Related Experiment Video
Updated: Dec 27, 2025
08:55
Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
Published on: June 7, 2018
8.8K
Microcanonical coarse-graining of the kinetic Ising model
Daniel Sigg1, Vincent A Voelz2, Vincenzo Carnevale3
1dPET, Spokane, Washington 99223, USA.
The Journal of Chemical Physics
|March 2, 2020
Summary
We developed a coarse-graining method for the Ising model, improving rate constant accuracy by analyzing barrier fluctuations. This spectral analysis corrects errors from dynamical memory loss in microcanonical projections.
Area of Science:
- Statistical Mechanics
- Computational Physics
Background:
- Ising lattices exhibit complex dynamics with free energy barriers.
- Coarse-graining simplifies these dynamics but can introduce errors.
Purpose of the Study:
- To develop and validate a coarse-graining scheme for the 2-D kinetic Ising model using the microcanonical ensemble.
- To accurately compute rate constants for barrier crossing.
Main Methods:
- Projecting Ising model dynamics onto the microcanonical ensemble.
- Computing forward rate constants using Monte Carlo simulations.
- Applying spectral decomposition of the diffusion coefficient to correct for memory effects.
Main Results:
- Coarse-graining without correction resulted in rate constants 50% larger than true values due to lost dynamical memory.
- Spectral analysis successfully corrected the rate constants in 2-D and 3-D Ising lattices.
- Error in 3-D Ising lattice was reduced to 6%.
Conclusions:
- Microcanonical coarse-graining combined with spectral analysis accurately describes barrier crossing dynamics.
- This method is effective for both 2-D and 3-D Ising models, even with diminished memory effects.
Related Concept Videos
01:24One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation
1.0K
This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
On...
On...
1.0K
01:29Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving
234
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
234
01:12Kinetic Theory of an Ideal Gas
4.5K
A mole is defined as the amount of any substance that contains as many molecules as there are atoms in exactly 12 grams of carbon-12. An Italian scientist Amedeo Avogadro (1776–1856) formed the hypothesis that equal volumes of gas at equal pressure and temperature contain equal numbers of molecules, independent of the type of gas. Later, the hypothesis was developed to form the SI unit for measuring the amount of any substance.
The number of molecules in one mole is called...
The number of molecules in one mole is called...
4.5K
02:43Basic Postulates of Kinetic Molecular Theory: Particle Size, Energy, and Collision
37.2K
The ideal-gas equation, which is empirical, describes the behavior of gases by establishing relationships between their macroscopic properties. For example, Charles’ law states that volume and temperature are directly related. Gases, therefore, expand when heated at constant pressure. Although gas laws explain how the macroscopic properties change relative to one another, it does not explain the rationale behind it.
37.2K
02:54Trends in Lattice Energy: Ion Size and Charge
26.3K
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:
26.3K
01:21Mechanistic Models: Overview of Compartment Models
299
Mechanistic models, a category encompassing both physiological and compartmental modeling, differ from empirical models' approaches to incorporating known factors about the systems being modeled. Empirical models describe data with minimal assumptions, while mechanistic models aim to provide a robust description of available data by specifying assumptions and integrating known factors about the system. Compartmental analysis is a key example of a mechanistic model in pharmacokinetics and...
299