Step length adaptation on ridge functions

Step length adaptation is central to evolutionary algorithms in real-valued search spaces. This paper contrasts several step length adaptation algorithms for evolution strategies on a family of ridge functions. The algorithms considered are cumulative step length adaptation, a variant of mutative self-adaptation, two-point adaptation, and hierarchically organized strategies. In all cases, analytical results are derived that yield insights into scaling properties of the algorithms. The influence of noise on adaptation behavior is investigated. Similarities and differences between the adaptation strategies are discussed.     

Tensile testing of microfabricated thin films

 Mechanical properties of titanium thin films of 0.5 μm thickness and aluminum thin films of 1.0 μm thickness, microfabricated by magnetron sputtering, were measured by using a novel tensile machine. These thin films are difficult to handle because they are fragile, so the thin film specimens were fabricated by using semiconductor manufacturing technology in a silicon frame to protect them. The test section of these specimens was 300 μm in width and 1400 μm in gauge length. By gripping the thin film specimen with a new device using a micrometer, it could be mounted on the tensile machine easily. The stress-strain diagrams of both thin films were measured continuously in the atmosphere at room temperature. The experimental results indicated that the titanium thin film and the aluminum thin film had a smaller breaking elongation although they had a larger tensile strength than bulk pure titanium and bulk pure aluminum, respectively. Received: 31.10.96/Accepted: 14.11.96     

A New Approach for Predicting the Final Outcome of Evolution Strategy Optimization Under Noise

Differential-geometric methods are applied to derive steady state conditions for the (μ/μ _I ,λ)-ES on the general quadratic test function disturbed by fitness noise of constant strength. A new approach for estimating the expected final fitness deviation observed under such conditions is presented. The theoretical results obtained are compared with real ES runs, showing a surprisingly excellent agreement.     

Performance analysis of evolutionary optimization with cumulative step length adaptation

Iterative algorithms for continuous numerical optimization typically need to adapt their step lengths in the course of the search. While some strategies employ fixed schedules, others attempt to adapt dynamically in response to the outcome of trial steps or the history of the search process. Evolutionary algorithms are of the latter kind. A control strategy that is commonly used in evolution strategies is the cumulative step length adaptation approach. This paper presents a theoretical analysis of that adaptation strategy. The analysis includes the practically relevant case of noise interfering in the optimization process. Recommendations are made with respect to choosing appropriate population sizes.     

Optimum tracking with evolution strategies

Evolutionary algorithms are frequently applied to dynamic optimization problems in which the objective varies with time. It is desirable to gain an improved understanding of the influence of different genetic operators and of the parameters of a strategy on its tracking performance. An approach that has proven useful in the past is to mathematically analyze the strategy's behavior in simple, idealized environments. The present paper investigates the performance of a multiparent evolution strategy that employs cumulative step length adaptation for an optimization task in which the target moves linearly with uniform speed. Scaling laws that quite accurately describe the behavior of the strategy and that greatly contribute to its understanding are derived. It is shown that in contrast to previously obtained results for a randomly moving target, cumulative step length adaptation fails to achieve optimal step lengths if the target moves in a linear fashion. Implications for the choice of population size parameters are discussed.     

Fabrication of compliant high aspect ratio silicon microelectrode arrays using micro-wire electrical discharge machining

This paper reports on the fabrication of high aspect ratio silicon microelectrode arrays by micro-wire electrical discharge machining (μ-WEDM). Arrays with 144 electrodes on a 400 μm pitch were machined on 6 and 10 mm thick p-type silicon wafers to a length of 5 and 9 mm, respectively. Machining parameters such as voltage and capacitance were varied for different wire types to maximize the machining rate and to obtain uniform electrodes. Finite element analysis was performed to investigate electrode shapes with reduced lateral rigidity. These compliant geometries were machined using μ-WEDM followed by a two step chemical etching process to remove the recast layer and to reduce the cross sections of the electrodes.     

Experiments on opto-electrically generated microfluidic vortices

Strong microfluidic vortices are generated when a near-infrared (1,064 nm) laser beam is focused within a microchannel and an alternating current (AC) electric field is simultaneously applied. The electric field is generated from a parallel-plate, indium tin oxide (ITO) electrodes separated by 50 μm. We present the first μ-PIV analysis of the flow structure of such vortices. The vortices exhibit a sink-type behavior in the plane normal to the electric field and the flow speeds are characterized as a function of the electric field strength and biasing AC signal frequency. At a constant AC frequency of 100 kHz, the fluid velocity increases as the square of the electric field strength. At constant electric field strength fluid velocity does not change appreciably in the 30–50 kHz range and it decreases at larger frequencies (>1 MHz) until at approximately 5 MHz when Brownian motion dominates the movement of the 300 nm μ-PIV tracer particles. Presence of strongly focused laser beams in an interdigitated-electrode configuration can also lead to strong microfluidic vortices. When the center of the illumination is focused in the middle of an electrode strip, particles experiencing negative dielectrophoresis are carried towards the illumination and aggregate in this area.     

