Efficient circular arc interpolation based on active tolerance control

In this paper, we present an efficient sub-optimal algorithm for fitting smooth planar parametric curves by G¹ arc splines. To fit a parametric curve by an arc spline within a prescribed tolerance, we first sample a set of points and tangents on the curve adaptively as well as with enough density, so that an interpolation biarc spline curve can be with any desired high accuracy. Then, we construct new biarc curves interpolating local triarc spirals explicitly based on the control of permitted tolerances. To reduce the segment number of fitting arc spline as much as possible, we replace the corresponding parts of the spline by the new biarc curves and compute active tolerances for new interpolation steps. By applying the local biarc curve interpolation procedure recursively and sequentially, the result circular arcs with no radius extreme are minimax-like approximation to the original curve while the arcs with radius extreme approximate the curve parts with curvature extreme well too, and we obtain a near optimal fitting arc spline in the end. Even more, the fitting arc spline has the same end points and end tangents with the original curve, and the arcs will be jointed smoothly if the original curve is composed of several smooth connected pieces. The algorithm is easy to be implemented and generally applicable to circular arc interpolation problem of all kinds of smooth parametric curves. The method can be used in wide fields such as geometric modeling, tool path generation for NC machining and robot path planning, etc. Several numerical examples are given to show the effectiveness and efficiency of the method.     

A practicable approach to G biarc approximations for making accurate, smooth and non-gouged profile features in CNC contouring

Extensive research on G¹ biarc approximations to free-form curves has been conducted for the production of accurate, smooth and non-gouged profile features in CNC contouring. However, all the published work has only focused on improving the fitting accuracy between the biarc curve and the nominal free-form curve of a profile and minimizing the biarc number; as a result, the radii of the concave arcs of some biarcs could be less than the pre-determined tool radius, and the tool would overcut these arcs in machining, eventually gouging the profile. In this work, a new, practicable approach is proposed to completely solve this problem. The main feature of this approach is to find the gouging-free parameter interval of a biarc family, among which the radii of all the concave arcs are larger than the tool radius, and then to search in this interval for a best fitting biarc so that its approximation accuracy is within the tolerance. This approach is robust and easy to implement and can substantially promote the use of G¹ biarc curves for CNC machining.     

Bismuth film electrodes for heavy metals determination

Bismuth film electrodes (BiFEs) have a potential to replace toxic mercury used most frequently for determination of heavy metals (Cd, Pb, Zn) by anodic stripping voltammetry. We prepared a graphite disc electrode (0.5 mm in diameter) from a pencil-lead rod and developed a nitrogen doped diamond-like carbon (NDLC) microelectrode array consisting of 50,625 microdiscs with 3 μm in diameter and interelectrode distances of 20 μm on a highly conductive silicon substrate as a support for BiFEs. The disc graphite BiFE was used for simultaneous determination of Pb(II), Cd(II) and Zn(II) by square wave voltammetry (SWV) in an aqueous solution. We found the optimum bismuth-to-metal concentration ratio in the solution to be 20. The dependence of the stripping responses on the concentration of target metals was linear in the range from 1 × 10⁻⁸ to 1.2 × 10⁻⁷ mol/L. Detection limits 2.4 × 10⁻⁹ mol/L for Pb(II), 2.9 × 10⁻⁹ mol/L for Cd(II) and 1.2 × 10⁻⁸ mol/L for Zn(II) were estimated. A bismuth-plated NDLC microelectrode array was used for Pb(II) determination by differential pulse voltammetry (DPV) in an aqueous solution. We found that the stripping current for bismuth-plated NDLC array was linear in the concentration range of Pb(II) from 2 × 10⁻⁸ to 1.2 × 10⁻⁷ mol/L. The detection limit 2.2 × 10⁻⁸ mol/L was estimated from a calibration plot.     

