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Perturbative computation of nonlinear harvesting through a path integral approach
Martín E Giuliano1, Bruno Combi1, Matías G dell'Erba1
1IFIMAR-CONICET Universidad Nacional de Mar del Plata, 7600 Mar del Plata, Argentina.
Physical Review. E
|February 17, 2024
Summary
Statistical field theories analyze kinetic energy harvester dynamics driven by colored noise. Nonlinearity
Area of Science:
- Statistical physics
- Dynamical systems
- Energy harvesting
Background:
- Complex dynamical systems analysis often requires advanced theoretical tools.
- Kinetic energy harvesters are crucial for energy scavenging applications.
- Stochastic nonlinear differential equations model complex system behaviors.
Purpose of the Study:
- To analyze the dynamics of a kinetic energy harvester using statistical field theories.
- To investigate the effects of colored noise and nonlinearity on harvester performance.
- To provide an analytical framework for understanding energy harvesting dynamics.
Main Methods:
- Application of statistical field theories, specifically Martin-Siggia-Rose response fields.
- Utilizing path integrals in phase space for analytical solutions.
- Employing Feynman diagrams to represent physical observables.
- Perturbative expansion to analyze nonlinear effects.
- Numerical simulations for validation.
Main Results:
- Analytical solutions derived for the kinetic energy harvester model.
- Comparison with linear case validates the analytical method.
- First-order effect of nonlinearity on energy harvest quantified.
- Numerical simulations support the analytical findings.
Conclusions:
- Statistical field theories offer a robust framework for analyzing kinetic energy harvesters.
- The study provides insights into the impact of nonlinearity and colored noise.
- The developed analytical approach can be extended to other complex systems.
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