A variotherm mold for micro metal injection molding

In this paper, a variotherm mold was designed and fabricated for the production of 316L stainless steel microstructures by micro metal injection molding (MIM). The variotherm mold incorporated a rapid heating/cooling system, vacuum unit, hot sprue and cavity pressure transducer. The design of the variotherm mold and the process cycle of MIM using the variotherm mold were described. Experiments were conducted to evaluate the molded microstructures produced using variotherm mold and conventional mold. The experiments showed that microstructures of higher aspect ratio such as 60 m × height 191 m and 40 m × height 174 m microstructures could be injection molded with complete filling and demolded successfully using the variotherm mold. Molded microstructures with dimensions of 60 m × height 191 m were successfully debound and sintered without visual defects.     

Generating Boolean \mu-expressions

In this paper, we consider the class of Boolean -functions, which are the Boolean functions definable by -expressions (Boolean expressions in which no variable occurs more than once). We present an algorithm which transforms a Boolean formulaE into an equivalent -expression-if possible-in time linear in E times , where E is the size ofE andn _m is the number of variables that occur more than once inE. As an application, we obtain a polynomial time algorithm for Mundici's problem of recognizing -functions fromk-formulas [17]. Furthermore, we show that recognizing Boolean -functions is co-NP-complete for functions essentially dependent on all variables and we give a bound close to co-NP for the general case.     

Metallic microgripper with SU-8 adaptor as end-effectors for heterogeneous micro/nano assembly applications

This paper presents design, fabrication, and characterization of easy-to-handle electroplated nickel microgrippers with SU-8 adaptors for heterogeneous micro/nano assembly applications. Two distinctive designs of microgrippers as end-effectors of micro/nano assembly applications have been developed in this work. The first design is 200 m thick electroplated nickel microgripper with a plastic mechanical displacement amplifier that is driven by a piezoelectric actuator. The piezoelectric actuator is capable of creating 5 m displacement which is amplified to 10 m by the plastic mechanical amplifier and finally such displacement generates 50–139 m microgripper tip displacement. The second design is 20 m thick electroplated nickel microgripper embedded in SU-8 adaptor for easy-to-handle operation. The second design is electro-thermally actuated using a set of joule-heated bent beams. With applied actuation voltage in the range of 2–4 V, the microgripper generates tip displacement of 4–32 m. Extensive thermal and mechanical finite element modeling have been carried out and measurement results were compared with the simulation results. Such developed easy-to-handle microgrippers can be used for micro/nano pick-and-place assembly applications.This work was supported by the National Institute of Standards and Technology-Advanced Technology Program (NIST-ATP 70NANB1H3021). The authors would like to thank the members of Design Engineering Group at Zyvex Corporation, Mr. Yohannes Desta from the Center for Advanced Microstructures and Devices (CAMD) at Louisiana State University for the valuable technical discussions, and the members of Micro and Nano Device and Systems (MiNDS) Laboratory and Cleanroom staffs at the University of Texas at Dallas.     

Deep sub micron high aspect ratio polymer structures produced by hard X-ray lithography

Microfabrication using X-ray lithography is a well established process in many laboratories worldwide. Radiation spectra, mask technology and process conditions are optimized for patterning resist thicknesses of several hundred micrometers with lateral dimensions of a few microns. This article provides first results as to how far these technologies can be extended to form structures with sub-micrometer lateral dimensions in resist layers of a few micrometers thickness. Available equipment and processes of the 2.5 GeV electron storage ring ANKA and the process technology of the Institut für Mikrostrukturtechnik (IMT) in Karlsruhe, Germany, have been applied. An X-ray mask with a 2.7 m Ti-membrane and 20 m thick Au-absorbers is used to expose 1.6 m PMMA resist on silicon wafers. As the smallest features on the mask are 2 m, a double exposure with an intermediate deliberate relative movement between mask and resist generated sub-micron resist test structures. Smallest feature sizes are between 300 and 400 nm. They are not yet limited by diffraction, but by different process conditions that lead to adhesion loss, resist cracking and surface rounding. It has been shown that an intermediate layer of 1.2 m thick polyimide between resist and substrate significantly enhances adhesion and reduces resist cracking. Reducing the beam power impinging onto the sample from typically 21 to 0.4 W leads to a 50% reduction of the surface rounding at the top of the microstructures. To demonstrate the capability to pattern thicker resist layers, first samples with an increased resist thickness of 4.1 m and an aspect ratio of up to 8 were processed. Finally, a metal mesh with 2 m thick Au-absorbers and 900 nm hexagonal holes was applied to pattern showpieces of sub micron features using a reduced electron energy of 1.3 GeV.The high resolution metal mesh was provided by R. Fettig of IMT.     