New PCG based algorithms for the solution of Hermitian Toeplitz systems

In order to solve Toeplitz linear systems A_n(f)x=b generated by a nonnegative integrable function f, through use of the preconditioned conjugate gradient (PCG) method, several authors have proposed A_n(g) as preconditioner in the case where g is a trigonometric polynomial [10, 14, 27, 12, 28]. In preceding works, we studied the distribution and the extremal properties of the spectrum of the preconditioned matrix G=A _n ⁻¹ (g) A_n(f). In this paper we prove that the union of the spectra of all the G_n is dense on the essential range of f/g, i.e.,ER(f/g) and we obtain asymptotic information about the rate of convergence of the smallest eigenvalue λ _l ⁿ of G_n to r (and of λ _n ⁿ to R). As a consequence of this second order result, it is possible to handle the case where f has zeros of any order θ, through the PCG methods proposed in [10, 14]. This is a noteworthy extension since the techniques developed in [10, 14, 27, 12, 28] are shown to be effective only when f has zeros of even orders. The cost of this procedure is O(n^1+c(θ) log n) arithmetic operations (ops) where the quantity c(θ) belongs to interval [0,2⁻¹] and takes the maximum value 2⁻¹ when f has a zero of odd order. Finally, for the special case of zeros of odd orders, we propose a further algorithm which makes use of the PCG techniques proposed in [10, 14, 27, 12, 28] for theeven order case, reducing the cost to O(n long n) ops.     

Volume hologram recording in diarylethene doped polymer

Volume hologram recording is implemented experimentally in the bulk of diarylethene dyedoped polymeric host-guest material. A wide range of reciprocity for holographic imaging is demonstrated, ranging from as low as 0.55 mW/cm² up to more than 200 mW/cm². At a dye concentration of 2 × 10⁻³ M and spatial frequency of 2000 mm⁻¹, refractive index modulations Δn of 2 × 10⁻⁵ at λ = 514.5 nm and 1 × 10⁻⁵ at λ = 830 nm were attained. Increasing the dye concentration to 3.8 × 10⁻² M resulted in higher Δn values of 3.8 × 10⁻⁴ at λ = 514.5 nm and 2.1 × 10⁻⁴ at λ = 830 nm. The high fatigue resistance of the dye allows multiple record/erase cycles without degradation. The thermal stability of the dye allows for durability of the recording material at temperatures above 115°C. At temperatures above 57°C, the hologram is found to exhibit thermal degradation at a rate far exceeding that caused by thermochromism. It is suggested that diffusion of the dye in the polymer matrix is responsible for the increased sensitivity of the hologram to elevated temperatures, which may be applied in reusable holographic thermal sensors. The text was submitted by the author in English.     

Vibration perception and excitatory direction for haptic devices

Vibration feedback is one of the most popular ways to communicate between human and haptic interfaces nowadays. In order to deliver a wider variety of information accurately and efficiently, significant design factors of the vibration need to be investigated and applied to haptic devices. In this study, the excitatory direction was examined as a design factor of the vibration in terms of sensitivity and emotion. We conducted two experiments. In the first experiment, the sensitivities of three excitatory directions—X (lateral), Y (fore-and-aft) and Z (vertical) axes were estimated by the absolute thresholds of the vibration perception with two frequency levels (150 and 280 Hz). Based on ten participants’ estimated absolute thresholds, we conclude that the vibration with X axis is less sensitive than Z axis at the frequency of 150 Hz, while the vibration with Y axis is less sensitive than Z axis at the frequency of 280 Hz. In the second experiment, the agreeability of 29 emotional expressions to the vibrations was measured by a 7-point scale with a total of 12 conditions (2 frequencies × 2 amplitudes (i.e., 50 × 10⁻³ and 500 × 10⁻³ g) × 3 excitatory directions). Based on 20 participants’ responses, it is concluded that at the frequency of 150 Hz and the amplitude of 50 × 10⁻³ g, the vibration is perceived as ‘light’, and as even ‘lighter’ if the vibration is with Y axis rather than with Z axis. Likewise, at the frequency of 150 Hz and the amplitude of 500 × 10⁻³ g, the vibration is perceived as ‘repulsive’, and as even ‘more repulsive’ if the vibration is with Y or Z axis rather than with X axis. Therefore, three excitatory directions can be selectively utilized to design the distinguishable vibration by its sensitivity and emotion.     

