On a numerical bifurcation analysis of a particle reaction-diffusion model for a motion of two self-propelled disks

Theoretical analysis using mathematical models is often used to understand a mechanism of collective motion in a self-propelled system. In the experimental system using camphor disks, several kinds of characteristic motions have been observed due to the interaction of two camphor disks. In this paper, we understand the emergence mechanism of the motions caused by the interaction of two self-propelled bodies by analyzing the global bifurcation structure using the numerical bifurcation method for a mathematical model. Finally, it is also shown that the irregular motion, which is one of the characteristic motions, is chaotic motion and that it arises from periodic bifurcation phenomena and quasi-periodic motions due to torus bifurcation.

On the Thermal Dynamics of Metallic and Superconducting Wires. Bifurcations, Quench, the Destruction of Bistability and Temperature Blowup

In the present study, a numerical bifurcation analysis is carried out in order to investigate the multiplicity and the thermal runaway features of metallic and superconducting wires in a unified framework. The analysis reveals that the electrical resistance, combined with the boiling curve, are the dominant factors shaping the conditions of bistability—which result in a quenching process—and the conditions of multistability—which may lead to a temperature blowup in the wire. An interesting finding of the theoretical analysis is that, for the case of multistability, there are two ways that a thermal runaway may be triggered. One is associated with a high current value (“normal” runaway) whereas the other one is associated with a lower current value (“premature” runaway), as has been experimentally observed with certain types of superconducting magnets. Moreover, the results of the bifurcation analysis suggest that a static criterion of a warm or a cold thermal wave propagation may be established based on the limit points obtained.

Numerical Bifurcation Analysis of a Film Flowing over a Patterned Surface through Enhanced Lubrication Theory

The bifurcation analysis of a film falling down an hybrid surface is conducted via the numerical solution of the governing lubrication equation. Instability phenomena, that lead to film breakage and growth of fingers, are induced by multiple contamination spots. Contact angles up to 75∘ are investigated due to the full implementation of the free surface curvature, which replaces the small slope approximation, accurate for film slope lower than 30∘. The dynamic contact angle is first verified with the Hoffman–Voinov–Tanner law in case of a stable film down an inclined plate with uniform surface wettability. Then, contamination spots, characterized by an increased value of the static contact angle, are considered in order to induce film instability and several parametric computations are run, with different film patterns observed. The effects of the flow characteristics and of the hybrid pattern geometry are investigated and the corresponding bifurcation diagram with the number of observed rivulets is built. The long term evolution of induced film instabilities shows a complex behavior: different flow regimes can be observed at the same flow characteristics under slightly different hybrid configurations. This suggest the possibility of controlling the rivulet/film transition via a proper design of the surfaces, thus opening the way for relevant practical application.

Disconnected stationary solutions for 3D Kolmogorov flow problem: preliminary results

The extension of the classical A.N. Kolmogorov’s flow problem for the stationary 3D Navier-Stokes equations on a stretched torus for velocity vector function is considered. A spectral Fourier method with the Leray projection is used to solve the problem numerically. The resulting system of nonlinear equations is used to perform numerical bifurcation analysis. The problem is analyzed by constructing solution curves in the parameter-phase space using previously developed deflated pseudo arc-length continuation method. Disconnected solutions from the main solution branch are found. These results are preliminary and shall be generalized elsewhere.

A geometric analysis of the SIRS epidemiological model on a homogeneous network

We study a fast–slow version of an SIRS epidemiological model on homogeneous graphs, obtained through the application of the moment closure method. We use GSPT to study the model, taking into account that the infection period is much shorter than the average duration of immunity. We show that the dynamics occurs through a sequence of fast and slow flows, that can be described through 2-dimensional maps that, under some assumptions, can be approximated as 1-dimensional maps. Using this method, together with numerical bifurcation tools, we show that the model can give rise to periodic solutions, differently from the corresponding model based on homogeneous mixing.

Multiple stage hydra effect in a stage-structured prey-predator model

In this work, we show by means of numerical bifurcation that two alternative stable states exhibit a hydra effect in a continuous-time stage-structured predator-prey model. We denote this behavior as a stage multiple hydra effect. This concomitant effect can have significant implications in population dynamics as well as in population management.