The Yarkovsky effect as a heat engine

We show how the Yarkovsky effect can be understood as a heat engine. The output of the engine, manifested in the rate of change in semimajor axis of the body, has a maximum at an intermediate heat capacity, depending on the rotation rate of the body. This maximum arises because the work output depends on the product of the solar heat absorbed by the body and transported from its morning to evening side (this am-pm heat flux increases with heat capacity) and the Carnot efficiency (which declines with heat capacity).     

Directions and possibilities of mathematical geology

This paper considers the present state of mathematical geology. Three directions are recognized: applied, theoretical, and mathematical. Applied mathematical geology includes formal use of mathematics to solve problems and computer processing of data. Success is achieved by a correspondence of mathematical methods used to the nature of geological data. This correspondence can be demonstrated by purely mathematical means. Theoretical mathematical geology uses mathematics as a language of geology; however, a number of methodological problems must be solved: formalization of initial geological concepts and creation of a strict conceptual basis, substantiation of initial principles of mathematical simulation, creation of theoretical geological models, problems of elementary and coincidence in geology, and methodological substantiations of possibilities of any mathematical model to approximate geological models. The essense and significance of these problems are considered. The main task of mathematical geology is to prove its correspondence to the nature of the geological objects studied, geological data obtained, and geological problems solvable. Finally, the main problems of mathematical geology are not so much mathematical as geological and methodological.     

Heat capacity and phase equilibria of wadeite-type K2Si4O9

The low-temperature heat capacity (C _p) of Si-wadeite (K₂Si₄O₉) synthesized with a piston cylinder device was measured over the range of 5–303 K using the heat capacity option of a physical properties measurement system. The entropy of Si-wadeite at standard temperature and pressure calculated from the measured heat capacity data is 253.8 ± 0.6 J mol⁻¹ K⁻¹, which is considerably larger than some of the previous estimated values. The calculated phase transition boundaries in the system K₂O–Al₂O₃–SiO₂ are generally consistent with previous experimental results. Together with our calculated phase boundaries, seven multi-anvil experiments at 1,400 K and 6.0–7.7 GPa suggest that no equilibrium stability field of kalsilite + coesite intervenes between the stability field of sanidine and that of coesite + kyanite + Si-wadeite, in contrast to previous predictions. First-order approximations were undertaken to calculate the phase diagram in the system K₂Si₄O₉ at lower pressure and temperature. Large discrepancies were shown between the calculated diagram compared with previously published versions, suggesting that further experimental or/and calorimetric work is needed to better constrain the low-pressure phase relations of the K₂Si₄O₉ polymorphs. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Offshore marine conservation policies in the North East Atlantic: Emerging tensions and opportunities

An inherent tension exists between legal approaches to nature conservation and fisheries management in the European Union, as the former remains the remit of Member States while the latter is under the exclusive legislative jurisdiction of the European Community (EC). This tension is of particular importance when addressing the conservation of habitats or species that are under threat from fishing activities. This article examines recent developments in offshore marine conservation in the North-East Atlantic in light of the legislative developments and political frameworks that are currently evolving. By analysing the emergency closure of the Darwin Mounds area of cold-water corals and the UK pair-trawl ban, it becomes evident that the precautionary principle is a key factor in the tension between fisheries management and marine nature conservation, and is not always taken into account.     

比较原理在多有理数时滞区间系数离散系统的应用

应用多组有理数时滞离散系统的比较原理和频域法,将多组有理数时滞区间系数离散系统化为多组有理数时滞定常离散系统,以判定其时滞无关稳定性,并举例说明了新定理的有效性和实用性。     

A Unified Variational Principle of Fluid Mechanics and Application on Solitary Subdomain or Point

-According to basic equations of fluid mechanics, this paper presents a unified variational principle of fluid mechanics (UVPFM) by using the optimization method of weighted residuals (OMWR). The advantages are as follows, the establishment of the functional and the variational principle is easy, it can change various problems of fluid mechanics derived by basic equations into a unified optimization problem, and the solution is the optimum one in some sense. According to the OMWR for the solitary subdomain, this paper uses UVPFM onto any solitary subdomain and gives the solution of the hydrodynamics equation which is suitable only for that solitary subdomain. According to the OMWR for solitary point, this paper uses UVPFM to any solitary point and gives the solution of the hydrodynamics equation (point solution) which is suitable only for that solitary point. As the solution for the solitary subdomain or solitary point is developed independently, the compatibility with other subdomain or other points, do     

Optimum Sample Size to Detect Perturbation Effects: The Importance of Statistical Power Analysis – A Critique

Abstract. The current article describes statistical power analysis as an efficient strategy for the estimation of the optimum sample size. The principle aim is constructively to criticise and enrich the results presented by Mouillot et al. (1999) , who estimate the optimum sample size for evaluating possible perturbations. The authors did not make any reference to statistical power analysis, even though their objective clearly went beyond a simple stock evaluation to assess management strategies in a particular marine ecosystem. Surprisingly, they proposed (a priori) an ANOVA design to test a hypothesis considering both space and temporal scales. However, the authors did not cover important topics related with power analysis and the precautionary principle, both used into environment impact assessment programmes for marine ecosystems. Based on their results and on statistical power analysis, it is demonstrated that the variability (dispersion statistics), a key factor they used to estimate the sample size, is less relevant than the magnitude of perturbation (effect size). Therefore, a greater effort must be devoted to estimate the effect size of a particular phenomenon rather than a desired variability.     

一类广义Sine-Gordon方程的概周期解

用最大值原理和Banach压缩映像原理研究一类广义Sine-Gordon方程的概周期解问题,证明概周期解的存在‖u‖L∞<π2中的唯一性。     

Surface Elevation Distribution of Sea Waves Based on the Maximum Entropy Principle

A probability density function of surface elevation is obtained through improvement of the method introduced by Cieslikiewicz who employed the maximum entropy principle to investigate the surface elevation distribution. The density function can be easily extended to higher order according to demand and is non-negative everywhere, satisfying the basic behavior of the probability. Moreover because the distribution is derived without any assumption about sea waves, it is found from comparison with several accepted distributions that the new form of distribution can be applied in a wider range of wave conditions. In addition, the density function can be used to fit some observed distributions of surface vertical acceleration although something remains unsolved.