Nonaxisymmetric Shapes Research Articles

Scattering-Point-Guided Oriented RepPoints for Ship Detection

Ship detection finds extensive applications in fisheries management, maritime rescue, and surveillance. However, detecting nearshore targets in SAR images is challenging due to land scattering interference and non-axisymmetric ship shapes. Existing SAR ship detection models struggle to adapt to oriented ship detection in complex nearshore environments. To address this, we propose an oriented-reppoints target detection scheme guided by scattering points in SAR images. Our method deeply integrates SAR image target scattering characteristics and designs an adaptive sample selection scheme guided by target scattering points. This incorporates scattering position features into the sample quality measurement scheme, providing the network with a higher-quality set of proposed reppoints. We also introduce a novel supervised guidance paradigm that uses target scattering points to guide the initialization of reppoints, mitigating the influence of land scattering interference on the initial reppoints quality. This achieves adaptive feature learning, enhancing the quality of the initial reppoints set and the performance of object detection. Our method has been extensively tested on the SSDD and HRSID datasets, where we achieved mAP scores of 89.8% and 80.8%, respectively. These scores represent significant improvements over the baseline methods, demonstrating the effectiveness and robustness of our approach. Additionally, our method exhibits strong anti-interference capabilities in nearshore detection and has achieved state-of-the-art performance.

Investigation of non-axisymmetric endwall contouring in a high loaded turbine stator cascade

The intensity and structure of the secondary flows have significant influences on the turbine cascade losses. Combining with the extension method of Non-linear Programming by Quadratic Lagrangian (NLPQLP), two endwall parametric methods respectively based on the B-spline surface and Fourier series are used to optimize the aerodynamic losses of a turbine cascade. The optimization processes are based on Computational Fluid Dynamics (CFD) analysis and two final designs are obtained by different methods. The endwall profile generated by the B-spline surface method (EW-B1) appears to relatively reduce the total pressure loss by 16.58% and the secondary kinetic energy coefficient ( C SKE) by 27.08%, while the endwall profile generated by the Fourier series method (EW-F1) relatively reduces the loss by 16.18% but increases C SKE by 8.99%. The radial movement of upper Passage Vortex (PV) and the weakening of the pressure branch of the Horseshoe Vortex (HVps) are confirmed to be the reasons of loss reduction in EW-B1, while the movement of PV is the main reason for EW-F1 to decrease the total pressure loss. In EW-B1, the weakening of HVps has a much more significant effect on the decrease in loss, which is affected by the non-axisymmetric shapes upstream of the vortex trajectory and the drop in C SKE generation near the throat.

Dynamics of Drop Formation in the Presence of Interfacial Mass Transfer.

The dynamics of drop formation have been investigated in the presence of interfacial mass transfer through controlled flow visualization experiments. The mixtures of n-hexane (solvent) and acetone (solute) were used as a dispersed phase, having different initial compositions varying over a broad range. Drops were formed at the submerged position in the continuous phase (water) at the same operating flow conditions. The unsteady force balance model is developed to analyze the implications of the simultaneously occurring interfacial transfer of the solute on the formation dynamics in real time, and predictions are validated with experimental results. Based on initial compositions, the analysis of the transient drop shape shows a sharp transition in the drop formation regime. At lower initial solute concentrations, i.e., ϕ0 < 0.2, axisymmetric drop formation occurs and the interfacial solute transfer has negligible effects on the formation dynamics. Over an intermediate range of solute concentrations, i.e., 0.2 < ϕ0 < 0.5, Marangoni instability is triggered along the evolving interface, and therefore, the interface deformations and contractions occur during the drop formation. At ϕ0 = 0.5, the drop takes highly nonaxisymmetric shapes and remains away from equilibrium until its detachment from an orifice. For ϕ0 > 0.5, the spontaneous ejection of plumes of the solute results in the rapid generation of multiple droplets of smaller size. This work shows that higher solute concentration gradients not only lead to faster solute transport but also induce strong interfacial instability simultaneously. Thus, the coupled effects of transient change in composition and fluid properties govern the drop size and its formation time in such systems under non-equilibrium.

Terahertz Constant Velocity Flying Spot for 3D Tomographic Imaging.

