Gaussian skewness approximation for dynamic rate multi-server queues with abandonment

Energy function of 2D and 3D dynamical systems

With the rise of some concepts such as “Digital Earth” and “digital city,” how to realize the three-dimensional reconstruction and visualization of the urban art landscape is becoming a current research hotspot. This study takes the VR-Platform as the development platform and combines it with 3dsMax technology to study the dynamic simulation technology of urban 3D art landscapes. Additionally, this study combines the dynamic simulation technology of urban three-dimensional artistic landscape, designs the urban three-dimensional artistic landscape dynamic simulation system from the aspects of landscape modeling, texture mapping, drive integration, and so on, and finally realizes the basic functions such as roaming interaction, map navigation, information measurement, and visual display of the urban three-dimensional artistic landscape dynamic simulation system, which has a certain practical application value.

The aim of this study was to measure the facial motion of patients with facial paralysis using a three-dimensional dynamic quantitative analysis system of facial motion (3D ASFM) and analyze its correlation with subjective grading systems. We included 30 healthy volunteers and 50 patients with unilateral facial paralysis. After placing landmarks on the faces, the facial motions of the patients were measured using the 3D ASFM. The regional symmetry ratios(SRs) and gross scores of different parameters were calculated. Then a comparison with four subjective grading systems(House-Brackmann, Sunnybrook, Facial Nerve Grading System 2.0, Fisch) was performed. The entire test could be completed within five minutes. The normal range of healthy volunteers were obtained, the gross score of which was 91.9±1.5. The SRs of the maximal moving distance(MMD) were most strongly correlated with regional subjective grading systems, followed by the SRs of the maximal moving velocity (MMV). The SRs of the maximal moving acceleration (MMA) were either poorly correlated or uncorrelated with the subjective grading systems. Moreover, the Spearman coefficients with four subjective grading systems were -0.630(House-Brackmann), -0.728(Facial Nerve Grading System 2.0), 0.697(Sunnybrook), and 0.617(Fisch)respectively(P<0.05). The 3D ASFM is a convenient method to rapidly assess facial paralysis. It not only overcomes the shortcomings of conventional subjective grading systems, but also correlates well with them.

Traveling waves in a quintic BBM equation under both distributed delay and weak backward diffusion

Three-dimensional Discrete Element Method simulation system of the interaction between irregular structure wheel and lunar soil simulant

As tropical forests are complex systems, they tend to be modelled either roughly via scaling relationships or in a detailed manner as high-dimensional systems with many variables. We propose an approach which lies between the two whereby succession in a tropical forest is viewed as a trajectory in the configuration space of a dynamical system with just three dependent variables, namely, the mean leaf-area index (LAI) and its standard deviation (SD) or coefficient of variation along a transect, and the mean diameter at breast height (DBH) of trees above the 90th percentile of the distribution of tree DBHs near the transect. Four stages in this forest succession are identified: (I) naturally afforesting grassland: the initial stage with scattered trees in grassland; (II) very young forest: mostly covered by trees with a few remaining gaps; (III) young smooth forest: almost complete cover by trees of mostly similar age resulting in a low SD; and (IV) old growth or mature forest: the attracting region in configuration space characterized by fluctuating SD from tree deaths and regrowth. High-resolution LAI measurements and other field data from Khao Yai National Park, Thailand show how the system passes through these stages in configuration space, as do simple considerations and a crude cellular automaton model.

This paper uses the theory of bifurcations of dynamical systems, considering R&D input competition model in oligopoly market with heterogeneous rationality. We assume that cooperation, as well as competition, exists among the oligarchs, which are closer to reality and different from previous studies. On the basis of analyzing the stabilities of four fixed points in the three-dimensional dynamic system, a local stable region of Nash equilibrium is obtained. Simulation results show that the adjustment of R&D input speed has an obvious impact on the complexity of competition, and also show that the system profit will decrease when it is in chaos. So this paper discusses the application of parameters control method when the model is in chaos and then allows the oligarchs to eliminate the negative effects.

