Stability of equilibrium points in the generalized perturbed restricted three-body problem

This paper studies the existence and stability of equilibrium points under the influence of small perturbations in the Coriolis and the centrifugal forces, together with the non-sphericity of the primaries. The problem is generalized in the sense that the bigger and smaller primaries are respectively triaxial and oblate spheroidal bodies. It is found that the locations of equilibrium points are affected by the non-sphericity of the bodies and the change in the centrifugal force. It is also seen that the triangular points are stable for 0<μ<μ _c and unstable for \(\mu_{c}\le\mu <\frac{1}{2}\), where μ _c is the critical mass parameter depending on the above perturbations, triaxiality and oblateness. It is further observed that collinear points remain unstable.     

Fuel optimization for low-thrust Earth–Moon transfer via indirect optimal control

The problem of designing low-energy transfers between the Earth and the Moon has attracted recently a major interest from the scientific community. In this paper, an indirect optimal control approach is used to determine minimum-fuel low-thrust transfers between a low Earth orbit and a Lunar orbit in the Sun–Earth–Moon Bicircular Restricted Four-Body Problem. First, the optimal control problem is formulated and its necessary optimality conditions are derived from Pontryagin’s Maximum Principle. Then, two different solution methods are proposed to overcome the numerical difficulties arising from the huge sensitivity of the problem’s state and costate equations. The first one consists in the use of continuation techniques. The second one is based on a massive exploration of the set of unknown variables appearing in the optimality conditions. The dimension of the search space is reduced by considering adapted variables leading to a reduction of the computational time. The trajectories found are classified in several families according to their shape, transfer duration and fuel expenditure. Finally, an analysis based on the dynamical structure provided by the invariant manifolds of the two underlying Circular Restricted Three-Body Problems, Earth–Moon and Sun–Earth is presented leading to a physical interpretation of the different families of trajectories.     

The Problem of the Height Dependence of Magnetic Fields in Sunspots

To understand the physics of sunspots, it is important to know the properties of their magnetic field, and especially its height stratification plays a substantial role. There are mainly two methods to assess this stratification, but they yield different magnetic gradients in the photospheric layers. Determinations based on the several spectral lines of different formation heights and the slope of their profiles result in gradients of ?2 to ?3 G?km^?1, or even steeper. This is similar for the total magnetic field strength and for the vertical component of the magnetic field. The other option is to determine the horizontal partial derivatives of the magnetic field, and with the condition \(\operatorname{div} {{\boldsymbol {B}}} = 0\) also the vertical derivative is known. With this method, gradients of ?0.5 G?km^?1 and even shallower are obtained. Obviously, these results do not agree. If chromospheric spectral lines are included, only shallow gradients around ?0.5 G?km^?1 are obtained. Shallow gradients are also found from gyro-resonance measurements in the radio wave range 300?–?2000 GHz.Some indirect methods are also considered, but they cannot clarify the total picture. An analysis of a numerical simulation of a sunspot indicates a shallow gradient over a wide height range, but with slightly steeper gradients in deep layers.Several ideas to explain the discrepancy are also discussed. With no doubts cast on Maxwell’s equations, the first one is to look at the uncertainties of the formation heights of spectral lines, but a wider range of these heights would require an extension of the solar photosphere that is incompatible with observations and the theory of stellar atmospheres. Submerging and rising magnetic flux might play a role in the outer penumbra, if the resolution is too low to separate them, but it is not likely that this effect acts also in the umbra. A quick investigation assuming a spatial small scale structure of sunspots together with twist and writhe of individual flux tubes shows a reduction of the measured magnetic field strength for spectral lines sensitive to a larger height range. However, sophisticated investigations are required to prove that the explanation for the discrepancy lies here, and the problem of the height gradient of the magnetic field in sunspots is still not solved.     

The smoke is rising but where is the fire? Exploring effective online map design for wildfire warnings

The current study sought to offer guidance for developing effective web-based mapping tools for wildfire warnings by identifying (1) the important content for facilitating individuals’ decision-making, and (2) the optimal interface design for ensuring usability and ease of information access. A map-based warning tool was prototyped in the Australian context, followed by a usability and effectiveness evaluation through individual interviews and verbal protocol analysis to assess participants’ interaction with the mapping interface and information in response to the simulated warning scenario. The results demonstrated variations in participants’ approaches to wildfire warning response, revealing varied information needs. Specifically, most participants relied on their own assessment of the prospective threat, requiring specific wildfire-related information before eliciting a response. In contrast, the decision of a minority of the participants was motivated by response guidance from agencies, and accurate wildfire information was less important for their response. Imperative information for both types of residents therefore needs to be highlighted in a map-based warning tool to cater to a wide audience. Furthermore, a number of heuristics were identified for designing effective interactive functions to facilitate the control of, and access to, the various maps and textual information presented on the map-based warning interface.     

