Anomalous Diffusion and Relaxations in Liquid Crystals: Fractal and Fractional Behavior

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Complexity".

Deadline for manuscript submissions: 31 December 2024 | Viewed by 435

Special Issue Editors

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Guest Editor
Departmento de Física, Universidade Tecnológica Federal do Paraná, Campus de Apucarana, Apucarana 86812-460, PR, Brazil
Interests: liquid crystals; pattern formation; chirality; impedance; anomalous diffusion; fractional diffusion

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Guest Editor
Departamento de Física, Universidade Estadual de Ponta Grossa, Ponta Grossa 84030-900, PR, Brazil
Interests: anomalous diffusion; liquid crystals; impedance; fractional dynamics; nonextensive thermostatistics
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Special Issue Information

Dear Colleagues,

Liquid crystals stand as extraordinary and profoundly interdisciplinary materials. Mastery of their myriad mesophases demands expertise spanning mathematics, physics, engineering, and biology. Positioned between conventional liquids and crystalline solids, they find versatile applications in display technology, sensors, and emerging fields, even serving as synthetic analogs to mimic naturally occurring materials. Unsurprisingly, these unique materials, boasting exceptional properties, also exhibit distinctive dynamical phenomena, such as anomalous diffusion and relaxation processes, both of which lie at the heart of their application in technology such as displays, photonic and optical devices, sensors and biosensors, and many more.

This Special Issue is dedicated to delving into the anomalous diffusion and relaxation processes within liquid crystal materials. This expansive and captivating topic lies at the core of cutting-edge applications of liquid crystals, including the development of molecular motors and responsiveness to external stimuli. Contributors are warmly welcomed to explore anomalous behaviors in liquid crystals stemming from factors such as doping, geometric confinement, active dopants, external stimuli, defect coarsening, and more.

The focal point of this Special Issue revolves around dynamic behaviors that defy conventional, Debye-like relaxation, ultimately invoking fractional or fractal-like descriptions. Emphasis is placed on exploring their connections with established properties of liquid crystals and potential applications. Due to the extensive range of applications of liquid crystals, authors are encouraged to explore the potential unraveling of their findings in diverse fields, including but not limited to technology, engineering, materials science, and biological applications.

This Special Issue aims to propel research on anomalous relaxation phenomena in liquid crystal phases, fostering advancements in theory, experiments, computer simulations, and practical applications. Submissions are encouraged on a broad spectrum of topics, including (but not limited to):

  • Diffusion through modulated and non-modulated liquid crystal media;
  • Anomalous relaxation;
  • Coarsening defect dynamics;
  • Pattern formation;
  • Fractal aspects of liquid crystal phases;
  • Polymer growth and anomalous relaxation of polymer-stabilized phases;
  • Non-linear response to external stimuli;
  • Memory effects;
  • Anomalous shear-induced dynamics;
  • Anomalous response time;
  • Anomalous viscoelasticity and scaling;
  • Applications of anomalous behavior in liquid crystals;
  • Fractal and fractional modeling of liquid crystals.

We eagerly anticipate your valuable contributions to enrich our understanding of these intriguing phenomena, propelling the field towards new horizons.

Prof. Dr. Rafael Soares Zola
Prof. Dr. Ervin K. Lenzi
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fractal and Fractional is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2700 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.


  • anomalous diffusion
  • non-Debye relaxation
  • modulated liquid crystal phases
  • coarsening dynamics
  • pattern formation
  • fractal and fractional calculus
  • anomalous scaling
  • memory effects

Published Papers

This special issue is now open for submission, see below for planned papers.

Planned Papers

The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.

A Brief Review on Fractional Calculus as a Tool for Applications in Liquid Crystals: Adsorption Phenomena and Electrical Impedance
——Prof. Dr. Rafael Soares Zola and Prof. Dr. Ervin K. Lenzi
Fractal Hausdorff Derivative for Modeling Polymer-Stabilized Nematic Liquid Crystal Response Time
——Prof. Dr. Rafael Soares Zola and Prof. Dr. Ervin K. Lenzi
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