Finite Distance Research Articles

Overlap of parafermionic zero modes at a finite distance

Parafermion bound states (PBSs) are generalizations of Majorana bound states (MBSs) and have been predicted to exist as zero-energy eigenstates in proximitized fractional quantum Hall edge states. Similarly to MBSs, a finite distance between the PBS can split the ground state degeneracy. However, parafermionic modes have a richer exchange statistics than MBSs, so several interaction terms are allowed by the underlying $\mathbb{Z}_{2n}$ symmetry, rendering the effective Hamiltonian governing a pair of PBSs at a finite distance nontrivial. Here, we use a combination of analytical techniques (semiclassical instanton approximation) and numerical techniques (quantum Monte Carlo simulations) to determine the effective coupling Hamiltonian. For this purpose, we go beyond the dilute one-instanton gas approximation and show how finite-size effects can give rise to higher-order parafermion interactions. We find excellent agreement between the analytical results and Monte Carlo simulations. We estimate that these finite-size corrections should be observable in some of the recently proposed experiments to observe PBSs in strongly correlated systems.

A process-data-driven BP neural network model for predicting interval-valued fatigue life of metals

The experimental observations of fatigue life of metals always exhibit uncertainty even under the same settings. How to effectively capture the uncertainty when predicting fatigue life of metals? This paper proposes an interval-valued fatigue life prediction model for coping with the challenge of uncertainty. First, a novel back-propagation (BP) neural network model is established, where the data extracted from fatigue failure process of metals is used. The fatigue life of metals is predicted as an interval by considering the measurement errors of mechanical loadings and geometry of materials. Second, the low cycle fatigue life of un-notched/notched Q235 steel is predicted using the proposed model. The real- and interval-valued predictions of fatigue life are reported and compared with the experimental observations. It is found that the prediction accuracy is enhanced by extracting the data from fatigue failure process. Third, the performance of the proposed method is analyzed under different data sets and numbers of neurons together with network layers. The appropriate numbers of neurons, network layers and cycles are reported for predicting fatigue life with enough accuracy. Comparisons with finite element method (FEM) and critical distance method (CDM) reveal the advantages of the proposed model in predicting fatigue life of metals.

Hypersonic Boundary-Layer Transition on Cold-Wall Canonical Geometries with Quantified Distributed Roughness Elements

Given the challenges of obtaining a natural turbulent boundary layer on common test model geometries in a shock tunnel, this work aims to investigate the influence of roughness elements on the boundary layer with respect to transition to turbulence. The experiments were conducted in the High Enthalpy Shock Tunnel Göttingen at the German Aerospace Center on a 1100-mm-long, 7°-half-angle cone and a 602-mm-long flat plate at Mach 7.4. Roughness elements were applied on the nosetip of the cone and near the leading edge of the flat plate. The roughness elements were scanned with a laser profilometer, allowing their specification in terms of a roughness Reynolds number based on the 70th-percentile element height and an exceedance probability distribution. Transition was examined for the cone geometry using streamwise-aligned coaxial thermocouples on the 0° meridian. This assisted sizing the roughness elements required for transition to occur as far upstream as detectable. Breakdown of roughness-induced vortical structures generated by the roughness elements with a similar roughness Reynolds number was then examined using the flat plate geometry with temperature-sensitive paint applied downstream of the roughness elements. It was found that roughness-induced vortices required a finite distance (persistence length) to break down into turbulent structures. The persistence length was successfully reduced by interspersing roughness elements with smaller ones.

Mechanical signaling cascades.

Mechanical computing has seen resurgent interest recently owing to the potential to embed sensing and computation into new classes of programmable metamaterials. To realize this, however, one must push signals from one part of a device to another and do so in a way that can be reset robustly. We investigate the propagation of signals in a bistable mechanical cascade uphill in energy. By identifying a penetration length for perturbations, we show that signals can propagate uphill for finite distances and map out parameters for this to occur. Experiments on soft elastomers corroborate our results.

A numerical method for resolving finite mixtures of three-dimensional inter-site distance distributions measured by single-molecule localization microscopy.