This work reports on a terahertz tomography technique using constant velocity flying spot scanning as illumination. This technique is essentially based on the combination of a hyperspectral thermoconverter and an infrared camera used as a sensor, a source of terahertz radiation held on a translation scanner, and a vial of hydroalcoholic gel used as a sample and mounted on a rotating stage for the measurement of its absorbance at several angular positions. From the projections made in 2.5 h and expressed in terms of sinograms, the 3D volume of the absorption coefficient of the vial is reconstructed by a back-projection method based on the inverse Radon transform. This result confirms that this technique is usable on samples of complex and nonaxisymmetric shapes; moreover, it allows 3D qualitative chemical information with a possible phase separation in the terahertz spectral range to be obtained in heterogeneous and complex semitransparent media.

Giant Impacts and Debris Disk Morphology

Certain debris disks have nonaxisymmetric shapes in scattered light which are unexplained. The appearance of a disk depends on how its constituent Keplerian ellipses are arranged. The more the ellipses align apsidally, the more nonaxisymmetric the disk. Apsidal alignment is automatic for fragments released from a catastrophic collision between solid bodies. We synthesize scattered light images, and thermal emission images, of such giant impact debris. Depending on the viewing geometry, and if and how the initial apsidal alignment is perturbed, the remains of a giant impact can appear in scattered light as a one-sided or two-sided “fork,” a lopsided “needle,” or a set of “double wings.” The last shape is difficult to reproduce in other scenarios involving gravitational forcing or gas drag, which do not align orbits as well. We compare our images with observations and offer a scorecard assessing whether the scattered light asymmetries in HD 15115, HD 32297, HD 61005, HD 111520, HD 106906, β Pic, and AU Mic are best explained by giant impacts, gravitational perturbations, or sculpting by the interstellar medium.

Stability of drawing of microstructured optical fibres

We consider the stability of the drawing of a long and thin viscous thread with an arbitrary number of internal holes of arbitrary shape that evolves due to axial drawing, inertia and surface tension effects. Despite the complicated geometry of the boundaries, we use asymptotic techniques to determine a particularly convenient formulation of the equations of motion that is well-suited to stability calculations. We will determine an explicit asymptotic solution for steady states with (a) large surface tension and negligible inertia, and (b) large inertia. In both cases, we will show that complicated boundary layer structures can occur. We will use linear stability analysis to show that the presence of an axisymmetric hole destabilises the flow for finite capillary number and which answers a question raised in the literature. However, our formulation allows us to go much further and consider arbitrary hole structures or non-axisymmetric shapes, and show that any structure with holes will be less stable than the case of a solid axisymmetric thread. For a solid axisymmetric thread, we will also determine a closed-form expression that delineates the unconditional instability boundary in which case the thread is unstable for all draw ratios. We will determine how the detailed effects of the microstructure affect the stability, and show that they manifest themselves only via a single function that occurs in the stability problem and hence have a surprisingly limited effect on the stability.

Contact Angle Measurement on Curved Wetting Surfaces in Multiphase Lattice Boltzmann Method.

Contact angle is an essential physical quantity that characterizes the wettability of a substrate. Although it is widely used in the studies of surface wetting, capillary phenomena, and moving contact lines, the contact angle measurements in simulations and experiments are still complicated and time-consuming. In this paper, we present an efficient scheme for the measurement of contact angle on curved wetting surfaces in lattice Boltzmann simulations. The measuring results are in excellent agreement with the theoretical predictions without considering the gravity effect. A series of simulations with various drop sizes and surface curvatures confirm that the present scheme is grid-independent. Then, the scheme is verified in gravitational environments by simulating the deformations of sessile and pendent droplets on the curved wetting surface. The numerical results are highly consistent with experimental observations and support the theoretical analysis that the microscopic contact angle is independent of gravity. Furthermore, the method utilizes only the microscopic geometry of the contact angle and does not depend on the droplet profile; therefore, it can be applied to nonaxisymmetric shapes or moving contact lines. The scheme is applied to capture the dynamic contact angle hysteresis on homogeneous or chemically heterogeneous curved surfaces. Importantly, the accurate contact angle measurement enables the dynamic mechanical analysis of moving contact lines. The present measurement is simple and efficient and can be extended to implementations in various multiphase lattice Boltzmann models.

