Academic literature on the topic 'Jacobi correction functions'

We discuss the thermodynamics of the noncommutative inspired Kerr black hole by means of a reformulated Hamilton–Jacobi method and a dimensional reduction technique. In order to investigate the effect of the angular momentum of the tunneling particle, we calculate the wave function to the first order of the WKB ansatz. Then, using a density matrix technique we derive the radiation spectrum from which the radiation temperature can be read out. Our results show that the radiation of this noncommutative inspired black hole corresponds to a modified temperature which involves the effect of noncommutativity. However, the angular momentum of the tunneling particle has no influence on the radiation temperature. Moreover, we analyze the entropy spectrum and verify that its quantization is modified neither by the noncommutativity of spacetime nor by the quantum correction of wave functions.

Luminosity functions of planetary nebulae contain information about the central star mass distributions, nebular, central star, and progenitor evolution, stellar death rates, and a galaxy's star formation and chemical evolution histories. Appropriate observing strategies can be used in combination with various models to extract some of the parameters of these functions. The principal results from these studies are that the central star mass distribution is narrow (σ ∼ 0.02–0.04M⊙), the number of PN in a galaxy depends on galaxy color, and the number of PN in the Galaxy is ∼ 104.The most extensive application of luminosity function studies has been exploiting the bright end cutoff as a distance indicator. Distances for 25 galaxies have been measured using the methodology outlined by Jacoby, Ciardullo, and collaborators. The PNLF method compares extremely well with other techniques, and is accurate to ∼ 5%. In fact, there is no evidence for systematic effects of any kind, although a small (5–10%) metallicity correction needs to be applied for metal-poor systems.

An interface-corrected diffuse interface method is presented in this work for the simulation of incompressible multiphase flows with large density ratios. In this method, an interface correction term together with a mass correction term is introduced into the diffuse-interface Cahn–Hilliard model to maintain both mass conservation and interface shapes between binary fluids simultaneously. The interface correction term is obtained by connecting the signed distance functions in the Hamilton–Jacobian equation with the order parameter of the Cahn–Hilliard model. In addition, an improved multiphase lattice Boltzmann flux solver is introduced, in which the fluxes are obtained by considering the contributions of the particle distribution functions before and after the streaming process through a local switch function. The proposed method is validated by simulating multiphase flows, such as the Laplace law, the evolution of a square bubble, the merging of two bubbles, Rayleigh–Taylor instability, and a droplet impacting on a film with a density ratio of 1000. Numerical results show that the presented method can not only reduce the interface diffusion but also has good control over the interface thickness and mass conservation. The improved numerical method has great potential for use in practical applications involving multiphase flows.

David Bohm had shown that the Schrödinger equation, that is a "visiting card" of quantum mechanics, can be decomposed onto two equations for real functions — action and probability density. The first equation is the Hamilton–Jacobi (HJ) equation, a "visiting card" of classical mechanics, is modified by the Bohmian quantum potential. This potential is a nonlinear function of the probability density. And the second is the continuity equation. The latter can be transformed to the entropy balance equation. The Bohmian quantum potential is transformed into two Bohmian quantum correctors. The first corrector modifies the kinetic energy term of the HJ equation, and the second one modifies the potential energy term. The unification of the quantum HJ equation and the entropy balance equation gives a complexified HJ equation containing complex kinetic and potential terms. The imaginary parts of these terms have an order of smallness about the Planck constant. The Bohmian quantum corrector is an indispensable term modifying the Feynman's path integral by expanding coordinates and momenta to an imaginary sector. The difference between the Bohmian and Feynman's trajectories is that the former satisfies the principle of least action and they bifurcate on interfaces. The latter covers all possible paths from a source to a detector. They can split and annihilate.