Fabrication of microfluidic devices for packaging CMOS MEMS impedance sensors

This work presents a polydimethylsiloxane (PDMS) microfluidic device for packaging CMOS MEMS impedance sensors. The wrinkle electrodes are fabricated on PDMS substrates to ensure a connection between the pads of the sensor and the impedance instrument. The PDMS device can tolerate an injection speed of 27.12 ml/h supplied by a pump. The corresponding pressure is 643.35 Pa. The bonding strength of the device is 32.44 g/mm². In order to demonstrate the feasibility of the device, the short circuit test and impedance measurements for air, de-ionized water, phosphate buffered saline (PBS) at four concentrations (1, 2 × 10⁻⁴, 1 × 10⁻⁴, and 6.7 × 10⁻⁵ M) were performed. The experimental results show that the developed device integrated with a sensor can differentiate various samples.     

Rapid quantification of bio-particles based on image visualisation in a dielectrophoretic microfluidic chip

We studied an imaging-based technique for the rapid quantification of bio-particles in a dielectrophoretic (DEP) microfluidic chip. Label-free particles could be successively sorted and trapped in a continuous flow manner under the applied alternating current (AC) conditions. Both 2 and 3 μm polystyrene beads at a concentration of 1.0 × 10⁷ particles ml⁻¹ could be rapidly quantified within 5 min in our DEP system. Capturing efficiencies higher than 95% could be 2 μm polystyrene beads with a linear flow speed, applied voltage and frequency of 0.89 mm s⁻¹, 20 V_p-p and 5 MHz. Yeast cells (Candida glabrata and Candida albicans) could also be captured even at a lower concentration of 2.5 × 10⁵ cells ml⁻¹. Images of aggregative particles taken from the designed trapping area were further processed based on the intensity of relative greyscale followed by correction of the particle numbers. The imaging-based quantification method showed higher agreement than that of the conventional counting chamber method and proved the stability and feasibility of our AC DEP system.     

Wavelength Assignment for Realizing Parallel FFT on Regular Optical Networks

Routing and wavelength assignment (RWA) is a central issue to increase efficiency and reduce cost in Wavelength Division Multiplexing (WDM) optical networks. In this paper, we address the problem of wavelength assignment for realizing parallel FFT on a class of regular optical WDM networks. We propose two methods for sequential mapping and shift-reversal mapping of FFT communication pattern to the optical WDM networks concerned. By sequential mapping, the numbers of wavelengths required to realize parallel FFT with 2ⁿ nodes on WDM linear arrays, rings, 2-D meshes and 2-D tori are 2^{n − 1}, 2^{n − 1}, 2^{max (k,n − k) − 1} and 2^{max (k,n − k) − 1} respectively. By shift-reversal mapping, the numbers of wavelengths required are max (3× 2^{n − 3},2), 2^{n − 2}, max (3× 2^{max (k,n − k) − 3},2) and 2^{max (k,n − k) − 2}. These results show that shift-reversal mapping outperforms sequential mapping. Our results have a clear significance for applications because FFT represents a common computation pattern shared by a large class of scientific and engineering problems and WDM optical networks as a promising technology in networking has an increasing popularity.     

Problems of measurement of the Newtonian gravitational constant

Due to weakness of gravity, the accuracy of the Newtonian gravitational constant G is essentially below the accuracy of other fundamental constants. The current value of G, recommended by CODATA in 2006, based on all results available at the end of 2006, is G = (6.67428 ± 0.00067) × 10⁻¹¹ m³ kg⁻¹ s⁻² with a relative error of 100 ppm. New experiments at a level of accuracy of 10 to 30 ppm are now in progress in some world gravitational laboratories. One of the problems of improving the accuracy of G is a precision measurement of the period of eigen oscillations of the torsion balance. In this work, numerical modelling of torsion and swing oscillations is under the condition that the torsion system is subject to randomnoise. A newmethod of high-precision estimation of the period of torsion oscillations has been developed. The dependence of the torsion period value and the error of its estimation on the level of the acting seismic noise has been studied. To measure the Newtonian gravitational constant at the accuracy level of 10 ppm, the environmental seismic noise must be below 10⁻² mGal. Talk given at the International Conference RUSGRAV-13, June 23–28, 2008, PFUR, Moscow.     