Local determinacy of abstract local dynamical systems

O. Hájek proved in his book Dynamical Systems in the Plane (Chapter III) that there isat most one abstract local dynamical system which is locally equivalent to, or equivalently an extension of, a given elementary dynamical system, and suggested a question of finding reasonable conditions on the latter for the existence ofat least one such abstract local dynamical system. An elementary dynamical system is said to satisfy the No-Intersection Axiom and is called an abstract germ if(x ₁, t) = (x ₂,t) impliesx ₁ =x ₂. We show that is (uniquely) extendable to an abstract local dynamical system if and only if is an abstract germ, and hence the question is completely answered. After introducing various kinds of isomorphisms of abstract germs and abstract local dynamical systems corresponding to those of continuous germs and continuous local dynamical systems, we obtain some sufficient conditions for extendability of isomorphisms and possibility of restriction of them, and thus establish the local determinacy of abstract local dynamical systems up to isomorphisms in some wider categories.Dedicated to Professor Yusuke HAGIHARA in Commemoration of His Seventy-Seventh Anniversary     

Thermal bubble powered microactuators

Thermal bubble powered micro mechanical actuators have been successfully demonstrated in working liquids. Micro mechanical plates which function as the mechanical actuators are 70×60×2 m³ in size. They have been fabricated by surface-micromachining technology and suspended 2 m above the substrate by the supports of cantilever beams. Micro thermal bubbles which are generated by heavily phosphorus doped polysilicon line resistive heaters have been used to lift the mechanical plates in a controllable manner. The typical current required to generate a single, spherical thermal bubble as the actuation source on top of the micro line resistors (60×2×0.3 m³ in size) is 8.4 mA (80 m Watt) in FC 43 liquid (an inert, dielectrical fluid available from the 3M company). The thermal bubbles have been demonstrated to actuate the mechanical plate perpendicularly to the substrate with a maximum elevation distance of 140 m and a maximum actuation force of 2 N. This new actuation mechanism is expected to find applications for micro fluidic devices.The authors would like to thank Prof. V.P. Carey, Mechanical Engineering department, U.C. Berkeley and Dr. A.P. Lee for valuable discussions. The devices were fabricated in the UC Berkeley Microfabrication Laboratory and the FC liquid was provided by 3M company. This work has been supported by Berkeley Sensor and Actuator Center, an NSF/Industry/University Co-operative Research Center.     

Anisotropic Si deep beam etching with profile control using SF6/O2 Plasma

This paper presents the results of dry plasma etching of single crystal silicon using SF₆ and O₂ as process gases in a traditional Reactive Ion Etcher. The highly anisotropic profiles are achieved for a deep beam feature with depths in excess of 100 m. The effect of O₂ concentration on both etch rate and etch profile is investigated across a range of chamber pressures. Etch profile anisotropy can be controlled through appropriate variations in O₂ and SF₆ flow rate and SEM images are provided to show this effect over a range of chamber pressures and RF powers. Our results indicate O₂ concentration to be the primary factor influencing etch profile, while system pressure is shown to have a strong influence over etch rate. Shadowing effect also has been discussed for the possible application of releasing the freestanding beams. These results aided in the formulation of a suitable process for fabricating long-travel electrothermally actuated beam structures with the depth and width of 100 m and 20 m. The ratio of beam depth to the mask-undercut is 10:1. This etching technique is resulting in the successful fabrication of thermoelectrically-driven long-travel beam structures.The author would like to thank Professor R. R. A. Syms and Mr Michael Larsson for encouraging and useful discussions during this work. This project is supported by the EPSRC under grant GR/R07844/01.     

Deep X-ray lithography using mask with integrated electrothermal actuator

We present a deep X-ray mask with integrated bent-beam electrothermal actuator for the fabrication of 3D microstructures with curved surface. The mask absorber is electroplated on the shuttle mass, which is supported by a pair of 20-m-thick single crystal silicon bent-beam electrothermal actuators and oscillated in a rectilinear direction due to the thermal expansion of the bent-beams. The width of each bent-beam is 10 m or 20 m and the length and bending angle are 1 mm and 0.1 rad, respectively, and the shuttle mass size is 1 mm × 1 mm. For 10-m-wide bent-beams, the shuttle mass displacement is around 15 m at 180 mW (3.6 V) dc input power. For 20-m-wide bent-beams, the shuttle mass displacement is around 19 m at 336 mW (4.2 V) dc input power. Sinusoidal cross-sectional PMMA microstructures with a pitch of 40 m and a height of 20 m are fabricated by 0.5 Hz, 20-m-amplitude sinusoidal shuttle mass oscillation.This research, under the contract project code MS-02-338-01, has been supported by the Intelligent Microsystem Center, which carries out one of the 21st centurys Frontier R & D Projects sponsored by the Korea Ministry of Science & Technology. Experiments at PLS were supported in part by MOST and POSCO.     

