithophores, capable of calcifying elaborate external skeletons (coccoliths s.l.) which differ morphologically depending on the phase of the life cycle considered, and the locus (intra- or extracellular) of mineralization. No study is currently available that analyzes the impact of these differences on coccolith morphology. An analysis of the assembly of their crystals is conducted here in search of the following: (1) identical traits across life cycles; (2) fossil records diagnostic of extracellular calcification; and (3) influence of the geometry of biomineralization during the diploid phase on the long-term evolution of a clade. This study shows patterns such as correlation of characters and structural imprint that unify the haploid and diploid phases, indicating a strong cellular integrity and offering potent means to determine life cycles in living and fossil communities. It also shows that differences in diversity patterns and longevity among families and orders depend on coccolith geometry, concentric geometry being more favorable to stability, and superposition geometry facilitating morphological diversification. Extinction occurs when the potential for diversification is attained. Finally, I propose that the evolution of biomineralization in the calcareous nannoplankton may have been more complex than initially thought, with intra- and extracellular calcification evolving independently. Full article

The Mateur aquifer system in Northern Tunisia was examined using data from 19 water boreholes, 69 vertical electrical sounding (VES) stations, and a Sentinel-2 satellite image. Available boreholes and their corresponding logs were compared to define precisely the multi-layer aquifer system, including the Quaternary and Campanian aquifers of the Mateur plain. Quantitative interpretation and qualitative evaluation of VES data were conducted to define the geometry of these reservoirs. These interpretations were enhanced by remote sensing imagery processing, which enabled the identification of the Mateur plain’s superficial lineaments. Based on well log information, the lithological columns show that the Quaternary series in the Ras El Ain region contains a layer of clayey, pebbly, and gravelly limestone. Additionally, in the Oued El Tine area, a clayey lithological unit has been identified as a multi-layer aquifer. The study area, exhibiting apparent resistivity values ranging between 20 and 170 Ohm·m, appears to be rich in groundwater resources. The correlation between the lithological columns and the interpreted VES data, presented as geoelectrical cross-sections, revealed variations in depth (8–106 m), thickness (10 to 55 m), and resistivity (20–98 Ohm·m) of a coarse unit corresponding to the Mateur aquifer. Twenty-three superficial lineaments were extracted from the Sentinel-2 image. Their common superposition indicated that both of them are in a good coincidence; these could be the result of normal faults, creating an aquifer system divided into raised and sunken blocks. Full article

Precise electrochemical machining (PECM) is being used increasingly to produce turbine blades (high-pressure compressors) from difficult-to-machine materials such as Inconel. However, the challenges associated with PECM are particularly pronounced for filigree workpieces characterized by high aspect ratios and thin-walled geometries. The need for high-pressure flushing within the working gap to renew the electrolyte poses a dilemma because it induces unwanted deflection in these thin-walled structures. This problem is intensified by the mechanical oscillation of the tool applied to promote flushing efficiency. The superposition of mechanical tool oscillation and turbulent flushing, which exacerbate fluid–structure interaction, has been identified as the essential cause of workpiece deflection. The aim of this paper is to present an experimental setup coupled with numerical methods to better investigate the phenomenon of workpiece deflection during PECM. In the first part of this work, a novel tool system for investigating the phenomenon of workpiece deflection in PECM is presented. The tool system combines typical PECM tool–workpiece arrangements for double-sided machining and a unique electrolytic mask that provides optical access to the working gap, allowing in situ measurements. After validating the tool system by experimental tests, the workpiece deflection is investigated using high-speed imaging. In a next step, analytical studies of the flushing conditions during machining operations are carried out. These investigations are followed by a structural investigation of the workpiece to improve the understanding of the deflection behavior of the workpiece. In addition, the effect on the blade tip caused by the continuously decreasing moment of inertia of the blade due to their thinning during machining is analyzed. Full article

The manufacturing geometrical variability in axial compressors is a stochastic source of uncertainty, implying that the real geometry differs from the nominal design. This causes the real geometry to lose the ideal axial symmetry. Considering the aerofoils of a stator vane, the geometrical variability affects the flow traversing it. This impacts the downstream rotor, especially when considering the aeroelastic excitation forces. Optical surface scans coupled with a parametrisation method allow for acquiring the information relative to the real aerofoils geometries. The measured data are included in a multi-passage and multi-stage CFD setup to represent the mistuned flow. In particular, low excitation harmonics on the rotor vane are introduced due to the geometrical deviations of the upstream stator. The introduced low engine orders, as well as their amplitude, depend on the stator geometries and their order. A method is proposed to represent the phenomena in a reduced CFD domain, limiting the size and number of solutions required to probabilistically describe the rotor excitation forces. The resulting rotor excitation forces are reconstructed as a superposition of disturbances due to individual stator aerofoils geometries. This indicates that the problem is linear in the combination of disturbances from single passages. Full article

