Special Issue "Theory and Applications of Hyperbolic Diffusion and Shannon Entropy"
Deadline for manuscript submissions: 15 December 2023 | Viewed by 197
Interests: stochastic processes; disorder; non-equilibrium statistical mechanics; quantum open system
Diffusion is ubiquitous in science, while a model of instantaneous propagation for the process itself is a matter of discussion in the real natural world. Examples of finite-velocity diffusion are heat waves in simple and complex materials, transport in special relativity, biological space-dependent population models, competition, and coupled systems in ecological transport, run-and-tumble biological motion, the geophysical earth's climate problems, neuroscience and its transport electric brain behavior, and transport in electronic circuits and in guide waves, as well as in the socio-economic propagation of information models.
The use of the canonical Fick law to study the behavior of such a system has acquired significant importance in the pioneer works of transport theory, while the Cattaneo–Fick’s law is focused on considering the finite-velocity diffusion propagation. In a related context, the telegrapher’s equation—in the wave propagation approach—addresses the important interest of describing electromagnetic transport in conducting media from a theoretical and/or experimental viewpoint. Additionally, surface gravitational waves on random media are describes by the telegrapher’s equation.
The application of information theory to study these diffusion-like systems is an open statistics problem. Further progress on this matter calls for new statistical techniques based on the Shannon entropy theory, as well as for an improved understanding of the hyperbolic diffusion problem and the waves in the stochastic telegrapher’s equation for complex systems. Contributions addressing any of these issues are very welcome.
This Special Issue aims to be a forum for the presentation of improved techniques for these kinds of finite-velocity diffusion-like systems. The analysis and interpretation of the hyperbolic diffusion using statistical tools based on the Shannon information theory fall within the scope of this Special Issue.
Prof. Dr. Manuel O. Cáceres
Manuscript Submission Information
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- finite-velocity diffusion
- wave telegrapher’s equation
- stochastic and random media
- statistics information theory
- complex transport
- random waves and dispersion
- earth sciences
- social sciences