Recurrent traveling waves in a two-dimensional saw-toothed cylinder and their average speed

We study a curvature-dependent motion of plane curves in a two-dimensional infinite cylinder with spatially undulating boundary. The law of motion is given by V=κ+A$V=\kappa +A$, where V is the normal velocity of the curve, κ is the curvature, and A is a positive constant. The boundary undulation is assumed to be almost periodic, or, more generally, recurrent in a certain sense. We first introduce the definition of recurrent traveling waves and establish a necessary and sufficient condition for the existence of such traveling waves. We then show that the traveling wave is asymptotically stable if it exists. Next we show that a regular traveling wave has a well-defined average speed if the boundary shape is strictly ergodic. Finally we study what we call “virtual pinning”, which means that the traveling wave propagates over the entire cylinder with zero average speed. Such a peculiar situation can occur only in non-periodic environments and never occurs if the boundary undulation is periodic.     

Hom-Orthogonal Partial Tilting Modules for Dynkin Quivers

We count the number of isomorphism classes of hom-orthogonal partial tilting modules over path algebras of Dynkin quiver of type 𝔸 _n , 𝔻 _n , 𝔼 _n . This number is independent on the choice of an orientation of the arrows, and the number for 𝔸 _n or 𝔻 _n -type can be expressed as a special value of a hypergeometric function. As a consequence of our theorem, we obtain a minimum value of the number of basic relative invariants of corresponding regular prehomogeneous vector spaces.     

Axial non-mechanical scan in laser doppler velocimeter using single diffraction grating

An axial non-mechanical scan in the laser Doppler velocimeter (LDV) using a single diffraction grating is demonstrated. The measurement position in this LDV is axially scanned using a wavelength change and a dispersion function of the grating. The experimental result using a sensor probe setup indicates that a scanning function is successfully obtained with a simpler arrangement than that of the LDV previously reported, and the ratio of the scanning range to the working distance can be enhanced by virtue of using larger angular dispersion.     

An estimation of the baseband transfer function of multimode optical fibers

This paper discusses an alternative criterion for estimating the baseband transfer function of multimode optical fibers. The optical fibers having little mode conversions show that the baseband frequency characteristics are affected strongly by the launching condition of an input optical pulse. In the criterion presented here, the baseband transfer function in such fibers is estimated by considering the launching condition that excites all fiber modes uniformly in amplitudes. In order to obtain such a transfer function, the actual responses affected by the launching conditions are measured together with the modal power distributions for different kinds of launching conditions. A numerical procedure is then presented that enables us to derive the baseband transfer function independently of modal power distributions. Experimental results at λ x= 633 nm and 856 nm are presented for step index fibers (0.1 and 0.2 km long) having a core radius of 30 pm (its refractive index is 1.452) and a refractive index difference of 0.7%.     

Recent developments of optical fiber sensors for automotive use

Optical fiber sensing technologies are expected to apply for many future electronic control systems in automobiles, because of their inherent outstanding features, such as high noise immunity, high heat resistance, and flexible light propagation paths which can be applied to measure the movements and directions of the mobiles. In this paper, two typical applications of fiber sensing technologies in automobiles are described in detail. The combustion flame detector is one of the typical applications of a fiber spectroscopic technology which utilizes the feature of high noise and heat resistibility and remote sensibility. Measurement of engine combustion conditions, such as the detonation, the combustion initiation, and the air-fuel ratio, have been demonstrated in an experimental fiber sensing method. Fiber interferometers, such as a fiber gyroscope, have great possibilities in future mobile applications because they are applicable to many kinds of measurements for movements and physical variables. An optical fiber gyroscope utilizing the single polarized optical fiber and other optical devices has been developed. Quite an accurate measurement of vehicle position was displayed on a prototype navigation system which installed the fiber gyroscope as a rotational speed sensor.     

Synchronization engineering: theoretical framework and application to dynamical clustering

A method for engineering the global behavior of populations of rhythmic elements is presented. The framework, which is based on phase models, allows a nonlinear time-delayed global feedback signal to be constructed which produces an interaction function corresponding to the desired behavior of the system. It is shown theoretically and confirmed in numerical simulations that a polynomial, delayed feedback is a versatile tool to tune synchronization patterns. Dynamical states consisting of one to four clusters were engineered to demonstrate the application of synchronization engineering in an experimental electrochemical system.     

Development and testing of a CW-EPR apparatus for imaging of short-lifetime nitroxyl radicals in mouse head

This article describes a method for reducing the acquisition time in three-dimensional (3D) continuous-wave electron paramagnetic resonance (CW-EPR) imaging. To visualize nitroxyl spin probes, which have a short lifetime in living organisms, the acquisition time for a data set of spectral projections should be shorter than the lifetime of the spin probes. To decrease the total time required for data acquisition, the duration of magnetic field scanning was reduced to 0.5 s. Moreover, the number of projections was decreased by using the concept of a uniform distribution. To demonstrate this faster data acquisition, two kinds of nitroxyl radicals with different decay rates were measured in mice. 3D EPR imaging of 4-hydroxy-2,2,6,6-tetramethylpiperidine-d₁₇-1-¹⁵N-1-oxyl in mouse head was successfully carried out. 3D EPR imaging of nitroxyl spin probes with a half-life of a few minutes was achieved for the first time in live animals.     

A loop resonator for slice-selective in vivo EPR imaging in rats

A loop resonator was developed for 300 MHz continuous-wave electron paramagnetic resonance (CW-EPR) spectroscopy and imaging in live rats. A single-turn loop (55 mm in diameter) was used to provide sufficient space for the rat body. Efficiency for generating a radiofrequency magnetic field of 38 microT/W(1/2) was achieved at the center of the loop. For the resonator itself, an unloaded quality factor of 430 was obtained. When a 350 g rat was placed in the resonator at the level of the lower abdomen, the quality factor decreased to 18. The sensitive volume in the loop was visualized with a bottle filled with an aqueous solution of the nitroxide spin probe 3-carbamoyl-2,2,5,5-tetramethyl-3-pyrrolin-1-yloxy (3-CP). The resonator was shown to enable EPR imaging in live rats. Imaging was performed for 3-CP that had been infused intravenously into the rat and its distribution was visualized within the lower abdomen.     

New aplysiatoxin derivatives from the Okinawan cyanobacterium Moorea producens

The marine cyanobacterium Moorea producens is a rich source of diverse compounds that possess a variety of biological activities. In the present study, eight new aplysiatoxin derivatives, namely 6, 8–13, and 15, along with aplysiatoxin (1), debromoaplysiatoxin (2), 3-methoxyaplysiatoxin (3), anhydroaplysiatoxin (4), anhydrodebromoaplysiatoxin (5), oscillatoxin B2 (7), and 30-methyloscillatoxin D (14) were isolated and identified from the Okinawan M. producens. In cytotoxicity and diatom growth inhibition tests, the fifteen compounds tested (1–15) showed moderate or no activity at a concentration of 10?μg/mL.