Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Sums of Power01:22

Sums of Power

In definite integration, Riemann sums approximate the area under a curve by dividing it into subintervals and summing the areas of rectangles. When these approximations follow predictable numerical patterns, such as arithmetic or polynomial sequences, sum formulas offer a more efficient and accurate way to compute the result. In particular, the sum of consecutive integers, squares, and cubes plays an essential role in simplifying these calculations, especially when dealing with uniform...
Dimensional Analysis03:40

Dimensional Analysis

Dimensional analysis, also known as the factor label method, is a versatile approach for mathematical operations. The main principle behind this approach is: the units of quantities must be subjected to the same mathematical operations as their associated numbers. This method can be applied to computations ranging from simple unit conversions to more complex and multi-step calculations involving several different quantities and their units.
Conversion Factors and Dimensional Analysis
The unit...
Dimensional Analysis01:27

Dimensional Analysis

Dimensional analysis is a valuable technique in fluid mechanics for simplifying complex problems by reducing them into dimensionless groups. These groups capture the essential relationships between the variables involved, allowing researchers and engineers to analyze fluid flow without dealing with each variable individually. This approach reduces the number of independent variables, allowing for easier analysis and better understanding of physical phenomena.
In fluid mechanics, dimensional...
Dimensional Analysis01:23

Dimensional Analysis

Dimensional analysis is a powerful tool that is used in physics and engineering to understand and predict the behavior of physical systems. The basic idea behind dimensional analysis is to express physical quantities in terms of fundamental dimensions such as the mass, length, and time. Derived dimensions like the velocity, acceleration, and force are derived from the combinations of these fundamental dimensions.
Dimensional analysis allows us to analyze and compare physical quantities on a...
Dimensional Analysis02:19

Dimensional Analysis

The concept of dimension is important because every mathematical equation linking physical quantities must be dimensionally consistent, implying that mathematical equations must meet the following two rules. The first rule is that, in an equation, the expressions on each side of the equal sign must have the same dimensions. This is fairly intuitive since we can only add or subtract quantities of the same type (dimension). The second rule states that, in an equation, the arguments of any of the...
Euler's Formula for Pin-Ended Columns01:21

Euler's Formula for Pin-Ended Columns

In structural engineering, the stability of columns under compressive axial loads is a critical consideration, described as buckling. A typical example involves a column PQ, which is pin-connected at both ends and subjected to a centric axial load F applied at one end, with a reaction force of F' = -F at the other end. Here, it is crucial to understand that when an applied load exceeds the critical load, buckling occurs as the system becomes unstable.
To calculate the critical load, envision...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Thermodynamics of a one-dimensional self-gravitating gas with periodic boundary conditions.

Physical review. E·2017
Same author

Path integral Monte Carlo on a lattice. II. Bound states.

Physical review. E·2016
Same author

Dynamics of Coulombic and gravitational periodic systems.

Physical review. E·2016
Same author

Cosmology in one dimension: Vlasov dynamics.

Physical review. E·2016
Same author

Regular and chaotic dynamics of a piecewise smooth bouncer.

Chaos (Woodbury, N.Y.)·2015
Same author

Chaotic dynamics of one-dimensional systems with periodic boundary conditions.

Physical review. E, Statistical, nonlinear, and soft matter physics·2015
Same journal

Tension on dsDNA bound to ssDNA-RecA filaments may play an important role in driving efficient and accurate homology recognition and strand exchange.

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Amplitude-phase coupling drives chimera states in globally coupled laser networks [Phys. Rev. E 91, 040901(R) (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Erratum: Shapes of sedimenting soft elastic capsules in a viscous fluid [Phys. Rev. E 92, 033003 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Erratum: Attenuation of excitation decay rate due to collective effect [Phys. Rev. E 90, 022142 (2014)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Role of connectivity and fluctuations in the nucleation of calcium waves in cardiac cells [Phys. Rev. E 92, 052715 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Lattice Boltzmann approach for complex nonequilibrium flows [Phys. Rev. E 92, 043308 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
See all related articles

Related Experiment Video

Updated: Jun 5, 2026

Analysis of SEC-SAXS data via EFA deconvolution and Scatter
10:59

Analysis of SEC-SAXS data via EFA deconvolution and Scatter

Published on: January 28, 2021

Ewald sums for one dimension.

Bruce N Miller1, Jean-Louis Rouet

  • 1Department of Physics and Astronomy, Texas Christian University, Fort Worth, Texas 76129, USA. b.miller@tcu.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 15, 2011
PubMed
Summary
This summary is machine-generated.

This study presents analytic solutions for one-dimensional systems, developing efficient simulation algorithms and exploring boundary condition effects on cosmic structure evolution. Results clarify differences in simulation approaches for periodic systems.

Related Experiment Videos

Last Updated: Jun 5, 2026

Analysis of SEC-SAXS data via EFA deconvolution and Scatter
10:59

Analysis of SEC-SAXS data via EFA deconvolution and Scatter

Published on: January 28, 2021

Area of Science:

  • Physics
  • Computational Physics
  • Cosmology

Background:

  • Periodic boundary conditions are crucial in simulating large systems.
  • Analytic solutions for one-dimensional systems are less explored than higher dimensions.
  • Ewald summation is a common technique for handling long-range interactions.

Purpose of the Study:

  • To derive analytic solutions for potential and field in 1D systems with periodic boundary conditions.
  • To develop efficient simulation algorithms for such systems.
  • To investigate the impact of different periodic boundary condition approaches on cosmological clustering evolution.

Main Methods:

  • Derivation of analytic solutions for potential and field.
  • Development of simulation tools and algorithms.
  • Comparison of two distinct periodic boundary condition implementations in cosmological simulations.

Main Results:

  • Analytic solutions for 1D Ewald sums were obtained.
  • An efficient simulation algorithm was constructed.
  • Two boundary condition approaches yielded similar clustering evolution until small cluster numbers, where boundary effects became significant.

Conclusions:

  • The derived analytic solutions and simulation methods offer valuable tools for 1D systems.
  • Understanding boundary condition influence is critical for accurate cosmological simulations, especially at late times.
  • This work clarifies discrepancies in previous studies related to periodic boundary conditions.