Residual Modes Research Articles

Neumann boundary control of a coupled transport-diffusion system with boundary observation

We study the Neumann boundary stabilization problem of a coupled transport-diffusion system in the case where the observation is done at the boundary. In the recent paper of Sano and Nakagiri [H. Sano, S. Nakagiri, Stabilization of a coupled transport-diffusion system with boundary input, J. Math. Anal. Appl. 363 (2010) 57–72], we treated the stabilization problem for the case with Neumann boundary control and distributed observation. The novelty of this paper is the formulation of the boundary observation equation in a Hilbert space. We have an interesting result of its being expressed by using an A1γ-bounded operator with γ∈(12,1). Moreover, it is shown that a reduced-order model with a finite-dimensional state variable is controllable and observable. This means that one can always construct a finite-dimensional stabilizing controller for the original infinite-dimensional system by using a residual mode filter (RMF) approach.

How predictable is the northern hemisphere summer upper-tropospheric circulation?

The retrospective forecast skill of three coupled climate models (NCEP CFS, GFDL CM2.1, and CAWCR POAMA 1.5) and their multi-model ensemble (MME) is evaluated, focusing on the Northern Hemisphere (NH) summer upper-tropospheric circulation along with surface temperature and precipitation for the 25-year period of 1981–2005. The seasonal prediction skill for the NH 200-hPa geopotential height basically comes from the coupled models’ ability in predicting the first two empirical orthogonal function (EOF) modes of interannual variability, because the models cannot replicate the residual higher modes. The first two leading EOF modes of the summer 200-hPa circulation account for about 84% (35.4%) of the total variability over the NH tropics (extratropics) and offer a hint of realizable potential predictability. The MME is able to predict both spatial and temporal characteristics of the first EOF mode (EOF1) even at a 5-month lead (January initial condition) with a pattern correlation coefficient (PCC) skill of 0.96 and a temporal correlation coefficient (TCC) skill of 0.62. This long-lead predictability of the EOF1 comes mainly from the prolonged impacts of El Nino-Southern Oscillation (ENSO) as the EOF1 tends to occur during the summer after the mature phase of ENSO. The second EOF mode (EOF2), on the other hand, is related to the developing ENSO and also the interdecadal variability of the sea surface temperature over the North Pacific and North Atlantic Ocean. The MME also captures the EOF2 at a 5-month lead with a PCC skill of 0.87 and a TCC skill of 0.67, but these skills are mainly obtained from the zonally symmetric component of the EOF2, not the prominent wavelike structure, the so-called circumglobal teleconnection (CGT) pattern. In both observation and the 1-month lead MME prediction, the first two leading modes are accompanied by significant rainfall and surface air temperature anomalies in the continental regions of the NH extratropics. The MME’s success in predicting the EOF1 (EOF2) is likely to lead to a better prediction of JJA precipitation anomalies over East Asia and the North Pacific (central and southern Europe and western North America).

Dynamical decompactification and three large dimensions

We study string gas dynamics in the early universe and seek to realize the Brandenberger - Vafa mechanism - a goal that has eluded earlier works - that singles out three or fewer spatial dimensions as the number which grow large cosmologically. Considering wound string interactions in an impact parameter picture, we show that a strong exponential suppression in the interaction rates for d > 3 spatial dimensions reflects the classical argument that string worldsheets generically intersect in at most four spacetime dimensions. This description is appropriate in the early universe if wound strings are heavy - wrapping long cycles - and diluted. We consider the dynamics of a string gas coupled to dilaton-gravity and find that a) for any number of dimensions the universe generically stays trapped in the Hagedorn regime and b) if the universe fluctuates to a radiation regime any residual winding modes are diluted enough so that they freeze-out in d > 3 large dimensions while they generically annihilate for d = 3. In this sense the Brandenberger-Vafa mechanism is operative.

