One-dimensional Line Research Articles

Slender body theories for rotating filaments

Slender fibres are ubiquitous in biology, physics and engineering, with prominent examples including bacterial flagella and cytoskeletal fibres. In this setting, slender body theories (SBTs), which give the resistance on the fibre asymptotically in its slenderness $\epsilon$ , are useful tools for both analysis and computations. However, a difficulty arises when accounting for twist and cross-sectional rotation: because the angular velocity of a filament can vary depending on the order of magnitude of the applied torque, asymptotic theories must give accurate results for rotational dynamics over a range of angular velocities. In this paper, we first survey the challenges in applying existing SBTs, which are based on either singularity or full boundary integral representations, to rotating filaments, showing in particular that they fail to consistently treat rotation–translation coupling in curved filaments. We then provide an alternative approach which approximates the three-dimensional dynamics via a one-dimensional line integral of Rotne–Prager–Yamakawa regularized singularities. While unable to accurately resolve the flow field near the filament, this approach gives a grand mobility with symmetric rotation–translation and translation–rotation coupling, making it applicable to a broad range of angular velocities. To restore fidelity to the three-dimensional filament geometry, we use our regularized singularity model to inform a simple empirical equation which relates the mean force and torque along the filament centreline to the translational and rotational velocity of the cross-section. The single unknown coefficient in the model is estimated numerically from three-dimensional boundary integral calculations on a rotating, curved filament.

Review of Research on the Three-Dimensional Transition Process of Large-Scale Low-Lift Pump

Due to the uneven distribution of water resources, there are many water diversion projects around the world, such as the South-to-North Water Diversion Project in China, especially in some plain areas. To transfer water from low to high areas, large low-head pumps have been widely used. The transition process of the pumping station is mainly caused by the sudden change in the flow velocity and pressure of the fluid in the pipeline of the pumping station system caused by the start-up and shutdown processes. The previous research has mainly been based on the one-dimensional characteristic line method. However, due to the characteristics of the low-lift pumping station, the flow passage is short and irregular, and the calculation results often cannot guarantee the accuracy of the calculation. In addition to some faults in the actual operation process, in some pumping stations, accidents or operation-scheduling faults are caused by transient processes, such as a high degree of water hammer, the inability to initiate backward flow, the shutdown load rejection runaway exceeding the standard, and decreased hydraulic efficiency. To avoid transition process failures in the newly designed pumping stations and the modified pumping stations, it is necessary to carry out a research review of the three-dimensional transition process of large low-lift pumps. Especially with the development of computing technology, CFD numerical simulation technology has become the main research method for analyzing the pump transition process. The research on the transition process is mainly based on the combination of numerical simulations and experiments. The reliability of a numerical simulation is verified by an experiment. A numerical simulation can measure some parameters that cannot be measured by an experiment. Dynamic mesh technology has become the main technical means for using CFD numerical simulation to study the three-dimensional transition process, and the secondary development of computing software has become the main trend of future development. This paper analyzes and summarizes the research status of the start–stop transition process of large low-lift pump stations and provides a reference for the protection of the start–stop transition process of pump stations.

Tunable interface states between Floquet-Weyl semimetals

Weyl semimetals and nodal line semimetals are characterized by linear electronic bands touching at zero-dimensional points and one-dimensional lines, respectively. Recently, it has been predicted that nodal line semimetals can be driven into tunable Floquet-Weyl semimetals by circularly polarized light. Here, we study the occurrence of interface states between two regions of a nodal line semimetal shined by two beams of light with opposite circular polarizations. Within a minimal model, we find remarkable modifications of the energy structure by tuning the polarized light, such as the possible generation of van Hove singularities. Moreover, by adding a $\delta$-doping of magnetic impurities along the interfacial plane, we show the occurrence of a switchable and topologically non-trivial, vortex-like pseudo-spin pattern of the interface states.

