Related papers: Saddle-node bifurcation in interfacial morphology …
Effective passivation of lithium metal surfaces, and prevention of battery-shorting lithium dendrite growth, are critical for implementing lithium-metal-anodes for batteries with increased power densities. Nanoscale surface heterogeneities…
Steady states of the Swift--Hohenberg equation are studied. For the associated four--dimensional ODE we prove that on the energy level $E=0$ two smooth branches of even periodic solutions are created through the saddle-node bifurcation. We…
In this paper, we investigate saddle-node to saddle separatrix--loops that we term SNICeroclinic bifurcations. They are generic codimension-two bifurcations involving a heteroclinic loop between one non-hyperbolic and one hyperbolic saddle.…
Lithium ion batteries (LIB) can feature reactive anodes that operate at low potentials, such as lithium metal or silicon, passivated by solid electrolyte interphase (SEI) films. SEI is known to evolve over time as cycling proceeds. In this…
We study homoclinic bifurcations in an interval map associated with a saddle-focus of (2, 1)-type in $\mathbb{Z}_2$-symmetric systems. Our study of this map reveals the homoclinic structure of the saddle-focus, with a bifurcation unfolding…
We study the effect of external forcing on the saddle-node bifurcation pattern of interval maps. By replacing fixed points of unperturbed maps by invariant graphs, we obtain direct analogues to the classical result both for random forcing…
As the parameters of a piecewise-smooth system of ODEs are varied, a periodic orbit undergoes a bifurcation when it collides with a surface where the system is discontinuous. Under certain conditions this is a grazing-sliding bifurcation.…
In this report, we consider a semi-infinite discrete nonlinear Schr\"odinger equation driven at one edge by a driving force. The equation models the dynamics of coupled waveguide arrays. When the frequency of the forcing is in the…
In this paper, we present a general framework for constructively proving the existence and stability of stationary localized 1D solutions and saddle-node bifurcations in activator--inhibitor systems using computer-assisted proofs.…
The necking instability is a precursor to tensile failure and rupture of materials. A quasistatically loaded free-standing uniaxial specimen typically exhibits necking at a single location, corresponding to a long wavelength bifurcation…
Silicon is a promising anode material for next-generation lithium-ion batteries due to its exceptionally high specific capacity (3600 mAh g$^{-1}$), significantly exceeding that of conventional graphite. However, its practical application…
We investigate localised bulging or necking in an incompressible, hyperelastic cylindrical tube under axial stretching and surface tension. Three cases are considered in which the tube is subjected to different constraints. In case 1 the…
The Solid-Electrolyte Interphase, SEI, formed on a battery electrode has been a central area of research for decades. This thin, complex layer profoundly impacts the electrochemical deposition morphology and stability of the metal in…
Bifurcations mark qualitative changes of long-term behavior in dynamical systems and can often signal sudden ("hard") transitions or catastrophic events (divergences). Accurately locating them is critical not just for deeper understanding…
In this paper, we report the bifurcations of mode-locked periodic orbits occurring in maps of three or higher dimensions. The `torus' is represented by a closed loop in discrete time, which contains stable and unstable cycles of the same…
In this paper for the first time we report the results of molecular dynamics simulation of electrode/electrolyte interface of Li-O2 cathode under potential close to experimental values in 1M dimethyl sulfoxide (DMSO) solution of LiPF6 salt.…
A generic saddle-node bifurcation is proposed to modelize fast transitions of finite amplitude arising in geophysical (and perhaps other) contexts, when they result from the intrinsic dynamics of the system. The fast transition is…
Sulci are localized furrows on the surface of soft materials that form by a compression-induced instability. We unfold this instability by breaking its natural scale and translation invariance, and compute a limiting bifurcation diagram for…
We focus on the existence and persistence of families of saddle periodic orbits in a four-dimensional Hamiltonian reversible ordinary differential equation derived using a travelling wave ansatz from a generalised nonlinear Schr{\"o}dinger…
A 3D mechanical stable scaffold is shown to accommodate the volume change of a high specific capacity nickel-tin nanocomposite Li-ion battery anode. When the nickel-tin anode is formed on an electrochemically inactive conductive scaffold…