A general mixed boundary model reduction method for component mode synthesis

A classic issue in component mode synthesis (CMS) methods is the choice for fixed or free boundary conditions at the interface degrees of freedom (DoF) and the associated vibration modes in the components reduction base. In this paper, a novel mixed boundary CMS method called the "Mixed Craig-Bampton" method is proposed. The method is derived by dividing the substructure DoF into a set of internal DoF, free interface DoF and fixed interface DoF. To this end a simple but effective scheme is introduced that, for every pair of interface DoF, selects a free or fixed boundary condition for each DoF individually. Based on this selection a reduction basis is computed consisting of vibration modes, static constraint modes and static residual flexibility modes. In order to assemble the reduced substructures a novel mixed assembly procedure is developed. It is shown that this approach leads to relatively sparse reduced matrices, whereas other mixed boundary methods often lead to full matrices. As such, the Mixed Craig-Bampton method forms a natural generalization of the classic Craig-Bampton and more recent Dual Craig-Bampton methods. Finally, the method is applied to a finite element test model. Analysis reveals that the proposed method has comparable or better accuracy and superior versatility with respect to the existing methods.

Low-splicing-loss polarization-maintaining photonic-crystal-fiber-based Sagnac interferometer and its cladding-mode effect

A low-splicing-loss polarization-maintaining photonic-crystal-fiber (PMPCF)-based optical fiber Sagnac interferometer (OFSI) and its cladding-mode effect are demonstrated experimentally and analytically. An OFSI with minimum splicing loss of about 2.6 dB is achieved. The weak cladding modes induced by residual mode field diameter mismatch at the fusion splice cause a filtering effect on the transmission spectra of the OFSIs. This is especially noticeable for short length PMPCF-based OFSIs. Experimental results show that the relatively maximum ripple fluctuation induced by the cladding mode can reach 5.7%. The cladding-mode effect can be eliminated by slightly bending the PMPCF, but this introduces additional insertion loss.

SIMTON: A Simulator for Transparent Optical Networks

In this article we present a software to simulate Transparent Optical Networks (SIMTON). SIMTON is an eventdriven simulation software implemented in C++ which takes into account optical device characteristics for the evaluation of network blocking probability in wavelength routed transparent optical networks. The simulator uses a physical layer model that considers the following effects: device losses, fiber attenuation, four wave mixing, residual chromatic dispersion and polarization mode dispersion in optical fibers, gain saturation in optical amplifiers (Erbium Doped Fiber Amplifier), dependence of the amplified spontaneous emission noise with the input power in EDFA, in-band crosstalk in optical switches, and source spontaneous emission noise of the laser transmitter. By using SIMTON it is possible to adjust the parameters of the optical devices, as well as to choose the routing and wavelength assignment algorithm. Moreover, the tool has a graphical interface. We also present some examples of network analysis results obtained from SIMTON.

Characterisation of residual stress and interface degradation in TBCs by photo-luminescence piezo-spectroscopy

Residual stress in the TGO in two different TBC systems, one with a Pt aluminide (β structure) bond coat and another with a Pt diffusion (γγ′ structure) bond coat, were studied using photo-luminescence piezo-spectroscopy (PLPS). The luminescence spectra and TGO morphology were investigated progressively with thermal cycling at 1135 °C. The two TBC systems were found to have distinctly different TGO residual stresses and different failure modes. Several stress relaxation mechanisms were found to be operative in the Pt aluminide system, while no stress relaxation was evident in the Pt diffusion system until close to the end of life (spallation). Luminescence spectral shape evolution has been quantitatively analysed and correlated with TBC system degradation processes. Both TBC systems showed clear spectral shape changes as a result of the formation of interface cracks when they reached approximately 75% lifetime. Characteristic spectral shape changes in response to different types of interface crack were demonstrated experimentally. The correlation between spectral shape evolution and interface degradation opens a new avenue for studies of degradation and lifetime assessment of TBCs.

Conversion of a TEM_10 beam into two nearly Gaussian beams

To achieve high output power and/or high efficiencies, laser systems are often designed to operate with either high-order or multiorder transverse modes. This comes at the expense of beam quality. Herein, a technique for converting the two lobes of a higher-order (Hermite-Gaussian TEM(10)) beam into two TEM(00) beams is discussed. It is shown that nearly 94% of the power in a single lobe of the TEM(10) beam spatially overlaps an appropriately chosen TEM(00) beam. Beam quality (defined by the M(2) beam quality factor) is increased by separating the two TEM(10) lobes with an edge aperture. A single-mode optical fiber can be used as a spatial filter to eliminate residual higher-order mode content. This study suggests that more than 90% of the power in a TEM(10) beam can be converted into two separate TEM(00) beams.

