Optimization of photonic crystal structures

We report on the numerical structural optimization of two-dimensional photonic crystal (PhC) power dividers by using two different classes of optimization algorithms, namely, a modified truncated Newton (TN) gradient search as deterministic local optimization scheme and an evolutionary optimization representing the probabilistic global search strategies. Because of the severe accuracy requirements during optimization, the proper PhC device has been simulated by using the multiple-multipole program that is contained in the MaX-1 software package. With both optimizer classes, we found reliable and promising solutions that provide vanishing power reflection and perfect power balance at any specified frequency within the photonic bandgap. This outcome is astonishing in light of the discrete nature inherent in the underlying PhC structure, especially when the optimizer is allowed to intervene only within a very small volume of the device. Even under such limiting constraints structural optimization is not only feasible but has proven to be highly successful.     

Semi-intelligible Isar Proofs from Machine-Generated Proofs

Sledgehammer is a component of the Isabelle/HOL proof assistant that integrates external automatic theorem provers (ATPs) to discharge interactive proof obligations. As a safeguard against bugs, the proofs found by the external provers are reconstructed in Isabelle. Reconstructing complex arguments involves translating them to Isabelle’s Isar format, supplying suitable justifications for each step. Sledgehammer transforms the proofs by contradiction into direct proofs; it iteratively tests and compresses the output, resulting in simpler and faster proofs; and it supports a wide range of ATPs, including E, LEO-II, Satallax, SPASS, Vampire, veriT, Waldmeister, and Z3.     

Proof Pearl: Mechanizing the Textbook Proof of Huffman’s Algorithm

Huffman’s algorithm is a procedure for constructing a binary tree with minimum weighted path length. Our Isabelle/HOL proof closely follows the sketches found in standard algorithms textbooks, uncovering a few snags in the process. Another distinguishing feature of our formalization is the use of custom induction rules to help Isabelle’s automatic tactics, leading to very short proofs for most of the lemmas. This work was supported by the DFG grant NI 491/11-1.     

Experimental determination of the fundamental-mode diameter in solid-state lasers

A method to determine directly the radius of the fundamental mode in a laser crystal has been developed. The radius is measured by comparison of the distribution of the spontaneous emission in the pumped region during laser operation with the fluorescence distribution without laser emission. Measuring the mode radius with various pump powers enables one to optimize the overlap between the pump and the cavity beam and to determine the dioptric power of the thermally induced lens.     

Single subject image analysis using the complex general linear model--an application to functional magnetic resonance imaging with multiple inputs

A linear time invariant model is applied to functional fMRI blood flow data. Based on traditional time series analysis, this model assumes that the fMRI stochastic output sequence can be determined by a constant plus a linear filter (hemodynamic response function) of several fixed deterministic inputs and an error term assumed stationary with zero mean. The input function consists of multiple exponential distributed (time delay between images) visual stimuli consisting of negative and erotic images. No a priori assumptions are made about the hemodynamic response function that, in essence, is calculated at each spatial position from the data. The sampling rate for the experiment is 400 ms in order to allow for filtering out higher frequencies associated with the cardiac rate. Since the statistical analysis is carried out in the Fourier domain, temporal correlation problems associated with inference in the time domain are avoided. This formal model easily lends itself to further development based on previously developed statistical techniques.     

Development of Nano-Composite Microstructures in ZrO2-Al2O3 via the Solution Precursor Method

Aqueous mixtures of zirconium acetate and aluminum nitrate were pyrolyzed and crystallized to form a metastable solid solution, Zr_{1- x} Al _x O_{2− x /2} ( x < 0.57). The initial, metastable phase partitions at higher temperatures to form two metastable phases, viz., t −ZrO₂+γ-Al₂O₃ with a nano-scale microstructure. The microstructural observations associated with the γ- →α-Al₂O₃ phase transformation in the t -ZrO₂ matrix are reported for compositions containing 10, 20, and 40 mol% A1₂O₃. During this phase transformation, the α-Al₂O₃ grains take the form of a colony of irregular, platelike grains, all with a common crystallographic orientation. The plates contain ZrO₂ inclusions and are separated by ZrO₂ grains. The volume fraction of A1₂O₃ and the heat treatment conditions influence the final microstructure. At lower volume fractions of A1₂O₃, the colonies coarsen to single, irregular plates, surrounded by polycrystalline ZrO₂. Interpenetrating microstructures produced at high volume fractions of A1₂O₃ exhibit very little grain growth for periods up to 24 h at 1400°C.     

