Path Equation Research Articles

Nonlinear Path Following Method

This paper develops a new guidance logic for a vehicle to converge to a specified, desired path of general shape in three dimensions. Conditions are found that ensure exponential convergence to the path for any initial vehicle position and velocity vector, excluding only the velocity vector normal to the desired path. The guidance logic includes a ghost vehicle that follows the desired path. The command accelerations are derived from fictitious forces that act in a frame of reference that moves with the ghost. The forces comprise a springlike force between vehicle and ghost and a drag force created by a fictitious medium that moves with the ghost. The motion of the ghost is determined indirectly by a nonlinear constraint that controls the real vehicle speed and leads to a differential-algebraic system of equations. The path equations are formulated in terms of differential geometry, in which time is replaced by distance along the vehicle path. The geometric equations are transformed into standard form differential equations. These are transformed again into kinetic equations for both a fixed medium and a moving medium. The transformed equations provide more explicit formulas for command accelerations and are used to ensure that commands do not exceed the capabilities of the vehicle. Often, the vehicle limitation is more constraining than the convergence conditions. Simulations of a miniature aircraft, using these equations, illustrate the effectiveness of the method. Other methods are compared.

Optical path control of solitary waves in dye-doped nematic liquid crystals

The light-induced steering of spatial optical solitary waves in dye-doped nematic liquid crystals is analyzed. Shining a control beam through the cell results in a boundary mediated change in the orientation of the molecular director, thereby a perturbation in the refractive index of the medium. This re-orientational effect can optically steer spatial solitary waves propagating in an orthogonal plane within the liquid crystal layer. The equations governing this steering are solved using a Lagrangian formulation, resulting in modulation equations for the self-trapped beam path. Very good agreement is obtained between solutions of the modulation equations and numerical solutions of the full governing equations. Full Text: PDF

The stochastic dance of circling sperm cells: sperm chemotaxis in the plane

Biological systems such as single cells must function in the presence of fluctuations. It has been shown in a two-dimensional experimental setup that sea urchin sperm cells move toward a source of chemoattractant along planar trochoidal swimming paths, i.e. drifting circles. In these experiments, a pronounced variability of the swimming paths is observed. We present a theoretical description of sperm chemotaxis in two dimensions which takes fluctuations into account. We derive a coarse-grained theory of stochastic sperm swimming paths in a concentration field of chemoattractant. Fluctuations enter as multiplicative noise in the equations for the sperm swimming path. We discuss the stochastic properties of sperm swimming and predict a concentration-dependence of the effective diffusion constant of sperm swimming which could be tested in experiments.

Pathways to enhanced value creation from the international technology transfer process in Thai construction projects

PurposeInternational technology transfer (TT) initiatives are essential for developing the necessary infrastructure which underpins the sustainable development of economics and living standards in newly industrialised and developing countries. However, these initiatives have rarely translated into enhanced capabilities and competitiveness within host country firms, resulting in a sustained reliance on foreign firms. With few clues as to how to effectively manage the TT process, many stakeholders from the construction sectors of developing countries lack direction on how to more rapidly diffuse best‐practice technology. This paper aims to address the issues.Design/methodology/approachIn an attempt to better understand, the international TT process on Thai construction projects a path model was developed and later implemented. The path model development stage utilised the questionnaire survey response of 162 Thai construction and engineering professionals that had exposure to construction projects which incorporated international TT initiatives. A rigorous statistical analysis process which employed ANOVA, exploratory factor analysis, confirmatory factor analysis and structural equation modelling was followed to formulate the robust path model. The path model implementation stage utilised a series of case studies to validate the significant path equations in the developed model. This stage solicited questionnaire survey responses from 47 Thai construction and engineering professionals working for five domestic firms which were contractually involved with foreign partners on four large construction projects.FindingsThe findings provide evidence that transferors must have appropriate characteristics (i.e. willingness, knowledge base, experience, management, etc.) for establishing solid relationships with the transferee. Moreover, relationship building (RB) between the transferor and transferee (i.e. trust, understanding, communication, etc.) is the key enabler to TT induced value creation for the host construction sector.Originality/valueThe developed model empirically explains interactions between TT process enablers and outcome factors in the construction context. The model can assist government and private sector organisations from developing and newly industrialised countries to better evaluate the TT induced value creation process for the host construction sector. In this context, improved TT evaluation can help such organisations to devise targeted strategies for accelerating rates of TT, which will ultimately decrease their reliance on foreign firms when procuring large‐scale infrastructure projects.

