Euler-Lagrange Theory Research Articles

Experimental and theoretical evaluation of tubing cutting with rotating particle jet in oil and gas borehole operation

The rotating particle jet cutting technology is an efficient way to deal with downhole stuck tubing efficiently in oil and gas borehole operation. To make full use of the rotating particle jet energy, a thorough understanding of the cutting process is needed. In this work, the Euler-Lagrange theory was utilized to establish the Computational Fluid Dynamics (CFD) model of tubing cutting with a rotary particle jet. A field-scale testing apparatus was developed to investigate the cutting effect achieved by rotating particle jet impact. The flow field characteristics of tubing cutting with a rotary particle jet were studied. The effects of operating parameters on the cutting efficiency were analyzed and the key cutting parameters were optimized. Validation of the theoretical model was carried out. The results show that the highest pressure is achieved when the rotating particle jet impacts the tubing wall. The average erosion rate increases with increasing standoff distance when the standoff distance is less than 7 mm. When the particle concentration is greater than 6%, the average erosion rate of tubing begins to increase slowly. The recommended particle diameter is 0.6–0.8 mm. This work can provide a theoretical foundation for field application of the rotating particle jet cutting technology.

Is the system reliability profitable for retailing and consumer service of a dynamical system under cross-price elasticity of demand?

Retailing strategy is one of the most crucial factors for industries. A proper retailing strategy can help to enhance consumer service and increase the industry's profit. An improved approach to retailing is suggested in this research to deliver superior customer service while maximizing profits in a dynamic system. The study analyzes a retailing strategy for a demand with cross-price elasticity upon the retail price. A product's cross-price elasticity and the system reliability are critical factors in retailing. Understanding the cross-price elasticity of demand between products helps retailers to make pricing decisions that maximize profits by maintaining demand. Imperfect products are produced due to an imperfect production system. The imperfect ones must be adjusted with some costs to make them perfect for better retailing. The system failure rate is crucial for retailing under cross-price elasticity of demand patterns. Production system reliability, cross-price elasticity of demand, and consumer service are all essential factors that can impact a company's success in the market. The production rate is considered time- and system failure rate-dependent. Contradictory to the literature, a dynamical system is proposed for improved retail management, which is solved using the Euler-Lagrange theory. Finally, one can achieve the expected maximum profit for this retail system with optimum selling prices for different products by reducing the system failure rate. Some numerical illustrations with graphical representations are provided to validate the current study. Numerical examples show that applying cross-price elasticity of demand for more than two identical products provides 35% more profit for the retail industry than a single type of product.

A rotating auxetic energy harvester for vehicle wheels

In this paper, a rotating auxetic vibration energy harvester (RAVEH) is proposed to provide a new solution for battery-free technology for intelligent tires. This RAVEH is self-adjusting at different vehicle speeds through centrifugal force generated by rotational motion. A dynamic model for RAVEH is established based on Euler-Lagrange theory to predict the energy harvesting performances and experimentally verified. A comparison between the RAVEH and traditional rotating flat energy harvester is conducted and the effects of the geometric parameters are also discussed thoroughly. It is found that RAVEH can increase the peak voltage by 42.90%, the peak power by 139.14%, the bandwidth by 54.55%, and the power range by 80.95% compared with a flat energy harvester. The designed RAVEH is capable of powering the sensors corresponding to the intelligent tires and realizing the battery-free technology.

Numerical simulation and experimental study of the influence of coaxial powder feeding laser cladding process parameters on gas-powder flow

Laser cladding is an advanced manufacturing technology for preparing high-performance metallurgical coatings on metal substrates that is widely used in industrial production. In order to improve the powder utilization rate and reduce the waste of powder in the coaxial powder feeding laser cladding process, the Euler–Lagrange theory was used to establish the simulation model of gas-powder two-phase flow in laser cladding. Fluent was used to simulate the powder particle size, powder particle shape factor, carrier gas flow rate, and powder feed rate under different process conditions, and the results were verified by experiments. Through analysis, under the process parameters of a carrier gas flow rate of 4 L / min and a powder feed rate of 15 g / min, the powder utilization rate was high and the surface of the cladding layer was smooth. When the particle size was 100 mesh and the particle shape factor approached 1.0, the concentration of powder focus was higher and the convergence effect was the best. The influence of powder process parameters on powder convergence was comprehensively analyzed, which is of great significance for the subsequent optimization design of nozzle and the improvement of powder utilization in the laser cladding process.

