Generation of Micro Mechanical Devices Using Stereo Lithography

A high resolution machining setup for creating three-dimensional precision components from a UV-curable photo-resin has been developed. By using frequency-converted diode-pumped solid state lasers, functional micro-mechanical devices are directly fabricated in a successive layer-bylayer fashion. Within this paper, the direct generation of micro assemblies having moving components without further assembly of parts will be presented. The micro system design is based on user-defined 3D-CAD data and will completively be built up within the fabrication cycle. By using specially developed μSL materials with suitable properties for micromechanical parts, the development from Rapid Prototyping towards Rapid Production of small series is intended.Mechanical Engineerin

Stochastic Matrix Product States

The concept of stochastic matrix product states is introduced and a natural form for the states is derived. This allows to define the analogue of Schmidt coefficients for steady states of non-equilibrium stochastic processes. We discuss a new measure for correlations which is analogous to the entanglement entropy, the entropy cost $S_C$, and show that this measure quantifies the bond dimension needed to represent a steady state as a matrix product state. We illustrate these concepts on the hand of the asymmetric exclusion process

Asymptotic approximations to the nodes and weights of Gauss-Hermite and Gauss-Laguerre quadratures

Asymptotic approximations to the zeros of Hermite and Laguerre polynomials are given, together with methods for obtaining the coefficients in the expansions. These approximations can be used as a standalone method of computation of Gaussian quadratures for high enough degrees, with Gaussian weights computed from asymptotic approximations for the orthogonal polynomials. We provide numerical evidence showing that for degrees greater than $100$ the asymptotic methods are enough for a double precision accuracy computation ($15$-$16$ digits) of the nodes and weights of the Gauss--Hermite and Gauss--Laguerre quadratures.Comment: Submitted to Studies in Applied Mathematic

Computation of the Marcum Q-function

Methods and an algorithm for computing the generalized Marcum $Q-$function ($Q_{\mu}(x,y)$) and the complementary function ($P_{\mu}(x,y)$) are described. These functions appear in problems of different technical and scientific areas such as, for example, radar detection and communications, statistics and probability theory, where they are called the non-central chi-square or the non central gamma cumulative distribution functions. The algorithm for computing the Marcum functions combines different methods of evaluation in different regions: series expansions, integral representations, asymptotic expansions, and use of three-term homogeneous recurrence relations. A relative accuracy close to $10^{-12}$ can be obtained in the parameter region $(x,y,\mu) \in [0,\,A]\times [0,\,A]\times [1,\,A]$, $A=200$, while for larger parameters the accuracy decreases (close to $10^{-11}$ for $A=1000$ and close to $5\times 10^{-11}$ for $A=10000$).Comment: Accepted for publication in ACM Trans. Math. Soft

Impact of foods with health logo on ssaturated fat, sodium and sugar intake of young Dutch adults

Objective Health logos are introduced to distinguish foods with ‘healthier’ nutrient composition from regular foods. In the present study, we evaluated the effects of changed food compositions according to health logo criteria on the intake of saturated fat, sugar and sodium in a Dutch population of young adults. Design Foods in the Dutch food composition table were evaluated against nutrient criteria for logo eligibility. Three replacement scenarios were compared with the nutrient intake ‘as measured’ in the Dutch consumption survey. The foods not complying with health logo criteria were replaced either by ‘virtual’ foods exactly complying with the health logo criteria, with real 2007 market shares (scenario I) and 100 % market shares (scenario II), or by existing similar foods with a composition that already complied with the health logo criteria (scenario III). Results The percentage reduction in nutrient intake with the current 2007 market shares of ‘health logo foods’ was -2·5 % for SFA, 0 % for sodium and -1 % for sugar. With a 100 % market share these reductions would be -10 % for SFA, -4 % for sodium and -6 % for sugar. This may lead to a reduction of -40 % for SFA, -23 % for sodium and -36 % for sugar in the most optimal replacement scenario. Conclusions With ‘health logo foods’, available in 2007 and current consumption patterns, small reductions can be achieved for SFA and sugar. For additional reductions, lowering the fat/sodium content of meat (products) towards health logo criteria and drinks without sugar towards limits far below health logo criteria would be the most effective reformulation strategy

Non-equilibrium dynamics of a Bose-Einstein condensate in an optical lattice

The dynamical evolution of a Bose-Einstein condensate trapped in a one-dimensional lattice potential is investigated theoretically in the framework of the Bose-Hubbard model. The emphasis is set on the far-from-equilibrium evolution in a case where the gas is strongly interacting. This is realized by an appropriate choice of the parameters in the Hamiltonian, and by starting with an initial state, where one lattice well contains a Bose-Einstein condensate while all other wells are empty. Oscillations of the condensate as well as non-condensate fractions of the gas between the different sites of the lattice are found to be damped as a consequence of the collisional interactions between the atoms. Functional integral techniques involving self-consistently determined mean fields as well as two-point correlation functions are used to derive the two-particle-irreducible (2PI) effective action. The action is expanded in inverse powers of the number of field components N, and the dynamic equations are derived from it to next-to-leading order in this expansion. This approach reaches considerably beyond the Hartree-Fock-Bogoliubov mean-field theory, and its results are compared to the exact quantum dynamics obtained by A.M. Rey et al., Phys. Rev. A 69, 033610 (2004) for small atom numbers.Comment: 9 pages RevTeX, 3 figure

Computer based human-centered display system

A human centered informational display is disclosed that can be used with vehicles (e.g. aircraft) and in other operational environments where rapid human centered comprehension of an operational environment is required. The informational display integrates all cockpit information into a single display in such a way that the pilot can clearly understand with a glance, his or her spatial orientation, flight performance, engine status and power management issues, radio aids, and the location of other air traffic, runways, weather, and terrain features. With OZ the information is presented as an integrated whole, the pilot instantaneously recognizes flight path deviations, and is instinctively drawn to the corrective maneuvers. Our laboratory studies indicate that OZ transfers to the pilot all of the integrated display information in less than 200 milliseconds. The reacquisition of scan can be accomplished just as quickly. Thus, the time constants for forming a mental model are near instantaneous. The pilot's ability to keep up with rapidly changing and threatening environments is tremendously enhanced. OZ is most easily compatible with aircraft that has flight path information coded electronically. With the correct sensors (which are currently available) OZ can be installed in essentially all current aircraft

Resonantly enhanced pair production in a simple diatomic model

A new mechanism for the production of electron-positron pairs from the interaction of a laser field and a fully stripped diatomic molecule in the tunneling regime is presented. When the laser field is turned off, the Dirac operator has resonances in both the positive and the negative energy continua while bound states are in the mass gap. When this system is immersed in a strong laser field, the resonances move in the complex energy plane: the negative energy resonances are pushed to higher energies while the bound states are Stark shifted. It is argued here that there is a pair production enhancement at the crossing of resonances by looking at a simple 1-D model: the nuclei are modeled simply by Dirac delta potential wells while the laser field is assumed to be static and of finite spatial extent. The average rate for the number of electron-positron pairs produced is evaluated and the results are compared to the single nucleus and to the free cases. It is shown that positrons are produced by the Resonantly Enhanced Pair Production (REPP) mechanism, which is analogous to the resonantly enhanced ionization of molecular physics. This phenomenon could be used to increase the number of pairs produced at low field strength, allowing the study of the Dirac vacuum.Comment: 11 pages, 4 figure