A Study on the Nonlinear Stability of Fronts in the Ocean on a Sloping Continental Shelf

The baroclinic nonlinear stability of fronts in the ocean on a sloping continental shelf is studied, the model equations, called the frontal geostrophic model, developed by Cushman—Roisin et al.(1992) for describing the dynamics of surface density fronts in the ocean are developed and the two—layer frontal geostrophic model for fronts on a sloping continental shelf is first obtained. The nonlinear stability criteria for the fronts on a sloping bottom are obtained by using Arnol’d (1965, 1969) variational principle and a prior estimate method. It is shown that our result is better than the former works. Key words Fronts in the ocean - Frontal geostrophic model - Nonlinear stability This Work was supported by “ the National Key Programme for Developing Basic Sciences” G199804901-1 and the National Natural Science Foundation of China “ Research Programme for Excellent State Key Laboratory” under Grant No. 49823002 and No. 49805002.

On the stability of fronts near shelfbreak

Using a two-dimensional semi-geostrophic model. the stability of fronts near shelf break (shelfbreak font, western boundary current front) and its mechanism are studied. We find that the stability of the front is related to the frontal structure. In general, the increase of the lower layer depth lowers the unstable growth rate (a1). (1) The shelfbreak front is baroclinically unstable and ai increases with the increase of the bottom slope, different from the conclusion of Flagg and Beardsley (1978). (2) A western boundary current front with uniform vorticity in the upper layer is barotropically unstable, due to the strong horizontal shear of the mean current. The unstable growth rate of this front for a realistic topography is only one seventh of that of the flat bottom case. (3) For a western boundary current front with hyperbolic tangent structure, we find its wave propagation speed to be about 0. 5 m/s, in agreement with the observed values. The front is baroclinically unstable. (4)The unstable growth rate of a domed structure front and its wave speed do not seem to be related to its wavelength. The front is baroclinically unstable.

STABILITY OF TIME-PERIODIC TRAVELING FRONTS IN BISTABLE REACTION-ADVECTION-DIFFUSION EQUATIONS

This paper is concerned with the global exponential stability of time periodic traveling fronts of reaction-advection-diffusion equations with time periodic bistable nonlinearity in infinite cylinders. It is well known that such traveling fronts exist and are asymptotically stable. In this paper, we further show that such fronts are globally exponentially stable. The main difficulty is to construct appropriate supersolutions and subsolutions.

Macroregulation in all-around recovery:Maintain stability and orient to long-term priorities

Since last October, loose monetary and credit policies and the stimulus package have produced desired results. The economy has entered into a "V-shaped" recovery in the second quarter of this year after hitting the bottom in the first quarter, with various economic indicators rising fast, rescue missions completed and short-term objectives basically met. In this context, the next step of macro-regulation should focus on long-term objectives, speed up institutional innovation and restructuring, control the intensity, pattern and pace of short-term policy loosening and prevent inflation and wild swings in the economy so as to achieve a new round of sustained and rapid economic growth.

Multidimensional Governance Logic and Path to Maintain Social Stability

With China’s reform and development entering a critical period,the interweaving of various interest relations and the superimposing of the old and new contradictions have intensified social risks.Based on the concept of“pluralism,sharing,participation,cooperation and tolerance”,social stability can be maintained by the balanced protection of civil rights and the full realization of the development strategy.In addition,with the guidance of comprehensive legal thinking and core socialist values,the legal regulation of administrative behavior and rights-protection behavior is strengthened.In this way,the win-win of maintaining rights and stability can be realized in the positive-sum game that will help resolve social risks and achieve high-quality social stability.

On stability of elastic domain during isothermal solid-solid phase transformationin a tube configuration

Under isothermal quasi-static stretching the phase transition of a superelastic NiTi tube involves the formation （during loading） and vanishing （in unloading） of a high strain （martensite） domain. The two events are accompanied by a rapid stress drop/rise due to the formation/vanishing of do- main fronts. From a thermodynamic point of view, both are instability phenomena that occur once the system reaches its critical state. This paper investigates the stability of a shrink- ing cylindrical domain in a tube configuration during unload- ing. The energetics and thermodynamic driving force of the cylindrical domain are quantified by using an elastic inclu- sion model. It is demonstrated that the two domain fronts ex- hibit strong interaction when they come close to each other, which brings a peak in the total energy and a sign change in the thermodynamic driving force. It is proved that such domain front interaction plays an important role in control- ling the stability of the domain and in the occurrence of stress jumps during domain vanishing. It is also shown that the pro- cess is governed by two nondimensional length scales （the normalized tube length and normalized wall-thickness） and that the length scale dependence of the critical domain length and stress jump for the domain vanishing can be quantified by the elastic inclusion model.

