Bifurcation of a modified railway wheelset model with nonlinear equivalent conicity and wheel–rail force

This paper presents the bifurcation behaviors of a modified railway wheelset model to explore its instability mechanisms of hunting motion. Equivalent conicity data measured from China high-speed railway vehicle are used to modify the wheelset model. Firstly, the relationships between longitudinal stiffness, lateral stiffness, equivalent conicity and critical speed are taken into account by calculating the real parts of the eigenvalues of the Jacobian matrix and Hurwitz criterion for the corresponding linear model. Secondly, measured equivalent conicity data are fitted by a nonlinear function of the lateral displacement rather than are considered as a constant as usual. Nonlinear wheel–rail force function is used to describe the wheel–rail contact force. Based on these modifications, a modified railway wheelset model with nonlinear equivalent conicity and wheel–rail force is set up, and then, some instability mechanisms of China high-speed train vehicle are investigated based on Hopf bifurcation, fold (limit point) bifurcation of cycles, cusp bifurcation of cycles, Neimark–Sacker bifurcation of cycles and 1:1 resonance. In particular, fold bifurcation of cycles can produce a vast effect on the hunting motion of the modified wheelset model. One of the main reasons leading to hunting motion is due to the fold bifurcation structure of cycles, in which stable limit cycles and unstable limit cycles may coincide, and multiple nested limit cycles appear on a side of fold bifurcation curve of cycles. Unstable hunting motion mainly depends on the coexistence of equilibria and limit cycles and their positions; if the most outward limit cycle is stable, then the motion of high-speed vehicle should be safe in a reasonable range. Otherwise, if the initial values are chosen near the most outward unstable limit cycle or the system is perturbed by noises, the high-speed vehicle will take place unstable hunting motion and even lead to serious train derailment events. Therefore, in order to control hunting motions, it may be the easiest way in theory to guarantee the coexistence of the inner stable equilibrium and the most outward stable limit cycle in a wheelset system.

     

Oil phase evaporation-induced self-assembly of hydrophobic nanoparticles into spherical clusters with controlled surface chemistry in an oil-in-water dispersion and comparison of behaviors of individual and clustered iron oxide nanoparticles

We report a general method for preparing nanoparticle clusters (NPCs) in an oil-in-water emulsion system mediated by cetyl trimethylammonium bromide (CTAB), where previously only individual nanoparticles were obtained. NPCs of magnetic, metallic, and semiconductor nanoparticles have been prepared to demonstrate the generality of the method. The NPCs were spherical and composed of densely packed individual nanoparticles. The number density of nanoparticles in the oil phase was found to be critical for the formation, morphology, and yield of NPCs. The method developed here is scalable and can produce NPCs in nearly 100% yield at a concentration of 5 mg/mL in water, which is approximately 5 times higher than the highest value reported in the literature. The surface chemistry of NPCs can also be controlled by replacing CTAB with polymers containing different functional groups via a similar procedure. The reproducible production of NPCs with well-defined shapes has allowed us to compare the properties of individual and clustered iron oxide nanoparticles, including magnetization, magnetic moments, and contrast enhancement in magnetic resonance imaging (MRI). We found that, due to their collective properties, NPCs are more responsive to an external magnetic field and can potentially serve as better contrast enhancement agents than individually dispersed magnetic NPs in MRI.     

Seed-mediated shape evolution of gold nanomaterials: from spherical nanoparticles to polycrystalline nanochains and single-crystalline nanowires

We studied the kinetics of the reduction of a gold precursor (HAuCl₄) and the effect of the molar ratio (R) of sodium citrate, which was introduced from a seed solution, and the gold precursor on the shape evolution of gold nanomaterials in the presence of preformed 13 nm gold nanoparticles as seeds. The reduction of the gold precursor by sodium citrate was accelerated due to the presence of gold seeds. Nearly single-crystalline gold nanowires were formed at a very low R value (R = 0.16) in the presence of the seeds as a result of the oriented attachment of the growing gold nanoparticles. At a higher R value (R = 0.33), gold nanochains were formed due to the non-oriented attachment of gold nanoparticles. At a much higher R value (R = 1.32), only larger spherical gold nanoparticles grown from the seeds were found. In the absence of gold seeds, no single-crystalline nanowires were formed at the same R value. Our results indicate that the formation of the 1D nanostructures (nanochains and nanowires) at low R values is due to the attachment of gold nanoparticles along one direction, which is driven by the surface energy reduction, nanoparticle attraction, and dipole–dipole interaction between adjacent nanoparticles.