The "information revolution" of our time affects our entire generation. While a vision of the "Information Society," with its financial, legal, business, privacy, and other aspects has emerged in the past few years, the "traditional scene" of information technology, that is, industrial automation, maintained its significance as a field of unceasing development. Since the old-fashioned concept of "Hard Automation" applicable only to industrial processes of fixed, repetitive nature and manufacturing large batches of the same product1)was thrust to the background by keen market competition, the key element of this development remained the improvement of "Machine Intelligence". In spite of the fact that L. A. Zadeh already introduced the concept of "Machine Intelligence Quotient" in 1996 to measure machine intelligence2) , this term remained more or less of a mysterious meaning best explicable on the basis of practical needs. The weak point of hard automation is that the system configuration and operations are fixed and cannot be changed without incurring considerable cost and downtime. Mainly it can be used in applications that call for fast and accurate operation in large batch production. Whenever a variety of products must be manufactured in small batches and consequently the work-cells of a production line should be quickly reconfigured to accommodate a change in products, hard automation becomes inefficient and fails due to economic reasons. In these cases, new, more flexible way of automation, so-called "Soft Automation," are expedient and suitable. The most important "ingredient" of soft automation is its adaptive ability for efficiently coping with changing, unexpected or previously unknown conditions, and working with a high degree of uncertainty and imprecision since in practice increasing precision can be very costly. This adaptation must be realized without or within limited human interference: this is one essential component of machine intelligence. Another important factor is that engineering practice often must deal with complex systems of multiple variable and multiple parameter models almost always with strong nonlinear coupling. Conventional analysis-based approaches for describing and predicting the behavior of such systems in many cases are doomed to failure from the outset, even in the phase of the construction of a more or less appropriate mathematical model. These approaches normally are too categorical in the sense that in the name of "modeling accuracy," they try to describe all structural details of the real physical system to be modeled. This significantly increases the intricacy of the model and may result in huge computational burden without considerably improving precision. The best paradigm exemplifying this situation may be the classic perturbation theory: the less significant the achievable correction is, the more work must be invested for obtaining it. Another important component of machine intelligence is a kind of "structural uniformity" giving room and possibility to model arbitrary particular details a priori not specified and unknown. This idea is similar to that of the ready-to-wear industry, whose products can later be slightly modified in contrast to the custom-tailors' made-to-measure creations aiming at maximum accuracy from the beginning. Machines carry out these later corrections automatically. This "learning ability" is another key element of machine intelligence. To realize the above philosophy in a mathematically correct way, L. A. Zadeh separated Hard Computing from Soft Computing. This revelation immediately resulted in distinguishing between two essential complementary branches of machine intelligence: Hard Computing based Artificial Intelligence and Soft Computing based Computational Intelligence. In the last decades, it became generally known that fuzzy logic, artificial neural networks, and probabilistic reasoning based Soft Computing is a fruitful orientation in designing intelligent systems. Moreover, it became generally accepted that soft computing rather than hard computing should be viewed as the foundation of real machine intelligence via exploiting the tolerance for imprecision, uncertainty and partial truth to achieve tractability, robustness, low solution cost and better rapport with reality. Further research in the past decade confirmed the view that typical components of present soft computing such as fuzzy logic, neurocomputing, evolutionary computation and probabilistic reasoning are complementary and best results can be obtained by their combined application. These complementary branches of Machine Intelligence, Artificial Intelligence and Computational Intelligence, serve as the basis of Intelligent Engineering Systems. The huge number of scientific results published in journals and conference proceedings worldwide substantiates this statement. Three years ago, a new series of conferences in this direction was initiated and launched with the support of several organizations including the IEEE Industrial Electronics Society and IEEE Hungary Section in technical cooperation with IEEE Robotics & Automation Society. The first event of the series hosted by Bdnki Dondt Polytechnic, Budapest, Hungary, was called "19997 IEEE International Conference on Intelligent Engineering Systems " (INES'97). The Technical University of Vienna, Austria hosted the next event of the series in 1998, followed by INES'99 held by the Technical University of Kosice, Slovakia. The present special issue consists of the extended and revised version of the most interesting papers selected out of the presentations of this conference. The papers exemplify recent development trends of intelligent engineering systems. The first paper pertains to the wider class of neural network applications. It is an interesting report of applying a special Adaptive Resonance Theory network for identifying objects in multispectral images. It is called "Extended Gaussian ARTMAP". The authors conclude that this network is especially advantageous for classification of large, low dimensional data sets. The second paper's subject belongs to the realm of fuzzy systems. It reports successful application of fundamental similarity relations in diagnostic systems. As an example failure detection of rolling-mill transmission is considered. The next paper represents the AI-branch of machine intelligence. The paper is a report on an EU-funded project focusing on the storage of knowledge in a corporate organizational memory used for storing and retrieving knowledge chunks for it. The flexible structure of the system makes it possible to adopt it to different SMEs via using company-specific conceptual terms rather than traditional keywords. The fourth selected paper's contribution is to the field of knowledge discovery. For this purpose in the first step, cluster analysis is done. The method is found to be helpful whenever little or no information on the characteristics of a given data set is available. The next paper approaches scheduling problems by the application of the multiagent system. It is concluded that due to the great number of interactions between components, MAS seems to be well suited for manufacturing scheduling problems. The sixth selected paper's topic is emerging intelligent technologies in computer-aided engineering. It discusses key issues of CAD/CAM technology of our days. The conclusion is that further development of CAD/CAM methods probably will serve companies on the competitive edge. The seventh paper of the selection is a report on seeking a special tradeoff between classical analytical modeling and traditional soft computing. It nonconventionally integrates uniform structures obtained from Lagrangian Classical Mechanics with other simple elements of machine intelligence such as saturated sigmoid transition functions borrowed from neural nets, and fuzzy rules with classical PID/ST, and a simplified version of regression analysis. It is concluded that these different components can successfully cooperate in adaptive robot control. The last paper focuses on the complexity problem of fuzzy and neural network approaches. A fuzzy rule base, be it generated from expert operators or by some learning or identification schemes, may contain redundant, weakly contributing, or outright inconsistent components. Moreover, in pursuit of good approximation, one may be tempted to overly assign the number of antecedent sets, thereby resulting in large fuzzy rule bases and much problems in computation time and storage space. Engineers using neural networks have to face the same complexity problem with the number of neurons and layers. A fuzzy rule base and neural network design, hence, have two important objectives. One is to achieve a good approximation. The other is to reduce the complexity. The main difficulty is that these two objectives are contradictory. A formal approach to extracting the more pertinent elements of a given rule set or neurons is, hence, highly desirable. The last paper is an attempt in this direction. References 1)C. W. De Silva. Automation Intelligence. Engineering Application of Artificial Intelligence. Vol. 7. No. 5. 471-477 (1994). 2)L. A. Zadeh. Fuzzy Logic, Neural Networks and Soft Computing. NATO Advanced Studies Institute on Soft Computing and Its Application. Antalya, Turkey. (1996). 3)L. A. Zadeh. Berkeley Initiative in Soft Computing. IEEE Industrial Electronics Society Newsletter. 41, (3), 8-10 (1994).

