Immersion freezing (ice nucleation by particles immersed in supercooled water) is a key process for forming ice in mixed-phase clouds. Immersion freezing experiments with particles in microliter-sized (millimeter-sized) water droplets are often applied to detecting very small numbers of ice nucleating particles (INPs). However, the application of such large droplets remains confined to the dete...

This paper presents studies on applying the novel weak Galerkin finite element method (WGFEM) to a two-phase model for subsurface flow, which couples the Darcy equation for pressure and a transport equation for saturation in a nonlinear manner. The coupled problem is solved in the framework of operator decomposition. Specifically, the Darcy equation is solved by theWGFEM, whereas the saturation...

[1] This study investigates the effects of cloud condensation nuclei (CCN) and ice nuclei (IN) on ice formation in mixed-phase clouds using an adiabatic parcel model. The simulations with lower updrafts represent mixed-phase stratiform clouds, and those with higher updrafts represent deep convective clouds. Increasing CCN concentration can lead to more ice crystals with smaller sizes, but does ...

This paper investigates the integrated optimization of production, distribution and inventory decisions related to supplying multiple retailers from a central production facility. A single-item uncapacitated lot-sizing problem is defined for optimizing production decisions and inventory management. The optimization of daily distribution is modeled as a traveling salesman problem or a vehicle ro...

The two-phase issue in the O(n) non-linear σ-model: a Monte-Carlo study Our paper [1] has motivated a comment [2] by A. Patrascioiu and E. Seiler which we reply in this note. The remarks in [2] concern three statements that the authors select from our paper: i) " The results for O(8) support the asymptotic freedom scenario ". The authors in [2] recall that at small˜β ≡ β/N the 1/N expansion is ...

In this paper we derive rates of convergence for regularizations of the multidimensional two-phase Stefan problem and use the regularized problems to define backward-difference in time and C° piecewise-linear in space Galerkin approximations. We find an L2 rate of convergence of order \^ in the e-regularization and an L rate of convergence of order (h2/e + Ai/ \6F) in the Galerkin estimates whi...

In this paper, we derive a model for the two-phase freezing process of supercooled uids. Especially, we take density changes along the phase interfaces into account. Thus, besides heat diiusion and the interface phenomena, mass transport and convection in the uid phase which is given by the full Navier{Stokes equations has to be considered. For the 2D case we implemented an algorithm for the nu...

We consider a stationary two-phase Stefan problem with convection. The problem is governed by a coupled system involving a nonlinear Darcy law and the energy balance equation with second member in L 1. We prove existence of at least one weak solution of the problem, using the penalty method and the Schauder xed point principle.