Quadratic Algorithm Research Articles

A Direct Numerical Simulation of Annular Two-Phase Laminar Flow and Heat Transfer in a Circular Pipe

An accurate finite-volume based numerical method is developed for the direct numerical simulation of two-phase flow dynamics and heat transfer in a circular pipe consisting of a liquid slug translating in a non-reacting gas. This method is built on a sharp interface concept and developed on an Eulerian-Cartesian fixed-grid system with a cut-cell scheme and marker points to track the moving interface. The unsteady, axisymmetric Navier-Stokes equations in both liquid and gas phases are solved separately. The mass continuity and momentum flux conditions are explicitly matched at the true surface phase boundary to determine the interface shape and movement. A quadratic curve fitting algorithm with marker points is used to yield smooth and accurate information of the interface curvatures. Two-phase flow and heat transfer characteristics are predicted for air-water flows under low and high Weber numbers to evaluate the heat transfer enhancement levels due to the moving liquid slug and the effects of surface tension force. The method reported in this paper offers, for the first time, a new capability of simulating two-phase gas-liquid flow dynamics and heat transfer directly without any modeling. This numerical simulation involves liquid phase deformation, moving interface boundary, curvature variations due to surface tension, property jumps, and heat transfer at the interface.

A Quadratic Algorithm for Finding Next-to-Shortest Paths in Graphs

Given an edge-weighted undirected graph G and two prescribed vertices u and v, a next-to-shortest (u,v)-path is a shortest (u,v)-path amongst all (u,v)-paths having length strictly greater than the length of a shortest (u,v)-path. In this paper, we deal with the problem of computing a next-to-shortest (u,v)-path. We propose an ${\mathcal{O}}(n^{2})$ time algorithm for solving this problem, which significantly improves the bound of a previous one in ${\mathcal{O}}(n^{3})$ time where n is the number of vertices in G.

On the link between Markovian trees and tree-structured Markov chains

Abstract In this paper, we describe a link between Markovian binary trees (MBT) and tree-like quasi-birth-and-death processes (TLQBD) by associating a specific TLQBD to each MBT. The algorithms to compute the matrices G k in the TLQBD then correspond to the algorithms calculating the extinction probability vector of the MBT. This parallelism leads to a new quadratic algorithm, based on the Newton iteration method, which converges to the extinction probability of an MBT. We also present a one-to-one correspondence between a general Markovian tree (GMT) and a scalar tree-structured M/G/1-type Markov chain. This allows us to prove the equivalence between the main result on the positive recurrence, null recurrence or transience of a scalar tree-structured M/G/1-type Markov chain and the criticality of a GMT.

Optimization of Secondary-Air Addition in a Continuous One-Dimensional Spray Combustor

A framework is established for optimal control of continuous combustors using the sequential linear quadratic algorithm. An analysis is presented for liquid-fuel vaporization and burning in a continuous combustor with secondary-air addition at downstream locations. A steady one-dimensional flow is portrayed and a system of nonlinear ordinary differential equations is established. Three combustion models are presented with different rate-controlling processes: vaporization, vaporization-mixing, and vaporization-mixing-reaction. The models have a sufficient number of characteristic times and sufficient nonlinearity to provide a challenge to an optimization procedure. The proposed method yields an optimal distribution of secondary-air addition.

Reliability based limit design of steel frames with limited residual strain energy capacity

AbstractThe aim of this paper is to take into consideration the influence of the limited load carrying capacity of the connections on the plastic limit state of elasto‐plastic steel (or composite) framed structures under multi‐parameter stochastic loading and probabilistically given conditions. In addition to the plastic limit design to control the plastic behaviour of the structure, bound on the complementary strain energy of the residual forces is also applied. This bound has significant effect for the load parameter. If the design uncertainties (manufacturing, strength, geometrical) are expressed by the calculation of the complementary strain energy of the residual forces a reliability based extended limit design problem is formed. The formulations of the problems yield to nonlinear mathematical programming which are solved by the use of sequential quadratic algorithm. The bi‐level optimization procedure governed by the reliability index calculation. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Optimization problems for periodic systems

