3D Fractals, Axiom of Algebra (Δn)n = +1

After having laid down the Axiom of Algebra, bringing the creation of the square root of -1 by Euler to the entire circle and thus authorizing a simple notation of the nth roots of unity, the author uses it to organize homogeneous divisions of the limited development of the exponential function, that is opening the way to the use of a whole bunch of new primary functions in Differential Calculus. He then shows how new supercomplex products in dimension 3 make it possible to calculate fractals whose connexity depends on the product considered. We recall the geometry of convex polygons and regular polygons.

A Novel Flux-weakening Control Method with Quadrature Voltage Constrain for Electrolytic Capacitorless PMSM Drives

In electrolytic capacitorless permanent magnet synchronous motor(PMSM) drives, the DC-link voltage will fluctuate in a wide range due to the use of slim film capacitor. When the flux-weakening current is lower than-ψf/Ld during the high speed operation, the flux-weakening control loop will transform to a positive feedback mode, which means the reduction of flux-weakening current will lead to the acceleration of the voltage saturation, thus the whole system will be unstable. In order to solve this issue, this paper proposes a novel flux-weakening method for electrolytic capacitorless motor drives to maintain a negative feedback characteristic of the control loop during high speed operation. Based on the analysis of the instability mechanism in flux-weakening region, a quadrature voltage constrain mechanism is constructed to stabilize the system.Meanwhile, the parameters of the controller are theoretically designed for easier industrial application. The proposed algorithm is implemented on a 1.5 kW electrolytic capacitorless PMSM drive to verify the effectiveness of the flux-weakening performance.

Passively spatiotemporal gain-modulation-induced stable pulsing operation of a random fiber laser

Unlike a traditional fiber laser with a defined resonant cavity, a random fiber laser(RFL), whose operation is based on distributed feedback and gain via Rayleigh scattering(RS) and stimulated Raman scattering in a long passive fiber, has fundamental scientific challenges in pulsing operation for its remarkable cavity-free feature. For the time being, stable pulsed RFL utilizing a passive method has not been reported. Here, we propose and experimentally realize the passive spatiotemporal gain-modulation-induced stable pulsing operation of counterpumped RFL. Thanks to the good temporal stability of an employed pumping amplified spontaneous emission source and the superiority of this pulse generation scheme, a stable and regular pulse train can be obtained.Furthermore, the pump hysteresis and bistability phenomena with the generation of high-order Stokes light is presented, and the dynamics of pulsing operation is discussed after the theoretical investigation of the counterpumped RFL. This work extends our comprehension of temporal property of RFL and paves an effective novel avenue for the exploration of pulsed RFL with structural simplicity, low cost, and stable output.

Stable single-mode operation of a distributed feedback quantum cascade laser integrated with a distributed Bragg reflector

We report an index-coupled distributed feedback quantum cascade laser by employing an equivalent phase shift(EPS) of quarter-wave integrated with a distributed Bragg reflector(DBR) at λ~5.03 μm. The EPS is fabricated through extending one sampling period by 50% in the center of a sampled Bragg grating. The key EPS and DBR pattern are fabricated by conventional holographic exposure combined with the optical photolithography technology, which leads to improved flexibility, repeatability, and cost-effectiveness. Stable single-mode emission can be obtained by changing the injection current or heat sink temperature even under the condition of large driving pulse width.

An experimental study of a single-piston free piston linear generator

Free piston linear generator(FPLG)is a promising range extender for the electrical vehicle with unparallel advantages,such as compact structure,higher system efficiency,and reduced maintenance cost.However,due to the lack of the mechanic crankshaft,the related piston motion control is a challenge for the FPLG which causes problems such as misfire and crash and limits its widespread commercialization.Aimed at resolving the problems as misfire,a single-piston FPLG prototype has been designed and manufactured at Shanghai Jiao Tong University(SJTU).In this paper,the development process and experimental validation of the related control strategies were detailed.From the experimental studies,significant misfires were observed at first,while the FPLG operated in natural-aspiration conditions.The root cause of this misfire was then identified as the poor scavenging process,and a compressed air source was leveraged to enhance the related scavenging pressure.Afterward,optimal control parameters,in terms of scavenging pressure,air-fuel equivalence ratio,and ignition position,were then calibrated in this charged-scavenging condition.Eventually,the FPLG prototype has achieved a continuous stable operation of over 1000 cycles with an ignition rate of 100%and a cycle-to-cycle variation of less than 0.8%,produced an indicated power of 2.8 kW with an indicated thermal efficiency of 26%and an electrical power of 2.5 kW with an overall efficiency of 23.2%.