Optimal piezoelectric actuator and sensor location for active vibration control, using genetic algorithm

This paper deals with the optimization of piezoelectric actuators and sensors locations for active vibration control. Two modified optimization criteria are used, ensuring good observability or controllability of the structure, and considering residual modes to limit the spillover effect. Two optimization variables are considered for each piezoelectric device: the location of its center and its orientation. Genetic algorithms are used to find the optimal configurations. Several simulations are presented for a simply supported plate.

Fuzzy State-Space Modeling and Robust Observer-Based Control Design for Nonlinear Partial Differential Systems

In this paper, a robust fuzzy control design is proposed for the stabilization of nonlinear partial differential systems (NPDSs). Based on Galerkin's method, a Takagi-Sugeno (T-S) fuzzy PDS is first proposed to model an NPDS. Then, the T-S fuzzy PDS can be represented by a finite-dimensional T-S fuzzy subsystem in controlled mode and a coupled infinite-dimensional T-S fuzzy subsystem in residual mode. Therefore, the NPDS can be partitioned into a finite-dimensional T-S fuzzy slow state-space subsystem to be controlled and a coupled infinite-dimensional fast residual subsystem to be tolerated. Based on the small-gain theorem, a robust fuzzy observer-based controller is developed to tolerate the coupled residual subsystem to asymptotically stabilize the NPDS. Furthermore, based on the dissipative theory, an Hinfin control design is proposed to attenuate the effects of external disturbances and measurement noises on the robust stabilization of NPDSs. The MATLAB linear matrix inequality toolbox can be employed to efficiently solve the optimal Hinfin fuzzy observer-based control design problem of NPDSs. Finally, a simulation example is given to illustrate the design procedure and confirm the performance of the proposed robust fuzzy observer-based control method for the perturbative NPDSs.

Stabilization of a coupled transport-diffusion system with boundary input

We consider the problem of stabilizing a coupled transport-diffusion system with boundary input. The system is described by two linear transport-diffusion equations and is not asymptotically stable. In order to stabilize the system with boundary input, sensor influence functions are assumed to be located at interior of the domain. First, we formulate the system as an evolution equation with unbounded output operators in a Hilbert space, using variable transformation. Next, we derive a reduced-order model with a finite-dimensional state variable for the infinite-dimensional system. Then, a stabilizing controller is constructed for the reduced-order model under an additional assumption. It is shown that the finite-dimensional controller together with a residual mode filter plays a role of a finite-dimensional stabilizing controller for the original infinite-dimensional system, if the order of the residual mode filter is chosen sufficiently large. Finally, the validity of the design method is demonstrated through a numerical simulation.

H ∞ Control with μ-analysis of a Piezoelectric Actuated Plate

This paper presents the development of a multimodal H∞controller for piezoelectric actuated plates designed to simultaneously suppress vibrational components of the first two modes. The controller is developed for a reduced structural model. The closed-loop control scheme is subject to both uncertainties due to control and observation spillover in the unmodeled residual modes and to parametric errors in the structural model. The closed-loop stability and performance robustness is analyzed using μ-analysis, and numerical investigations indicate that the controller tolerates uncertainties of significant size.

Detailed Theoretical and Experimental Characterization of 10 Gb/s Clock Recovery Using a Q-Switched Self-Pulsating Laser

A detailed characterization of the clock recovery properties of a self-pulsating, three-section distributed feedback laser is presented by directly comparing simulation and experimental results for the dependence of the RMS timing jitter of the recovered clock signal on important properties of the input signal. These properties include the duty cycle, peak power, extinction ratio, state-of-polarization, optical signal-to-noise ratio (OSNR), and waveform distortion due to residual group velocity dispersion and polarization mode dispersion. The permissible range for each of these is identified in terms of the RMS timing jitter of the recovered clock signal being less than 2 ps. In particular, the self-pulsating laser is effective for input signals degraded by amplified spontaneous emission noise as it provides this level of jitter performance for input OSNRs larger than 8.8 dB (0.1 nm noise bandwidth).

