A Fractional LC − RC Circuit

Mathematics Subject Classification: 26A33, 30B10, 33B15, 44A10, 47N70, 94C05We suggest a fractional differential equation that combines the simple harmonic oscillations of an LC circuit with the discharging of an RC circuit. A series solution is obtained for the suggested fractional differential equation. When the fractional order α = 0, we get the solution for the RC circuit, and when α = 1, we get the solution for the LC circuit. For arbitrary α we get a general solution which shows how the oscillatory behavior (LC circuit) go over to a decay behavior (RC circuit) as grows from 0 to 1, and vice versa. An explanation of the behavior is proposed based on the idea of the evolution of a resistive property in the inductor giving a new value to the inductance that affects the frequency of the oscillator

Supramolecular Interactions Involved in the Solid State Structure of N,N\u27-[bis(pyridin-2-yl)formylidene]ethane-1,2-diamine

The structure of the symmetrical Schiff base, N,N\u27-[bis(pyridin-2-yl)formylidene]ethane-1,2-diamine (bpfd) has been characterized by single crystal X-ray diffraction. The non-covalent supramolecular chemistry involved in the crystal structure of this ligand has been carefully investigated. The structure adopted different motifs of nitrogen-hydrogen interactions that led to the formation of centrosymmetric dimers. In addition, edge-edge and face-face nitrogen-nitrogen interactions were ob-served and reported. The Schiff base (bpfd) ligand crystallizes in a monoclinic space group C12/c1 with a = 19.128(2) Å; b = 5.8776(6) Å; c = 13.1403(15) Å; α = 90o; β = 121.970o(4); γ = 90o and z = 4. This structure is an example of compounds with many symmetry-independent molecules in the asymmetric unit cell (Z > 2)

Sensitive detection schemes for small variations in the damping coefficient based on the Duffing-Holmes oscillator with a potential application in magnetic sensing

In this work we proposed two detection schemes based on the non-linear properties of the Duffing-Holmes oscillator for the detection of small variations in the damping coefficient. Theoretically, variations in the damping coefficient up to 0.001% with the possibility to be pushed further can be detected based on our model. A potential on-off magnetic sensor suitable for biomedical applications is suggested by implementing these two schemes with Giant Magnetoresistance based magnetic sensors