Rectilinear Path Research Articles

The Hampered [formula omitted]-Median Problem with Neighbourhoods

This paper deals with facility location problems in a continuous space with neighbours and barriers. Each one of these two elements, neighbours and barriers, makes the problems harder than their standard counterparts. Combining all together results in a new challenging problem that, as far as we know, has not been addressed before, but has applications for inspection and surveillance activities and the delivery industry assuming uniformly distributed demand in some regions. Specifically, we analyse the k-Median problem with neighbours and polygonal barriers in two different situations. None of these problems can be seen as a simple incremental contribution since in both cases the tools required to analyse and solve them go beyond any standard overlapping of techniques used in the separated problems. As a first building block, we deal with the problem assuming that the neighbourhoods are not visible from one another and therefore there are no rectilinear paths that join two of them without crossing barriers. Under this hypothesis, we derive a valid mixed-integer linear formulation. Removing that hypothesis leads to a more general and realistic problem, but at the price of making it more challenging. Adapting the elements of the first formulation, we also develop another valid mixed-integer bilinear formulation. Both formulations rely on tools borrowed from computational geometry that allow to handle polygonal barriers and neighbours that are second-order cone (SOC) representable, which we preprocess and strengthen with valid inequalities. These mathematical programming formulations are also instrumental to derive an adapted matheuristic algorithm that provides good quality solutions for both problems in short computing time. The paper also reports extensive computational experience, counting 2400 experiments, showing that our exact and heuristic approaches are useful: the exact approach can solve optimally instances with up to 50 neighbourhoods and different number of barriers within one hour of CPU time, whereas the matheuristic approach always returns good feasible solutions in less than 300 s.

Advancements in the Understanding of Single‐Bubble Dynamics: Integrated Experimental and Simulation Studies

Because of wake instability, bubbles always ascend along an unstable path, which is not considered when simulating their movement in steel refining and continuous casting systems. Utilizing the 3D shadow image method, a quantitative characterization of the bubble trajectories is conducted to establish a bubble path oscillation model considering the zigzag lateral movement of bubbles due to asymmetric wake shedding. This model is incorporated into a rectilinear bubble motion model within the Lagrangian framework and then used to simulate the free ascent of single bubbles within the 2.15–2.55 mm range. The predicted bubble ascent velocities and trajectories agree well with the experimental. The spatial position, velocity, acceleration, forces, volume swept by bubbles, and bubble residence time are discussed. The results shown that the dominant force in the horizontal direction is the lateral force, followed by the drag and virtual mass force. Compared to the rectilinear path model, the volume swept by bubbles with initial diameters of 2.15, 2.25, 2.34, 2.45, and 2.55 mm in this model increases by 30.8%, 32.0%, 34.0%, 31.5%, and 29.6%, respectively. These findings help accurately predict the path of bubbles and also may contribute to a better understanding of bubble dynamics in bubble metallurgy and clean steel production.

Flow-induced vibrations with and without structural restoring force: convergence under the effect of path curvature

When a cylinder is free to move along a transverse rectilinear path within a current, the vibrations developing with and without structural restoring force (SRF) noticeably deviate: if the elastic support is removed, their onset is delayed from a Reynolds number ( $Re$ , based on the body diameter and inflow velocity) value of approximately 20 to 30, and their peak amplitudes and frequency bandwidths are substantially reduced. The present study examines the influence of a curved path on this deviation by considering that the cylinder, mounted on an elastic support or not, is free to translate along a circular path whose radius is varied. The investigation is carried out numerically at $Re=25$ and $100$ , i.e. subcritical and postcritical values relative to the threshold of $47$ that marks the onset of flow unsteadiness for a fixed body. The principal result of this work is that the behaviours of the flow–structure systems with and without SRF tend to converge under the effect of path curvature. Beyond a certain curvature magnitude, both systems explore the same vibration ranges and the presence or absence of SRF becomes indiscernible. This convergence is accompanied by an enhancement of the responses appearing without SRF. It is analysed in light of the evolution of the effective added mass which determines the subset of responses reached with SRF that remain accessible without SRF. The apparent continuity of the physical mechanisms between the subcritical- and postcritical- $Re$ values suggests that the convergence phenomenon uncovered here could persist at higher $Re$ .