Quadratic optimization algorithms for discrete-time linear periodic systems are discussed. Consideration is given to the conventional linear-quadratic problem statement where the optimal controller is found by solving the discrete algebraic Riccati equation and to input-feedback controller design problems. Considerable attention is focused on the synthesis of a reliable controller with a guaranteed stability margin. The following inverse problem is solved: given plant and controller matrices, find the weight matrices of the functional being optimized. The efficiency of the algorithms is demonstrated by way of examples

Evaluation of a photovoltaic energy mechatronics system with a built-in quadratic maximum power point tracking algorithm

The historically high cost of crude oil price is stimulating research into solar (green) energy as an alternative energy source. In general, applications with large solar energy output require a maximum power point tracking (MPPT) algorithm to optimize the power generated by the photovoltaic effect. This work aims to provide a stand-alone solution for solar energy applications by integrating a DC/DC buck converter to a newly developed quadratic MPPT algorithm along with its appropriate software and hardware. The quadratic MPPT method utilizes three previously used duty cycles with their corresponding power outputs. It approaches the maximum value by using a second order polynomial formula, which converges faster than the existing MPPT algorithm. The hardware implementation takes advantage of the real-time controller system from National Instruments, USA. Experimental results have shown that the proposed solar mechatronics system can correctly and effectively track the maximum power point without any difficulties.

A note on a quadratic algorithm for the 2-cyclic robotic scheduling problem

Recently, Pablo Sáez (2009) [1] has developed a quadratic algorithm for a 2-cyclic robotic scheduling problem. In this note we uncover that the algorithm handles a special version of the problem only and fails to solve the general 2-cyclic robotic scheduling problem.

Adaptive content-based music retrieval system

This paper presents a tunable content-based music retrieval (CBMR) system suitable the for retrieval of music audio clips. The audio clips are represented as extracted feature vectors. The CBMR system is expert-tunable by altering the feature space. The feature space is tuned according to the expert-specified similarity criteria expressed in terms of clusters of similar audio clips. The main goal of tuning the feature space is to improve retrieval performance, since some features may have more impact on perceived similarity than others. The tuning process utilizes our genetic algorithm. The R-tree index for efficient retrieval of audio clips is based on the clustering of feature vectors. For each cluster a minimal bounding rectangle (MBR) is formed, thus providing objects for indexing. Inserting new nodes into the R-tree is efficiently performed because of the chosen Quadratic Split algorithm. Our CBMR system implements the point query and the n-nearest neighbors query with the O(logn) time complexity. Different objective functions based on cluster similarity and dissimilarity measures are used for the genetic algorithm. We have found that all of them have similar impact on the retrieval performance in terms of precision and recall. The paper includes experimental results in measuring retrieval performance, reporting significant improvement over the untuned feature space.

Aqua MODIS Thermal Emissive Band On-Orbit Calibration, Characterization, and Performance

The NASA's Earth Observing System Aqua Moderate Resolution Imaging Spectroradiometer (MODIS) has continued to operate with satisfactory performance since its launch in May 2002, exceeding its nominal six-year design lifetime. Its continuous Earth observations have been used to generate many science data products for studies of the Earth's system. MODIS has 36 spectral bands: 20 reflective solar bands and 16 thermal emissive bands (TEBs). All TEB observations are made at 1-km nadir spatial resolution with spectral wavelengths from 3.7 to 14.4 mum. Primary applications of MODIS TEB include surface, cloud, and atmospheric temperatures, water vapor, and cloud top altitude. MODIS TEB on-orbit calibration uses a quadratic algorithm with its calibration coefficients derived using an onboard blackbody (BB). This paper will present Aqua MODIS TEB on-orbit calibration, characterization, and performance over its six-year mission. Examples of instrument thermal behavior, BB temperature stability, detector short-term stability, and changes in long-term response (or system gain) will be presented. Comparisons will also be made with Terra MODIS, launched in December 1999. On-orbit results show that Aqua MODIS and its focal plane temperatures have behaved normally. BB temperature has remained extremely stable with typical scan-to-scan variations of less than plusmn0.15 mK. Most TEB detectors continue to exceed their specified signal-to-noise ratio requirements, exhibiting excellent short-term stability and calibration accuracy. Excluding a few noisy detectors, either identified prelaunch or occurring postlaunch, on-orbit changes in TEB responses have been less than 0.5% on an annual basis. By comparison, the overall Aqua TEB performance has been better than that of Terra MODIS.

