MATHEMATICAL MODELS and METHODS in APPLIED SCIENCES (original) (raw)

Advanced Learning Techniques for Chemometric Modelling

2017

The European chemical industry is the world leader in its field. 8 out of the 15 largest chemical companies are EU based. Furthermore, 29 % of the worldwide chemical sales originate from the EU. These industries face future challenges such as rising costs and scarcity of raw materials, an increase in the price of energy, and an intensified competition from Asian countries. Process Analytical Chemistry represents one of the most significant developments in chemical and process engineering over the past decade. Chemical information is of increasing importance in today's chemical industry. It is required for efficient process development, scale-up and production. It is used to assure product quality and compliance with regulations that govern chemical production processes. If reliable analytical information on the chemical process under investigation is available, adjustments and actions can be undertaken immediately in order to assure maximum yield and product quality while minimi...

The deductive solution of chemical problems by computer programs on the basis of a mathematical model of chemistry

Pure and Applied Chemistry, 2000

A mathematical model of constitutional chemistry is described which is well suited as a theoretical basis for the deductive solution of a variety of chemical problems by computer programs. Within this framework the chemical constitution of molecules and ensembles of molecules (EM) is represented by BE-matrices, whose rows and columns are assigned to the considered atomic cores, and whose entries represent covalent bonds and free valence electrons. Chemical reactions are represented by transforming the BE-matrix B of the beginning EM into the BE-matrix E of the end EM by addition of an R-matrix R according to the master equation B + R = E of the present theory. With a given initial matrix B, those R-matrices R whose addition to B represent chemical reactions can be generated mathematically without any information on individual chemical reactions. Tie applications of this approach are synthesis design and he prediction of the products which may conceivably be formed from combinations of listed chemical compounds. When the basis elements of the R-matrices are used in a successive mode in this context, results may be obtained which take into account mechanistic aspects of chemical reacttions.

MANUFACTURING CAPABILITY OF MATHEMATICAL MODELING OF CHEMICAL PROCESSES

Processes of petrochemistry and oil-refining, 2016

An overview about the modern state of mathematical modeling and optimization of chemical-engineering systems was given. An explanation to the concept “computer chemistry” was supplied and using in chemical structures identification. Chemical processes software is based on programs such as InvensysProcessSystems, AspenTechnologies, ChemStations. AspenPlus и HYSYS, Chemcad which permit not only occurring computing on high level, but also transfer from laboratory experiment to industry adoption of processes on basis of database of physicochemical equation and chemically pure products.

Data-driven construction of mathematical models.

Mathematical models have become crucial tools in describing and understanding many scientific processes in which complex dynamics between many metabolites are present. Systems biology in particular has received a great deal of interest in the last decade because of its potential to describe large metabolic networks. The fundamental problem in modelling a complex network is the inherently large number of unknown parameters in the proposed mathematical model. Because of a limited data set, many of these parameters cannot be uniquely determined. In this project we study the so-called inverse problem which attempts to identify and estimate parameters in a mathematical model from experimental data.

A Method to Discover Admissible Model Equations from Observed Data

Most conventional law equation discovery systems such as BACON require experimental environments to acquire their necessary data. The mathematical techniques such as linear system identication and neural network tting presume the classes of equations to model given observed data sets. The study reported in this paper proposes a novel method to discover an admissible model equation from a given set of observed data, while the equation is ensured to reect rst principles governing the objective system. The power of the proposed method comes from the use of the scale-types of the observed quantities, a mathematical property of identity and quasi-bi-variate tting to the given data set. Its principles and algorithm are described with moderately complex examples, and its practicality is demonstrated through a real application to psychological and sociological law equation discovery.