Narrow Results

A consumer behavior model is considered in the context of a network of interacting individuals in an energy market. We propose and analyze a simple dynamical model of an ensemble of coupled active elements mimicking consumers' behavior, where "word-of-mouth" interactions between individuals are important. A single element is modeled using the automatic control system framework. Assuming local (nearest neighbor) coupling we study the evolution of chains and lattices of the model consumers when varying the coupling strength and initial conditions. The results are interpreted as the dynamics of the decision-making process by the energy-market consumers. We demonstrate that a pitchfork bifurcation to the homogeneous solution leads to bistability of stationary regimes, while the autonomous system is always monostable. In the presence of inhomogeneities, this results in the formation of clusters of sharply positive and negative opinions. We also find that, depending on the coupling strength, the perturbations caused by inhomogeneities can be exponentially localized in space or delocalized. In the latter case, the coarse-graining of opinion clusters occurs.

N-body simulations of dark matter halos show that the density is cusped near the center of the halo. The density profile behaves as r^–γ in the inner parts, where γ ≃ 1 for the NFW model and γ ≃ 1.5 for the Moore model, but in the outer parts the two models agree with each other in the asymptotic behavior of the density profile. The simulations also show information about the anisotropy parameter β(r) of the velocity distribution: β ≈ 0 in the inner part and β ≈ 0.5 (radially anisotropic) in the outer part of the halo. We provide some distribution functions F(E, L) with the constant anisotropy parameter β for the two spherical models of dark matter halos: a new generalized NFW model and a generalized Moore model. There are two parameters α and ∊ for those two generalized models to determine the asymptotic behavior of the density profile. In this paper, we concentrate on the situation of β(r) = 1/2 from the viewpoint of the simulation.

A dynamical model is employed to determine some peculiar properties of the scission neutrons, i.e., those emitted at the rupture of the neck between the fragments during low energy nuclear fission. Thus, by a specially adapted procedure, we calculate the time-dependent decay rate. This, defines the character of the emission process: pulsed or exponentially. From the time dependence of the survival probability, we deduced the “half-life” of the scission neutron emission. The angular distribution of the scission neutrons with respect to the fission axis is calculated as well. This is obtained for sets of neutron wave functions defined by a given quantum number $\mathrm{\Omega }$ (projection of the total angular momentum on the symmetry axis). A strong dependence on $\mathrm{\Omega }$ was found, namely, wave functions with different $\mathrm{\Omega }$ have different most probable emission angles: from emission along the fission axis (1/2) to emission perpendicular to the fission axis (9/2). This result leads to a new interpretation of the measured angular distribution of the prompt fission neutrons. Finally, an extension of the dynamical model (i.e., with a time-dependent potential also after scission) is presented.

A mathematical model for Intra-Venous Glucose Tolerance Test (IVGTT) with explicit glucose–insulin interaction is presented as a system of delay differential equation with discrete time delays and its important mathematical features are analyzed. This model includes the positivity and boundedness of the solution. An unique equilibrium point is found and its local stability is investigated. Using the Lyapunov functional approach, we show the global stability of the unique equilibrium point. The length of delay that preserves the stability is estimated. Sensitivity analysis is performed on a delay differential equation model for IVGTT that suggests the parameter value has a major impact on the model dynamics. Numerical calculations are performed to support and elaborate the analytical findings.

Hemorrhagic fever with renal syndrome (HFRS) spreading from rodent to human beings is a major public health problem in China, which causes high mortality rate. Data obtained from the China Ministry of Health shows that cases of HFRS in China exhibited monthly periodic outbreak. To well reveal the mechanisms about the outbreak of HFRS, we established a dynamical model to explain the periodic behaviors of HFRS in China. We obtained the basic reproduction number $R_0$, analyzed the dynamical behavior of the model, and used the model to fit the monthly data of HFRS cases. Our results demonstrated that periodic transmission rates and rodent periodic birth rate of HFRS in China can give rise to the periodic outbreak of HFRS, hence providing insights into taking measures to control HFRS in China.

With its good flexibility and adaptability to the environment, soft robot has been attached great importance by the majority of researchers in recent years, and is widely used in rehabilitation treatment, flexible grasping and other fields. However, the existing actuators have disadvantages such as single deformation mode, poor flexibility and insufficient environmental adaptability. The reason is that the actuator structure is too simple to meet the complex application scenarios. In this paper, an omnidirectional bending multi-segment soft actuator is proposed, and the parameter analysis and dynamic analysis models are given. Meanwhile, the prestressed modal analysis of the proposed model is carried out to better characterize the dynamic behavior. A numerical study of a climbing motion verifies the novelty and validity of the proposed structure.

To investigate the dynamical load sharing behaviors of multi-floating components in the heavy load planetary gear system, a multi-floating planetary gear system that includes a floating central component and a quasi-floating planet flexible supporting pin is employed. Then a 21 degree of freedom lumped parameters dynamical model of this system is presented to study the dynamical load sharing behaviors. Some influencing factors, such as supporting stiffness, positions error of sun or carrier, and external input load are analyzed on the dynamical load sharing of the planetary gear system with multi-floating components. The results demonstrate that the load sharing condition of the system is best when both the sun gear and planet gears are multi-floating at the same time. When the planet gear position errors remain constant, reducing the flexible pin stiffness of planet gear or increasing external input load can effectively improve the load sharing. These conclusions are verified by the relevant experiments.

In industrial production, the industrial manipulator's end-effector is required to produce movements according to a desired track to execute tasks. However, high nonlinearity and coupling are exhibited in the dynamic characteristic of manipulators because of the constrained relationship brought on by the desired track. This makes it hard to build dynamical equations with the traditional Lagrange equation. Targeted at industrial manipulators subject to constraint, this paper presents a generalized constrained relationship and found its analytical formulas. The dynamical equation of a system under a certain desired track constraint was then acquired based on the Udwadia–Kalaba equation, overcoming the disadvantages of doing so using the traditional Lagrange equation and multiplier. The simulation results proved that the dynamical equation established by this method fits the empirical data.

The possibility of synthesizing a doubly magic superheavy nucleus, ²⁹⁸Fl₁₈₄ at the Center of Island Stability, is investigated on the basis of fluctuation-dissipation dynamics. In this study, we employ the three-dimensional Langevin equation for fusion process and survival process. We take into account the neutron evaporations during the whole process and the change of the potential energy due to the neutron evaporations. We obtained the fusion cross section and showed the advantage of producing ³⁰⁴Fl as high excited compound nucleus. It means that the dynamical mechanism, which was discussed in [1], works even in the three-dimensional Langevin calculation.

The possibility of synthesizing a doubly magic superheavy nucleus, ²⁹⁸Fl₁₈₄, is investigated on the basis of fluctuation-dissipation dynamics. In order to synthesize this nucleus, we must generate more neutron-rich compound nuclei because of the neutron emissions from excited compound nuclei. The compound nucleus ³⁰⁴Fl has two advantages to achieving a high survival probability. First, because of low neutron separation energy and rapid cooling, the shell correction energy recovers quickly. Secondly, owing to neutron emissions, the neutron number in the nucleus approaches that of the double closed shell and the nucleus attains a large fission barrier. Because of these two effects, the survival probability of ³⁰⁴Fl does not decrease until the excitation energy E^*= 50 MeV. These properties lead to a rather high evaporation residue cross section. Also, using the dynamical model, we study fission fragment mass distributions from the fission of U and Pu isotopes at low excitation energies. It was found that the shell effect of the potential-energy landscape has a dominant role in determining the mass distribution. The present approach can serve as a basis for more refined analysis.