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Related Concept Videos

Atomic Nuclei: Nuclear Relaxation Processes01:23

Atomic Nuclei: Nuclear Relaxation Processes

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In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis,  the precessing magnetic moments are randomly oriented around the z-axis.
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Related Experiment Videos

Entrainment in the master equation.

Michael Margaliot1, Lars Grüne2, Thomas Kriecherbauer2

  • 1School of Electrical Engineering and the Sagol School of Neuroscience, Tel-Aviv University, Tel-Aviv 69978, Israel.

Royal Society Open Science
|May 17, 2018
PubMed
Summary
This summary is machine-generated.

The master equation, crucial in many fields, entrains to periodic excitations. Solutions converge to a periodic state matching the excitation

Keywords:
Metzler matrixasymmetric simple exclusion processcontractive systemscooperative dynamical systemsfirst integralstability

Related Experiment Videos

Area of Science:

  • Mathematical Physics
  • Systems Biology
  • Statistical Mechanics

Background:

  • The master equation models dynamic systems across diverse scientific disciplines.
  • Periodic transition rates can arise from external periodic forces, such as daily cycles or traffic signals.

Purpose of the Study:

  • To analyze the behavior of master equations with periodic transition rates.
  • To demonstrate the phenomenon of entrainment or phase locking to periodic excitations.

Main Methods:

  • Application of systems and control theory.
  • Mathematical analysis of master equation solutions.

Main Results:

  • Convergence of all solutions to a periodic solution.
  • The period of the solution matches the period of the transition rates.
  • Demonstration of entrainment (phase locking) to periodic driving forces.

Conclusions:

  • Master equations with periodic rates exhibit predictable entrainment behavior.
  • Theoretical results have implications for statistical mechanics and epidemiology models.