In the five-axis machining, the dual nonuniform rational B-spline (NURBS) interpolator performs better than the conventional linear interpolator in improving machining efficiency and quality. However, a successful dual NURBS interpolator faces with two aspects of issues. First, the feedrate should be reasonably scheduled according to axial drive constraints. Furthermore, the axial trajectories should be precisely and rapidly calculated according to the scheduled feedrate. To schedule the feedrate, existing methods use either overall constant speed or frequent time-varying speed. However, the former one is adverse to the motion efficiency, while the latter one is adverse to the motion stability. To deal with these issues, this study schedules feedrate-sensitive and nonsensitive regions and plans constant speed at the sensitive regions and smooth transition speed within the nonsensitive regions, thus balancing the motion stability and the efficiency. In addition, to calculate the axial trajectories, existing methods, using inverse kinematics, result in multiple solutions due to the existence of antitrigonometric functions, and this requires complicated selection of the solutions, otherwise the axial positions will be discontinuity. To deal with this issue, this study proposes a Jacobi matrix-based Adams prediction–correction numerical algorithm, which uses the incremental value of the tool pose to calculate the consecutive unique solution of the five-axis positions directly. By integrating above techniques, a systematic five-axis dual NURBS interpolator with the constant speed at feedrate-sensitive regions under axial drive constraints is presented. Experimental tests are conducted to evaluate the effectiveness of the proposed method.

AbstractWe compute partition functions of Chern–Simons type theories for cylindrical spacetimes $$I \times \Sigma $$ I × Σ , with I an interval and $$\dim \Sigma = 4l+2$$ dim Σ = 4 l + 2 , in the BV-BFV formalism (a refinement of the Batalin–Vilkovisky formalism adapted to manifolds with boundary and cutting–gluing). The case $$\dim \Sigma = 0$$ dim Σ = 0 is considered as a toy example. We show that one can identify—for certain choices of residual fields—the “physical part” (restriction to degree zero fields) of the BV-BFV effective action with the Hamilton–Jacobi action computed in the companion paper (Cattaneo et al., Constrained systems, generalized Hamilton–Jacobi actions, and quantization, arXiv:2012.13270), without any quantum corrections. This Hamilton–Jacobi action is the action functional of a conformal field theory on $$\Sigma $$ Σ . For $$\dim \Sigma = 2$$ dim Σ = 2 , this implies a version of the CS-WZW correspondence. For $$\dim \Sigma = 6$$ dim Σ = 6 , using a particular polarization on one end of the cylinder, the Chern–Simons partition function is related to Kodaira–Spencer gravity (a.k.a. BCOV theory); this provides a BV-BFV quantum perspective on the semiclassical result by Gerasimov and Shatashvili.

