On the Gröbner basis triangularization of constraint equations in natural coordinates

Efficient dynamic simulation code is essential in many situations (including hardware-in-the-loop and model-predictive control applications), and highly beneficial in others (such as design optimization, sensitivity analysis, parameter identification, and controller tuning tasks). When the number of modeling coordinates n exceeds the degrees-of-freedom of the system f, as is often the case when closed kinematic chains are present, the governing dynamic equations consist of n second-order ordinary differential equations (ODEs) coupled with m=n?f algebraic constraint equations. This set of n+m index-3 differential-algebraic equations can be difficult to solve in an efficient yet accurate manner. Embedding (or generalized coordinate partitioning) can be used to obtain f ODEs (one for each independent acceleration), which are generally more amenable to numerical integration; however, the dependent positions are typically computed from the independent positions at each time step. Newton–Raphson iteration is often used for solving the position-level kinematics, but only provides solutions to within a specified tolerance, and can require several iterations to converge. In this work, Gröbner bases are used to obtain recursively solvable symbolic solutions for the dependent positions, which can then be evaluated to within machine precision using a fixed number of arithmetic operations. Natural coordinates are particularly attractive in this context, since the resulting constraint equations are maximally quadratic polynomials and are, therefore, easily triangularized. The proposed approach is suitable for use in an automated formulation procedure and, as demonstrated by three examples, is capable of generating highly efficient simulation code with minimal additional effort required at the formulation stage.     

Local structure and concentration in Al-Mn alloy electrodeposits

The structures of f.c.c. crystalline and amorphous phases coexisting in Al-Mn alloy electrodeposits containing 11–30 wt% were examined by using the grazing-incidence X-ray diffraction (GIXD) method, high-resolution transmission electron microscopy combined with energy dispersive X-ray spectrometry (HRTEM/EDS), and the manganese K-edge extended X-ray absorption fine-structure (EXAFS) technique. The amorphous and f.c.c. phases were homogeneously distributed in the through-thickness direction of the electrodeposits, although the amorphous phase increased and the f.c.c. phase decreased with increasing manganese total concentration. The decrease of Mn-content in the f.c.c. crystalline phases with increasing manganese total concentration was revealed by the lattice constant measurement of the f.c.c. crystalline phase. This result was also supported by the microarea elemental analysis by HRTEM/EDS. The EXAFS result has indicated that the manganese local structures in the amorphous phases are almost identical in different manganese total concentration electrodeposits. This suggests that the Mn-content in the amorphous phases hardly changes with increasing manganese total concentration. These results have revealed that a peculiar elemental partition occurs in the amorphous and crystalline phases of Al-Mn alloy electrodeposits.     

High‐resolution technology for FPD manufacturing

Using shorter wavelength for exposure light is one way to achieve high resolution while keeping sufficient depth of focus. We show exposure results for high resolution to confirm the effect of deep UV exposure light. With deep UV light, 1.2‐µm line and space pattern and 1.8‐µm contact hole pattern are resolved while keeping sufficient depth of focus.     

Basic study about cooperative movement between a human and an agent with entrainment

The use of an agent in the environment, as in medical treatment, welfare, the construction field, and the home, is examined. It is necessary for the agent to be able to work cooperatively with a human, and that may be a problem. Therefore, this study pays attention to the phenomenon that is called entrainment. This is the phenomenon where the rhythm of a certain person and the partner in the communication is synchronized. The purpose of this study is to perform a basic examination into applying an entrainment in order to realize cooperation in operations between a human and an agent. Since many human rhythms are expressed by a nonlinear oscillator, we simulated limited cycle oscillators, which are one of two nonlinear oscillators that cause interactions between agents, as the basic examination for this achievement. Consequently, entrainment of limited cycle oscillators with rhythms which differ has been checked in certain conditions. As a result, the possibility that cooperative movement could be gained was suggested.     