The Claremont Shakespeare Authorship Clinic: How Severe Are the Problems?

Ward Elliott (from 1987) and Robert Valenza (from 1989) set out to the find the true Shakespeare from among 37 anti-Stratfordian Claimants. As directors of the Claremont Shakespeare Authorship Clinic, Elliott and Valenza developed novel attributional tests, from which they concluded that most Claimants are not-Shakespeare. From 1990-4, Elliott and Valenza developed tests purporting further to reject much of the Shakespeare canon as not-Shakespeare (1996a). Foster (1996b) details extensive and persistent flaws in the Clinic's work: data were collected haphazardly; canonical and comparative text-samples were chronologically mismatched; procedural controls for genre, stanzaic structure, and date were lacking. Elliott and Valenza counter by estimating maximum erosion of the Clinic's findings to include five of our 54 tests, which can amount, at most, to half of one percent (1998). This essay provides a brief history, showing why the Clinic foundered. Examining several of the Clinic's representative tests, I evaluate claims that Elliott and Valenza continue to make for their methodology. A final section addresses doubts about accuracy, validity and replicability that have dogged the Clinic's work from the outset.     

One problem of mathematical optimal control theory

The necessary conditions obtained by the author in a previous study for the extremum of a functional that depends on the control function on the compact set and on a -measurable subset in (where is the ordinary Lebesgue measure) subject to functional equality and inequality constraints are generalized here to an arbitrary continuous Radon measure.Translated from Kibernetika, No. 4, pp. 69–73, July–August, 1990.     

Conditions for the Light-Traffic Insensitivity to Loss Probability in a GI/G/m/0 Queueing System

A loss queueing system GI/G/m/0 is considered. Let a(x) be a p.d.f. of interarrival intervals. Assume that this function behaves like cx^-1 for small x. Further let B(x) be a d.f. of service time; (1/) be the mean service time. Conditions are derived for the light-traffic insensitivity of the loss probability to the form of B(x) as (/ ) 0. In particular, the condition = 1 is necessary. Estimates for the loss probability are obtained.     

Context-free text grammars

A text is a triple=(, ₁, ₂) such that is a labeling function, and ₁ and ₂ are linear orders on the domain of ; hence may be seen as a word (, ₁) together with an additional linear order ₂ on the domain of . The order ₂ is used to give to the word (, ₁) itsindividual hierarchical representation (syntactic structure) which may be a tree but it may be also more general than a tree. In this paper we introducecontext-free grammars for texts and investigate their basic properties. Since each text has its own individual structure, the role of such a grammar should be that of a definition of a pattern common to all individual texts. This leads to the notion of ashapely context-free text grammar also investigated in this paper.     

A probabilistic analysis of the height of tries and of the complexity of triesort

Summary We consider binary tries formed by using the binary fractional expansions of X ₁, ...,X _n, a sequence of independent random variables with common density f on [0,1]. For H _n, the height of the trie, we show that either E(H_n)21og₂ n or E(H_n)= for all n2 according to whether f ²(x)dx is finite or infinite. Thus, the average height is asymptotically twice the average depth (which is log₂ n when f ²(x)dx>). The asymptotic distribution of H _n is derived as well.If f is square integrable, then the average number of bit comparisons in triesort is nlog₂ n+0(n), and the average number of nodes in the trie is 0(n).Research of the author was supported in part by FCAC Grant EQ-1678     

Formalizing process algebraic verifications in the calculus of constructions

This paper reports on the first steps towards the formal verification of correctness proofs of real-life protocols in process algebra. We show that such proofs can be verified, and partly constructed, by a general purpose proof checker. The process algebra we use isCRL, ACP augmented with data, which is expressive enough for the specification of real-life protocols. The proof checker we use is Coq, which is based on the Calculus of Constructions, an extension of simply typed lambda calculus. The focus is on the translation of the proof theory ofCRL andCRL-specifications to Coq. As a case study, we verified the Alternating Bit Protocol.     

