General Method Of Solution Research Articles

Curved and stretched flames: the two Markstein numbers

AbstractThe analytical result concerning the Markstein number of adiabatic flames was obtained in 1982 with the one-step Arrhenius model in the limit of a large activation energy. This result is not relevant for real flames. The form of the law expressing the flame velocity in terms of the total stretch rate of the flame front through a single Markstein length is not conserved when the location of the front (surface of zero thickness) changes within the flame thickness. It is shown in this paper that two different Markstein numbers ${\mathscr{M}}_{I} \not = {\mathscr{M}}_{II} $ characterize usual wrinkled flames sustained by a multiple-step chemical network, ${\mathscr{M}}_{I} $ for the modification of the flame velocity due to the curvature of the front and ${\mathscr{M}}_{II} $ for the effect of the flow strain rate. In contrast to ${\mathscr{M}}_{I} $, ${\mathscr{M}}_{II} $ depends on the location of the flame surface within the flame thickness, in such a way that the final result for the flame dynamics is not depending on this choice. The first part of the paper is devoted to present a general method of solution, valid for any multiple-step chemical network. The two Markstein numbers for two-step chain-branching models representing rich hydrogen–air flames and lean hydrocarbon–air flames are then computed analytically in the second part.

Designing domestic institutions for international monetary policy cooperation: A Utopia?

In a wide variety of international macroeconomic models monetary policy cooperation is optimal, non-cooperative policies are inefficient, but optimal policies can be attained non-cooperatively by optimal design of domestic institutions/contracts. We show that given endogenous institutional design, inefficiencies of non-cooperation cannot and will not be eliminated. We model the delegation stage explicitly and show that subgame perfect, credible contracts (chosen by governments based on individual rationality) are non-zero, but are different from optimal contracts and hence lead to inefficient equilibria. Optimal contracts require cooperation at the delegation stage, which is inconsistent with the advocated non-cooperative nature of the solution. A general solution method for credible contracts and an example from international monetary policy cooperation are considered. Our results feature delegation as an equilibrium phenomenon, explain inefficiencies of existing delegation schemes and hint to a potentially stronger role for supranational authorities in international policy coordination.

A New General Iterative Method for Solution of a New General System of Variational Inclusions for Nonexpansive Semigroups in Banach Spaces

We introduce a new general system of variational inclusions in Banach spaces and propose a new iterative scheme for finding common element of the set of solutions of the variational inclusion with set‐valued maximal monotone mapping and Lipschitzian relaxed cocoercive mapping and the set of fixed point of nonexpansive semigroups in a uniformly convex and 2‐uniformly smooth Banach space. Furthermore, strong convergence theorems are established under some certain control conditions. As applications, finding a common solution for a system of variational inequality problems and minimization problems is given.

Optimal Trading Execution with Nonlinear Market Impact: An Alternative Solution Method

We consider the optimal trade execution strategies for a large portfolio of single stocks proposed by Almgren (2003). This framework accounts for a nonlinear impact of trades on average market prices. The results of Almgren (2003) are based on the assumption that no shares of assets per unit of time are trade at the beginning of the period. We propose a general solution method that accomodates the case of a positive stock of assets in the initial period. Our findings are twofold. First of all, we show that the problem admits a solution with no trading in the opening period only if additional parametric restrictions are imposed. Second, with positive asset holdings in the initial period, the optimal execution time depends on trading activity at the beginning of the planning period.

Nonequilibrium response from the dissipative Liouville equation

The problem of response of nonequilibrium systems is currently under intense investigation.We propose a general method of solution of the Liouville equation for thermostattedparticle systems subjected to external forces which retains only the slow degrees offreedom, by projecting out the majority of fast variables. Response formulae, extending theGreen–Kubo relations to dissipative dynamics, are provided, and comparison withnumerical data is presented.

A General Method of Solution for the Cluster Variation Method in Ionic Solids, with Application to Diffusionless Transitions in Yttria-Stabilized Zirconia

A new, general method of solution for the cluster variation method using a reduced conjugate gradient approach with a truncated line-search algorithm is presented. The method is generally convergent. Additionally, the truncation of the line-search algorithm may increase the speed of convergence considerably, as the size of the problem is progressively reduced (especially for strongly ordered phases), opening up the possibility of a considerable increase in the size of maximal clusters. The method is successfully demonstrated for a single, eight-atom maximal cluster in the fluorite lattice. Using pairwise defect interaction energies calculated for cubic, yttria-doped zirconia and fixed defect concentrations, a pair of metastable states are found in a composition and temperature range which is experimentally characterized by metastable, diffusionless phase transitions.