Collapse-free thermal bonding technique for large area microchambers in plastic lab-on-a-chip applications

Bonding is an essential step to form microchannels or microchambers in lab-on-a-chip applications. In this paper, we present a novel plastic thermal bonding technique to seal and form large area microchambers (planar characteristic width and length on the order of 1 mm and characteristic thickness on the order of 10–100 μm) without collapse by introducing a holed pressure equalizing plate (HPEP) that includes holes of the same size and shape as the microchambers. To demonstrate the proposed technique, two types of large area microchambers [(1) 20 × 10 mm and 40 μm thick and (2) 12 × 2.5 mm and 120 μm thick] with microchannels were designed and replicated on plastic substrates by means of hot embossing and injection molding processes with prepared two nickel mold inserts. The replicated large area microchambers as well as the microchannels in the plastic lab-on-a-chip were successfully sealed (i.e., no leakage) and formed without any collapse by the proposed thermal bonding technique with the help of the HPEP.     

Geometrical strengthening and tip-sharpening of a microneedle array fabricated by X-ray lithography

A novel fabrication method for LIGA (from the German “Lithographie”, “Galvanik”, and “Abformung”) microneedles with through holes is presented. Such microneedles are in demand by most bio-medical MEMS applications and in some fluidic MEMS applications. We propose a technique that combines conventional deep X-ray lithography, plane-pattern to cross-section transfer (PCT) process, and alignment X-ray lithography. The technique provides precise hole alignment with ± 3 μm tolerance. Finite-element simulations on various hole locations were performed to determine the optimum position. We previously fabricated a microneedle with a 100-μm base and a 300-μm height by a right-triangular mask. The resultant microneedle had a very sharp tip but was excessively steep, and thus resulted in a very low strength. Improved strength and tip sharpness was consequently achieved by changing the mask-pattern from a triangular pattern to a polygonal mask and changing the dimensions of the microneedle to have a 300-μm base with various heights between 350 and 800 μm. Using the proposed technique, we could produce a total of 100 hollow microneedles on a 5 × 5 mm² chip. Moreover, we successfully fabricated sharpened microneedles that were stronger than that we have fabricated so far. The molding process or electroplating and the cost list of the LIGA microneedle will also be included.     

Fabrication and analysis of the reflowed microlens arrays using JSR THB-130 N photoresist with different heat treatments

This paper reports that the fabrication of the reflowed microlens by the negative tone JSR THB-130 N photoresist can be treated with different thermal treatments using hotplate and oven. The different disk or thin cylinder arrays with diameters of 40–70 μm and thickness of about 7.4 μm were patterned using photolithography technology, and baked at 220°C by two kinds of thermal treatments using hotplate and oven to form reflowed microlens arrays. The spot size of the refractive microlens was then measured by optical microscopy and the total focal length of refractive microlens was simulated by curve fitting the lens profiles. The resolution of the microlens arrays approaches to 400 dpi as coated with Hexamethyldisilizane material. The smallest spot size of about 2.72 μm at the nominal 40 μm microlensis is obtained by the oven heat treatment, and the shortest total focal length of about 150 μm at the nominal 40 μm microlens is achieved by the hotplate heat treatment. The reduced spot size and total focal length of the microlens could improve the density and performance of optical devices and imaging systems.     

Characterization of an electro-thermal micro gripper and tip sharpening using FIB technique

A micromachined electro-thermal gripper, first introduced by Ivanova et al. (Microelectron Eng 83:1393–1395, 2006), represents a promising candidate for the manipulation and handling of micro or even nano-scaled objects. To further optimize the performance of the device, a detailed electrical and mechanical characterization is needed. Due to the so-called duo-action gripper approach (i.e., a separate actuator for closing and opening action) these investigations focused on the maximum (minimum) opening width being 11.5 μm (3.3 μm), while in rest position a value of 4 μm is feasible. The maximum, electrical input power is limited to 80 mW/actuator element, resulting in a current density of up to 1.27 MA cm⁻² in the corresponding metal layers. When applying, however, larger current densities the probability of device failure increases substantially as in combination with an enhanced temperature of about 200°C electromigration effects occur in the metallization. Furthermore, the cut-off frequency and parasitic effects during actuation such as the z-deflection and the increase in length of each arm both showing values of up to 3 μm have been investigated as a function of operation parameters. Finally, the tips of the gripper were sharpened using Focused Ion Beam technique to a radius of less than 1 μm for gripping operations in space-restricted environments or for the manipulation or handling of sub-μm scaled objects.     