Wall effect on single bubble rising in a Hele–Shaw cell

Single air bubble rising near vertical wall in a Hele–Shaw cell was investigated experimentally. Bubbles with a large range of size from 4.46 mm to 21.68 mm were generated. A vertical wall was introduced in the cell, and the initial distance between the wall and the bubble releasing position was varied systematically to study the wall effect on the rising dynamics. Rising trajectory, bubble morphology, and rising characteristics were analyzed. Bubble will migrates away from the wall, and the trajectory transits from rectilinear path to zigzag. Two mechanisms of zigzag were revealed as “rigid zigzag” for the small bubble and “contracting zigzag” for the large bubble. It is always easier to zigzag for a more rounded bubble, and migration is always stronger with a smaller normalized initial distance.

An evaluation of predictive correlations for the terminal rising velocity of a single bubble in quiescent clean liquid

Evaluation work was carried out on widely used correlations for predicting the terminal velocities of single bubbles rising in quiescent liquids against a database with 758 data points. The data were collected from the experiments of air bubbles rising in pure water with diameters covering 0.02–66.97 mm. The correlations are firstly categorized into three groups according to their application ranges: group 1 for spherical and ellipsoidal bubbles with rectilinear paths, group 2 for ellipsoidal bubbles with unstable paths and spherical-cap bubbles and group 3 for bubbles of all sizes. Evaluation results show that among group 1 correlations, the Moore (1965) correlation demonstrates the best MAE of 2.9% within its application range (Re ¿ 50). The Chen et al. correlation and Rastello et al. correlation, with the broadest application range in group 1, yield good overall MAEs of 7.0% and 5.0%, respectively. The Lehrer correlation gives the smallest MAE of 4.3% in group 2. In group 3, the Dijkhuizen et al. correlation and Baz-Rodríguez et al. correlation achieve the highest accuracy against all the experimental data, with global MAEs of 7.7% and 8.7%, respectively. Although present prediction methods have achieved good agreement with the experimental results, predicting the terminal velocity of ellipsoidal bubbles with unstable paths is the most intractable and lacks satisfactory methods, and it still remains challenging to develop a unified correlation.

Path curvature enhances the flow-induced vibrations of a cylinder without structural restoring force

A cylinder immersed in a current and free to translate along a circular arc is considered to investigate the impact of path curvature on the flow-induced vibrations (FIV) occurring without structural restoring force. Path curvature magnitude ( $\kappa$ , inverse of path radius non-dimensionalized by the body diameter $D$ ) is varied from $0$ (transverse rectilinear path) to $20$ , over a wide range of values of the structure to displaced fluid mass ratio, $m^\star \in [0.05,10]$ . The exploration is carried out numerically at subcritical and postcritical values of the Reynolds number ( $Re$ , based on $D$ and the inflow velocity), i.e. below and above the critical value $47$ for the onset of flow unsteadiness when the body is fixed, up to $100$ . Path curvature triggers a desynchronized regime of the flow–body system in addition to the synchronized regime typical of vortex-induced vibrations, and alters the composition of fluid forcing. The most prominent effect uncovered here is, however, a global enhancement of FIV, with three principal results: (i) vibrations and flow unsteadiness are found to arise at lower subcritical $Re$ along a curved path, down to $19.5$ versus $31$ for $\kappa =0$ ; (ii) the $m^\star$ range where substantial responses develop is considerably extended and encompasses the entire interval under study, which contrasts with the narrow band of low $m^\star$ identified for $\kappa =0$ ; (iii) the vibrations are amplified, $+45\,\%$ relative to the peak amplitude measured along a rectilinear path at $Re =100$ .