The recently synthetically prepared endohedral CH₄@C₆₀ was characterized here using calculations—namely its structure, energetics, thermodynamics, and vibrational spectrum. The calculations were carried out with DFT (density-functional theory) methods, namely by the DFT M06-2X functional and MP2, as well as B2PLYPD advanced correlated, treatments with the standard 6-31++G** and 6-311++G** basis sets, corrected for the basis set superposition error evaluated using the approximative Boys–Bernardi counterpoise method. The symmetry of the endohedral obtained in the geometry optimizations was tetrahedral T. The energetics of CH₄ encapsulation into C₆₀ was attractive (i.e., with a negative encapsulation-energy term), producing a substantial energy gain of −13.94 kcal/mol at the most advanced computational level, B2PLYPD/6-311++G**. The encapsulation equilibrium constants for CH₄@C₆₀ were somewhat higher than previously found with the CO@C₆₀ system. For example at 500 K, the encapsulation equilibrium constant for CH₄@C₆₀ had a value one order of magnitude larger than for CO@C₆₀. The encapsulation thermodynamic characteristics suggest that high-pressure and high-temperature synthesis could in principle also be possible for CH₄@C₆₀. Full article

This study investigates the impact of fluid loads on the elastic deformation and dynamic response of linear structures. A weakly coupled modal solver is presented, which involves the solution of a dynamic equation of motion with external loads. The mode superposition method is used to find the dynamic response, utilizing predetermined mode shapes and natural frequencies associated with the structure. These essential parameters are pre-calculated and provided as input for the simulation. Integration of the weakly coupled modal solver is accomplished with the Lagrangian Differencing Dynamics (LDD) method. This method can directly use surface mesh as boundary conditions, so it is much more convenient than other meshless CFD methods. It employs Lagrangian finite differences, utilizing a strong formulation of the Navier–Stokes equations to model an incompressible free-surface flow. The elastic deformation of the structure, induced by fluid forces obtained from the flow solver, is computed within the modal coupling algorithm through direct numerical integration. Subsequently, this deformation is introduced into the flow solver to account for changes in geometry, resulting in updated flow pressure and velocity fields. The flow particles and vertices of the structure are advected in Lagrangian coordinates, resulting in Lagrangian–Lagrangian coupling in spaces with weak or explicit coupling in time. The two-way coupling between fluid and structure is successfully validated through various FSI benchmark cases. The efficiency of the LDD method is highlighted as it operates directly on surface meshes, streamlining the simulation setup. Direct coupling of structural deformation eliminates the conventional step of mapping fluid results onto the structural mesh and vice versa. Full article

Research and development of the DEMOnstration power plant (DEMO) breeder blanket (BB) has been performed in recent years based on a predefined DEMO tritium breeding ratio (TBR) requirement, which determines a loss of wall surface due to non-breeding in-vessel components (IVCs) which consume plasma-facing wall surface and do not contribute to the breeding of tritium. The integration of different IVCs, such as plasma limiters, neutral beam injectors, electron cyclotron launchers and diagnostic systems, requires cut-outs in the BB, resulting in a loss of the breeder blanket volume, TBR and power generation, respectively. The neutronic analyses presented here have the goal of providing an assessment of the TBR losses associated with each IVC. Previously performed studies on this topic were carried out with simplified, homogenized BB geometry models. To address the effect of the detailed heterogeneous structure of the BBs on the TBR losses due to the inclusion of the IVCs in the tokamak, a series of blanket geometry models were developed for integration in the latest DEMO base model. The assessment was performed for both types of BBs currently developed within the EUROfusion project, the helium-cooled pebble bed (HCPB) and water-cooled lead–lithium (WCLL) concepts, and for the water-cooled lead and ceramic breeder (WLCB) hybrid BB concept. The neutronic simulations were performed using the MCNP6.2 Monte Carlo code with the Joint Evaluated Fission and Fusion File (JEFF) 3.3 data library. For each BB concept, a 22.5° toroidal sector of the DEMO tokamak was developed to assess the TBR and nuclear power generation in the breeder blankets. For the geometry models with the breeder blanket space filled only with blankets without considering IVCs, the results of the TBR calculations were 1.173, 1.150 and 1.140 for the HCPB, WCLL and WLCB BB concepts, respectively. The TBR impact of all IVCs and the losses of the power generation were estimated as a superposition of the individual effects. Full article

