Proximal methods for nonlinear programming: double regularization and inexact subproblems

This paper describes the first phase of a project attempting to construct an efficient general-purpose nonlinear optimizer using an augmented Lagrangian outer loop with a relative error criterion, and an inner loop employing a state-of-the art conjugate gradient solver. The outer loop can also employ double regularized proximal kernels, a fairly recent theoretical development that leads to fully smooth subproblems. We first enhance the existing theory to show that our approach is globally convergent in both the primal and dual spaces when applied to convex problems. We then present an extensive computational evaluation using the CUTE test set, showing that some aspects of our approach are promising, but some are not. These conclusions in turn lead to additional computational experiments suggesting where to next focus our theoretical and computational efforts.

Discontinuous Galerkin approximation of two-phase flows in heterogeneous porous media with discontinuous capillary pressures

We design and investigate a sequential discontinuous Galerkin method to approximate two-phase immiscible incompressible flows in heterogeneous porous media with discontinuous capillary pressures. The nonlinear interface conditions are enforced weakly through an adequate design of the penalties on interelement jumps of the pressure and the saturation. An accurate reconstruction of the total velocity is considered in the Raviart-Thomas(-Nedelec) finite element spaces, together with diffusivity-dependent weighted averages to cope with degeneracies in the saturation equation and with media heterogeneities. The proposed method is assessed on one-dimensional test cases exhibiting rough solutions, degeneracies, and capillary barriers. Stable and accurate solutions are obtained without limiters. (C) 2010 Elsevier B.V. All rights reserved.

Limits to phase resolution in matter-wave interferometry

We study the quantum dynamics of a two-mode Bose-Einstein condensate in a time-dependent symmetric double-well potential using analytical and numerical methods. The effects of internal degrees of freedom on the visibility of interference fringes during a stage of ballistic expansion are investigated varying particle number, nonlinear interaction sign and strength, as well as tunneling coupling. Expressions for the phase resolution are derived and the possible enhancement due to squeezing is discussed. In particular, the role of the superfluid-Mott insulator crossover and its analog for attractive interactions is recognized.

Fingerprint recognition system using hybrid matching techniques

With an increasing emphasis on the emerging automatic person identification application, biometrics based, especially fingerprint-based identification, is receiving a lot of attention. This research developed an automatic fingerprint recognition system (AFRS) based on a hybrid between minutiae and correlation based techniques to represent and to match fingerprint; it improved each technique individually. It was noticed that, in the hybrid approach, as a result of an improvement of minutiae extraction algorithm in post-process phase that combines the two algorithms, the performance of the minutia algorithm improved. An improvement in the ridge algorithm that used centre point in fingerprint instead of reference point was also observed. Experiments indicate that the hybrid technique performs much better than each algorithm individually.

Dynamic pacing strategies during the cycle phase of an ironman triathlon

Introduction: A nonlinear dynamic systems model has previously been proposed to explain pacing strategies employed during exercise.

Purpose: This study was conducted to examine the pacing strategies used under varying conditions during the cycle phase of an Ironman triathlon.

Methods: The bicycles of six well-trained male triathletes were equipped with SRM power meters set to record power output, cadence, speed, and heart rate. The flat, three-lap, out-and-back cycle course, coupled with relatively consistent wind conditions (17-30 km·h-1), enabled comparisons to be made between three consecutive 60-km laps and relative wind direction (headwind vs tailwind).

Results: Participants finished the cycle phase (180 km) with consistently fast performance times (5 h, 11 ± 2 min; top 10% of all finishers). Average power output (239 ± 25 to 203 ± 20 W), cadence (89 ± 6 to 82 ± 8 rpm), and speed (36.5 ± 0.8 to 33.1 ± 0.8 km·h-1) all significantly decreased with increasing number of laps (P < 0.05). These variables, however, were not significantly different between headwind and tailwind sections. The deviation (SD) in power output and cadence did not change with increasing number of laps; however, the deviations in torque (6.8 ± 1.6 and 5.8 ± 1.3 N·m) and speed (2.1 ± 0.5 and 1.6 ± 0.3 km·h-1) were significantly greater under headwind compared with tailwind conditions, respectively. The median power frequency tended to be lower in headwind (0.0480 ± 0.0083) compared with tailwind (0.0531 ± 0.0101) sections.