<p style='text-indent:20px;'>Mechanical systems (i.e., one-dimensional field theories) with constraints are the focus of this paper. In the classical theory, systems with infinite-dimensional targets are considered as well (this then encompasses also higher-dimensional field theories in the hamiltonian formalism). The properties of the Hamilton–Jacobi (HJ) action are described in details and several examples are explicitly computed (including nonabelian Chern–Simons theory, where the HJ action turns out to be the gauged Wess–Zumino–Witten action). Perturbative quantization, limited in this note to finite-dimensional targets, is performed in the framework of the Batalin–Vilkovisky (BV) formalism in the bulk and of the Batalin–Fradkin–Vilkovisky (BFV) formalism at the endpoints. As a sanity check of the method, it is proved that the semiclassical contribution of the physical part of the evolution operator is still given by the HJ action. Several examples are computed explicitly. In particular, it is shown that the toy model for nonabelian Chern–Simons theory and the toy model for 7D Chern–Simons theory with nonlinear Hitchin polarization do not have quantum corrections in the physical part (the extension of these results to the actual cases is discussed in the companion paper [<xref ref-type="bibr" rid="b21">21</xref>]). Background material for both the classical part (symplectic geometry, generalized generating functions, HJ actions, and the extension of these concepts to infinite-dimensional manifolds) and the quantum part (BV-BFV formalism) is provided.</p>

Abstract In [1] we have studied the single-particle free energy of a class of Little String Theories of A-type, which are engineered by N parallel M5-branes on a circle. To leading instanton order (from the perspective of the low energy U(N) gauge theory) and partially also to higher order, a decomposition was observed, which resembles a Feynman diagrammatic expansion: external states are given by expansion coefficients of the N = 1 BPS free energy and a quasi-Jacobi form that governs the BPS-counting of an M5-brane coupling to two M2-branes. The effective coupling functions were written as infinite series and similarities to modular graph functions were remarked. In the current work we continue and extend this study: working with the full non-perturbative BPS free energy, we analyse in detail the cases N = 2, 3 and 4. We argue that in these cases to leading instanton order all coupling functions can be written as a simple combination of two-point functions of a single free scalar field on the torus. We provide closed form expressions, which we conjecture to hold for generic N. To higher instanton order, we observe that a decomposition of the free energy in terms of higher point functions with the same external states is still possible but a priori not unique. We nevertheless provide evidence that tentative coupling functions are still combinations of scalar Greens functions, which are decorated with derivatives or multiplied with holomorphic Eisenstein series. We interpret these decorations as corrections of the leading order effective couplings and in particular link the latter to dihedral graph functions with bivalent vertices, which suggests an interpretation in terms of disconnected graphs.

Today, the main research field for the automotive industry is to find solutions for active safety. In order to perceive the surrounding environment, tracking nearby traffic objects plays an important role. Validation of the tracking performance is often done in staged traffic scenarios, where additional sensors, mounted on the vehicles, are used to obtain their true positions and velocities. The difficulty of evaluating the tracking performance complicates its development. An alternative approach studied in this thesis, is to record sequences and use non-causal algorithms, such as smoothing, instead of filtering to estimate the true target states. With this method, validation data for online, causal, target tracking algorithms can be obtained for all traffic scenarios without the need of extra sensors. We investigate how non-causal algorithms affects the target tracking performance using multiple sensors and dynamic models of different complexity. This is done to evaluate real-time methods against estimates obtained from non-causal filtering. Two different measurement units, a monocular camera and a LIDAR sensor, and two dynamic models are evaluated and compared using both causal and non-causal methods. The system is tested in two single object scenarios where ground truth is available and in three multi object scenarios without ground truth. Results from the two single object scenarios shows that tracking using only a monocular camera performs poorly since it is unable to measure the distance to objects. Here, a complementary LIDAR sensor improves the tracking performance significantly. The dynamic models are shown to have a small impact on the tracking performance, while the non-causal application gives a distinct improvement when tracking objects at large distances. Since the sequence can be reversed, the non-causal estimates are propagated from more certain states when the target is closer to the ego vehicle. For multiple object tracking, we find that correct associations between measurements and tracks are crucial for improving the tracking performance with non-causal algorithms.

Adaptive control systems are one of the most significant research directions of modern control theory. It is well known that every mechanical appliance’s behavior noticeably depends on environmental changes, functioning-mode parameter changes and changes in technical characteristics of internal functional devices. An adaptive controller involved in control process allows reducing an influence of such changes. In spite of this such type of control methods is applied seldom due to specifics of a controller designing. The work presented in this paper shows the design process of the adaptive controller built by Lyapunov’s function method for a hydraulic servo system. The modeling of the hydraulic servo system were conducting with MATLAB® software including Simulink® and Symbolic Math Toolbox™. In this study, the Jacobi matrix linearization of the object’s mathematical model and derivation of the suitable reference models based on Newton’s characteristic polynomial were applied. In addition, an intelligent adaptive control algorithm and system model including its nonlinearities was developed to solve Lyapunov’s equation. Developed algorithm works properly and considered plant is met requirement of functioning with. The results shows that the developed adaptive control algorithm increases system performance in use devices significantly and might be used for correction of system’s behavior and dynamics.