The modpn library

We investigate the integration of C implementation of fast arithmetic operations into Maple, focusing on triangular decomposition algorithms. We show substantial improvements over existing Maple implementations; our code also outperforms Magma on many examples. Profiling data show that data conversion can become a bottleneck for some algorithms, leaving room for further improvements. Since the early days of computer algebra systems, their designers have investigated many aspects of this kind of software. For systems born in the 70’s and 80’s, such as AXIOM and Maple, the primary concerns were probably the expressiveness of the programming language and the convenience of the user interface; the implementation of modular methods for operations such as polynomial GCD or factorization was also among these concerns. Computer algebra systems and libraries born in the 90’s, such as Magma and NTL, have brought forward a new priority: the implementation of asymptotically fast arithmetic for polynomials and matrices. They have demonstrated that, for relatively small input data size, FFT-based polynomial operations could outperform operations based on classical quadratic algorithms or on the Karatsuba trick. This increased in a spectacular manner the range of solvable problems. Meanwhile, AXIOM and Maple remain highly attractive: the former one by its programming environment and the latter one by its users community. In previous work [6, 9, 11] we have investigated the integration of asymptotically fast arithmetic operations into AXIOM. Since AXIOM is based today on GNU Common Lisp (GCL), we realized optimized implementations of these fast routines in C and

An Efficient Computation of the Equation K-automaton of a Regular K-expression

The aim of this paper is to describe a quadratic algorithm for computing the equation K-automaton of a regular K-expression as defined by Lombardy and Sakarovitch. Our construction is based on an extension to regular K-expressions of the notion of c-continuation that we introduced to compute the equation automaton of a regular expression as a quotient of its position automaton.

A quadratic algorithm for the 2-cyclic robotic scheduling problem

We improve on an O ( n 5 log n ) algorithm by Kats and Levner [V. Kats, E. Levner, A polynomial algorithm for 2-cyclic robotic scheduling, in: Gelbukh, Reyes-García (Eds.), Proceedings of MICAI’06, in: LNAI, vol. 4293, Springer Verlag, 2006, pp. 439–449] for 2-cyclic robotic scheduling. We provide in this work an O ( n 2 log n ) algorithm for this problem.

Robust processing method for data smooth

There exist deviations of error distribution and exceptional dots in practical data measurement.However the classical methods of shift smooth processing of 2k+1 dots are not robust.In order to deal with this problem,the paper utilized M robust quadratic polynomial linearity space regression algorithm to deal with the robust smooth progressing.Lastly,the full robustness of the algorithm is demonstrated by analyzing the IF.

Efficient inclusion for a class of XML types with interleaving and counting

Inclusion between XML types is important but expensive, and is much more expensive when unordered types are considered. We prove here that inclusion for XML types with interleaving and counting can be decided in polynomial time in the presence of two important restrictions: no element appears twice in the same content model, and Kleene star is only applied to disjunctions of single elements. Our approach is based on the transformation of each such content model into a set of constraints that completely characterizes the generated language. We then reduce inclusion checking to constraint implication. We exhibit a quadratic algorithm to perform inclusion checking on a RAM machine.

