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An analytical study on crease formations in a swelling gel layer is conducted. By exploring the smallness of the layer thickness and using a method of coupled series-asymptotic expansions, the original nonlinear eigenvalue problem of partial differential equations is reduced to one of ordinary differential equations. The latter problem is then solved analytically to obtain closed-form solutions for all the post-bifurcation branches. With the available analytical results, a number of deep insights on crease formations are provided, including the unveiling of three pathways to crease (depending on the layer thickness), determination of the bifurcation type, establishment of a lower bound for mode numbers and two scaling laws. Also, a number of experimental results are captured, which are then nicely interpreted based on the analytical solutions. In particular, it is shown that some critical physical quantities are invariant with respect to the thickness at the moment of crease formation. It appears that the present work offers a comprehensive understanding on crease formation, a widely-spread phenomenon.
A single closed-form analytical solution of the driven nonlinear Schr{o}dinger equation is developed, reproducing a large class of the behaviors in Kerr-comb systems, including bright-solitons, dark-solitons, and a large class of periodic wavetrains.
The growth dynamics of an air finger injected in a visco-elastic gel (a PVA/borax aqueous solution) is studied in a linear Hele-Shaw cell. Besides the standard Saffmann-Taylor instability, we observe - with increasing finger velocities - the existenc
Bottle brushes are polymeric macromolecules made of a linear polymeric backbone grafted with side chains. The choice of the grafting density {sigma}g, the length ns the grafted side chains and their chemical nature fully determines the properties of
We use numerical simulations and an athermal quasi-static shear protocol to investigate the yielding of a model colloidal gel. Under increasing deformation, the elastic regime is followed by a significant stiffening before yielding takes place. A spa
We perform large scale three-dimensional molecular dynamics simulations of unlinked and unknotted ring polymers diffusing through a background gel, here a three-dimensional cubic lattice. Taking advantage of this architecture, we propose a new method