242,665 research outputs found

    Phase diagrams for quantum Brownian motion models on two-dimensional Bravais lattices

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    We study quantum Brownian motion (QBM) models for a particle in a dissipative environment coupled to a periodic potential. We review QBM for a particle in a one-dimensional periodic potential and extend the study to that for a particle in two-dimensional (2D) periodic potentials of four Bravais lattice types: square, rectangular, triangular (hexagonal), and centered rectangular. We perform perturbative renormalization group analyses to derive the zero temperature flow diagrams and phase boundaries for a particle in these potentials, and observe localization behavior dependent on the anisotropy of the lattice parameters.Comment: 16 pages, 5 figure

    Phase-field modeling droplet dynamics with soluble surfactants

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    Using lattice Boltzmann approach, a phase-field model is proposed for simulating droplet motion with soluble surfactants. The model can recover the Langmuir and Frumkin adsorption isotherms in equilibrium. From the equilibrium equation of state, we can determine the interfacial tension lowering scale according to the interface surfactant concentration. The model is able to capture short-time and long-time adsorption dynamics of surfactants. We apply the model to examine the effect of soluble surfactants on droplet deformation, breakup and coalescence. The increase of surfactant concentration and attractive lateral interaction can enhance droplet deformation, promote droplet breakup, and inhibit droplet coalescence. We also demonstrate that the Marangoni stresses can reduce the interface mobility and slow down the film drainage process, thus acting as an additional repulsive force to prevent the droplet coalescence