Coherence and Large-Scale Pattern Formation in Coupled Logistic-Map Lattices via Computer Algebra Systems

2014 ◽  
pp. 230-241
Author(s):  
Maciej Janowicz ◽  
Arkadiusz Orłowski
Keyword(s):  
Pattern Formation ◽  
Computer Algebra ◽  
Large Scale ◽  
Logistic Map ◽  
Computer Algebra Systems

Utilization of Mathematical Software Packages in Chemical Engineering Research

2005 ◽  
Vol 5 (2) ◽  
pp. 125
Author(s):  
Ang Wee Lee ◽  
Nayef Mohamed Ghasem ◽  
Mohamed Azlan Hussain
Keyword(s):  
Differential Equations ◽  
Computer Algebra ◽  
Large Scale ◽  
Chemical Engineering ◽  
Nonlinear Differential Equations ◽  
Differential Algebraic Equations ◽  
Good Choice ◽  
Computer Algebra Systems ◽  
Algebraic Equations ◽  
Starting Point

Using Fortran taken as the starting point, we are now on the sixth decade of high-level programming applications. Among the programming languages available, computer algebra systems (CAS) appear to be a good choice in chemical engineering can be applied easily. Until the emergence of CAS, the assistance from a specialized group for large-scale programming is justified. Nowadays, it is more effective for the modern chemical engineer to rely on his/her own programming ability for problem solving. In the present paper, the abilities of Polymath, Maple, Matlab, Mathcad, and Mathematica in handling differential equations are illustrated for differential-algebraic equations, large system of nonlinear differential equations, and partial differential equations. The programming of solutions with these CAS are presented, contrasted, and discussed in relation to chemical engineering problems. Keywords: Computer algebra systems (CAS),computer simulation,Mathcad, Mathematica,Mathlab and numerical methods.

scholarly journals New ideas for handling of loop and angular integrals in D-dimensions in QCD

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Valery E. Lyubovitskij ◽  
Fabian Wunder ◽  
Alexey S. Zhevlakov
Keyword(s):  
Computer Algebra ◽  
Cross Sections ◽  
Orthogonal Basis ◽  
Computer Algebra Systems ◽  
Covariant Formalism ◽  
Linear Combinations ◽  
Recursion Relations ◽  
New Ideas ◽  
Rotational Invariant ◽  
Geometric Picture

Abstract We discuss new ideas for consideration of loop diagrams and angular integrals in D-dimensions in QCD. In case of loop diagrams, we propose the covariant formalism of expansion of tensorial loop integrals into the orthogonal basis of linear combinations of external momenta. It gives a very simple representation for the final results and is more convenient for calculations on computer algebra systems. In case of angular integrals we demonstrate how to simplify the integration of differential cross sections over polar angles. Also we derive the recursion relations, which allow to reduce all occurring angular integrals to a short set of basic scalar integrals. All order ε-expansion is given for all angular integrals with up to two denominators based on the expansion of the basic integrals and using recursion relations. A geometric picture for partial fractioning is developed which provides a new rotational invariant algorithm to reduce the number of denominators.

Dynamic Polygon Generation for Flexible Pattern Formation in Large-Scale UAV Swarm Networks

2020 ◽  
Author(s):  
Gunasekaran Raja ◽  
Kottilingam Kottursamy ◽  
Ajay Theetharappan ◽  
Korhan Cengiz ◽  
Aishwarya Ganapathisubramaniyan ◽  
...  
Keyword(s):  
Pattern Formation ◽  
Large Scale ◽  
Uav Swarm

The Fischer-Clifford Matrices and Character Table of a Maximal Subgroup of Fi24

2010 ◽  
Vol 17 (03) ◽  
pp. 389-414 ◽  
Author(s):  
Faryad Ali ◽  
Jamshid Moori
Keyword(s):  
Automorphism Group ◽  
Conjugacy Class ◽  
Maximal Subgroup ◽  
Computer Algebra ◽  
Character Table ◽  
Computer Algebra Systems ◽  
Split Extension ◽  
Sporadic Group ◽  
Local Subgroup ◽  
Fischer Group

The Fischer group [Formula: see text] is the largest 3-transposition sporadic group of order 2510411418381323442585600 = 222.316.52.73.11.13.17.23.29. It is generated by a conjugacy class of 306936 transpositions. Wilson [15] completely determined all the maximal 3-local subgroups of Fi24. In the present paper, we determine the Fischer-Clifford matrices and hence compute the character table of the non-split extension 37· (O7(3):2), which is a maximal 3-local subgroup of the automorphism group Fi24 of index 125168046080 using the technique of Fischer-Clifford matrices. Most of the calculations are carried out using the computer algebra systems GAP and MAGMA.

Mechanical Patterning in Animal Morphogenesis

2021 ◽  
Vol 37 (1) ◽  
Author(s):  
Yonit Maroudas-Sacks ◽  
Kinneret Keren
Keyword(s):  
Pattern Formation ◽  
Large Scale ◽  
Coarse Grained ◽  
Annual Review ◽  
Publication Date ◽  
Biochemical Processes ◽  
Substantial Progress ◽  
Biological Pattern Formation ◽  
Effective Theories ◽  
Biochemical Signals

Morphogenesis is one of the most remarkable examples of biological pattern formation. Despite substantial progress in the field, we still do not understand the organizational principles responsible for the robust convergence of the morphogenesis process across scales to form viable organisms under variable conditions. Achieving large-scale coordination requires feedback between mechanical and biochemical processes, spanning all levels of organization and relating the emerging patterns with the mechanisms driving their formation. In this review, we highlight the role of mechanics in the patterning process, emphasizing the active and synergistic manner in which mechanical processes participate in developmental patterning rather than merely following a program set by biochemical signals. We discuss the value of applying a coarse-grained approach toward understanding this complex interplay, which considers the large-scale dynamics and feedback as well as complementing the reductionist approach focused on molecular detail. A central challenge in this approach is identifying relevant coarse-grained variables and developing effective theories that can serve as a basis for an integrated framework for understanding this remarkable pattern-formation process. Expected final online publication date for the Annual Review of Cell and Developmental Biology, Volume 37 is October 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Genetic analysis of pattern formation in the Arabidopsis embryo

Development ◽  
1991 ◽  
Vol 113 (Supplement_1) ◽  
pp. 27-38 ◽  
Author(s):  
Gerd Jürgens ◽  
Ulrike Mayer ◽  
Torres Ruiz Ramon A. ◽  
Thomas Berleth ◽  
Simon Miséra
Keyword(s):  
Pattern Formation ◽  
Large Scale ◽  
Early Embryo ◽  
Flowering Plant ◽  
Abnormal Development ◽  
Mutant Seedling ◽  
Basic Body ◽  
Plant Embryo ◽  
Embryonic Pattern Formation ◽  
Plant Arabidopsis Thaliana

Virtually nothing is known about the mechanisms that generate the basic body pattern in plant embryogenesis. As a first step towards the analysis of pattern formation, we have isolated and begun to characterise putative pattern mutants in the flowering plant, Arabidopsis thaliana. A large-scale screen for morphologically abnormal seedling mutants yielded about 250 lines for further study, and genetic evidence suggests saturation of the genome for this kind of mutation. The phenotypes of putative pattern mutants fall into distinct categories, classes and groups, which may reflect specific aspects of embryonic pattern formation. Mutant seedling phenotypes result from abnormal development in the early embryo. The implications of our findings are discussed with regard to the prospects for a mechanistic understanding of pattern formation in the plant embryo.

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