Solid phase extraction and removal of 2,4-dichlorophenol from aqueous samples using magnetic graphene nanocomposite

A magnetic graphene nanocomposite (Fe₃O₄-GNC) was prepared and used for the solid phase extraction (SPE) and removal of 2,4-dichlorophenol from aqueous solutions. The physicochemical properties were investigated using SEM, EDX, FTIR, and TGA. Different factors affecting sorption capacity were studied systematically. Results for kinetics studies revealed that 2,4-dichlorophenol sorption followed pseudo-second-order kinetics and the q_e value (987.45 mg/g) was in close agreement with experimental value (1000 mg/g). Thermodynamic study showed that the sorption is endothermic (?Hº = +56.116 kJ/mol) and spontaneous. The desorption studies were carried out for the reusability and extraction of 2,4-dichlorophenol from aqueous samples and 94% recoveries were obtained. The method was found feasible for the removal and preconcentration of trace analysis of 2,4-dichlorophenol in environmental water samples.     

A 3-level autonomous mobile robot navigation system designed by using reasoning/search approaches

This paper describes how soft computing methodologies such as fuzzy logic, genetic algorithms and the Dempster–Shafer theory of evidence can be applied in a mobile robot navigation system. The navigation system that is considered has three navigation subsystems. The lower-level subsystem deals with the control of linear and angular volocities using a multivariable PI controller described with a full matrix. The position control of the mobile robot is at a medium level and is nonlinear. The nonlinear control design is implemented by a backstepping algorithm whose parameters are adjusted by a genetic algorithm. We propose a new extension of the controller mentioned, in order to rapidly decrease the control torques needed to achieve the desired position and orientation of the mobile robot. The high-level subsystem uses fuzzy logic and the Dempster–Shafer evidence theory to design a fusion of sensor data, map building, and path planning tasks. The fuzzy/evidence navigation based on the building of a local map, represented as an occupancy grid, with the time update is proven to be suitable for real-time applications. The path planning algorithm is based on a modified potential field method. In this algorithm, the fuzzy rules for selecting the relevant obstacles for robot motion are introduced. Also, suitable steps are taken to pull the robot out of the local minima. Particular attention is paid to detection of the robot’s trapped state and its avoidance. One of the main issues in this paper is to reduce the complexity of planning algorithms and minimize the cost of the search. The performance of the proposed system is investigated using a dynamic model of a mobile robot. Simulation results show a good quality of position tracking capabilities and obstacle avoidance behavior of the mobile robot.     

Monitoring the Polymorphic Transformation of a Palm Kernel-Based Emulsion Using Ultrasound

Ultrasonic spectrometry was used to monitor the changes in polymorphism of palm kernel fat present in two tempered non-dairy emulsions with different globule sizes. Laser diffraction and differential scanning calorimetry (DSC) were performed to characterize the emulsions. X-ray diffraction (XRD) and nuclear magnetic resonance (NMR) were used to determine the polymorphic state and solid fat content (SFC) of fully hydrogenated palm kernel oil during tempering of the emulsions. The ultrasonic instrument generated a “chirp” signal, which is characterized by its bandwidth. The ultrasonic measurements were carried out using two different pairs of transducers with different center frequencies, 2.25 and 0.5 MHz, and bandwidths. 3D plots were generated disputing time, frequency, and signal strength. The whole tempering process, from start to finish, was better characterized with the 2.25-MHz center frequency transducers. The ultrasonic velocity through the emulsions was always higher for the more stable β′ polymorph than for the α polymorph (p?<?0.05) regardless of the pair of transducers used. The 2.25-MHz transducer revealed no significant difference (p?>?0.05) on the ultrasound velocities obtained for the two globule sizes. Monitoring of polymorphic changes in emulsions using ultrasonic spectrometry could be used for an online measurement system for industrial manufacturing.