Finite Length Research Articles

On the importance of the cracking process description for dynamic crack initiation simulation

A dynamic implementation of the coupled criterion under quasi-static loading, based only on the mean velocity during crack initiation, is proposed. It relies on a simultaneous node release method. It consists of computing the dynamic incremental energy release rate by simultaneously opening a crack of a finite length during a given time increment rather than progressively opening smaller crack increments following a velocity profile as in the progressive node release method. Both methods result in significantly different kinetic energy variations as a function of the crack length, and thus different incremental energy release rates for large enough crack velocities, for which the kinetic energy magnitude is similar to the elastic strain energy magnitude. Both simultaneous node release method and progressive node release method can however be equivalently used for small enough crack velocities since similar incremental energy release rates are obtained with both methods. Inverse identification of fracture properties based on dynamic crack initiation at a hole in Brazilian disk specimens yields critical energy release rates in the same order of magnitude as the one obtained based on dynamic crack propagation modeling.

Revisiting the time-ordering issue of TMD soft factors: causality, coordinate space analyticity and new equalities

We show that as a result of causality-constrained coordinate space analyticity, the Drell-Yan-shape transverse-momentum dependent soft factor in the exponential regulator allows Euclidean-type parametric representations without cuts, to all orders in perturbation theory. Moreover, it is identical to another soft factor defined with a single time-ordering that has a natural interpretation as a space-like form factor. Furthermore, this relation continues to hold for a larger class of TMD soft factors that interpolate between three different rapidity regulators: the off-light-cone regulator, the finite light-front length regulator, and the exponential regulator.

Mapping the Slow Stabilization of End States with Length along a Laterally Extended Graphene Nanoribbon.

With a lateral bisnaphtho-extended chemical structure, finite 7-13 carbon atom wide armchair graphene nanoribbons (7-13-aGNRs) were on-surface synthesized. For all lengths up to N = 7 monomer units, low-temperature ultrahigh vacuum scanning tunneling spectroscopy and spatial dI/dV maps were recorded at each captured tunneling resonance. The degeneracy of the two central electronic end states (ESs) occurs in a slowly decaying regime with N converging toward zero for N = 6 long 7-13-aGNR (12 bonded anthracenes), while it is N = 2 (4 bonded anthracenes) for seven carbon atoms wide armchair GNRs (7-aGNRs). The two end dI/dV conductance maxima of ESs are also shifted away from strictly two ends of the 7-13-aGNR compared to the 7-aGNR. Using the quantum topology graph filiation between finite length polyacetylene and 7-13-aGNRs wires, we show that this slow decay of 7-13-aGNR ESs is coming from the property of the topological Hückel band matrix that expels the ESs into its eigenvalue spectrum gaps to keep harmony in the core spectrum.

Concerning the Parameterization of Geometric and Criticality Effects on Detonation Amplification

This study investigates the role of geometric effects and detonation criticality on the behavior of a detonation transition through an area expansion of finite length. Three reinitiation behaviors that result in an amplified pressure impulse were observed and are referred to as steady, spike, and endwall amplification. Steady amplification was characterized by an amplification event with a peak pressure impulse 2 times that of the inlet detonation, followed by a near-linear attenuation toward Chapman–Jouguet conditions. Spike amplification displayed a larger peak pressure amplification that was 3 to 5 times greater than the inlet detonation, followed by a rapid and nonlinear attenuation. Endwall behavior represents a Craven–Grieg deflagration to detonation transition scenario. These behaviors are shown to be factors of area expansion ratio and the degree to which the incoming detonation is subcrtical. A decoupling parameter, Ψd, was devised to combine these effects into a single correlation metric. The finite length of the expansion chamber also plays a role in the reinitiation behavior as observed by the endwall reinitiation behavior. A critical chamber length parameter was devised to explain this behavior and then theorized to have a relationship to Ψd with this being explored theoretically and with the limited data set available.