LOCAL STABILITY OF TRAVELLING FRONTS FOR A DAMPED WAVE EQUATION

The paper is concerned with the long-time behaviour of the travelling fronts of the damped wave equation αutt ＋ut = uxx -V′（u） on R. The long-time asymptotics of the solutions of this equation are quite similar to those of the corresponding reaction-diffusion equation ut = uxx - V′（u）. Whereas a lot is known about the local stability of travelling fronts in parabolic systems, for the hyperbolic equations it is only briefly discussed when the potential V is of bistable type. However, for the combustion or monostable type of V, the problem is much more complicated. In this paper, a local stability result for travelling fronts of this equation with combustion type of nonlinearity is established. And then, the result is extended to the damped wave equation with a case of monostable pushed front.

Compressible Rayleigh-Taylor Instability with Preheat in Inertial Confinement Fusion

The compressible Rayleigh-Taylor instability of accelerated ablation front is analysed in consideration of the preheat effects, and the corresponding eigen-problem is solved numerically using the fourth-order accurate two- point compact difference scheme. Both the growth rate and perturbation profiles are obtained, and the obtained growth rate is close to the results of direct numerical simulation. Our results show that the growth rate is more reduced and the cutoff wave length becomes longer as preheat increases.

Weak Nonlinearity of Ablative Rayleigh-Taylor Instability

The weakly nonlinear regime of single mode ablative Rayleigh-Taylor instability is studied, with consideration of preheat effect and the width of the ablation front. The Rayleigh-Taylor linear growth rate agrees well with the direct numerical simulation. For the density perturbation, the amplitude distribution of the fundamental mode has one peak value whereas those of the second and third harmonics have two and three peak values, respectively. Harmonics generation versus wave number is also given and it is close to the result of direct numerical simulation.

Dyeing and printing industry:Scientific and technical progress,energy-saving and environmental protection have achieved balanced development Interview with Chen Zhihua,president of China Dyeing and Printing Association

The general operation of dyeing and printing industry maintained a trend of slow stabilization during the 12th Five-Year Program period with obvious results in science and technology,management,energy conservation and environmental protection as well as the balanced development of the industries.Chen Zhihua,president of China Dyeing and Printing Association(CDPA),said that the dyeing and printing industry has in-

Detection of early-stage research fronts——An example of complex networks research

Purpose:This study aims to detect research fronts of a scientific field in its early development stage using bibliometric indicators developed based on the features of research fronts.Design/methodology/approach:We first focused on conceptualization of'research fronts'and outlined 4 indicators to measure different aspects of the concept:Innovation,timeliness,stability and interdisciplinarity.Then research specialties obtained based on direct citation networks were evaluated with the 4 indicators and research fronts were identified.Finally,methodology was illustrated and verified in the research domain of complex networks.Findings:The results indicate that the proposed method is useful in detecting research fronts in a specific field which is at an early development stage.Research limitations:The quality of clustering results was not assessed.It needs to be further studied whether the method can be applicable to the fields that evolve slowly such as mathematics or are highly specialized like entomology and zoology.Practical implications:This study helps researchers keep abreast of emerging trends and policy-makers formulate science and technology policies and strategic plans.Originality/value:This research provides insights into a quantitative assessment method to detect research fronts of a scientific field in its early development stage.

Cellular Chemical Field and Cellular Homeostasis

1.Introduction Cell structure and function are controlled by a complex regulatory networking process,in which molecular adaptation and interaction are essential to maintain cellular homeostasis following dynamic multi-omics rules and multi-systematic changes.This complex chemical process is an important mechanism for stabilizing the cell microenvironment.

Association between balloon atrial septostomy and prostaglandin E1 therapy until repair of transposition of the great arteries in neonates

The standard of care in the management of d-transposition of the great arteries(TGA)includes the arterial switch operation(ASO).1,2 Although some institutions have begun to publish the results of performing the ASO within the first few hours of life,most centers continue to"electively"delay ASO for several days to allow for a reduction in pulmonary vascular resistance and the stabilization of renal and liver function.1,2 The early initiation of prostaglandin E1(PGE)infusion to maintain ductal patency is a nearly universal component of therapy in order to maintain adequate arterial oxygen saturation and systemic oxygen delivery during the pre-operative period via intercirculatory mixing at the atrial septal and patent ductus arteriosus levels1,3.

