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Cosmic plasmas are considered as the most abundant form of ordinary matter in the Universe while observations of the cosmic dust in different regions provide an insight into the Universe's recyclin...

In oceanography, acoustics and hydrodynamics, people pay attention to the Burgers-type equations for different wave processes, one of which is an extended coupled (2+1)-dimensional Burgers system hereby under investigation. Based on the scaling transformation, Bell polynomials, Hirota operators and symbolic computation, we structure out two hetero-Backlund transformations, each of which to a solvable linear partial differential equation, and construct two sets of the bilinear forms, with the relevant one- and two-soliton solutions. Results rely on the coefficients in the original system.

Tanshinones are the bioactive nor-diterpenoid constituents of the Chinese medicinal herb Danshen (Salvia miltiorrhiza). These groups of chemicals have the characteristic furan D-ring, which differentiates them from the phenolic abietane-type diterpenoids frequently found in the Lamiaceae family. However, how the 14,16-epoxy is formed has not been elucidated. Here, we report an improved genome assembly of Danshen using a highly homozygous genotype. We identify a cytochrome P450 (CYP71D) tandem gene array through gene expansion analysis. We show that CYP71D373 and CYP71D375 catalyze hydroxylation at carbon-16 (C16) and 14,16-ether (hetero)cyclization to form the D-ring, whereas CYP71D411 catalyzes upstream hydroxylation at C20. In addition, we discover a large biosynthetic gene cluster associated with tanshinone production. Collinearity analysis indicates a more specific origin of tanshinones in Salvia genus. It illustrates the evolutionary origin of abietane-type diterpenoids and those with a furan D-ring in Lamiaceae., Salvia miltiorrhiza is a medicinal plant that can produce the bioactive tanshinones. Here, the authors report the improved genome assembly and reveal the possible roles of three CYP71Ds in catalyzing the reactions leading to the formation of the characteristic furan D-ring of transhinones.

Two-layer fluids are seen in fluid mechanics, thermodynamics and medical sciences. Lattices are seen in solid-state physics. In a two-layer liquid or a lattice, a ( $$3+1$$ )-dimensional generalised Yu–Toda–Sasa–Fukuyama equation is hereby studied with symbolic computation. Via the Hirota method, bilinear form and bilinear auto-Backlund transformation under certain coefficient constraints are obtained. Breather solutions are worked out based on the Hirota method and extended homoclinic test approach. Considering that the periods of breather solutions tend to infinity, we derive the lump solutions under a limit procedure. We observe that the amplitudes of the breather and lump remain unchanged during the propagation. Furthermore, we graphically present the breathers and lumps under the influence of different coefficients in the equation.

Oceanic water-wave studies are attractive. Hereby, with a view to modelling the nonlinear and dispersive long gravity waves in two horizontal directions on the shallow water of an open sea or a wide channel of finite depth, we inquire into a generalized (2+1)-dimensional dispersive long-wave system, by virtue of the scaling transformations we hereby obtain, Bell polynomials and symbolic computation. As for the horizontal velocity and wave elevation above the undisturbed water surface, we find two branches of the hetero-Backlund transformations, two branches of the bilinear forms and two branches of the N -soliton solutions, with N as a positive integer. What we have obtained relies on the coefficients in the system.

The resonant nonlinear Schrodinger equation (RNLSE) with competing weakly nonlocal nonlinearity and fractional temporal evolution, which describes the propagation of optical solitons along the nonl...

Accurate quantum dynamics calculations have been carried out for the Na(3S) + DF(ν = 1–4, j = 0) → NaF + D, Na(3P) + DF(ν = 0, j = 0) → NaF + D/Na(3S) + DF and Na(3S) + HF(ν = 2–4, j = 2,4,6,9) → NaF + H reactions. The isotopic substitution decreases the reactivity remarkably in both Na(3S) + HF and Na(3P) + HF. The calculation also shows that effects of the initial rotational excitations for Na(3S) + HF are different between the process with threshold (v = 2) and those without thresholds (v = 3–4).

In this paper, Lie symmetry method is applied to investigate the invariance properties of the time fractional Kolmogorov–Petrovskii–Piskunov equation with Riemann–Liouville derivative. In view of p...

In this paper, a (2+1)-dimensional generalized Hirota-Satsuma-Ito equation for the water waves is investigated. We obtain the N-soliton solutions according to the bilinear form. The M-lump solutions are obtained based on the N-soliton solutions, where N and M are the positive integers. We take $$M=2$$ and 3 to get the two- and three-lump solutions. Besides, three types of the hybrid solutions are discussed graphically, which contain the hybrid solutions between the one-lump wave and two-kink solitons, between the two-lump wave and one-kink soliton, and between the one-lump wave and breather wave.