Conclusion: These data show evidence that a nonlinear dynamic pacing strategy is used by well-trained triathletes throughout various segments and conditions of the Ironman cycle phase. Moreover, an increased variation in torque and speed was found in the headwind versus the tailwind condition.

Stereo image matching using wavelet scale-space representation

A multi-resolution technique for matching a stereo pair of images based on translation invariant discrete multi-wavelet transform is presented. The technique uses the well known coarse to fine strategy, involving the calculation of matching points at the coarsest level with consequent refinement up to the finest level. Vector coefficients of the wavelet transform modulus are used as matching features, where modulus maxima defines the shift invariant high-level features (multiscale edges) with phase pointing to the normal of the feature surface. The technique addresses the estimation of optimal corresponding points and the corresponding 2D disparity maps. Illuminative variation that can exist between the perspective views of the same scene is controlled using scale normalization at each decomposition level by dividing the details space coefficients with approximation space and then using normalized correlation. The problem of ambiguity, explicitly, and occlusion, implicitly, is addressed by using a geometric topological refinement procedure and symbolic tagging.

Robust nonlinear distributed controller design for active and reactive power sharing in islanded microgrids

This paper presents a robust nonlinear distributed controller design for islanded operation of microgrids in order to maintain active and reactive power balance. In this paper, microgrids are considered as inverter-dominated networks integrated with renewable energy sources (RESs) and battery energy storage systems (BESSs), where solar photovoltaic generators act as RESs and plug-in hybrid electric vehicles as BESSs to supply power into the grid. The proposed controller is designed by using partial feedback linearization and the robustness of this control scheme is ensured by considering structured uncertainties within the RESs and BESSs. An approach for modeling the uncertainties through the satisfaction of matching conditions is also provided in this paper. The proposed distributed control scheme requires information from local and neighboring generators to communicate with each other and the communication among RESs, BESSs, and control centers is developed by using the concept of the graph theory. Finally, the performance of the proposed robust controller is demonstrated on a test microgrid and simulation results indicate the superiority of the proposed scheme under different operating conditions as compared to a linear-quadratic-regulator-based controller.

Observations on the nonlinear unloading behavior of advanced high strength steels

The unloading behavior was compared for three different steel grades: a dual-phase steel, a transformation-induced plasticity steel, and a twinning-induced plasticity steel. Steels that harden by phase transformation or deformation twinning exhibited a smaller component of microplastic strain during unloading and a smaller reduction in the chord modulus compared to the conventional hardening steel. As a result, unloading is closer to pure elastic unloading when the TRIP effect or TWIP effect is active.

A nonlinear adaptive backstepping approach for coordinated excitation and steam-valving control of synchronous generators

Steam-valving and excitation systems play an important role to maintain the transient stability of power systems with synchronous generators when power systems are subjected to large disturbances and sudden load changes. This paper presents a nonlinear adaptive backstepping approach for controlling excitation and steam-valving systems of synchronous generators. In this paper, the proposed excitation and steam-valving controllers are designed in a coordinated manner so that they can work under several and most severe operating conditions. Both excitation and steam-valving controllers are designed by considering some critical parameters as unknown. The effectiveness of the proposed coordinated control scheme is evaluated on a single machine infinite bus system under different operating conditions such as load changes and three-phase short circuit faults at the generator terminal. Finally, performance of the proposed scheme is compared to that of a similar nonlinear adaptive backstepping excitation controller without any coordination and simulation results demonstrate the superiority of the proposed one.

Nonlinear excitation control of synchronous generators based on adaptive backstepping method

n this paper, the design of a nonlinear excitation control of a synchronous generator is presented where the generator is connected to a single machine infinite bus (SMIB) system. An adaptive backstepping method is used to design the excitation controller with an objective of enhancing the overall dynamic stability of the SMIB system under different contingencies. In this paper, two types of contingencies are considered- i) unknown parameters and physical quantities during the controller design process and ii) controller performance evaluation under different system configurations such as three-phase short circuit faults. The adaption law, which is mainly based on the formulation of Lyapunov function, is used to estimate the unknown parameters which guarantee the convergence of different physical quantities of synchronous generators, e.g., the relative speed, terminal voltage, etc. The effectiveness of the proposed scheme is evaluated under different system configurations as mentioned in the second contingency and compared to that of an existing adaptive backstepping controller and a conventional power system stabilizer (PSS). Simulation results demonstrate the superiority of the proposed control scheme over the existing controllers.

