Quantum dynamics within curved thin layers with deviation

Combining the deviation between thin layers' adjacent surfaces with the confining potential method applied to the quantum curved systems,we derive the effective Schr?dinger equation describing the particle constrained within a curved layer,accompanied by a general geometric potential V_(gq) composed of a compression-corrected geometric potential V_(gq)~*and a novel potential V_(gq)~(**) brought by the deviation.Applying this analysis to the cylindrical layer emerges two types of deviation-induced geometric potential,resulting from the the cases of slant deviation and tangent deviation,respectively,which strongly renormalizes the purely geometric potential and contribute to the energy spectrum based on a very substantial deepening of bound states they offer.

Bending results of graphene origami reinforced doubly curved shell

The present work investigates higher order stress,strain and deformation analyses of a shear deformable doubly curved shell manufactures by a Copper(Cu)core reinforced with graphene origami auxetic metamaterial subjected to mechanical and thermal loads.The effective material properties of the graphene origami auxetic reinforced Cu matrix are developed using micromechanical models cooperate both material properties of graphene and Cu in terms of temperature,volume fraction and folding degree.The principle of virtual work is used to derive governing equations with accounting thermal loading.The numerical results are analytically obtained using Navier's technique to investigate impact of significant parameters such as thermal loading,graphene amount,folding degree and directional coordinate on the stress,strain and deformation responses of the structure.The graphene origami materials may be used in aerospace vehicles and structures and defence technology because of their low weight and high stiffness.A verification study is presented for approving the formulation,solution methodology and numerical results.

Deep structure of the Southeast Asian curved subduction system and its dynamic process

The deep structure,material circulation,and dynamic processes in the Southeast Asia have long been an elusive scientific puzzle due to the lack of systematic scientific observations and recognized theoretical models.Based on the deep seismic tomography using long-period natural earthquake data,in this study,the deep structure and material circulation of the curved subduction system in Southeast Asia was studied,and the dynamic processes since 100 million years ago was reconstructed.It is pointed out that challenges still exist in the precise reconstruction of deep mantle structures of the study area,the influence of multi-stage subduction on deep material exchange and shallow magma activity,as well as the spatiotemporal evolution and coupling mechanism of multi-plate convergence.Future work should focus on high-resolution land-sea joint 3-D seismic tomography imaging of the curved subduction system in the Southeast Asia,combined with geochemical analysis and geodynamic modelling works.

Effect of boundary slip on electroosmotic flow in a curved rectangular microchannel

The aim of this study is to numerically investigate the impact of boundary slip on electroosmotic flow(EOF) in curved rectangular microchannels. Navier slip boundary conditions were employed at the curved microchannel walls. The electric potential distribution was governed by the Poisson–Boltzmann equation, whereas the velocity distribution was determined by the Navier–Stokes equation. The finite-difference method was employed to solve these two equations. The detailed discussion focuses on the impact of the curvature ratio, electrokinetic width, aspect ratio and slip length on the velocity. The results indicate that the present problem is strongly dependent on these parameters. The results demonstrate that by varying the dimensionless slip length from 0.001 to 0.01 while maintaining a curvature ratio of 0.5 there is a twofold increase in the maximum velocity. Moreover, this increase becomes more pronounced at higher curvature ratios. In addition, the velocity difference between the inner and outer radial regions increases with increasing slip length. Therefore, the incorporation of the slip boundary condition results in an augmented velocity and a more non-uniform velocity distribution. The findings presented here offer valuable insights into the design and optimization of EOF performance in curved hydrophobic microchannels featuring rectangular cross-sections.

Effective dynamics for a spin-1/2 particle constrained to a curved layer with inhomogeneous thickness

We derive an effective Hamiltonian for a spin-1/2 particle confined within a curved thin layer with non-uniform thickness using the confining potential approach.Our analysis reveals the presence of a pseudo-magnetic field and effective spin–orbit interaction(SOI)arising from the curvature,as well as an effective scalar potential resulting from variations in thickness.Importantly,we demonstrate that the physical effect of additional SOI from thickness fluctuations vanishes in low-dimensional systems,thus guaranteeing the robustness of spin interference measurements to thickness imperfection.Furthermore,we establish the applicability of the effective Hamiltonian in both symmetric and asymmetric confinement scenarios,which is crucial for its utilization in one-side etching systems.