A low-dimensional subsurface model for saturated and unsaturated flow processes: ability to address heterogeneity

A low-dimensional model that describes both saturated and unsaturated flow processes in a single equation is presented. Subsurface flow processes in the groundwater, the vadose zone, and the capillary fringe are accounted for through the computation of aggregated hydrodynamic parameters that result from the integration of the governing flow equations from the bedrock to the land surface. The three-dimensional subsurface flow dynamics are thus described by a two-dimensional equation, allowing for a drastic reduction of model unknowns and simplification of the model parameterizations. This approach is compared with a full resolution of the Richards equation in different synthetic test cases. Because the model reduction stems from the vertical integration of the flow equations, the test cases all use different configurations of heterogeneity for vertical cross-sections of a soil-aquifer system. The low-dimensional flow model shows strong consistency with results from a complete resolution of the Richards equation for both the water table and fluxes. The proposed approach is therefore well suited to the accurate reproduction of complex subsurface flow processes.     

路堤下软土地基侧向位移与沉降关系分析研究

总结了软土地基下侧向位移的研究现状,从路堤中最大侧向位移和路中沉降之间的比例关系出发进行了分析研究。利用有限单元法,建立了路堤下软土地基的计算模型。计算结果表明,在路堤填筑期间最大侧向位移和路中沉降的增量大致相等,而在固结期两者的比例关系在0.14左右。不同的加载方式在数值上也有所不同。计算结果对路堤下地基侧向变形的计算分析具有一定的指导作用。     

A simulation study of capillary transport,preferential retention and distribution of salts in historic sandstone buildings

Salt crystallisation is a major problem of deterioration in historic stone buildings, monuments and sculptures. The capillary rise of soil water is one of the primary sources of salts in stone structures, which evaporates leaving the salts behind. It has been noted that the spatial distribution profile of different species of salts crystallised in historic stone buildings is not homogeneous, i.e. different salts crystallise at different locations. The capillary transport and inhomogeneous spatial distribution of different salts in the porous building materials has been considered to be a result of solubility-dependent crystallisation; however, the factors responsible for this phenomenon are not clearly known. This paper aims to investigate the factors influencing the differential distribution of salts during capillary rise of soil water. In this study, the capillary transport of salts was simulated on two different sandstones—Locharbriggs, a Permo–Triassic, red sandstone and Stoke Hall, a Carboniferous, buff sandstone. The experiments were carried out under controlled environmental conditions to eliminate the possibility of evaporation-driven crystallisation of salts depending on their solubilities. The results indicate that fractionation or differential distribution of salts takes place even in the absence of evaporation and crystallisation. The sandstones exhibit properties like an ion exchange column, and ionic species present in the salt solution show differential distribution within the porous network of sandstone.     

Markov Chain Random Fields for Estimation of Categorical Variables

Multi-dimensional Markov chain conditional simulation (or interpolation) models have potential for predicting and simulating categorical variables more accurately from sample data because they can incorporate interclass relationships. This paper introduces a Markov chain random field (MCRF) theory for building one to multi-dimensional Markov chain models for conditional simulation (or interpolation). A MCRF is defined as a single spatial Markov chain that moves (or jumps) in a space, with its conditional probability distribution at each location entirely depending on its nearest known neighbors in different directions. A general solution for conditional probability distribution of a random variable in a MCRF is derived explicitly based on the Bayes’ theorem and conditional independence assumption. One to multi-dimensional Markov chain models for prediction and conditional simulation of categorical variables can be drawn from the general solution and MCRF-based multi-dimensional Markov chain models are nonlinear.     

二维有限元大地电磁正演模拟在Matlab上的实现

Matlab高级语言开发平台对矩阵的计算简便快速,并且绘图输出文件方便。以这些特点为契机,在Matlab平台上,讨论利用有限单元法实现二维大地电磁正演的问题,推导出相应的公式,计算地表或海底视电阻率及相位,并与解析解以及主流方法结果对比,证实了本文方法的正确性。     

一种改进的基于非高斯性最大化的预测反褶积算法

The predictive deconvolution algorithm （PD）, which is based on second-order statistics, assumes that the primaries and the multiples are implicitly orthogonal. However, the seismic data usually do not satisfy this assumption in practice. Since the seismic data （primaries and multiples） have a non-Gaussian distribution, in this paper we present an improved predictive deconvolution algorithm （IPD） by maximizing the non-Gaussianity of the recovered primaries. Applications of the IPD method on synthetic and real seismic datasets show that the proposed method obtains promising results.