Noise-Induced Spatial Pattern Formation in Stochastic Reaction-Diffusion Systems

This paper is concerned with stochastic reaction-diffusion kinetics governed by the reaction-diffusion master equation. Specifically, the primary goal of this paper is to provide a mechanistic basis of Turing pattern formation that is induced by intrinsic noise. To this end, we first derive an approximate reaction-diffusion system by using linear noise approximation. We show that the approximated system has a certain structure that is associated with a coupled dynamic multi-agent system. This observation then helps us derive an efficient computation tool to examine the spatial power spectrum of the intrinsic noise. We numerically demonstrate that the result is quite effective to analyze noise-induced Turing pattern. Finally, we illustrate the theoretical mechanism behind the noise-induced pattern formation with a H2 norm interpretation of the multi-agent system

Turing Instability in Reaction-Diffusion Systems with a Single Diffuser: Characterization Based on Root Locus

Cooperative behaviors arising from bacterial cell-to-cell communication can be modeled by reaction-diffusion equations having only a single diffusible component. This paper presents the following three contributions for the systematic analysis of Turing instability in such reaction-diffusion systems. (i) We first introduce a unified framework to formulate the reaction-diffusion system as an interconnected multi-agent dynamical system. (ii) Then, we mathematically classify biologically plausible and implausible Turing instabilities and characterize them by the root locus of each agent's dynamics, or the local reaction dynamics. (iii) Using this characterization, we derive analytic conditions for biologically plausible Turing instability, which provide useful guidance for the design and the analysis of biological networks. These results are demonstrated on an extended Gray-Scott model with a single diffuser

Existence of Oscillations in Cyclic Gene Regulatory Networks with Time Delay

This paper is concerned with conditions for the existence of oscillations in gene regulatory networks with negative cyclic feedback, where time delays in transcription, translation and translocation process are explicitly considered. The primary goal of this paper is to propose systematic analysis tools that are useful for a broad class of cyclic gene regulatory networks, and to provide novel biological insights. To this end, we adopt a simplified model that is suitable for capturing the essence of a large class of gene regulatory networks. It is first shown that local instability of the unique equilibrium state results in oscillations based on a Poincare-Bendixson type theorem. Then, a graphical existence condition, which is equivalent to the local instability of a unique equilibrium, is derived. Based on the graphical condition, the existence condition is analytically presented in terms of biochemical parameters. This allows us to find the dimensionless parameters that primarily affect the existence of oscillations, and to provide biological insights. The analytic conditions and biological insights are illustrated with two existing biochemical networks, Repressilator and the Hes7 gene regulatory networks

Moment of Inertia Dependence of Vertical Axis Wind Turbines in Pulsating Winds

Vertical Axis Wind Turbines (VAWTs) are unaffected by changes in wind direction, and they have a simple structure and the potential for high efficiency due to their lift driving force. However, VAWTs are affected by changes in wind speed, owing to effects originating from the moment of inertia. In this study, changes in the rotational speed of a small VAWT in pulsating wind, generated by an unsteady wind tunnel, are investigated by varying the wind cycle and amplitude parameters. It is shown that the responses observed experimentally agree with simulations based on torque characteristics obtained under steady rotational conditions. Additionally, a simple equation expressing the relationship between the rotational change width and amplitude of the pulsating wind is presented. The energy efficiency in a pulsating wind remains constant with changes in both the moment of inertia and the wind cycle; however, the energy efficiency decreases when the wind amplitude is large

Wind Tunnel Experiments on Interaction between Two Closely Spaced Vertical-Axis Wind Turbines in Side-by-Side Arrangement

This study aimed to determine the optimal rotor spacing of two vertical-axis wind turbines, which are simulated by miniature models arranged side-by-side with a relatively low aspect ratio. Wind tunnel experiments with a pair of 3-D printed model rotors were conducted at a uniform velocity. A series of experiments were conducted involving both incremental adjustments to the rotor gaps, g, and the rotational direction of each rotor. Increases in the power and the related flow patterns were observed in all three arrangements: Co-Rotating (CO), Counter-Up (CU), and Counter-Down (CD). The maximum phase-synchronized rotational speed occurs at the narrowest gap in the CD arrangement. Meanwhile, local maxima arise in the CO and CU arrangements at g/D < 1, where D is the rotor diameter. From an engineering perspective, the optimal rotor spacing is g/D = 0.2 with the CO arrangement, using the same two rotors rotating in the same direction. Based on flow visualization using a smoke-wire method at a narrower gap opening of 0.2D, the wake width in the case of the CU arrangement was remarkably narrower than those obtained in the CO and CD arrangements. In the CU arrangement, a movement towards the center of the rotor pair of the nominal front-stagnation point of each rotor was confirmed via flow visualization. This finding explains a reduction tendency in the rotational speed of the rotors via a reduction in the lift in the CU arrangement

Collective oscillation period of inter-coupled biological negative cyclic feedback oscillators

A number of biological rhythms originate from networks comprised of multiple cellular oscillators. But analytical results are still lacking on the collective oscillation period of inter-coupled gene regulatory oscillators, which, as has been reported, may be different from that of an autonomous oscillator. Based on cyclic feedback oscillators, we analyze the collective oscillation pattern of coupled cellular oscillators. First we give a condition under which the oscillator network exhibits oscillatory and synchronized behavior. Then we estimate the collective oscillation period based on a novel multivariable harmonic balance technique. Analytical results are derived in terms of biochemical parameters, thus giving insight into the basic mechanism of biological oscillation and providing guidance in synthetic biology design.Comment: arXiv admin note: substantial text overlap with arXiv:1203.125

Analytical Model for Phase Synchronization of a Pair of Vertical-Axis Wind Turbines

The phase-synchronized rotation of a pair of closely spaced vertical-axis wind turbines has been found in wind tunnel experiments and computational fluid dynamics (CFD) simulations. During phase synchronization, the two wind turbine rotors rotate inversely at the same mean angular velocity. The blades of the two rotors pass through the gap between the turbines almost simultaneously, while the angular velocities oscillate with a small amplitude. A pressure drop in the gap region, explained by Bernoulli’s law, has been proposed to generate the interaction torque required for phase synchronization. In this study, an analytical model of the interaction torques was developed. In our simulations using the model, (i) phase synchronization occurred, (ii) the angular velocities of the rotors oscillated during the phase synchronization, and (iii) the oscillation period became shorter and the amplitude became larger as the interaction became stronger. These observations agree qualitatively with the experiments and CFD simulations. Phase synchronization was found to occur even for a pair of rotors with slightly different torque characteristics. Our simulation also shows that the induced flow velocities influence the dependence of the angular velocities during phase synchronization on the rotation directions of the rotors and the distance between the rotors