Interplane charge dynamics in high-temperature superconductors; Charge confinement and spin gap

We have studies optical and transport properties of the prototypical high-T_c system La_2–xSr_xCuO₄ in the direction perpendicular to the CuO₂ planes (c-axis direction). In the normal state, it is found that the c-axis spectral weight is suppressed over a wide energy range. This is a demonstration of charge confinement in the real material which has been proposed theoretically by Anderson. Upon reducing temperature the low-energy spectral weight of the underdoped compound is further reduced, due perhaps to spin gap effect. The suppressed spectral weight results in completely different out-of-plane charge transport in the normal state and leads to the appearance of a superconducting plasma edge within the gap region in the superconducting state.     

Revolving Vernier Mechanism Controls Size of Linear Homomultimer

A new kind of the Vernier mechanism that is able to control the size of linear assembly of DNA origami nanostructures is proposed. The mechanism is realized by mechanical design of DNA origami, which consists of a hollow cylinder and a rotatable shaft in it connected through the same scaffold. This nanostructure stacks with each other by the shape complementarity at its top and bottom surfaces of the cylinder, while the number of stacking is limited by twisting angle of the shaft. Experiments have shown that the size distribution of multimeric assembly of the origami depends on the twisting angle of the shaft; the average lengths of the multimer are decamer, hexamer, and tetramer for 0°, 10°, and 20° twist, respectively. In summary, it is possible to affect the number of polymerization by adjusting the precise shape and movability of a molecular structure.     

Detection of microspotted carcinoembryonic antigen on a glass substrate by scanning electrochemical microscopy

Microspots of carbinoembryonic antigen (CEA) on glass substrates were characterized by scanning electrochemical microscopy (SECM). CEA was immobilized via a sandiwch method using horseradish peroxidase (HRP)-labeled anti-CEA. The reduction current of the oxidized form of ferrocenylmethanol generated by the HRP reaction was monitored to view SECM images. This method detects as low as ～10(4) CEA molecules in a single 20-μm-radius spot.     

The Somatropin Reference Standard (Control 951) of the National Institute of Health Sciences

Somatropin material was examined for preparation of the "Somatropin Reference Standard". The candidate material was evaluated by a domestic collaborative study in which eight laboratories participated. The protein content was determined to be 4.5 mg/Vial based on amino acid analysis. Because of the possibility of application as a chemical reference standard for assay by the HPLC method, a physico-chemical evaluation of the candidate material was also performed. By SE-HPLC, the content of polymer, dimer were determined to be 0.54%, 0.98%, respectively. By RP-HPLC, the early peak area ascribed to desamido and sulfoxide form was 1.07% of the total peak area. And for informational data, the potency of the candidate material, being estimated by three different biological methods, weight gain assay, tibia test and adiposeconversion assay is 14.8 IU/vial. Based on the above results, the candidate was authorized as the Somatropin Reference Standard of the National Institute of Health Sciences.     

Parameter identification in dynamic systems using the homotopy optimization approach

Identifying the parameters in a mathematical model governed by a system of ordinary differential equations is considered in this work. It is assumed that only partial state measurement is available from experiments, and that the parameters appear nonlinearly in the system equations. The problem of parameter identification is often posed as an optimization problem, and when deterministic methods are used for optimization, one often converges to a local minimum rather than the global minimum. To mitigate the problem of converging to local minima, a new approach is proposed for applying the homotopy technique to the problem of parameter identification. Several examples are used to demonstrate the effectiveness of the homotopy method for obtaining global minima, thereby successfully identifying the system parameters.     

Fast Particle‐based Visual Simulation of Ice Melting

The visual simulation of natural phenomena has been widely studied. Although several methods have been proposed to simulate melting, the flows of meltwater drops on the surfaces of objects are not taken into account. In this paper, we propose a particle‐based method for the simulation of the melting and freezing of ice objects and the interactions between ice and fluids. To simulate the flow of meltwater on ice and the formation of water droplets, a simple interfacial tension is proposed, which can be easily incorporated into common particle‐based simulation methods such as Smoothed Particle Hydrodynamics. The computations of heat transfer, the phase transition between ice and water, the interactions between ice and fluids, and the separation of ice due to melting are further accelerated by implementing our method using CUDA. We demonstrate our simulation and rendering method for depicting melting ice at interactive frame‐rates.