Related papers: High-order WENO scheme for Polymerization-type equ…
The three-dimensional organization of chromatin is thought to play an important role in controlling gene expression. Specificity in expression is achieved through the interaction of transcription factors and other nuclear proteins with…
Weighted essentially non-oscillatory (WENO) reconstruction schemes are presented that preserve cylindrical symmetry for radial flows on an equal-angle polar mesh. These new WENO schemes are used with a Lagrangian discontinuous Galerkin (DG)…
A high-order well-balanced scheme for the Euler equations with gravitation is presented. The scheme is able to preserve a spatially high-order accurate discrete representation of a large class of hydrostatic equilibria. It is based on a…
This paper proposes high-order accurate, oscillation-eliminating Hermite weighted essentially non-oscillatory (OE-HWENO) finite volume schemes for hyperbolic conservation laws. The OE-HWENO schemes apply an OE procedure after each…
Protein folding is a problem of large interest since it concerns the mechanism by which the genetic information is translated into proteins with well defined three-dimensional (3D) structures and functions. Recently theoretical models have…
The weighted essentially non-oscillatory (WENO) schemes are widely used for hyperbolic conservation laws due to the ability to resolve discontinuities and maintain high-order accuracy in smooth regions at the same time. For hyperbolic…
Predictive modeling is the key factor for saving time and resources with respect to manufacturing processes such as fermentation processes arising e.g.\ in food and chemical manufacturing processes. According to Zhang et al. (2002), the…
A new method for sequence optimization in protein models is presented. The approach, which has inherited its basic philosophy from recent work by Deutsch and Kurosky [Phys. Rev. Lett. 76, 323 (1996)] by maximizing conditional probabilities…
In this work, we illustrate the underlying mathematical structure of mixed-dimensional models arising from the composition of graphs and continuous domains. Such models are becoming popular in applications, in particular, to model the human…
The protein folding problem has attracted an increasing attention from physicists. The problem has a flavor of statistical mechanics, but possesses the most common feature of most biological problems -- the profound effects of evolution. I…
This paper presents a method of reconstruction a primary structure of a protein that folds into a given geometrical shape. This method predicts the primary structure of a protein and restores its linear sequence of amino acids in the…
We propose a simple modification of standard WENO finite volume methods for Cartesian grids, which retains the full spatial order of accuracy of the one-dimensional discretization when applied to nonlinear multidimensional systems of…
In this paper, we introduce second order and fourth order space discretization via finite difference implementation of the finite element method for solving Fokker-Planck equations associated with irreversible processes. The proposed…
In nature the three-dimensional structure of a protein is encoded in the corresponding gene. In this paper we describe a new method for encoding the three-dimensional structure of a protein into a binary sequence. The feature of the method…
Hamiltonian systems are known to conserve the Hamiltonian function, which describes the energy evolution over time. Obtaining a numerical spatio-temporal scheme that accurately preserves the discretized Hamiltonian function is often a…
A hybrid LDG-HWENO scheme is proposed for the numerical solution of KdV-type partial differential equations. It evolves the cell averages of the physical solution and its moments (a feature of Hermite WENO) while discretizes high order…
Polymerization is a fundamental chemical process enabling large-scale production of material components across modern industries. By transforming a monomer mixture into a cross-linked polymer network, polymerization induces changes in…
Mass spectrometry is the dominant technology in the field of proteomics, enabling high-throughput analysis of the protein content of complex biological samples. Due to the complexity of the instrumentation and resulting data, sophisticated…
Based on the understandings regarding linear upwind schemes with flux splitting to achieve free-stream preservation (Q. Li, etc. Commun. Comput. Phys., 22 (2017) 64-94), a series of WENO interpolation-based and upwind-biased nonlinear…
This work presents arbitrary high order well balanced finite volume schemes for the Euler equations with a prescribed gravitational field. It is assumed that the desired equilibrium solution is known, and we construct a scheme which is…