Concepts for estimating all types of diffusion coefficients of NiCoFeCr multi-principal element alloys using two dissimilar or a combination of ideal and non-ideal pseudo-ternary diffusion couples

The estimation of diffusion coefficients in multicomponent system is facilitated by strategically designing diffusion couples with constrained diffusion paths. We have demonstrated methods of estimating tracer diffusion coefficients following three different combinations of diffusion profiles: (i) By intersecting a pseudo-ternary diffusion path with a rectilinear pseudo-binary diffusion path, (ii) by considering a combination of two dissimilar pseudo-ternary diffusion paths, and (iii) considering a combination of ideal and non-ideal pseudo-ternary diffusion paths with uphill diffusion characteristics. Equation schemes required for such analyses depending on the type of diffusion profiles are explained in detail. This approach relies on the availability of reliable thermodynamic data for the estimation of the tracer diffusion coefficients. Following, as demonstrated, one can calculate the intrinsic and interdiffusion coefficients of all the elements for a conventional diffusion couple in which all the elements would produce the diffusion profiles.

Adaptive closed-loop maneuver planning for low-thrust spacecraft using reinforcement learning

Autonomy is an increasingly essential component of future space missions, and new technologies are necessary to accommodate off-nominal occurrences onboard that may pose risks to mission success. Identifying a suitable maneuver plan for onboard, low-thrust mission applications in cislunar space remains challenging, particularly in the case of unanticipated events. This investigation addresses this challenge by demonstrating artificial neural networks as promising tools for accurately estimating startup solutions for a conventional targeting-based iterative guidance and control algorithm. This blended approach produces a robust ‘hybrid’ architecture that simultaneously benefits from the computational simplicity of neural networks and the robustness of differential corrections to satisfy mission requirements. In this paradigm, a multiple shooting scheme is incorporated directly into a reinforcement learning process, tasking the resulting neural network controller with convergence basin identification for trajectory recovery. Rapid low-thrust maneuver planning is demonstrated in a ‘runaway’ spacecraft scenario, where deviation over time from a planned near rectilinear halo orbit path renders stationkeeping ineffective and demands an alternative approach to determine an effective recovery plan. The proposed Neural Network-Initialized Targeting (NNIT) algorithm significantly extends the recovery window compared to a crossing-control orbit maintenance approach and exhibits promising results in identifying both the timing and control components for low-thrust maneuver plans.

Flow-induced vibrations of a cylinder along a circular arc

An elastically mounted circular cylinder, immersed in a cross-current and free to move along a rectilinear path, is subjected to vortex-induced vibrations (VIV). These vibrations develop through a mechanism referred to as lock-in, where body motion and vortex shedding synchronize at a frequency that may deviate both from the oscillator natural frequency and from the vortex shedding frequency past a fixed cylinder. The present numerical study aims at extending the analysis to curved trajectories, by considering that the cylinder is free to translate along a circular path. The Reynolds number based on the body diameter ( $D$ ) and current velocity ( $U$ ) is set to $100$ . A wide range of path radii, from $0.05D$ to $10D$ , and values of the reduced velocity (inverse of the oscillator natural frequency non-dimensionalized by $D$ and $U$ ) up to $30$ are examined, for the concave and convex configurations, i.e. the circular path centre located upstream or downstream of the cylinder. Path curvature results in a major alteration of the flow–body system behaviour compared with rectilinear VIV, with substantially different evolutions in the concave and convex configurations. In addition to the typical lock-in mechanism, two subharmonic forms of synchronization, at half and one third of vortex formation frequency, are uncovered in the convex configuration. They coexist with a desynchronized regime where the body and the flow oscillate at incommensurable frequencies. The four interaction regimes exhibit contrasted trends in terms of structural response, spatiotemporal organization of the wake and associated forces. They particularly differ by their symmetry properties, which are closely linked to the possible reconfiguration of the oscillator due to mean fluid forcing.