Some comments on “A simple method to compute economic order quantities”

Abstract In this note, we emphasize that the arithmetic–geometric-mean-inequality approach proposed by Teng [Teng, J.T., 2008. A simple method to compute economic order quantities. European Journal of Operational Research. doi:10.1016/j.ejor.2008.05.019 ] is not a general solution method. Teng’s approach happens to work and give the correct results when the two terms in an objective function are any functions such that their product is a constant. The classical EOQ model works fine since the product of the two terms is indeed a constant! When the product is not a constant, Teng’s approach is of little use. This is exemplified in Comment 1 via solving the EOQ model with complete backorders (where the model is regarded as having two decision variables). Comment 2 is generally valid for an algebraic method when it is used to solve an objective function with two decision variables.

Ionic Ingress and Charge‐Neutralization Phenomena of Conducting‐Polymer Films

Ionic ingress and diffusion through a conducting-polymer (CP) film containing embedded charges under potential and concentration gradients is studied. Electroneutrality, a common assumption in modeling of similar systems, is not justified in this case or similar diffusion-limited processes, as the timescale of ionic diffusion in the solid matrix is quite large. Counter ions therefore cannot move instantaneously for effective neutralization of excess charges. Poisson-Nernst-Planck (PNP) equations have to be solved for such cases without any simplifying assumption. Analytical solution shows the existence of a charge boundary layer, which limits and strongly influences the ionic flux. A general numerical method for solution is also developed for the dynamic modeling, analysis, and design of these types of systems. The numerical results are validated by comparison with analytical solutions as well as with some experimental results available in the literature. With this modeling framework, the basic features of controlled release of molecules across a CP film under an applied electrical potential can be explained quantitatively.

Faster Converging Global Heuristic for Continuous Network Design Using Radial Basis Functions

In light of the demand for more complex network models and general solution methods, this research introduces a radial basis function-based method as a faster alternative global heuristic to a genetic algorithm method for the continuous network design problem. Two versions of the algorithm are tested against the genetic algorithm in three experiments: the Sioux Falls, South Dakota, network with standard origin–destination flows; the same network with double the flows to test performance under a more congested scenario; and an illustrative experiment with the Anaheim, California, network to compare the scalability of performance. To perform the experiments, parameters for the network design problem were developed for the Anaheim network. The Anaheim test would be the first instance of testing the radial basis function methods on a 31-dimensional network design problem. Results indicate that the multistart local radial basis function method performs notably better than the genetic algorithm in all three experiments and would therefore be an attractive method to apply to more complicated network design models involving larger networks and more complex constraints, objectives, and representations of the time dimension.

Direct growth of high-rate capability and high capacity copper sulfide nanowire array cathodes for lithium-ion batteries

A general solution method for the growth of highly ordered large-scale Cu2S nanowire arrays onto the copper metal current collector substrates has been developed. The electrochemical behaviors of Cu2S nanowire array cathodes for lithium-ion battery applications reveal that they exhibit stable lithium-ion insertion/extraction reversibility, high reversible lithium storage capacity, long cycle life and outstanding rate capability. The superb electrochemical performance can be attributed to the nanowire arrays having increased reaction sites, improved cycle life in the face of mechanical strain and efficient charge transport. With the simplicity of fabrication and good electrochemical properties, the Cu2S nanowire arrays are promising cathode materials for the practical use in the next generation lithium-ion batteries.