For the Earth, water is at the core of sustainable development and at the heart of adaptation to climate change. For the Enceladus, the sixth-largest moon of the Saturn, Cassini spacecraft discovers a possible global ocean of liquid water beneath an icy crust. Oceanic water waves are one of the most common phenomena in nature. Hereby, on the Whitham–Broer–Kaup system for the dispersive long waves in the oceanic shallow water, with respect to the horizontal velocity of the water wave and height of the deviation from the equilibrium position of the water, our binary Bell polynomials and symbolic computation lead to two sets of the bilinear forms, two sets of the N-soliton solutions and two sets of the auto-Backlund transformations with the sample solitons, where N is a positive integer. Our bilinear forms and auto-Backlund transformations are different from those reported in the existing literatures. All of our results are dependent on the coefficients in the system which represent different oceanic-water-wave dispersion/diffusion powers.

Of current interest, the paper commented [i.e., Eur. Phys. J. Plus (2020) 135:272] has investigated the $$(3+1)$$ -dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt equation in ocean dynamics, fluid mechanics and plasma physics. However, the story that the paper commented has caused could be made more complete. Hereby, for the same equation, via the Bell polynomials, we work out the same bilinear form as that in the paper commented, but the ways of derivation are different. With symbolic computation, we also construct two auto-Backlund transformations for the same equation with some solitons. Our results are with respect to the amplitude or elevation of the relevant wave in ocean dynamics, fluid mechanics and plasma physics.

We report on the fabrication and characterization of AlGaN/GaN metal-insulator-semiconductor (MIS) capacitors and high-electron-mobility transistors (MIS-HEMTs) using a 5 nm thick Al2O3 dielectric deposited by cost-effective and environmental-friendly mist chemical vapor deposition (mist-CVD) technique. Practically hysteresis-free capacitance–voltage profiles were obtained from the fabricated two-terminal MIS-capacitors indicating high quality of the mist-Al2O3/AlGaN interface. Compared with reference Schottky-gate HEMTs, mist MIS-HEMTs exhibited much improved performance including higher drain current on-to-off ratio, much lower gate leakage current in both forward and reverse directions and lower subthreshold swing. These results demonstrate the potential and viability of non-vacuum mist-CVD Al2O3 in the development of high-performance GaN-based MIS-HEMTs.

Based on a new global potential energy surface of SiH 2 + ( X 2 A 1 ) , the exact quantum dynamical calculation for the H(2 S) + SiH+(X1Σ+) → H2 + Si+ reaction has been carried out by using the Chebyshev wave packet method. The initial state specified (ν i = 0, j i = 0) probabilities, integral cross sections (ICS) and thermal rate constants of the title reaction are calculated. All partial wave contributions up to J = 90 are calculated in exact quantum calculation including the full Coriolis coupling (CC) effect. The dynamical behaviors of probabilities, ICSs and rate constants are found to be in accord with an exothermic reaction without potential barrier. By comparing the probabilities of CC with the corresponding centrifugal sudden (CS) approximation ones, it can be concluded that neglecting CC effect will decrease the collision time, increase the amplitude of oscillation and lead to overestimation or underestimation of the reaction probability. For ICSs and rate constants, it is found that the deviation of CC and CS ICSs is small in the most of collision energy range except for the range of 0 eV–0.05 eV, while the deviation of both rate constants is considerable in the temperature range of 16 K–1000 K.

Water waves attract people’s attention. For the water waves, a ( 2 + 1 )-dimensional generalized variable-coefficient Boiti–Leon–Pempinelli system is hereby studied. As for the horizontal velocity and elevation of the water wave, on the one hand, with the scaling transformations and symbolic computation, a set of the hetero-Backlund transformations is constructed, linking the original system with a known generalized variable-coefficient Burgers equation. As for the horizontal velocity and elevation of the water wave, on the other hand, with symbolic computation, a set of the similarity reductions is constructed, from the original system to a known ordinary differential equation. All our results depend on the variable coefficients in the original system.

Water waves, one of the most common phenomena in nature, play an important role in the marine/offshore engineering, hydraulic engineering, energy development, mechanical engineering, etc. Hereby, for the shallow water waves near an ocean beach or in a lake, we study a Boussinesq-Burgers system. With respect to the water-wave horizontal velocity and height deviating from the equilibrium position of water, we find out (1) two hetero-Backlund transformations via the Bell polynomials and symbolic computation, and (2) a set of the similarity reductions via symbolic computation, to a known ordinary differential equation, for which we also construct some solutions. The results rely on the oceanic water-wave dispersive power. We hope that our hetero-Backlund transformations and similarity reductions could help the researchers investigate certain modes of the shallow water waves near an ocean beach.

