966 resultados para VARIATIONAL-CUMULANT EXPANSION
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A self-consistent equilibrium calculation, valid for arbitrary aspect ratio tokamaks, is obtained through a direct variational technique that reduces the equilibrium solution, in general obtained from the 2D Grad-Shafranov equation, to a 1D problem in the radial flux coordinate rho. The plasma current profile is supposed to have contributions of the diamagnetic, Pfirsch-Schluter and the neoclassical ohmic and bootstrap currents. An iterative procedure is introduced into our code until the flux surface averaged toroidal current density (J(T)), converges to within a specified tolerance for a given pressure profile and prescribed boundary conditions. The convergence criterion is applied between the (J(T)) profile used to calculate the equilibrium through the variational procedure and the one that results from the equilibrium and given by the sum of all current components. The ohmic contribution is calculated from the neoclassical conductivity and from the self-consistently determined loop voltage in order to give the prescribed value of the total plasma current. The bootstrap current is estimated through the full matrix Hirshman-Sigmar model with the viscosity coefficients as proposed by Shaing, which are valid in all plasma collisionality regimes and arbitrary aspect ratios. The results of the self-consistent calculation are presented for the low aspect ratio tokamak Experimento Tokamak Esferico. A comparison among different models for the bootstrap current estimate is also performed and their possible Limitations to the self-consistent calculation is analysed.
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The methodology based on the association of the variational method with supersymmetric quantum mechanics is used to evaluate the energy states of the confined hydrogen atom. (C) 2002 Elsevier B.V. B.V. All rights reserved.
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We have investigated and extensively tested three families of non-convex optimization approaches for solving the transmission network expansion planning problem: simulated annealing (SA), genetic algorithms (GA), and tabu search algorithms (TS). The paper compares the main features of the three approaches and presents an integrated view of these methodologies. A hybrid approach is then proposed which presents performances which are far better than the ones obtained with any of these approaches individually. Results obtained in tests performed with large scale real-life networks are summarized.
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The simulated annealing optimization technique has been successfully applied to a number of electrical engineering problems, including transmission system expansion planning. The method is general in the sense that it does not assume any particular property of the problem being solved, such as linearity or convexity. Moreover, it has the ability to provide solutions arbitrarily close to an optimum (i.e. it is asymptotically convergent) as the cooling process slows down. The drawback of the approach is the computational burden: finding optimal solutions may be extremely expensive in some cases. This paper presents a Parallel Simulated Annealing, PSA, algorithm for solving the long term transmission network expansion planning problem. A strategy that does not affect the basic convergence properties of the Sequential Simulated Annealing algorithm have been implementeded and tested. The paper investigates the conditions under which the parallel algorithm is most efficient. The parallel implementations have been tested on three example networks: a small 6-bus network, and two complex real-life networks. Excellent results are reported in the test section of the paper: in addition to reductions in computing times, the Parallel Simulated Annealing algorithm proposed in the paper has shown significant improvements in solution quality for the largest of the test networks.
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We show how the zero-temperature result for the heat-kernel asymptotic expansion can be generalized to the finite-temperature one. We observe that this general result depends on the interesting ratio square-root tau/beta, where tau is the regularization parameter and beta = 1/T, so that the zero-temperature limit beta --> infinity corresponds to the cutoff limit tau --> 0. As an example, we discuss some aspects of the axial model at finite temperature.
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It is demonstrated, contrary to various claims, that the phase shifts calculated via variational principles involving the Green function may exhibit anomalous behavior. These anomalies may appear in variational principles for the K matrix (Schwinger variational principle) of potential V, for (K-V) (Kohn-type and Newton variational principles), and other variational principles of higher order (Takatsuka-McKoy variational principle).
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The usefulness of the application of heuristic algorithms in the transportation model, first proposed by Garver, is analysed in relation to planning for the expansion of transmission systems. The formulation of the mathematical model and the solution techniques proposed in the specialised literature are analysed in detail. Starting with the constructive heuristic algorithm proposed by Garver, an extension is made to the problem of multistage planning for transmission systems. The quality of the solutions found by heuristic algorithms for the transportation model is analysed, as are applications in problems of planning transmission systems.
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The paper presents a constructive heuristic algorithm (CHA) for solving directly the long-term transmission-network-expansion-planning (LTTNEP) problem using the DC model. The LTTNEP is a very complex mixed-integer nonlinear-programming problem and presents a combinatorial growth in the search space. The CHA is used to find a solution for the LTTNEP problem of good quality. A sensitivity index is used in each step of the CHA to add circuits to the system. This sensitivity index is obtained by solving the relaxed problem of LTTNEP, i.e. considering the number of circuits to be added as a continuous variable. The relaxed problem is a large and complex nonlinear-programming problem and was solved through the interior-point method (IPM). Tests were performed using Garver's system, the modified IEEE 24-Bus system and the Southern Brazilian reduced system. The results presented show the good performance of IPM inside the CHA.
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The data of four networks that can be used in carrying out comparative studies with methods for transmission network expansion planning are given. These networks are of various types and different levels of complexity. The main mathematical formulations used in transmission expansion studies-transportation models, hybrid models, DC power flow models, and disjunctive models are also summarised and compared. The main algorithm families are reviewed-both analytical, combinatorial and heuristic approaches. Optimal solutions are not yet known for some of the four networks when more accurate models (e.g. The DC model) are used to represent the power flow equations-the state of the art with regard to this is also summarised. This should serve as a challenge to authors searching for new, more efficient methods.
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The formalism of supersymmetric quantum mechanics is used to determine trial functions in order to obtain eigenvalues for the Lennard-Jones (12, 6) potential from variational method. The superpotential obtained provides an effective potential which can be directly comparable to the original one.
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A branch and bound (B& B) algorithm using the DC model, to solve the power system transmission expansion planning by incorporating the electrical losses in network modelling problem is presented. This is a mixed integer nonlinear programming (MINLP) problem, and in this approach, the so-called fathoming tests in the B&B algorithm were redefined and a nonlinear programming (NLP) problem is solved in each node of the B& B tree, using an interior-point method. Pseudocosts were used to manage the development of the B&B tree and to decrease its size and the processing time. There is no guarantee of convergence towards global optimisation for the MINLP problem. However, preliminary tests show that the algorithm easily converges towards the best-known solutions or to the optimal solutions for all the tested systems neglecting the electrical losses. When the electrical losses are taken into account, the solution obtained using the Garver system is better than the best one known in the literature.
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Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)