Related papers: An analytic derivation of the bifurcation conditio…
Slender elastic objects such as a column tend to buckle under loads. While static buckling is well understood as a bifurcation problem, the evolution of shapes during dynamic buckling is much harder to study. Elastic rings under normal…
Axisymmetric viscoelastic pipe flow of Oldroyd-B fluids has been recently found to be linearly unstable by Garg et al. Phys. Rev. Lett., 121.024502 (2018). From a nonlinear point of view, this means that the flow can transition to…
The linear eigenvalue problem governing the stability of the mechanical equilibrium of the fluid in a electrohydrodynamic (EHD) convection problem is investigated. The analytical study is one of bifurcation. This allows us to regain the…
We study the effect of a magnetic field on the behaviour of a conducting elastic rod subject to a novel set of boundary conditions that, in the case of a transversely isotropic rod, give rise to exact helical post-buckling solutions. The…
The paper deals with a problem of interaction between hydrodynamics and mechanics of nonlinear elastic bodies. The existence question for two-dimensional symmetric steady waves travelling on the surface of a deep ocean beneath a heavy…
We investigate the link between the geometric environment of particles, the local deformations of the solvent, and the bulk effective viscosity in non-Brownian suspensions. First, we discuss the caging of particles by their neighbors,and…
It is shown that a channel flow of a dilute polymer solution between two widely spaced cylinders hindering the flow is an important paradigm of an unbounded flow in the case in which the channel wall is located sufficiently far from the…
The sudden arrest of motion due to confinement is commonly observed via the clogging transition in the flow of particles through a constriction. We present results of a simple experiment to elucidate a similar transition in the…
We analyze the implication of tristability on localization phenomena in one-dimensional extended dissipative systems. In this context, localized states appear due to the interaction and locking of front waves connecting different extended…
We study the conditions on the physical parameters in the Helfrich bending energy of lipid bilayer vesicles. Among embedded surfaces with a biconcave axisymmetric shape, the variation equation is analyzed in detail. This leads to simple…
We perform traction experiments on viscous liquids highly confined between parallel plates, a geometry known as the probe-tack test in the adhesion community. Direct observation during the experiment coupled to force measurement shows the…
The growth of an elastic film adhered to a confining substrate might lead to the formation of delimitation blisters. Many results have been derived when the substrate is flat. The equilibrium shapes, beyond small deformations, are…
We study the initiation and evolution of aneurysmal morphology in a pressurized soft tube where the elastic modulus is non-uniform in the radial direction. The primary deformation prior to instability is characterized within the framework…
The bifurcation problem of a circular Euler-Bernoulli rod subject to a uniform radial force distribution is investigated under three distinct loading conditions: (i.) hydrostatic pressure, (ii.) centrally-directed, and (iii.) dead load.…
Using numerical simulations, we study the failure of an amorphous solid under quasi-static expansion starting from a homogeneous high-density state. During the volume expansion, we demonstrate the existence of instabilities manifesting via…
We investigate the equilibrium configurations of closed planar elastic curves of fixed length, whose stiffness, also known as the bending rigidity, depends on an additional density variable. The underlying variational model relies on the…
We re-examine the procedure of adiabatic elimination of fast relaxing variables near a bifurcation point when some of the parameters of the system are stochastically modulated. Approximate stationary solutions of the Fokker-Planck equation…
The postulate of the existence of a jamming phase diagram (Liu and Nagel, Nature 396, 21 EP (1998aa)) provides a theoretical basis for the classification of a wide range of amorphous solids (colloidal, molecular and emulsion glasses,…
We study tangent bifurcation of band edge plane waves in nonlinear Hamiltonian lattices. The lattice is translationally invariant. We argue for the breaking of permutational symmetry by the new bifurcated periodic orbits. The case of two…
The buckling of thin elastic sheets is a classic mechanical instability that occurs over a wide range of scales. In the extreme limit of atomically thin membranes like graphene, thermal fluctuations can dramatically modify such mechanical…