Estimation of diffusion coefficients by intersecting different types of diffusion paths in a multi-principal element alloy

A unique method for estimating all types of diffusion coefficients in a multicomponent system is proposed by intersecting only two but different types of diffusion paths. This concept circumvents the limitations of the recently proposed diffusion couple methods, such as pseudo-binary, pseudo-ternary, and the body diagonal method, when practiced individually. Here the diffusion coefficients of all the elements can be estimated as compared to the estimation of diffusivities associated with only two or three elements which develop the diffusion profiles following the pseudo-binary and pseudo-ternary methods, respectively. This also reduces the laborious effort required to bring all the serpentine body diagonal diffusion paths close to each other to estimate the diffusivities with an unknown uncertainty when they do not intersect exactly. On the other hand, as proposed in this study, a serpentine conventional (or body diagonal) diffusion path can be intersected by a rectilinear pseudo-binary diffusion path with relative ease at a specific composition. The modification of the equation schemes for the application of different types of diffusion paths in the estimation of tracer, intrinsic, and interdiffusion coefficients is explained in detail. This method is demonstrated in a model NiCoFeCr multi-principal element system at a composition very close to the equiatomic composition. The influence of the vacancy wind effect on intrinsic and interdiffusion coefficients is described in detail.

Motor vehicles’ problems with keeping the straight driving direction; analysis of selected case

The article presents issues related to the testing and verification of the keeping of straight driving direction by motor vehicles. The subjective feelings of drivers were assigned specific values of physical quantities describing the rectilinear path of motion, i.e. the steering wheel angle and the force vector applied to the steering wheel of the vehicle under test while driven along a straight path. This made it possible to determine the limit values enabling the assessment whether the object under test has a tendency to move straight ahead without any unusual steering corrections. The cases analysed relate to the situations where measurements of wheel geometry settings do not show significant deviations from the standard but, in spite of that, the vehicle requires unusual steering corrections by the driver to maintain a straight path.

Joint formation mechanism of different laser transmission welding paths

Abstract In this study, the rectilinear, sine, and spiral paths of polymer transmission welding were used to perform welding comparative experiments, and the influence of various parameters in the polymer transmission welding of different laser paths on the joint performance and the formation of molten pool was discussed. The spiral path exhibited the highest joint strength, that increased by more than 50% compared with conventional rectilinear welding. The molten pool formed by spiral welding had a high depth-to-width ratio. Microscope observations revealed that the glass fiber flow signs in the molten pool were obvious, the glass fiber in the molten pool was abundant, and the bubble generation rate in the molten pool was lower. In this paper, Fortran language was used to construct Gaussian body heat source movement model with different paths. Results show that the spiral welding had higher welding stability than traditional rectilinear welding, welding defects caused by the lack of heat in the previous period can be properly compensated by selecting the appropriate welding period, Therefore, good joint performance can be achieved. In addition, amplitude and period are two important process parameters of spiral welding, and their sizes have important effects on joint strength and molten pool formation

Analysis of the Refraction Effect in Ultrasound Breast Tomography

Ultrasound breast tomography (UBT) is a promising quantitative imaging method. It allows for precise analysis of ultrasound velocity distribution, which is related to tissue density and elasticity, enabling cancer detection. Only a few centers around the world have a prototype of the device for in vivo breast ultrasound tomography imaging. The quality of images reconstructed from measurements of ultrasound pulse transit times is adversely affected by the refraction of beam rays on the breast immersed in water. Refraction can be reduced using waveform tomography, ray-tracing, and ray-linking methods. However, this requires the acquisition of a pre-reconstructed pattern and is limited by extreme computational costs. In this study, the effect of refraction on transit time measurements of ultrasound passing through the female breast was analyzed under immersion conditions in water. It was found that the refraction causes the highest measurement errors in the area of the water/breast interface, and these can be reduced by adjusting the water temperature and changing the breast geometry. The results allow us to improve the quality of breast images reconstructed using an efficient transformation algorithm that assumes rectilinear ultrasound propagation paths between transmitters and receivers. In vivo breast studies were performed on the developed hybrid UBT scanner.