Research on Asymmetric and Negative Offset Mechanism of Large-Scale Steel Plate Rolling Shear

According to revised Cailikefu’s rolling shear force formula, motion path equation of spatial seven-bar path is built, and mechanical model, with such new structural features as asymmetric and negative offset, is thus successfully established for 2800 mm heavy shear of some Iron&Steel Company. Shear force and bar force of steel plate, before and after adoption of asymmetric and negative offset structure, are analyzed, as well as horizontal force component of mechanism that influences pure rolling shear and back-wall push force that keeps blade clearance. The discovery is that back-wall push force could be kept large enough at rolling start-up (i.e. the time that the maximum rolling shear produces), meanwhile, back-wall push force is the most approximate to side forces with adoption of 60mm~100mm offset. Theoretical results and on-site shear quality both indicate that new structural features such as asymmetric and negative offset plays an important role in ensuring pure rolling shear and keeping blade clearance constant, which provide an effective means to improve quality of steel plate.

Effective process times for multi-server flowlines with finite buffers

An Effective Process Time (EPT) approach is proposed for the building of aggregate models to represent multi-server tandem queues with finite buffers. EPT distributions of the workstations in the flow line are measured without identifying the contributing factors. A sample path equation is used to compute the EPT realizations from arrival and departure events of lots at the respective workstations. If the amount of blocking in the line is high, the goodness of fits of the EPT distribution determines the accuracy of the EPT-based aggregate model. Otherwise, an aggregate model based on just the first two moments of the EPT distributions is sufficient to obtain accurate predictions. The approach is illustrated in an industrial case study using both simulation and analytical queueing approximations as aggregate models.

Principle of Asymmetric Crank Mechanism of New-type Rolling Shear

Based on rolling-cut simulation,a 3 000 mm single-shaft,double-eccentricity and cut-to-length rolling shear of a certain large-scale iron steel company that adopts asymmetric new-type structure is used as the calculation model by establishing motion path equation of spatial shear mechanism.After comparing and analyzing the shear force on steel plates with asymmetric front and rear,connecting rod force,and horizontal force component of connecting rod,the asymmetric formula is deduced.The asymmetric crank structure can decrease the horizontal force component of connecting rod during rolling-cut process,increase the effective drive force of connecting rod at the period of the maximum shear force,and decrease the extrusion of blade arc on steel plate edge as well. Theoretical analysis results and on-spot steel plate shear quality show that the asymmetric structure is an important means to improve shear capability,decrease blade wear,prolong blade life and improve shear quality.

Performance measurement and lumped parameter modeling of single server flow lines subject to blocking: An effective process time approach

The present paper extends the so-called effective process time (EPT) approach to single server flow lines with finite buffers and blocking. The power of the EPT-approach is that it quantifies variability in workstation process times without the need to identify each of the contributing disturbances, and that it directly provides an algorithm for the actual computation of EPTs. It is shown that EPT-realizations can be simply obtained from arrival and departure times of lots, by using sample path equations. The measured EPTs can be used for bottleneck analysis and for lumped parameter modeling. Simulation experiments show that for lumped parameter modeling of flow lines with finite buffers, in addition to the mean and variance, offset is also a relevant parameter of the process time distribution. A case from the automotive industry illustrates the approach.

A base function for generating contour traversal paths in stereolithography apparatus applications

The technique of layered manufacturing in rapid prototyping is to fabricate product prototype by scanning the cross-sectional contours of the product using a laser beam layer by layer. The outlines of geometrical objects on each layer are different, and each layer may contain several geometrical objects. In order to simplify the problem, each geometrical object on the same plane is approximating by its own minimum circumscribed circle. Therefore, the minimum traversal path of circles can be the based model of the minimum traversal path of scanning geometrical objects. Furthermore, the minimum traversal path of three circles is the degenerated case of the minimum traversal path of plural circles. And the problem of the minimum traversal path of three circles can be transferred to the problem of the minimum traversal path of one circle and two points in this paper. By using the concepts of reflection of light in physics and geometrical mathematics, the equation of the minimum traversal path of three circles is derived in this paper. This equation can be easily implemented in many areas of application, including robotic motion planning and path planning for submarine, ship, and airplane.

