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Related Concept Videos

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...
Non-conservative Forces01:17

Non-conservative Forces

Non-conservative forces are dissipative forces such as friction or air resistance. These forces take energy away from a system as it progresses. Unlike conservative forces, non-conservative forces do not have potential energy associated with them. This is because the energy is lost to the system and cannot be turned into useful work later.
Also unlike their conservative counterparts, they are path-dependent; where the object starts and stops does matter. For example, a grinding wheel applies a...
Simplification of a Force and Couple System: II01:23

Simplification of a Force and Couple System: II

In a three-dimensional system, multiple forces can act on an object. These forces can be combined into a single equivalent force, known as the resultant force. Similarly, the moments generated by these forces can be combined into a single equivalent moment, the resultant couple moment. In certain situations, these two entities may not be mutually perpendicular, meaning they do not have a 90-degree angle between them. This unique condition requires a deeper understanding of the interplay between...
Central-Force Motion01:17

Central-Force Motion

The central force system operates by exerting a force on an object directed towards a fixed point, typically the origin, with the force magnitude determined by the object's distance from this fixed point. In the context of an object with mass 'm,' polar coordinates are employed to express the equation of motion. Notably, the azimuthal component of force is nonexistent in this system. A comprehensive rewrite and integration of this equation reveal that the product of the squared radial distance...
Simplification of a Force and Couple System I01:18

Simplification of a Force and Couple System I

The concept of reducing a system of forces and couple moments to an equivalent system is essential in simplifying the analysis of rigid bodies. This reduction allows for more straightforward computation and understanding of the external effects produced by the system. In particular, systems with an equivalent resultant force and a resultant couple moment having perpendicular lines of action can be further reduced to a single equivalent resultant force acting along a new line of action. There...
Two-Dimensional Force System01:20

Two-Dimensional Force System

A two-dimensional system in mechanical engineering involves the analysis of motion and forces in a plane. A two-dimensional force vector can be resolved into its components as:

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Related Experiment Video

Updated: Jul 8, 2026

Realistic Membrane Modeling Using Complex Lipid Mixtures in Simulation Studies
07:31

Realistic Membrane Modeling Using Complex Lipid Mixtures in Simulation Studies

Published on: September 1, 2023

A Force-Kernel Reformulation of the Extended-System Adaptive Biasing Force for Free-Energy Calculations.

Christopher Kang1, Rahul Verma1, Aditya Sonpal1

  • 1Department of Chemical and Biomolecular Engineering, North Carolina State University, Raleigh, North Carolina 27695, United States.

Journal of Chemical Theory and Computation
|July 7, 2026
PubMed
Summary
This summary is machine-generated.

We developed force-kernel extended-system adaptive biasing force (FK-eABF), a novel method for molecular simulations. FK-eABF accelerates free-energy landscape exploration and achieves accurate results faster than existing techniques.

Related Experiment Videos

Last Updated: Jul 8, 2026

Realistic Membrane Modeling Using Complex Lipid Mixtures in Simulation Studies
07:31

Realistic Membrane Modeling Using Complex Lipid Mixtures in Simulation Studies

Published on: September 1, 2023

Area of Science:

  • Computational Chemistry
  • Molecular Dynamics
  • Biophysics

Background:

  • Enhanced sampling methods are crucial for molecular simulations.
  • Conventional methods like eABF rely on histogram-based accumulators, which can be slow to converge.
  • There is a need for methods that provide faster convergence and accurate free-energy landscapes.

Purpose of the Study:

  • Introduce force-kernel extended-system adaptive biasing force (FK-eABF), a novel force-based kernel reformulation of eABF.
  • To demonstrate FK-eABF's efficiency and accuracy in molecular simulations.
  • To compare FK-eABF performance against established enhanced sampling techniques.

Main Methods:

  • Developed FK-eABF, replacing histogram-based mean-force accumulation with Gaussian kernels and Nadaraya-Watson regression.
  • Implemented an auxiliary, self-attenuating exploration force derived from the same kernel population.
  • Benchmarked FK-eABF on N-acetyl-N'-methylalanylamide, Abl1 kinase transitions, and 1,3-butadiene electrocyclic ring closure.

Main Results:

  • FK-eABF achieved faster free-energy landscape coverage compared to WT-MetaD, OPES, and WTM-eABF for N-acetyl-N'-methylalanylamide.
  • The method demonstrated long-time accuracy, accurately reproducing the near-isoenergetic balance for Abl1 kinase transitions.
  • FK-eABF recovered the free-energy landscape for 1,3-butadiene within 30 ps at the ab initio molecular dynamics level.

Conclusions:

  • FK-eABF offers faster early-time convergence in molecular simulations.
  • The method maintains quantitative accuracy over long simulation times.
  • FK-eABF represents a significant advancement in enhanced sampling techniques for computational chemistry.