Mathematical Analysis of the Concomitance of Illicit Drug Use and Banditry in a Population

One of the majors global health and social problem facing the world today is the use of illicit drug and the act banditry. The two problems have resulted into lost of precious lives, properties and even a devastating effects on the economy of some countries where such acts were been practiced. Of interest in this work is to study the global stability of illicit drug use spread dynamics with banditry compartment using a dynamical system theory approach. Illicit drug use and banditry reproduction number was evaluated analytically, which measures the potential spread of the illicit drug use and banditry in the population. The system exhibits supercritical bifurcation property, telling us that local stability of an illicit drug and banditry-present equilibrium exist and it is unique. In addition, the illicit drug and banditry-free and illicit drug and banditry-present equilibria were shown to be global asymptotically stable, this was achieved by construction of suitable Lyapunov functions. Sensitivity analysis was carried out to know the impact of each parameter on the dynamical spread of illicit drug use and banditry in a population. Numerical simulations were used to validate the obtained quantitative results, and examine the effects of some key parameters on the system. It was discovered that, to reduce the burden of banditry in the population, stringent control measures must be put in place to reduce the use of illicit drug in a population. Suggested control measures to use in curtail the menace of the illicit drug use and banditry were recommends.

IMPACT OF DOWNSTREAM POTENTIAL PERTURBATIONS ON THE NONLINEAR STABILITY OF A GENERIC FAN

The dependence of the aerodynamic stability of fan blades with amplitude and nodal diameter of potential perturbations associated with the presence of pylons is studied. The analysis is conducted using a novel block-wise spatial Fourier decomposition of the reduced-passages to reconstruct the full-annulus solution. The method represents very efficiently unsteady flows generated by outlet static pressure non-uniformities. The explicit spatial Fourier approximation is exploited to characterize the relevance of each nodal diameter of outlet perturbations in the fan stall process, and its nonlinear stability is studied in a harmonic by harmonic basis filtering the nonlinear contribution of the rest. The methodology has been assessed for the NASA rotor 67. The maximum amplitude of the downstream perturbation at which the compressor becomes unstable and triggers a stall process has been mapped. It is concluded that the fan stability dependence with the amplitude of the perturbation is weaker than in the case of intake distortion. For perturbations with an odd number of nodal diameters, the nonlinear stability analysis leads to the same conclusions as to the small amplitude linear stability analysis. However, if the perturbations have an even number nodal diameters, the flow exhibits a supercritical bifurcation and have a stabilizing effect.

Nonlinear Vibration Analysis of a Flexible Rotor Supported by a Journal Bearing Considering Journal Angular Motion

The effect of bearing length to diameter (L/D) ratio and large disk position on nonlinear vibration of a flexible rotor-bearing system was investigated. The rotor consisted of a shaft modeled by one-dimensional finite elements (FEs) and disks. It was supported by a self-aligning ball bearing (BB) and an axial-groove journal bearing (JB). Two JB's L/D ratios of 0.4 and 0.6, two large disk positions of 340 and 575 mm measured from the BB, and two bearing models that consider both journal's lateral and angular motion (model A) and consider only journal's lateral motion (model B) were investigated. The degrees-of-freedom (DOF) of the equation of motion (EOM) were reduced to those of the boundary DOF by real mode component mode synthesis (CMS) that retains only the first forward and backward modes of the internal DOF. Shooting method and Floquet multiplier analysis were applied to the reduced EOM to obtain limit cycles and their stability, which indicates Hopf bifurcation type. Numerical results indicated that supercritical bifurcation only occurred in the case of L/D = 0.4 and large disk position 575 mm for both bearing models. Otherwise, the subcritical bifurcation occurred except the case of L/D = 0.6 with the large disk position 575 mm that supercritical bifurcation occurred if model B was used. The experiment with the same parameters used in the calculation was conducted as verification. The experimental results showed the same bifurcation type as calculated by using model A.

Buoyancy-Driven Rayleigh–Taylor Instability in a Vertical Channel

Suppose that a vertical tube is composed of two chambers that are separated by a retractable thermally insulated thin membrane. The upper and lower chambers are filled with an incompressible fluid and maintained at temperatures {T_{c}} and {T_{h}}>{T_{c}}, respectively. Upon removal of the membrane, the two fluid masses form an unstably stratified Rayleigh–Taylor-type configuration with cold and heavy fluid overlying a warmer and lighter fluid and separated by an interface across which there is a discontinuity in the density. Due to the presence of an initial discontinuity between two homogeneous states, this problem is mathematically homologous to that of the shock tube problem with the thermal expansion playing the role of pressure. When the two fluid regions are brought directly into contact with each other and the transient interfacial fluctuations have subsided, we show the emergence of a stationary state of convection through a supercritical bifurcation provided a threshold value for the temperature difference is exceeded. We suggest a possible way for the experimental testing of the theoretical results put forth in this paper.

A flow on the verge of turbulent breakdown

Stably stratified sheared flows are ubiquitous in geophysical flows from the ocean to the stars, and the route to turbulence in these flows remains an open question. The article by Lefauve et al. (J. Fluid Mech., vol. 848, 2018, pp. 508–544) is an invitation to this journey. With impressive experimental precision mastered by few teams in the world, the nature of the coherent structure that dominates the flow on the verge of turbulent breakdown is revealed and analysed through one- or two-dimensional modern stability analysis of an experimentally obtained base flow. The effect of confinement is surprisingly strong, advocating for leaving the textbook flows, inhomogeneous in only one direction, for the more complex shores of real flows, now accessible to analysis of multidimensional stability problems. The route explored by Lefauve et al. (2018) renews with the long tradition of the supercritical bifurcation scenario, it revisits the linear stability theory with possibility of resonances, critical layers and more to be imagined, since complex base flows are now available to explore both experimentally and analytically.

On the Critical Speed, Supercritical Bifurcation, and Stability Problems of Certain Type of High-Speed Rail Vehicle

Recently, Chinese engineers have proposed a simple way to find the vehicles’ critical speed, which is similar to the ramping method. In this article, through an example of vehicle of supercritical properties, it is proved that the new easier way is not scientifically justified and should not be used in engineering practice. In addition, the ramping way also yields inaccurate critical speed. Then one abnormal vibration phenomenon which appears on Beijing-Shanghai high-speed line is studied. The results demonstrate that it is car body hunting but not bogie hunting. Finally, through the computation and comparison of the lateral ride indices under different conditions, one stability problem about stochastic limit cycle banding is tentatively discussed.