One dimensional normal consolidation line equation

Abstract Many empirical equations have been proposed in the past to predict the parameters of the one-dimensional normal consolidation line (1D-NCL) for soils. However, applications of these equations are limited to specific range of pressure and plasticity soils. General empirical equations for 1D-NCL for large range of pressure and plasticity soils are presented in this study. It is assumed that the 1D-NCL has up to three slopes and these slopes start at different stresses depending on liquid limit (LL) of soils. The 1D-NCL of 59 different soils for a large range of LL (19–520%) was used to establish the initial part of 1D-NCL. The soils were categorized based on their LL into two groups: (i) LL < 110% and (ii) LL > 110%. The equations for initial part of 1D-NCL were compared with the previous empirical 1D-NCL equations. The comparisons showed that the new 1D-NCL equations have a better agreement with tests results, especially for highly plastic soils. Moreover, two soils with different plasticity were used to verify the new 1D-NCL equations. The verifications showed a good agreement between the experimental and the predicted results.

On the Computation of Hierarchical Control results for One-Dimensional Transmission Line

In this paper, motivated by a physics problem, we investigate some numerical and computational aspects for the problem of hierarchical controllability in a one-dimensional wave equation in domains with a moving boundary. Some controls act in part of the boundary and define a strategy of equilibrium between them, considering a leader control and a follower. Thus, we introduced the concept of hierarchical control to solve the problem and mapped the Stackelberg Strategy between these controls. A total discretization of the problem is presented for a numerical evaluation in spaces of finite dimension, an algorithm for evaluation of the problem is presented as the combination of finite element method (FEM) and finite difference method (FDM). The algorithm efficiency and computational results are illustrated for some experiments using the softwares Freefem++ and MatLab.

A new strategy to one-step construct polyoxometalate/semiconductor one-dimensional tandem heterojunctions toward optimized conductometric sensing performances of ethanol gas

Gas sensing performances of homogenous semiconductors materials are limited by their high carriers recombination rate. Polyoxometalates (POMs), as a kind of electron acceptors, comes into sight in gas sensing field. In this study, three series of SnO2 @POMs@WO3 layered core-middle-shell nanofibers with tandem heterojunctions are first prepared utilizing one-step coaxial electrospinning. The tandem heterojunctions are continuously distributed in a one-dimensional line along the nanofibers. For the first time the gas sensing performances of one-dimensional tandem heterojunctions are investigated. Furthermore, the effects of different contents and types of POMs on gas sensing performance are studied. The response of POMs-modified nanofibers can be significantly improved compared to SnO2 @WO3 nanofibers. The optimized response to 100 ppm ethanol can reach 8.8. The enhancement can be attributed to that the addition of POMs electron acceptor, the construction of POMs/semiconductor tandem heterojunctions and the one-dimensional nano-structure can together promote the separation of carriers, which could remarkably improve gas sensing performances. These results provide a new strategy for developing high-performance gas sensors by synthesizing one-dimensional tandem heterojunctions as well as introducing POMs.

Impedance tube method for characterization of one-dimensional electro-momentum coupled materials

Electro-momentum coupling is a macroscopically observable material response resulting from heterogeneous piezoelectric media with microscale asymmetries that produce unique cross-coupling between the bulk momentum of the material and the generated electric field. Recently, Pernas-Salomon et al. used a one-dimensional transmission line model to demonstrate that the electro-momentum coupling effect must be considered in order to retrieve physically meaningful effective properties of heterogeneous media with subwavelength asymmetries [Wave Motion 106, 102797, (2021)]. This work presents the specialization of their transmission line model to the classical impedance tube measurement technique in which the scattering coefficients and the spatial averages of the mechanical and electrical fields of a one-dimensional material can be measured in order to obtain estimates of the frequency-dependent effective properties of an electro-momentum coupled sample. We investigate an idealized analytical approximation and then a finite element model of the realistic impedance tube configurations in order to link the analytical model to realistic experimental conditions and geometry. We then provide preliminary test results extracted from an electro-momentum coupled unit cell in a water-filled impedance tube. [Research sponsored by the Defense Advance Research Project Agency and the Army Research Office and was accomplished under Grant No. W911NF-20-1-0349.]

