Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Metallic Solids

Metallic Solids

Metallic solids such as crystals of copper, aluminum, and iron are formed by metal atoms. The structure of metallic crystals is often described as a uniform distribution of atomic nuclei within a “sea” of delocalized electrons. The atoms within such a metallic solid are held together by a unique force known as metallic bonding that gives rise to many useful and varied bulk properties.
All metallic solids exhibit high thermal and electrical conductivity, metallic luster, and malleability. Many...

Lattice Centering and Coordination Number

Lattice Centering and Coordination Number

The structure of a crystalline solid, whether a metal or not, is best described by considering its simplest repeating unit, which is referred to as its unit cell. The unit cell consists of lattice points that represent the locations of atoms or ions. The entire structure then consists of this unit cell repeating in three dimensions. The three different types of unit cells present in the cubic lattice are illustrated in Figure 1.
Types of Unit Cells
Imagine taking a large number of identical...

Bewley Lattice Diagram

Bewley Lattice Diagram

The Bewley lattice diagram, developed by L. V. Bewley, effectively organizes the reflections occurring during transmission-line transients. It visually represents how voltage waves propagate and reflect within a transmission line, making it easier to understand the complex interactions that occur.

Lattice Energies of Ionic Crystals

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...

Properties of Laplace Transform-II

Properties of Laplace Transform-II

Time differentiation, convolution, integration, and periodicity are fundamental concepts in analyzing functions and signals over time. Each concept provides a unique perspective on how functions evolve, interact, and repeat, offering essential tools for various scientific and engineering applications.
Time differentiation involves analyzing the rate of change of a function over time. Mathematically, it is the derivative of a function with respect to time. This concept can be likened to tracking...

Structures of Solids

Structures of Solids

Solids in which the atoms, ions, or molecules are arranged in a definite repeating pattern are known as crystalline solids. Metals and ionic compounds typically form ordered, crystalline solids. A crystalline solid has a precise melting temperature because each atom or molecule of the same type is held in place with the same forces or energy. Amorphous solids or non-crystalline solids (or, sometimes, glasses) which lack an ordered internal structure and are randomly arranged. Substances that...

You might also read

Related Articles

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

Sort by

Same author

Cluster percolation and dynamical scaling in the Baxter-Wu model.

Physical review. E·2026

Same author

Partition Function Zeros of the Frustrated <i>J</i><sub>1</sub>-<i>J</i><sub>2</sub> Ising Model on the Honeycomb Lattice.

Entropy (Basel, Switzerland)·2024

Same author

Universal Fragility of Spin Glass Ground States under Single Bond Changes.

Physical review letters·2024

Same author

Thermodynamic properties of quasi-one-dimensional fluids.

The Journal of chemical physics·2024

Same author

Resampling schemes in population annealing: Numerical and theoretical results.

Physical review. E·2024

Same author

Geometric clusters in the overlap of the Ising model.

Physical review. E·2023

Same journal

Erratum: Spectroscopy and Ground-State Transfer of Ultracold Bosonic ^{39}K^{133}Cs Molecules [Phys. Rev. Lett. 135, 203401 (2025)].

Physical review letters·2026

Same journal

Erratum: Lifetime of the ^{2}F_{7/2} Level in Yb^{+} for Spontaneous Emission of Electric Octupole Radiation [Phys. Rev. Lett. 127, 213001 (2021)].

Physical review letters·2026

Same journal

Laser-Plasma Based Seeded Free Electron Laser in the High-Gain Regime.

Physical review letters·2026

Same journal

Parent Hamiltonians for Stabilizer Quantum Many-Body Scars.

Physical review letters·2026

Same journal

Properties of Heavy Cosmic Nuclei Phosphorus, Chlorine, Argon, Potassium, and Calcium: Results from the Alpha Magnetic Spectrometer.

Physical review letters·2026

Same journal

Role of Spin-Isospin Symmetries in Nuclear β-Decays.

Physical review letters·2026

See all related articles

Search research articles

Related Experiment Video

Updated: May 26, 2026

Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials

Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials

Published on: September 26, 2014

Regular packings on periodic lattices.

Tadeus Ras¹, Rolf Schilling, Martin Weigel

¹Institut für Physik, Johannes Gutenberg-Universität Mainz, Germany.

Physical Review Letters

|December 21, 2011

Summary

This summary is machine-generated.

This study explores dense packing of identical objects on lattices, calculating maximum packing fractions for various shapes and dimensions. Results reveal continuous packing fractions with infinite singular points, offering insights into geometrical frustration.

More Related Videos

Rapid in-silico Battery Electrolyte Electrochemical Reaction Generation using 3T-VASP Multi-Scale Energy Minimization

Rapid in-silico Battery Electrolyte Electrochemical Reaction Generation using 3T-VASP Multi-Scale Energy Minimization

Published on: August 22, 2025

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Related Experiment Videos

Last Updated: May 26, 2026

Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials

Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials

Published on: September 26, 2014

Rapid in-silico Battery Electrolyte Electrochemical Reaction Generation using 3T-VASP Multi-Scale Energy Minimization

Rapid in-silico Battery Electrolyte Electrochemical Reaction Generation using 3T-VASP Multi-Scale Energy Minimization

Published on: August 22, 2025

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Area of Science:

Physics
Materials Science
Geometry

Background:

Understanding how objects pack efficiently is crucial in materials science and physics.
Regular lattices provide a fundamental framework for studying packing phenomena.

Purpose of the Study:

To investigate the densest packing of identical hard objects on regular lattices in d dimensions.
To calculate the maximum packing fraction (φ(d)(X)) for specific shapes (rectangles, ellipses, biaxial ellipsoids) at a given aspect ratio (X).

Main Methods:

Restricting object configurations to parallel alignment.
Calculating the maximum packing fraction for objects on square and simple cubic lattices.
Analyzing the continuity and singular points of the packing fraction function.

Main Results:

The maximum packing fraction φ(d)(X) is continuous with an infinite number of singular points.
In 2D, all maxima have equal height; for ellipsoids, a unique global maximum exists.
The packing fraction's form relates to geometrical frustration, contact number transitions, and number theory.

Conclusions:

The study provides a detailed analysis of dense packing for specific objects and lattice types.
Findings offer insights into geometrical frustration and number-theoretical aspects of packing.
The framework can be extended to more general packing problems.