Related Experiment Video
Updated: Jul 8, 2026
08:19
Asymmetric Walkway: A Novel Behavioral Assay for Studying Asymmetric Locomotion
Published on: January 15, 2016
A growth walk model for estimating the canonical partition function of interacting self-avoiding walk
S L Narasimhan1, P S R Krishna, M Ponmurugan
1Solid State Physics Division, Bhabha Atomic Research Centre, Mumbai 400085, India. slnoo@magnum.barc.gov.in
The Journal of Chemical Physics
|January 15, 2008
Summary
The canonical partition function of interacting self-avoiding walks (ISAW) is equivalent to interacting growth walk (IGW) averages. Temperature-dependent growth rules affect available configurations, impacting thermodynamic behavior analysis.
Area of Science:
- Statistical Mechanics
- Polymer Physics
- Computational Physics
Background:
- The canonical partition function is central to understanding thermodynamic properties.
- Interacting self-avoiding walks (ISAW) model complex systems.
- Growth walks offer an alternative perspective on ISAW.
Purpose of the Study:
- To demonstrate the exact equivalence between ISAW partition functions and interacting growth walk (IGW) configurational averages.
- To investigate the implications of temperature-dependent local growth rules on the partition function.
- To analyze the temperature dependence of IGW configurations.
Main Methods:
- Theoretical analysis of partition functions.
- Development of growth walk models.
- Monte Carlo simulations on a diamond lattice.
Main Results:
- Established the exact equivalence between ISAW and IGW under specific averaging conditions.
- Showed that the density of states cannot always be factored out when growth rules are temperature-dependent.
- Monte Carlo results revealed temperature-dependent IGW configurations.
Conclusions:
- The study provides a theoretical framework linking ISAW and IGW.
- Temperature-dependent growth rules introduce complexities in analyzing thermodynamic behavior.
- Despite configuration variations, IGW averages correctly predict ISAW thermodynamic properties.
Related Concept Videos
01:24One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation
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...
01:27Growth Models with Integration: Problem Solving
In population modeling, integration provides a systematic way to determine accumulated quantities from known rates of change. One such application arises in ecology, where the total weight of a fish population in a body of water is referred to as its biomass. When the rate of growth of this biomass is known as a function of time, calculus can be used to determine the total biomass at a future date.Growth Rate and Biomass FunctionLet the growth rate of the fish population be represented by a...
01:14Multicompartment Models: Overview
Multicompartment models are mathematical constructs that depict how drugs are distributed and eliminated within the body. They segment the body into several compartments, symbolizing various physiological or anatomical areas connected through drug transfer processes such as absorption, metabolism, distribution, and elimination.
These models offer a more comprehensive representation of drug behavior in the body than one-compartment models. They accommodate the complexity of drug distribution,...
These models offer a more comprehensive representation of drug behavior in the body than one-compartment models. They accommodate the complexity of drug distribution,...
01:29Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving
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...
01:26Exponential Equations for Modeling Growth
Exponential models are essential for describing rapid, multiplicative changes in natural systems, such as population growth. When a population doubles at regular intervals, the process can be modeled using a suitable base. For instance, a bacterial culture that doubles every three hours follows the model n(t)=n0⋅2t/3, where n(t) is the population at the time t.A more general model uses the natural base e, especially for continuous growth. This takes the form n(t)=n0⋅ert, where r is the relative...
01:14Compartment Models: Single-Compartment Model
The single-compartment model serves as a simplified representation of the human body. This model assumes that the body functions as a single, well-mixed open compartment. When a drug is administered intravenously, it enters the body and quickly distributes uniformly. The drug then undergoes biotransformation and elimination, ultimately leaving the body. The volume of this compartment is referred to as the apparent volume of distribution into which the drug can uniformly distribute. In this...