The three-dimensional (3D) inter-site distance can be measured by single-molecule localization microscopy. Existing theories and analysis tools for 3D inter-site distance measurement only consider the simplest case where all measured distances are from an identical 3D Rician distribution. There are many problems where the 3D inter-site distance measurement result is made up of multiple components, for example, the measurement of intramolecular distances of deoxyribonucleic acid with multiple possible conformations. In these cases, the overall distance distributions become finite mixtures of 3D Rician distributions (or 3D Rician mixtures). Here, we provide a numerical method using the 3D Rician mixture model to resolve the finite 3D inter-site distance mixtures, which is based on the expectation-maximization algorithm. The proposed method has been tested on simulation data of finite 3D inter-site distance mixtures. The result using the Gaussian mixture model in the developed method is also discussed for comparison.

Finite Fracture Mechanics extension to dynamic loading scenarios

The coupled criterion of Finite Fracture Mechanics (FFM) has already been successfully applied to assess the brittle failure initiation in cracked and notched structures subjected to quasi-static loading conditions. The FFM originality lies in addressing failure onset through the simultaneous fulfilment of a stress requirement and the energy balance, both computed over a finite distance ahead of the stress raiser. Accordingly, this length results to be a structural parameter, thus able to interact with the geometry under investigation. This work aims at extending the FFM failure criterion to dynamic loadings. To this end, the general requisites of a proper dynamic failure criterion are first shortlisted. The novel Dynamic extension of FFM (DFFM) is then put forward assuming the existence of a material time interval that is related to the coalescence period of microcracks upon macroscopic failure. On this basis, the DFFM model is investigated in case a one-to-one relation between the external solicitation and both the dynamic stress field and energy release rate holds true. Under such a condition, the DFFM is also validated against suitable experimental data on rock materials from the literature and proven to properly catch the increase of the failure load as the loading rate rises, thus proving to be a novel technique suitable for modelling the rate dependence of failure initiation in brittle and quasi-brittle materials.

Elliptic K3 surfaces at infinite complex structure and their refined Kulikov models

Motivated by the Swampland Distance and the Emergent String Conjecture of Quantum Gravity, we analyse the infinite distance degenerations in the complex structure moduli space of elliptic K3 surfaces. All complex degenerations of K3 surfaces are known to be classified according to their associated Kulikov models of Type I (finite distance), Type II or Type III (infinite distance). For elliptic K3 surfaces, we characterise the underlying Weierstrass models in detail. Similarly to the known two classes of Type II Kulikov models for elliptic K3 surfaces we find that the Weierstrass models of the more elusive Type III Kulikov models can be brought into two canonical forms. We furthermore show that all infinite distance limits are related to degenerations of Weierstrass models with non-minimal singularities in codimension one or to models with degenerating generic fibers as in the Sen limit. We explicitly work out the general structure of blowups and base changes required to remove the non-minimal singularities. These results form the basis for a classification of the infinite distance limits of elliptic K3 surfaces as probed by F-theory in the companion paper [1]. The Type III limits, in particular, are (partial) decompactification limits as signalled by an emergent affine enhancement of the symmetry algebra.

Dual diffeomorphisms and finite distance asymptotic symmetries in 3D gravity

We study the finite distance boundary symmetry current algebra of the most general first order theory of 3d gravity. We show that the space of quadratic generators contains diffeomorphisms but also a notion of dual diffeomorphisms, which together form either a double Witt or centreless BMS$_3$ algebra. The relationship with the usual asymptotic symmetry algebra relies on a duality between the null and angular directions, which is possible thanks to the existence of the dual diffeomorphisms.

Deflection and gravitational lensing of null and timelike signals in the Kiselev black hole spacetime in the weak field limit

