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Related Concept Videos

Conservation of Energy in Control Volume01:14

Conservation of Energy in Control Volume

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Consider a turbine operating under steady-flow conditions. The control volume is drawn around the turbine, with fluid entering at one point and exiting at another. The turbine extracts energy from the fluid, which performs mechanical work (shaft work).
For steady flow systems, the time derivative of the stored energy becomes zero since there is no energy accumulation within the control volume. This simplifies the energy equation to:
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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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Stormwater detention basins are essential in managing runoff during heavy rainfall, particularly in urban areas where impervious surfaces increase the risk of flooding. Understanding the conservation of mass in these systems allows engineers to optimize basin performance, balancing inflow, outflow, and water storage.
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The terms 'conserved quantity' and 'conservation law' have specific scientific meanings in physics, which differ from the meanings associated with their everyday use. For example, in everyday usage, water could be conserved by not using it, by using less of it, or by re-using it. However, in scientific terms, a conserved quantity of a system stays constant, changes by a definite amount that is transferred to other systems, and is converted into other forms of that...
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Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration; but it is important to remember that these conditions are relative. For instance, an object may be at rest when viewed from one frame of reference, but that same object would appear to be in motion when viewed by someone moving at a constant velocity.
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Conservation-Law-Based Global Bounds to Quantum Optimal Control.

Hanwen Zhang1,2, Zeyu Kuang1,2, Shruti Puri1,3

  • 1Department of Applied Physics, Yale University, New Haven, Connecticut 06511, USA.

Physical Review Letters
|September 24, 2021
PubMed
Summary
This summary is machine-generated.

This study introduces a new framework for quantum control, establishing fundamental speed limits for quantum systems. These bounds accurately predict performance, even with complex dynamics and constraints.

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Area of Science:

  • Quantum Physics
  • Quantum Information Science
  • Control Theory

Background:

  • Active control of quantum systems is crucial for quantum computation and molecular process manipulation.
  • Existing speed bounds for quantum control are often imprecise due to coarse system information and complex dynamics.

Purpose of the Study:

  • To develop a systematic framework for identifying fundamental limits in any quantum control scenario.
  • To establish accurate and universally applicable bounds for quantum control performance.

Main Methods:

  • Formulating conservation laws in quantum dynamics using integral equations.
  • Developing a systematic framework based on these integral equations to derive control bounds.

Main Results:

  • Demonstrated the utility of the derived bounds in three distinct scenarios: three-level driving, decoherence suppression, and maximum-fidelity gate implementation.
  • Showcased that the derived bounds are tight or nearly tight across these diverse quantum control applications.

Conclusions:

  • The integral-equation-based framework provides a robust method for determining fundamental limits in quantum control.
  • These global bounds effectively complement local optimization designs, offering a clearer understanding of achievable and unsurpassable performance levels in quantum systems.