Continuum soft tissue models from upscaling of arrays of hyperelastic cells

Constitutive models for soft tissue mechanics are typically constructed by fitting phenomenological models to experimental measurements. However, a significant challenge is to rationally construct soft tissue models that encode the properties of the constituent cells and their extracellular matrix. This work presents a framework to derive multiscale soft tissue models that incorporate properties of individual cells without assuming homogeneity or periodicity at the cell level. We consider a viscoelastic model for each cell (which can deform, grow and divide), that we couple to form a network description of a one-dimensional line of cells. We use a discrete-to-continuum approach to form (nonlinear) continuum partial differential equation models for the tissue. These models elucidate the contrasting role of the two forms of dissipation: substrate dissipation localizes the deformation to the neighbourhood of the free boundary and inhibits morphoelastic growth, whereas internal cell dissipation promotes spatial uniformity and does not influence the elongation length. Furthermore, cell division is shown to increase the rate of elongation of the array compared with growth alone, provided the substrate dissipation is proportional to the cell surface area.

Electrostatic shape energy differences of one-dimensional line charges

We investigate the electrostatic energy of one-dimensional line charges, focusing on the energy difference between lines of different shapes. The self-energy of a strictly one-dimensional charge is infinite, but one can quantify the energy by considering geometries that approach a one-dimensional curve, for example, thin wires, thin strips, or chains of close point charges. In each model, the energy diverges logarithmically as the geometry approaches a perfect one-dimensional curve, but the energy also contains a finite term depending on the shape of the line—the “shape energy.” The difference in shape energy between a straight line and a circle is checked to be the same using a range of models. To calculate the shape energy of more complex shapes numerically, we propose a line integral where the singularity in the integrand is canceled. This integral is used to calculate the shape energy of a helix.

Rapid performance prediction model of axial turbine with coupling one-dimensional inverse design and direct analysis

The reasonable and rapid prediction of turbine performance based on design targets such as mass flow rate and pressure ratio is indispensable in the preliminary and conceptual design stage for gas turbine engines in the aviation and power generation industry. However, the lack of detailed geometrical and aerodynamic parameters in this stage significantly challenges the reasonable evaluation of turbine characteristics. The present work proposes a rapid prediction method of axial turbine performance by coupling the inverse design and direct analysis. Firstly, according to the one-dimensional mean line design theory with empirical loss and deviation correlation models, the basic aerodynamic and geometrical parameters are quickly obtained by solving the inverse problem to fulfill the design targets such as mass flow rate and pressure ratio with optimized efficiency. Then, by adopting the loss and deviation correlation models in the off-design conditions, the turbine characteristics in a wide range of operating conditions are obtained by solving the direct analysis problem. Thus, the reasonable and rapid prediction of the turbine characteristics can be realized by coupling the inverse design with direct analysis. Based on the built prediction model, the effect of various deviation models on the predicted turbine characteristics, which was not systematically investigated in previous studies, is clarified by comparing the predicted performance with published test results. Finally, an optimization method of the empirical coefficients in turbine loss and deviation models based on the Genetic Algorithm (GA) is introduced. This method employs optimization theory and existing experimental data to improve the prediction accuracy. The results show that the averaged prediction discrepancies of output powers and mass flow rates in a wide range of operating conditions are no more than 2% and 2.5% for test cases after the optimization of model coefficients. Therefore, this optimization method is expected to be used for updating the empirical coefficients to improve the model prediction accuracy, accompanying the evolution of turbine design strategy at present or in the future.