A computational study for the title reaction is carried out employing recent ab initio potential energy surface. J = 0 reaction probability is obtained using both quasiclassical trajectory (QCT) and wave packet methods. The total and state resolved integral as well as differential cross sections are also obtained by means of QCT method. Dynamics of the title reaction shows qualitative similarity with its isotopic counterpart, the H + CaCl reaction, but quantitatively, reactivity is significantly enhanced in the title reaction. In addition, the effect of initial rotational state excitation on H + CaCl reaction is investigated.

People pay attention to the oceans crossing the Solar System: the Earth, Enceladus and Titan. Hereby, on a variable-coefficient nonlinear dispersive-wave system for the shallow oceanic environment, (A) nonlinear-water-wave symbolic computation and Bell polynomials lead to two hetero-Backlund transformations and (B) nonlinear-water-wave symbolic computation gives rise to a similarity reduction, both depending on the variable coefficients representing the wave elevation and surface velocity of the water wave. This paper might be of some use for the future oceanic studies on the Solar System.

Nowadays, the Burgers-type equations are seen in oceanography, gas dynamics, shock-wave formation, hydrodynamic turbulence, boundary-layer behavior, continuum-traffic simulation, convection-dominated diffusion, wave formation in the thermo-elastic media, vorticity transport, dispersion in the porous media, acoustic transmission structure, particle sedimentation in fluid suspension, colloid evolution, and so forth. In this Letter, we investigate an extended (2+1)-dimensional coupled Burgers system in fluid mechanics. With symbolic computation and with reference to the velocity components in fluid-related problems, we construct a hetero-Backlund transformation and a similarity reduction, depending on the coefficients in the system.

Oceanic water waves are actively studied. Hereby, taking into account the nonlinear and dispersive long gravity waves in two horizontal directions on the shallow water of an open sea or a wide channel of finite depth, we investigate a generalized (2+1)-dimensional dispersive long-wave system. With symbolic computation while with respect to the horizontal velocity and wave elevation above the undisturbed water surface, we work out two non-auto-Backlund transformations and two auto-Backlund transformations with solitons. All of our results are dependent on the constant coefficients in the original system.

We carried out accurate quantum wave packet as well as quasi-classical trajectory (QCT) calculations for H + CaCl (νi = 0, ji = 0) reaction occurring on an adiabatic ground state using the recent ab initio potential energy surface to obtain the quantum and QCT reaction probabilities for several partial waves (J = 0, 10, and 20) as well as state resolved QCT integral and differential cross sections. The complete list of vibrational energy levels supported by the intermediate HCaCl complex is also obtained using the Lanczos algorithm. The QCT reaction probabilities show excellent agreement with the quantum ones except for the failure in reproducing the highly oscillatory resonance structure. Despite the fact that the reaction is exothermic and the existence of a barrier that is energetically lower than the bottom of the reactant valley, the reaction probability for J = 0 shows threshold-like behavior and the reactivity all through the energies is very low (0.1). The dynamical features at two different energy regions (0.35 eV and0.35 eV) are found to be different drastically from each other. The analyses of these results suggest that the reaction is governed by one of the two different types of reaction mechanism, one is the direct mechanism at the high energy region and the other is the indirect mechanism at the low energy region by which the reaction proceeds through the long-lived intermediate complex followed by a statistical dissociation into asymptotic channels.

Under investigation in this paper is an inhomogeneous nonlinear Schrödinger-Maxwell-Bloch system with variable dispersion and nonlinear effects, which describes the propagation of optical pulses in an inhomogeneous erbium-doped fiber. Under certain coefficient constraints, multi-soliton solutions are obtained by the Hirota method and symbolic computation. Evolution and interaction of the solitons are plotted, and the self-induced transparency effect caused by the doped erbium atoms is found to lead to the change of the soliton velocity and phase. Overall phase shift can be observed when the parameter accounting for the interaction between the silica and doped erbium atoms is taken as a constant.

Fusion and fission phenomena for solitary waves have been discovered theoretically and experimentally. In this paper, the (2 + 1)-dimensional variable-coefficient Broer–Kaup system is symbolically investigated. By employing the bilinear method, new solitary solutions with arbitrary functions are obtained. At the same time, the non-elastic interactions of solitary solutions are graphically studied. Furthermore, soliton fusion and fission phenomena are revealed by choosing appropriate functions.

By means of symbolic computation, a new application of Riccati equation is presented to obtain novel exact solutions of some nonlinear evolution equations, such as nonlinear Klein–Gordon equation, generalized Pochhammer–Chree equation and nonlinear Schrodinger equation. Comparing with the existing tanh methods and the proposed modifications, we obtain the exact solutions in the form as a non-integer power polynomial of tanh (or tan) functions by using this method, and the availability of symbolic computation is demonstrated.

