p-Adic Models of Ultrametric Diffusion Constrained by Hierarchical Energy Landscapes

Abstract

We demonstrate that p-adic analysis is a natural basis for the construction of a wide variety of the ultrametric diffusion models constrained by hierarchical energy landscapes. A general analytical description in terms of p-adic analysis is given for a class of models. Two exactly solvable examples, i.e. the ultrametric diffusion constraned by the linear energy landscape and the ultrametric diffusion with reaction sink, are considered. We show that such models can be applied to both the relaxation in complex systems and the rate processes coupled to rearrangenment of the complex surrounding.

14 pages, 6 eps figures, LaTeX 2.09

Cited by in corpus (52)

• p-Adic Mathematical Physics
• p-Adic description of characteristic relaxation in complex systems
• $p$-Adic Mathematical Physics: The First 30 Years
• A p-Adic Model of DNA Sequence and Genetic Code
• p-Adic pseudodifferential operators and p-adic wavelets
• Replica symmetry breaking related to a general ultrametric space I: replica matrices and functionals
• p-Adic Modelling of the Genome and the Genetic Code
• Quantization of the Riemann Zeta-Function and Cosmology
• Nonlocal Operators, Parabolic-type Equations, and Ultrametric Random Walks
• Replica symmetry breaking related to a general ultrametric space II: RSB solutions and the n\to0 limit
• First Passage Time Distribution and Number of Returns for Ultrametric Random Walk
• Replica symmetry breaking related to a general ultrametric space III: the case of general measure
• Ultrametric pseudodifferential operators and wavelets for the case of non homogeneous measure
• Parabolic Type Equations and Markov Stochastic Processes on Adeles
• Non-Degenerate Ultrametric Diffusion
• $p$-Adic multidimensional wavelets and their application to $p$-adic pseudo-differential operators
• Some estimates for p-adic rough multilinear Hausdorff operators and commutators on weighted Morrey-Herz type spaces
• p-adic Cellular Neural Networks
• Ultrametric Diffusion, Rugged Energy Landscapes and Transition Networks
• Fractal globule as an artificial molecular machine
• p-adic Cellular Neural Networks: Applications to Image Processing
• p-Adic Statistical Field Theory and Deep Belief Networks
• Chaotic Hamiltonian systems revisited: Survival probability
• On the chaotic behavior of a generalized logistic $p$-adic dynamical system
• Eigen's Paradox and the Quasispecies Model in a Non-Archimedean Framework
• On scale-free and poly-scale behaviors of random hierarchical network
• On metric structure of ultrametric spaces
• Some aspects of the $m$-adic analysis and its applications to $m$-adic stochastic processes
• Ultrametric theory of conformational dynamics of protein molecules in a functional state and the description of experiments on the kinetics of CO binding to myoglobin
• Non-Archimedean Replicator Dynamics and Eigen's Paradox
• Graphs, local zeta functions, Log-Coulomb Gases, and phase transitions at finite temperature
• $p$-Adic Brownian Motion is a Scaling Limit
• Genetic Code and Number Theory
• $p$-Adic Haar multiresolution analysis
• Random Hierarchical Matrices: Spectral Properties and Relation to Polymers on Disordered Trees
• p-Adic Structure of the Genetic Code
• How the Quasispecies Evolution Depends on the Topology of the Genome Space
• Hierarchical Wilson-Cowan Models and Connection Matrices
• Reaction-diffusion Equations on Complex Networks and Turing Patterns, via p-Adic Analysis
• Random walk on p-$adics in glassy systems
• Estimates of linearization discs in $p$-adic dynamics with application to ergodicity
• Ultrametric dynamics for the closed fractal-cluster resource models
• Some classes of non-archimedean radial probability density functions associated with energy landscapes
• Time-Varying Energy Landscapes and Temperature paths: Dynamic Transition Rates in locally Ultrametric Complex Systems
• Spectral properties of pseudo-differential operators over the compact group of $p$-adic integers and compact Vilenkin groups
• The Haar Wavelet Transform of a Dendrogram: Additional Notes
• Non-algebraic first return probability of a stretched random walk near a convex boundary and its effect on adsorption
• Non-Archimedean Coulomb Gases
• On Rational $P$-Adic Dyanamical Systems
• Landscape dynamics, interbasin kinetics and ultrametric diffusion
• $p$-adic singular integral and their commutator in generalized Morrey space
• A $p$-adic Reaction--Diffusion Model of Branching Coral Growth and Calcification Dynamics