Effects of correction by heating/pressing on mechanical behavior of steel bridge pier

A series of experiments was conducted in order to elucidate effects of correction by heating/pressing on mechanical behavior of steel bridge piers. Local buckling deformation of specimens due to loading considering the situation of an earthquake was corrected by heating/pressing, with or without water-cooling. Some out-of-plane deformations were inevitably left to avoid cracking in the welds. This geometric imperfection was defined as residual imperfection. After the correction, the same loading experiment was conducted. From the results, no deterioration was confirmed in mechanical properties of the steel even with water-cooling only if heating temperature was kept below A1 transformation temperature. Although it is ideal to have local buckling deformation repaired within the allowance of initial deflection in correction by heating/pressing, it was elucidated that making the residual imperfection mode opposite to local buckling mode was reasonable for guarantee of the maximum load of the corrected structure.

Correction of complex lower extremity deformities with the use of the Ilizarov -Taylor spatial frame

We evaluated the effectiveness of the Taylor spatial frame (Smith & Nephew, Memphis, TN, USA) in the treatment of complex lower extremity deformities. The Taylor spatial frame (TSF) was applied to 29 bone segments of 25 patients (12 females, 13 males; mean age 17 years). Indications for the TSF were congenital disorders (n=12), rickets (n=6), physeal injuries (n=4), stiff nonunions (n=3), malunions (n=3), and sequela from septic arthritis of the knee (n=1). Applications involved the tibia (n=15), femur (n=9), foot (n=4), and knee (n=1) with (n=24) or without (n=5) osteotomies. Following acute correction with the use of the TSF and internal osteosynthesis by plating or nailing, the fixator was removed in six cases. The chronic mode was used in six cases who underwent acute correction. The remaining deformities were gradually corrected using the "total residual mode". The follow-up period ranged from eight months to 42 months (mean 29 months). The mean duration of external fixator was 24.5 weeks (range 18 to 37 weeks) in 13 tibial and five femoral segments. In all cases, correction was applied until the mechanical axis reached normal limits. Complete consolidation was achieved in all osteotomized segments, including three cases of nonunion. A plantigrade foot was obtained in all foot deformities. Recurrence was seen in one case in which knee contracture and subluxation were treated with soft tissue distraction without osteotomy. The Taylor spatial frame is a safe and practical method with excellent results in the treatment of nonunions and deformities complicated especially by translation and rotation providing correct clinical data are derived and used.

Trace gas measurements using optically resonant cavities and quantum cascade lasers operating at room temperature

Achieving the high sensitivity necessary for trace gas detection in the midinfrared molecular fingerprint region generally requires long absorption path lengths. In addition, for wider application, especially for field measurements, compact and cryogen free spectrometers are definitely preferable. An alternative approach to conventional linear absorption spectroscopy employing multiple pass cells for achieving high sensitivity is to combine a high finesse cavity with thermoelectrically (TE) cooled quantum cascade lasers (QCLs) and detectors. We have investigated the sensitivity limits of an entirely TE cooled system equipped with an ∼0.5 m long cavity having a small sample volume of 0.3 l. With this spectrometer cavity enhanced absorption spectroscopy employing a continuous wave QCL emitting at 7.66 μm yielded path lengths of 1080 m and a noise equivalent absorption of 2×10−7 cm−1 Hz−1/2. The molecular concentration detection limit with a 20 s integration time was found to be 6×108 molecules/cm3 for N2O and 2×109 molecules/cm3 for CH4, which is good enough for the selective measurement of trace atmospheric constituents at 2.2 mbar. The main limiting factor for achieving even higher sensitivity, such as that found for larger volume multi pass cell spectrometers, is the residual mode noise of the cavity. On the other hand the application of TE cooled pulsed QCLs for integrated cavity output spectroscopy and cavity ring-down spectroscopy (CRDS) was found to be limited by the intrinsic frequency chirp of the laser. Consequently the accuracy and advantage of an absolute internal absorption calibration, in theory inherent for CRDS experiments, are not achievable.