Multiple dimensions of spin-gapless semiconducting states in tetragonal Sr2CuF6

Spin-gapless semiconductors (SGSs), with intrinsic magnetism, $100%$ spin polarization, and zero-gap band crossing points, have attracted great scientific interest owing to their potential applications in spintronics. In this Letter, using first-principles calculations and symmetry analysis, we demonstrate that the realistic material ${\mathrm{Sr}}_{2}{\mathrm{CuF}}_{6}$ is a spintronic material with multiple dimensions of spin-gapless semiconducting states. Tetragonal ${\mathrm{Sr}}_{2}{\mathrm{CuF}}_{6}$ has a zero-dimensional zero-gap nodal point, a one-dimensional zero-gap nodal line, and a two-dimensional nearly zero-gap nodal surface in one spin direction. Moreover, it hosts a wide band gap in the other spin direction. Our results extend the SGS members from nodal point SGSs and nodal line SGSs to nodal surface SGSs. Furthermore, we report a SGS candidate in an experimentally realized material exhibiting different dimensions of zero-gap points in momentum space. It is hoped that spintronic materials with multiple dimensions of spin-gapless semiconducting states may have significant applications in new-generation spintronics.

Advanced impedance modeling for micropatterned polymer electrolyte membrane fuel cells

Cathode patterning is an effective means of improving the oxygen reduction reaction in polymer electrolyte membrane fuel cells. Because the conventional one-dimensional transmission line model cannot be applied to micropatterned electrodes, impedance modeling for micropatterned electrodes is conducted using a two-dimensional transmission line matrix model. In this study, the charge transfer resistance is considered a function of proton potential in the equivalent circuit based on the Butler–Volmer equation. Micropatterned membrane electrode assemblies (MEAs) with three different pattern depths are fabricated, and electrochemical measurements are performed on them. The measured and simulated impedances are evaluated using the distribution of relaxation times analysis results. This study validates the proposed model by comparing the simulated and measured impedances of the MEAs. The experimental and matrix model simulation results confirm that cathode patterning reduces both the charge transfer and proton conduction resistances. For each MEA, the charge transfer resistances obtained by fitting the matrix model to the measured impedances are plotted on a straight line; thus, the Tafel slope is obtained. The matrix model demonstrated in this study leads to the design of patterned electrodes through the impedance analysis of various patterned electrodes.

Probabilistic analysis and simulation of crack propagation in concrete pavements and surfaces

The surface of concrete pavement is susceptible to cracking. The propagation of a crack in a concrete structure may take the form of a one-dimensional line crack, a two-dimensional surface crack, or a three-dimensional volume crack. Predicting crack propagation in a concrete pavement surface is a complicated task. The whole process of formation, propagation, and orientation of cracks can be considered a stochastic process that necessitates a probabilistic investigation approach. In the present study, crack propagation in concrete pavements is studied from a probabilistic point of view using the concepts of multinomial Markov Chains using Random Walks. The study is based on actual probabilities of propagation and orientation of cracks obtained by tracing crack paths from a large dataset of images using custom-built software. Two random walker models are developed using the trinomial and multinomial Markov Chains. The master equation is developed assuming the trinomial Markov Chain, which has been brought for further theoretical and numerical developments. Examples of inferences and numerical simulations are presented to showcase the potential uses and applications of the proposed probabilistic approach for the design and scheduling of inspection visits and maintenance/rehabilitation strategies of concrete pavements and surfaces.

A large anomalous Hall conductivity induced by Weyl nodal lines in Fe70Al30

Materials with one-dimensional Weyl nodal lines are attracting much attention because of rich exotic properties. In this work, based on the first-principles calculations, we predict the existence of Weyl nodal lines in Fe70Al30. A large intrinsic anomalous Hall conductivity is calculated to be −374 S/cm, which stems from the net Berry curvature induced by Weyl nodal lines. To confirm our calculated results, high quality Fe70Al30 has been prepared and did possess a large anomalous Hall conductivity, where the intrinsic Berry curvature plays a role.