Nuclear Fuel Recycling, the Value of the Separated Transuranics and the Levelized Cost of Electricity

We analyze the levelized cost of electricity (LCOE) for three different fuel cycles: a Once-Through Cycle, in which the spent fuel is sent for disposal after one use in a reactor, a Twice-Through Cycle, in which the spent fuel is recycled for a second use in a light water reactor after which the spent fuel is sent for disposal, and a Fast Reactor Recycle in which all of the transuranics are repeatedly recycled in fast reactors. We carefully define the LCOE and provide a simple solution method that involves simultaneously calculating the value of the recycled materials, whether plutonium or the transuranics. We parameterize our formulas and calculate the LCOEs. Earlier reports do not provide general formulas and solution methods for calculating the LCOE. We contrast our methodology with the definitions and solution methods employed in various prior reports, and we compare our parameter inputs and resulting LCOEs. For example, we show that the ‘equilibrium cost’ of fast reactor systems as calculated in other studies exaggerates the LCOE. Our calculations show that, based on current estimates of the costs for the various activities, recycling increases the LCOE by between 1.7 and 2.8 mills/kWh. This is an approximately 20-34% increase in the fuel cycle cost of the Once-Through Cycle, which we estimate at 8.28 mill/kWh. This is an approximately 2-4% increase in the total LCOE of the Once-Through Cycle, which we estimate at 75.32 mill/kWh. For the Twice-Through Cycle, the separated plutonium has a negative value, meaning that a reactor will have to be paid to take the recycled plutonium. For the Fast Reactor Cycle, the separated transuranics have a negative value, meaning that a fast reactor will have to be paid to take the transuranics.

Motivating Computer Engineering Freshmen Through Mathematical and Logical Puzzles

As in many other fields of science and technology, college students in computer engineering do not come into full contact with the key ideas and challenges of their chosen discipline until the third year of their studies. This situation poses a problem in terms of keeping the students motivated as they labor through their foundational, basic science, and general education coursework. At the University of California, Santa Barbara, the computer engineering program has sought to remedy this problem by offering a required freshman seminar, entitled "ten puzzling problems in computer engineering." This pass/not-pass seminar, which meets once a week and is graded based solely on attendance, introduces the students to some of the most challenging problems faced by computer engineers in their daily professional endeavors and at the frontiers of research. To accomplish this feat in a nontechnical way, these problems are related to popular mathematical and logical puzzles. Each class session (60-75 min) begins by introducing the students to puzzles of a particular kind and letting them participate in formulating solutions. General solution methods for the puzzles are then discussed by the instructor, who then proceeds to demonstrate how the puzzles and their solution strategies are related to real technical challenges in computer engineering. The new one-unit course was well received during its first two offerings in spring 2007 and spring 2008, and its continuation is planned.

ELASTIC ANALYSIS OF A GRIFFITH CRACK IN ICOSAHEDRAL QUASICRYSTAL Al-Pd-Mn QUASICRYSTAL

The elastic analysis of a Griffith crack in an icosahedral quasicrystal is performed using the general solution and systematic Fourier transform-dual integral equations method, the analytic expressions for the displacement and stress fields are obtained. The asymptotic behavior of the stress field around the crack tip indicates that the stress near the crack tip exhibits the square root singularity. The singularity in the phason stress field arising from those of the phonon and phonon–phason coupling is also discussed. The most important physical quantities of fracture theory, crack stress intensity factor and energy release rate, are determined.

Solving the ordered one-median problem in the plane

In this paper, we propose a general approach solution method for the single facility ordered median problem in the plane. All types of weights (non-negative, non-positive, and mixed) are considered. The big triangle small triangle approach is used for the solution. Rigorous and heuristic algorithms are proposed and extensively tested on eight different problems with excellent results.

The big cube small cube solution method for multidimensional facility location problems

In this paper we propose a general solution method for (non-differentiable) facility location problems with more than two variables as an extension of the Big Square Small Square technique (BSSS). We develop a general framework based on lower bounds and discarding tests for every location problem. We demonstrate our approach on three problems: the Fermat–Weber problem with positive and negative weights, the median circle problem, and the p -median problem. For each of these problems we show how to calculate lower bounds and discarding tests. Computational experiences are given which show that the proposed solution method is fast and exact.

On the heterogeneous multiscale method with various macroscopic solvers

The heterogeneous multiscale method (HMM) is a general method for efficient numerical solution of problems with multiscales. It consists of two components: an overall macroscopic solver for macrovariables on a macrogrid and an estimation of the missing macroscopic data from the microscopic model. In this paper we present a state-of-the-art review of the HMM with various macroscopic solvers, including finite differences, finite elements, discontinuous Galerkin, mixed finite elements, control volume finite elements, nonconforming finite elements, and mixed covolumes. The first four solvers have been studied in the HMM setting; the others are not. As example, the HMM with the nonconforming finite element macroscopic solver for nonlinear and random homogenization problems is also studied here.

