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

Second Derivatives and Laplace Operator

Second Derivatives and Laplace Operator

The first order operators using the del operator include the gradient, divergence and curl. Certain combinations of first order operators on a scalar or vector function yield second order expressions. Second-order expressions play a very important role in mathematics and physics. Some second order expressions include the divergence and curl of a gradient function, the divergence and curl of a curl function, and the gradient of a divergence function.
Consider a scalar function. The curl of its...

Entropy Change in Reversible Processes

Entropy Change in Reversible Processes

In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.

Poisson's And Laplace's Equation

Poisson'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.

Region of Convergence of Laplace Tarnsform

Region of Convergence of Laplace Tarnsform

The Region of Convergence (ROC) is a fundamental concept in signal processing and system analysis, particularly associated with the Laplace transform. The ROC represents an area in the complex plane where the Laplace transform of a given signal converges, determining the transform's applicability and utility.
Consider a decaying exponential signal that begins at a specific time. When deriving its Laplace transform, the time-domain variable is replaced with a complex variable. This...

Propagation of Uncertainty from Random Error

Propagation of Uncertainty from Random Error

An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...

Linear Approximation in Time Domain

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...

You might also read

Related Articles

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

Sort by

Same author

Weak solutions to gradient flows of functionals with inhomogeneous growth in metric spaces.

Journal of evolution equations·2025

Same author

The trace space of anisotropic least gradient functions depends on the anisotropy.

Mathematische annalen·2023

Same journal

Automorphisms of relatively hyperbolic groups and the Farrell-Jones conjecture.

Mathematische annalen·2026

Same journal

Groups acting on trees with Tits' independence property (P): With an appendix by Stephan Tornier.

Mathematische annalen·2026

Same journal

A note on integrated local energy decay estimates for spherically symmetric black hole spacetimes.

Mathematische annalen·2026

Same journal

Higher-order regularity for a structurally damped plate equation on rough domains.

Mathematische annalen·2026

Same journal

The shifted convolution problem in function fields.

Mathematische annalen·2026

Same journal

<math><mi>b</mi></math> -Hurwitz numbers from refined topological recursion.

Mathematische annalen·2026

See all related articles

Search research articles

Related Experiment Video

Updated: Sep 13, 2025

Following the Dynamics of Structural Variants in Experimentally Evolved Populations

Following the Dynamics of Structural Variants in Experimentally Evolved Populations

Published on: February 3, 2023

Evolution problems with perturbed 1-Laplacian type operators on random walk spaces.

W Górny^1,2, J M Mazón³, J Toledo³

¹Faculty of Mathematics, Universität Wien, Oskar-Morgerstern-Platz 1, 1090 Vienna, Austria.

Mathematische Annalen

|August 4, 2025

Summary

This summary is machine-generated.

This study explores evolution problems on random walk spaces with multiple structures. It analyzes functionals with varying growth rates across different random walk components and partitions.

More Related Videos

WheelCon: A Wheel Control-Based Gaming Platform for Studying Human Sensorimotor Control

WheelCon: A Wheel Control-Based Gaming Platform for Studying Human Sensorimotor Control

Published on: August 15, 2020

$Fourier-Based Diffraction Analysis of Live Caenorhabditis elegans$

Fourier-Based Diffraction Analysis of Live Caenorhabditis elegans

Published on: September 13, 2017

Related Experiment Videos

Last Updated: Sep 13, 2025

Following the Dynamics of Structural Variants in Experimentally Evolved Populations

Following the Dynamics of Structural Variants in Experimentally Evolved Populations

Published on: February 3, 2023

WheelCon: A Wheel Control-Based Gaming Platform for Studying Human Sensorimotor Control

WheelCon: A Wheel Control-Based Gaming Platform for Studying Human Sensorimotor Control

Published on: August 15, 2020

$Fourier-Based Diffraction Analysis of Live Caenorhabditis elegans$

Fourier-Based Diffraction Analysis of Live Caenorhabditis elegans

Published on: September 13, 2017

Area of Science:

Partial Differential Equations (PDEs)
Stochastic Processes
Mathematical Analysis

Background:

Random walk spaces provide a versatile framework for studying PDEs.
These spaces encompass discrete settings like weighted graphs and continuous nonlocal scenarios with kernels on R^N.
Existing research often focuses on single random walk structures.

Purpose of the Study:

To investigate evolution problems on random walk spaces featuring two distinct random walk structures.
To analyze the behavior of associated functionals exhibiting different growth properties on each structure.
To examine functionals with varied growth rates across a partitioned random walk space.

Main Methods:

Development of a theoretical framework for analyzing evolution problems on composite random walk spaces.
Application of functional analysis techniques to study growth properties of functionals.
Mathematical modeling of systems with multiple interacting random walk dynamics.

Main Results:

Established conditions for the well-posedness of evolution problems with dual random walk structures.
Characterized the impact of differing functional growth rates on solution behavior.
Demonstrated how partitioning a random walk affects functional analysis.

Conclusions:

The framework effectively handles complex evolution problems on multi-structured random walks.
Understanding functional growth variations is crucial for analyzing PDEs in these settings.
This research extends the applicability of random walk theory to more intricate mathematical models.