Pattern formation in finite size non-equilibrium systems and models of morphogenesis

Two canonical pattern forming systems, the Rayleigh-Benard convection and the Turing mechanism for biological pattern formation, are compared. The similarity and fundamental differences in the mathematical structure of the two systems are addressed, with special emphasis on how the linear onset of patterns is affected by the finite size and the boundary conditions. Our analysis is facilitated by continuously varying the boundary condition, from one that admits simple algebraic solution of the problem but is unrealistic to another which is physically realizable. Our investigation shows that the size dependence of the convection problem can be considered generic, in the sense that for the majority of boundary conditions the same trend is to be observed, while for the corresponding Turing mechanism one will rely crucially on the assumed boundary conditions to ensure that a particular sequence of patterns be picked up as the system grows in size. This suggests that, although different systems might exhibit similar pattern forming features, it is still possible to distinguish them by characteristics which are specific to the individual models

Boundary conditions and linear analysis of finite-cell Rayleigh–Bénard convection

The linear stability of finite-cell pure-fluid Rayleigh–Bénard convection subject to any homogeneous viscous and/or thermal boundary conditions is investigated via a variational formalism and a perturbative approach. Some general properties of the critical Rayleigh number with respect to change of boundary conditions or system size are derived. It is shown that the chemical reaction–diffusion model of spatial-pattern-forming systems in developmental biology can be thought of as a special case of the convection problem. We also prove that, as a result of the imposed realistic boundary conditions, the nodal surfaces of the temperature of a nonlinear stationary state have a tendency to be parallel or orthogonal to the sidewalls, because the full fluid equations become linear close to the boundary, thus suggesting similar trend for the experimentally observed convective rolls

Finite-size effects on linear stability of pure-fluid convection

The linear stability of pure-fluid Rayleigh-Benard convection in a finite cell of arbitrary geometry can be formulated as a self-adjoint eigenvalue problem. This, when coupled with perturbation theory, allows one to deduce how the sidewalls affect its stability. In particular, it is shown that for almost all boundary conditions the difference between the onset Rayleigh number and its infinite-cell limit scales like L^-2 as the cell dimension L tends to infinity, and near the sidewall the temperature and velocity are of order L^-1 compared to their bulk values. The validity of replacing the true thermal boundary condition by a frequently used mathematically simpler homogeneous one is also demonstrated

THE EFFECT OF TENNIS RACKET STRING VIBRATION ABSORBER PLACEMENT ON TENNIS RACKET VIBRATIONS

The purpose of this research was to analyze the vibration effect of tennis racket caused by impact on different locative vibration absorber and locations. In this experiment, The tennis racket was fixed and kept the face horizontalized to the ground with 50 Ib on strings. A tennis ball was dropped from one meter height to impact three locations of the racket. The different locative vibration absorber was fixed on the racket. It was installed an accelerometer to capture the vibration signal of the handle of the racket. After the experiment, the data was used logarithmic decrement to calculate damping ratio. It was illustrated when the vibration absorber in Back and Tip to have obvious effect. But in Side, it could not effectively decrease the vibration compared with the racket without absorber

Design, Modeling and Development of a Serial Hybrid Motorcycle with HCCI Engine

This paper discusses the design, modeling, and development of small motorcycle equipped with a HCCI engine in an series hybrid configuration. A mathematical model was developed using MATLAB/Simulink and used to size the powertrain components and to predict fuel economy. A conventional 125 cc spark ignition engine was modified to run in HCCI combustion mode and integrated into a prototype vehicle. Dual-fuel and external EGR strategies were used to upgrade the engine speed and torque capabilities of the engine to meet the requirements of the powertrain. An electrical generator, hub-motor, battery pack and other power electronics devices were used to form the electrical system for the vehicle. The advantages of the proposed design compared to the original motorcycle with SI engine and CVT transmission are: 1) a reduction in noxious emissions due to the HCCI combustion, and 2) higher fuel economy in city driving because of the HCCI engine and series hybrid powertrain. Fuel economy was measured by driving the motorcycle on a chassis dynamometer using a sequence of ECE-40 driving cycles. The overall fuel economy was measured to be 73.7km/L which represents a 139.3% increase in fuel economy over the baseline vehicle

Large expert-curated database for benchmarking document similarity detection in biomedical literature search

Document recommendation systems for locating relevant literature have mostly relied on methods developed a decade ago. This is largely due to the lack of a large offline gold-standard benchmark of relevant documents that cover a variety of research fields such that newly developed literature search techniques can be compared, improved and translated into practice. To overcome this bottleneck, we have established the RElevant LIterature SearcH consortium consisting of more than 1500 scientists from 84 countries, who have collectively annotated the relevance of over 180 000 PubMed-listed articles with regard to their respective seed (input) article/s. The majority of annotations were contributed by highly experienced, original authors of the seed articles. The collected data cover 76% of all unique PubMed Medical Subject Headings descriptors. No systematic biases were observed across different experience levels, research fields or time spent on annotations. More importantly, annotations of the same document pairs contributed by different scientists were highly concordant. We further show that the three representative baseline methods used to generate recommended articles for evaluation (Okapi Best Matching 25, Term Frequency-Inverse Document Frequency and PubMed Related Articles) had similar overall performances. Additionally, we found that these methods each tend to produce distinct collections of recommended articles, suggesting that a hybrid method may be required to completely capture all relevant articles. The established database server located at https://relishdb.ict.griffith.edu.au is freely available for the downloading of annotation data and the blind testing of new methods. We expect that this benchmark will be useful for stimulating the development of new powerful techniques for title and title/abstract-based search engines for relevant articles in biomedical research.Peer reviewe