Reviews of modern physics, ISSN 1539-0756, 2008, Volume 80, Issue 4, pp. 1275 - 1335

The combination of the compactness of networks, featuring small diameters, and their complex architectures results in a variety of critical effects...

STATISTICAL-MECHANICS | PHYSICS, MULTIDISCIPLINARY | SMALL-WORLD | FERROMAGNETIC ISING-MODEL | EXACTLY SOLVABLE MODEL | diseases | ORDER PHASE-TRANSITION | complex networks | RANDOM GRAPHS | synchronisation | ecology | K-CORE | SPIN MODELS | Ising model | POTTS-MODEL | CRITICAL-BEHAVIOR | Network architecture | Evaluation | Usage | Graph theory | Phase transformations (Statistical physics) | Analysis

STATISTICAL-MECHANICS | PHYSICS, MULTIDISCIPLINARY | SMALL-WORLD | FERROMAGNETIC ISING-MODEL | EXACTLY SOLVABLE MODEL | diseases | ORDER PHASE-TRANSITION | complex networks | RANDOM GRAPHS | synchronisation | ecology | K-CORE | SPIN MODELS | Ising model | POTTS-MODEL | CRITICAL-BEHAVIOR | Network architecture | Evaluation | Usage | Graph theory | Phase transformations (Statistical physics) | Analysis

Journal Article

The European physical journal. ST, Special topics, ISSN 1951-6401, 2014, Volume 223, Issue 11, pp. 2307 - 2321

... TOPICS Review Recent advances and open challenges in percolation N. Ara´ ujo 1,a , P. Grassberger 2,b , B. Kahng 3,c ,K . J .S c h r e n k 4,d , and R.M. Ziﬀ 5,e 1...

Condensed Matter Physics | Measurement Science and Instrumentation | Materials Science, general | Atomic, Molecular, Optical and Plasma Physics | Physics, general | Physics | Classical Continuum Physics | CLUSTER-SIZE | RANGE CORRELATED PERCOLATION | PHYSICS, MULTIDISCIPLINARY | 3-DIMENSIONAL POLYMERS | PHASE-TRANSITIONS | BOND PERCOLATION | STATE POTTS-MODEL | URBAN-GROWTH PATTERNS | EXPLOSIVE PERCOLATION | MOLECULAR-SIZE DISTRIBUTION | 2 DIMENSIONS | Physics - Statistical Mechanics

Condensed Matter Physics | Measurement Science and Instrumentation | Materials Science, general | Atomic, Molecular, Optical and Plasma Physics | Physics, general | Physics | Classical Continuum Physics | CLUSTER-SIZE | RANGE CORRELATED PERCOLATION | PHYSICS, MULTIDISCIPLINARY | 3-DIMENSIONAL POLYMERS | PHASE-TRANSITIONS | BOND PERCOLATION | STATE POTTS-MODEL | URBAN-GROWTH PATTERNS | EXPLOSIVE PERCOLATION | MOLECULAR-SIZE DISTRIBUTION | 2 DIMENSIONS | Physics - Statistical Mechanics

Journal Article

Journal of Difference Equations and Applications, ISSN 1023-6198, 09/2017, Volume 23, Issue 9, pp. 1542 - 1561

In the present paper, by conducting research on the dynamics of the p-adic generalized Ising mapping corresponding to renormalization group associated with the p-adic Ising-Vannemenus model...

p-adic numbers | chaos | periodic | p-adic dynamical system | JULIA SETS | SYSTEM | MATHEMATICS, APPLIED | MAPS | RATIONAL FUNCTIONS | PHASE-TRANSITIONS | DYNAMICS | POTTS-MODEL | Ising model | Fixed points (mathematics) | Mapping | Applied mathematics | Mathematics - Dynamical Systems

p-adic numbers | chaos | periodic | p-adic dynamical system | JULIA SETS | SYSTEM | MATHEMATICS, APPLIED | MAPS | RATIONAL FUNCTIONS | PHASE-TRANSITIONS | DYNAMICS | POTTS-MODEL | Ising model | Fixed points (mathematics) | Mapping | Applied mathematics | Mathematics - Dynamical Systems

Journal Article

Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena, ISSN 0960-0779, 12/2017, Volume 105, pp. 260 - 270

We consider a family of (2, 2)-rational functions given on the set of complex p-adic field Cp...