Учет трения в математических моделях диссипативных систем

Obtaining models of mechanical processes with dissipation based on the Euler-Lagrange theory has undoubted advantages over Newton's theory due to the smaller size of the considered vector of variables included in the equations. However, the Euler-Lagrange variation theory is not applicable to the description of the motion of systems with dissipation. The aim of the work is to demonstrate the possibility of using the Euler-Lagrange theory in relation to dissipative systems with different types of friction. Mathematical models of systems with dissipation are based on the superposition of mechanical and thermodynamic Lagrangians. To obtain a mathematical description of dissipative systems it is proposed to use the field theory as applied to the thermodynamics of dissipative processes within the framework of the Lagrange formalism. The Euler-Lagrange equations are obtained for the Stokes and Coulomb friction models. As it was referred to the research results obtained there is possibility of accounting the energy dissipation in the Lagrange formalism. The mathematical models proposed describe dynamic processes in heterogeneous structures with friction based on the Euler-Lagrange theory. There are presented mathematical transformations that allow transition from models based on the Lagrange formalism to models based on Newtonian mechanics

Numerical simulation and experimental investigation of the influence of process parameters on gas-powder flow in laser metal deposition

Uniform, stable and highly converged powder feeding is crucial to guarantee the compact structure, uniform composition and smooth surface of parts in laser metal deposition. Numerical gas-powder flow model for four-stream nozzle was established on the basis of Euler-Lagrange theory. Employing the gas-powder flow model, flow distributions for TC4 and 304L metal powder feeding were obtained respectively in FLUENT. The consistency of simulation and experimental results proved the validity and reliability of the model. Accordingly, influence of powder flow rate, particle properties (particle size, density, sphericity) and other processing parameters on powder flow concentration was studied through numerical simulations and experiments. It was found that metal powder could be transported efficiently with a powder flow rate ranging from 2.5–3.5 kg/h and a carrier gas flow rate of 6 L/min. With the optimized parameters, powder utilization could be improved while the focal length was increased. With the increase of particle size and its shape factor, the concentration of powder flow was increased and focal point was raised. Metal particle sizes of 120 mesh and 100 mesh were found to be suitable for powder utilization. Dispersion of powder flow was controlled more obviously when the shape factor of the particle approached 1.0. And besides, focal position moved up and focal length became shorter with the increase of particle density. Employing the optimized powder flow process parameter for 304L powder with particle size of 75–150 µm, single-track cladding experiment was performed. This study was significant for matching processing parameters with high deposition rate and for further study on nozzle optimization design in laser metal deposition.

Variable order and stepsize in general linear methods

This paper describes the implementation of a class of IRKS methods (Wright 2002). These GLM algorithms are practical with reliable error estimators (Butcher and Podhaisky, Appl. Numer. Math. 56, 345–357 2006). The current robust ODE solvers in variable stepsize as well as in variable-order mode are based upon heuristics. In this paper, we examine an optimisation approach, based on Euler-Lagrange theory (Butcher, IMA J. Numer. Anal. 6, 433–438 1986), (Butcher, Computing 44, 209–220 1990), to control the stepsize as well as the order and implement the GLMs in an efficient manner. A set of nonstiff to mildly stiff problems have been used to investigate this approach in fixed-order and variable-order modes.

Numerical simulation of the oil spilling diffusion in waterway engineering

Taking Guangli waterway engineering of Dongying Port as background, based on hydrodynamic and Euler-Lagrange theory, a numerical model of two-dimensional tidal current and oil spill diffusion is established and verified by measured data. According to different meteorological conditions, choose representative scenes, the drift range of oil film after oil spill accident and its influence on the surrounding water environment are predicted. Results show that: the range and track of oil film are closely related to the oil spilling time and wind direction. Under no wind condition, the oil sweep area is between 45 km2 and 65 km2 in 24h; Under strong wind direction of NW, the furthest distance to the southeast can be up to 23 km, and the oil sweep area is between 70 km2 and 135 km2 in 24h. Oil spills will have different effects on adjacent reserves. It is suggested that emergency response measures should be taken quickly in case of oil spills to minimize the adverse effects on the surrounding marine environment.