The slot opening function, also called relative air gap permeance, is a function which, multiplied by the flux density distribution of a slotless geometry, gives the flux density distribution of a slotted configuration. Here, the magnetic field inside the air gap of a multi-slot surface facing a smooth one was studied, by solving the Laplace equation inside the air gap, in terms of a Fourier series. To obtain the Fourier coefficients, at first, the conformal mapping analytical solution of a single-slot configuration along the smooth surface, was considered. Then, the principle of superposition of the single-slot lost flux density distributions was applied to obtain the multi-slot distribution. The approach is valid in general, and in the case of interference among the flux density distributions of adjacent slots, where their mutual effect cannot be neglected. The field distributions obtained by using the proposed slot opening functions were compared with FEM simulations, showing satisfactory agreement. The numerical accuracy limits were also analysed and discussed. Full article

We study order, chaos and ergodicity in the Bohmian trajectories of a 2D quantum harmonic oscillator. We first present all the possible types (chaotic, ordered) of Bohmian trajectories in wavefunctions made of superpositions of two and three energy eigenstates of the oscillator. There is no chaos in the case of two terms and in some cases of three terms. Then, we show the different geometries of nodal points in bipartite Bohmian systems of entangled qubits. Finally, we study multinodal wavefunctions and find that a large number of nodal points does not always imply the dominance of chaos. We show that, in some cases, the Born distribution is dominated by ordered trajectories, something that has a significant impact on the accessibility of Born’s rule $P={\left|\mathrm{\Psi }\right|}^2$ by initial distributions of Bohmian particles with $P_0\ne {\left|{\mathrm{\Psi }}_0\right|}^2$. Full article

Shearing high-strength steels often leads to a subpar cut quality and excessive stress on the tool components. To enhance the quality of the cut surface, intricate techniques like fine blanking are commonly employed. However, for applications with lower quality requirements, precision shear cutting offers an alternative solution. This research paper introduces a novel approach to directly superimpose radial stress on a workpiece during the precision shear cutting process and showcases for the first time how the application of direct stress superimposition can impact the cut surface by concurrently modifying the shear cutting edge and punch surface. A statistical experimental design is employed to investigate the interrelationships between the parameters and their effects. The results indicate that the overall cut quality, including cylindricity, clean-cut angle, rollover height, and tool stress, defined by punch force and retraction force, is influenced by the superimposed stress. Regarding the clean-cut zone, the statistical significance of direct radially superimposed stress was not observed, except when interacting with sheet thickness and clearance. Additionally, the sheet thickness and cutting gap emerged as significant parameters affecting the overall quality of the cut surface. Full article

Unusual optical properties of laser-ablated metal surfaces arise from the excitation of local plasmon resonances in nano- and microstructures produced by laser-processing and from the mutual interaction of those structures through surface plasmon polariton (SPP) waves. This interaction provides a synergistic effect, which can make the optical properties of the composite nanostructure drastically different from the properties of its elements. At the same time, the prediction and analysis of these properties are hampered by the complexity of the analytical solution to the problem of SPP excitation by surface objects of arbitrary configuration. Such a problem can be reduced to a simpler one if one considers the geometry of a structured surface as a superposition of harmonic Fourier components. Therefore, the analytical solution to the problem of surface plasmon polariton excitation through the scattering of light by a sinusoidally perturbed plasmonic metal/vacuum boundary becomes very important. In this work, we show that this problem can be solved using a well-known method for calculating guided-mode amplitudes in the presence of current sources, which is used widely in the waveguide theory. The calculations are carried out for the simplest 2D cases of (1) a sinusoidal current of finite length and (2) a finite-length sinusoidal corrugation on a plasmonic metal surface illuminated by a normally incident plane wave. The analytical solution is compared with the results of numerical simulations. It is shown that, in the first case, the analytical and numerical solutions agree almost perfectly. In the second case, the analytical solution correctly predicts the optimum height of the corrugation $x_{\mathrm{opt}}$, providing the maximum SPP excitation efficiency. At the same time, the analytical and numerical values of the SPP amplitude agree very well when the corrugation height x turns out to be $x\ll x_{\mathrm{opt}}$ or $x\gg x_{\mathrm{opt}}$ (at least up to $3x_{\mathrm{opt}}$); at $x=x_{\mathrm{opt}}$, the mismatch of those does not exceed 25%. The limitations of the analytical model leading to such a mismatch are discussed. We believe that the presented approach is useful for modeling various phenomena associated with SPP excitation. Full article