A FAST AND EFFECTIVE TIMING-DRIVEN PLACEMENT TOOL FOR FPGAs

In this paper, we present TQPF, a Timing-Driven Quadratic-based Placement Tool for FPGAs. Quadratic placement algorithms try to minimize total squared wire length by solving linear equations. The resulting placement tends to locate all cells near the center of the chip with a large amount of overlap. Also, since squared wire length is only an indirect measure of linear wire length, the resulting total wire length may not be minimized. We propose methods to alleviate the above two problems that give high-quality results while minimizing the total run time. We incorporate multiple iterations of equation-solving process together with a technique for pulling nodes out of the dense area while minimizing linear wire length. Experimental results using 20 Microelectronics Center of North Carolina (MCNC) benchmark circuits show that, on average, TQPF is approximately three times faster than the well-known Versatile Placement and Routing tool for FPGAs (VPR). The estimated total wire length, on average, is only 1.4% longer, and the critical path delay is 4.9% lower.

On the tiling by translation problem

On square or hexagonal lattices, tiles or polyominoes are coded by words. The polyominoes that tile the plane by translation are characterized by the Beauquier-Nivat condition. By using the constant time algorithms for computing the longest common extensions in two words, we provide a linear time algorithm in the case of pseudo-square polyominoes, improving the previous quadratic algorithm of Gambini and Vuillon. We also have a linear algorithm for pseudo-hexagon polyominoes not containing arbitrarily large square factors. The results are extended to more general tiles.

A Hybrid Automaton Model of the Cement Mill Control

Cement milling circuits are controlled by linear quadratic strategies with the purpose of retaining the circuit stability. Generally, the controlled variables of milling circuits present discontinuities over the range of values they take during the plant operation. The design of linear quadratic control algorithms is based on linear approximations of the nonlinear differential equations that hold over the continuous time ranges of the controlled variables. These approximations make the practical implementation of these algorithms less effective than expected and for this reason there is the need to verify the range of the variable values over which the algorithms can retain the circuit stability before commissioning them. In this paper, an alternative model to that of the nonlinear differential equations is developed for the verification of the milling circuit stability. The model is based on the rectangular hybrid automata formalism. This formalism provides a more systematic and formal way of modeling the plant operation over different ranges of variables presenting discontinuities and does not require to develop informal textual description of the conditions under which different sets of differential equations model the plant operation within the different continuous ranges of the variables. In order to use this model for verifying the circuit stability, the requirements for the circuit stability are expressed in the form of a logical proposition of the ranges of the values within which certain variables of the cement milling circuit must remain. The circuit stability is verified by finding whether the states that are defined by the logical proposition are included in the state space of the automaton. There are, however, cases in which existing algorithms that search into the state space either do not terminate or take very long times in identifying the existence or not of the desired state. After the elapse of a significant portion of time the analyst does not know whether this long time is due to algorithm termination problem or to the very large number of remaining computations. In this paper, a new algorithm was developed which does not search into the state space of the automaton as most of the other algorithms do, but computes the number of automaton iterations required for reaching a state. If this is a finite number one can conclude that the desired state is reachable. This algorithm was used in verifying the circuit stability.

A HIGH-ORDER RECURSIVE QUADRATIC ALGORITHM FOR LINEAR-IN-THE-PARAMETER MODELS

In this paper, a high-order Recursive Quadratic (RQ) algorithm is introduced, and the features of this algorithm are thoroughly studied and illustrated. In addition, a robust RQ algorithm is also developed in the presence of general bounded noisy data to enhance model robustness. A numerical example is included to demonstrate the efficiency of RQ algorithms by comparing the results with both the projection algorithm and the conventional recursive least squares algorithm. Also some simulations are carried out to illustrate the effectiveness of the RQ and robust RQ algorithms.

Quadratic Interpolation Algorithm for Minimizing Tabulated Function

Problem statement: The problem of finding the minimum value of objective function, when we know only some values of it, is needed in more practical fields. Quadratic interpolation algorithms are the famous tools deal with this kind of these problems. These algorithms interested with the polynomial space in which the objective function is approximated. Approach: In this study we approximated the objective function by a one dimensional quadratic polynomial. This approach saved the time and the effort to get the best point at which the objective is minimized. Results: The quadratic polynomial in each one of the steps of the proposed algorithm, accelerate the convergent to the best value of the objective function without taking into account all points of the interpolation set. Conclusion: Any n-dimensional problem of finding a minimal value of a function, given by some values, can be converted to one dimensional problem easier in deal.