https://www.cell.com/biophysj/pdf/S0006-3495(04)74439-2.pdf

Automatic and Quantitative Measurement of Protein-Protein Colocalization in Live Cells

We present a general theory for polymer adsorption using a quasi-crystalline lattice model. The partition function for a mixture of polymer chains and solvent molecules near an interface is evaluated by adopting the Bragg-Williams approximation of random mixing within each layer parallel to the surface. The interaction between segments and solvent molecules is taken into account by use of the Flory-Huggins parameter x; that between segments and the interface is described in terms of the differential adsorption energy parameter xs. No approximation was made about an equal contribution of all the segments of a chain to the segment density in each layer. By differentiating the partition function with respect to the number of chains having a particular conformation an expression is obtained that gives the numbers of chains in each conformation in equilibrium. Thus also the train, loop, and tail size distribution can be computed. Calculations are carried out numerically by a modified matrix procedure as introduced by DiMarzio and Rubin. Computations for chains containing up to lo00 segments are possible. Data for the adsorbed amount r, the surface coverage 0, and the bound fraction p = O/r are given as a function of xs, the bulk solution volume fraction c#J,, and the chain length r for two x values. The results are in broad agreement with earlier theories, although typical differences occur. Close to the surface the segment density decays roughly exponentially with increasing distance from the surface, but at larger distances the decay is much slower. This is related to the fact that a considerable fraction of the adsorbed segments is present in the form of long dangling tails, even for chains as long as r = 1000. In previous theories the effect of tails was usually neglected. Yet the occurrence of tails is important for many practical applications. Our theory can be easily extended to polymer in a gap between two plates (relevant for colloidal stability) and to copolymers.

Statistical Theory of the Adsorption of Interacting Chain Molecules. 1. Partition Function, Segment Density Distribution, and Adsorption Isotherms

Computer-optimized decoupling scheme for wideband applications and low-level operation

In this paper, we present an overview of the evolution of the discontinuous Galerkin methods since their introduction in 1973 by Reed and Hill, in the framework of neutron transport, until their most recent developments. We show how these methods made their way into the main stream of computational fluid dynamics and how they are quickly finding use in a wide variety of applications. We review the theoretical and algorithmic aspects of these methods as well as their applications to equations including nonlinear conservation laws, the compressible Navier-Stokes equations, and Hamilton-Jacobi-like equations.

/pdf/the-development-of-discontinuous-galerkin-methods-17hxfhour7.pdf

The Development of Discontinuous Galerkin Methods

In this paper the solution of nonlinear programming problems by a Sequential Quadratic Programming (SQP) trust-region algorithm is considered. The aim of the present work is to promote global convergence without the need to use a penalty function. Instead, a new concept of a “filter” is introduced which allows a step to be accepted if it reduces either the objective function or the constraint violation function. Numerical tests on a wide range of test problems are very encouraging and the new algorithm compares favourably with LANCELOT and an implementation of Sl1QP.

D. A. H. Jacobs

Papers

The State of the Art in Numerical Analysis.