The variable-coefficient Korteweg–de Vries (KdV)-typed models, although often hard to be studied, are of current interest in describing various real situations. Under investigation hereby is a large class of the generalized variable-coefficient KdV models with external-force and perturbed/dissipative terms. Recent examples of this class include those in blood vessels and circulatory system, arterial dynamics, trapped Bose–Einstein condensates related to matter waves and nonlinear atom optics, Bose gas of impenetrable bosons with longitudinal confinement, rods of compressible hyperelastic material and semiconductor heterostructures with positonic phenomena. In this Letter, based on symbolic computation, four transformations are proposed from this class either to the cylindrical or standard KdV equation when the respective constraint holds. The constraints have nothing to do with the external-force term. Under those transformations, such analytic solutions as those with the Airy, Hermit and Jacobian elliptic functions can be obtained, including the solitonic profiles. The roles for the perturbed and external-force terms to play are observed and discussed. Investigations on this class can be performed through the properties of solutions of cylindrical and standard KdV equations.

A new ab initio potential energy surface (PES) for the ground state of Li + HCl reactive system has been constructed by three-dimensional cubic spline interpolation of 36 654 ab initio points computed at the MRCI+Q/aug-cc-pV5Z level of theory. The title reaction is found to be exothermic by 5.63 kcal/mol (9 kcal/mol with zero point energy corrections), which is very close to the experimental data. The barrier height, which is 2.99 kcal/mol (0.93 kcal/mol for the vibrationally adiabatic barrier height), and the depth of van der Waals minimum located near the entrance channel are also in excellent agreement with the experimental findings. This study also identified two more van der Waals minima. The integral cross sections, rate constants, and their dependence on initial rotational states are calculated using an exact quantum wave packet method on the new PES. They are also in excellent agreement with the experimental measurements.

The product rotational polarizations of reaction Li+HF→LiF+H at different collision energies, as well as at the different vibrational states and rotational states, are calculated by using the quasi-classical trajectory method based on a new potential energy surface constructed by Aguado et al. [J. Chem. Phys. 119 (2003) 10088]. We investigate the alignment and the orientation of the product molecule by calculating the P(θr, r) distributions describing polar angle distribution, the P(θr) distributions describing the k–j' correlation and the P(r) distributions describing the k–k'–j' correlation. We also explore the dependence of reaction probabilities and cross sections on the rotational and vibrational quantum number of the title reaction. It is concluded that the vibrational state has more important impact on the angular distribution, reaction probability and cross section.

The detailed stereodynamics of the reaction Li+HF(v=0–3) with different collision energy and in different vibration-excited state has been carried out by using the quasi-classical trajectory (QCT) method based on a new potential energy surface constructed by Aguado and Pariagua (Aguado and Paniagua J. Chem. Phys., Vol. 119, No. 19, 2003). The correlated k-j', k-k'-j' angular distributions and the polarization-dependent differential cross sections (PDDCSs) are discussed in detail. The results indicate that the collision energy has more impact on the P(θr) distributions describing the k-j' correlation than the vibration excitation. The distributions of P(φr) describing the k-k'-j' correlation, as well as the polarization-dependent generalized differential cross-sections, are sensitive to the vibration excitation. Meanwhile, the collision energy also has more influence on them.

The product rotational polarizations of reactions Li+HF/DF/TF at different collision energies are calculated using the quasi-classical trajectory method based on a new potential energy surface constructed by Aguado and Paniagua [J. Chem. Phys. 119(2003) 10088]. We investigate the P(θr) distributions describing the k–j' correlation, the P(r) distributions describing the k–k'–j' correlation, and the four polarization-dependent generalized differential cross sections. Furthermore, we compare the influences of mass factor and collision energy in detail and find that the isotope substitution has more impact on the distribution of the product's angular momentum vectors than the collision energy.

A copper nitride (Cu3N) thin film is deposited on a Si substrate by the reactive magnetron sputtering method. The XPS measurements of the composite film indicate that the Cu content in the film is increased to 80.82 at. % and the value of the Cu/N ratio to 4.2:1 by introducing 4% H2 into the reactive gas. X-ray diffraction measurements show that the film is composed of Cu3N crystallites with an anti-ReO3 structure. The effects of the increase of copper content on the field emission characteristics of the Cu3N thin film are investigated. Significant improvement in emission current density and emission repeatability could be attributed to the geometric field enhancement, caused by numerous surface nanotips, and the decrease of resistivity of the film.

Diamond-like carbon (DLC) and carbon nitride (CNx) films were deposit ed successfully by the electrochemical method.The conditions of deposition were discussed also.Scanning electron microscope and Fourier transform infrared technigue were used to investigate the surface morphology and the bonding structure.The results of the field emission show that the turn-on fields of DLC films and CNx films are 88 and 10V/μm respectively.Under the field of 23V/μm,their current densities are as high as 10 and 037 mA/cm2, respectively .