Nonlinear dynamics of a circular curved cantilevered pipe conveying pulsating fluid based on the geometrically exact model

Due to the novel applications of flexible pipes conveying fluid in the field of soft robotics and biomedicine,the investigations on the mechanical responses of the pipes have attracted considerable attention.The fluid-structure interaction(FSI)between the pipe with a curved shape and the time-varying internal fluid flow brings a great challenge to the revelation of the dynamical behaviors of flexible pipes,especially when the pipe is highly flexible and usually undergoes large deformations.In this work,the geometrically exact model(GEM)for a curved cantilevered pipe conveying pulsating fluid is developed based on the extended Hamilton's principle.The stability of the curved pipe with three different subtended angles is examined with the consideration of steady fluid flow.Specific attention is concentrated on the large-deformation resonance of circular pipes conveying pulsating fluid,which is often encountered in practical engineering.By constructing bifurcation diagrams,oscillating shapes,phase portraits,time traces,and Poincarémaps,the dynamic responses of the curved pipe under various system parameters are revealed.The mean flow velocity of the pulsating fluid is chosen to be either subcritical or supercritical.The numerical results show that the curved pipe conveying pulsating fluid can exhibit rich dynamical behaviors,including periodic and quasi-periodic motions.It is also found that the preferred instability type of a cantilevered curved pipe conveying steady fluid is mainly in the flutter of the second mode.For a moderate value of the mass ratio,however,a third-mode flutter may occur,which is quite different from that of a straight pipe system.

Beyond boundaries:Feasibility of curved linear array echoendoscope in appendiceal neoplasm detection

We recently read with great interest a study by Zhang et al in the World Journal of Gastroenterology.In our practice,we focus specifically on examining appendiceal mucinous neoplasms(AMNs)with endoscopic ultrasound(EUS)using different scopes.AMNs are rare neoplastic lesions characterized by an accumulation of mucin inside a cystic dilatation of the appendix.Clinically,they can present as nonspecific acute appendicitis.AMNs can turn into a life-threatening condition,termed pseudomyxoma peritonei,in which the ruptured appendix causes accumulation of mucin in the abdomen.Therefore,accurate and rapid diagnosis of AMN is essential.EUS is able to confirm and stage AMNs;although,EUS examination was once limited to the rectal and anal regions due to the conven-tional oblique-view scopes.With the emergence of new forward-view linear echoendoscopes and instruments like EUS miniprobes and overtubes,the scope of examination is changing.Herein,we discuss the feasibility of using the curved linear array echoendoscopes to examine cecal and appendiceal orifice lesions.

Resilient performance of self-centering hybrid rocking walls with curved interface under pseudo-static loading

Frame and rocking wall(FRW)structures have excellent resilient performance during earthquakes.However,the concrete at interfacial corners of rocking walls(RWs)is easily crushed due to local extreme compression during the rocking process.An innovative RW with a curved interface is proposed to prevent interfacial corners from producing local damage,enhancing its earthquake resilient performance(ERP).The precast wall panel with a curved interface is assembled into an integral self-centering hybrid rocking wall(SCRW)by two post-tensioned unbonded prestressed tendons.Moreover,two ordinary energy dissipation steel rebars and two shear reinforcements are arranged to increase the energy dissipation capacity and lateral resistance.Two SCRW specimens and one monolithic reinforced concrete(RC)shear wall(SW)were tested under pseudo-static loading to compare the ERPs of the proposed SCRW and the SW,focusing on studying the effect of the curved interface on the SCRW.The key resilient performance of rocking effects,failure modes,and hysteretic properties of the SCRW were explored.The results show that nonlinear deformations of the SCRW are concentrated along the interface between the SCRW and the foundation,avoiding damage within the SCRW.The restoring force provided by the prestressed tendons can effectively realize self-centering capacity with small residual deformation,and the resilient performance of the SCRW is better than that of monolithic SW.In addition,the curved interface of the SCRW makes the rocking center change and move inward,partially relieving the stress concentration and crush of concrete.The rocking range of the rocking center is about 41.4%of the width of the SCRW.

