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.     

Decompositions of polyhedral products for shifted complexes

The conjecture of Bahri, Bendersky, Cohen and Gitler (2010)  [3] on wedge decompositions of polyhedral products of shifted complexes is settled affirmatively. As a corollary, it is proved that the homotopy type of the complement of a coordinate subspace arrangement associated with a shifted complex, tensored with R^r${\mathbb{R}}^r$ for any r≥1$r\ge 1$, has the homotopy type of a wedge of spheres.     

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.     

Study of Neutron-Rich Hypernuclei by the (π −, K +) Reaction at J-PARC

We are planning to perform an experiment at J-PARC and produce new neutron-rich Λ hypernuclei by using the (π ^?, K ⁺) reaction (J-PARC E10). As the first step, we are planning to produce ${^6_{\Lambda}{\rm H}}$ hypernuclei with a ⁶Li target. To conduct this experiment, we are developing new detectors, those are scintillating fiber tracker, and silicon strip detector, for high rate operation to aim at increasing beam intensity up to 10⁷/spill. As a result of beam test in Jun 2012, we are going to use high-rate beam at least 10⁷/spill.     

Wave propagation along a non-principal direction in a compressible pre-stressed elastic layer

The dispersive behavior of small amplitude waves propagating along a non-principal direction in a pre-stressed, compressible elastic layer is considered. One of the principal axes of stretch is normal to the elastic layer and the direction of propagation makes an angle θ with one of the in-plane principal axes. The dispersion relations which relate wave speed and wavenumber are obtained for both symmetric and anti-symmetric motions by formulating the incremental boundary value problem for a general strain energy function. The behavior of the dispersion curves for symmetric waves is for the most part similar to that of the anti-symmetric waves at the low and high wavenumber limits. At the low wavenumber limit, depending on the pre-stress and propagation angle, it may be possible for both the fundamental mode and the next lowest mode to have finite phase speeds, while other higher modes have an infinite phase speed. At the high wavenumber limit, the phase speeds of the fundamental mode and the higher modes tend to the Rayleigh surface wave speed and the limiting wave speeds of the layer, respectively. Numerical results are presented for a Blatz–Ko material and the effect of the propagation angle is clearly illustrated.     

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.