The Geometrical Nature of the Cosmological Inflation in the Framework of the Weyl-Dirac Conformal Gravity Theory

The nature of the scalar field responsible for the cosmological inflation, the \qo{inflaton}, is found to be rooted in the most fundamental concept of the Weyl's differential geometry: the parallel displacement of vectors in curved space-time. The Euler-Lagrange theory based on a scalar-tensor Weyl-Dirac Lagrangian leads straightforwardly to the Einstein equation admitting as a source the characteristic energy-momentum tensor of the inflaton field. Within the dynamics of the inflation, e.g. in the slow roll transition from a \qo{false} toward a \qo{true vacuum}, the inflaton's geometry implies a temperature driven symmetry change between a highly symmetrical \qo{Weylan} to a low symmetry \qo{Riemannian} scenario. Since the dynamics of the Weyl curvature scalar, constructed over differentials of the inflaton field, has been found to account for the quantum phenomenology at the microscopic scale, the present work suggests interesting connections between the \qo{micro} and the \qo{macro} aspects of our Universe.

On two conjectures that shaped the historiography of indeterminate analysis: Strachey and Chasles on Sanskrit sources

This paper is part of a research project on the historiography of mathematical proof in ancient traditions. Its purpose is to shed light on the various ways in which nineteenth-century European scholars attempted to make sense of Sanskrit mathematical sources dealing with indeterminate analysis. Attention will be paid to the historical processes by which these different strands interwove into a cumulative historiography of the field. The focus is on two interpretive conjectures that shaped alternative readings of an evolving corpus of texts, with significantly different emphases and viewpoints.The British scholar and East India Company servant Edward Strachey first identified a consistent algebraic theory in Bhāskara's Bīja-gaṇita, which he translated from a seventeenth-century Persian manuscript. While reading his sources through the lens of the Euler–Lagrange theory of periodic continued fraction expansions for quadratic irrationals, he offered an insightful interpretation of the so-called cakravāla, or “cyclic method”. Two decades later, in the context of his investigations on the historiography of geometry, the French geometer Michel Chasles delved into Henry Thomas Colebrooke's translations of Bhāskara and Brahmagupta, from the Sanskrit original, which had become authoritative all over Europe in the meantime. While working out an overall interpretation of Brahmagupta's theory of quadrilaterals, Chasles incidentally spotted a geometrical construction which opened the way to a geometrical solution of the indeterminate equation Cx2±A=y2. He conjectured that this geometrical way may have been the Sanskrit path to indeterminate analysis. Furthermore, on the basis of textual reconstruction, he supplemented his rigorous interpretive conjecture with a more sweeping historical assumption about a possible transmission of this geometrical approach to algebra, from Sanskrit to European mathematics, through the Arabs and Fibonacci. Owing to further scholarship by Baldassare Boncompagni, Franz Woepcke and others, the wheat would be sorted out from the chaff.

An imperfect production process for time varying demand with inflation and time value of money – An EMQ model

The paper deals with an economic manufacturing quantity (EMQ) model for time-dependent (quadratic) demand pattern. Every manufacturing sector wants to produce perfect quality items. But in long run process, there may arise different types of difficulties like labor problem, machinery capabilities problems, etc., due to that the machinery systems shift from in-control state to out-of-control state as a result the manufacturing systems produce imperfect quality items. The imperfect items are reworked at a cost to become the perfect one. The rework cost may be reduced by improvements in product reliability i.e., the production process depend on time and also the reliability parameter. We want to determine the optimal product reliability and production rate that achieves the biggest total integrated profit for an imperfect manufacturing process using Euler–Lagrange theory to build up the necessary and sufficient conditions for optimality of the dynamic variables. Finally, a numerical example is discussed to test the model which is illustrated graphically also.

Superposition of selfdual functionals in non-homogeneous boundary value problems and differential systems

Selfdual variational theory -- developed in [8] and [9] -- allows for the superposition of appropriate 'boundary' Lagrangians with 'interior' Lagrangians, leading to a variational formulation and resolution of problems with various linear and nonlinear boundary constraints that are not amenable to standard Euler-Lagrange theory. The superposition of several selfdual Lagrangians is also possible in many natural settings, leading to a variational resolution of certain differential systems. These results are applied to nonlinear transport equations with prescribed exit values, Lagrangian intersections of convex-concave Hamiltonian systems, initial-value problems of dissipative systems, as well as evolution equations with periodic and anti-periodic solutions.