Formulation and Numerical Solution of the Stability Loss Problem of Elastic-Plastic Shells of Revolution with an Elastic Filler under Combined Axisymmetric and Torsional Loadings

A dynamic statement and a method for numerically solving the buckling problems of elastoplastic shells of revolution with filler in axisymmetric and non-axisymmetric shapes under quasi-static and dynamic loading are presented within the framework of two approaches. In the first approach, the problem of elastic-plastic deformation and buckling of shells of revolution with an elastic filler under combined axisymmetric loading with torsion is formulated in a two-dimensional (generalized axisymmetric) formulation based on the hypotheses of the shells theory of the Timoshenko type and the Winkler foundation. The constitutive relations are written in the cylindrical system of Euler coordinates. For each shell element, a local Lagrangian coordinate system is introduced. Kinematic relations are recorded in the current state metric. The distribution of the displacement velocity components over the shell thickness and strain rate tensors in the local basis is written as the sum of the momentless and moment components, which, in turn, are written as the sum of the symmetric and asymmetric parts in the local and in the general basis. The elastoplastic properties of the shell material are taken into account within the framework of the theory of flow with nonlinear isotropic hardening. To take into account non-axisymmetric forms of buckling, the desired functions (both displacements and forces, moments, contact pressure) are expanded into a Fourier series in the circumferential direction. The variational equations of shell motion are derived from the general equation of dynamics. The contact between the shell and the deformable filler is modeled based on the conditions of non-penetration along the normal and free slip along the tangent. The variational equations of shell dynamics for axisymmetric and nonaxisymmetric processes are interconnected through the physical relations of the theory of plasticity. They take into account large axisymmetric shape changes and the instantaneous stress-strain state of the shell. At the initial stage of the nonaxisymmetric buckling process, the deflections are small; therefore, the equations of nonaxisymmetric buckling are obtained as linearized with respect to nonaxisymmetric forms. To initiate nonaxisymmetric buckling modes, initial nonaxisymmetric deflections are introduced. To solve the defining system of equations, a finite-difference method and an explicit time integration scheme of the “cross” type are used. The second approach is based on continuum mechanics hypotheses and implemented in a three-dimensional setting. Both approaches make it possible to simulate the nonlinear subcritical deformation of shells of revolution with an elastic filler, to determine the ultimate (critical) loads in a wide range of loading rates, taking into account geometric shape imperfections, to study the processes of buckling in axisymmetric and non-axisymmetric shapes under dynamic and quasi-static complex loading by tension, compression, torsion, internal and external pressure. The results of numerical simulation are compared with experimental data on the torsion of steel cylindrical elastoplastic shells ( R / h = 1.45) with an elastic filler.

Transient shape morphing of active gel plates: geometry and physics.

The control of shape in active structures is a key problem for the realization of smart sensors and actuators, which often draw inspiration from natural systems. In this context, slender structures, such as thin plates, have been studied as a relevant example of shape morphing systems where curvature is generated by in-plane incompatibilities. In particular, in hydrogel plates these incompatibilities can be programmed at fabrication time, such that a target configuration is attained at equilibrium upon swelling or shrinking. While these aspects have been examined in detail, understanding the transient morphing of such active structures deserves further investigation. In this study, we develop a geometrical model for the transient shaping of thin hydrogel plates by extending the theory of non-Euclidean plates. We validate the proposed model using experiments on gel samples that are programmed to reach axisymmetric equilibrium shapes. Interestingly, our experiments show the emergence of non-axisymmetric shapes for early times, as a consequence of boundary layer effects induced by solvent transport. We rationalize these observations using numerical simulations based on a detailed poroelastic model. Overall, this work highlights the limitations of purely geometrical models and the importance of transient, reduced theories for morphing plates that account for the coupled physics driving the evolution of shape. Computational approaches employing these theories will allow to achieve accurate control on the morphing dynamics and ultimately advance 4D printing technologies.