Boij-Söderberg conjectures for differential modules

Boij-Söderberg theory gives a combinatorial description of the set of Betti tables belonging to finite length modules over the polynomial ring S=k[x1,…,xn]. We posit that a similar combinatorial description can be given for analogous numerical invariants of graded differential S-modules, which are natural generalizations of chain complexes. We prove several results that lend evidence in support of this conjecture, including a categorical pairing between the derived categories of graded differential S-modules and coherent sheaves on Pn−1 and a proof of the conjecture in the case where S=k[t].

Free Vibrations of Thin-Walled Gas Pipelines Taking into Account the Influence of Longitudinal Force During Trench Laying

A numerical experiment was carried out to determine the frequencies of free oscillations of an inhomogeneous pipeline at various mechanical and geometric parameters.This made it possible to establish the influence of factors such as longitudinal force, thickness of the reinforced concrete shell, internal working pressure and the coefficient of the soil bed on the system’s own vibrations. For calculations, a model of an inhomogeneous cylindrical two-layer shell of finite length consisting of a steel pipe and a protective reinforced concrete layer was chosen.

Effects of 2.5-D ultra-low and ultra-high velocity zones on flip-reverse-stacking (FRS) of the ScS wavefield

SUMMARY Within the last decade, thin ultra-low velocity zone (ULVZ) layering, sitting directly on top of the core–mantle boundary (CMB), has begun to be investigated using the flip-reverse-stack (FRS) method. In this method, pre- and post-cursor arrivals that are symmetrical in time about the ScS arrival, but with opposite polarities, are stacked. This same methodology has also been applied to high velocity layering, with indications that ultra-high velocity zones (UHVZs) may also exist. Thus far, studies using the FRS technique have relied on 1-D synthetic predictions to infer material properties of ULVZs. 1-D ULVZ models predominantly show a SdS precursor that reflects off the top of the ULVZ and an ScscS reverberation within the ULVZ that arrives as a post-cursor. 1-D UHVZ models are more complex and have a different number of arrivals depending on a variety of factors including UHVZ thickness, velocity contrast, and lateral extent. 1-D modelling approaches assume that lower mantle heterogeneity is constant and continuous everywhere across the lower mantle. However, lower mantle features display lateral heterogeneity and are either finite in extent or display local thickness variations. We examine the interaction of the ScS wavefield with ULVZs and UHVZs in 2.5-D geometries of finite extent. We show that multiple additional arrivals exist that are not present in 1-D predictions. In particular, multipath ScS arrivals as well as additional post-cursor arrivals are generated. Subsequent processing by the FRS method generates complicated FRS traces with multiple peaks. Furthermore, post-cursor arrivals can be generated even when the ScS ray path does not directly strike the heterogeneity from above. Analysing these predictions for 2.5-D models using 1-D modelling techniques demonstrates that a cautious approach must be adopted in utilization and interpretation of FRS traces to determine if the ScS wavefield is interacting with a ULVZ or UHVZ through a direct strike on the top of the feature. In particular, traveltime delays or advances of the ScS arrival should be documented and symmetrical opposite polarity arrivals should be demonstrated to exist around ScS. The latter can be quantified by calculation of a time domain multiplication trace. Because multiple post-cursor arrivals are generated by finite length heterogeneities, interpretation should be confined to single layer models rather than to interpret the additional peaks as internal layering. Furthermore, strong trade-offs exist between S-wave velocity perturbation and thickness making estimations of ULVZ or UHVZ elastic parameters highly uncertain. We test our analysis methods using data from an event occurring in the Fiji-Tonga region recorded in North America. The ScS bounce points for this event sample the CMB region to the southeast of Hawaii, in a region where ULVZs have been identified in several recent studies. We see additional evidence for a ULVZ in this region centred at 14°N and 153°W with a lateral scale of at least 250 km × 360 km. Assuming a constant S-wave velocity decrease of −10 or −20 per cent with respect to the PREM model implies a ULVZ thickness of up to 16 or 9 km, respectively.

