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This paper considers the problem: if coexistence occurs in the long run when a third species w invades an ecosystem consisting of two species u and v on , where u, v and w compete with one another. Under the assumption that the influence of w on u and v is small and other suitable conditions, we show that the three species can coexist as a non-monotone travelling wave. Such type of non-monotone waves plays an important role in the study of three-species phenomena. However, fewer results are known for the existence of such waves in the literature. Our approach, based on the method of sub- and super-solutions and bifurcation theory, provides a new approach to construct non-monotone waves of this type. Moreover, we show that the waves we construct are stable. To the best of our knowledge, this is the first rigorous result of stability for such type of waves.

In vertebrates, sperm is generated in testicular tube-like structures called seminiferous tubules. The differentiation stages of spermatogenesis exhibit a dynamic spatiotemporal wavetrain pattern. There are two types of pattern-the vertical type, which is observed in mice, and the helical type, which is observed in humans. The mechanisms of this pattern difference remain little understood. In the present study, we used a three-species reaction-diffusion model to reproduce the wavetrain pattern observed in vivo. We hypothesized that the wavelength of the pattern in mice was larger than that in humans and undertook numerical simulations. We found complex patterns of helical and vertical pattern frequency, which can be understood by pattern selection using boundary conditions. From these theoretical results, we predicted that a small number of vertical patterns should be present in human seminiferous tubules. We then found vertical patterns in histological sections of human tubules, consistent with the theoretical prediction. Finally, we showed that the previously reported irregularity of the human pattern could be reproduced using two factors: a wider unstable wavenumber range and the irregular geometry of human compared with mouse seminiferous tubules. These results show that mathematical modeling is useful for understanding the pattern dynamics of seminiferous tubules in vivo.

We consider a two-variable partial differential equations model of cardiac excitation and study spiral wave instability in a one-parameter family of solutions. We investigate numerically the existence of periodic traveling wave solution and show the front and the back interaction far away from the bifurcation point in one dimension. In two dimensions, we show the emergence of a stable spiral pattern before the bifurcation point. The most complex spatiotemporal pattern is called ventricular fibrillation when the breakup of one spiral wave makes another wave and the medium becomes chaotic. We show spiral wave instability and periodic traveling wave instability in the same computational settings. It is found that the pattern of the front–back interaction in two dimensions is similar with that of in the one dimension.

One parameter family of rectangular periodic traveling wave solutions are known to exists in a perturbed system of the modified KdV equation. The rectangular periodic traveling wave consists basically of front and back transitions. It turns out that the rectangular traveling wave becomes unstable as its period becomes large. More precisely, torus bifurcation occurs successively along the branch of the rectangular traveling wave solutions. And, as a result, a “rippling rectangular wave” appears. It is roughly the rectangular traveling wave on which small pulse wave trains are superimposed. The bifurcation branch is constructed by a numerical torus continuation method. The instability is explained by using the accumulation of eigenvalues on the essential spectrum around the stationary solutions. Moreover, the critical eigenfunctions which correspond to the torus bifurcation can be characterized theoretically.

A cascoded GaN half-bridge with a wide-band galvanically isolated current sensor is proposed. A 650 V depletion-mode GaN field-effect transistor is switched by a low-propagation-delay gate driver in active-mode. The standby and active modes are switched by a 25 V N-ch laterally diffused MOS (LDMOS). The current sensor uses the LDMOS as a shunt resistor, gm-cell-based sense amplifier and a mixer-based isolation amplifier for wider bandwidth. PVT variations of on-resistance of the current-detecting MOSFET are compensated using a reference MOSFET. A digital calibration loop across the isolation is formed to keep the current sensor gain constant within ± 1.5 % across the whole temperature range. The wide-band current sensor can measure the power device switching current. In this study, a cascoded GaN half-bridge switching and inductor current sensing using low-side and high-side device current are demonstrated. The proposed techniques show the possibility of implementing a GaN half-bridge module with an isolated current sensor in a package.

The Belousov-Zhabotinsky (BZ) reaction is a famous experimental model for chemical oscillatory reaction and pattern formation. We herein study a diffusive coupled system of two oscillators with global feedback using the photosensitive BZ reaction both experimentally and theoretically. The coupled oscillator showed in-phase and antiphase oscillations depending on the strength of diffusive coupling and light feedback. Moreover, we analyzed our model to locate the bifurcational origin and found the reconnection of the bifurcation branches for antiphase oscillation, which was induced by the competition between global feedback and the diffusion effect.