Complex p-adic field | Invariant set | Ergodic | Siegel disk | Rational dynamical systems | Fixed point | MINIMAL DECOMPOSITION | ERGODICITY | PHYSICS, MULTIDISCIPLINARY | RATIONAL FUNCTIONS | CHAOTIC BEHAVIOR | PHYSICS, MATHEMATICAL | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | POTTS-MODEL | Mathematics - Dynamical Systems

Complex p-adic field | Invariant set | Ergodic | Siegel disk | Rational dynamical systems | Fixed point | MINIMAL DECOMPOSITION | ERGODICITY | PHYSICS, MULTIDISCIPLINARY | RATIONAL FUNCTIONS | CHAOTIC BEHAVIOR | PHYSICS, MATHEMATICAL | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | POTTS-MODEL | Mathematics - Dynamical Systems

Journal Article

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, ISSN 1078-0947, 01/2018, Volume 38, Issue 1, pp. 231 - 245

In the previous investigations of the authors the renormalization group method to p-adic models on Cayley trees has been developed...

MATHEMATICS, APPLIED | chaos | CAYLEY TREE | Ising-Potts function | PHASE-TRANSITIONS | shift | GIBBS MEASURES | MODEL | p-adic numbers | JULIA SETS | MATHEMATICS | REDUCTION | MAPS | DYNAMICAL-SYSTEMS | Q(P)

MATHEMATICS, APPLIED | chaos | CAYLEY TREE | Ising-Potts function | PHASE-TRANSITIONS | shift | GIBBS MEASURES | MODEL | p-adic numbers | JULIA SETS | MATHEMATICS | REDUCTION | MAPS | DYNAMICAL-SYSTEMS | Q(P)

Journal Article

Bulletin of mathematical biology, ISSN 1522-9602, 2013, Volume 75, Issue 8, pp. 1377 - 1399

htmlabstractAngiogenesis, the formation of new blood vessels sprouting from existing ones, occurs in several situations like wound healing, tissue remodeling...

cellular Potts model | Angiogenesis | extracellular matrix | Branching growth | Life Sciences, general | Mathematical and Computational Biology | Cellular Potts model | MMPs | Extracellular matrix | Mathematics | Cell Biology | FIBROBLAST | VASCULOGENESIS | VEGF | DIFFERENTIAL ADHESION | PROLIFERATION | TUMOR-INDUCED ANGIOGENESIS | IN-VITRO | GROWTH | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | CLINICAL-IMPLICATIONS | CAPILLARY FORMATION | Animals | Models, Cardiovascular | Extracellular Matrix - physiology | Humans | Neovascularization, Pathologic | Mathematical Concepts | Systems Biology | Vascular Endothelial Growth Factor A - physiology | Endothelial Cells - physiology | Neovascularization, Physiologic | Cell Movement | Models | Tumors | Endothelium | Original

cellular Potts model | Angiogenesis | extracellular matrix | Branching growth | Life Sciences, general | Mathematical and Computational Biology | Cellular Potts model | MMPs | Extracellular matrix | Mathematics | Cell Biology | FIBROBLAST | VASCULOGENESIS | VEGF | DIFFERENTIAL ADHESION | PROLIFERATION | TUMOR-INDUCED ANGIOGENESIS | IN-VITRO | GROWTH | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | CLINICAL-IMPLICATIONS | CAPILLARY FORMATION | Animals | Models, Cardiovascular | Extracellular Matrix - physiology | Humans | Neovascularization, Pathologic | Mathematical Concepts | Systems Biology | Vascular Endothelial Growth Factor A - physiology | Endothelial Cells - physiology | Neovascularization, Physiologic | Cell Movement | Models | Tumors | Endothelium | Original

Journal Article

Physical Review B - Condensed Matter and Materials Physics, ISSN 1098-0121, 03/2012, Volume 85, Issue 10

We study an M-p-spin spin glass model with p = 3 and M = 3 in three dimensions using the Migdal-Kadanoff renormalization group approximation (MKA...

