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Conservation of Mass in Finite Cotrol Volume01:16

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The principle of conservation of mass is a fundamental law in fluid mechanics and is applied using the continuity equation. We apply the concept to a finite control volume to derive the continuity equation.
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The principle of conservation of mass is fundamental in fluid dynamics and is crucial for analyzing flow within fixed control volumes, such as pipes or ducts. This principle states that the total mass within a control volume remains constant unless altered by the inflow or outflow of mass through the control surfaces. This results in a vital relationship for steady, incompressible flow where the mass entering a system equals the mass leaving it.
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Carbonation is a process used to dissolve carbon dioxide gas in a liquid, commonly used in the production of carbonated beverages. Achieving efficient carbonation requires careful control of temperature, pressure, and flow conditions. By adjusting these parameters, carbonation efficiency can be maximized, producing a higher concentration of CO2 in the liquid.
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Related Experiment Video

Updated: May 16, 2025

Forming, Confining, and Observing Microtubule-Based Active Nematics
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Achieving designed texture and flows in bulk active nematics using optimal control theory.

Saptorshi Ghosh1, Aparna Baskaran1, Michael F Hagan1

  • 1Martin A. Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02453, USA.

The Journal of Chemical Physics
|April 1, 2025
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Summary
This summary is machine-generated.

Scientists developed an optimal control theory to guide active materials. This framework uses light-generated activity to steer complex systems toward desired functions, overcoming chaotic dynamics.

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Area of Science:

  • Physics
  • Materials Science
  • Nonlinear Dynamics

Background:

  • Active materials, inherently out of equilibrium, offer unique functional capabilities beyond passive systems.
  • However, their complex dynamics often lead to chaotic states, hindering practical applications and work generation.
  • Controlling these systems to achieve specific, stable dynamical states remains a significant scientific challenge.

Purpose of the Study:

  • To develop a theoretical framework for controlling the dynamics of active materials using spatiotemporal light patterns.
  • To investigate the ability of optimal control theory to direct active nematic systems toward desired steady states.
  • To explore the potential for creating novel functions and stable emergent behaviors in active materials through external control.

Main Methods:

  • Formulated an optimal control theory framework tailored for active nematic systems.
  • Utilized spatiotemporal sequences of light-generated activity as the control input.
  • Simulated and analyzed the system's response to computed control fields to assess dynamical state selection and stabilization.

Main Results:

  • Demonstrated that optimal control can effectively redirect the dynamics of active nematics away from chaotic states.
  • Showcased the ability to drive the system into prescribed dynamical steady states and alternative functional programs.
  • Successfully stabilized emergent behaviors that are inherently unstable in the absence of control.
  • Illustrated dynamic reconfiguration between different system states.

Conclusions:

  • Optimal control theory provides a powerful and rational approach to designing and manipulating active materials.
  • Optogenetic control strategies, guided by this framework, can unlock new functionalities and overcome inherent dynamical instabilities.
  • This research offers a roadmap for engineering active materials with tailored structures, dynamics, and functions for diverse applications.