Related Experiment Video
Updated: Aug 10, 2026
08:04
Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
Published on: May 27, 2020
Exactly solvable model with an absorbing state and multiplicative colored Gaussian noise
S I Denisov1, Werner Horsthemke
1Department of Mechanics and Mathematics, Sumy State University, 2, Rimskiy-Korsakov Street, 40007 Sumy, Ukraine. denisov@ssu.sumy.ua
Summary
This study analyzes systems with absorbing states driven by state-dependent colored Gaussian noise. We derived exact expressions for probability densities and absorption times, revealing noise correlation
Area of Science:
- Complex systems dynamics
- Stochastic processes
- Statistical physics
Background:
- Systems with absorbing states are fundamental in many scientific fields.
- Understanding the dynamics of such systems under external noise is crucial.
- Colored Gaussian noise introduces temporal correlations that complicate system evolution.
Purpose of the Study:
- To investigate the temporal evolution of a system with an absorbing state driven by state-dependent colored Gaussian noise.
- To derive exact analytical expressions for system and absorption time probability density functions.
- To analyze the impact of noise correlation function properties on system behavior.
Main Methods:
- Derivation of exact analytical expressions for probability density functions.
- Calculation of numerical characteristics, including fractional moments and mean absorption time.
- Analysis of the system's behavior based on the functional form of the noise correlation function.
Main Results:
- Exact analytical expressions for the probability density functions of the system state and absorption time were obtained.
- Fractional moments of the system and the mean absorption time were calculated.
- The influence of the noise correlation function's form on system dynamics was analyzed.
Conclusions:
- The study provides a comprehensive analytical framework for understanding stochastic systems with absorbing states under colored noise.
- The derived expressions and analyses offer insights into the role of noise characteristics in system evolution and absorption phenomena.
- This work contributes to the theoretical understanding of complex systems driven by correlated noise.
Related Concept Videos
01:09Poisson Probability Distribution
A Poisson probability distribution is a discrete probability distribution. It gives the probability of a number of events occurring in a fixed interval of time or space if these events happen at a known average rate and independently of the time since the last event. For example, a book editor might be interested in the number of words spelled incorrectly in a particular book. It might be that, on average, there are five words spelled incorrectly in 100 pages. The interval is 100 pages.
The...
The...
01:25Poisson's And Laplace's Equation
The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.
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...
01:29Mathematical Modeling: Problem Solving
Mathematical modeling transforms real-world scenarios into mathematical expressions, allowing for structured problem-solving and analysis. This process involves defining the situation, assigning variables to measurable quantities, selecting an appropriate model, and solving the resulting equation. Such models are invaluable in finance, providing precise methods to evaluate investments, loans, and repayment structures.A widely used example is the calculation of fixed monthly payments on a loan,...
01:30Gaussian Elimination: Problem Solving
Systems of linear equations in several variables are pivotal in modeling complex scenarios involving multiple unknowns and constraints. Such systems are widely used in various fields to represent relationships where several conditions must be simultaneously satisfied. Each variable in the system corresponds to an unknown quantity, while each equation imposes a linear constraint, leading to a structured approach for analyzing and solving real-world problems.A system of three equations with three...
01:25Modeling with Differential Equations
Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...