TRANSITION | POTTS | PHYSICS, CONDENSED MATTER | CONNECTIONS | TIME-REVERSAL SYMMETRY

TRANSITION | POTTS | PHYSICS, CONDENSED MATTER | CONNECTIONS | TIME-REVERSAL SYMMETRY

Journal Article

1980, ISBN 9070265826, 155

Book

Antimicrobial agents and chemotherapy, ISSN 1098-6596, 2018, Volume 62, Issue 5

Segregation of bacteria based on their metabolic activities in biofilms plays an important role in the development of antibiotic resistance. Mushroom-shaped...

Cell proliferation | Mushroom-shaped biofilm | Cell motility | Biofilms | Cellular Potts model | Antibiotic resistance | Pseudomonas aeruginosa | Chemotaxis | BACTERIA | cell proliferation | TOLERANCE | MICROBIOLOGY | cellular Potts model | TRANSPOSON MUTANT LIBRARY | cell motility | mushroom-shaped biofilm | TOBRAMYCIN | SUBPOPULATION | antibiotic resistance | MULTICELLULAR STRUCTURES | RESISTANCE | COLISTIN | IV PILI | PHARMACOLOGY & PHARMACY | biofilms | chemotaxis | MOTILITY

Cell proliferation | Mushroom-shaped biofilm | Cell motility | Biofilms | Cellular Potts model | Antibiotic resistance | Pseudomonas aeruginosa | Chemotaxis | BACTERIA | cell proliferation | TOLERANCE | MICROBIOLOGY | cellular Potts model | TRANSPOSON MUTANT LIBRARY | cell motility | mushroom-shaped biofilm | TOBRAMYCIN | SUBPOPULATION | antibiotic resistance | MULTICELLULAR STRUCTURES | RESISTANCE | COLISTIN | IV PILI | PHARMACOLOGY & PHARMACY | biofilms | chemotaxis | MOTILITY

Journal Article

Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, 05/2015, Volume 2015, Issue 5

In this paper, we continue an investigation of the p-adic Ising-Vannimenus model on the Cayley tree of an arbitrary order k (k >= 2...

phase diagrams (theory) | solvable lattice models | SYSTEM | FIELDS | MECHANICS | PHASE-TRANSITIONS | LAMBDA-MODEL | GENERAL ULTRAMETRIC SPACE | GIBBS MEASURES | STATE | POTTS-MODEL | PHYSICS, MATHEMATICAL

phase diagrams (theory) | solvable lattice models | SYSTEM | FIELDS | MECHANICS | PHASE-TRANSITIONS | LAMBDA-MODEL | GENERAL ULTRAMETRIC SPACE | GIBBS MEASURES | STATE | POTTS-MODEL | PHYSICS, MATHEMATICAL

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 02/2014, Volume 47, Issue 7, pp. 1 - 12

We investigate the generalized p-spin models that contain arbitrary diagonal operators (U...

64.70.Q | glass transition | replica symmetry breakingPACS numbers: 64.60.-i | spin glasses | frustration | replica symmetry breaking | PHASE | PHYSICS, MULTIDISCIPLINARY | EXACTLY SOLVABLE MODEL | MEAN-FIELD POTTS | STATE | REPLICA-SYMMETRY-BREAKING | PHYSICS, MATHEMATICAL | RANDOM-ENERGY MODEL | Glass transition | Operators | Mathematical analysis | Glass | Mathematical models | Reflection | Quadrupoles | Crossovers | Symmetry