Dynamic and electrical responses of a curved sandwich beam with glass reinforced laminate layers and a pliable core in the presence of a piezoelectric layer under low-velocity impact

The dynamic responses and generated voltage in a curved sandwich beam with glass reinforced laminate(GRL)layers and a pliable core in the presence of a piezoelectric layer under low-velocity impact(LVI)are investigated.The current study aims to carry out a dynamic analysis on the sandwich beam when the impactor hits the top face sheet with an initial velocity.For the layer analysis,the high-order shear deformation theory(HSDT)and Frostig's second model for the displacement fields of the core layer are used.The classical non-adhesive elastic contact theory and Hunter's principle are used to calculate the dynamic responses in terms of time.In order to validate the analytical method,the outcomes of the current investigation are compared with those gained by the experimental tests carried out by other researchers for a rectangular composite plate subject to the LVI.Finite element(FE)simulations are conducted by means of the ABAQUS software.The effects of the parameters such as foam modulus,layer material,fiber angle,impactor mass,and its velocity on the generated voltage are reviewed.

A Review of the Key Points in the Design of Small-Radius Curved Ramp Bridges

This article explores the fundamentals of small-radius curved ramp bridges.It covers the selection of box girder spans,support methods,and forms,along with design optimization techniques for this type of bridge structure.The purpose of this paper is to provide robust support for enhancing the design quality of these bridges and ensuring their efficacy in real-world applications.

Regularity classification and corresponding analysis method requirements of horizontally curved bridges with unequal pier heights

The seismic behavior of horizontally curved bridges,particularly with unequal height piers,is more complicated than that of straight bridges due to their geometric properties.In this study,the seismic responses of several horizontally curved single-column-bent viaducts with various degrees of curvature and different pier heights have been investigated,employing three different analysis approaches:namely,modal pushover analysis,uniform load method,and nonlinear time history analysis.Considering the investigated bridge configurations and utilizing the most common regularity indices,the results indicate that viaducts with 45-degree and 90-degree deck subtended angles can be categorized as regular and moderately irregular,respectively,while the bridges with 180-degree deck subtended angle are found to be highly irregular.Furthermore,the viaducts whose pier heights are asymmetric may be considered as irregular for almost all ranges of the deck subtended angles.The effects of higher transverse and longitudinal modes are discussed and the minimum analysis requirements are identified to assess the seismic response of such bridge configurations for design purposes.Although the Regularity Indices used here are useful tools to distinguish between regular and irregular bridges,further studies are needed to improve their reliability.

Impact of backwater on water surface profile in curved channels

Owing to extensive construction of dams, the impact of backwater on flow may lead to navigation or flood control issues in curved channels. To date, the impact of backwater on the water surface profile in curved channels remains unknown and requires investigation. In this study, experiments were conducted in a glass-walled recirculating flume with a length of 19.4 m, a width of 0.6 m, and a depth of 0.8 m, and the impact of backwater on the water surface profile in a 90° channel bend was investigated. The experimental results showed that the backwater degree had a significant impact on the transverse and longitudinal flow depth distributions in the bend. The transverse slope of the flow (Jr) increased linearly with an increase in the Froude number of the approach flow upstream of the bend. Jr increased with the longitudinal location parameter ξ when −0.2 < ξ < 0.5, and decreased with ξ when 0.5 < ξ < 1.2. Furthermore, the results showed that Jr asymptotically decreased to zero with an increase in the degree of backwater. An equation was formulated to estimate the transverse slope of the flow in a 90° bend in backwater zones.

Flume Experiment Investigation on Propagation Characteristics of Tidal Bore in A Curved Channel

Tidal bore is a special and intensive form of flow movement induced by tidal effect in estuary areas, which has complex characteristics of profile, propagation and flow velocity. Although it has been widely studied for the generation mechanism, propagation features and influencing factors, the curved channel will complicate the characteristics of tidal bore propagation, which need further investigation compared with straight channel. In this study, the flume experiments for both undular and breaking bores’ propagation in curved channel are performed to measure the freesurface elevation and flow velocity by ultrasonic sensors and ADV respectively. The propagation characteristics,including tidal bore height, cross-section surface gradient, tidal bore propagation celerity, and flow velocity are obtained for both sides of the curved channel. And three bore intensities are set for each type of tidal bores. The freesurface gradients are consistently enlarged in high-curvature section for undular and breaking bores, but have distinct behaviors in low-curvature section. The spatial distributions of tidal bore propagation celerity and flow velocity are compared between concave and convex banks. This work will provide experimental reference for engineering design of beach and seawall protection, erosion reduction and siltation promotion in estuary areas with the existence of tidal bores.

