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

Crystallographic Point Groups01:29

Crystallographic Point Groups

Crystallographic point groups represent the various symmetry operations that can occur within crystals. They are unique in that at least one point will always remain unchanged during these actions. For instance, consider the triclinic system. This system, devoid of any axis or plane of symmetry, aligns with the C1 and Ci point groups.where Cᵢ is characterized solely by a center of inversion.Contrastingly, the monoclinic system introduces an element of symmetry. This system with one plane and...
Lattice Energies of Ionic Crystals01:27

Lattice Energies of Ionic Crystals

Lattice energy represents the energy released when gaseous cations and anions combine to form an ionic solid, reflecting the strength of electrostatic interactions within the crystal. This process is fundamentally governed by Coulombic attraction between oppositely charged ions, where the potential energy varies inversely with the interionic distance and directly with the product of ionic charges. As ions approach one another, the electrostatic energy becomes increasingly negative, indicating a...
The Seven Crystal Systems: Overview01:24

The Seven Crystal Systems: Overview

Crystals with various point group symmetries belong to different crystal classes, which are synonymous terms. Despite being in the same class, crystals may have distinct shapes, like cubes and octahedra. There are 32 three-dimensional point groups, all of which are systematically divided into seven crystal systems.The basic cubic crystal system, exemplified by NaCl, features orthogonal vectors (α = β = �� = 90°) of equal lengths (a = b = c). When specific requirements are not imposed on the...
Trends in Lattice Energy: Ion Size and Charge02:54

Trends in Lattice Energy: Ion Size and Charge

An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure of the strength of this attraction. The lattice energy (ΔHlattice) of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid sodium chloride, the lattice energy is the enthalpy change of the process:
Symmetry Elements in a Crystal01:27

Symmetry Elements in a Crystal

Crystal symmetry operations are isometric transformations that map objects onto indistinguishable copies while preserving distances, angles, and volumes. The simplest symmetry operation is translation, which shifts the entire infinite crystal lattice parallelly by a translation vector.Crystallographic rotations involve rotations by an angle of 2π/n around an axis without changing the positions of points on the axis. It is called the rotational axis of the symmetry, denoted by n. The combination...
Determination of Crystal Structures01:29

Determination of Crystal Structures

In the late 1800s, the revelation that light extended beyond visible wavelengths led to the discovery of X-rays by Wilhelm Roentgen. Recognized as high-energy electromagnetic radiation with short wavelengths, X-rays prompted exploration into their interaction with crystals. Max von Laue proposed in 1912 that the periodic arrangement of atoms, ions, or molecules in crystals would cause them to diffract X-rays, a hypothesis confirmed through experiments with copper sulfate and zinc sulfide...

You might also read

Related Articles

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

Sort by
Same author

Thick-panel origami structures forming seamless surfaces.

Nature communications·2025
Same author

Group-theoretic analysis of symmetry-preserving deployable structures and metamaterials.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2024
Same author

Rate of Entropy Production in Stochastic Mechanical Systems.

Entropy (Basel, Switzerland)·2022
Same author

A Mosquito Pick-and-Place System for PfSPZ-based Malaria Vaccine Production.

IEEE transactions on automation science and engineering : a publication of the IEEE Robotics and Automation Society·2021
Same author

Continuous body 3-D reconstruction of limbless animals.

The Journal of experimental biology·2021
Same author

Black-Scholes Theory and Diffusion Processes on the Cotangent Bundle of the Affine Group.

Entropy (Basel, Switzerland)·2020

Related Experiment Video

Updated: Jul 11, 2026

Microfluidic Chips for In Situ Crystal X-ray Diffraction and In Situ Dynamic Light Scattering for Serial Crystallography
11:48

Microfluidic Chips for In Situ Crystal X-ray Diffraction and In Situ Dynamic Light Scattering for Serial Crystallography

Published on: April 24, 2018

Torsional random walk statistics on lattices using convolution on crystallographic motion groups.

Aris Skliros1, Gregory S Chirikjian

  • 1A. Skliros is with the Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA,

Polymer
|September 28, 2007
PubMed
Summary

A new algorithm efficiently generates lattice polymer conformational statistics by convolving pose distributions of chain segments. This method drastically reduces computational complexity compared to brute-force enumeration for polymer modeling.

More Related Videos

Derivatization of Protein Crystals with I3C using Random Microseed Matrix Screening
14:04

Derivatization of Protein Crystals with I3C using Random Microseed Matrix Screening

Published on: January 16, 2021

Picometer-Precision Atomic Position Tracking through Electron Microscopy
15:04

Picometer-Precision Atomic Position Tracking through Electron Microscopy

Published on: July 3, 2021

Related Experiment Videos

Last Updated: Jul 11, 2026

Microfluidic Chips for In Situ Crystal X-ray Diffraction and In Situ Dynamic Light Scattering for Serial Crystallography
11:48

Microfluidic Chips for In Situ Crystal X-ray Diffraction and In Situ Dynamic Light Scattering for Serial Crystallography

Published on: April 24, 2018

Derivatization of Protein Crystals with I3C using Random Microseed Matrix Screening
14:04

Derivatization of Protein Crystals with I3C using Random Microseed Matrix Screening

Published on: January 16, 2021

Picometer-Precision Atomic Position Tracking through Electron Microscopy
15:04

Picometer-Precision Atomic Position Tracking through Electron Microscopy

Published on: July 3, 2021

Area of Science:

  • Computational physics
  • Polymer science
  • Statistical mechanics

Background:

  • Lattice polymer models are crucial for understanding polymer behavior.
  • Generating conformational statistics for these models is computationally intensive.
  • Existing methods often rely on brute-force enumeration, leading to exponential complexity.

Purpose of the Study:

  • To develop a novel, efficient algorithm for computing conformational statistics of lattice polymer models.
  • To overcome the computational limitations of existing methods for polymer conformation generation.
  • To provide a framework for analyzing polymer behavior in various lattice structures.

Main Methods:

  • The algorithm divides polymer chains into segments and performs generalized convolutions of pose distribution functions.
  • Convolutions are computed with respect to the crystallographic space group of the lattice.
  • The method incorporates excluded volumes and pairwise conformational energies for realistic simulations.

Main Results:

  • The algorithm achieves polynomial time complexity, O(n^(D+1)), for generating conformational statistics in D-dimensions.
  • For 3D lattices, including conformational energy effects, the complexity is O(z^4n^4).
  • This represents a significant improvement over the exponential complexity of brute-force methods.

Conclusions:

  • The developed algorithm offers a computationally efficient approach to lattice polymer conformational analysis.
  • It enables easier calculation of end-to-end distance distributions and average radius of gyration.
  • The method is demonstrated on various lattice types, showcasing its versatility.