In this work we study the deflection and gravitational lensing of null and timelike signals in the Kiselev spacetime in the weak field limit, to investigate the effects of the equation of state parameter ω and the matter amount parameter α. In doing this, we extend a perturbative method previously developed for asymptotically flat spacetimes whose metric functions have integer-power asymptotic expansions to the case that may or may not be asymptotically flat but with non-integer power expansions. It is found that in the asymptotically flat case (−1/3 < ω < 0) the deflection angles are expressable as quasi-power series of the dimensionless quantities M/b, b/r s,d and α/M 1+3ω where M, b, r s,d are respectively the lens mass, impact parameter and source/detector radius. A similar series exists for the non-asymptotically flat case of (−1 < ω < −1/3), but with the closest radius r 0 replacing b. In the asymptotically flat (or non-flat) case, the increase of α or decrease of ω will increase (or increase) the deflection angle. Since the obtained deflection angles naturally take into account the finite distance effect of the source and the detector, we can establish an exact gravitational lensing equation, from which the apparent angles of the images and their magnifications are solved. It is found that generally for the asymptotically flat case, increasing α or decreasing ω will increase the apparent angles of the images. While for the non-asymptotically flat case, increasing α or ω will both lead to smaller apparent angles.

Method for Calculating the Instrument Function of a Medical Hyperspectrometer

Hyperspectral imaging technology offers great opportunities in noninvasive disease diagnostics and scientific research. Medical hyperspectrometer operation is based on the light ability to be reflected from biological tissue and depends on how strongly the tissue absorbs/reflects the light. Knowledge of the reflected and scattered light from tissues makes it possible to accurately interpret the state of health of a patient. Hyperspectrometer was considered consisting of projection lens that takes a picture of the patient's body from the finite distance, imaging spectrometer, as well as of calibrated radiation sources to illuminate the areas under study. Image decomposition into spectrum was implemented in the scheme of a classical spectrometer, which entrance slit was the exposure slit of the imaging lens. To ensure scanning, it was supposed to use displacement either of the spectrometer or of the patients under examination on a conveyor belt. A technique is proposed for determining the instrument function of a medical hyperspectrometer taking into account the scattering function influence of optical system, slit, optical radiation receiver, image displacement relative to the slit and electronics. By analyzing the instrument function, it becomes possible to implement various methods for assessing the optical image quality, such as modulation transfer function and spatial and spectral resolution, which is required for correct use of the device and image interpretation. The instrument design process involves optimization of the main circuit and design solutions according to the criterion of their influence on the instrument function and the generated image quality. An example of instrument design was considered involving optimization of the basic circuitry and design solutions

The determination of secondary ray-aberration coefficients for axis-symmetrical optical systems

The ray-aberrations in axis-symmetrical systems are conventionally derived from wavefront functions or characteristic functions using classical approximate partial derivatives. However, the resulting aberrations typically have fifth-order errors, as described by Restrepo et al. (2017) [1]. Accordingly, in the present study, the secondary ray-aberration coefficients for object placed at finite distance are determined using the fifth-order Taylor series expansion of a skew ray. Notably, the derived expressions are exact since they are determined without any approximations. It is found that some of the aberration coefficients are not constants, but are functions of the polar angle of the entrance pupil. It is additionally found that, once the required derivative matrices have been generated, determination of the secondary aberration coefficients is straightforward without iteration, and incurs only a low computational cost.

Electron transport in quantum channels with spin–orbit interaction: effects of the sign of the Rashba coupling and applications to nanowires

We investigate the effects of the sign of the Rashba spin–orbit coupling (RSOC) on electron transmission through a single-channel nanowire (NW) in the quantum coherent regime. We show that, while for a finite length NW with homogeneous RSOC contacted to two electrodes the sign of its RSOC does not affect electron transport, the situation can be quite different in the presence of an inhomogeneous RSOC and a magnetic field applied along the NW axis. By analyzing transport across an interface between two regions of different RSOC we find that, if the two regions have equal RSOC signs, the transmission within the magnetic gap energy range is almost perfect, regardless of the ratio of the spin–orbit energies to the Zeeman energy. In contrast, when the two regions have opposite RSOC signs and are Rashba-dominated, the transmission gets suppressed. Furthermore, we discuss the implementation on a realistic NW setup where two RSOC regions are realized with suitably coupled gates separated by a finite distance. We find that the low-temperature NW conductance exhibits a crossover from a short distance behavior that strongly depends on the relative RSOC sign of the two regions to a large distance oscillatory behavior that is independent of such relative sign. We are thus able to identify the conditions where the NW conductance mainly depends on the sign of the RSOC and the ones where only the RSOC magnitude matters.