A New Dynamics Analysis Model for Five-Axis Machining of Curved Surface Based on Dimension Reduction and Mapping

The equipment used in various fields contains an increasing number of parts with curved surfaces of increasing size.Five-axis computer numerical control(CNC)milling is the main parts machining method,while dynamics analysis has always been a research hotspot.The cutting conditions determined by the cutter axis,tool path,and workpiece geometry are complex and changeable,which has made dynamics research a major challenge.For this reason,this paper introduces the innovative idea of applying dimension reduction and mapping to the five-axis machining of curved surfaces,and proposes an efficient dynamics analysis model.To simplify the research object,the cutter position points along the tool path were discretized into inclined plane five-axis machining.The cutter dip angle and feed deflection angle were used to define the spatial position relationship in five-axis machining.These were then taken as the new base variables to construct an abstract two-dimensional space and establish the mapping relationship between the cutter position point and space point sets to further simplify the dimensions of the research object.Based on the in-cut cutting edge solved by the space limitation method,the dynamics of the inclined plane five-axis machining unit were studied,and the results were uniformly stored in the abstract space to produce a database.Finally,the prediction of the milling force and vibration state along the tool path became a data extraction process that significantly improved efficiency.Two experiments were also conducted which proved the accuracy and efficiency of the proposed dynamics analysis model.This study has great potential for the online synchronization of intelligent machining of large surfaces.

Unsteady Flow and Heat Transfer of a Casson Micropolar Nanofluid over a Curved Stretching/Shrinking Surface

We present the results of an investigation into the behavior of the unsteady flow of a Casson Micropolar nanofluid over a shrinking/stretching curved surface,together with a heat transfer analysis of the same problem.The body force acting perpendicular to the surface wall is in charge of regulating the fluid flow rate.Curvilinear coordinates are used to account for the considered curved geometry and a set of balance equations for mass,momentum,energy and concentration is obtained accordingly.These are turned into ordinary differential equations using a similarity transformation.We show that these equations have dual solutions for a number of different combinations of various parameters.The stability of such solutions is investigated by applying perturbations on the steady states.It is found that high values of the Micropolar and Casson parameters cause the flow to move more slowly.However,when compared to a shrunken surface,a stretched surface produces a greater Micro-rotation flux.

High-Order Method with Moving Frames to Compute the Covariant Derivatives of Vectors on General 2D Curved Surfaces

The covariant derivative is a generalization of differentiating vectors.The Euclidean derivative is a special case of the covariant derivative in Euclidean space.The covariant derivative gathers broad attention,particularly when computing vector derivatives on curved surfaces and volumes in various applications.Covariant derivatives have been computed using the metric tensor from the analytically known curved axes.However,deriving the global axis for the domain has been mathematically and computationally challenging for an arbitrary two-dimensional(2D)surface.Consequently,computing the covariant derivative has been difficult or even impossible.A novel high-order numerical scheme is proposed for computing the covariant derivative on any 2D curved surface.A set of orthonormal vectors,known as moving frames,expand vectors to compute accurately covariant derivatives on 2D curved surfaces.The proposed scheme does not require the construction of curved axes for the metric tensor or the Christoffel symbols.The connectivity given by the Christoffel symbols is equivalently provided by the attitude matrix of orthonormal moving frames.Consequently,the proposed scheme can be extended to the general 2D curved surface.As an application,the Helmholtz‐Hodge decomposition is considered for a realistic atrium and a bunny.

Microstructure and mechanical properties of curved AZ31 magnesium alloy profiles produced by differential velocity sideways extrusion

