Three-body problem, its Lagrangian points and how to exploit them using an alternative transfer to L4 and L5

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Revisiting the S-matrix approach to the open superstring low energy effective lagrangian

The conventional S-matrix approach to the (tree level) open string low energy effective lagrangian assumes that, in order to obtain all its bosonic alpha'(N) order terms, it is necessary to know the open string (tree level) (N + 2)-point amplitude of massless bosons, at least expanded at that order in alpha'. In this work we clarify that the previous claim is indeed valid for the bosonic open string, but for the supersymmetric one the situation is much more better than that: there are constraints in the kinematical bosonic terms of the amplitude (probably due to Spacetime Supersymmetry) such that a much lower open superstring n-point amplitude is needed to find all the alpha'(N) order terms. In this 'revisited' S-matrix approach we have checked that, at least up to alpha'(4) order, using these kinematical constraints and only the known open superstring 4-point amplitude, it is possible to determine all the bosonic terms of the low energy effective lagrangian. The sort of results that we obtain seem to agree completely with the ones achieved by the method of BPS configurations, proposed about ten years ago. By means of the KLT relations, our results can be mapped to the NS-NS sector of the low energy effective lagrangian of the type II string theories implying that there one can also find kinematical constraints in the N -point amplitudes and that important informations can be inferred, at least up to alpha'(4) order, by only using the (tree level) 4-point amplitude.

Lagrangian heuristic for a class of the generalized assignment problems

A Lagrangian based heuristic is proposed for many-to-many assignment problems taking into account capacity limits for task and agents. A modified Lagrangian bound studied earlier by the authors is presented and a greedy heuristic is then applied to get a feasible Lagrangian-based solution. The latter is also used to speed up the subgradient scheme to solve the modified Lagrangian dual problem. A numerical study is presented to demonstrate the efficiency of the proposed approach. (C) 2010 Elsevier Ltd. All rights reserved.

A Lagrangian relaxation approach to a coupled lot-sizing and cutting stock problem

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A decentralized approach for optimal reactive power dispatch using a Lagrangian decomposition method

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Bounds on contact interactions from LEP1 data and high-Q2 HERA events

A contact four-fermion interaction between light quarks and electrons has been evoked as a possible explanation for the excess of events observed by HERA at high-Q2. We explore the 1-loop effects of such interaction in Γ(Z0 → e+e-) measured at LEP and impose strong bounds on the lower limit of the effective scale. Our results are able to discard some of the contact interactions as possible explanation for the HERA events. © 1997 Elsevier Science B.V.

Limits on anomalous couplings from higgs boson production at the fermilab tevatron collider

We estimate the attainable limits on the coefficients of dimension-6 operators from the analysis of Higgs boson phenomenology, in the framework of a SU L(2) × U y(1) gauge-invariant effective Lagrangian. Our results, based on the data sample already collected by the collaborations at Fermilab Tevatron, show that the coefficients of Higgs-vector boson couplings can be determined with unprecedented accuracy. Assuming that the coefficients of all blind operators are of the same magnitude, we are also able to impose mere restrictive bounds on the anomalous vector-boson triple couplings than the present limit from double gauge boson production at the Tevatron collider.

Bounds on Higgs and gauge-boson interactions from LEP2 data

We derive bounds on Higgs and gauge-boson anomalous interactions using the LEP2 data on the production of three photons and photon pairs in association with hadrons. In the framework of SU(2)L ⊗ U(1)Y effective Lagrangians, we examine all dimension-six operators that lead to anomalous Higgs interactions involving γ and Z. The search for Higgs boson decaying to γγ pairs allow us to obtain constrains on these anomalous couplings that are comparable with the ones originating from the analysis of pp̄ collisions at the Tevatron. Our results also show that if the coefficients of all blind operators are assumed to have the same magnitude, the indirect constraints on the anomalous couplings obtained from this analysis, for Higgs masses MH ≲ 140 GeV, are more restrictive than the ones coming from the W+W- production. © 1998 Elsevier Science B.V. All rights reserved.

Testing anomalous Higgs couplings in triple photon production at the Tevatron collider

We derive bounds on Higgs and gauge-boson anomalous interactions using the CDF data for the process pp̄ → γγγ + X. We use a linearly realized SU L(2) X U Y(1) invariant effective Lagrangian to describe the bosonic sector of the Standard Model, keeping the fermionic couplings unchanged. All dimension-six operators that lead to anomalous Higgs interactions involving γ and Z are considered. We also show the sensitivity that can be achieved for these couplings at Fermilab Tevatron upgrades. © 1998 Published by Elsevier Science B.V. All rights reserved.

Three jet events and new strong couplings at LEP and NLC

We study the effects of new dimension-6 operators, resulting from a general SU(3)C ⊗ SU(2)L ⊗ U(1)Y invariant effective Lagrangian, on three jet production at LEP and at the Next Linear Collider. Contributions to the total event rate and to some event shape variables are analysed in order to establish bounds on these operators. © 1999 Elsevier Science B.V. All rights reserved.