Effect of particle spin on trajectory deflection and gravitational lensing

Spin of a test particle is a fundamental property that can affect its motion in a gravitational field. In this work we consider the effect of particle spin on its deflection angle and gravitational lensing in the equatorial plane of arbitrary stationary and axisymmetric spacetimes. To do this we developed a perturbative method that can be applied to spinning signals with arbitrary asymptotic velocity and takes into account the finite distance effect of the source and the observer. The deflection angle Δφ and total travel time Δt are expressed as (quasi-)power series whose coefficients are polynomials of the asymptotic expansion coefficients of the metric functions. It is found that when the spin and orbital angular momenta are parallel (or antiparallel), the deflection angle is decreased (or increased). Apparent angles θ of the images in gravitational lensing and their time delays are also solved. In Kerr spacetime, spin affects the apparent angle θK in a way similar to its effect on ΔφK . The time delay between signals with opposite spins is found to be proportional to the signal spin at leading order. These time delays might be used to constrain the spin to mass ratio of neutrinos.

Dehnen halo effect on a black hole in an ultra-faint dwarf galaxy

There had been recent advancement toward the detection of ultra-faint dwarf galaxies, which may serve as a useful laboratory for dark matter exploration since some of them contains almost 99% of pure dark matter. The majority of these galaxies contain no black hole that inhabits them. Recently, there had been reports that some dwarf galaxies may have a black hole within. In this study, we construct a black hole solution combined with the Dehnen dark matter halo profile, which is commonly used for dwarf galaxies. We aim to find out whether there would be deviations relative to the standard black hole properties, which might allow determining whether the dark matter profile in an ultra-faint dwarf galaxy is cored or cuspy. To make the model more realistic, we applied the modified Newman-Janis prescription to obtain the rotating metric. We analyzed the black hole properties such as the event horizon, ergoregion, geodesics of time-like and null particles, and the black hole shadow. Using these observables, the results indicate the difficulty of distinguishing whether the dark matter is cored or cuspy. To find an observable that can potentially distinguish these two profiles, we also calculated the weak deflection angle to examine the effect of the Dehnen profile in finite distance and far approximation. Our results indicate that using the weak deflection angle is far better, in many orders of magnitude, in potentially differentiating these profiles. We conclude that although dwarf galaxies are dark matter-dominated places, the effect on the Dehnen profile is still dependent on the mass of the black hole, considering the method used herein.

Secondary Kinetic Peak in the Kohn-Sham Potential and Its Connection to the Response Step.

We consider a prototypical 1D model Hamiltonian for a stretched heteronuclear molecule and construct individual components of the corresponding KS potential, namely, the kinetic, the N - 1, and the conditional potentials. These components show very special features, such as peaks and steps, in regions where the density is drastically low. Some of these features are quite well-known, whereas others, such as a secondary peak in the kinetic potential or a second bump in the conditional potential, are less or not known at all. We discuss these features building on the analytical model treated in Giarrusso et al. J. Chem. Theory Comput. 2018, 14, 4151. In particular, we provide an explanation for the underlying mechanism which determines the appearance of both peaks in the kinetic potential and elucidate why these peaks delineate the region over which the plateau structure, due to the N - 1 potential, stretches. We assess the validity of the Heitler-London Ansatz at large but finite internuclear distance, showing that, if optimal orbitals are used, this model is an excellent approximation to the exact wave function. Notably, we find that the second natural orbital presents an extra node very far out on the side of the more electronegative atom.

Simple Unsupervised Graph Representation Learning

In this paper, we propose a simple unsupervised graph representation learning method to conduct effective and efficient contrastive learning. Specifically, the proposed multiplet loss explores the complementary information between the structural information and neighbor information to enlarge the inter-class variation, as well as adds an upper bound loss to achieve the finite distance between positive embeddings and anchor embeddings for reducing the intra-class variation. As a result, both enlarging inter-class variation and reducing intra-class variation result in small generalization error, thereby obtaining an effective model. Furthermore, our method removes widely used data augmentation and discriminator from previous graph contrastive learning methods, meanwhile available to output low-dimensional embeddings, leading to an efficient model. Experimental results on various real-world datasets demonstrate the effectiveness and efficiency of our method, compared to state-of-the-art methods. The source codes are released at https://github.com/YujieMo/SUGRL.