Lightweight curved profiles are widely utilised in the transportation industry considering the increasing need for improving aerodynamic efficiency,aesthetics and cutting emissions.In this paper,curved AZ31 Mg alloy profiles were manufactured in one operation by a novel process,differential velocity sideways extrusion(DVSE),in which two opposed rams were used.Effects of extrusion temperature and velocity(strain rate) on curvature,microstructure,and mechanical properties of the formed profiles were examined.Profile curvature was found to be more readily controlled by the velocity ratio of the bottom ram v2to the top ram v1,whereas extrusion temperature(T=250,300,350℃)and extrusion velocity(v_(1)=0.1,1 mm/s) slightly affect curvature for a given velocity ratio.A homogeneous microstructure with equiaxed grains(~4.5 μm) resulted from dynamic recrystallisation(DRX),was observed after DVSE(v_(2)/v_(1)=1/2) at 300 ℃ and v_(1)=0.1 mm/s,where the initial billet had an average grain size of ~25 um.Increasing extrusion temperature leads to grain growth(~5 μm) at 350 ℃ and v_(1)=0.1 mm/s.DRX is incomplete at the relatively low temperature of 250℃(v_(1)=0.1 mm/s),and higher strain rate with v1=1mm/s(T=300℃),resulting in inhomogeneous bi-modal necklace pattern grains ranging in size around 1-25 μm for the former and 2-20μm for the latter.Grain refinement is attributed to DRX during the severe plastic deformation(SPD) arising in DVSE,and initiates at the prior boundaries of coarse grains in a necklace-like manner.Compared with the billet,micro-hardness and ultimate tensile strength of the profiles have been enhanced,which is compatible with grain refinement.Also,an obvious increase in tensile ductility was found.However,yield strength slightly decreases except for the complete DRXed case(300℃,v_(1)=0.1 mm/s),where a slightly higher value was found,indicating strengthening by grain refinement is greater than softening caused by texture modification.The initial billet had a strong basal texture wherein the {0002} basal plane is oriented parallel to the extrusion direction(’hard’ orientation),while DVSE results in the profiles having weak basal textures and the {0002} basal plane oriented ~5-10° to the extrusion direction(i.e.towards the orientation for easier slip).This significantly modified texture contributes to the softening of the profiles in the extrusion direction,in which tensile tests were performed,and the related elongation improvement.

Flow Structure and Short-Term Riverbed Evolution in Curved Flumes

River bending is the major effect responsible for bed topography and bank changes.In this study,fluid velocity(measured by a three-dimensional Doppler advanced point current meter)and bed topographical data have been collected in 40 sections of an experimental model.The whole flume was composed of an organic glass bend,upstream and downstream water tanks,two transition straight sections,a circulation pump,and a connection pipeline.Each section has been found to be characterized by a primary circulation and a small reverse circulation,with some sections even presenting three more or more circulation structures.The minimum circulation intensity has been detected in proximity to the top of the curved channel,while a region with small longitudinal velocity has been observed near the concave bank of each bend,corresponding to the flat bed formed after a short period of scouring.The maximum sediment deposition and scour depth in the presence of a uniform distribution of living flexible vegetation within 10 cm of the flume wall have been found to be smaller than those observed in the tests conducted without vegetation.

A Fourth-Order Unstructured NURBS-Enhanced Finite Volume WENO Scheme for Steady Euler Equations in Curved Geometries

In Li and Ren(Int.J.Numer.Methods Fluids 70:742–763,2012),a high-order k-exact WENO finite volume scheme based on secondary reconstructions was proposed to solve the two-dimensional time-dependent Euler equations in a polygonal domain,in which the high-order numerical accuracy and the oscillations-free property can be achieved.In this paper,the method is extended to solve steady state problems imposed in a curved physical domain.The numerical framework consists of a Newton type finite volume method to linearize the nonlinear governing equations,and a geometrical multigrid method to solve the derived linear system.To achieve high-order non-oscillatory numerical solutions,the classical k-exact reconstruction with k=3 and the efficient secondary reconstructions are used to perform the WENO reconstruction for the conservative variables.The non-uniform rational B-splines(NURBS)curve is used to provide an exact or a high-order representation of the curved wall boundary.Furthermore,an enlarged reconstruction patch is constructed for every element of mesh to significantly improve the convergence to steady state.A variety of numerical examples are presented to show the effectiveness and robustness of the proposed method.

Inverse design of mechanical metamaterial achieving a prescribedconstitutive curve

Besides exhibiting excellent capabilities such as energy absorption,phase-transforming metamaterials offer a vast design space for achieving nonlinear constitutive relations.This is facilitated by switching between different patterns under deformation.However,the related inverse design problem is quite challenging,due to the lack of appropriate mathematical formulation and the convergence issue in the post-buckling analysis of intermediate designs.In this work,periodic unit cells are explicitly described by the moving morphable voids method and effectively analyzed by eliminating the degrees of freedom in void regions.Furthermore,by exploring the Pareto frontiers between error and cost,an inverse design formulation is proposed for unit cells.This formulation aims to achieve a prescribed constitutive curve and is validated through numerical examples and experimental results.The design approach presented here can be extended to the inverse design of other types of mechanical metamaterials with prescribed nonlinear effective properties.