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We present analytical results for the emerging structure of networks that evolve via a combination of growth (by node addition and random attachment) and contraction (by random node deletion). To this end we consider a network model in…
We present systematic wetting experiments and numerical simulations of gravity driven liquid drops sliding on a plane substrate decorated with a linear chemical step. Surprisingly, the optimal direction to observe crossing is not the one…
The idea of contact angle was generalized by using the principle of minimum total energy. The problems of the shape of the two-dimensional sessile drop and the drop on an inclined surface are considered. The differential equations…
The time distribution of relaxation events in an aging system is investigated via molecular dynamics simulations. The focus is on the distribution functions of the first passage time, $p_1(\Delta t)$, and the persistence time, $p(\tau)$. In…
Classical hydrodynamic models predict that infinite work is required to move a three-phase contact line, defined here as the line where a liquid/vapor interface intersects a solid surface. Assuming a slip boundary condition, in which the…
Sessile droplets of aqueous poly(ethylene oxide) solution, with average molecular weight of 100 kDa, are monitored during evaporative drying at ambient conditions over a range of initial concentrations $c_0$. For all droplets with $c_0 \geq…
We numerically study the coalescence dynamics of two sessile droplets with radii $R_0$. The droplets are placed on top of a rigid substrate with a contact angle of $\theta_{eq.} = \pi/9$. Having a highly wettable substrate ($\theta_{eq} \ll…
We studied the step dynamics during sublimation and growth in the presence of electromigration force acting on the adatoms. In the limit of fast surface diffusion and slow kinetics of atom attachment-detachment at the steps we formulate a…
We study the motion of a particle sliding under the action of an external field on a stochastically fluctuating one-dimensional Edwards-Wilkinson surface. Numerical simulations using the single-step model shows that the mean-square…
We investigate the motion of a spherical drop in a general quadratic flow acted upon by an arbitrarily oriented externally applied uniform electric field. The drop and media are considered to be leaky dielectrics. The flow field affects the…
Normal incidence ion irradiation at elevated temperatures, when amorphization is prevented, induces novel nanoscale patterns of crystalline structures on elemental semiconductors by a reverse epitaxial growth mechanism: on Ge surfaces…
In this paper, we introduce the concept of Developmental Partial Differential Equation (DPDE), which consists of a Partial Differential Equation (PDE) on a time-varying manifold with complete coupling between the PDE and the manifold's…
For atoms and crystals with an ideal symmetry, the optical selection rules for electronic transitions are well covered in physics textbooks. However, in studies of material systems one often encounters systems with a weakly distorted…
Nucleation plays a critical role in the birth of crystals and is associated with a vast array of phenomena such as protein crystallization and ice formation in clouds. Despite numerous experimental and theoretical studies, many aspects of…
The evolution of the liquid bridge formed between two coalescing sessile yield-stress drops is studied experimentally. We find that the height of the bridge evolves similar to a viscous Newtonian fluid, $h_0\sim t$, before arresting at long…
We study closed systems of particles that are subject to stochastic forces in addition to the conservative forces. The stochastic equations of motion are set up in such a way that the energy is strictly conserved at all times. To ensure…
The spreading of a cap-shaped spherical droplet on a completely wettable spherical substrate is studied. The non-equilibrium thermodynamic formulation is used to derive the thermodynamic driving force of spreading including the line-tension…
Chemical selectivity, as quantified by a branching ratio, is a phenomenon relevant for many organic chemical reactions. It may be exhibited on a potential energy surface that features a valley-ridge inflection point in the region between…
Desorption of deposited species plays a role in determining the evolution of surface morphology during crystal growth when the desorption time constant is short compared to the time to diffuse to a defect site, step edge or kink. However,…
Mathematical model that allows for direct tracking of the homoepitaxial crystal growth out of the window etched in the solid, pre-deposited layer on the substrate is described. The growth is governed by the normal (to the crystal-vapor…