The present study aims to establish a mathematical model for the stability analysis of a viscous compressible liquid jet in a homogeneous wind field, utilizing linear stability theory. Furthermore, the validity of the proposed mathematical model and its solution method are subsequently verified. The findings indicate that the homogeneous wind field exerts an equal influence on both the axisymmetric disturbance and the non-axisymmetric disturbance, with the latter being the predominant form of disturbance. The compressibility of the gas phase has a detrimental effect on the stability of jet flow, while the compressibility of the liquid phase has negligible impact on the stability of jet flow. The impact of a homogeneous wind field on jet stability is primarily manifested in two key dimensions. The presence of a tailwind field has the potential to enhance the stability of jets and impede the likelihood of splitting and atomization. The presence of the deadwind field has the potential to diminish the stability of the jet flow and facilitate the occurrence of splitting and atomization.

The implementation flow of processing incompressible Navier-Stokes equations based on velocity-correction schemes is introduced, and velocity-correction schemes based on Picard iteration is developed by introducing Picard linearization to process the convection term in the velocity governing equation. Compared with the traditional method, the projection method after Picard linearization can be solved with a larger time step, which improves the stability of the solution method, and the convergence accuracy meets the requirements, which confirms the reliability of the solution method.

Based on the smoothed particle hydrodynamics (SPH) method, the SPH method without kernel function derivative (KDF-SPH) is applied to the numerical solution of the time fractional convection-diffusion equation. In the simulation process of the time fractional convection-diffusion equation, the finite difference method (FDM) is used for the Caputo time fractional derivative, and the KDF-SPH method and SPH method are used for the spatial derivative respectively. The results show that the error of KDF-SPH method is much smaller than that of SPH method. Compared with the SPH method, KDF-SPH retains all the advantages of SPH (meshless, Lagrangian and particle properties). This method plays a great role in reducing errors and maintaining stability, and numerical approximation can be carried out regardless of whether the kernel gradient exists or not. It avoids the calculation of the derivative of the kernel function, reduces the requirement for the derivability of the kernel function, improves the calculation efficiency and is easy to be programmed. It is easy to expand the calculation of high-dimensional problems and has good practical application value.

The nonlinear properties of natural convection in the space of an eccentric annulus are investigated using the lattice Boltzmann method (LBM). Firstly, the system is mathematically determined to develop into a chaotic state at high Rayleigh numbers through the maximum Lyapunov exponent spectrum and run test. Then, the process of the system transitioning to chaos is characterized based on the characteristics of numerical solution phase diagram and power spectral density (PSD). The results show that with the increase of Rayleigh number Ra, the solution of the eccentric annular system changes from deterministic steady-state solution to periodic oscillation solution through Hopf bifurcation, and the phase diagram trajectory changes from fixed point to limit cycle. With further increase of Rayleigh number, the stable limit cycle bifurcates into a two-dimensional torus, and the system enters a quasi-periodic state. When Rayleigh number Ra reaches a critical value, the phase diagram trajectory of the system exhibits rapid exponential separation, becomes extremely complex, and many incommensurable fundamental frequencies appear in its power spectral density. Chaotic attractors emerge, Hopf bifurcation occurs again, and eventually chaos is reached.

The propagation characteristics of intense femtosecond laser pulses underwater are numerically investigated and modulated by the input energy, lens focal length and beam waist width.The results indicate that, when the system parameters are appropriately selected, the generation of filament can be effectively controlled by the focal length of lens in range of 1 meter to 10 meters underwater, and the filament length reaches the meter scale. With increase of the focal distance (such as f=10 m), the generated plasma filament will oscillate strongly, which is disadvantage to the underwater detection of spectrum. At this time, by increasing the waist width of the beam, the filament can be transmitted more stably at a distant target position underwater. The attenuation effect of the impurities in seawater on pulse energy can be balanced by increasing input power, so as to realize the long-distance transmission of filaments.

