CMDS-12

Buckling of elastic structures subject to tensile dead load
D.Bigoni*, G. Noselli*, D. Misseroni*, D. Zaccaria**
* University of Trento, ** University of Trieste

Buckling of a straight elastic column subject to compressive end thrust occurs at a critical load for which the straight configuration of the column becomes unstable and simultaneously ceases to be the unique solution of the elastic problem (so that instability and bifurcation are concomitant phenomena). Buckling is known from ancient times: it has been experimentally investigated in a systematic way by Pieter van Musschenbrok (1692-1761) and mathematically solved by Leonhard Euler (1707-1783), who derived the differential equation governing the behaviour of a thin elastic rod suffering a large bending, the so-called `elastica' (see Love, 1927).

Through centuries, engineers have experimented and calculated complex structures, such as frames, plates and cylinders, manifesting instabilities and bifurcations of various forms (Timoshenko and Gere, 1961). Until now structures exhibiting bifurcation and instability under tensile load of fixed direction and point of application (in other words `dead') have never been found, so that the word `buckling' is commonly associated by engineers to compressive loads.

We show that structures buckling in tension exist and we substantiate this statement with both theoretical and experimental proofs.

Melting and freezing of colloidal crystals
Yilong Han
The Hong Kong University of Science and Technology, Hong Kong

We experimentally studied the melting and freezing behaviors of colloidal crystals composed of diameter tunable microgel spheres by bright-field and confocal video microscopies. The melting behaviors of three-dimensional (3D), two-dimensional (2D) and multilayer thin films of both single crystals and polycrystals were systematically studied with single-particle dynamics. Thick films (>4 layers) melt heterogeneously, while thin films (<5 layers) melt homogeneously even in polycrystals. A novel heterogeneous melting at dislocation is discovered in 5- to 12-layer films. The equilibrium phase behaviors are different in three thickness regimes: thick films have a liquid-solid coexistence regime which decreases with the film thickness and vanishes at 4 layers, thin films melt into the liquid phase in one step, while monolayers melt in two steps with an intermediate hexatic phase. Superheated crystals and homogeneous melting in 3D were directly visualized and studied by locally heating single crystals with a focused beam of light. In the freezing studies, we experimentally tested four empirical 2D freezing criteria in a thermal system for the first time and suggested four new freezing criteria. The critical nucleus size and the line tension in 2D nucleation have also been measured for the first time.

References:
[1] Y. Peng, Z.-R. Wang, A. Alsayed, A. Yodh, and Y. Han, Phys. Rev. Lett. 104, 205703 (2010)
[2] Z.-R. Wang, A. Alsayed, A. Yodh, and Y. Han, J. Chem. Phys. 132, 154501 (2010)
[3] Y. Han, N. Y Ha, A. Alsayed, and A. Yodh, Phys. Rev. E 77, 041406 (2008)

A variational approach to the moving contact line hydrodynamics
Tiezheng Qian
Department of Mathematics, Hong Kong University of Science and Technology

In immiscible two-phase flows, contact line denotes the intersection of the fluid-fluid interface with the solid wall. When one fluid displaces the other, the contact line moves along the wall. A classical problem in continuum hydrodynamics is the incompatibility between the moving contact line and the no-slip boundary condition, as the latter leads to a non-integrable singularity. The recently discovered generalized Navier boundary condition (GNBC) offers an alternative to the no-slip boundary condition which can resolve the moving contact line conundrum. We present a variational derivation of the GNBC through the principle of minimum energy dissipation (entropy production), as formulated by Onsager for small perturbations away from the equilibrium. Through numerical implementation of a continuum hydrodynamic model, it is demonstrated that the GNBC can quantitatively reproduce the moving contact line slip velocity profiles obtained from molecular dynamics simulations. In particular, the transition from complete slip at the moving contact line to near-zero slip far away is shown to be governed by a power-law partial slip regime, extending to mesoscopic length scales.

Stochastic population oscillations in spatial predator-prey models
Uwe C. Tauber
Department of Physics, Virginia Tech, Blacksburg, VA 24061-0435

It is well established that including spatial structure and stochastic noise in models for predator-prey interactions invalidates the classical deterministic Lotka-Volterra picture of neutral population cycles. In contrast, stochastic models yield long-lived, but ultimately decaying erratic population oscillations, which can be understood through a resonant amplification mechanism for density fluctuations. Monte Carlo simulations of spatial stochastic predator-prey systems yield striking complex spatio-temporal structures. These spreading activity fronts induce persistent correlations between predators and prey species. We employ field-theoretic methods based on the Doi-Peliti representation of the master equation for stochastic particle interaction models to address fluctuation-induced renormalizations of the oscillation frequency and damping.

References:
- M. Mobilia, I.T. Georgiev, and U.C.T., J. Stat. Phys. 128, 447 (2007) [q-bio.PE/0512039]
- U.C.T., in preparation (2010)