Discrete fractional order system vibrations

A theory of free vibrations of discrete fractional order (FO) systems with a finite number of degrees of freedom (dof) is developed. A FO system with a finite number of dof is defined by means of three matrices: mass inertia, system rigidity and FO elements. By adopting a matrix formulation, a mathematical description of FO discrete system free vibrations is determined in the form of coupled fractional order differential equations (FODE). The corresponding solutions in analytical form, for the special case of the matrix of FO properties elements, are determined and expressed as a polynomial series along time. For the eigen characteristic numbers, the system eigen main coordinates and the independent eigen FO modes are determined. A generalized function of visoelastic creep FO dissipation of energy and generalized forces of system with no ideal visoelastic creep FO dissipation of energy for generalized coordinates are formulated. Extended Lagrange FODE of second kind, for FO system dynamics, are also introduced. Two examples of FO chain systems are analyzed and the corresponding eigen characteristic numbers determined. It is shown that the oscillatory phenomena of a FO mechanical chain have analogies to electrical FO circuits. A FO electrical resistor is introduced and its constitutive voltage–current is formulated. Also a function of thermal energy FO dissipation of a FO electrical relation is discussed.

Rapid automated method for on-site determination of sulfadiazine in fish farming: a stainless steel veterinary syringe coated with a selective membrane of PVC serving as a potentiometric detector in a flow-injection-analysis system

Sulfadiazine is an antibiotic of the sulfonamide group and is used as a veterinary drug in fish farming. Monitoring it in the tanks is fundamental to control the applied doses and avoid environmental dissemination. Pursuing this goal, we included a novel potentiometric design in a flow-injection assembly. The electrode body was a stainless steel needle veterinary syringe of 0.8-mm inner diameter. A selective membrane of PVC acted as a sensory surface. Its composition, the length of the electrode, and other flow variables were optimized. The best performance was obtained for sensors of 1.5-cm length and a membrane composition of 33% PVC, 66% onitrophenyloctyl ether, 1% ion exchanger, and a small amount of a cationic additive. It exhibited Nernstian slopes of 61.0 mV decade-1 down to 1.0×10-5 mol L-1, with a limit of detection of 3.1×10-6 mol L-1 in flowing media. All necessary pH/ionic strength adjustments were performed online by merging the sample plug with a buffer carrier of 4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid, pH 4.9. The sensor exhibited the advantages of a fast response time (less than 15 s), long operational lifetime (60 days), and good selectivity for chloride, nitrite, acetate, tartrate, citrate, and ascorbate. The flow setup was successfully applied to the analysis of aquaculture waters. The analytical results were validated against those obtained with liquid chromatography–tandem mass spectrometry procedures. The sampling rate was about 84 samples per hour and recoveries ranged from 95.9 to 106.9%.