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Related Concept Videos

Energy Conservation and Bernoulli's Equation01:16

Energy Conservation and Bernoulli's Equation

Applying the conservation of energy principle or the work-energy theorem to an incompressible, inviscid fluid in laminar, steady, irrotational flow leads to Bernoulli's equation. It states that the sum of the fluid pressure, potential, and kinetic energy per unit volume is constant along a streamline.
All the terms in the equation have the dimension of energy per unit volume. The kinetic energy per unit volume is called the kinetic energy density, and the potential energy per unit volume is...
Conservation of Energy in Control Volume01:14

Conservation of Energy in Control Volume

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:
Accelerating Fluids01:17

Accelerating Fluids

When a fluid is in constant acceleration, the pressure and buoyant force equations are modified. Suppose a beaker is placed in an elevator accelerating upward with a constant acceleration, a. In the beaker, assume there is a thin cylinder of height h with an infinitesimal cross-sectional area, ΔS.
The motion of the liquid within this infinitesimal cylinder is considered to obtain the pressure difference. Three vertical forces act on this liquid:
Fast Decoupled and DC Powerflow01:24

Fast Decoupled and DC Powerflow

The fast decoupled power flow method addresses contingencies in power system operations, such as generator outages or transmission line failures. This method provides quick power flow solutions, essential for real-time system adjustments. Fast decoupled power flow algorithms simplify the Jacobian matrix by neglecting certain elements, leading to two sets of decoupled equations:
Work and Energy for Variable Forces01:10

Work and Energy for Variable Forces

When an object is acted upon by a variable force, the amount of work done and the change in energy of the object can be more complex to calculate compared to when a constant force is applied. Work is the product of force and displacement, while energy is the capacity of a system to do work. When a constant force is applied to an object, the work done can be calculated as the product of the force and the distance moved in the direction of the force. However, when a variable force is applied, the...
Newtonian Fluid: Problem Solving01:18

Newtonian Fluid: Problem Solving

Newtonian fluids exhibit a constant viscosity, meaning their shear stress and shear strain rate are directly proportional. This property ensures a predictable and stable response to applied forces, maintaining a linear relationship between force and flow. Examples include water, air, and light oils, consistently demonstrating this proportional behavior regardless of external conditions.
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Optical Coherence Tomography Based Biomechanical Fluid-Structure Interaction Analysis of Coronary Atherosclerosis Progression
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Escorted free energy simulations: improving convergence by reducing dissipation.

Suriyanarayanan Vaikuntanathan1, Christopher Jarzynski

  • 1Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USA.

Physical Review Letters
|June 4, 2008
PubMed
Summary

This study introduces a new method to improve free energy calculations in simulations by reducing dissipation. The technique uses an artificial flow field to guide systems along near-equilibrium paths, enhancing accuracy and convergence.

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Published on: January 15, 2022

Area of Science:

  • Computational chemistry
  • Statistical mechanics
  • Physical chemistry

Background:

  • Nonequilibrium methods for free energy calculations often suffer from poor convergence due to dissipative effects.
  • Accurate estimation of equilibrium free energy differences (ΔF) is crucial in various scientific domains.

Purpose of the Study:

  • To develop a novel method for improving the convergence and accuracy of free energy estimates in nonequilibrium simulations.
  • To address the challenge of dissipation in fast-switching simulations.

Main Methods:

  • Proposed a method involving an artificial flow field coupled to system coordinates and the external parameter.
  • Derived a new identity for ΔF based on trajectories generated with the artificial flow field.
  • Generated trajectories with reduced dissipation by effectively escorting the system along a near-equilibrium path.

Main Results:

  • The artificial flow field method was shown to reduce dissipation in simulations.
  • Near-equilibrium path generation led to efficient and accurate free energy estimates.
  • Demonstrated the method's effectiveness on a model system.

Conclusions:

  • The proposed method offers a significant improvement over traditional nonequilibrium techniques for free energy calculations.
  • The approach is generally applicable to various systems requiring accurate free energy determination.
  • Reduced dissipation is key to achieving reliable and efficient free energy estimates.