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Related Concept Videos

Electrostatic Boundary Conditions01:16

Electrostatic Boundary Conditions

Consider an external electric field propagating through a homogeneous medium. When the electric field crosses the surface boundary of the medium, it undergoes a discontinuity. The electric field can be resolved into normal and tangential components. The amount by which the field changes at any boundary is given by the difference between the field components above and below the surface boundary.
The surface integral of an electric field is given by Gauss's law in integral form and is related to...
Force and Potential Energy in One Dimension01:13

Force and Potential Energy in One Dimension

Force can be calculated from the expression for potential energy, which is a function of position. The component of a conservative force, in a particular direction, equals the negative of the derivative of the corresponding potential energy with respect to the displacement in that direction. For regions where potential energy changes rapidly with displacement, the work done and force is maximum. Also, when force is applied along the positive coordinate axis, the potential energy decreases with...
Continuous Charge Distributions01:17

Continuous Charge Distributions

Imagine a bucket of water. It contains many molecules, of the order of 1026 molecules. Thus, although it contains discrete elements (molecules) at the microscopic level, macroscopically, it can be considered continuous. Small volume elements of water, infinitesimal compared to the bulk of the bucket's volume, still contain many molecules. Under this framework, quantized matter is approximated as continuous for practical purposes.
The electric charge can also be subjected to an analogical...
Improper Integrals: Discontinuous Integrands01:28

Improper Integrals: Discontinuous Integrands

Evaluating Areas Under Curves with DiscontinuitiesA definite integral is considered improper when the integrand is discontinuous at one of the limits of integration. This occurs when the function is undefined or becomes infinite at an endpoint, making the corresponding region under the curve unbounded. Such behavior is commonly associated with vertical asymptotes at the boundary of the interval. To properly define and evaluate these integrals, a limiting process is used to determine whether a...
Magnetostatic Boundary Conditions01:28

Magnetostatic Boundary Conditions

An electric field suffers a discontinuity at a surface charge. Similarly, a magnetic field is discontinuous at a surface current. The perpendicular component of a magnetic field is continuous across the interface of two magnetic mediums. In contrast, its parallel component, perpendicular to the current, is discontinuous by the amount equal to the product of the vacuum permeability and the surface current. Like the scalar potential in electrostatics, the vector potential is also continuous...
Limits with Oscillating Discontinuities01:19

Limits with Oscillating Discontinuities

An oscillating discontinuity is a type of discontinuity in which a function’s values fluctuate infinitely often as the input approaches a particular point. Unlike jump discontinuities, where the function suddenly shifts between two values, or infinite discontinuities, where the function diverges without bound, an oscillating discontinuity arises from rapid back-and-forth variation. Because the function never stabilizes toward a single value, no finite limit exists at that point.One of the most...

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Related Experiment Video

Updated: May 10, 2026

Finite Element Modelling of a Cellular Electric Microenvironment
08:23

Finite Element Modelling of a Cellular Electric Microenvironment

Published on: May 18, 2021

Constant-force approach to discontinuous potentials.

Pedro Orea1, Gerardo Odriozola

  • 1Programa de Ingeniería Molecular, Instituto Mexicano del Petróleo, Eje Central Lázaro Cárdenas 152, 07730 México D.F., Mexico.

The Journal of Chemical Physics
|June 14, 2013
PubMed
Summary
This summary is machine-generated.

We introduce a constant repulsive force method to simulate hard-core systems using molecular dynamics. This approach accurately predicts thermodynamic properties like vapor-liquid coexistence and surface tension.

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Area of Science:

  • Thermodynamics
  • Computational Physics
  • Materials Science

Background:

  • Standard molecular dynamics simulations struggle to accurately model hard-core systems due to discontinuous potentials.
  • Accurate simulation of hard-core systems is crucial for understanding material properties.

Purpose of the Study:

  • To develop a novel method for simulating thermodynamical properties of hard-core systems using molecular dynamics.
  • To replace discontinuous pair potentials with a continuous, repulsive constant-force function.

Main Methods:

  • A repulsive constant-force method was implemented, replacing the discontinuity of pair potentials with a linear function.
  • The method was tested on a triangle potential of short range.
  • Replica exchange molecular dynamics (REMD) simulations were performed and compared with discontinuous potentials and replica exchange Monte Carlo (REMC).

Main Results:

  • The proposed method successfully models quasi-hard-core behavior.
  • Remarkable agreement was found between the constant-force method and discontinuous potentials for vapor-liquid coexistence densities.
  • The surface tension results also showed excellent agreement.

Conclusions:

  • The repulsive constant-force method is a viable and accurate approach for simulating thermodynamical properties of hard-core systems.
  • This method offers a practical alternative for standard molecular dynamics simulations of such systems.