Related Experiment Video
Updated: Feb 19, 2026
11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
9.1K
Fast and slow thermal processes in harmonic scalar lattices.
V A Kuzkin1,2, A M Krivtsov1,2
1Peter the Great Saint Petersburg Polytechnical University, Polytechnicheskaya st. 29, Saint Petersburg, Russia.
Summary
This study presents an analytical method to describe thermal processes in scalar lattices. It reveals that temperature evolution involves fast, high-frequency oscillations and slow, ballistic heat transfer.
Area of Science:
- Condensed matter physics
- Statistical mechanics
- Solid-state physics
Background:
- Understanding thermal transport in crystalline solids is crucial for materials science and nanotechnology.
- Lattice dynamics governs heat propagation, but analytical solutions for complex lattice interactions are challenging.
Purpose of the Study:
- To develop an analytical approach for describing thermal processes in harmonic scalar lattices.
- To investigate the evolution of the initial temperature field in infinite lattices.
- To derive and solve the continuum equation governing temperature evolution.
Main Methods:
- Analytical description of longitudinal, transverse, and out-of-plane vibrations in 1D and 2D lattices.
- Derivation of an exact evolution equation for the temperature field.
- Continualization of the lattice equation to a continuum form.
- Analytical solution of the continuum equation.
Main Results:
- The kinetic temperature is a sum of short-time (fast) and large-time (slow) components.
- Fast process: High-frequency oscillations due to energy redistribution (kinetic/potential).
- Slow process: Ballistic heat transfer, with temperature fields propagating as waves.
Conclusions:
- The derived analytical solution accurately describes both fast and slow thermal processes.
- The theory provides insights into irreversible thermal behavior in lattices.
- Numerical simulations confirm the accuracy of the analytical model for temperature field evolution.
Related Concept Videos
01:28Atomic Nuclei: Types of Nuclear Relaxation
1.0K
Nuclear relaxation restores the equilibrium population imbalance and can occur via spin–lattice or spin–spin mechanisms, which are first-order exponential decay processes.
In spin–lattice or longitudinal relaxation, the excited spins exchange energy with the surrounding lattice as they return to the lower energy level. Among several mechanisms that contribute to spin–lattice relaxation, magnetic dipolar interactions are significant. Here, the excited nucleus transfers...
In spin–lattice or longitudinal relaxation, the excited spins exchange energy with the surrounding lattice as they return to the lower energy level. Among several mechanisms that contribute to spin–lattice relaxation, magnetic dipolar interactions are significant. Here, the excited nucleus transfers...
1.0K
02:54Trends in Lattice Energy: Ion Size and Charge
26.8K
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:
26.8K
01:16Thermal Sigmatropic Reactions: Overview
2.6K
Sigmatropic rearrangements are a class of pericyclic reactions in which a σ bond migrates from one part of a π system to another. These are intramolecular rearrangements where the total number of σ and π bonds remain unchanged.
Sigmatropic shifts are classified based on an order term [i, j ], where i and j indicate the number of atoms across which each end of the σ bond migrates. Below are examples of a [3,3] sigmatropic shift in 1,5-hexadiene, referred...
Sigmatropic shifts are classified based on an order term [i, j ], where i and j indicate the number of atoms across which each end of the σ bond migrates. Below are examples of a [3,3] sigmatropic shift in 1,5-hexadiene, referred...
2.6K
01:28Standing Waves in a Cavity
1.5K
A household microwave and lasers are examples of standing electromagnetic waves in a cavity. When two conducting metal plates are placed parallel at the nodal planes, it creates a cavity where standing waves are formed. The cavity between the two planes is analogous to a stretched string held at the points x = 0 and x = L. Here, the distance 'L' between the two planes must be an integer multiple of half of the wavelength. The wavelengths that satisfy this condition are given by:
1.5K
01:23Atomic Nuclei: Nuclear Relaxation Processes
1.3K
In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis, the precessing magnetic moments are randomly oriented around the z-axis.
1.3K
01:14Atomic Nuclei: Nuclear Spin State Population Distribution
2.4K
Near absolute zero temperatures, in the presence of a magnetic field, the majority of nuclei prefer the lower energy spin-up state to the higher energy spin-down state. As temperatures increase, the energy from thermal collisions distributes the spins more equally between the two states. The Boltzmann distribution equation gives the ratio of the number of spins predicted in the spin −½ (N−) and spin +½ (N+) states.
2.4K