Related papers: Continuous Spin Fractionation: A large scale metho…
Polymer mixtures fractionate between phases depending on their molecular weight. Consequently, by varying solvent conditions, a polydisperse polymer sample can be separated between phases so as to achieve a particular molecular weight…
In this work, a framework for deriving theoretical equations for mean squared displacement (MSD) and fractional Fokker-Planck (FFP) is developed for any arbitrary rheological model. The obtained general results are then specified for…
The aim of this paper is to investigate the distribution of a continuous polymer in the presence of an attractive finitely supported potential. The most intricate behavior can be observed if we simultaneously and independently vary two…
The prediction of the three-dimensional native structure of proteins from the knowledge of their amino acid sequence, known as the protein folding problem, is one of the most important yet unsolved issues of modern science. Since the…
The kinetics of collective rearrangements in solution, such as protein folding and nanocrystal phase transitions, often involve free energy barriers that are both long and rough. Applying methods of transition path sampling to harvest…
Polymer composite materials require softening to reduce their glass transition temperature and improve processability. To this end, plasticizers, which are small organic molecules, are added to the polymer matrix. The miscibility of these…
Solvation is a notoriously difficult and nagging problem for the rigorous theoretical description of chemistry in the liquid phase. Successes and failures of various approaches ranging from implicit solvation modeling through dielectric…
Self-consistent field theory (SCFT) has proven to be a powerful tool for modeling equilibrium microstructures of soft materials, particularly for multiblock polymers. A very successful approach to numerically solving the SCFT set of…
Along with the flourish of the information age, massive amounts of data are generated day by day. Due to the large-scale and high-dimensional characteristics of these data, it is often difficult to achieve better decision-making in…
We consider an inextensible, semiflexible polymer or worm-like chain which is confined in the transverse direction by a parabolic potential and subject to a longitudinal force at the ends, so that the polymer is stretched out and…
Markov chain sampling methods that automatically adapt to characteristics of the distribution being sampled can be constructed by exploiting the principle that one can sample from a distribution by sampling uniformly from the region under…
In the classic circle packing problem, one asks whether a given set of circles can be packed into a given container. Packing problems like this have been shown to be $\mathsf{NP}$-hard. In this paper, we present new sufficient conditions…
We study the problem of partitioning a given simple polygon $P$ into a minimum number of connected polygonal pieces, each of bounded size. We describe a general technique for constructing such partitions that works for several notions of…
A new technique for the separation of macromolecules is proposed and investigated. A thin mesh with pores comparable to the radius of gyration of a free chain is used to filter chains according to their length. Without a field it has…
The width of the distribution of species in a polydisperse system is employed in a small-variable expansion, to obtain a well-controlled and compact scheme by which to calculate phase equilibria in multi-phase systems. General and universal…
Suppose X is a multivariate diffusion process that is observed discretely in time. At each observation time, a transformation of the state of the process is observed with noise. The smoothing problem consists of recovering the path of the…
The possibilities to fractionate copolymers with respect to their chemical composition on a preparative scale by means of the establishment of liquid/liquid phase equilibria were studied for random copolymers of styrene and acrylonitrile…
Polar slice sampling (Roberts & Rosenthal, 2002) is a Markov chain approach for approximate sampling of distributions that is difficult, if not impossible, to implement efficiently, but behaves provably well with respect to the dimension.…
The most efficient way to pack equally sized spheres isotropically in 3D is known as the random close packed state, which provides a starting point for many approximations in physics and engineering. However, the particle size distribution…
Generative models excel at synthesizing high-fidelity samples from complex data distributions, but they often violate hard constraints arising from physical laws or task specifications. A common remedy is to project intermediate samples…