Analysis of transformations nucleated on non-random sites simulated by cellular automata in three dimensions

Cellular automata simulation in three dimensions is carried out to simulate microstrutural evolution for nuclei distribution ranging from a periodic arrangement to clusters of nuclei. The effect of clustering in three dimensions is found to be much more difficult to detect using conventional microstructural path analysis than in two dimensions. Microstructural path equations fit simulated data well, even when the nuclei are non-randomly located. However, the parameters obtained by means of this fitting lead to erroneous time dependent velocities. Therefore, measuring a descriptor that is sensitive to non-randomness such as the contiguity is even more important in three than in two dimensions.

Mechanical and oxygen barrier properties of organoclay‐polyethylene nanocomposite films

AbstractAn organically modified montmorillonite was compounded with ethylene vinyl acetate copolymer (EVA), low density polyethylene (LDPE), and high density polyethylene (HDPE) in a twin‐screw extruder. The resulting organoclay‐polyethylene nanocomposites were then blown into films. Tensile properties and oxygen permeability of these nanocomposite films were investigated to understand the effects of organoclay on different types of polyethylene. It was found that the clay enhancing effects are function of the matrix. The mechanical and oxygen barrier properties of clay/EVA systems increased with clay loading. Both the tensile modulus and oxygen barrier of EVA doubled at 5 wt% clay. Maleic anhydride grafted polyethylene (MAPE) usually is used as a compatibilizer for LDPE and HDPE‐based nanocomposites. However, the MAPEs were found to weaken the oxygen barrier of the PEs, especially for HDPE. This is believed to be a result of less compactness caused by the large side groups and the increase in polarity of the MAPEs. Incorporating 5 wt% clay improves the oxygen barrier by 30% and the tensile modulus by 37% for the LDPE/MAPE system. Incorporation of clay does not enhance the properties of the HDPE‐based systems, likely due to large domain structure and poor bonding. Halpin–Tsai equation and the tortuous path equation were used to model the tensile modulus and oxygen permeability of the clay/EVA nanocomposite films. POLYM. ENG. SCI., 47:1101–1107, 2007. © 2007 Society of Plastics Engineers

Mechanical Properties of New Type Negative Offset Structure During Shearing Process of Heavy Steel Plate

Abstract According to the revised Cailikefu's rolling shear force formula, motion path equation of spatial seven-bar path was built, and a mechanical model, with the new structural feature of negative offset, was thus successfully established for 2 800 mm heavy shear of some iron and steel company. Shear and bar forces of steel plate, before and after the adoption of negative offset structure, were analyzed, as well as horizontal force component of mechanism that influences pure rolling shear and back-wall push force that keeps blade clearance. It was found that the back-wall push force keeps large even at the time that the maximum rolling shear was obtained; meanwhile, back-wall push force is the most approximate to side forces when 60 – 100 mm of offset was adopted. Both theoretical results and on-site shear quality show that the negative offset plays an important role in ensuring the stability of pure rolling shear and keeping blade clearance constant.

Study of thermal effects, considering birefringence, on phase distortion of beam in a side pumped Nd:YAG rod using BEM

The present study uses boundary element method (BEM) in linear approximation to solve heat transfer equation. Differential equations of displacement are numerically solved through BEM to obtain strain tensor in an Nd:YAG crystal diode transversely pumped in a three fold geometry. Variation of refractive index, due to the temperature distribution and induced birefringence, which arises from photo-elastic effect, is obtained in the volume of the rod. Then the phase shift imposed on emerging beam from the rod is calculated by solving the equation of path of ray along the laser rod. Using the obtained results, effective focal distance and astigmatism of the beam for different types of polarization are calculated.

The Vector Function for Distance Travelled in Great Circle Navigation

Traditionally, on a great circle, the latitude or longitude of a waypoint is found by inspection. In this paper, using an elementary knowledge of vector algebra including linear combination of vectors and vector basis, we provide an easy method for finding the equation of a great circle path as a parameterized curve. By use of this vector function of distance travelled, the latitude and longitude of waypoints can be found based on the distance from departure point along a great circle. The approach is intended to appeal to the navigator who is interested in the mathematics of navigation and who, nowadays, solves his navigation problems with a personal computer.

