Spatiotemporal dynamics analysis and optimal control method for an SI reaction-diffusion propagation model

In the new social media era, it is becoming increasingly important to explore the propagation rules for rumors in social networks. This article is concerned with investigating a diffusive susceptible-infected rumor propagation model with a nonlinear propagation function in a spatially heterogeneous environment. We establish the uniform persistence and analyze the asymptotic behavior of the rumor-spreading steady state for the spatially heterogeneous model when one of the diffusion coefficients tends to zero. Moreover, to better reflect the effect of a time delay on the process of rumor propagation, we establish a spatially homogeneous model with a time delay and prove the existence and local stability of the corresponding equilibrium point. Furthermore, the optimal control in the spatially homogeneous environment case is derived. Finally, several numerical simulations are performed to verify the theoretical results in both spatially heterogeneous and spatially homogeneous systems.     

康德区分开了理由与原因吗

后期维特根斯坦所做出的最为独特的哲学贡献是将理由与原因严格地区别开来。正是基于这个区分,他对遵守规则现象及语言现象的本性做出了独特的说明。此区分不仅在维特根斯坦后期哲学中居于核心的位置,而且也在当代哲学特别是道德哲学和行动哲学的讨论中占有着一个非常重要的位置。维特根斯坦是哲学史上第一个明确地做出这种区别的哲学家。不过,这个断言与一些哲学史家的观点相背。著名康德专家艾利森声称,康德在其著名的理知因致性学说或自由学说中就已经做出了−至少应该做出了−维特根斯坦意义上的理由与原因之分。这种解读是错误的。     

Dynamical Analysis and Control Strategies of Rumor Spreading Models in Both Homogeneous and Heterogeneous Networks

In recent years, rumor propagation in social networks attracts more researchers’ attention. In this paper, we have established I2S2R rumor spreading models in both homogeneous networks and heterogeneous networks considering the effect of time delay. In the homogeneous network model, we obtain the basic reproduction number by means of the next-generation matrix. Besides, the local stability and the global stability of the equilibrium points are discussed by linearization approach of nonlinear systems and Lyapunov function. In the heterogeneous network model, we calculate the basic reproduction number through algebraic method. In addition, Lyapunov functional method and Lasalle invariance principle are applied to study the stability of equilibrium points in the complex network model. Further, we put forward some useful strategies to control the spreading of rumor based on the complex network theory. Finally, we take advantage of numerical simulations to verify the theory above and come up with necessary conclusions.

     

Multiple fire interactions: A further investigation by burning rate data of square fire arrays

This paper presents the first effort to explore the spatial distributions of the burning rates in group fires consisting of a large number of fire points, by analyzing burn-out time data from experimental square fire arrays ranging from 3 × 3 to 15 × 15. A new concept termed fire layer is introduced and defined to characterize the spatial locations of fire points by which the complex spatial variations of burning rates, under different conditions, are analyzed and physically interpreted. Analysis shows that the fire layer burning rates vary from outer to inner in definite nonlinear modes. This indicates that the two fire interaction effects, heat feedback enhancement and air supply restriction, involve distinct spatial fluctuations in fire arrays. The spatial fluctuations of the two interaction effects are significantly affected by the two major parameters, fire spacing and fire array size. Definite spatial regions and parameter ranges for the spatial fluctuations and high competitions of the two interaction effects are clearly distinguished. It is demonstrated that the average burning rates of all fire layers involve consistent variations versus fire spacing or fire array size, especially with high comparability to the entire fire array. It is found that by varying fire spacing, the average burning rates for all fire layers vary linearly versus the fire area ratio, within the same ranges as the entire fire array, while there exist different fluctuation modes of fire layer burning rates with respect to fire array size. Furthermore, analysis shows that the burning rates of all fire layers will be significantly affected by fire merging when it occurs. Finally, a new approach is presented to simulate fire propagation among discrete fuel sources, by which the positive effect of the surrounding new fire points on the burning rates of the original ones is definitely indicated.     