In this research article, we investigate a three-dimensional dynamical system governed by fractal-fractional-order evolution differential equations subject to terminal boundary conditions. We derive existence and uniqueness results using Schaefer’s and Banach’s fixed-point theorems, respectively. Additionally, the Hyers–Ulam stability approach is employed to analyze the system’s stability. We employ vector terminology for the proposed problem to make the analysis simple. To illustrate the practical relevance of our findings, we apply the derived results to a numerical example and graphically illustrate the solution for different fractal-fractional orders, emphasizing the effect of the derivative’s order on system behavior.

A general method by which to investigate nonlinear dynamical systems close to a stability threshold is presented. This method combines a proper orthogonal decomposition and a subsequent Galerkin projection. This technique is applied to three-dimensional resistive ballooning plasma fluctuations in a tokamak. The corresponding dynamical system belongs to a large family of convective fluid systems including Rayleigh-Benard convection. A proper orthogonal decomposition of the fluctuating signal obtained by numerical simulation shows that the relevant modes are close to the linear (global) modes. The Galerkin projection provides a low-dimensional system that allows the study of shear flow generation, its subsequent fluctuation reduction, and the evolution to oscillating states.

Vehicles crossing bridges at high speeds can cause significant dynamic effects and must be studied by accurately simulating the interactive, dynamic responses of the bridge deck and the load-applying vehicles. Specifically, a multi-span, orthotropic, bridge deck during truck loading is investigated to better understand the dynamic interaction between moving vehicles with tandem axles and highway bridge decks. The vehicle is modeled by a three-dimensional dynamic system with tandem axles with 9 degrees of freedom. The bridge deck is modeled by a thin, orthotropic, multi-span plate. The road surface irregularities are modeled by a random function characterized by a spectral roughness coefficient and power spectral density. The modal method is used to solve the equation of motion of the bridge deck. Equations of motion of the vehicle are obtained using a virtual work principle. The coupled equations of motion vehicle/bridge deck are integrated numerically by Newmark’s method. A computational algorithm in FORTRAN is used to solve the integrated equations of motion in a decoupled, iterative process. A numerical example of an orthotropic, three-span bridge deck, excited in nine degrees of freedom truck is presented. The resulting distribution of the Dynamic Amplification Factor on the bridge deck does not reflect any particular trend, because high values of the DAF can be obtained at points where the vertical displacement is small. The DAF is significant only under the interaction force. Thus, the road surface roughness had a significant influence on the dynamic vehicle/bridge deck interaction forces.Keywordsdynamic interactionorthotropic bridge deckvehicletandem axles

Horseshoe chaos and topological entropy estimation in a palaeoclimate dynamical model

A neo-Kaleckian model of capital accumulation, income distribution and financial fragility

The carbon market is the least-cost tool to reduce carbon emissions. This study explores the evolution of the carbon price in the carbon market from a dynamic system perspective. A three-dimensional carbon price dynamic system is established to quantify the interactions among the carbon price, energy price, and economic growth. The system built in this study presents various dynamic characteristics including chaotic attractors and stable equilibria. Specifically, the existence of chaos in the system is verified by Lyapunov exponents spectrum and bifurcation diagram. In contrast, the system tends to be stable in the case of China after identifying the system parameters through the genetic algorithm. Furthermore, evolutionary trends of the carbon price are analyzed when the system parameters are perturbed. The results show that the carbon price is positively correlated with energy price as well as energy price policy. Besides, the level of the carbon price is negatively correlated with government control in the short term and positively correlated in the long term. This study can help analyze trends in the carbon price in the mid-term to long-term.

The problem of finding integrals of motion of three-dimensional dynamical systems is analysed. The authors introduce a new type of direct method in the search of parameter values for which an integral of motion exists. This method consists in proposing an ansatz for the integral that explicitly shows the dependence with respect to one of the phase space coordinates of the system. They apply this procedure to the reduced three-wave interaction problem and to the Rabinovich system. For both models new integrals of motion are found.

The paper deals with bifurcations of dynamic systems having noncoarse homoclinical contours. Cases are singled out when the bifurcation surface corresponding to the appearance of a noncoarse homoclinical contour can separate a Morse-Smiley system from a system with a countable set of periodic motions. An example is adduced of the existence of a countable set of stable periodic motions.