Dynamics of Biostructures on a Fractal/Multifractal Space-Time Manifold

A theory of space-time is built on a fractal/multifractal variety. Thus, considering that both the spatial coordinates and the time are fractal/multifractal, it is shown that both the energy and the non-differentiable mass of any biostructure depend on both the “state” of the biostructure and a speed limit of constant value. For the dynamics on Peano fractal/multifractal curves and Compton scale resolutions, it is shown that our results are reduced to those of Einstein relativity. In such a context, it has been shown that the “chameleon effect” of cholesterol corresponds to the HDL-LDL state transfer dictated by the spontaneous symmetry breaking through a fractal/multifractal tunnel effect. Then both HDL and LDL become distinct states of the same biostructure as in nuclear physics where proton and neutron are distinct states of the same nucleon

Complex Systems with Self‐Elimination of Dissipation with Implication in Bio‐Structural Behavior Via Nondifferentiability

In the present chapter, we show that the use of the nondifferentiable mathematical procedures, developed in the Scale Relativity Theory with constant arbitrary fractal dimension, simplifies very much the dynamics analyses in the case of complex systems. By applying such a procedure to various complex systems dynamics (biological structures, ablation or discharge plasmas, etc.), we are able to observe that it starts from a steady (oscillating state) and as the external factor is varied the system undergoes significant changes. The systems evolve asymptotically through various transition, toward a chaotic regime (like bifurcations or intermittencies), but never reaching it. Another important reveal from the study of the system’s dynamics was the presence of various steady states depending on the resolution scale at which the theoretical investigations are performed

Turbulence Removal in Atmospheric Dynamics through Laminar Channels

El método adoptado en este paper para describir la dinámica atmosférica ha implicado el desarrollo de estructuras geométricas invariantes al tiempo con lo que implican que puede modelizarse de forma fractal/multifractal. Los escenarios evaluados tipo Schrödinger y Madelung conducen a un comportamiento atmosférico de las turbulencias que se puede describir en términos de modulación y discretización. A traves de estos modelos se establece que los canales laminares en toda la atmósfera actúan como un medio superconductor de masas. Para ello se han usado datos experimentales de un ceilómetro y una plataforma de radar que confirma mediante la dinámica vertical de enjambres de insectos que el modelo funciona.Dynamics in atmospheric structures are analyzed using the Scale Relativity Theory in Schrödinger-type and Madelung-type scenarios. In the Schrödinger-type scenario, the group invariances of the special linear group SL(2R)-type under Riccati-type gauges implies morphological atmospheric manifestations through frequency modulation, particularly through period doubling. In the Madelung-type scenario, the same group invariances type, manifested through harmonic mappings, implies the functionality of atmospheric mass conductions through mass superconducting-type by scale transition from nondifferentiable atmospheric dynamics to differentiable atmospheric dynamics. The compatibility of these two scenarios under the correlations of atmospheric morphologiesfunctionalities implies Stoler-type coherences of the atmospheric dynamics through the removal of atmospheric turbulence by means of laminar channels. Finally, these theories are successfully employed to analyze the vertical atmospheric dynamics of cases of insect swarms.19 páginas 26 notas bibliográfica

METHOD FOR STUDY MYOCARDIAL TISSUE IN VITRO: APPLICATION OF NANOSECOND PULSED ELECTRIC FIELDS (nsPEFs)

Nanosecond pulsed electric fields (nsPEFs) were used to investigate the different responses arising in myocardial tissues when exposed to a 100 ns electrical pulse and to understand the influence of the electrical parameters on induced phenomena. Nanosecond pulse electric fields can affect the intracellular structures of cells in vitro. Nanosecond pulse electric fields applied to the cardiac tissue are considered to be a possible tool for treatment of arrhythmias or to improve blood circulation inside the myocardial tissue. For this study were used myocardial tissue surgically removed from Wistar rats. The tissue was suspended in KrebsHenseleit solution, placed under an electrode and subjected to 100 ns voltage pulses (2.5 – 10 kV/cm). 300 and 500 pulses at 0.5 Hz were applied. For an early indication in particular, histological investigations of the myocardial tissues exposed to nanosecond pulsed electric fields (nsPEFs) were performed to determine the extent of the morphological modifications produced at the cellular level. After exposure, tissues were prepared for optical microscopy, in order to observe any changes in cell morphology. Histopathological assessment has shown important modifications, such as significant capillary congestion, an aspect which may be explored as a potential application for treating the myocardial ischemia