Experimental research on flame revolution and precession of fire whirls

This paper presents the first experimental effort to explore the large scale 3-D flame instabilities of fire whirls, including the inclined flame revolution during the transition from a general pool fire to fire whirl, and the swirling flame precession in a quasi-steady fire whirl. The experimental medium-scale fire whirls were produced by a fixed-frame facility. Experimental observations indicate that flame revolution is an important flame instability during the formation of fire whirl, showing that the entire flame is inclined and revolves around the geometrical axis of symmetry with increasing angular velocity until the critical point, without the self-rotation of the flame. It is found that the inlet velocity fluctuates synchronously with the flame revolution. As soon as the fire whirl forms, the erect swirling flame starts to precess around the geometrical axis of symmetry. Analysis indicates that during flame precession the periodic fluctuations of inlet velocity disappear and a local annular external recirculation zone (ERZ) is produced outside the flame (vortex core), while the flow is upward inside. It is found that the inlet velocities are nearly constant within the continuous flame in order to maintain a stable generating eddy. A good linear correlation exists between the average inlet velocities and average ambient circulations for all fuel pan sizes. The precession frequency is relatively stable during one test. The frequencies of flame revolution and precession are both proportional to the average inlet velocity, and the corresponding Strouhal numbers are constants of 0.42 and 0.80, respectively. The flame revolves and precesses in the same direction as the self-rotation of the fire whirl flame in all tests. The flame revolution is related to the periodical fluctuations of inlet flow, while the flame precession is considered to be linked to the occurrence of ERZ in fire whirls.     

Experimental research on combustion dynamics of medium-scale fire whirl

The medium-scale fire whirl was extensively investigated by experimental means, in order to establish correlations of the burning rate, flame height and flame temperature of fire whirl, and to clarify the difference between fire whirls and general pool fires. Experimental observations and data confirmed that a free burning fire whirl is a highly stable burning phenomenon with large quasi-steady periods. Burning rates of fire whirls depend on pool diameter similarly to those of general pool fires; however the transition turbulent burning occurs sooner as the pool diameter increases. The lip height seems to have little effect on the burning rate of fire whirls. The correlation was proposed to couple the height of fire whirl to the fire release rate and ambient circulation. It correlates the data from both this work and the literature. Radial temperature profiles in the continuous region of the fire whirl were confirmed to be hump-type, implying the existence of fuel-rich inner core. The pool diameter and heat release rate do not significantly affect the radial temperature profiles in non-dimensional radial coordinates. It was found that the fire plume of fire whirl involves three distinct zones just like that of pool fire, but with different normalized ranges. Fire whirls maintain a higher ratio of continuous flame height to the overall flame height, and also higher maximum centerline excess temperature in continuous flame region, as compared to general pool fires. It was further demonstrated that the fire whirl plume at its origin behaves like a turbulent jet with moderate swirling, and then tends to become buoyancy dominated downstream, with slight swirling. With an increase in dimensionless height adjusted by the plume origin, the plume centerline excess temperature decays rapidly and approaches the theoretical value of −5/3 for free buoyancy plume.     

SIS Model of Rumor Spreading in Social Network with Time Delay and Nonlinear Functions

With the advent of the information age of networks, the study about rumor propagation in social networks has become increasingly significant. In this paper, a rumor propagation model with nonlinear functions and time delay in social networks is proposed. First, according to the nextgeneration matrix method, we work out the basic reproduction number. Second, we discuss the existence of the rumor-prevailing equilibrium points. Third, we demonstrate the stabilities of equilibrium points and analyze the sufficient conditions for Hopf bifurcation. Finally, the correctness of the theory is verified and several vital conclusions are obtained by numerical simulations.     

Modeling the COVID-19 epidemic and awareness diffusion on multiplex networks

The coronavirus disease 2019(COVID-19)has been widely spread around the world,and the control and behavior dynamics are still one of the important research directions in the world.Based on the characteristics of COVID-19’s spread,a coupled disease-awareness model on multiplex networks is proposed in this paper to study and simulate the interaction between the spreading behavior of COVID-19 and related information.In the layer of epidemic spreading,the nodes can be divided into five categories,where the topology of the network represents the physical contact relationship of the population.The topological structure of the upper network shows the information interaction among the nodes,which can be divided into aware and unaware states.Awareness will make people play a positive role in preventing the epidemic diffusion,influencing the spread of the disease.Based on the above model,we have established the state transition equation,through the microscopic Markov chain approach(MMCA),and proposed the propagation threshold calculation method under the epidemic model.Furthermore,MMCA iteration and the Monte Carlo method are simulated on the static network and dynamic network,respectively.The current results will be beneficial to the study of COVID-19,and propose a more rational and effective model for future research on epidemics.     

论康德哲学中的过度决定问题

康德认为,人的行动一方面是特定的自然原因的结果,另一方面又是一种独特的理知原因的结果。在此,自然原因与理知原因分别对应着作为显象的人与作为物本身的人（主体本身或我本身）。一些解释者认为,康德的这种观点会让其陷入“过度决定”困境。这种批评是不可接受的,因为在康德这里,理知原因、自然原因和人的行动构成了一个因果链条：理知原因首先引起（因致）作为一种自然原因的意志决定和意志行为;意志决定和意志行为接着引起（因致）人的行动。