IT enhanced project information management in construction: Pathways to improved performance and strategic competitiveness

Continuous process improvement via the strategic implementation of innovative information and communication technologies is essential for the long-term survival of construction firms. Some have successfully grasped the opportunities enabled by IT enhanced information management systems to develop new low-cost business models. However, not all proactive construction businesses have been satisfied with their IT investments, largely due to their limited ability to evaluate the degree of IT-induced valued added to operational and business performance. This article builds upon recently published work by the author, by empirically investigating the link between ‘Construct IT’ Balanced Scorecard (BSC) perspectives, utilizing structural equation modeling. Moreover, the validity of developed path equations for predicting IT-induced business performance and strategic competitiveness is reinforced through benchmarking studies, conducted on two large infrastructure projects constructed in Australia, where innovative web-based collaboration platforms were implemented.

Targeting Techniques for Enhancing Process Yield

A hierarchical procedure is developed to identify maximum targets for the overall yield of the process. First, we identify the key causes for loss in overall process yield. Then, several mass integration strategies are proposed to attain maximum yield. These include rerouting of raw materials, optimization of reaction yield, rerouting of product from undesirable outlets to desirable outlets, and recycle of unreacted raw materials. Path equations are tailored to provide the appropriate level of details for modelling the process performance as a function of the optimization variables pertaining to design and operating variables. Interval analysis is used as an inclusion technique that provides rigorous bounds regardless of the process nonlinearities. The proposed procedure is systematic, rigorous, and computationally efficient. A case study is used to illustrate the applicability of the proposed procedure.

Book Review: Latent Variable Models: An Introduction to Factor, Path, and Structural Equation Analysis (4th ed.)

Book Review: Latent Variable Models: An Introduction to Factor, Path, and Structural Equation Analysis (4th ed.)

A comparison of the radar ray path equations and approximations for use in radar data assimilation

The radar ray path equations are used to determine the physical location of each radar measurement. These equations are necessary for mapping radar data to computational grids for diagnosis, display and numerical weather prediction (NWP). They are also used to determine the forward operators for assimilation of radar data into forecast models. In this paper, a stepwise ray tracing method is developed. The influence of the atmospheric refractive index on the ray path equations at dierent locations related to an intense cold front is examined against the ray path derived from the new tracing method. It is shown that the radar ray path is not very sensitive to sharp vertical gradients of refractive index caused by the strong temperature inversion and large moisture gradient in this case. In the paper, the errors caused by using the simplified straight ray path equations are also examined. It is found that there will be significant errors in the physical location of radar measurements if the earth’s curvature is not considered, especially at lower elevation angles. A reduced form of the equation for beam height calculation is derived using Taylor series expansion. It is computationally more ecient and also avoids the need to use double precision variables to mitigate the small dierence between two large terms in the original form. The accuracy of this reduced form is found to be sucient for modeling use.

Planetary and light motions from Newtonian theory: an amusing exercise

We attempt to see how closely we can formally obtain the planetary and light path equations of general relativity by employing certain operations on the familiar Newtonian equation. This paper is intended neither as an alternative to nor as a tool for grasping Einstein's general relativity. Though the exercise can be understood by readers at large, it is especially recommended to teachers of relativity for an appreciative understanding of its peculiarity as well as its pedagogical value in the teaching of differential equations.

A NEW CLASS OF PATH EQUATIONS IN AP-GEOMETRY

In the present work, it is shown that the application of the Bazanski approach to Lagrangians, written in AP-geometry and including the basic vector of the space, gives rise to a new class of path equations. The general equation representing this class contains four extra terms, when vanished reduces this equation to the geodesic one. If the basic vector of the AP-geometry is considered as playing the role of the electromagnetic potential, as done in a previous work, then the second term (of the extra terms) will represent Lorentz force while the fourth term gives a direct effect of the electromagnetic potential on the motion of the charged particle. This last term may give rise to an effect similar to the Aharanov–Bohm effect. It is to be considered that all extra terms will vanish if the spacetime used is torsion-less.