Global Robust Control of an Aeroelastic System Using Output Feedback

A EROELASTIC systems exhibit a variety of phenomena including instability, limit cycle, and even chaotic vibration. Researchers in aerodynamics, structures, materials, and control have made interesting contributions to the analysis and control of aeroelastic systems [1]. Readers may refer to an excellent article by Mukhopadhyay [2] for the analysis and control of aeroelastic systems. A benchmark active control technology (BACT) windtunnel model has been designed at the NASA Langley Research Center and control algorithms for flutter suppression have been developed [3–5]. At Texas A&Ma 2-degrees-of-freedom aeroelastic model has been developed and tests have been performed in a wind tunnel to examine the effect of nonlinear structural stiffness, and control systems have been designed using linear control theory, feedback linearizing technique, and adaptive control strategies [6– 10]. Based on the Euler–Lagrange theory, control of an aeroelastic model has been considered [11]. The state variable and output feedback designs of [8–10] are based on adaptive control techniques. The synthesis of adaptive controllers is not simple because a large number of parameters must be updated in the dynamic feedback loop. It is also well known that unmodeled dynamics of the system can cause parameter divergence and instability in the closed-loop system. Therefore, it is interesting to design nonadaptive control systems for uncertain aeroelastic models which can be synthesized relatively easily. The contribution of this paper lies in the design of a robust control system for the global regulation of an aeroelastic system which describes the plunge and pitch motion of a wing. The model has polynomial type structural nonlinearity and only the pitch angle is measured for feedback. It is assumed that all the system parameters are unknown to the designer, but the bounds on uncertainties are known. For the purpose of design, afirst-order dynamic compensator is introduced and a “chained” structure of the aeroelastic model including the dynamic compensator is obtained by an appropriate coordinate transformation. Then using the Lyapunov stability theory, a control law for robust output regulation of the transformed system including the compensator is derived. In the closed-loop system, the controller accomplishes global robust stabilization of the aeroelastic system and system trajectories converge to the origin. Simulation results for various flow velocities and elastic axis locations are obtainedwhich show that the control system is effective in flutter suppression in spite of the large parameter uncertainties. An attractive feature of this control system lies in its simplicity from the point of view of implementation.

Third sound and stability of thinHe3−He4films

We study third sound in thin $^{3}\mathrm{He}\text{\ensuremath{-}}^{4}\mathrm{He}$ mixture films from first-principles, microscopic theory and compare these results to the usual film-averaged, hydrodynamic approach. The hydrodynamic approach yields third-sound speeds that depend only on the thickness of the superfluid film and the distribution of impurities---i.e., $^{3}\mathrm{He}$. In very thin films, this result clearly must be modified to account for the effects of nonuniform $^{4}\mathrm{He}$ film density. Utilizing the variational, hypernetted-chain--Euler-Lagrange theory as applied to inhomogeneous boson systems, we calculate accurate chemical potentials for both the $^{4}\mathrm{He}$ superfluid film and the physisorbed $^{3}\mathrm{He}$. Numerical density derivatives of the chemical potentials lead to the sought-after third-sound speeds that clearly reflect a layered structure of at least seven oscillations. We are thus able to gauge the range of applicability of the film-averaged hydrodynamic results as applied to thin quantum liquid films. We study third sound on two model substrates: Nuclepore and glass. We compute the change in third-sound speed as a function of $^{3}\mathrm{He}$ coverage in the linear (low-concentration) regime, which is then studied for the two substrates as a function of $^{4}\mathrm{He}$ film thickness and compared to existing experiments.$^{3}\mathrm{He}$ density profiles are calculated as a function of $^{4}\mathrm{He}$ film thickness, and we show explicitly the smooth transition from Andreev states in the thick-film limit to lateral mixtures in the submonolayer limit. This effect was first seen by Noiray et al. [Phys. Rev. Lett. 53, 2421 (1984)]. Our results predict that the addition of a small amount of $^{3}\mathrm{He}$ can increase, as well as decrease, the third-sound speed relative to that of the pure $^{4}\mathrm{He}$ film. Further, we show that the addition of a small amount of $^{3}\mathrm{He}$ can destabilize the film and drive a phase separation into lateral regions of $^{3}\mathrm{He}$-rich and $^{3}\mathrm{He}$-poor patches. This latter result may help explain the phase transitions reported by Bhattacharyya and Gasparini [Phys. Rev. Lett. 49, 919 (1982)] and Cs\'athy, Kim, and Chan [Phys. Rev. Lett. 88, 045301 (2002)] in thin mixture films.