The flow resistance of single DNA-grafted colloids as measured by optical tweezers

In rheological experiments, the flow resistance of single blank or DNA-grafted colloids is determined and compared. The length of the double-stranded-DNA varies amongst 1,000, 4,000 and 6,000 base pairs (bp) corresponding to contour lengths varying between 340 and 2,040 nm at a grafting density of 0.03±0.01 μm²/chain. The degree of swelling of the grafted DNA is adjusted by exchanging the ion concentration of the surrounding medium. For all examined flow velocities ranging between 100 and 1,200 μm/s, one observes an interesting deviation from Stokes law which can be traced back to a shear-dependent conformational change of the brush layer. The ratio of the effective hydrodynamic radii of DNA-grafted and blank colloids shows a pronounced dependence on the flow velocity, but as well on the length of the grafted DNA and the ionic strength of the solvent. The experimental findings are in qualitative agreement with hydrodynamic simulations based on an elastically jointed chain model.     

Collector of noncoherent electromagnetic energy distributed in space

In this abstract, the collector of noncoherent electromagnetic energy distributed in space is considered. This device, according to the plan, can be presented as a converter of electromagnetic noise (mainly from the infrared area with a wave length of about 10 μm) in a constant or nearly constant current of the useful load. The schematic design and results of a computational experiment are presented. The promotion of this device assumes its nanotechnological prospects.     

Relationships between process, microstructure and properties of molded zirconia micro specimens

Due to size effects the mechanical behavior of micro-components with dimensions in the range of some 100 μm and structure details of about 10 μm differs markedly from those of larger components. This is a crucial aspect for the design of micro-components for applications where demands for high strength are critical. The present study, which was performed in the frame of the Collaborative Research Centre 499 (SFB 499), approaches this issue by investigating the relationship between production process, microstructure and the mechanical properties of micro-specimens made from zirconia using two different feedstocks. The specimens were produced by a sintering process. The sintering temperature was varied between 1,300 and 1,500°C. Mechanical and tribological behavior of the specimens was determined by three-point bending tests as well as static and sliding friction tests, respectively. Properties derived from these tests were then correlated to the surface states in the specimens such as porosity, edge radius and roughness. The strength of the micro-specimens was found to be significantly influenced by these surface features. Whilst low porosity alone is not sufficient for high strength, notch effects resulting from pores as well as surface roughness can lower the strength. With increasing edge radius the strength of the material also increases. The porosity, edge radius and surface roughness were mathematically correlated with the strength to allow for a forecast. Within the SFB 499 feedstocks with specific properties were designed and reliable processes were developed to guarantee desirable surface roughness and porosity in the specimens. A characteristic bending strength of about 2,000 MPa is realizable in the micro-specimens within a good statistical reliability. The tribological tests revealed that the wear properties of the zirconia micro-components are strongly dependent on the quality of the feedstock.     

Fabrication of intermediate mask for deep x-ray lithography

 This paper presents the fabrication of intermediate x-ray mask for deep x-ray lithography. In order to have working mask with absorbers thickness larger than 10 μm, the intermediate mask should have absorbers of 0.7 μm in thickness. To demonstrate intermediate mask fabrication, x-ray zone plates are fabricated on the 1.2 μm low-stress silicon-rich silicon nitride (SiN_x) membrane with the tri-layer Chromium-Tungsten-Chromium (Cr–W–Cr) as the x-ray absorbers. The chromium layers both 200 angstroms are used as adhesion and for stress relief. The SiN_x film is deposited with low pressure chemical vapor deposition (LPCVD) and the free standing membrane are formed by KOH silicon backside etching. With the e-beam lithography and reactive ion etching, width of 0.8 μm of outmost zone of the x-ray zone plates has been achieved on the membrane. The scanning electron microscopy (SEM) images of the x-ray zone plates and pictures of intermediate masks are demonstrated. Received: 25 August 1997/Accepted: 3 September 1997     

On the robustness of a multigrid method for anisotropic reaction-diffusion problems