An active/reactive predispatch model incorporating ramp rate constraints solved by dual decomposition/lagrangian relaxation

The Predispatch model (PD) calculates a short-term generation policy for power systems. In this work a PD model is proposed that improves two modeling aspects generally neglected in the literature: voltage/reactive power constraints and ramp rate constraints for generating units. Reactive power constraints turn the PD into a non-linear problem and the ramp rate constraints couple the problem dynamically in time domain. The solution of the PD is turned into a harder task when such constraints are introduced. The dual decomposition/ lagrangian relaxation technique is used in the solution approach for handing dynamic constraints. As a result the PD is decomposed into a series of independent Optimal Power Flow (FPO) sub problems, in which the reactive power is represented in detail. The solution of the independent FPO is coordinated by means of Lagrange multipliers, so that dynamic constraints are iteratively satisfied. Comparisons between dispatch policies calculated with and without the representation of ramp rate constraints are performed, using the IEEE 30 bus test system. The results point-out the importance of representing such constraints in the generation dispatch policy. © 2004 IEEE.

Analysis of numeric conditioning of Hessian matrix of Lagrangian via singular values

This paper presents an analyze of numeric conditioning of the Hessian matrix of Lagrangian of modified barrier function Lagrangian method (MBFL) and primal-dual logarithmic barrier method (PDLB), which are obtained in the process of solution of an optimal power flow problem (OPF). This analyze is done by a comparative study through the singular values decomposition (SVD) of those matrixes. In the MBLF method the inequality constraints are treated by the modified barrier and PDLB methods. The inequality constraints are transformed into equalities by introducing positive auxiliary variables and are perturbed by the barrier parameter. The first-order necessary conditions of the Lagrangian function are solved by Newton's method. The perturbation of the auxiliary variables results in an expansion of the feasible set of the original problem, allowing the limits of the inequality constraints to be reached. The electric systems IEEE 14, 162 and 300 buses were used in the comparative analysis. ©2007 IEEE.

Interaction between wave and coastal structure: Validation of two lagrangian numerical models with experimental results marine 2011

Numerical modeling of the interaction among waves and coastal structures is a challenge due to the many nonlinear phenomena involved, such as, wave propagation, wave transformation with water depth, interaction among incident and reflected waves, run-up / run-down and wave overtopping. Numerical models based on Lagrangian formulation, like SPH (Smoothed Particle Hydrodynamics), allow simulating complex free surface flows. The validation of these numerical models is essential, but comparing numerical results with experimental data is not an easy task. In the present paper, two SPH numerical models, SPHysics LNEC and SPH UNESP, are validated comparing the numerical results of waves interacting with a vertical breakwater, with data obtained in physical model tests made in one of the LNEC's flume. To achieve this validation, the experimental set-up is determined to be compatible with the Characteristics of the numerical models. Therefore, the flume dimensions are exactly the same for numerical and physical model and incident wave characteristics are identical, which allows determining the accuracy of the numerical models, particularly regarding two complex phenomena: wave-breaking and impact loads on the breakwater. It is shown that partial renormalization, i.e. renormalization applied only for particles near the structure, seems to be a promising compromise and an original method that allows simultaneously propagating waves, without diffusion, and modeling accurately the pressure field near the structure.

Optimal low cost transfer to L4 and L5 lagrangian points

Lagrangian points L4 and L5 lie at 60 degrees ahead of and behind Moon in its orbit with respect to the Earth. Each one of them is a third point of an equilateral triangle with the base of the line defined by those two bodies. These Lagrangian points are stable for the Earth-Moon mass ratio. Because of their distance electromagnetic radiations from the Earth arrive on them substantially attenuated. As so, these Lagrangian points represent remarkable positions to host astronomical observatories. However, this same distance characteristic may be a challenge for periodic servicing mission. In this work, we introduce a new low-cost orbital transfer strategy that opportunistically combine chaotic and swing-by transfers to get a very efficient strategy that can be used for servicing mission on astronomical mission placed on Lagrangian points L4 or L5. This strategy is not only efficient with respect to thrust requirement, but also its time transfer is comparable to others known transfer techniques based on time optimization. Copyright ©2010 by the International Astronautical Federation. All rights reserved.

Optimal low-cost transfer to L4 and L5 lagrangian points based on G-family of periodic orbits

An alternative transfer strategy to send spacecrafts to stable orbits around the Lagrangian equilibrium points L4 and L5 based in trajectories derived from the periodic orbits around LI is presented in this work. The trajectories derived, called Trajectories G, are described and studied in terms of the initial generation requirements and their energy variations relative to the Earth through the passage by the lunar sphere of influence. Missions for insertion of spacecrafts in elliptic orbits around L4 and L5 are analysed considering the Restricted Three-Body Problem Earth- Moon-particle and the results are discussed starting from the thrust, time of flight and energy variation relative to the Earth. Copyright© (2012) by the International Astronautical Federation.