Theoretical wind clumping predictions from 2D LDI models of O-star winds at different metallicities

Context.Hot, massive (OB) stars experience strong line-driven stellar winds and mass loss. As the majority of efficient driving lines are metallic, the amount of wind driving and mass loss is dependent on the stellar metallicityZ.In addition, line-driven winds are intrinsically inhomogeneous and clumpy. However, to date, neither theoretical nor empirical studies of line-driven winds have investigated how such wind clumping may also depend onZ.Aims.We theoretically investigated the degree of wind clumping due to the line-deshadowing instability (LDI) as a function ofZMethods.We performed two-dimensional hydrodynamic simulations of the LDI with an assumed one-dimensional radiation line force for a grid of O-star wind models with fixed luminosity, but with different metal contents by varying the accumulative line strengthQ̄describing the total ensemble of driving lines.Results.We find that, for this fixed luminosity, the amount of wind clumping decreases with metallicity. The decrease is clearly seen in the statistical properties of our simulations, but is nonetheless rather weak; a simple power-law fit for the dependence of the clumping factorfcl≡ 〈ρ2〉 / 〈ρ〉2on metallicity yieldsfcl∝Z0.15±0.01. This implies that empirically derived power-law dependencies of mass-loss rateṀon metallicity – which were previously inferred from spectral diagnostics effectively depending onṀ√fclbut without having any constraints onfcl(Z) – should be only modestly altered by clumping. We expect that this prediction can be directly tested using new data from theHubbleSpace Telescope Ultraviolet Legacy Library of Young Stars as Essential Standards (ULLYSES) project.

Designing transit-oriented multi-modal transportation systems considering travelers’ choices

One goal of future transit-oriented transportation systems is to promote door-to-door mobility for travelers by integrating different public transportation modes into a whole. We propose a mathematical design framework for such a transit-oriented multi-modal transportation system from a societal aspect considering three categories of public transportation modes, i.e., general on-demand modes, local on-demand modes, and fixed-schedule modes. A system-state equilibrium is brought up to describe travelers’ rational travel choices and their reverse effects on agency service levels using the continuous approximation method, and a centralized system designer then manages to achieve a system-beneficial outcome with the minimum cost. To solve the design problem, we prove that the transportation system reaches a unique equilibrium when decision variables are given. By this discovery, we construct a global search framework based on the DIRECT algorithm to solve the optimal design. In analyzing the problem property, we rigorously prove that in the designed systems, the bus service as a fixed-schedule mode is absent from the design scheme under the cases with sufficiently low demands, and the design problem thus reduces to a one-dimensional line search. The ride-hailing service as a general on-demand mode is similarly proved to be excluded when the demand is sufficiently high. In this context, the approximate design parameters of the bus service and the total system cost are developed analytically. The local on-demand mode, bike-sharing service, as an option of bus feeders, is proved to be efficient under a realistic setting. Extensive numerical examples provide evidence verifying the preceding analyses and indicating the behavior of travelers and agencies. Further sensitivity tests show that the subway is favorable for intensive demands and autonomous vehicles may promote the ride-hailing industry. For completeness, an immediate application of the proposed framework in generalized cases validates the model reliability.

Ultrafast two-photon fluorescence imaging of cerebral blood circulation in the mouse brain in vivo

Characterizing blood flow dynamics in vivo is critical to understanding the function of the vascular network under physiological and pathological conditions. Existing methods for hemodynamic imaging have insufficient spatial and temporal resolution to monitor blood flow at the cellular level in large blood vessels. By using an ultrafast line-scanning module based on free-space angular chirped enhanced delay, we achieved two-photon fluorescence imaging of cortical blood flow at 1,000 two-dimensional (2D) frames and 1,000,000 one-dimensional line scans per second in the awake mouse. This orders-of-magnitude increase in temporal resolution allowed us to measure cerebral blood flow at up to 49 mm/s and observe pulsatile blood flow at harmonics of heart rate. Directly visualizing red blood cell (RBC) flow through vessels down to >800 µm in depth, we characterized cortical layer–dependent flow velocity distributions of capillaries, obtained radial velocity profiles and kilohertz 2D velocity mapping of multifile blood flow, and performed RBC flux measurements from penetrating blood vessels.