Electron vortex beams (EVBs, also known as twisted electron beams) possess an intrinsic orbital angular momentum (OAM) with respect to their propagation direction. This intrinsic OAM represents a new degree of freedom that provides new insights into investigating the dynamics of electron impact ionization. In this communication, we present, in the first Born approximation (FBA), the angular profiles of the triple differential cross section (TDCS) for the (e, 2e) process on CH${}_4$ and NH${}_3$ molecular targets in the coplanar asymmetric geometry. We compare the TDCS of the EVB for different values of OAM number m with that of the plane wave. For a more realistic scenario, we investigate the average TDCS for macroscopic targets to explore the influence of the opening angle ${\theta }_p$ of the twisted electron beam on the TDCS. In addition, we also present the TDCS for the coherent superposition of two EVBs. The results demonstrate that the twisted (e, 2e) process retrieves the p-type character of the molecular orbitals, which is absent in the plane wave TDCS for the given kinematics. The results for the coherent superposition of two Bessel beams show the sensitivity of TDCS toward the OAM number m. Full article

The LNG cargo containment system used in membrane-type LNG cargo tanks must have sufficient dynamic strength to withstand the impact of sloshing loads. However, performing direct dynamic nonlinear transient finite element assessments against design sloshing impact loads with different design specifications can be complicated and time-consuming. To address this, it is effective to use linear superposition methods, such as the triangular impulse response function (TIRF) method, to conduct dynamic transient FE assessments of LNG cargo containment systems. However, as LNG cargo containment systems have a high level of nonlinearities in terms of geometry, material, and boundary effects, it is necessary to evaluate the applicability of the TIRF method in advance. This study investigates the dynamic responses of an LNG cargo containment system using the TIRF method and compares the ultimate value of the structural responses and impulses with that obtained using direct dynamic nonlinear transient assessments. Based on a comparison of a series of FE analyses, the study proposes a design for the partial safety factors for calculating the ultimate bending and shear capacities of an LNG cargo containment system, taking into consideration the dynamic impact of sloshing loads using the TIRF method. Finally, the ultimate shear and bending capacities are calculated using the proposed method and compared with those obtained through direct dynamic nonlinear transient assessments. The results show that the proposed method provides conservative estimates against direct nonlinear finite element simulations, with a difference of around 10% for the mean minus two standard deviations. This approach can be practically applied for early basic design purposes in the shipbuilding industry. Full article

Twenty-five molecule–anion complex systems [I₄Tt···X⁻] (Tt = C, Si, Ge, Sn and Pb; X = F, Cl, Br, I and At) were examined using density functional theory (ωB97X-D) and ab initio (MP2 and CCSD) methods to demonstrate the ability of the tetrel atoms in molecular entities, I₄Tt, to recognize the halide anions when in close proximity. The tetrel bond strength for the [I₄C···X⁻] series and [I₄Tt···X⁻] (Tt = Si, Sn; X = I, At), was weak-to-moderate, whereas that in the remaining 16 complexes was dative tetrel bond type with very large interaction energies and short Tt···X close contact distances. The basis set superposition error corrected interaction energies calculated with the highest-level theory applied, [CCSD(T)/def2-TZVPPD], ranged from −3.0 to −112.2 kcal mol⁻¹. The significant variation in interaction energies was realized as a result of different levels of tetrel bonding environment between the interacting partners at the equilibrium geometries of the complex systems. Although the ωB97X-D computed intermolecular geometries and interaction energies of a majority of the [I₄Tt···X⁻] complexes were close to those predicted by the highest level of theory, the MP2 results were shown to be misleading for some of these systems. To provide insight into the nature of the intermolecular chemical bonding environment in the 25 molecule–anion complexes investigated, we discussed the charge-density-based topological and isosurface features that emanated from the application of the quantum theory of atoms in molecules and independent gradient model approaches, respectively. Full article