Nutation-based longitudinal-sensing protocols for high-field NMR with nitrogen-vacancy centers in diamond

Nitrogen-vacancy (N-V) centers in diamond enable nuclear magnetic resonance (NMR) spectroscopy of samples at the nano- and microscale. However, at typical tesla-scale NMR magnetic field strengths, N-V–NMR protocols become difficult to implement due to the challenge of driving fast N-V pulse sequences sensitive to nuclear Larmor frequencies above a few megahertz. We perform simulations and theoretical analysis of the experimental viability of N-V NMR at tesla-scale magnetic fields using a measurement protocol called DRACAERIS (Double Rewound ACquisition Amplitude Encoded Radio Induced Signal). DRACAERIS detects the longitudinal magnetization of the NMR sample at a much lower driven Rabi frequency, more suitable technically for N-V detection. We discuss how pulse errors, finite pulse lengths, and nuclear spin-spin couplings affect the resulting NMR spectra. We find that DRACAERIS is less susceptible to pulse imperfections and off-resonance effects than previous protocols for longitudinal magnetization detection. We also identify reasonable parameters for experimental implementation. Published by the American Physical Society 2024

Local-to-non-local transition laws for stiffness-tuneable monoatomic chains preserving springs mass.

Recently, non-local configurations have been proposed by adding beyond nearest neighbour couplings among elements in lattices to obtain roton-like dispersion relations and phase and group velocities with opposite signs. Even though the introduction of non-local elastic links in metamaterials has unlocked unprecedented possibilities, literature models and prototypes seem neither to provide criteria to compare local and non-local lattices nor to discuss any related rules governing the transition between the two configurations. A physically reasonable principle that monoatomic one-dimensional chains must obey to pass from single- to multi-connected systems is here proposed through a mass conservation law for elastic springs thereby introducing a suitable real dimensionless parameter [Formula: see text] to tune stiffness distribution. Therefore, the dispersion relations as a function of [Formula: see text] and of the degree of non-locality [Formula: see text] are derived analytically, demonstrating that the proposed principle can be rather interpreted as a general mechanical consistency condition to preserve proper dynamics, involving the spring-to-bead mass ratio. Finally, after discussing qualitative results and deriving some useful inequalities, numerical simulations and two-dimensional FFTs are performed for some paradigmatic examples to highlight key dynamics features exhibited by chains with finite length as the parameters [Formula: see text] and [Formula: see text] vary.This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'.

Categorical resolutions of filtered schemes

We give an alternative proof of the theorem by Kuznetsov and Lunts, stating that any separated scheme of finite type over a field of characteristic zero admits a categorical resolution of singularities. Their construction makes use of the fact that every variety (over a field of characteristic zero) can be resolved by a finite sequence of blow-ups along smooth centres. We merely require the existence of (projective) resolutions. To accomplish this we put the \mathcal{A} -spaces of Kuznetsov and Lunts in a different light, viewing them instead as schemes endowed with finite filtrations. The categorical resolution is then constructed by gluing together differential graded categories obtained from a hypercube of finite length filtered schemes.

Non-Hermitian zero-energy pinning of Andreev and Majorana bound states in superconductor-semiconductor systems

The emergence of Majorana bound states in finite length superconductor-semiconductor hybrid systems has been predicted to occur in the form of oscillatory energy levels with parity crossings around zero energy. Each zero-energy crossing is expected to produce a quantized zero-bias conductance peak but several studies have reported conductance peaks pinned at zero energy over a range of Zeeman fields, whose origin, however, is not clear. In this work, we consider superconducting systems with spin-orbit coupling under a Zeeman field and demonstrate that non-Hermitian effects, due to coupling to ferromagnet leads, induce zero-energy pinning of Majorana and trivial Andreev bound states. We find that this zero-energy pinning effect occurs due to the formation of non-Hermitian spectral degeneracies known as exceptional points, whose emergence can be controlled by the interplay of non-Hermiticity, the applied Zeeman field, and chemical potentials. Moreover, depending on the non-Hermitian spatial profile, we find that non-Hermiticity changes the single point Hermitian topological phase transition into a flattened zero energy line bounded by exceptional points from multiple low energy levels. This seemingly innocent change notably enables a gap closing well below the Hermitian topological phase transition, which can be in principle simpler to achieve. Furthermore, we reveal that the energy gaps separating Majorana and trivial Andreev bound states from the quasicontinuum remain robust for the values that give rise to the zero-energy pinning effect. While reasonable values of non-Hermiticity can be indeed beneficial, very strong non-Hermitian effects can be detrimental as it might destroy superconductivity. Our findings can be therefore useful for understanding the zero-energy pinning of trivial and topological states in Majorana devices. Published by the American Physical Society 2024

