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Hyperbolas01:30

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A hyperbola is a conic section produced when a double-napped cone is intersected by a plane at an angle steeper than the slope of the cone, such that it cuts through both nappes. This intersection yields two separate, mirror-image curves known as branches, which open away from each other along the transverse axis. The nearest points on each branch to the hyperbola’s center are termed vertices, and the distance from the center to a vertex is denoted by a. Perpendicular to the transverse axis is...
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Updated: May 18, 2026

Introduction to Solid Supported Membrane Based Electrophysiology
19:56

Introduction to Solid Supported Membrane Based Electrophysiology

Published on: May 11, 2013

Anomalous transport induced by nonhyperbolicity.

S R Lopes1, J D Szezech, R F Pereira

  • 1Departamento de Física, Universidade Federal do Paraná, Curitiba, PR, Brazil. lopes@fisica.ufpr.br

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 26, 2012
PubMed
Summary

Deterministic system features enable direct particle transport in quasisymmetric potentials. Nonhyperbolic regions in phase space are key to particle acceleration and harnessing unbiased fluctuations for useful work.

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Last Updated: May 18, 2026

Introduction to Solid Supported Membrane Based Electrophysiology
19:56

Introduction to Solid Supported Membrane Based Electrophysiology

Published on: May 11, 2013

Area of Science:

  • Physics
  • Nonlinear Dynamics
  • Statistical Mechanics

Background:

  • Understanding particle transport in complex systems is crucial.
  • Quasisymmetric potentials and weak dissipation present unique challenges.
  • Exploiting nonequilibrium fluctuations remains an active research area.

Purpose of the Study:

  • To investigate the role of deterministic features in direct transport.
  • To analyze particle acceleration mechanisms in quasisymmetric potentials.
  • To explore the potential for extracting useful work from fluctuations.

Main Methods:

  • Analysis of deterministic features within a quasisymmetric potential.
  • Study of particle dynamics in the presence of weak dissipation.
  • Identification and characterization of nonhyperbolic regions in phase space.

Main Results:

  • Deterministic features facilitate direct transport in the studied system.
  • Nonhyperbolic regions around acceleration areas are critical for particle acceleration.
  • Direct transport is achievable over a wide parameter range of weak asymmetry.

Conclusions:

  • Nonhyperbolic dynamics are essential for direct transport and particle acceleration.
  • The findings suggest possibilities for work extraction from unbiased fluctuations.
  • This research offers insights into harnessing nonequilibrium effects in physical systems.