The present study concerns the homogenization and fingering instability of a microgravity smoldering combustion problem with radiative heat transfer. The major premise of the homogenization procedure is the slow exothermic fuel oxidation of a reactive porous medium at the pore level. The porous medium consists of ϵ -periodically distributed cells, with ϵ a suitable scale parameter. A nonlinear reaction rate of Arrhenius type accounts for the relationship between the reactants and the heat that sustains the smoldering process. At the gas–solid interface, the balance of thermal fluxes is given by the heat production rate due to the reaction and the radiative heat losses at the interface. Since the size of the inclusions is small with respect to ϵ , we derive a kinetic model for fuel conversion in the region occupied by the solid inclusions and hence complete the description of a single-step chemical kinetics. The derived macroscopic model shows a close correspondence to a previous phenomenological reaction-diffusion model, within a suitable choice of parameters. We perform numerical simulations on the microscopic and homogenized models in order to verify the efficiency of the homogenization process in the slow smoldering regime. We show that the results of the macroscopic model capture the distinct fingering states reminiscent of microgravity smoldering combustion. We also show qualitative results that confirm the close relationship between the radiative heat losses and the characteristic length scales of the instability.

Developments in wireless LAN technology have resulted in the proliferation of various types of mobile terminal devices with wireless LAN implemented. The services used by these terminals include conventional web access and e-mail, as well as multimedia services and various application s, such as voice and video communication.Multimedia applications require high communication quality. Therefore, delay time and packet loss rate for packet transmission must be reduced, and communication bandwidth and t hroughput must be guaranteed. I propose a novel access control method that improves the communication quality of the various applications that utiliz e wireless LANs. In addition, I propose improvements to the communication quality of the access control method for next-generation wireless transmission technology.

Although passive response control design is a popular method, an arrangement methodology for energy-dissipating devices in spatial structures has not been established yet. In this study, optimization techniques are applied to arrangements of energy-dissipating devices in truss tower structures. First, a response prediction rule using the response spectrum and the equivalent linearization method is proposed. Then, a genetic algorithm is applied to select the optimal arrangement of viscoelastic damper devices in truss tower structures. Additionally, the device arrangements determined by empirical design methods are compared with the optimal solutions.

It is known that the electrical activities in the cardiac cells give rise to periodic action potentials in one dimension. So, in order to understand the heart dysfunction, one needs to study the behavior of periodic signals in the myocardium cells of the heart wall. The propagation of these periodic signals is called periodic traveling waves. This paper study the bifurcation behavior in the periodic waves in a two-component FitzHugh-Nagumo type reaction-diffusion system. We show the existence and stability of the periodic traveling waves in a one-parameter family of solutions. An Eckhaus bifurcation is found to occur between stable and unstable periodic traveling waves. We explain the stability by the numerical calculation of essential spectra of the periodic traveling wave solutions. In two dimensions, it is found that a stable spiral pattern bifurcates to a complicated spatiotemporal pattern in the same computational settings.

It is well known from experiments that a sample of thin porous material burning against an oxidizing air under microgravity exhibits various finger-like char patterns. The patterns are classified into three distinct types depending on the oxidizer flow rate. (I) Sparse fingers; (II) tip-splitting fingers; (III) connected front. We presently extend our modeling strategy based on the homogenization approach, which has been applied for the case of isotropic porous media, to analyze the pattern behavior on anisotropic porous media. In order to understand the characteristic features of the patterns based on the influence of the local structure, we simply rely on fixed anisotropic two-dimensional geometries representative of the microstructure of interest. Thus, we illustrate numerically the consequence of the material anisotropy on the fingering patterns based on effective diffusion tensors calculated using the homogenization method and the mechanism of thermal-diffusion instability. Besides revealing new insights on the experimental observations, our numerical results show that material anisotropy can influence the uniformity on the patterns, but the distinct fingering regimes are independent of the local microstructure of materials. This effect is consistent with the qualitative experimental findings from Zik and Moses (1999). Keywords: Reverse smoldering; Anisotropy; Homogenization; Combustion instability; Fingering pattern