In this paper, we consider a reaction-diffusion boundary value problem in a three-dimensional thin domain. The very different length scales in the geometry result in an anisotropy effect. Our study is motivated by a parabolic heat conduction problem in a thin foil leading to such anisotropic reaction-diffusion problems in each time step of an implicit time integration method [7]. The reaction-diffusion problem contains two important parameters, namely ε >0 which parameterizes the thickness of the domain and μ >0 denoting the measure for the size of the reaction term relative to that of the diffusion term. In this paper we analyze the convergence of a multigrid method with a robust (line) smoother. Both, for the W- and the V-cycle method we derive contraction number bounds smaller than one uniform with respect to the mesh size and the parameters ε and μ.      

A numerical study of an electrothermal vortex enhanced micromixer

Temperature gradients aroused from the Joule heating in a non-uniform electrical field can induce inhomogeneities of electric conductivity and permittivity of the electrolyte, thus causing an electrothermal force that generates flow motion. A 2D numerical investigation of a micromixer, utilizing electrothermal effect to enhance its mixing efficiency, is proposed in this paper. Results for temperature and velocity distributions, as well as sample concentration distribution are obtained for an electrolyte solution in a microchannel with different pairs of electrodes under AC potentials with various frequencies. Numerical solutions were first carried out for one pair of electrodes, with a length of 10 μm separated by a gap of 10 μm, on one side wall of a microchannel having a length of 200 μm and a height of 50 μm. It is found that the electrothermal flow effect, in the frequency range for which Coulomb force is predominant, induces vortex motion near the electrodes, thus stirring the flow streams and enhancing its mixing efficiency. If more than one pair of electrodes is located on the opposite walls of the microchannel, the mixing efficiency depends on the AC potential applied pattern and the electrodes arrangement pattern. The distance between two pairs of electrodes on two opposite walls is then optimized numerically. Sample mixing efficiencies, using KCl solutions as the working fluid in microchannels with different number of electrodes pairs at optimal electrodes arrangement pattern, are also investigated. If root mean squared voltages of 10 V in an AC frequency range of 0.1–10 MHz are imposed on 16 pairs of electrodes separated at an optimal distance, the numerical results show that a mixing efficiency of 98% can be achieved at the end of the microchannel having a length of 700 μm and a height of 50 μm at Re = 0.01 Pe _C = 100, and Pe _T = 0.07. However, the mixing efficiency decreases sharply at a frequency higher than 10 MHz owing to the drastically decrease in the Coulomb force.     

Anti-scattering X-ray grid

 Various optical or x-ray applications require reduction of scattered radiation on the imaging detector to produce sharper images. The scattered radiation is reduced when the radiation impacting on the detector is from a chosen small solid angle. This requires a mask in front of the detector with small holes and high aspect ratio. We are applying the SLIGA process to perform a proof-of-principle demonstration with the capability of making a large and high area anti-scattering grid. The approach is by assembling and stacking small pieces of grid. To maintain high throughput of the desired radiation, the wall of the grid has to be thin. We designed and fabricated four grid patterns all with 20 μm thick walls and 80 μm×80 μm holes. The individual pieces were 210 μm high and made of nickel. The pieces were assembled and stacked to make a 5 mm×5 mm grid 2.1 mm high. Much larger grids can be made by the SLIGA process, which was chosen because of its capability to fabricate high aspect ratio devices with precision. Received: 25 August 1997/Accepted: 24 October 1997     

Local performance of the (1 + 1)-ES in a noisy environment

While noise is a phenomenon present in many real world optimization problems, the understanding of its potential effects on the performance of evolutionary algorithms is still incomplete. This paper investigates the effects of fitness proportionate Gaussian noise for a (1 + 1)-ES with isotropic normal mutations on the quadratic sphere in the limit of infinite search-space dimensionality. It is demonstrated experimentally that the results provide a good approximation for finite space dimensionality. It is shown that overvaluation as a result of failure to re-evaluate parental fitness leads to both reduced success probabilities and improved performance. Implications for mutation strength adaptation rules are discussed and optimal re-sampling rates are computed     

Experimental investigation of noise suppression using the modified up-and-down method

The noise suppression efficiency is experimentally investigated for discrete stroboscopic signal transformation providing 5–15 μV (RMS) sensitivity. A balanced comparator based on tunnel diodes is used as a clocked comparator. Ordinary and modified up-and-down methods are used to measure the instantaneous signal values. The experimental results are compared to the theoretical calculations.