基于Mein-Larson入渗模型的凹形边坡稳定性分析

坡面形态对边坡表面应力状态影响显著,而应力状态与边坡稳定性密切相关。以往的降雨入渗模型仅考虑直线形态的边坡,并没有考虑边坡为曲线形态的情况。将Mein-Larson入渗模型与坡形函数相结合,推导降雨作用下凹形边坡的入渗函数,结合极限平衡分析方法,提出一种凹形边坡稳定性计算模型。同时根据坡形拟合与坡形简化的思路,将实际边坡分别当作成凹形边坡和直线边坡进行研究。研究结果表明:湿润锋入渗深度与降雨时间呈线性关系,湿润锋面在不同降雨时刻下均与坡面平行。将实际边坡当作凹形边坡进行分析时,其降雨入渗规律更符合实际情况;当降雨时间为10天时,浅层斜坡模型得到的计算结果为0.95,而本文计算模型与数值模拟得到的稳定性系数分别为1.004和1.003,相对误差不超过1%。因此与以往提出的计算模型相比,该模型不仅考虑了实际边坡的坡面形态,而且具有计算简便、可靠度较高等特点。

Existence, uniqueness and stability of pyramidal traveling fronts in reaction-diffusion systems

In the one-dimensional space, traveling wave solutions of parabolic differential equations have been widely studied and well characterized. Recently, the mathematical study on higher-dimensional traveling fronts has attracted a lot of attention and many new types of nonplanar traveling waves have been observed for scalar reaction-diffusion equations with various nonlinearities. In this paper, by using the comparison argument and constructing appropriate super- and subsolutions, we study the existence, uniqueness and stability of three- dimensional traveling fronts of pyramidal shape for monotone bistable systems of reaction-diffusion equations in R3. The pyramidal traveling fronts are characterized as either a combination of planar traveling fronts on the lateral surfaces or a combination of two-dimensional V-form waves on the edges of the pyramid. In particular, our results are applicable to some important models in biology, such as Lotk,u-Volterra competition-diffusion systems with or without spatio-temporal delays, and reaction-diffusion systems of multiple obligate mutualists.

ACTIVE FRONT STEERING DURING BRAKING PROCESS

An active front steering （AFS） intervention control during braking for vehicle stability is presented. Based on the investigation of AFS mechanism, a simplified model of steering system is established and integrated with vehicle model. Then the AFS control on vehicle handling dynamics during braking is designed. Due to the difficulties associated with the sideslip angle measurement of vehicle, a state observer is designed to provide real time estimation. Thereafter, the controller with the feedback of both sideslip and yaw angle is implemented. To evaluate the system control, the proposed AFS controlled vehicle has been tested in the Hardware-in-the-loop-simulation （HILS） system and compared with that of conventional vehicle. Results show that AFS can improve vehicle lateral stability effectively without reducing the braking performance.

Linear and Quadratic Leap-and-Land Trajectory Tracking Algorithms

Considered in this note are numerical tracking algorithms for the accurate following of implicit curves. We start with a fixed point on the curve, and then systematically place on it additional points, one after the other. In this note we first go over the basic procedure of moving forward tangentially from an already placed point then orthogonally returning to the curve. Next, we further consider higher order forward stepping procedures for greater accuracy. We note, however, that higher order methods, desirable for greater accuracy, may harbor latent instabilities. This note suggests ways of holding such instabilities in check, to have stable and highly accurate tracing methods. The note has several supporting numerical examples, including the rounding of a dynamical “snap-through” point.

What to Expect at the Brasilia BRICS Summit

THE end of BRICS’s first decade takes place in a different international context from that of its early years.At its inception,BRICS countries maintained high growth rates and enjoyed greater political and social stability.The economic crisis of 2008,which had the United States as its epicenter,gave rise to the need for greater participation of emerging economies in the process of defining the global economy’s direction.

A NEW ONLINE NORMAL

China and Thailand established diplomatic relations on July 1,1975.Over the past 45 years,the China-Thailand relationship has maintained sound momentum of stability,and the convergence of interests and cooperation between the two countries have deepened and broadened.Thanks to the care and guidance of leaders of the two countries,both peoples have supported and helped each other.Traditional and everlasting friendship has made the two countries as close as family as it thrives in a comprehensive,wide-ranging,deep,and multidimensional way.

CHINESE ECONOMIC PROSPECTS IN 2022

The Chinese economy is estimated to have maintained a high growth rate of about 8 percent with the COVID-19 pandemic basically under control in 2021.At the same time,the triple pressures of demand contraction,supply shock,and weakening expectations gradually emerged as the quarterly economic growth rate endured an obvious downward slope,an indication that China’s economic development will face more difficulties in 2022.Therefore,the Central Economic Work Conference held in December 2021 noted that economic work should“prioritize stability while pursuing progress,”which set“stability”as the tone for economic development in 2022.