Nonlinear adaptive excitation controller design for multimachine power systems

This paper presents a nonlinear adaptive excitation control scheme to enhance the dynamic stability of multimachine power systems. The proposed controller is designed based on the adaptive backstepping technique where the mechanical power input to the generators and the damping coefficient of each generator are considered as unknown. These unknown quantities are estimated through the adaption laws. The adaption laws are obtained from the formulation of Lyapunov functions which guarantee the convergence of different physical quantities of generators such as the relative speed, terminal voltage, and electrical power output. The proposed scheme is evaluated by applying a three-phase short-circuit fault at one of the key transmission lines in an 11-bus test power system and compared with an existing backstepping controller and conventional power system stabilizer (CPSS). Simulation results show that the proposed scheme is much more effective than existing controllers.

Nonlinear controller design for vehicle-to-grid systems with output LCL filters

This paper presents a nonlinear controller design for vehicle-to-grid (V2G) systems with LCL output filters. The V2G systems are modeled with LCL output filters in order to eliminate harmonics for improving power qualities and the nonlinear controller is designed based on the feedback linearization. The feasibility of using the appropriate feedback linearization approaches, either partial or exact, is also investigated through the feedback linearizability of V2G systems. In this paper, partial feedback linearization is used to design the controller with a capability of sharing both active and reactive power in V2G systems. The performance of the proposed controller controller is evaluated on a single-phase full-bridge converter-based V2G system with an LCL output filter and compared to that of without any filter. Simulation results clearly demonstrate the harmonic elimination capabilities of the proposed V2G structure with the proposed control scheme.

Improved Fault Location on Distribution Feeders Based on Matching During-Fault Voltage Sags

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Superfluid Fermi-Fermi mixture: Phase diagram, stability, and soliton formation

We study the phase diagram for a dilute Bardeen-Cooper-Schrieffer superfluid Fermi-Fermi mixture (of distinct mass) at zero temperature using energy densities for the superfluid fermions in one (1D), two (2D), and three (3D) dimensions. We also derive the dynamical time-dependent nonlinear Euler-Lagrange equation satisfied by the mixture in one dimension using this energy density. We obtain the linear stability conditions for the mixture in terms of fermion densities of the components and the interspecies Fermi-Fermi interaction. In equilibrium there are two possibilities. The first is that of a uniform mixture of the two components, the second is that of two pure phases of two components without any overlap between them. In addition, a mixed and a pure phase, impossible in 1D and 2D, can be created in 3D. We also obtain the conditions under which the uniform mixture is stable from an energetic consideration. The same conditions are obtained from a modulational instability analysis of the dynamical equations in 1D. Finally, the 1D dynamical equations for the system are solved numerically and by variational approximation (VA) to study the bright solitons of the system for attractive interspecies Fermi-Fermi interaction in 1D. The VA is found to yield good agreement to the numerical result for the density profile and chemical potential of the bright solitons. The bright solitons are demonstrated to be dynamically stable. The experimental realization of these Fermi-Fermi bright solitons seems possible with present setups.

Nonlinear Schrodinger equation with power-law confining potential

Critical limits of a stationary nonlinear three-dimensional Schrodinger equation with confining power-law potentials (similar to r(alpha)) are obtained using spherical symmetry. When the nonlinearity is given by an attractive two-body interaction (negative cubic term), it is shown how the maximum number of particles N-c in the trap increases as alpha decreases. With a negative cubic and positive quintic terms we study a first order phase transition, that occurs if the strength g(3) of the quintic term is less than a critical value g(3c). At the phase transition, the behavior of g(3c) with respect to alpha is given by g(3c)similar to 0.0036+0.0251/alpha+0.0088/alpha(2).