Shinya Watanabe

Ibaraki University · Department of Mathematics and Informatics

The Soret effect is a phenomenon in which the components of mixed fluids are separated by a temperature gradient. This study investigated a simple and low-cost technique for extracting high concentration hydrogen (H2) by utilizing the Soret effect in a H2-carbon dioxide mixed gas. Previous research by the authors attempted to improve the efficiency...

In recent years, hydrogen energy, which does not emit carbon dioxide when used, has been attracting attention as a candidate solution to environmental issues. Hydrogen is produced as a mixture of hydrogen and carbon dioxide or other gases, mainly using fossil fuel reforming. Therefore, in order to use hydrogen as an energy source, the gas mixture m...

A new method for separating a binary gas mixture, such as hydrogen and carbon dioxide, is proposed and investigated numerically and experimentally. As a pressure driven flow of the mixture goes through a two-dimensional Burgers cascade, the components are separated due to thermal diffusion and the amplifying effect of the cascade. Unlike traditiona...

A new method for separating a binary gas mixture, such as hydrogen and carbon dioxide, is proposed and investigated numerically and experimentally. As a pressure driven flow of the mixture goes through a two-dimensional Burgers cascade, the components are separated due to thermal diffusion and the amplifying effect of the cascade. Unlike traditiona...

Recently, hydrogen has been paid attention as a clean energy because hydrogen has little environmental load and high energy conversion efficiency. However, hydrogen must be in high concentration when it is used for energy source such as fuel cells. In this study, we propose a simple hydrogen refinement method utilizing the Soret effect that the con...

Burgers equation in a one-dimensional bounded domain with no-flux boundary conditions at both ends is proven to be exactly solvable. Cole–Hopf transformation converts not only the governing equation to the heat equation with an extra damping but also the nonlinear mixed boundary conditions to Dirichlet boundary conditions. The average of the soluti...

Two ways of networking microseparators to almost completely separate, for example, hydrogen from a mixture are proposed. Each separator has two outlets for slightly higher and lower concentrations, whose difference is modeled by a quadratic map of the average concentration at its inlet. In the continuum, the networks are governed by the Burgers equ...

A simple constrained minimization problem with an integral constraint de-scribes a symmetry breaking of a circular front around a point source. As a single control parameter, the total flux φ from the source, is varied, apparently polygonal solutions with an arbitrary number of corners m are shown to bifur-cate from the circular solution. Our asymp...

Microbe can move smoothly in water environment with high efficiency, which could offer new ideas for future micro machines. In this study, we investigated the spiral moving behavior of flagellum by using Stoke's theory and experimental models. We simulated euglena's fluid environment of Re number of 10^<-4>. The optimal spiral shapes in terms of pr...

We propose a phenomenological model for the polygonal hydraulic jumps discovered by Ellegaard and co-workers [Nature (London) 392, 767 (1998); Nonlinearity 12, 1 (1999); Physica B 228, 1 (1996)], based on the known flow structure for the type-II hydraulic jumps with a "roller" (separation eddy) near the free surface in the jump region. The model co...

The Soret effect is a phenomenon in which a temperature gradient gives rise to a concentration gradient. In this study, we attempted a simple technique for the separation of hydrogen from a gas mixture by utilizing the Soret effect. A gas mixture of hydrogen and carbon dioxide was introduced into a metal mini tube in which a temperature gradient wa...

Microbe can move smoothly in water environment with high efficiency, which could offer new ideas for future micro machines. In this study, we investigated the spiral moving behavior of flagellum by using Stoke's theory and experimental models. We simulated euglena's fluid environment of Re number of 10-4. The optimal spiral shapes in terms of propu...

We derive a simplified model for two-dimensional (2D) channel flows with recirculated regions at moderate Reynolds numbers based on an extension of the boundary layer (BL) theory and averaging across the channel. The model reproduces symmetry-breaking bifurcations and resulting flow structures accurately. Analytical estimates for the decay rates to...

We study laminar thin film flows with large distortions in the free surface using the method of averaging across the flow. Two concrete problems are studied: the circular hydraulic jump and the flow down an inclined plane. For the circular hydraulic jump our method is able to handle an internal eddy and separated flow. Assuming a variable radial ve...

Parallel arrays of underdamped Josephson junctions are interesting due to their ability to produce coherent radiation. For a broad range of array parameters, we find that these arrays have solutions which can be represented as traveling waves with a small number of harmonics. We develop equivalent circuits for the DC and AC response using a harmoni...

This year's cover illustration shows an unexpected singular structure occurring in a flow seen in an ordinary household kitchen sink. When a vertical jet of liquid impinges on a flat surface it creates a ring discontinuity, the circular hydraulic jump, at a well-defined distance from the jet, where the depth of the fluid layer changes by an order o...

We present an experimental as well as theoretical study of kink motion in one-dimensional arrays of Josephson junctions connected in parallel by superconducting wires. The boundaries are closed to form a ring, and the waveform and stability of an isolated circulating kink is discussed. Two one-dimensional rings can be coupled which provides an inte...

