We study secondary structures of random RNA molecules by means of a renormalized field theory based on an expansion in the sequence disorder. We show that there is a continuous phase transition from a molten phase at higher temperatures to a low-temperature glass phase. The primary freezing occurs above the critical temperature, with local islands of stable folds forming within the molten phase...

This article describes a number of velocity-based moving mesh numerical methods for multidimensional nonlinear time-dependent partial differential equations (PDEs). It consists of a short historical review followed by a detailed description of a recently developed multidimensional moving mesh finite element method based on conservation. Finite element algorithms are derived for both mass-conser...

The dynamics of strongly disordered systems becomes extremely slow or glassy at low temperatures, which results in a characteristic aging scenario. This means that the outcome of measurements strongly depends on the history of the system within the glassy phase, even on macroscopic time scale like hours, weeks or years. This area of non-equilibrium dynamics in disordered systems became recently...

The answer to this question lies in knowing the moral standing of Phase IV studies and whether we ought to conduct them. And to know this, in part, we need to compare them to studies in Phases I, II, and III and then determine where Phase IV studies stand in relation to Phase I–III studies scientifically and commercially.

We present a hyperbolic-elliptic model problem related to the equations of two-phase fluid flow. The model problem is solved numerically, and properties of its solution are presented. The model equation is wellposed when linearized around a constant state, but there is a strong focusing effect, and very large solutions exists at certain times. We prove that the model problem has a smooth soluti...

We consider the nature of the fluid–solid phase transition in a polydisperse mixture of hard spheres. For a sufficiently polydisperse mixture (s.0.085) crystallization occurs with simultaneous fractionation. At the fluid–solid boundary, a broad fluid diameter distribution is split into a number of narrower fractions, each of which then crystallize. The number of crystalline phases increases wit...

We study secondary structures of random RNA molecules by means of a renormalized field theory based on an expansion in the sequence disorder. We show that there is a continuous phase transition from a molten phase at higher temperatures to a low-temperature glass phase. The primary freezing occurs above the critical temperature, with local islands of stable folds forming within the molten phase...

A percolation model is an infinite random graph model for phase transitions and critical phenomena. The percolation threshold corresponds to a phase transition point, such as a melting or freezing temperature. The exact value of the percolation threshold is not known for any three-dimensional percolation models, which are important for physical applications. Furthermore, rigorous bounds for the...

This study investigated the partitioning behavior of dissolved organic matter (DOM) in liquid and ice phases, as well as the changes in the optical properties and chlorine reactivity of DOM during the freezing processes of water. DOM was rejected from the ice phase and accumulated in the remaining liquid phase during water freezing. Moreover, the decrease in freezing temperature, as well as the...