Fractional order inductive phenomena based on the skin effect

The Maxwell equations play a fundamental role in the electromagnetic theory and lead to models useful in physics and engineering. This formalism involves integer-order differential calculus, but the electromagnetic diffusion points towards the adoption of a fractional calculus approach. This study addresses the skin effect and develops a new method for implementing fractional-order inductive elements. Two genetic algorithms are adopted, one for the system numerical evaluation and another for the parameter identification, both with good results.

Electrical skin phenomena: a fractional calculus analysis

The internal impedance of a wire is the function of the frequency. In a conductor, where the conductivity is sufficiently high, the displacement current density can be neglected. In this case, the conduction current density is given by the product of the electric field and the conductance. One of the aspects of the high-frequency effects is the skin effect (SE). The fundamental problem with SE is it attenuates the higher frequency components of a signal.

Electrical Skin Phenomena: A Fractional Calculus Analysis

The internal impedance of a wire is the function of the frequency. In a conductor, where the conductivity is sufficiently high, the displacement current density can be neglected. In this case, the conduction current density is given by the product of the electric field and the conductance. One of the aspects the high-frequency effects is the skin effect (SE). The fundamental problem with SE is it attenuates the higher frequency components of a signal. The SE was first verified by Kelvin in 1887. Since then many researchers developed work on the subject and presently a comprehensive physical model, based on the Maxwell equations, is well established. The Maxwell formalism plays a fundamental role in the electromagnetic theory. These equations lead to the derivation of mathematical descriptions useful in many applications in physics and engineering. Maxwell is generally regarded as the 19th century scientist who had the greatest influence on 20th century physics, making contributions to the fundamental models of nature. The Maxwell equations involve only the integer-order calculus and, therefore, it is natural that the resulting classical models adopted in electrical engineering reflect this perspective. Recently, a closer look of some phenomas present in electrical systems and the motivation towards the development of precise models, seem to point out the requirement for a fractional calculus approach. Bearing these ideas in mind, in this study we address the SE and we re-evaluate the results demonstrating its fractional-order nature.

Characterization and Biological Activities of Ocellatin Peptides from the Skin Secretion of the Frog Leptodactylus pustulatus

Eight new peptides were isolated from the skin secretion of the frog Leptodactylus pustulatus and their amino acid sequences determined by de novo sequencing and by cDNA cloning. Structural similarities between them and other antimicrobial peptides from the skin secretion of Leptodactylus genus frogs were found. Ocellatins-PT1 to -PT5 (25 amino acid residues) are amidated at the C-terminus, while ocellatins-PT6 to -PT8 (32 amino acid residues) have free carboxylates. Antimicrobial activity, hemolytic tests, and cytotoxicity against a murine fibroblast cell line were investigated. All peptides, except for ocellatin-PT2, have antimicrobial activity against at least one Gram negative strain. Ocellatin-PT8 inhibited the growth of Escherichia coli, Staphylococcus aureus, Klebsiella pneumoniae, and Salmonella choleraesuis strains with MICs in the 60−240 μM range. No significant effect was observed in human erythrocytes and in a murine fibroblast cell line after exposure to the peptides at MICs. A comparison between sequences obtained by both direct HPLC-MS de novo sequencing and cDNA cloning demonstrates the secretion of mature peptides derived from a pre-pro-peptide structure.