The interfacial profiles and interfacial tensions of phase-separated binary mixtures of Bose-Einstein condensates are studied theoretically. The two condensates are characterized by their respective healing lengths and £2 and by the interspecies repulsive interaction K. An exact solution to the Gross-Pitaevskii (GP) equations is obtained for the special case I 2/ I 1 = 1/2 and K = 3/2. Furthermore, applying a double-parabola approximation (DPA) to the energy density featured in GP theory allows us to define a DPA model, which is much simpler to handle than GP theory but nevertheless still captures the main physics. In particular, a compact analytic expression for the interfacial tension is derived that is useful for all f ,, | 2, and K. An application to wetting phenomena is presented for condensates adsorbed at an optical wall. The wetting phase boundary obtained within the DPA model nearly coincides with the exact one in GP theory.

The localized low-energy interfacial excitations, or Nambu-Goldstone modes, of phase-segregated binary mixtures of Bose-Einstein condensates are investigated analytically by means of a doubleparabola approximation (DPA) to the Lagrangian density in Gross-Pitaevskii theory for a system in a uniform potential. Within this model analytic expressions are obtained for the excitations underlying capillary waves or "ripplons" for arbitrary strength K (> 1) of the phase segregation.The dispersion relation ω ∝ k 3/2 is derived directly from the Bogoliubov-de Gennes equations in limit that the wavelength 2π/k is much larger than the healing length ξ. The proportionality constant in the dispersion relation provides the static interfacial tension. A correction term in ω(k) of order k 5/2 is calculated analytically, entailing a finite-wavelength correction factor (1 +). This prediction may be tested experimentally using (quasi-)uniform optical-box traps. Explicit expressions are obtained for the structural deformation of the interface due to the passing of the capillary wave. It is found that the amplitude of the wave is enhanced by an amount that is quadratic in the ratio of the phase velocity ω/k to the sound velocity c. For generic asymmetric mixtures consisting of condensates with unequal healing lengths an additional modulation is predicted of the common value of the condensate densities at the interface.

A three-phase contact line in a three-phase fluid system is modeled by a mean-field density functional theory. We use a variational approach to find the Euler-Lagrange equations. Analytic solutions are obtained in the two-phase regions at large distances from the contact line. We employ a triangular grid and use a successive overrelaxation method to find numerical solutions in the entire domain for the special case of equal interfacial tensions for the two-phase interfaces. We use the Kerins-Boiteux formula to obtain a line tension associated with the contact line. This line tension turns out to be negative. We associate line adsorption with the change of line tension as the governing potentials change.

Accurate and useful analytic approximations are developed for order parameter profiles and interfacial tensions of phase-separated binary mixtures of Bose-Einstein condensates. The pure condensates 1 and 2, each of which contains a particular species of atoms, feature healing lengths ξ 1 and ξ 2 . The inter-atomic interactions are repulsive. In particular, the effective inter-species repulsive interaction strength is K. A triple-parabola approximation (TPA) is proposed, to represent closely the energy density featured in Gross-Pitaevskii (GP) theory. This TPA allows us to define a model, which is a handy alternative to the full GP theory, while still possessing a simple analytic solution. The TPA offers a significant improvement over the recently introduced double-parabola approximation (DPA). In particular, a more accurate amplitude for the wall energy (of a single condensate) is derived and, importantly, a more correct expression for the interfacial tension (of two condensates) is obtained, which describes better its dependence on K in the strong segregation regime, while also the interface profiles undergo a qualitative improvement.

Cell development and behavior are driven by internal genetic programming, but the external microenvironment is increasingly recognized as a significant factor in cell differentiation, migration, and in the case of cancer, metastatic progression. Yet it remains unclear how the microenvironment influences cell processes, especially when examining cell motility. One factor that affects cell motility is cell mechanics, which is known to be related to substrate stiffness. Examining how cells interact with each other in response to mechanically differential substrates would allow an increased understanding of their coordinated cell motility. In order to probe the effect of substrate stiffness on tumor related cells in greater detail, we created hard–soft–hard (HSH) polydimethylsiloxane (PDMS) substrates with alternating regions of different stiffness (200 and 800 kPa). We then cultured WI-38 fibroblasts and A549 epithelial cells to probe their motile response to the substrates. We found that when the 2 cell types were exposed simultaneously to the same substrate, fibroblasts moved at an increased speed over epithelial cells. Furthermore, the HSH substrate allowed us to physically guide and separate the different cell types based on their relative motile speed. We believe that this method and results will be important in a diversity of areas including mechanical microenvironment, cell motility, and cancer biology.