Integrated micro Pirani gauge based hermetical package monitoring for uncooled VO x bolometer FPAs

This paper presents the design and fabrication of a micro Pirani gauge using VO _x as the sensitive material for monitoring the pressure inside a hermetical package for micro bolometer focal plane arrays (FPAs). The designed Pirani gauge working in heat dissipating mode was intentionally fabricated using standard MEMS processing which is highly compatible with the FPAs fabrication. The functional layer of the micro Pirani gauge is a VO _x thin film designed as a 100 × 200 μm pixel, suspended 2 μm above the substrate. By modeling of rarefied gas heat conduction using the Extended Fourier’s law, finite element analysis is used to investigate the sensitivity of the pressure gauge. Also the thermal interactions between the micro Pirani gauge and bolometer FPAs are verified. From the fabricated prototype, the measured device TCR is about −0.8% K⁻¹ and the sensitivity about 1.84 × 10⁻³ W K⁻¹ mbar⁻¹.     

Uniform trigonometric polynomial B-spline curves

This paper presents a new kind of uniform spline curve, named trigonometric polynomial B-splines, over space Ω = span{sini,cost, tk-3,tk-4, …,t, 1} of which k is an arbitrary integer larger than or equal to 3. We show that trigonometric polynomial B-spline curves have many similar properties to traditional B-splines. Based on the explicit representation of the curve we have also presented the subdivision formulae for this new kind of curve. Since the new spline can include both polynomial curves and trigonometric curves as special cases without rational form, it can be used as an efficient new model for geometric design in the fields of CAD/CAM.     

Status of the experiments on measurement of the Newtonian gravitational constant

Due to the weakness of gravity, the accuracy of the Newtonian gravitational constant G is essentially below the accuracy of other fundamental constants. The current value of G, recommended by CODATA in 2006, based on all results available at the end of 2006, is G = (6.67428 ± 0.00067) × 10⁻¹¹ m³ kg⁻¹ s⁻² with a relative error of 100 ppm. The accuracy of the best experimental results is 15–40 ppm, although the scatter of the results is large enough. Therefore new experiments at a level of accuracy of 10–30 ppm are rather topical. One of the problems of improving accuracy of G is a precision measurement of the period of eigen oscillations of a torsion balance. The nonlinear behavior of the torsion balance with five degrees of freedom has been studied. It was shown that swing modes are excited by the acting environmental noise. A coupling of the swing modes to the torsional mode has been revealed. Methods of suppressing the effect of mode couplings have been considered.     

Blaschke products and optimal recovery inH ∞

We examine the error in the optimal estimation of∫ ₋₁ ¹ f(t)w(t)dt by a quadrature formula using values off at equally spaced points of (−1, 1) or at the zeros of ultraspherical polynomials. Heref is known to be an analytic function in the unit disc which is bounded by l andw is a given weight function with prescribed behavior near ±1. A major role in our investigations is played by bounds on (−1, 1) from above and below for the finite Blaschke product which is based in the nodes of the quadrature formula. Optimal estimation of the functionf, rather than its integral, is also studied.     

Quantum model and memory of informative biomacromolecules

It is shown, that tubuline informative biomacromolecule has two-well structure potential energy relief for an electron responsible for the switching between conformations of molecules. Therefore the system of conformational excitation in informative biomacromolecules must be described as a two-level quantum system. The energy of the basic electron state ɛ₊ = 1.2 eV and frequency of electron tunneling ω = (6 × 10¹³–6 × 10¹¹) s⁻¹ in a tubuline molecule were calculated. The possibility of data recording by directly collapse of wave function in a two-level cell was shown, thus coherence of quantum state collapses only. The article is published in the original.     