Analytical model of an I-core coil inside a metal tube of finite length

An analytical solution is presented for the interaction of an I-core coil with a metal tube of finite length. Using the Truncated Region Eigenfunction Expansion (TREE) method, the impedance variation of the I-core coil is expressed in a closed form. Notably, the 1D finite element method (1D FEM) is adopted to calculate the complex eigenvalues and eigenfunctions of the steel tube, by which the overflow issue of complex eigenfunctions has been surmounted. And the 1D FEM also simplifies the calculation in the ferrite core region immensely. A performant algorithm is obtained due to the matrix formalization and the high speed of the sparse eigenvalue solver. The tubes made of aluminum alloy and stainless steel are investigated by the proposed method and tested in the experiment. The high reliability and efficiency of the proposed method are proved, and the results are also validated by the comparison with simulation and measurement data.

Analytical solutions for long-time steady state Boussinesq gravity currents flowing along a horizontal boundary of finite length

Analytical solutions for long-time steady state Boussinesq gravity currents flowing along a horizontal boundary of finite length

Locally cohomologically complete intersection ideals and cofiniteness

Let [Formula: see text] be a unitary commutative local Noetherian ring and [Formula: see text] be an ideal. The aim of this paper is twofold: In the first part of this paper, we consider locally cohomologically complete intersection ideals of pure height [Formula: see text]. Next, we deal with cofinite modules. In particular, we investigate conditions for cofiniteness of [Formula: see text] and conditions under which, the modules [Formula: see text] are of finite length for all [Formula: see text] and all finitely generated [Formula: see text]-module [Formula: see text].

Optimizing Production Stability while Safeguarding Information

The goal of Finite Time Stabilization is to finish a particular thing in a fixed time. Regardless of the system's original state, finite-time stabilisation refers to the regulation of a system so that it reaches a desired equilibrium or setpoint in a finite length of time. Finite-time stabilisation is essential for providing quick and effective control over a variety of variables in industrial processes, such as temperature, pressure, flow rate, or composition. By layering materials based on a computer model, 3D printing, sometimes referred to as additive manufacturing, creates three-dimensional items. Even though 3D printing technology has advanced significantly in recent years, manufacturing them still presents a number of difficulties. Some of the typical difficulties include: Cost: Due to the intricate parts and high level of precision needed when manufacturing 3D printers, the cost might be high. Quality parts, such as motors, electronics, and extruders, can be expensive to source. As a result, manufacturers may find it difficult to strike a balance between price and performance. So, as part of our process, we analyse the data and forecast the pricing to make things simple for the client. To make this prediction, we employed logistic regression. More than that those client data is secured through fernet algorithm.

Hot-wire spatial resolution issues in adverse pressure gradient turbulent boundary layers

The effect of a finite length of hot-wire probe sensor length on the measured streamwise velocity fluctuations is well understood in canonical wall-bounded flow, where the small-scale energy has been found to be universal and invariant with Reynolds number. A straightforward application of that assumption to non-canonical flows such as strong adverse pressure gradient (APG) flows has, however, been hampered since the effect of Re and APG could not conclusively be studied separately due to the lack of data with a clear scale separation. The present experimental investigation at Reτ≈4000 in weak, moderate and strong APGs with different wire length shows that spatial averaging effects are not only limited to the inner layer. A note of caution is hence warranted for measurements that seemingly try to take the bias effect of spatial attenuation into account by performing measurements with albeit long but fixed viscous-scaled wire length.