Acoustic scattering reduction of elliptical targets via pentamode near-cloaking based on transformation acoustics in elliptic coordinates

Cloaks for underwater applications designed for actual submarine acoustic stealth are still far from the technological advancement needed for being put in practice. Several challenges need to be overcome such as dealing with weight or non-axisymmetric shapes. In this paper, we introduce the use of elliptical coordinates to define quasi-symmetric transformations to retrieve the material properties of pentamode cloaks for elliptical shaped targets, along with a quantifiable approximation introduced by the rotation tensor being different from the identity. This is done analytically adopting transformation theory, in an attempt to generalize the usual approach for axisymmetric cloaks, with the aim of dealing with shapes closer to those of the actual cross section of a submarine. With respect to existing techniques for dealing with arbitrarily shaped pentamode cloaks, the introduced technique allows for a priori control on the principal directions of anisotropy and for enlarged design space in terms of possible combinations of material property distributions for the same geometry of the problem.

SPH simulations for shape deformation of rubble-pile asteroids through spinup: The challenge for making top-shaped asteroids Ryugu and Bennu

Asteroid 162173 Ryugu and asteroid 101955 Bennu, which were recently visited by spacecraft Hayabusa2 and OSIRIS-REx, respectively, are spinning top-shaped rubble piles. Other axisymmetric top-shaped near-Earth asteroids have been observed with ground-based radar, most of which rotate near breakup rotation periods of ∼3 h. This suggests that rotation-induced deformation of asteroids through rotational spinup produces top shapes. Although some previous simulations using the Discrete Element Method showed that spinup of rubble piles may produce oblate top shapes, it is still unclear what kinds of conditions such as friction angles of constituent materials and spinup timescales are required for top-shape formation. Here we show, through Smoothed Particle Hydrodynamics simulations of granular bodies spinning-up at different rates, that the rotation-induced deformation of spherical rubble piles before breakup can be classified into three modes according to the friction angle ϕd: quasi-static and internal deformation for ϕd≤40°, dynamical and internal deformation for 50°≤ϕd≤60°, and a set of surface landslides for ϕd≥70°. Note that these apparent large values of friction angle can be acceptable if we consider the effect of cohesion among blocks of a rubble pile under weak gravity. Bodies with ϕd≤60° evolve into oblate spheroids through internal deformation, but never form pronounced equators defining a top shape. In contrast, bodies with ϕd≥70° deform into axisymmetric top shapes through an axisymmetric set of surface landslides if spinup timescales are ≲ a few days. In addition, through slow spinups with timescales ≳1 month, bodies with ϕd≥70° deform into non-axisymmetric shapes via localized sets of landslides. We suggest that rapid spinup mechanisms are preferable for the formation of axisymmetric top shapes.

Generating biomembrane-like local curvature in polymersomes via dynamic polymer insertion

Biomembrane curvature formation has long been observed to be essential in the change of membrane morphology and intracellular processes. The significant importance of curvature formation has attracted scientists from different backgrounds to study it. Although magnificent progress has been achieved using liposome models, the instability of these models restrict further exploration. Here, we report a new approach to mimic biomembrane curvature formation using polymersomes as a model, and poly(N-isopropylacrylamide) to induce the local curvature based on its co-nonsolvency phenomenon. Curvatures form when poly(N-isopropylacrylamide) becomes hydrophobic and inserts into the membrane through solvent addition. The insertion area can be fine-tuned by adjusting the poly(N-isopropylacrylamide) concentration, accompanied by the formation of new polymersome-based non-axisymmetric shapes. Moreover, a systematic view of curvature formation is provided through investigation of the segregation, local distribution and dissociation of inserted poly(N-isopropylacrylamide). This strategy successfully mimicks biomembrane curvature formation in polymersomes and a detailed observation of the insertion can be beneficial for a further understanding of the curvature formation process. Furthermore, polymer insertion induced shape changing could open up new routes for the design of non-axisymmetric nanocarriers and nanomachines to enrich the boundless possibilities of nanotechnology.

2D finite-element modeling of 3D blade structures with axisymmetric and non-axisymmetric shapes

Prediction of the clearance between the components of a rotor and casing of a gas turbine is generally based on the two-dimensional (2D) finite-element analysis of the overall layout, the three-dimensional (3D) finite-element analysis of the local parts, and the deformation of the gas turbine components caused by other, unimportant 3D effects, such as cold-build clearances and ovalization. Using this, the variation of clearance, the minimum clearance, and the contact evaluation between the components with respect to the operation time are evaluated. Detailed 3D modeling of the overall shape for transient thermal-structural analysis for the prediction of clearances between components under the operating conditions of gas turbines with complex components, including both axisymmetric and non-axisymmetric shapes, is not economical in terms of computational time and cost. To address this problem, it is efficient to perform finite-element analysis by means of 2D modeling based on the crosssectional information of the gas turbine components. At this moment, the 2D finite-element modeling for the axisymmetric and non-axisymmetric structures of the gas turbine is important for predicting the correct and accurate deformation. In this paper, we show that 2D modeling can obtain results similar to those of 3D finite-element analysis for the original shape. The proposed 2D finite-element modeling method for rotor and support of a gas turbine that includes both axisymmetric and non-axisymmetric shapes will enable rapid and effective prediction of the components' behavior.

