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Nondisjunction

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Related Experiment Video

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Generation of Aggregates of Mouse Embryonic Stem Cells that Show Symmetry Breaking, Polarization and Emergent Collective Behaviour In Vitro

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Spontaneous symmetry breaking in amnestically induced persistence.

Marco Antonio Alves da Silva¹, G M Viswanathan, A S Ferreira

¹Departamento de Física e Química, FCFRP, Universidade de São Paulo, 14040-903 Ribeirão Preto, São Paulo, Brazil.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|June 4, 2008

Summary

This study explores a non-Markovian random walk model, revealing four distinct phases. Log-periodic persistence exhibits complex fractal dimensions and self-similarity, breaking continuous scale invariance.

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Area of Science:

Physics
Statistical Mechanics
Complex Systems

Background:

Non-Markovian random walks deviate from standard models by incorporating memory effects.
A recently proposed model introduces memory loss and persistence, leading to complex dynamics.

Purpose of the Study:

To fully characterize the phase diagram of the non-Markovian random walk model.
To analyze the symmetries and fractal properties of different phases, particularly log-periodic behavior.

Main Methods:

Numerical simulations were employed to explore the system's behavior.
Analytical techniques were used to derive the complete phase diagram and understand symmetries.

Main Results:

Identified four distinct phases: classical nonpersistence, classical persistence, log-periodic nonpersistence, and log-periodic persistence.
Demonstrated that log-periodicity breaks continuous scale invariance, exhibiting discrete scale invariance instead.
Observed complex fractal dimensions and evidence of statistical and geometric self-similarity in log-periodic persistence.

Conclusions:

The non-Markovian random walk model exhibits rich phase behavior beyond classical descriptions.
Log-periodic phases introduce novel symmetries and fractal characteristics, including complex dimensions.
The findings offer insights into systems with memory-dependent dynamics and self-similar structures.