Measurement-induced quantum walks.

We investigate a tight-binding quantum walk on a graph. Repeated stroboscopic measurements of the position of the particle yield a measured "trajectory," and a combination of classical and quantum mechanical properties for the walk are observed. We explore the effects of the measurements on the spreading of the packet on a one-dimensional line, showing that except for the Zeno limit, the system converges to Gaussian statistics similarly to a classical random walk. A large deviation analysis and an Edgeworth expansion yield quantum corrections to this normal behavior. We then explore the first passage time to a target state using a generating function method, yielding properties like the quantization of the mean first return time. In particular, we study the effects of certain sampling rates that cause remarkable changes in the behavior in the system, such as divergence of the mean detection time in finite systems and decomposition of the phase space into mutually exclusive regions, an effect that mimics ergodicity breaking, whose origin here is the destructive interference in quantum mechanics. For a quantum walk on a line, we show that in our system the first detection probability decays classically like (time)^{-3/2}. This is dramatically different compared to local measurements, which yield a decay rate of (time)^{-3}, indicating that the exponents of the first passage time depend on the type of measurements used.

The MUSE eXtremely Deep Field: Individual detections of Lyα haloes around rest-frame UV-selected galaxies at z ≃ 2.9–4.4

Hydrogen Lyα haloes (LAHs) are commonly used as a tracer of the circumgalactic medium (CGM) at high redshifts. In this work, we aim to explore the existence of Lyα haloes around individual UV-selected galaxies, rather than around Lyα emitters (LAEs), at high redshifts. Our sample was continuum-selected with F775W ≤ 27.5, and spectroscopic redshifts were assigned or constrained for all the sources thanks to the deepest (100- to 140-h) existing Very Large Telescope (VLT)/Multi-Unit Spectroscopic Explorer (MUSE) data with adaptive optics. The final sample includes 21 galaxies that are purely F775W-magnitude selected within the redshift range z ≈ 2.9 − 4.4 and within a UV magnitude range −20 ≤ M1500 ≤ −18, thus avoiding any bias toward LAEs. We tested whether galaxy’s Lyα emission is significantly more extended than the MUSE PSF-convolved continuum component. We find 17 LAHs and four non-LAHs. We report the first individual detections of extended Lyα emission around non-LAEs. The Lyα halo fraction is thus as high as 81.0−11.2+10.3%, which is close to that for LAEs at z = 3 − 6 in the literature. This implies that UV-selected galaxies generally have a large amount of hydrogen in their CGM. We derived the mean surface brightness (SB) profile for our LAHs with cosmic dimming corrections and find that Lyα emission extends to 5.4 arcsec (≃40 physical kpc at the midpoint redshift z = 3.6) above the typical 1σ SB limit. The incidence rate of surrounding gas detected in Lyα per one-dimensional line of sight per unit redshift, dn/dz, is estimated to be 0.76−0.09+0.09 for galaxies with M1500 ≤ −18 mag at z ≃ 3.7. Assuming that Lyα emission and absorption arise in the same gas, this suggests, based on abundance matching, that LAHs trace the same gas as damped Lyα systems (DLAs) and sub-DLAs.

Some Regularity Properties on Bolza problems in the Calculus of Variations

The paper summarizes the main core of the last results that we obtained in [8, 4, 17] on the regularity of the value function for a Bolza problem of a one-dimensional, vectorial problem of the calculus of variations. We are concerned with a nonautonomous Lagrangian that is possibly highly discontinuous in the state and velocity variables, nonconvex in the velocity variable and non coercive. The main results are achieved under the assumption that the Lagrangian is convex on the one-dimensional lines of the velocity variable and satisfies a local Lipschitz continuity condition w.r.t. the time variable, known in the literature as Property (S), and strictly related to the validity of the Erdmann–Du-Bois Reymond equation.