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Solution Transformations and Their Effects on the Systems with Open Boundary Conditions

Communications in Theoretical Physics 2002年第4期37卷 397-404页

作者： JUGuo－Xing ZhaoXian－Lin DepartmentofPhysics NanjingUniversityNanjing210093China DepartmentofPhysics HenanEducationCollegeZhengzhou450003China

The solution transformations and properties of the -matrices for two-component systems under these transformations are analyzed in details. Not all transformed -matrices can be put into the Skalyanin's formalism. For those -matrices with all required properties, the effects of solution transformations to the six- and eight-vertex systems with open boundary conditions are discussed. These effects can be one of the following types: The Hamiltonian is invariant or transposition-invariant or made in a similarity transformation, or its coupling coefficients are multiplied by an overall factor, or the spin of the system is rotated around the axis or/and reflected with respect to some plane. In these cases, the transformed systems remain to be integrable.

关键词： Hamiltonian solution transformation integrability vertex model boundary Yang-Baxter equation R-matrix K-matrix

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The Effects of Solution Transformations to the System with Color Parameters

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Communications in Theoretical Physics 2001年第5期35卷 539-542页

作者： JUGuo－Xing ZHAOXian－Lin CollegeofPhysicsandInformationEngineering HenanNormalUniversityXinxiang453002HenanProvinceChina DepartmentofPhysics HenanEducationCollegeZhengzhou450003China

The effects of solution transformations to the six- and eight-vertex systems are discussed. There are four kinds of effects, the Hamiltonian of the system is invariant, its coupling coefficients change, some additional terms appear in the Hamiltonian, and the spin of the system is rotated by some angle about axis under these transformations. In all the cases, the systems are still integrable if they are so before the transformation.

关键词： Hamiltonian solution transformation integrability vertex model

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Mathematical modeling of evolution of cell networks in epithelial tissues

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Quantitative Biology 2024年第3期12卷 286-300页

作者： Ivan Krasnyakov Department of Applied Physics Perm National Research Polytechnic UniversityPermRussia

Epithelial cell networks imply a packing geometry characterized by various cell shapes and distributions in terms of number of cell neighbors and *** such simple characteristics describing cell sheets,the formation of bubble-like cells during the morphogenesis of epithelial tissues remains poorly *** study proposes a topological mathematical model of morphogenesis in a squamous *** introduce a new potential that takes into account not only the elasticity of cell perimeter and area but also the elasticity of their internal ***,we incorporate an integral equation for chemical signaling,allowing us to consider chemo-mechanical cell *** addition to the listed factors,the model takes into account essential processes in real epithelial,such as cell proliferation and *** presented mathematical model has yielded novel insights into the packing of epithelial *** has been found that there are two main states:one consists of cells of the same size,and the other consists of“bubble”*** example is provided of the possibility of accounting for chemo-mechanical interactions in a multicellular *** introduction of a parameter determining the flexibility of cell shapes enables the modeling of more complex cell behaviors,such as considering change of cell *** developed mathematical model of morphogenesis of squamous epithelium allows progress in understanding the processes of formation of cell *** results obtained from mathematical modeling are of significant importance for understanding the mechanisms of morphogenesis and development of epithelial ***,the obtained results can be applied in developing methods to influence morphogenetic processes in medical applications.

关键词： bubble-like cells growth epithelial tissue mathematical model tissue modeling vertex model

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