Local Convergence of the Lavrentiev Method for the Cauchy Problem via a Carleman Inequality

The purpose is to perform a sharp analysis of the Lavrentiev method applied to the regularization of the ill-posed Cauchy problem, set in the Steklov-Poincaré variational framework. Global approximation results have been stated earlier that demonstrate that the Lavrentiev procedure yields a convergent strategy. However, no convergence rates are available unless a source condition is assumed on the exact Cauchy solution. We pursue here bounds on the approximation (bias) and the noise propagation (variance) errors away from the incomplete boundary where instabilities are located. The investigation relies on a Carleman inequality that enables enhanced local convergence rates for both bias and variance errors without any particular smoothness assumption on the exact solution. These improved results allows a new insight on the behavior of the Lavrentiev solution, look similar to those established for the Quasi-Reversibility method in [Inverse Problems 25, 035005, 2009]. There is a case for saying that this sort of ??super-convergence?? is rather inherent to the nature of the Cauchy problem and any reasonable regularization procedure would enjoy the same locally super-convergent behavior.     

Modeling and experimental investigation for electrolytic corrosion prevention in high frequency micro EDM using deionized water

The characteristics of the prevention of electrolytic corrosion during micro electrical discharge machining (EDM) using deionized water and high frequency bipolar pulse were investigated. Electrolytic corrosion during micro EDM using deionized water was analyzed using an equivalent electrical circuit based on the electrical double layer theory. Based on the analysis and experimental verification, a narrow positive pulse duration should be provided to the workpiece to prevent corrosion. A negative voltage with zero average applied voltage (V_{avg, app}) is also essential for this purpose. If V_{avg, app} is positive or negative, electrolytic corrosion occurs on the workpiece or tool, respectively. Micro holes and 3D structures without corrosion were successfully fabricated using a high frequency bipolar pulse with a pulse duration of 0.2?μs and a period of 1?μs, as well as V_{avg, app}?=?0?V.     

Severe motor disability affects functional cortical integration in the context of brain-computer interface (BCI) use

The purpose of this study was to investigate cortical interaction between brain regions in people with and without severe motor disability during brain-computer interface (BCI) operation through coherence analysis. Eighteen subjects, including six patients with cerebral palsy (CP) and three patients with amyotrophic lateral sclerosis (ALS), participated. The results showed (1) the existence of BCI performance difference caused by severe motor disability; (2) different coherence patterns between participants with and without severe motor disability during BCI operation and (3) effects of motor disability on cortical connections varying in the brain regions for the different frequency bands, indicating reduced cortical differentiation and specialisation. Participants with severe neuromuscular impairments, as compared with the able-bodied group, recruited more cortical regions to compensate for the difficulties caused by their motor disability, reflecting a less efficient operating strategy for the BCI task. This study demonstrated that coherence analysis can be applied to examine the ways cortical networks cooperate with each other during BCI tasks. PRACTITIONER SUMMARY: Few studies have investigated the electrophysiological underpinnings of differences in BCI performance. This study contributes by assessing neuronal synchrony among brain regions. Our findings revealed that severe motor disability causes more cortical areas to be recruited to perform the BCI task, indicating reduced cortical differentiation and specialisation.     

A 231-MHz, 2.18-mW 32-bit Logarithmic Arithmetic Unit for Fixed-Point 3-D Graphics System

A 32-bit fixed-point logarithmic arithmetic unit is proposed for the possible application to mobile three-dimensional (3-D) graphics system. The proposed logarithmic arithmetic unit performs division, reciprocal, square-root, reciprocal-square-root and square operations in two clock cycles and powering operation in four clock cycles. It can program its number range for accurate computation flexibility of 3-D graphics pipeline and eight -region piecewise linear approximation model for logarithmic and antilogarithmic conversion to reduce the operation error under 0.2%. Its test chip is implemented by 1-poly 6-metal 0.18-mum CMOS technology with 9-k gates. It operates at the maximum frequency of 231 MHz and consumes 2.18 mW at 1.8-V supply     

