The Role of Information in Managing Interactions from a Multifractal Perspective

In the framework of the multifractal hydrodynamic model, the correlations informational entropy–cross-entropy manages attractive and repulsive interactions through a multifractal specific potential. The classical dynamics associated with them imply Hubble-type effects, Galilei-type effects, and dependences of interaction constants with multifractal degrees at various scale resolutions, while the insertion of the relativistic amendments in the same dynamics imply multifractal transformations of a generalized Lorentz-type, multifractal metrics invariant to these transformations, and an estimation of the dimension of the multifractal Universe. In such a context, some correspondences with standard cosmologies are analyzed. Since the same types of interactions can also be obtained as harmonics mapping between the usual space and the hyperbolic plane, two measures with uniform and non-uniform temporal flows become functional, temporal measures analogous with Milne’s temporal measures in a more general manner. This work furthers the analysis published recently by our group in “Towards Interactions through Information in a Multifractal Paradigm”.     

A Theoretical Model for Release Dynamics of an Antifungal Agent Covalently Bonded to the Chitosan

The aim of the study was to create a mathematical model useful for monitoring the release of bioactive aldehydes covalently bonded to the chitosan by reversible imine linkage, considered as a polymer–drug system. For this purpose, two hydrogels were prepared by the acid condensation reaction of chitosan with the antifungal 2-formyl-phenyl-boronic acid and their particularities; influencing the release of the antifungal aldehyde by shifting the imination equilibrium to the reagents was considered, i.e., the supramolecular nature of the hydrogels was highlighted by polarized light microscopy, while scanning electron microscopy showed their microporous morphology. Furthermore, the in vitro fungicidal activity was investigated on two fungal strains and the in vitro release curves of the antifungal aldehyde triggered by the pH stimulus were drawn. The theoretical model was developed starting from the hypothesis that the imine-chitosan system, both structurally and functionally, can be assimilated, from a mathematical point of view, with a multifractal object, and its dynamics were analyzed in the framework of the Scale Relativity Theory. Thus, through Riccati-type gauges, two synchronous dynamics, one in the scale space, associated with the fungicidal activity, and the other in the usual space, associated with the antifungal aldehyde release, become operational. Their synchronicity, reducible to the isomorphism of two SL(2R)-type groups, implies, by means of its joint invariant functions, bioactive aldehyde compound release dynamics in the form of “kink–antikink pairs” dynamics of a multifractal type. Finally, the theoretical model was validated through the experimental data.     

The time dependent Ginzburg-Landau equation in fractal space-time

We use the hydrodynamic formulation of Scale Relativity Theory to analyze the TDGL equation. As a result, London equations come naturally from the system, when equating to zero the real velocity, the imaginary one turns real, the superconducting fluid act as a subquantum medium energy accumulator, the vector potential, the real and the imaginary velocity are all written in terms of the elliptic function. When solving the resulted system by means of WKBJ method, we get tunneling and quantization. In other words, scale transformation laws produce, on the motion equation of particles governed by the TDGL equation, under some peculiar assumptions, effects which are analogous to those of a “macroscopic quantum mechanics”.     

El Naschie’s ε space–time, hydrodynamic model of scale relativity theory and some applications

A generalization of the Nottale’s scale relativity theory is elaborated: the generalized Schrödinger equation results as an irrotational movement of Navier–Stokes type fluids having an imaginary viscosity coefficient. Then ψ simultaneously becomes wave-function and speed potential. In the hydrodynamic formulation of scale relativity theory, some implications in the gravitational morphogenesis of structures are analyzed: planetary motion quantizations, Saturn’s rings motion quantizations, redshift quantization in binary galaxies, global redshift quantization etc. The correspondence with El Naschie’s ε^(∞) space–time implies a special type of superconductivity (El Naschie’s superconductivity) and Cantorian-fractal sequences in the quantification of the Universe.     

Non-Differentiable Mechanical Model and Its Implications

Considering that the motions of the particles take place on fractals, a non-differentiable mechanical model is built. Only if the spatial coordinates are fractal functions, the Galilean version of our model is obtained: the geodesics satisfy a Navier-Stokes-type of equation with an imaginary viscosity coefficient for a complex speed field or respectively, a Schrödinger-type of equation or hydrodynamic equations, in the case of irrotational movements. Moreover, in this approach, the analysis of the fractal fluid dynamics generates conductive properties in the case of movements synchronization both on differentiable and fractal scales, and convective properties in the absence of synchronization (e.g. laser ablation plasma is analyzed). On the other hand, if both the spatial and temporal coordinates are fractal functions, it results that, the geodesics satisfy a Klein-Gordon-type of equation on a Minkowskian manifold.     

Synthesis of nanometer-scale polymeric structures on surfaces from template assisted admicellar polymerization: a comparative study with protein adsorption

A novel method for the formation of nanometer-scale polymer structures via template assisted admicellar polymerization (TAAP) is described. Admicellar polymerization uses a surfactant layer adsorbed on a surface to localize monomer to the surface prior to polymerization of the monomer. Nanostructures are formed by restricting adsorption to the uncovered sites of an already-templated surface, in this case to the interstitial sites between adsorbed latex spheres. Unlike most other process that form polymer nanostructures, polymer dimensions can be significantly smaller than the interstitial size because of sphere-surfactant interactions. Protein adsorption in the interstitial sites of colloidal arrays was also studied for three different proteins, and the results were compared with those obtained via admicellar polymerization.     

Al2O3 ceramics under high-fluence irradiation: plasma plume dynamics through space- and time-resolved optical emission spectroscopy

The expansion in vacuum of the plume generated by the UV ablation of a LiYF₄ crystal was analysed as a function of several parameters: distance from the target along the plume axis, laser fluency and angular dislocation with respect to the plume axis. The study was carried out by the optical time of flight technique. Time-resolved signals of the optical emission of the neutral as well as ionised species in the plume were recorded and analysed for different experimental situations. The most probable velocity for each species was calculated and confirmed by the Maxwell-Boltzmann distribution fits of the relative emission temporal profiles. An angular distribution of the ablated species could also be provided.     

The Cantorian structure of the background magnetic field and high temperature superconductors

One builds the solution of GL equation in terms of the elliptic cn function of complex argument. The real part of the complex action, , corresponds to the potential of a vortex lattice, and from here, through the elliptic function degeneration, to the vortex streets. Considering the vortex streets fixed on vacuum by a background magnetic field through pinning, from equating the current density to zero one determines the field structure: the mean value will be roughly equal to B_C2, and its flux will be fractional. The fractional flux will be associated to quasi-particles obeying the ‘anyonic’ statistics. At low temperatures and high external magnetic field, the structure of background field will be of Cantorian type.     

Gauge Gravitational Field in a Fractal Space-Time

Considering the fractal structure of space-time, the scale relativity theory in the topological dimension DT = 2 is built. In such a conjecture, the geodesics of this space-time imply the hydrodynamic model of the quantum mechanics. Subsequently, the gauge gravitational field on a fractal space-time is given. Then, the gauge group, the gauge-covariant derivative, the strength tensor of the gauge field, the gauge-invariant Lagrangean, the field equations of the gauge potentials and the gauge energy-momentum tensor are determined. Finally, using this model, a Reissner- Nordstrom type metric is obtained.