A New Method for Constructing Classifier Ensembles

Usage of recognition systems has found many applications in almost all fields. However, Most of classification algorithms have obtained good performance for specific problems; they have not enough robustness for other problems. Combination of multiple classifiers can be considered as a general solution method for pattern recognition problems. It has been shown that combination of classifiers can usually operate better than single classifier provided that its components are independent or they have diverse outputs. It was shown that the necessary diversity of an ensemble can be achieved manipulation of data set features. We also propose a new method of creating this diversity. The ensemble created by proposed method may not always outperforms all classifiers existing in it, it is always possesses the diversity needed for creation of ensemble, and consequently it always outperforms the simple classifier.

Oriented growth of large-scale nickel sulfide nanowire arrays via a general solution route for lithium-ion battery cathode applications

A general solution method for the oriented growth of large-scale Ni3S2nanowire arrays has been developed. The controlled oxidation scheme by combining ethylenediamine-chalcogens and hydrazine in alkali solution has been shown to have great advantages for the fabrication of metal chalcogenides with fewer instrumental limitations. This method is reliable and works in mild template-free conditions for the production of single-crystalline nanowire arrays. It provides a convenient route for the large-scale growth of pure-phase metal chalcogenide nanowire arrays on metal substrates. The electrochemical measurement results of Ni3S2nanowire arrays for lithium-ion battery electrode applications reveal that they have high reversible lithium storage capacity, long cycle life, good cyclic stability and high charge/discharge rate. With the simplicity of fabrication and good electrochemical performance, Ni3S2nanowire arrays are promising cathode materials for lithium-ion batteries.

Groundwater response to tidal forcing

The groundwater response to tidal forcing in a phreatic aquifer is modelled using a perturbation approach for the case of a shallow beach. The principal features of the groundwater response, namely the super-elevation of the water table, attenuation of the forcing wave and the asymmetry and phase shift in the fluctuations, is investigated and compared with earlier solutions. These results demonstrate the importance of correctly including the beach slope effects to prevent the exaggeration of observed features for shallow beaches. A general solution method is presented, which provides an efficient method for obtaining higher order solutions. References B. Ataie-Ashtiani, R. E. Volker, and D. A. Lockington. Tidal effects on groundwater dynamics in unconfined aquifers. Hydrological Processes, 15:655--669, 2001. doi:10.1002/hyp.183 P. Nielsen. Tidal dynamics of the water table in beaches. Water Resour. Res., 26(9):2127--2134, September 1990. J.R. Philip. Periodic nonlinear diffusion: An integral relation and its physical consequences. Aust. J. Phys., 26:513--519, 1973. H. T. Teo, D. S. Jeng, B. R. Seymour, D. A. Barry, and L. Li. A new analytical solution for water table fluctuations in coastal aquifers with sloping beaches. Adv. Wat. Res., 26:1239--1247, December 2003. doi:10.1016/j.advwatres.2003.08.004

A puzzle-based seminar for computer engineering freshmen1

We observe that recruitment efforts aimed at alleviating the shortage of skilled workforce in computer engineering must be augmented with strategies for retaining and motivating the students after they have enrolled in our educational programmes. At the University of California, Santa Barbara, we have taken a first step in this direction by offering a required freshman seminar entitled “Ten Puzzling Problems in Computer Engineering”. This one-unit pass/not-pass gateway course, which is graded based solely on attendance, introduces our students to some of the most challenging problems faced by computer engineers in their daily professional endeavors and at the frontiers of research. To accomplish this feat in a manner that is both understandable and appealing to freshmen, the problems are related to popular mathematical and logical puzzles. Each 1-hour class session begins by introducing the students to puzzles of a particular kind and letting them participate in formulating solutions. Historical context, background, and general solution methods for the puzzles are then discussed by the instructor, who finally proceeds to demonstrate how the puzzles and their solution strategies are related to real technical challenges in computer engineering. The new course, which has been offered twice already, is supported by a website containing complete lecture slides, class handouts, and reference information.