Computation of unsteady viscous flow and aeroacoustic noise of cross flow fans

Time-accurate viscous flow solutions are sought for the prediction of unsteady flow characteristics and associated aeroacoustic blade tonal noise of a cross flow fan. The two-dimensional incompressible Navier-Stokes equations in a moving coordinate are time-accurately solved by an unstructured finite-volume method on triangular meshes, and a sliding mesh technique is utilized at the interface between the domain rotating with blades and the stationary one for allowing the unsteady interactions. An accuracy assessment of the present method is made by comparing the fan performances with experimental data for a rotational speed at 1000 rpm and the Reynolds number 5300 based on blade tip speed and chord length. With the computed unsteady viscous flow solutions, sound pressure is predicted using Curle’s equation and narrow-band noise characteristics of three impellers with a uniform and two random pitch (type-A and -B) blades are compared by their sound pressure level spectra. Also, the frequency modulations of the blade passing frequency noise by random pitch fans are discussed.     

Performance of traveling-wave electroabsorption modulators depending on microwave properties of waveguides calculated using the FDTD method

We present a method to analyze electrical and optical characteristics of traveling-wave electroabsorption modulators (TW-EAMs) using the finite-difference time-domain method. We consider the interaction between electromagnetic fields and optical powers in waveguides in time domain to model electrical and optical behaviors of TW-EAMs. The effects of microwave properties of waveguides on modulation response and output optical power of TW-EAMs are analyzed by the proposed method. The characteristic impedance of TW-EAMs is more important than microwave index to obtain large modulation bandwidth of TW-EAMs when impedance matching techniques are not used. However, effective refractive index match between microwave and lightwave becomes important as the waveguide length increases. The microwave property closely related to the extinction ratio of output optical powers is the microwave loss. When impedance match is achieved by low-impedance termination, the velocity matching between microwave and lightwave becomes important.     

An approximate nonlinear observer with polynomial coordinatetransformation maps

The state equivalence condition to the nonlinear observer form is stated in terms of the exactness of one-form. Using the definition of the approximate closedness, we relax the equivalence condition, thereby obtaining a necessary and sufficient condition for the approximate observer error linearizability. This approximate observer theory extends the realm of applications. Another great advantage of this approximation method is that the coordinate transformation is directly obtainable as vectors of polynomials, while it is, in general, not possible with the existing method,     

Exact static element stiffness matrices of non‐symmetric thin‐walled curved beams

An evaluation procedure of exact static stiffness matrices for curved beams with non‐symmetric thin‐walled cross section are rigorously presented for the static analysis. Higher‐order differential equations for a uniform curved beam element are first transformed into a set of the first‐order simultaneous ordinary differential equations by introducing 14 displacement parameters where displacement modes corresponding to zero eigenvalues are suitably taken into account. This numerical technique is then accomplished via a generalized linear eigenvalue problem with non‐symmetric matrices. Next, the displacement functions of displacement parameters are exactly calculated by determining general solutions of simultaneous non‐homogeneous differential equations. Finally an exact stiffness matrix is evaluated using force–deformation relationships. In order to demonstrate the validity and effectiveness of this method, displacements and normal stresses of cantilever thin‐walled curved beams subjected to tip loads are evaluated and compared with those by thin‐walled curved beam elements as well as shell elements. Copyright © 2004 John Wiley & Sons, Ltd.     

A study on a generalized parametric interpolator with real-time jerk-limited acceleration

The impossibility of exact arc length computation for ‘standard’ parametric curves such as Bézier/B-spline curves makes it difficult to generate a feedrate profile with desired accelerations in real-time. This paper presents a new recursive trajectory generation method that estimates an admissible path increment and determines the initiation of the final deceleration stage according to the distance left to travel estimated at every sampling time, resulting in exact feedrate trajectory generation through jerk-limited acceleration profiles for the parametric curves. The proposed approach allows the feedrate profile to be dynamically adjusted according to geometrical path constraints for the curved path. The simulation result has been also provided to illustrate the generation of smooth feedrate profile encompassing a sequence of mixed NC blocks including traditional linear and circular blocks.