Building structure with elastoplastic bilinear model under multi-dimensional earthquake forces

Abstract Developed herein is an analysis procedure based on closed-form solutions to elastoplastic bilinear model of building structures accounted for different stiffnesses and yielding forces in different directions and rotated yield ellipses in different floor levels due to the layout of buildings and the complexity of structural members. The seismic design often considers earthquake forces on multiple floor levels but usually only in a single direction. However, in reality, the direction of the earthquake is not limited to one particular direction. Therefore, studying the influence of a two-way, furthermore multi-dimensional, earthquake on buildings is of great value. To estimate the total seismic demand on inelastic building structures subjected to multi-dimensional loading, this paper aims to find closed-form solution responses to an input rectilinear force path for the elastoplastic bilinear model of Hong and Liu (1999) which already has available closed-form solution responses to an input rectilinear displacement path. In this paper the elastoplastic bilinear model of building structures and Minkowski spacetime are adapted to accommodate such situations as different stiffnesses and yielding forces in different directions and rotated yield ellipses in different floor levels.

Minimum-link shortest paths for polygons amidst rectilinear obstacles

We compute shortest paths connecting two axis-aligned rectilinear simple polygons in the domain consisting of axis-aligned rectilinear obstacles in the plane. The bounding boxes, one defined for each polygon and one defined for each obstacle, are disjoint. We present an algorithm that computes a minimum-link rectilinear shortest path connecting the two polygons and avoiding the obstacles in O(nlog⁡n) time using O(n) space, where n is the total number of vertices of two polygons and obstacles in the domain.

Characteristics and Flow Dynamics of Bubble-in-Chain Rising in a Quiescent Fluid

In the present study, we experimentally investigated the freely rising of bubble-in-chain and the evolution of bubble-induced flow for a quiescent fluid. Quantitative data on bubble morphology, kinematics, and bubble-induced flow dynamics were obtained by combining the methods of shadowgraphy and laser-induced-fluorescence particle image velocimetry (PIV/LIF). Under the current experimental condition, after detached from the orifice, the rising of the bubble can be divided into three stages: rectilinear rising, transition regime and zigzagging. In the rectilinear rising stage (0 < y/Dn < 12), the bubble-induced flow is dominated by a pair of counter-rotating vortices, which rise together with the bubble moving, i.e., the standing eddies. Each bubble experiences an acceleration along the orifice centerline, and gradually becomes flattened with its aspect ratio increasing. At y/Dn ≈ 12, the bubble aspect ratio reaches the maximum (χ ≈ 4) and the induced wake vortices are significantly strengthened. Coupled with the destabilizing effect of disturbance from previous leading bubbles, the wake flow becomes unstable leading to the onset of wake vortex shedding that triggers the bubble path instability. As a result, the bubble deviates from the rectilinear path and goes into the transition regime. As rising to y/Dn ≈ 30, the bubble is strongly affected by the wake from previous bubbles since the vorticity has not been accumulated to trigger the next vortex shedding. Thus, the bubble enters in the zigzagging stage with its trajectory exhibiting significant differences among different bubbles. In particular, the bubble-induced flow in the zigzagging stage has the strong entrainment ability, which might be helpful for applications using bubbles for enhancing the mixing and transport of liquids.

Improving the navigational preparation of a bridge crew for entering/leaving a port, including activities in case of emergency

