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Fabrication and Characterization of Disordered Polymer Optical Fibers for Transverse Anderson Localization of Light

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Straight Disclinations in Fractional Nonlocal Medium.

Tamara Kyrylych¹, Yuriy Povstenko¹

¹Department of Mathematics and Computer Science, Faculty of Science and Technology, Jan Dlugosz University in Czestochowa, al. Armii Krajowej 13/15, 42-200 Czestochowa, Poland.

Materials (Basel, Switzerland)

|May 7, 2025

Summary

This summary is machine-generated.

This study introduces a new nonlocal elasticity theory using a fractional diffusion Green function kernel. It successfully models stress fields around disclinations without singularities, advancing continuum mechanics.

Keywords:

Caputo derivative Mittag–Leffler function fractional differential equation nonlocal elasticity nonlocality kernel twist disclination wedge disclination

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Area of Science:

Continuum Mechanics
Nonlocal Elasticity Theory
Mathematical Physics

Background:

Classical elasticity theory faces challenges with material behavior at small scales.
Nonlocal stress tensors are crucial for capturing size effects and singularities.
Integral formulations are essential for nonlocal constitutive relations.

Purpose of the Study:

To develop a novel nonlocal elasticity theory.
To model stress fields around straight wedge and twist disclinations.
To eliminate nonphysical singularities in stress fields.

Main Methods:

Utilizing a Green function of the fractional diffusion equation as the nonlocality kernel.
Applying Laplace integral transform with respect to the nonlocality parameter.
Analyzing solutions for disclinations in an infinite medium.

Main Results:

Derived stress fields for straight wedge and twist disclinations.
Demonstrated the transition from nonlocal to local behavior as the nonlocality parameter approaches zero.
Confirmed the absence of nonphysical singularities at disclination lines.

Conclusions:

The proposed nonlocal elasticity theory effectively models disclination stress fields.
The use of a fractional diffusion Green function kernel provides a physically meaningful approach.
This framework offers a singularity-free description of stress concentrations.