Tsunami inundation and flow velocity within a partially sheltered structural array

ABSTRACT This work examines tsunami run-up processes within a building array partially sheltered by a high-elevation, finite length, seawall. Work was performed using numerical modeling of 2D shallow water equations with varying seawall length, wave height, time scale, and structure size. Inundation depth and flow velocity were output at many locations of interest throughout the structural array. The most important influence on results when compared to the no-wall case was the sheltering or clearance angle as defined from the end of the wall. Behind the wall, inundation depth and cross-shore velocity declined significantly as sheltering angles increased (more sheltered). Alongshore inundation velocity (parallel to the seawall) increased strongly with increasing sheltering angle. A longer wave time scale resulted in significant increase in inundation depth and velocity especially at locations sheltered by the wall. Larger structure size or blockage ratio also led to increased inundation depth and flow velocity. However, varying wave height gave little change in inundation and velocity patterns. These results will serve to provide a better understanding of the wave inundation within a coastal urban region in a tsunami event when the seawall is breached, as well as the influence of coastal structure size and spacing on the tsunami inundation.

Forced Bending Vibrations of a Plane Rod Fixed on a Rigid Support Element of Finite Length Under the Action of an External Transverse Force Aplied to Its Free End

Forced Bending Vibrations of a Plane Rod Fixed on a Rigid Support Element of Finite Length Under the Action of an External Transverse Force Aplied to Its Free End

Variational approaches to the elasticity of deformable strings with and without mass redistribution

AbstractThe catenary is a curve that has played a significant role in the history of mathematics, finding applications in various disciplines such as mechanics, technology, architecture, the arts, and biology. In this paper, we introduce some generalizations by applying the variational method to deformable strings. We explore two specific cases: (i) in the first case, we investigate the nonlinear behavior of an elastic string with variable length, dependent on the applied boundary conditions; specifically, this analysis serves to introduce the variational method and demonstrate the process of finding analytical solutions; (ii) in the second case, we examine a deformable string with a constant length; however, we introduce mass redistribution within the string through nonlinear elastic interactions. In the first scenario, the deformation state of the string always describes elongation, as compression states prove to be unstable for fully flexible strings. In contrast, in the second scenario, the finite length constraint induces compressive states in specific configurations and regions of the string. However, it is worth noting that the solution to this problem exists only for values of the elastic constant that are not too low, a phenomenon that is studied in detail. We conduct here both analytical and graphical analyses of various geometries, comparing the elastic behavior of the two aforementioned types of strings. Understanding the elastic behavior of deformable strings, especially the second type involving mass redistribution, is crucial for enhancing comprehension in the study of biological filaments or fibers and soft matter. For instance, these investigations can contribute to understanding the mechanisms employed by cells to sense gravity or other mechanical conditions.

Analytic Prediction of Rotor Broadband Noise with Serrated Trailing Edges with Applications to Urban Air Mobility Aircraft

Theoretical predictions for broadband noise generated by rotors with serrated trailing edges are presented. This study extends Lyu and Ayton’s model for serrated trailing-edge noise to account for factors such as finite span length, the accurate acoustic attenuation rate of trailing-edge noise, modified spanwise wavenumber, and the proper scattering factor. This new model is implemented in the rotorcraft broadband noise tool, UCD‐QuietFly. The validation results demonstrate a satisfactory level of agreement with the experimental data for serrated trailing‐edge noise of a wing section, a hovering rotor, and a forward‐flight rotor. Next, the effects of serration parameters, such as the number of serrations, serrations starting radial location, serration geometry, and serration height, on rotor broadband noise are investigated. For example, it is observed that sine-wave, chopped peak, or sawtooth serration shapes provide the most significant noise reduction among the various shapes considered. Finally, broadband noise reduction through serrations is applied to two urban air mobility aircraft scenarios: a six‐passenger quadrotor and a quiet helicopter. For the quadrotor, serrated trailing edges show a noise reduction potential of over 9 dB, with higher reductions observed at higher tip speeds and fewer blades. A quiet helicopter equipped with serrated blades in forward flight achieves a maximum noise reduction of over 10 dB in the forward direction.