Large-displacement Closed-loop Control of Variable Area Electrostatic Actuation for Membrane Reflectors

Membrane mirrors may be attractive in some space applications where light weight, deployability, and conformability are desired. This article investigates large-displacement closed-loop control of electrostatically driven mirrors being used in focusing and steering of laser beams. The required transient response characteristics for the membrane response are achieved using a variable area, constant voltage actuation method, which may be advantageous in some applications. Our previous work on variable area control was restricted to membrane deflections not exceeding 1/3 (the available gap size), and assumed that a continuous area variation was available. In this article, the controller design is extended to enable deflections approaching the entire available gap size, which would help to bring down the voltage requirement for a prescribed deflection range. A Lyapunov function-based approach is used here along with a fully nonlinear dynamic model. Although a single-mode lumped parameter model is used, a feedforward technique to compensate for a class of residual modes is investigated in this paper. Also studied in this article is the use of a Lyapunov function-based framework to guide the design of a controller to handle step-wise/discrete area changes. A dynamic observer based on quad-cell beam-position detector measurements and a fully nonlinear plant model is also studied. The article discusses numerical simulation results, which show that the controllers under study are fairly successful at providing closed-loop deflections approaching the full gap size at the required bandwidth.

Characteristics of Daily Position Time Series from the Hong Kong Gps Fiducial Network

AbstractCharacteristics of daily position time series from January 2001 to August 2007 at 12 GPS stations in the Hong Kong GPS fiducial network are investigated. A spatial filtering algorithm based on principal component analysis is employed to remove the common mode errors from the daily position time series. The noise characteristics of the filtered position time series are assessed by the method of maximum likelihood estimation. Contributions from atmospheric, nontidal oceanic, snow and soil moisture mass loading are evaluated. The results indicate that spatial filtering is an effective way to improve the precision of GPS position time series. The common mode errors have strong seasonal variations. The about 3 mm annual vertical variation of the common mode errors can be explained by the joint contribution of the seasonal surface mass redistributions. After removing these surface mass loading effects, the residual common mode errors are highly related to the higher‐order ionospheric effects. The noise in the filtered position time series can be described as a combination of variable white noise and flicker noise. The velocity uncertainties are about 2~6 times larger if only variable white noise is assumed. The maximum relative horizontal velocity between the sites is 1.5 mm/yr, which indicates some local fault activities. In addition, there are obvious 1~2 mm local seasonal signals in the filtered position time series of some of the sites. The residual scatters of all filtered time series also show strong seasonal characteristics.

Between ‘Market’ and ‘Welfare’: Rent Restructuring Policy in the Housing Association Sector, England

This paper empirically evaluates the market and welfare impacts of rent restructuring policy in the housing association (RSL) sector. The focus is on the financial viability of housing associations in the north of England, the affordability problems of tenants in the south, and the changes of turnover rates of RSL tenancies that have resulted. Using data from the Regulatory and Statistical Returns and the CORE (COntinuous REcording) from 2001/02 to 2005/06, the analysis shows that the ‘market’ component of the rent formula plays a more substantial role in affecting the RSL rent levels despite the ‘welfare’ measures in the policy—the greater emphasis on local earnings, the restriction of annual rent increase and the imposition of rent ceilings. Given that social housing in England is essentially a residual mode of provision, it is argued that a more flexible approach in balancing these two conflicting principles in rent setting is needed.

Modal-based model reduction and vibration control for uncertain piezoelectric flexible structures

In piezoelectric flexible structures, the contribution of vibration modes to the dynamic response of system may change with the location of piezoelectric actuator patches, which means that the ability of actuators to control vibration modes should be taken into account in the development of modal reduction model. The spatial H2 norm of modes, which serves as a measure of the intensity of modes to system dynamical response, is used to pick up the modes included in the reduction model. Based on the reduction model, the paper develops the state-space representation for uncertain flexible structures with piezoelectric material as non-collocated actuators/sensors in the modal space, taking into account uncertainties due to modal parameters variation and unmodeled residual modes. In order to suppress the vibration of the structure, a dynamic output feedback control law is designed by simultaneously considering the conflicting performance specifications, such as robust stability, transient response requirement, disturbance rejection, actuator saturation constraints. Based on linear matrix inequality, the vibration control design is converted into a linear convex optimization problem. The simulation results show how the influence of vibration modes on the dynamical response of structure varies with the location of piezoelectric actuators, why the uncertainties should be considered in the reductiom model to avoid exciting high-frequency modes in the non-collcated vibration control, and the possiblity that the conflicting performance specifications are dealt with simultaneously.