The Euler–Lagrange theory for Schur's Algorithm: Algebraic exposed points

In this paper the ideas of Algebraic Number Theory are applied to the Theory of Orthogonal polynomials for algebraic measures. The transferring tool are Wall continued fractions. It is shown that any set of closed arcs on the circle supports a quadratic measure and that any algebraic measure is either a Szegö measure or a measure supported by a proper subset of the unit circle consisting of a finite number of closed arcs. Singular parts of algebraic measures are finite sums of point masses.

A theory of anti-selfdual Lagrangians: stationary case

We develop the concept of anti-self dual Lagrangians that seems inherent to many problems in mathematical physics, Riemannian geometry, and differential equations. On one hand, they represent gradients of convex functions which usually drive dissipative systems, and on the other, their structure is rich enough to also cover – certain representations of – skew-symmetric operators which normally generate unitary flows. These Lagrangians provide variational formulations and resolutions for several non-potential boundary value problems many of which do not fit in the Euler–Lagrange theory. Solutions are minima of functionals of the form L ( u , Λ u ) where L is an anti-self dual Lagrangian and where Λ is a skew-adjoint operator. However, and just like the self (antiself) dual equations of quantum field theory (e.g. Yang–Mills) the equations associated to minimal solutions of our variational problems are not derived from the fact they are critical points of the associated functionals, but because they are also zeroes of the corresponding Lagrangians. To cite this article: N. Ghoussoub, C. R. Acad. Sci. Paris, Ser. I 340 (2005).

A theory of anti-selfdual Lagrangians: dynamical case

We consider the class of time-dependent anti-selfdual Lagrangians, which – just like the stationary case announced in Ghoussoub [C. R. Acad. Sci. Paris, Ser. I 340 (2005)] – enjoys remarkable permanence properties and provides variational formulations and resolutions for several initial-value parabolic equations including gradient flows and other dissipative systems. Even though these evolutions do not fit in the standard Euler–Lagrange theory, we show that their solutions can be obtained as minima – but also as zeroes – of action functionals of the form ∫ 0 T L ( t , u ( t ) , u ˙ ( t ) + Λ t u ( t ) d t ) where L is a time-dependent anti-selfdual Lagrangian and where Λ t is a flow of skew-adjoint operators. To cite this article: N. Ghoussoub, C. R. Acad. Sci. Paris, Ser. I 340 (2005).

The global element method and its extension to parabolic problems

AbstractThis article describes the derivation of the global element method, originally proposed by Delves and Hall, using the classical Euler–Lagrange theory. The method is then extended so as to be applicable to parabolic partial differential equations. The main advantages of the method, the ease of adjusting its accuracy and applying it to problems with discontinuous coefficients and point singularities, are also discussed.

Elementary Characterization of Classical Minima

many introductory treatments and is consequently ignored). It is therefore surprising that several optima of classical interest usually treated through the calculus of variations can be characterized directly by analysis much more elementary than the Euler-Lagrange theory. We shall substantiate this assertion by using little more than the Cauchy-Schwarz vector inequality to provide direct access to the solutions of several well-known problems, including certain of those associated with the brachistochrone and the minimal surface. We begin with two almost trivial examples from the classical literature [2, pp. 178-180, 201], namely those of determining geodesics in space and on the surface of a sphere. To find the shortest space curve joining fixed points P0(= 0) and PI, we must minimize I jP'(t)ldt

Variational formulation of the geodetic boundary value problem

A variational principle for the Stokesian boundary value problem is derived using the Euler-Lagrange theory. The resulting variational principle is then transformed into an equation determining the semi-major axis of the best fitting ellipsoid which fulfills the condition U 0 =W 0 . The computations using three different geopotential models yields the semi-major axis of the earth ellipsoid as a=6378145.4 metres for the flattening f=1/298.2564. The corresponding equatorial gravity and the geopotential number are computed as γa=978029.59 mgals and U 0=W 0=6.26367371 106 kgalmeters respectively.