We study the dynamics of one-dimensional arrays of Josephson junctions connected in parallel by superconducting wires. These arrays are model systems for the discrete, damped sine-Gordon equation and excellent agreement between theory and experiment is obtained. The influence of boundary conditions and the coupling between two discrete sine-Gordon...

When a vertical jet of liquid from a nozzle hits a flat surface, as in tap water striking the kitchen sink, a discontinuity appears in a ring created by the flow. At this deformation the depth of the water alters abruptly (the 'circular hydraulic jump'1, 2, 3, 4, 5) at some distance from the jet. We have now discovered that if the jet contains a li...

We present theory and experiments on the circular hydraulic jump in the stationary regime. The theory can handle the situation in which the fluid flows over an edge far away from the jump. In the experiments the external height is controlled, and a series of transitions in the flow structure appears. First the steepening of the jump causes a transi...

When magnetic flux moves across layered or granular superconductor structures, the passage of vortices can take place along channels which develop finite voltage, while the rest of the material remains in the zero-voltage state. We present analytical studies of an example of such mixed dynamics: the row-switched (RS) states in underdamped two-dimen...

New resonance steps are found in the experimental current-voltage characteristics of long, discrete, one-dimensional Josephson junction arrays with open boundaries and in an external magnetic field. The junctions are underdamped, connected in parallel, and DC biased. Numerical simulations based on the discrete sine-Gordon model are carried out, and...

We present a simple viscous theory of free-surface flows in boundary layers, which can accommodate regions of separated flow. In particular, this yields the structure of stationary hydraulic jumps, both in their circular and linear versions, as well as structures moving with a constant speed. Finally, we show how the fundamental hydraulic concepts...

We have measured a novel phase-locked state in discrete parallel arrays of Josephson junctions which can be used for oscillator applications. Previous Josephson junction oscillators have been based on the Eck step, where a large-amplitude wave of nearly a single harmonic travels through the system. Multi-row systems biased on the Eck step could imp...

We study the dynamics of fully frustrated, underdamped Josephson arrays. Experiments reveal remarkable similarities among the dc current-voltage characteristics of several kinds of square and triangular arrays, where two resonant voltages are observed. Simulations indicate that a dynamical checkerboard solution underlies these similarities. By assu...

A mystery surrounds the stability properties of the splay-phase periodic solutions to a series array of N Josephson junction oscillators. Contrary to what one would expect from dynamical systems theory, the splay state appears to be neutrally stable for a wide range of system parameters. It has been explained why the splay state must be neutrally s...

We analyze the damped, driven, discrete sine-Gordon equation with periodic boundary conditions and constant forcing. Analytical and numerical results are presented about the existence, stability, and bifurcations of traveling waves in this system. These results are compared with experimental measurements of the current-voltage (I–V) characteristics...

We have measured and modeled the dynamics of inductively coupled discrete arrays of niobium Josephson junctions. We see splitting of the Eck step in the current‐voltage characteristic. Numerical simulations reproduce this splitting and are used to find an approximate solution for the junction phases at resonance. Using the technique of harmonic bal...

Circular arrays of underdamped Josephson junctions exhibit a series of resonant steps in the return path of the subgap region in the current-voltage characteristics. We show that the voltage locations of the steps can be predicted by studying the parametric instabilities of whirling periodic solutions, and experimentally verify the prediction in a...

We analyze the damped driven discrete sine-Gordon equation. For underdamped, highly discrete systems, we show that whirling periodic solutions undergo parametric instabilities at certain drive strengths. The theory predicts novel resonant steps in the current-voltage characteristics of discrete Josephson rings, occurring in the return path of the s...

We report the first observation of phase locking between a kink propagating in a highly discrete system and the linear waves excited in its wake. The current-voltage (I−V) characteristics of discrete rings of Josephson junctions have been measured. Resonant steps appear in the I−V curve, due to phase locking between a propagating vortex and its ind...

Superconducting systems built of underdamped Josephson junctions are of interest for ballistic and quantum vortex experiments. The dissipation in a Josephson tunnel junction can be extremely small because its subgap resistance can easily be made of the order of 1 MΩ which for a typical junction translates into a McCumber parameter as high as 107. I...

We report the first measurements of current-voltage (I–V) characteristics of discrete rings of Josephson junctions. As I is increased, resonant steps appear in the I–V curve, due to phase-locking between a propagating, trapped vortex and the linear waves excited in its wake. Unexpectedly, the phase velocity of the linear waves, not the group veloci...

We show that series arrays of N identical overdamped Josephson junctions have extremely degenerate dynamics. In particular, we prove that such arrays have N − 3 constants of motion for all N ⩾ 3. The analysis is based on a coordinate transformation that reduces the governing equations to an (N − 3)-parameter family of low-dimensional systems. In th...

A numerical method to study radially symmetric standing wave solutions (with arbitrarily large number of nodes) to the nonlinear Schrödinger equation is described and used to study several new geometric features of these waves. The method is based on numerically locating the basin boundary (separating surface) between two attracting invariant lines...

We show that a dynamical system of N phase oscillators with global cosine coupling is completely integrable. In particular, we prove that the N-dimensional phase space is foliated by invariant 2D tori, for all N greater than 3. Explicit expressions are given for the constants of motion and for the solitary waves that occur in the continuum limit. O...