On the Impact of Systematic Noise on the Evolutionary Optimization Performance—A Sphere Model Analysis

Quality evaluations in optimization processes are frequently noisy. In particular evolutionary algorithms have been shown to cope with such stochastic variations better than other optimization algorithms. So far mostly additive noise models have been assumed for the analysis. However, we will argue in this paper that this restriction must be relaxed for a large class of applied optimization problems. We suggest systematic noise as an alternative scenario, where the noise term is added to the objective parameters or to environmental parameters inside the fitness function. We thoroughly analyze the sphere function with systematic noise for the evolution strategy with global intermediate recombination. The progress rate formula and a measure for the efficiency of the evolutionary progress lead to a recommended ratio between and . Furthermore, analysis of the dynamics identifies limited regions of convergence dependent on the normalized noise strength and the normalized mutation strength. A residual localization error R can be quantified and a second to ratio is derived by minimizing R .     

On a Stroboscopic Approach to Quantum Tomography of Qudits Governed by Gaussian Semigroups

In this paper, we discuss the minimal number of observables Q ₁, ..., Q , where expectation values at some time instants t ₁, ..., t _r determine the trajectory of a d-level quantum system (qudit) governed by the Gaussian semigroup . We assume that the macroscopic information about the system in question is given by the mean values E _j(Q _i) = tr(Q _i(t _j)) of n selfadjoint operators Q ₁, ..., Q _n at some time instants t ₁ < t ₂ < ... < t _r, where n < d ²– 1 and r deg (, ). Here (, ) stands for the minimal polynomial of the generator of the Gaussian flow (t).     

Development of a novel self-sensitive atomic force microscope for nondestructive measurement of micro vertical surfaces

A novel Atomic Force Microscope for the nondestructive measurement of micro vertical surfaces have developed. This AFM have two cameras for the precise alignment of the cantilever and sample, self-sensitive cantilever that enables nondestructive measurement of micro vertical surfaces, and piezo-driven stage for minute movements of the cantilever and sample stage. With our developed AFM, we can nondestructively measure the sidewalls of dry-etched silicon wafers as small as 400 m wide and 100 m high.     

A Micro corona motor fabricated by a SU-8 built-on X-ray mask

A micro corona motor was fabricated using a membraneless built-on X-ray mask. Sharp stator electrodes of this motor ionize air molecules and ionized charges transfer onto the rotor surface, resulting in rotating rotor motions by Coulomb forces. For good performance, the stators electrodes should be wide (axial) and have sharp tips. Therefore, X-ray lithography was adopted for precise, high aspect ratio characteristics. To avoid the fabrication difficulty of a membrane X-ray mask, a built-on X-ray mask (conformal mask) technique was employed with negative toned SU-8 photoresist. SU-8 features X-ray fabrication compatibility, X-ray transparency and a large range of thickness. This technique may be suitable for fast fabrication of prototypes or very tall structures, which can be largely affected by printing gaps. For the X-ray built-on mask, 20 m SU-8 was patterned and 8 m gold absorber was electroplated on top of the 300 m PMMA resist. Tests showed good quality pattern transfer from the SU-8 pattern and smooth sidewalls.The authors would like to thank the National Science Foundation, Grant DMI-0115527, Manufacturing Machines and Equipment Program, Division of Design, Manufacture, and Industrial Innovation, and Atoz CompuNet Ltd. for support for this work. We also acknowledge partial support from Center for Nano and Molecular Science and Technology and Welch foundation in The University of Texas at Austin.     

Fabrication and preliminary testing of X-ray lenses in thick SU-8 resist layers

Deep X-ray lithography processing of SU-8 negative resist layers with thicknesses of up to 1 mm and physical-chemical properties of SU-8 polymer structures were investigated to find the optimum conditions for the fabrication of X-ray refractive lenses. The exposure was carried out at the ANKA storage ring in Karlsuhe, Germany. Experimental tests of the lenses were performed at the ESRF in Grenoble, France. First lenses showed a gain in the range of 20, a full width at half maximum of the focal spot intensity of approximately 2 m to 3 m and unique radiation stability of the optical characteristics.     

A system to measure 3-directional relative displacements for a biomedical application

A micro system for measuring the relative displacements between a bone and an implant in a prosthetic hip of a human being has been realized. Novel are the small dimensions of the system combined with the possibility to measure relative displacements in three directions. The system consists of a microsensor body, a mechanical transducer element made by precision mechanics, electronics, and the final package. The realization and test results of a prototype system are presented. Typical ranges for these prototypes are ±500 m for lateral directions and ±50 m in axial direction.