The process of rapid boiling of a two phase droplet rising in an immiscible liquid environment has been experimentally considered within a new range of superheats (normalized Jacob number, 0.2< Ja˜ <0.5). In the course of the research numerous water-column boiling experiments were conducted for liquid propane droplets in a water environment. Boiling was generally calm and very rapid, concluding within several milliseconds, due to high heat fluxes across the interface. This work deals with the effect of various initial conditions on this distinctive boiling process. The parameters considered, are: the host liquid temperature, background pressure, initial droplet size and the size of the vapor nucleus inside the droplet. Their separate and combined effects have been recognized, and a correction factor based on initial droplet and bubble size is proposed. Through the parametric study the limits of rapid boiling have been approximately defined — between explosive and slow “conduction” boiling. In all experiments considered mass boiling rate is given by a function of the normalized Jacob number Ja˜ and the correction factor, to good agreement. Furthermore, due to the special nature of this boiling process, by use of the proposed factor the rapid boiling curve may be predicted for a wide range of initial conditions, for liquid propane or similar hydrocarbons. This allows design of a rapid boiling curve for a required application. Suggested applications range from alternative marine propulsion, to rapid direct-contact heat exchange.

Abstract A key challenge in the gas turbine community is to adapt the engine model by matching measured data with simulation data. This study presents a procedure aiming to calibrate a certain type of gas turbine for power generation. To reproduce degradation, disturbance is injected into the healthy components maps at different time. Subsequently, six correction factors along with measured data and unmeasured parameters are coupled together using cooperative working equations and optimized based on primal-dual interior point method. When performing the adaptive procedure, Jacobian and hessian matrices are calculated using finite difference since the component maps have external, mapped, functions implemented as lookup-tables, and mode-switching statements. To improve the accuracy of first-order and second-order partial derivatives, the finite difference is enhanced by Richardson extrapolation method. The search scope of correction factors and unmeasured parameters are determined by the whole working conditions. Meanwhile, an adaptive update method of initial solution is proposed to make sure the convergence of the optimization procedure as quickly as possible. Finally, the proposed method is further applied to the on-line adaptation in case of performance degradation. The influence of measurement noise on optimization is also studied. It is demonstrated that the procedure is capable of refining the component maps progressively, which is significant for the model-based gas path diagnostics and prognostics.

The dynamic equations of motion for constrained multibody systems are frequently formulated using the Newton-Euler’s approach, which is augmented with the acceleration constraint equations. This formulation results in the establishment of a mixed set of differential and algebraic equations, which are solved in order to predict the dynamic behavior of general multibody systems. It is known that the standard resolution of the equations of motion is highly prone to constraints violation because the position and velocity constraint equations are not fulfilled. In this work, a general review of the main methods commonly used to control or eliminate the violation of the constraint equations in the context of multibody dynamics formulation is presented and discussed. Furthermore, a general and comprehensive methodology to eliminate the constraints violation at the position and velocity levels is also presented. The basic idea of this approach is to add corrective terms to the position and velocity vectors with the intent to satisfy the corresponding kinematic constraint equations. These corrective terms are evaluated as function of the Moore-Penrose generalized inverse of the Jacobian matrix and of the kinematic constraint equations.

A globally convergent and fully coupled magnetomechanical model for 3D magnetostrictive systems is presented. In magnetostrictive actuators, magnetic field and stress inputs generate magnetic flux density and strain. We refer to models that follow this scheme as direct models (no relation to the direct magnetomechanical effect). In certain design and control situations, inverse models are necessary in which the magnetic field and stress are found from specified magnetic flux density and strains. This inversion typically involves an iterative procedure, which may be prone to convergence issues. An inverse model approach is proposed for arbitrary magnetostrictive materials. The inversion requirement is a continuous and second order differentiable direct model for any chosen magnetostrictive material. The approach is globally convergent, which makes it ideal for use in finite element frameworks. The premise of the proposed iterative system model is to constitute a recursive correction formula based on second order approximations of a novel scalar error function which allows to achieve a faster convergence rate. A continuation approach is then used to achieve global convergence for arbitrary input parameters. To illustrate, Galfenol is chosen as the magnetostrictive material, and analytical derivations of the Jacobian and Hessian matrices are presented. Finally, the computational efficiency of the proposed approach is shown to compare favorably against existing models.