On Parabolic Boundary Layers for Convection–Diffusion Equations in a Channel: Analysis and Numerical Applications

In this article we discuss singularly perturbed convection–diffusion equations in a channel in cases producing parabolic boundary layers. It has been shown that one can improve the numerical resolution of singularly perturbed problems involving boundary layers, by incorporating the structure of the boundary layers into the finite element spaces, when this structure is available; see e.g. [Cheng, W. and Temam, R. (2002). Comput. Fluid. V.31, 453–466; Jung, C. (2005). Numer. Meth. Partial Differ. Eq. V.21, 623–648]. This approach is developed in this article for a convection–diffusion equation. Using an analytical approach, we first derive an approximate (simplified) form of the parabolic boundary layers (elements) for our problem; we then develop new numerical schemes using these boundary layer elements. The results are performed for the perturbation parameter ε in the range 10⁻¹–10⁻¹⁵ whereas the discretization mesh is in the range of order 1/10–1/100 in the x-direction and of order 1/10–1/30 in the y-direction. Indications on various extensions of this work are briefly described at the end of the Introduction.Dedicated to David Gottlieb on his 60th birthday.     

Two photon absorption coefficients and processing parameters for photoresists

The two photon absorption (TPA) process is currently used to write high resolution microstructures for a variety of applications. Key parameters required to predict the final structure formation for this process are experimentally determined and reported in this article for two commercially available resists, Ormocore and SU-8. The measured TPA coefficients measured at 800 nm for Ormocore and SU-8 are 27 ± 6 and 28 ± 6 cm TW⁻¹, respectively. For Ormocore and SU-8 the dose required to write 35 and 50 μm high structures, respectively, were 54 ± 8 and 3.5 ± 0.5 J cm⁻³, respectively, and the measured contrasts were 15 ± 2 μm per decade J⁻¹ cm³ and 55 ± 8 μm per decade J⁻¹ cm³, respectively.     

Low-voltage electroosmotic pumping using porous anodic alumina membranes

This study demonstrated electroosmotic pumping with high flow rate per unit area at a rather low applied voltage by using alumina nano-porous membrane. The platinum mesh electrode is perpendicular to, and has direct contact with the nano-channel inlet for proving uniform electric field and for reducing the electric voltage drop in the reservoir. The measured flow rate versus electrolyte (KCl) concentration reveals two distinct characteristics. First, the flow rate is usually high at low concentrations (10⁻⁵ to 10⁻⁷ M) in which a maximum value occurs. Second, a remarkable drop of flow rate is seen when the concentration surpasses 10⁻⁴ M. The maximum flow rate achieved from this study is 0.09 mL/min V cm² and the energy transfer efficiency is 0.43% at an operation voltage of 20 V. The mesh electrodes with 33 wire spacing are capable of providing an uniform electric field, the nano-porous membrane with a low electrolyte concentration provides the environment for strong overlapping of electric double layer, in association with the thin alumina membrane, leading to a high flow rate at a rather low applied voltage (20–80 V). The flow rate is comparable to the existing results whereas the corresponding operation voltage of this study is about one to two orders lower than most of the existing results.     

Simulation of lazer light propagation and thermal processes in red blood cells exposed to infrared laser tweezers (λ = 1064 nm)

Continuous-wave laser micro-beams are generally used as diagnostic tools in laser scanning microscopes or, in the case of near-infrared micro-beams, as optical traps for cell manipulation and force characterization. Because single beam traps are created with objectives of high numerical aperture, typical trapping intensities and photon flux densities are in the order of 10⁶ W/cm² and 10³ cm⁻² s⁻¹, respectively. These extremely high fields may induce two-photon absorption processes and anomalous biological effects. We studied effects occurring in red blood cells (RBCs) radiated by near-infrared laser tweezers λ = 1064 nm). The main idea of our study was to investigate the thermal reaction of RBCs irradiated by laser micro-beam. It is supported by the fact that many experiments have been carried out on RBCs using laser near infrared tweezers. Usually they are relatively long lasting and the thermal aspects of such experiments are not examined. In the present work it has been identified that the laser affects a RBC with a density of absorbed energy at approximately 10⁷ J/cm³, which causes a temperature rise in the cell of about 10–15°C.