Geometrical nonlinearity of circular plates and membranes: An alternative method

We apply the well-established theoretical method developed for geometrical nonlinearities of micro-/nano-mechanical clamped beams to circular drums. The calculation is performed under the same hypotheses, the extra difficulty being to analytically describe the (coordinate-dependent) additional stress generated in the structure by the motion. Specifically, the model applies to non-axisymmetric mode shapes. An analytic expression is produced for the Duffing (hardening) nonlinear coefficient, which requires only the knowledge of the mode shape functions to be evaluated. This formulation is simple to handle and does not rely on complex numerical methods. Moreover, no hypotheses are made on the drive scheme and the nature of the in-plane stress: it is not required to be of an electrostatic origin. We confront our predictions with both typical experimental devices and relevant theoretical results from the literature. Generalization of the presented method to Duffing-type mode-coupling should be a straightforward extension of this work. We believe that the presented modeling will contribute to the development of nonlinear physics implemented in 2D micro-/nano-mechanical structures.

Nonaxisymmetric Shapes of Biological Membranes from Locally Induced Curvature

In various biological processes such as endocytosis and caveolae formation, the cell membrane is locally deformed into curved morphologies. Previous models to study membrane morphologies resulting from locally induced curvature often only consider the possibility of axisymmetric shapes—an indeed unphysical constraint. Past studies predict that the cell membrane buds at low resting tensions and stalls at a flat pit at high resting tensions. In this work, we lift the restriction to axisymmetry to study all possible membrane morphologies. Only if the resting tension of the membrane is low, we reproduce axisymmetric membrane morphologies. When the resting tension is moderate to high, we show that 1) axisymmetric membrane pits are unstable and 2) nonaxisymmetric ridge-shaped structures are energetically favorable. Furthermore, we find the interplay between intramembrane viscous flow and the rate of induced curvature affects the membrane’s ability to transition into nonaxisymmetric ridges and axisymmetric buds. In particular, we show that axisymmetric buds are favored when the induced curvature is rapidly increased, whereas nonaxisymmetric ridges are favored when the curvature is slowly increased. Our results hold relevant implications for biological processes such as endocytosis and physical phenomena like phase separation in lipid bilayers.

Bending models of lipid bilayer membranes: Spontaneous curvature and area-difference elasticity

We present a computational study of bending models for the curvature elasticity of lipid bilayer membranes that are relevant for simulations of vesicles and red blood cells. We compute bending energy and forces on triangulated meshes and evaluate and extend four well established schemes for their approximation: Kantor and Nelson (1987), Jülicher (1996), Gompper and Kroll (1996) and Meyer et al. (2003), termed A, B, C, D. We present a comparative study of these four schemes on the minimal bending model and propose extensions for schemes B, C and D. These extensions incorporate the reference state and non-local energy to account for the spontaneous curvature, bilayer coupling, and area-difference elasticity models. Our results indicate that the proposed extensions enhance the schemes to account for shape transformation including budding/vesiculation as well as for non-axisymmetric shapes. We find that the extended scheme B is superior to the rest in terms of accuracy, and robustness as well as simplicity of implementation. We demonstrate the capabilities of this scheme on several benchmark problems including the budding-vesiculating process and the reproduction of the phase diagram of vesicles.

