Vortices, circumfluence, symmetry groups and Darboux transformations of the (2+1)-dimensional Euler equation

The Euler equation (EE) is one of the basic equations in many physical fields such as fluids, plasmas, condensed matter, astrophysics, oceanic and atmospheric dynamics. A symmetry group theorem of the (2+1)-dimensional EE is obtained via a simple direct method which is thus utilized to find \em exact analytical \rm vortex and circumfluence solutions. A weak Darboux transformation theorem of the (2+1)-dimensional EE can be obtained for \em arbitrary spectral parameter \rm from the general symmetry group theorem. \rm Possible applications of the vortex and circumfluence solutions to tropical cyclones, especially Hurricane Katrina 2005, are demonstrated.Comment: 25 pages, 9 figure

Metoda za optimizaciju tehničkih parametara liofilizacije

Vacuum freeze-drying is a technique that makes a material dehydrate at low temperature and low pressure, and it has many merits. A control system is designed and developed based on a certain area freeze-drying machine. A test by the control system is done to optimize the freeze-drying technical parameters. According to the test results, by the method of quadratic orthogonal experiment, the key parameters, including duration, temperature and vacuum of freeze-drying, are analysed and optimized. The test proves the optimized parameters valid for certain vacuum freeze-drying machines and certain bacterins. Furthermore, the optimized parameters show that the vacuum freeze-drying method is useful for any area vacuum freeze-drying machine and any bacterin.Liofilizacija u vakuumu postupak je koji dehidrira materijal pri niskoj temperaturi i niskom tlaku, što ima mnogo prednosti. Kontrolni sustav dizajniran je i razvijen za određeni uređaj za liofilizaciju. Kako bi se optimizirali tehnički parametri liofilizacije, provedeno je ispitivanje od strane nadzornog sustava. Prema rezultatima, metodom kvadratnog ortogonalnog eksperimenta, analizirani su i optimizirani ključni parametri uključujući trajanje, temperaturu i razinu vakuuma liofilizacije. Ispitivanje dokazuje da optimizirani parametri vrijede za određene uređaje za liofilizaciju i određene bakterine. Dodatno, optimizirani parametri pokazuju da je liofilizacija upotrebljiva za bilo koji uređaj za liofilizaciju u vakuumu i bilo koji bakterin

Spin injection from perpendicular magnetized ferromagnetic δ\delta-MnGa into (Al,Ga)As heterostructures

Electrical spin injection from ferromagnetic $\delta$-MnGa into an (Al,Ga)As p-i-n light emitting diode (LED) is demonstrated. The $\delta$-MnGa layers show strong perpendicular magnetocrystalline anisotropy, enabling detection of spin injection at remanence without an applied magnetic field. The bias and temperature dependence of the spin injection are found to be qualitatively similar to Fe-based spin LED devices. A Hanle effect is observed and demonstrates complete depolarization of spins in the semiconductor in a transverse magnetic field.Comment: 4 pages, 3 figure

Robust and clean Majorana zero mode in the vortex core of high-temperature superconductor (Li0.84Fe0.16)OHFeSe

The Majorana fermion, which is its own anti-particle and obeys non-abelian statistics, plays a critical role in topological quantum computing. It can be realized as a bound state at zero energy, called a Majorana zero mode (MZM), in the vortex core of a topological superconductor, or at the ends of a nanowire when both superconductivity and strong spin orbital coupling are present. A MZM can be detected as a zero-bias conductance peak (ZBCP) in tunneling spectroscopy. However, in practice, clean and robust MZMs have not been realized in the vortices of a superconductor, due to contamination from impurity states or other closely-packed Caroli-de Gennes-Matricon (CdGM) states, which hampers further manipulations of Majorana fermions. Here using scanning tunneling spectroscopy, we show that a ZBCP well separated from the other discrete CdGM states exists ubiquitously in the cores of free vortices in the defect free regions of (Li0.84Fe0.16)OHFeSe, which has a superconducting transition temperature of 42 K. Moreover, a Dirac-cone-type surface state is observed by angle-resolved photoemission spectroscopy, and its topological nature is confirmed by band calculations. The observed ZBCP can be naturally attributed to a MZM arising from this chiral topological surface states of a bulk superconductor. (Li0.84Fe0.16)OHFeSe thus provides an ideal platform for studying MZMs and topological quantum computing.Comment: 32 pages, 15 figures (supplementary materials included), accepted by PR

Approximate perturbed direct homotopy reduction method: infinite series reductions to two perturbed mKdV equations

An approximate perturbed direct homotopy reduction method is proposed and applied to two perturbed modified Korteweg-de Vries (mKdV) equations with fourth order dispersion and second order dissipation. The similarity reduction equations are derived to arbitrary orders. The method is valid not only for single soliton solution but also for the Painlev\'e II waves and periodic waves expressed by Jacobi elliptic functions for both fourth order dispersion and second order dissipation. The method is valid also for strong perturbations.Comment: 8 pages, 1 figur

A multiple exp-function method for nonlinear differential equations and its application

A multiple exp-function method to exact multiple wave solutions of nonlinear partial differential equations is proposed. The method is oriented towards ease of use and capability of computer algebra systems, and provides a direct and systematical solution procedure which generalizes Hirota's perturbation scheme. With help of Maple, an application of the approach to the $3+1$ dimensional potential-Yu-Toda-Sasa-Fukuyama equation yields exact explicit 1-wave and 2-wave and 3-wave solutions, which include 1-soliton, 2-soliton and 3-soliton type solutions. Two cases with specific values of the involved parameters are plotted for each of 2-wave and 3-wave solutions.Comment: 12 pages, 16 figure

Study on the multiple dendrite growth of Al – Si binary alloy using phase – field method (PFM)

Phase – field method offers the prospect of carrying out realistic numerical calculation on dendrite growth in metallic systems. The dendritic growth process of Al – 0,02mole % Si binary alloy was simulated by the coupling method of phase field and solute field. The effects of anisotropic parameters on the growth morphology of dendrite were studied. The results show that with the increase of the anisotropy magnitude, the secondary dendrite arms are more developed, and the dendrite tip is obvious oriented. For the multiple dendrite growth, the dendrites present the morphology from the tip splitting to the dendrite tip oriented. The multi dendritic branching and remelting states of Al – Si alloy were obtained and the directional solidification remelting and solute segregation were obtained under different anisotropic index conditions. And numerical simulations were conducted to investigate the growth of single and multiple dendrites under coupled conditions of phase field, solute field, and flow field