scholarly journals Classical and Quantum Models of Diffusion

2021 ◽  
Vol 03 (02) ◽  
pp. 1-1
Author(s):  
Angelo Morro ◽  
Keyword(s):  
Diffusion Models ◽  
Diffusion Equations ◽  
Classical Diffusion ◽  
Quantum Models ◽  
Classical Models ◽  
Quantum And Classical Models

The objective of the paper is twofold: first, to review the classical diffusion models and show the approximations at the origin of the parabolic character of the classical equations; second, to demonstrate a connection between the quantum and classical models of diffusion. As diffusion is inherently related to the motion of constituents, the consistent models are framed within the dynamics of mixtures. The derivation of diffusion equations is then determined based on the related, pertinent approximations.

Internal Noise Caused by the Memory

2011 ◽  
Vol 18 (04) ◽  
pp. 405-422 ◽  
Author(s):  
Karl-Heinz Fichtner ◽  
Lars Fichtner ◽  
Kei Inoue ◽  
Masanori Ohya
Keyword(s):  
Asymptotic Behaviour ◽  
Brain Research ◽  
Internal Noise ◽  
Eeg Mapping ◽  
Quantum Models ◽  
Classical Models

In modern brain research, an internal noise caused by the memory is represented by the output of EEG-measurement. However, based on classical models specialists in EEG-mapping cannot explain the observed properties of the internal noise. In this paper using the quantum models we consider the asymptotic behaviour of the internal noise caused by the memory.

scholarly journals A contraction-reaction-diffusion model for circular pattern formation in embryogenesis

2021 ◽  
Author(s):  
Tiankai Zhao ◽  
Yubing Sun ◽  
Xin Li ◽  
Mehdi Baghaee ◽  
Yuenan Wang ◽  
...  
Keyword(s):  
Pattern Formation ◽  
Cell Fate ◽  
Diffusion Model ◽  
Early Stage ◽  
Reaction Diffusion ◽  
Diffusion Models ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Reaction Diffusion Model ◽  
Stress Dependent

Reaction-diffusion models have been widely used to elucidate pattern formation in developmental biology. More recently, they have also been applied in modeling cell fate patterning that mimic early-stage human development events utilizing geometrically confined pluripotent stem cells. However, the traditional reaction-diffusion equations could not satisfactorily explain the concentric ring distributions of various cell types, as they do not yield circular patterns even for circular domains. In previous mathematical models that yield ring patterns, certain conditions that lack biophysical understandings had been considered in the reaction-diffusion models. Here we hypothesize that the circular patterns are the results of the coupling of the mechanobiological factors with the traditional reaction-diffusion model. We propose two types of coupling scenarios: tissue tension-dependent diffusion flux and traction stress-dependent activation of signaling molecules. By coupling reaction-diffusion equations with the elasticity equations, we demonstrate computationally that the contraction-reaction-diffusion model can naturally yield the circular patterns.

scholarly journals Parameter-free continuous drift–diffusion models of amorphous organic semiconductors

2015 ◽  
Vol 17 (35) ◽  
pp. 22778-22783 ◽  
Author(s):  
Pascal Kordt ◽  
Sven Stodtmann ◽  
Alexander Badinski ◽  
Mustapha Al Helwi ◽  
Christian Lennartz ◽  
...  
Keyword(s):  
Organic Semiconductors ◽  
Diffusion Models ◽  
Diffusion Equations ◽  
Atomistic Simulations ◽  
Drift Diffusion ◽  
Current Voltage ◽  
Current Voltage Characteristics ◽  
Semiconducting Film

Current–voltage characteristics of an organic semiconducting film via a direct parametrization of drift–diffusion equations by atomistic simulations.

scholarly journals Physical Limits on Self-Replication Processes

2006 ◽  
Vol 13 (02) ◽  
pp. 113-117 ◽  
Author(s):  
Robert Alicki
Keyword(s):  
Second Law Of Thermodynamics ◽  
Entangled States ◽  
Strongly Correlated ◽  
Classical Information ◽  
Composite Systems ◽  
Classical Models ◽  
Pure States ◽  
Self Replication ◽  
Quantum And Classical Models ◽  
Homogeneous Environment

Using few very general axioms which should be satisfied by any reasonable theory consistent with the Second Law of Thermodynamics we argue that: a) "no-cloning theorem" is meaningful for a very general theoretical scheme including both quantum and classical models, b) in order to describe self-replication, Wigner's "cloning" process should be replaced by a more general "broadcasting", c) "separation of species" is possible only in a non-homogeneous environment, d) "parent" and "offspring" must be strongly correlated. Motivated by the existing results on broadcasting which show that only classical information can self-replicate perfectly we discuss briefly a classical toy model with "quantum features" — overlapping pure states and "entangled states" for composite systems.

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