Fluctuating hydrodynamics and diffusion in amorphous solids

Cell clusters adopt a collective amoeboid mode of migration in confined nonadhesive environments

Cell migration is essential to living organisms and deregulated in cancer. Single cell's migration ranges from traction-dependent mesenchymal motility to contractility-driven propulsive amoeboid locomotion, but collective cell migration has only been described as a focal adhesion-dependent and traction-dependent process. Here, we show that cancer cell clusters, from patients and cell lines, migrate without focal adhesions when confined into nonadhesive microfabricated channels. Clusters coordinate and behave like giant super cells, mobilizing their actomyosin contractility at the rear to power their migration. This polarized cortex does not sustain persistent retrograde flows, of cells or actin, like in the other modes of migration but rather harnesses fluctuating cell deformations, or jiggling. Theoretical physical modeling shows this is sufficient to create a gradient of friction forces and trigger directed cluster motion. This collective amoeboid mode of migration could foster metastatic spread by enabling cells to cross a wide spectrum of environments.

Dependence of the configurational entropy on amorphous structures of a hard-sphere fluid

The free energy of a hard-sphere fluid for which the average energy is trivial signifies how its entropy changes with packing. The packing η_{f} at which the free energy of the crystalline state becomes lower than that of the disordered fluid state marks the freezing point. For packing fractions η>η_{f} of the hard-sphere fluid, we use the modified weighted density functional approximation to identify metastable free energy minima intermediate between uniform fluid and crystalline states. The distribution of the sharply localized density profiles, i.e., the inhomogeneous density field ρ(x) characterizing the metastable state is primarily described by a pair function g_{s}(η/η_{0}). η_{0} is a structural parameter such that for η=η_{0} the pair function is identical to that for the Bernal random structure. The configurational entropy S_{c} of the metastable hard-sphere fluid is calculated by subtracting the corresponding vibrational entropy from the total entropy. The extrapolated S_{c} vanishes as η→η_{K} and η_{K} is in agreement with other works. The dependence of η_{K} on the structural parameter η_{0} is obtained.

Linking density functional and mode coupling models for supercooled liquids

We compare predictions from two familiar models of the metastable supercooled liquid, respectively, constructed with thermodynamic and dynamic approaches. In the so called density functional theory the free energy F[ρ] of the liquid is a functional of the inhomogeneous density ρ(r). The metastable state is identified as a local minimum of F[ρ]. The sharp density profile characterizing ρ(r) is identified as a single particle oscillator, whose frequency is obtained from the parameters of the optimum density function. On the other hand, a dynamic approach to supercooled liquids is taken in the mode coupling theory (MCT) which predict a sharp ergodicity-non-ergodicity transition at a critical density. The single particle dynamics in the non-ergodic state, treated approximately, represents a propagating mode whose characteristic frequency is computed from the corresponding memory function of the MCT. The mass localization parameters in the above two models (treated in their simplest forms) are obtained, respectively, in terms of the corresponding natural frequencies depicted and are shown to have comparable magnitudes.

Metastable-state dynamics of a liquid: a free-energy landscape study

Using the time dependence of density fluctuations in a supercooled liquid obtained from the solutions of the equations of nonlinear fluctuating hydrodynamics (NFH), the evolution of the system in the free energy landscape is studied. A crossover from a continuous fluid type dynamics to that of hopping between different free energy minima is observed as the liquid is increasingly supercooled. We demonstrate that our results are also in agreement with equilibrium density functional analysis of the same system. The density field obtained in the numerical solution of the NFH equations are further analyzed to introduce complimentary density of voids in the supercooled liquid state and its static and dynamic correlations are computed. The nature of the relaxation of vacancy correlations are observed to be similar to that of the density fluctuations.

Fragility and elastic behavior of a supercooled liquid

A model for the supercooled liquid is considered by taking into account its solidlike properties. We focus on how the long time dynamics is affected due to the coupling between the slowly decaying density fluctuations and the local displacement variables in the frozen liquid. Results from our model agree with the recent observation of Novikov and Sokolov [Nature (London) 431, 961 (2004)] that the fragility index m of a glass forming material is linearly related to the corresponding ratio KG of the bulk and the shear moduli.

Metastable state dynamics and power law relaxation in a supercooled liquid

We consider glassy relaxation by using a model for supercooled liquid where the usual set of hydrodynamic variables is extended to include the presence of very slowly decaying defect densities. The long time limit of the density correlation function, the nonergodicity parameter, is studied in the vicinity of the dynamic transition point, and scaling exponents with respect to the distance from the critical point are obtained. In addition to the usual square root cusp, we also see a linear dependence on distance from transition with respect to the metastability parameters. We analyze the power law relaxation of the density correlation function at the initial stage of the dynamics, and obtain an exponent dependent on temperature. Results are compared with data obtained from light scattering experiments.