64.70.Q | glass transition | replica symmetry breakingPACS numbers: 64.60.-i | spin glasses | frustration | replica symmetry breaking | PHASE | PHYSICS, MULTIDISCIPLINARY | EXACTLY SOLVABLE MODEL | MEAN-FIELD POTTS | STATE | REPLICA-SYMMETRY-BREAKING | PHYSICS, MATHEMATICAL | RANDOM-ENERGY MODEL | Glass transition | Operators | Mathematical analysis | Glass | Mathematical models | Reflection | Quadrupoles | Crossovers | Symmetry

Journal Article

International Journal of Number Theory, ISSN 1793-0421, 08/2014, Volume 10, Issue 5, pp. 1171 - 1190

We provide a solvability criterion for a cubic equation in domains $\mathbb{Z}_{p}^{*}, \mathbb{Z}_p, \mathbb{Q}_p$ . We show that, in principal, the Cardano method is not always applicable for such equations...

p-adic Cardano formula | p-adic number | Cubic equation | solvability criterion | MATHEMATICS | DYNAMICAL-SYSTEMS | CAYLEY TREE | POTTS-MODEL | RESIDUES

p-adic Cardano formula | p-adic number | Cubic equation | solvability criterion | MATHEMATICS | DYNAMICAL-SYSTEMS | CAYLEY TREE | POTTS-MODEL | RESIDUES

Journal Article

Theoretical and Mathematical Physics, ISSN 0040-5779, 11/2017, Volume 193, Issue 2, pp. 1694 - 1702

Adapting some methods for real-valued Gibbs measures on Cayley trees to the p-adic case, we construct several p-adic distributions on the set...

Theoretical, Mathematical and Computational Physics | Cayley tree | p -adic measure | p -adic distribution | Applications of Mathematics | Physics | p -adic number | p-adic distribution | p-adic number | p-adic measure | PHYSICS, MULTIDISCIPLINARY | PHASE-TRANSITIONS | GIBBS MEASURES | STATE POTTS-MODEL | PHYSICS, MATHEMATICAL | UNIQUENESS

Theoretical, Mathematical and Computational Physics | Cayley tree | p -adic measure | p -adic distribution | Applications of Mathematics | Physics | p -adic number | p-adic distribution | p-adic number | p-adic measure | PHYSICS, MULTIDISCIPLINARY | PHASE-TRANSITIONS | GIBBS MEASURES | STATE POTTS-MODEL | PHYSICS, MATHEMATICAL | UNIQUENESS

Journal Article

Mathematical physics, analysis, and geometry, ISSN 1385-0172, 2012, Volume 16, Issue 1, pp. 49 - 87

In the present paper, we study a new kind of p-adic measures for q + 1-state Potts model, called p-adic quasi Gibbs measure...

82B26 | 12J12 | p -adic quasi Gibbs measure | Theoretical, Mathematical and Computational Physics | 46S10 | p -adic numbers | Potts model | Physics | Geometry | 47H10 | Analysis | Group Theory and Generalizations | Applications of Mathematics | 60K35 | 39A70 | Phase transition | p-adic numbers | p-adic quasi Gibbs measure | EXISTENCE | BREAKING | FIELDS | MATHEMATICS, APPLIED | SPACES | GIBBS MEASURES | STATE | PHYSICS, MATHEMATICAL | WAVELETS | Ferromagnetism | Models

82B26 | 12J12 | p -adic quasi Gibbs measure | Theoretical, Mathematical and Computational Physics | 46S10 | p -adic numbers | Potts model | Physics | Geometry | 47H10 | Analysis | Group Theory and Generalizations | Applications of Mathematics | 60K35 | 39A70 | Phase transition | p-adic numbers | p-adic quasi Gibbs measure | EXISTENCE | BREAKING | FIELDS | MATHEMATICS, APPLIED | SPACES | GIBBS MEASURES | STATE | PHYSICS, MATHEMATICAL | WAVELETS | Ferromagnetism | Models

Journal Article