Study on die-less spinning of cone–cylinder combined hollow parts

Die-less spinning can achieve the thin-walled parts with the regular shape of cone and cylinder or even some non-axisymmetric shapes. And it has advantages in forming some difficult demolding shapes. In this study, die-less spinning in a cone–cylinder combined hollow part and its forming mechanism were investigated. A ball-crown-shape roller was used to replace a conventional roller in the spinning process. The roller movement and spindle rotation were controlled by a computer numerical control spinning machine to achieve a planned roller path. The pass sets of tilted and horizontal lines were designed to form the cone and cylinder shape, respectively. Further, two methods were adopted to link the two forming pass sets and spin the cone–cylinder combined shape. One is to connect the cone and cylinder forming lines directly (Schemes A); the other is to connect the cone and cylinder forming lines by transition lines (Schemes B). The effects of two key parameters (roller path and feed ratio f) on the wrinkling and wall thickness distribution were analyzed. The product exhibited wrinkling on the wall using the roller path of Scheme A with f = 0.5 mm/r. f affected the occurrence of wrinkling considerably. Larger f made the flatness of the cylinder wall worse, no matter which roller path (in Scheme A or B) was used. When f was set to 0.25 mm/r (f was lower than LT1 in this study) with a blank thickness of 2.05 mm, wrinkling could be suppressed in the roller path of Scheme A. The product had an increasing thickness distribution on both the cone and the cylinder. The cylinder wall was even thicker than the disk blank with a blank thickness of 2.05 mm.

Problems of Hydrodynamics for a Triaxial Ellipsoid

Problems of motion of a triaxial ellipsoid in an ideal liquid and in a viscous liquid in the Stokes approximation and also equilibrium shapes of the rotating gravitating liquid mass are considered. Solutions of these problems expressed via four quadratures depending on four parameters are significantly simplified because they are expressed via the only function of two arguments. The efficiency of the proposed approach is demonstrated by means of analyzing the velocity and pressure fields in an ideal liquid, calculating the added mass of the ellipsoid, determining the viscous friction, and studying the equilibrium shapes and stability of the rotating gravitating capillary liquid. The pressure on the triaxial ellipsoid surface is expressed via the projection of the normal to the impinging flow velocity. The shape of an ellipsoid that ensures the minimum viscous drag at a constant volume is determined analytically. A simple equation in elementary functions is derived for determining the boundary of the domains of the secular stability of the Maclaurin ellipsoids. An approximate solution of the problem of equilibrium and stability of a rotating droplet is presented in elementary functions. A bifurcation point with non-axisymmetric equilibrium shapes branching from this point is found.

General Non-axisymmetric Shapes of Biological Membranes and their Importance in Understanding Endocytosis

Many important biological phenomena are mediated by cell membranes and the shapes accommodated by these membranes. For example, endocytosis involves bending to form a bud or a tube from a flat shaped membrane under the action of proteins such as clathrin or BAR and their coupling to actin pulling forces. Various morphological shapes of membranes are governed by thermodynamic parameters such as osmotic pressure drop across the membrane or membrane tension. Most theoretical studies focusing on understanding membrane bending involve either small deformations about a given configuration or axi-symmetric shape transitions. In this talk, using the recent advancements in theoretical and computational modeling of membranes, we show that axi-symmetric or small deformations are inadequate to understanding the morphological phase-diagrams of membranes governed by protein induced spontaneous curvature and membrane tension. In particular, we discuss how axi-symmetric analysis of membranes misguide our understanding and demonstrate that non-axisymmetric shape transitions are almost always energetically favorable to axi-symmetric ones. We apply these methods to understand the classical endocytosis phenomena in mammalian and yeast cells. With the newly found non-axisymmetric shapes, we discuss the physical principles governing endocytosis at varying levels of membrane tension.

Filament winding path generation based on the inverse process of stability analysis for non-axisymmetric mandrels

Obtaining reliable winding paths for non-axisymmetric shapes with current filament winding technologies is still a challenge. In this study, an algorithm was developed for generating geodesic and non-geodesic paths that are slippage- and bridging-free and can be applied to axisymmetric as well as non-axisymmetric mandrel models represented by triangular meshes. By performing a stability analysis on the winding path on a curved surface, the non-slipping and non-bridging conditions on a triangular mesh are deduced. Then, according to the inverse process of stability analysis, the next path point that satisfies the stability conditions is determined. In this method, the surface normal vector is calculated by a geodesic rather than via the weighted average method. Consequently, a stroke of the winding path is constructed by adding the next path point recursively. In addition, strategies for generating stable paths on a mandrel surface that includes concave regions are presented to avoid bridging.