Variation of singularity of earthquake-size distribution with respect to tectonic regime

Frequency-size relation of earthquakes in a region can be approximated by the Gutenberg-Richter law(GR). This power-law model involves two parameters: a-value measuring seismic activity or earthquake productivity, and b-value describing the relation between frequencies of small and large earthquakes.The spatial and temporal variations of these two parameters, especially the b-value, have been substantially investigated. For example, it has been shown that b-value depends inversely on differential stress. The b-value has also been utilized as earthquake precursor in large earthquake prediction.However, the physical meaning and properties of b-value including its value range still remain as an open fundamental question. We explore the property of b-value from frequency-size GR model in a new form which relates average energy release and probability of large earthquakes. Based on this new form of GR relation the b-value can be related to the singularity index(1-2/3 b) of fractal energy-probability power-law model. This model as applied to the global database of earthquakes with size M ≥ 5 from 1964 to 2015 indicates a systematic increase of singularity from earthquakes occurring on mid-ocean ridges, to those in subduction zones and in collision zones.

Uncertainty and universality in the power-law singularity as a precursor of catastrophic rupture

The prediction of catastrophic rupture of heterogeneous brittle material has been investigated by researchers in the past.In this work,the acoustic emission generated by marble samples under compression was analyzed to verify a power law singularity of index 1/2 as a catastrophe precursor.It is found that prior to catastrophe,the variation of the system response to the controlling parameter follows a power law of negative index,which proves the power law singularity as a common precursor of catastrophe.However,the power indexes vary with variables and samples.The uncertainty reflects sample specificity of an evolution induced catastrophe (EIC) process.

粗糙表面上的移动接触线和动态接触角

提出一个粗糙表面上移动接触线和动态接触角的数理模型 :毛细数较低时表观接触线前缘存在极薄的前驱膜 ,表观接触线在“湿”固体表面上移动 ,不同于传统模型中认为表观接触线在“干”固体表面上移动 .在Moffatt角区内部流动解的基础上 ,通过引入接触线特征参数表征表观接触线在前驱膜上的滑移程度 ,导出动态接触角的速度关系 .与不同研究者实验数据对比发现量纲 1特征参数反映固体材料特性和表面特性对动态湿润过程的影响 ,与液相的性质无关 .结合前期提出的滞后张力模型 ,对动态法和静态法测量静接触角产生的差异给出合理解释 .

动态接触角的初步分析

应用经典的Moffatt解,通过引入接触线特征参数λ给出接触线上的粘性剪切应力,导出动态接触角和接触线移动速度的关系,尝试解释文献中两种不同测量方法所得静态接触角不一致的现象,理论所揭示的动态接触角和接触线移动速度的关系曲线和以往文献中的曲线形式基本一致,通过和Hoffman试验数据的比较发现,λ与流体性质无关,是表征固壁性质的特征参数,并初步探讨了λ的数理意义。

Dynamics of Spreading of Liquid on Solid Surface

Based on assuming that there is the precursor film in the front of the apparent contact line （ACL）, a model was proposed to understand the dynamic wetting process and associated dynamic contact angle. The present model indicated that a new dimensionless characteristic parameter, 2, attects the dynamic wetting process and associated dynamic contact angle as well. However, the previous model suggested that the dynamic contact angle is dependent＇on the capillary number and static contact angle only. An experimental investigation was conducted to measure the dynamic wetting behavior of silicon oil moving over glass, aluminum and stainless steel surfaces. It concluded that when the value of 2 was selected as 0.07, 0.16 and 0.35 for glass, aluminum and stainless steel, respectively, the experimental results were in good accordance with the prediction of the model. Furthermore, the comparison of the model with Strom＇s experimental data showed that 2 is independent on the species of liquids. Apparently, 2 should be interpreted as the effect of the solid surface properties on the dynamic wetting process.Meanwhile, it is found in the present experiment that the Hoffman-Voinov-Tanner law, which is valid at very low capillary number （Ca 〈〈 1 or 80〈 10°） recommend by Cazabat, still holds for higher contact angles, even up to 70°-80°. This is explained by （he present model very well.

Dynamic wetting and stress singularity on contact line

A theoretical investigation is conducted to understand the contact linemovement and associated contact angle phenomena. Contact line is supposed to move on a thinprecursor film, and contact line has a velocity and is subject to viscous stress on the film orgeometrically on the solid surface. With the introduction of a characteristic parameter, λ', themovement of contact line and contact angle phenomena are very well described in both physics andmathematics. The viscous shearing stress exerted by liquid on solid surface was derived, and thebehavior of dynamic contact angle was recognized on rough solid surfaces. The analyses indicate thatcharacteristic parameter λ' is dependent upon solid wall intrinsic property and mechanicalperformance, and is irrelevant to liquid property. Theoretical predictions are in good agreementwith available experimental data in literature.

灾变破坏幂律奇异性前兆提取的奇异积分变换方法

1 研究背景幂律奇异性是材料灾变破坏及地震发生时的一个典型前兆特征(Voight,1989;Xue et al,2018)。在灾变破坏发生时,系统的响应函数R=du/dU发散到无穷大,表现出临界幂律奇异性(Xue et al,2018)。其中,u是系统响应量,U是系统的加载控制量。响应函数R的临界幂律奇异性是灾变破坏能量准则的体现,对大理岩、花岗岩试样进行的准静态单轴压缩实验表明,响应函数幂律奇异性指数分布在-1/2到-1之间。

Analysis of Onset and Development of Ore Formation in Dajishan Tungsten Ore Area,Jiangxi Province,China

The ＂theory of self-similar oscillatory finite-time singularities＂ of Sornette reflects accurately the spatio-temporal evolution and trends of development of events and processes in complex systems approaching to the singularities, and the effect of prediction for catastrophic events has been tested to be satisfactory. The authors take the contents of the chemical element tungsten as the carrier of positive feedback （or activator） in the ore formation, then try to apply the theory to studying and analyzing the onset and development of ore formation in the Dajishan （大吉山） tungsten ore area, Jiangxi （江西） Province, China. The results of the study show that during the spatio-temporal evolution from outside the ore area to its center, the contents of the chemical element tungsten and their loga- rithmic derivatives （local fractal dimension） manifest an obvious regularity： by way of the process of oscillation and the transition to power-law accelerating growth, they eventually approach the center of ore formation. The regularity makes clear that in the complex ore-forming system of the Dajishan tungsten ore deposit, the chemical element tungsten plays the role of carrier of positive and negative feedback, and by competing with each other, approaches to singularity in finite time by virtue of self-similar log-periodic oscillations and succeeded by power-law accelerating growth. In this way the onset of ore formation is realized. This regularity reflects correctly the dynamic process of ore formation of the studied ore deposit. The authors hold that Sornette＇s theory can be further applied to the prediction of perspective areas.