Related papers: Reversible stepwise condensation polymerization wi…
We develop a simple recursive approach to treat reversible condensation polymerization with cyclization. Based upon a minimum set of balance equations, the law of mass action, Gaussian chain statistics, and the assumption of independent…
This paper considers random graph approach to simulate irreversible step-growth polymerization. We study generalization of approach developed by Kryven~I. by introducing different types of bonds each with its own weight representing…
We give a construction of cyclic cocycles on convolution algebras twisted by gerbes over discrete translation groupoids. For proper \'etale groupoids, Tu and Xu provide a map between the periodic cyclic cohomology of a gerbe-twisted…
This paper presents a multi-temporal formulation for simulating elastoplastic solids under cyclic loading. We leverage the proper generalized decomposition (PGD) to decompose the displacements into multiple time scales, separating the…
It is argued that cluster methods provide a viable alternative to Wilson's momentum shell integration technique at the early stage of renormalization in the field-theoretic models with strongly coupled fields because these methods allow for…
Irreversible aggregation processes involving reactive and frozen clusters are investigated using the rate equation approach. In aggregation events, two clusters join irreversibly to form a larger cluster, and additionally, reactive clusters…
We discuss a problem of cyclization of a polymer molecule, which is an important example of reaction in a system showing strongly non-Markovian behavior on the timescales of interest. We show that the knowledge of the joint three-time…
We prove that the generalised non-crossing partitions associated to well-generated complex reflection groups of exceptional type obey two different cyclic sieving phenomena, as conjectured by Armstrong, respectively by Bessis and Reiner.…
We present a solution to the conjugacy decision problem and the conjugacy search problem in Garside groups, which is theoretically simpler than the usual one, with no loss of efficiency. This is done by replacing the well known cycling and…
The process of polymer condensation, i.e. the formation of bonds between reactive end-groups, is ubiquitous in both industry and biology. Here we study generic systems undergoing polymer condensation in competition with cyclisation. Using a…
We obtain exact, simple and very compact expressions for the linearization coefficients of the products of orthogonal polynomials; both the conventional Clebsch-Gordan-type and the modified version. The expressions are general depending…
A co-polycondensation reaction is discussed analytically and by Monte-Carlo simulations where two reactive units compete for reactions with an alternating third reactive unit, whereby irreversible reactions replace bonds which are able to…
While several Gaussian mixture models-based biclustering approaches currently exist in the literature for continuous data, approaches to handle discrete data have not been well researched. A multivariate Poisson-lognormal (MPLN) model-based…
In the first part of this paper, we propose new optimization-based methods for the computation of preferred (dense, sparse, reversible, detailed and complex balanced) linearly conjugate reaction network structures with mass action dynamics.…
A deterministic mathematical model for the polymerization of hyperbranched molecules accounting for substitution, cyclization, and shielding effect has been developed as a system of nonlinear population balances. The solution obtained by a…
l1 reweighting algorithms are very popular in sparse signal recovery and compressed sensing, since in the practice they have been observed to outperform classical l1 methods. Nevertheless, the theoretical analysis of their convergence is a…
We present a new simulation technique to study systems of polymers functionalized by reactive sites that bind/unbind forming reversible linkages. Functionalized polymers feature self-assembly and responsive properties that are unmatched by…
The reversible kinetics of copolymerization is solved analytically for the multistate mechanism proposed by B. D. Coleman and T. G. Fox [J. Chem. Phys. 38, 1065 (1963)] under low conversion conditions where the concentrations of monomeric…
Stochastic processes are a flexible and widely used family of models for statistical modeling. While stochastic processes offer attractive properties such as inclusion of uncertainty properties, their inference is typically intractable,…
A general framework for dealing with both linear regression and clustering problems is described. It includes Gaussian clusterwise linear regression analysis with random covariates and cluster analysis via Gaussian mixture models with…