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.

Power characteristics of a variable hydraulic transformer

Abstract The flow control of hydraulic transformers is a great challenge. To meet this challenge, a new kind of hydraulic transformer, variable hydraulic transformer （VHT）, is proposed in this work. This paper focuses on the power characteristics of the newly proposed VHT, including instanta neous power, average power, power pulsation, and efficiency. In the analyses, the concepts of efficiency, input power, output power, starting angle, and ceasing angle are defined or redefined. To investigate the power characteristics, their models are derived by considering the governing fac tors such as the control angle of the swash plate and the structure of the port plate. This work high lights that the load flow can be adjusted by adjusting the control angle of the swash plate, and the power characteristics at the Bport produce a remarkable change. In addition, the VHT has a starting angle and a ceasing angle, and these two angles can be adjusted by the influencing factors. The results reveal that the power pulsation and the jump points of the instantaneous power are the primary causes of a less smooth work. Then, it is shown that the control angle of the port plate, the control angle of the swash plate, and the pressures at the ports are the three key elements for a stable operation. The results also reveal that the adjustment of the influencing factors can improve the efficiency.

Three Dimensional Numerical Analysis of Flow within an Isolated Rotor with Stepped Blades

Every compressor works in a limited operational range. Surge as one of the sources of this limitation has been studied for many years. In this research, an isolated blade row of compressor rotor is numerically modeled and solved. In order to improve operational limit and postpone the surge occurrence, a stepped blade of RAF6E with higher stall angle of attack is used to investigate the near stall flow behavior. In this study, several location of step on blades are tried and the results are compared with the case with no step on blades. It is shown that, as the step moves toward the leading edge of blades, the effect of delay on surge is reduced and even efficiency is also decreased significantly. By moving the step towards the trailing edge, surge is delayed due to the reattachment of flow after the step. Efficiency is also decreased but not in the order of the previous case.

Numerical and Performance Analysis of one row Transonic Rotor with Sweep and Lean angle

In this study,aerodynamic behaviors of swept and leaned blades were investigated.Axial and tangential blade curvatures impacts on compressor's operating parameters were analyzed separately.A commercial CFD program which solves the Reynolds-averaged Navier-Stokes equations was used to find out the mentioned impact and the complicated flow field of transonic compressor-rotors.The CFD method that was used for solving flow field's equation was validated by experimental data of NASA Rotor 67.The results showed that the compressor with curved rotors had higher efficiency,rotor pressure ratio and stable operating range compared to the compressor with un-curved rotors.Using curved rotors mostly had higher impact on the overall stable operating range compared to the other operating parameters.Operating range involves choking point and stall point that were changed separately by using of bended blade.For finding the detailed impact of sweep and lean angle on transonic blades,various forms of lean and sweep angles were exerted to basic rotor.It was found that sweep angles increased overall operating range up to 30%,efficiency up to 2%and pressure ratio up to 1%.Leaning the blades increased the safe operating range,the pressure ratio and efficiency by 14%,4%and 2%respectively.

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%.