Statistical analysis of the causes of ship accidents showed that 10 % of accidents are due to the influence of irresistible force, about 15 % are the result of technical imperfection and sudden failure of ship equipment, and the remaining 75 % account for the «human factor» regardless of the cause of the accident. A detailed analysis of the causes of accidents reveals that they are caused by the actions of individuals, dominated by organizational errors by a group of operators in the preparation and execution of the maneuvering control process. At the same time, there is a gap between the complexity of modern equipment and the psychological capabilities of the human operator as an element of the human-machine system. Analysis of accidents in the Bugsky-Dnestrovsky Liman Canal over the past 20 years has shown that 58.5 % of accidents occurred in the dark and under conditions of limited visibility. There were two causes of accidents: grounding and allision, 84.3 %; collisions, 28.8 %. This indicates the insufficient preparation of bridge crews for navigating the canal. This paper has considered a procedure of bridge crew navigation training for planning safe motion coordinates while entering/leaving a port along the trajectory points, as well as actions in case of a pre-emergency and techniques to predict it. The coordinates of the travel points are determined at the intersection of rectilinear segments of the recommended safe rectilinear path on a chart. It is a relevant task to use new methods of planning the path and controlling the movement along it, taking into consideration the area for maneuvering, maneuverable properties of the vessel, as well as external influences, for timely detecting the deviation of parameters from those planned. The calculation of the planned coordinates is performed for the center of gravity of the vessel for the characteristic points of the path of movement (the beginning and end of a turn, the onset of braking) and trajectory points (rectilinear segments of the path through 0.2 cables, and curvilinear sections through 10 degrees). Coordinates of the assigned path are represented in the form of the linear matrices of the path rectilinear and curvilinear sections. The navigational motion control system consists of the devices to automatically determine deviations from planned coordinates and decision support systems to correct deviations detected. The proposed method to plan and control motion was investigated by computer simulation, the test was carried out under natural settings. Their results showed that the calculated optimal assigned trajectory enables accident-free guidance of the center of gravity along the predefined path by ship’s control means and meets the established criteria of optimality. The proposed method could be used in the development of controls for automated vessels and is the only possible one for vessels with unattended operation

Shortest rectilinear path queries to rectangles in a rectangular domain

Given a set of open axis-aligned disjoint rectangles, each of which plays as both an obstacle and a target, we seek to find shortest obstacle-avoiding rectilinear paths from a query to the nearest target and the farthest target. The distance to a target is determined by the point on the target achieving the minimum or maximum geodesic distance among all points on the boundary of the target. This problem arises in facility location and robot motion planning problems. We show how to construct data structures supporting such shortest path queries to the nearest and farthest neighbors efficiently.

Ferroelectric domain switching using passage of energetic charged particles

The passage of charged particles through ferroelectric medium produces localized changes in spontaneous polarization within the material. As the beam traverses the medium, it produces an electric field perpendicular to the direction of propagation of the beam. A theoretical approach is presented to estimate the electric field that is produced in the ferroelectric medium by passage of energetic electron beam and proton beam that can be probed to see the switching of ferroelectric domains. The transverse electric field produced by the 6 MeV electron beam is 183.6 MV/cm and for 25 MeV Proton beam is 14.79 MV/cm at a radial distance of 1 nm from the rectilinear path. This electric field so produced is large enough to cause the switching of ferroelectric domains. The method demonstrates a unique tool to probe the mechanism of ferroelectric domain switching along the large surface of the medium without any physical contact. This paper describes the method of theoretical estimation of transverse electric field and the ferroelectric domain switching time at and around phase transition of a known ferroelectric sample of Barium Titanate (BaTiO3) crystal.

Collision-free routing problem with restricted L-path

Given a set of vehicles that are allowed to move in a plane along a predefined directed rectilinear path, the collision-free routing problem seeks a maximum number of vehicles that can move without collision. This problem is known to be NP-hard (Ajaykumar et al., 2016). Here we study a variant of this problem called the constrained collision-free routing problem (in short, CCRP ). In this problem, each vehicle is allowed only to move in a directed L-shaped path. First, we show that CCRP is NP-hard. Further, we prove that any β -approximation algorithm for the maximum independent set problem in B 1 -VPG graphs would produce a β -approximation for CCRP . Also, we propose a 2-approximation algorithm for the maximum independent set problem on intersection graph of n unit-L frames (the union of a unit-length vertical and a unit-length horizontal line segment that shares an endpoint) with O ( n ) space and O ( n 2 ) time.