Post-bifurcation behaviour of elasto-capillary necking and bulging in soft tubes

Previous linear bifurcation analyses have evidenced that an axially stretched soft cylindrical tube may develop an infinite-wavelength (localized) instability when one or both of its lateral surfaces are under sufficient surface tension. Phase transition interpretations have also highlighted that the tube admits a final evolved ‘two-phase’ state. How the localized instability initiates and evolves into the final ‘two-phase’ state is still a matter of contention, and this is the focus of the current study. Through a weakly nonlinear analysis conducted for a general material model, the initial sub-critical bifurcation solution is found to be localized bulging or necking depending on whether the axial stretch is greater or less than a certain threshold value. At this threshold value, an exceptionally super-critical kink-wave solution arises in place of localization. A thorough interpretation of the anticipated post-bifurcation behaviour based on our theoretical results is also given, and this is supported by finite-element method simulations.

PT-symmetry and supersymmetry: interconnection of broken and unbroken phases

The broken and unbroken phases of P T and supersymmetry in optical systems are explored for a complex refractive index profile in the form of a Scarf potential, under the framework of supersymmetric quantum mechanics. The transition from unbroken to the broken phases of P T -symmetry, with the merger of eigenfunctions near the exceptional point is found to arise from two distinct realizations of the potential, originating from the underlying supersymmetry. Interestingly, in P T -symmetric phase, spontaneous breaking of supersymmetry occurs in a parametric domain, possessing non-trivial shape invariances, under reparametrization to yield the corresponding energy spectra. One also observes a parametric bifurcation behaviour in this domain. Unlike the real Scraf potential, in P T -symmetric phase, a connection between complex isospecrtal superpotentials and modified Korteweg-de Vries equation occurs, only with certain restrictive parametric conditions. In the broken P T -symmetry phase, supersymmetry is found to be intact in the entire parameter domain yielding the complex energy spectra, with zero-width resonance occurring at integral values of a potential parameter.

Bifurcation analysis of shear band in sand under true triaxial conditions with hypoplasticity

Predicting the onset of shear band is of significance in understanding the failureof geomaterials. The prediction accuracy is dictated by the constitutive modelused for the description of the pre-bifurcation behaviour. In this study, we firstmodify a recently proposed hypoplastic constitutive model by incorporating ageneral strength criterion and a stiffness function. We proceed to consider theonset of shear band in sand under true triaxial conditions. We demonstrate thatour analyses capture the pre-bifurcation stress–strain relationship at differentvalues of intermediate principal stress and predict fairly well the onset ofshear band. The acoustic tensor criterion generally adopted in elastoplasticapproaches is inadequate for hypoplastic approaches. No special non-coaxialtreatment is required for the present approach to yield a reasonable variationtrend of bifurcation strain with intermediate principal stress ratio 𝑏.

Indentation and bifurcation of inflated membranes

We study pneumatically inflated membranes indented by rigid indenters of different sizes and shapes. When the volume of the inflated membrane is beyond a critical value, a symmetric deformation mode becomes unstable and the system follows a path of asymmetric deformation. This bifurcation is analysed analytically for a two-dimensional membrane with either a line or plane indenter for which the stable deformation path is determined by computing the total system potential energy of different configurations. An axisymmetric membrane with indenters of different shapes and sizes is further investigated numerically. In this case, a cylindrical indenter can always trigger bifurcation while a small spherical indenter tends to be encapsulated rather than induce an asymmetric deformation mode. This result suggests that the observed bifurcation behaviour can be actively tuned and even triggered selectively by tuning indenter shape and size. We also demonstrate the effects of friction and biased bifurcation analytically through the example of a two-dimensional membrane with a line indenter.

Morphodynamic equilibrium of tidal bifurcations

<p>Deltas are fascinating landforms subject to riverine (input of water and sediments) and marine processes (waves, tides) where bifurcations are the building block controlling the distribution of water, nutrient and sediment fluxes among the distributary channels of the network. In this work we focus on the role of tides as a key factor in controlling bifurcation behaviour. Recently it has been suggested and observed that tidal deltas (i.e. delta influenced or totally dominated by the tides) have the tendency to less numerous but more stable branches in comparison to fluvial-dominated deltas [Hoitink et al., 2017]. River bifurcations subject to unidirectional flow have been widely studied in the last decades. However, in the case of tidal bifurcations, the acting physical mechanisms and controlling factors are still not well understood, and a theoretical framework is still lacking. In order to fill this gap and understand how the stability and evolution of a delta could be affected by the tides, we investigate through an analytical model, the equilibrium configurations and stability conditions of a tidal bifurcation under the hypothesis of small tidal oscillations. In particular, we extend to the tidal case the previous works of Bolla Pittaluga et al. [2015] and Seminara et al. [2012] relative to the equilibrium and stability of a single bifurcation, and to the equilibrium of a single river dominated estuary, respectively. Results show that higher tidal amplitude and a closer position of the junction node to the sea, tends to hamper the development of unstable solutions, reducing the asymmetries in water and sediment fluxes between branches obtained when the upstream width-to-depth ratio falls above a critical value. Field observations of natural deltas seems to corroborate our findings.</p>

Parameter inference in dynamical systems with co-dimension 1 bifurcations

Dynamical systems with intricate behaviour are all-pervasive in biology. Many of the most interesting biological processes indicate the presence of bifurcations, i.e. phenomena where a small change in a system parameter causes qualitatively different behaviour. Bifurcation theory has become a rich field of research in its own right and evaluating the bifurcation behaviour of a given dynamical system can be challenging. An even greater challenge, however, is to learn the bifurcation structure of dynamical systems from data, where the precise model structure is not known. Here, we study one aspects of this problem: the practical implications that the presence of bifurcations has on our ability to infer model parameters and initial conditions from empirical data; we focus on the canonical co-dimension 1 bifurcations and provide a comprehensive analysis of how dynamics, and our ability to infer kinetic parameters are linked. The picture thus emerging is surprisingly nuanced and suggests that identification of the qualitative dynamics—the bifurcation diagram—should precede any attempt at inferring kinetic parameters.