The Cracking Behavior of Two Dental Composite Materials Validated through Multifractal Analyzes

The aim of this in vitro study was to analyze, both experimentally and theoretically, the mechanical behavior of two types of composite materials used in restoring dental integrity. The samples of each composite resin, namely Filtek Supreme XT (3M ESPE, St. Paul, MN, USA) and Filtek Z250 (3M ESPE, St. Paul, MN, USA), were experimentally analyzed by determining their compressive strength and fracture behavior. The fractured fragments of the samples were subjected to surface evaluation by scanning electron microscopy. The compressive stress—compressive strain dependencies revealed stronger cracking of the Filtek Supreme XT composite than Filtek Z250 prior to fracture. Theoretically, the evaluation was made by means of holographic implementations of such types of composite materials. A Hooke-type equation in a differential form is presented, which links the proposed theoretical model with the experimentally obtained data

Theoretical and Experimental Designs of the Planetary Boundary Layer Dynamics through a Multifractal Theory of Motion

The accurate determination of atmospheric temperature with telemetric platforms is an active issue, one that can also be tackled with the aid of multifractal theory to extract fundamental behaviors of the lower atmosphere, which can then be used to facilitate such determinations. Thus, in the framework of the scale relativity theory, PBL dynamics are analyzed through the aid of a multifractal hydrodynamic scenario. Considering the PBL as a complex system that is assimilated to mathematical objects of a multifractal type, its various dynamics work as a multifractal tunnel effect. Such a treatment allows one to define both a multifractal atmospheric transparency coefficient and a multifractal atmospheric reflectance coefficient. These products are then employed to create theoretical temperature profiles, which lead to correspondences with real results obtained by radiometer data (RPG-HATPRO radiometer), with favorable results. Such methods could be further used and refined in future applications to efficiently produce atmospheric temperature theoretical profiles

Impact of the Liquid Crystal Order of Poly(azomethine-sulfone)s on the Semiconducting Properties

Organic semiconductors are an attractive class of materials with large application in various fields, from optoelectronics to biomedicine. Usually, organic semiconductors have low electrical conductivity, and different routes towards improving said conductivity are being investigated. One such method is to increase their ordering degree, which not only improves electrical conduction but promotes cell growth, adhesion, and proliferation at the polymer–tissue interface. The current paper proposes a mathematical model for understanding the influence of the ordering state on the electrical properties of the organic semiconductors. To this end, a series of aromatic poly(azomethine)s were prepared as thin films in both amorphous and ordered states, and their supramolecular and electrical properties were analyzed by polarized light microscopy and surface type cells, respectively. Furthermore, the film surface characteristics were investigated by atomic force microscopy. It was established that the manufacture of thin films from mesophase state induced an electrical conductivity improvement of one order of magnitude. A mathematical model was developed in the framework of a multifractal theory of motion in its Schrodinger representation. The model used the order degree of the thin films as a fractality measure of the physical system’s representation in the multifractal space. It proposed two types of conductivity, which manifest at different ranges of fractalization degrees. The mathematical predictions were found to be in line with the empirical data

Complex System Dynamics Through A Fractal Paradigm

Assimilating the complex with a fractal, non - differentiable behaviors in their dynamics are analyzed through a fractal paradigm. It results that complex system dynamics in the framework of hydrodynamic - type fractal regimes imply "holographic implementation" of the velocity fields at non - differentiable scale resolution, by means of fractal solitons, fractal solitons - fractal kinks and fractal minimal vortices. These vortices become turbulence sources in complex systems dynamics at non - differentiable scale resolutions

Boundary Layer via Multifractal Mass Conductivity through Remote Sensing Data in Atmospheric Dynamics

In this manuscript, multifractal theories of motion based on scale relativity theory are considered in the description of atmospheric dynamics. It is shown that these theories have the potential to highlight nondimensional mass conduction laws that describe the propagation of atmospheric entities. Then, using special operational procedures and harmonic mappings, these equations can be rewritten and simplified for their plotting and analysis to be performed. The inhomogeneity of these conduction phenomena is analyzed, and it is found that it can fluctuate and increase at certain fractal dimensions, leading to the conclusion that certain atmospheric structures and phenomena of either atmospheric transmission or stability can be explained by atmospheric fractal dimension inversions. Finally, this hypothesis is verified using ceilometer data throughout the atmospheric profiles