Attenuation of wave force on a floating dock by multiple porous breakwaters

The impact of an array of porous breakwaters for reducing wave forces on a floating dock is studied based on the small-amplitude water wave theory in finite water depth. The breakwater is approximated by a porous bottom-standing rectangular structure and an impermeable floating rectangular structure is placed at a finite distance on the lee-side representing a dock. The physical problem is solved analytically using Eigenfunction expansion method and numerically using a hybrid element multi domain boundary element method. Two scenarios are considered: (i) wave scattering by N porous structures and the floating dock and (ii) wave reflection by a dock attached to the impermeable wall in presence of N porous structures. The reflection, transmission and dissipation coefficients are evaluated and analyzed for various structural and wave parameters. The study reveals that the Bragg reflection occurs in the case of wave scattering by an array of porous structures in the absence of floating dock. It is also found that in the absence of dock N−2 sub-harmonic peaks occurs whereas, in the presence of dock the effect of Bragg resonance is clearly evident on hydrodynamic coefficients. Also, the study concludes that for four structures with larger height, 100% of wave energy can be dissipated and thus mitigate the wave force on the floating rigid dock. Furthermore, the height and width of the porous structure and spacing between the structures play a vital role to protect the floating platform.

Analytical and numerical solutions to describe water table fluctuations due to canal seepage and time-varying recharge

Abstract Hybrid finite analytic solution (HFAS), Galerkin's method based finite element solution (FES) and fully implicit finite difference solution (FIFDS) of one dimensional nonlinear Boussinesq equation and Analytical solution of Boussinesq equation linearized by Baumann's transformation (analytical solution I, AS I) as well as linearized by Werner's transformation (analytical solution II, AS II) were employed to obtain water table rise in a horizontal unconfined aquifer lying between two canals located at finite distance having different elevations and subjected to various patterns of recharge, i.e. zero recharge, constant recharge, as well as time varying recharge. Considering HFAS as benchmark solution, water table in mid region as obtained from FES followed by FIFDS was observed quite close to that obtained from HFAS and as per L2 and Tchebycheff norms computation, it was ranked at first and second place, respectively. Both AS I and AS II predicted higher water table at t = 5 days but at t = 10 days, AS I predicted lower and AS II predicted higher water table at all distances due to linearization effect. So, analytical solutions of linearized Boussinesq equation were rated lower than numerical solutions of nonlinear Boussinesq equation.

Capillary coalescence of two partially immersed slender structures

We study the onset of coalescence between two slender structures quasi-statically withdrawn from a liquid bath. When partially immersed, they interact with each other through the capillary force induced by their menisci. As they are removed from the bath, their dry length increases and they become easier to bend until the capillary force is strong enough to trigger contact. Surprisingly, the structures snap to contact from a finite distance at a critical dry length. The transition to coalescence is thus subcritical and exhibits a large hysteresis loop between two stable states. An analytical coalescence criterion is derived and agrees well with experimental data for rods and lamellae. This simple elastocapillary model is a first step to better understand the elastocapillary coalescence of slender structures in fluid capture systems.

1D Majorana Goldstinos and partial supersymmetry breaking in quantum wires

Realizing Majorana modes in topological superconductors, i.e., the condensed-matter counterpart of Majorana fermions in particle physics, may lead to a major advance in the field of topologically-protected quantum computation. Here, we introduce one-dimensional, counterpropagating, and dispersive Majorana modes as bulk excitations of a periodic chain of partially-overlapping, zero-dimensional Majorana modes in proximitized nanowires via periodically-modulated fields. This system realizes centrally-extended quantum-mechanical supersymmetry with spontaneous partial supersymmetry breaking. The massless Majorana modes are the Nambu-Goldstone fermions (Goldstinos) associated with the spontaneously broken supersymmetry. Their experimental fingerprint is a dip-to-peak transition in the zero-bias conductance, which is generally not expected for Majorana modes overlapping at a finite distance. Moreover, the Majorana modes can slide along the wire by applying a rotating magnetic field, realizing a “Majorana pump”. This may suggest new braiding protocols and implementations of topological qubits.