In order to explore key technologies to improve the combustion of agricultural internal combustion engine, characteristics and influencing factors of methane plasma in the coaxial dielectric barrier discharge process are analyzed. A two-dimensional axisymmetric actuator model is established, and the discharge process is numerically simulated by finite element method. The changes of electron density, electron temperature, CH₃ and H number density under different voltage amplitudes and different dielectric materials are analyzed. The simulation results show that voltage amplitude affects the change of current, and the change of electron density and electron temperature are affected by the current. When the input voltage changes, the energy of ionized methane changes with the voltage, and when the voltage amplitude increases, the electron density and electron temperature increase. When the energy consumed by the collision between particles is greater than the energy released by ionization, Electron density and temperature decreased; The number density of CH₃ and H increases with time, and the higher the voltage amplitude, the faster the growth rate. The electron density and the electron temperature increase with the increase of the relative dielectric constant, and the number density of CH₃ and H increases with the increase of the relative dielectric constant. Increasing voltage amplitude and relative dielectric constant will further intensify the ionization of methane.

A high sensitivity refractive index sensor have been proposed in this paper, which is composed by an M-shaped resonant cavity coupled with a baffle contained Metal-Dielectric-Metal (MDM) waveguide. The influence of structural parameter of M-shaped cavity and filled medium characteristics inside it on the transmission spectrum of MDM waveguide have been analyzed numerically through the finite element method. Simulation results show that four asymmetric transmission peaks with Fano line-shape are generated by the coupling interference between the four quasi Fabry-Perot (FP) resonant modes of the first to fourth orders inside M-shaped cavity and the reflected wave in MDM waveguide, moreover the four peak wavelengths redshift almost linearly with increasing cavity length or the refractive index of the filled medium, which can be used to design the refractive index sensor. The calculated sensitivities associated with the quadruple Fano transmission peaks are found to be proportional to the cavity length and the reciprocal of resonant order. As a consequence, a sensitive up to 4 900 nm/RIU has been realized by an M-shaped resonator in dimensions of 400 nm×400 nm. The results in the article provide an effective guidance for the design of high sensitivity sensors.

Based on the lattice Boltzmann method, the chemical reaction process of CO₂ absorption by tandem porous CaO particles is simulated at the scale of Representative Elementary Volume (REV) scale, and the influences of CaO porosity, particle diameter, and inter-particle arrangement of CaO particles on the conversion efficiency and the average conversion rate of particles are mainly investigated. The results show that the conversion efficiency of CaO particles first decreases and then increases with the increase of the porosity, which is attributed to differences in the initial amount of material and the internal gas-solid reaction rate of the particles due to the different porosities, and the competition between them affected the conversion efficiency. On the other hand, the larger the particle diameter, the lower the conversion efficiency. Specifically, the average conversion efficiency of the particles with 50 μm diameter is 8.4% higher than that of particles with 150 μm diameter, and the average conversion efficiency of particles with 150 μm diameter is 7.2% higher than that of the particles with 250 μm diameter. In addition, this work also investigates effect of the arrangement of particles on the average conversion rate. It is found that when the horizontal angle between particles changed from θ=0° to θ=10°, the average conversion rate can not be improved effectively with the increase of the angle due to the effect of the reflux vortex, and the average conversion rate is not improved with the increase of the angle between θ=10° and θ=40°. The average conversion between θ=0° and θ=10° is found not to be effectively improved due to the influence of the reflux vortex. And the average conversion between θ=10° and θ=40° is found to be significantly improved due to the fact that CaO particles at the rear are gradually moving away from the reflux zone, while the average conversion in the interval where the horizontal angle is larger than 40° is found to be maximized due to the fact that the average conversion is not changed with the angle. The simulation results can provide some theoretical guidance for CO₂ capture.

Utilizing density function theory (DFT), the structure, spectrum and dissociation properties of CH₂BrCl molecules are studied in the external electric field at MP2-(FC)/6-311+G(d, p)level, including the equilibrium structure, electric dipole moment, total energy, the highest occupied molecular orbital(HOMO) and the lowest unoccupied molecular orbital(LUMO), energy gap, infrared spectrum. The results show that the C-Br bond length extends and the electric dipole moment increases with the increase of electric field intensity, while the total energy and energy gap E_G decreases with increasing the electric field intensity. The external electric field influences the vibration frequency and absorption intensity of infrared spectrum of CH₂BrCl molecule to varying degree. Discussing the molecule dissociation in the external electric field, the potential well decreases and gradually vanishes with the increase of the external electric field, which implies the bound ability of C-Br bond of CH₂BrCl molecule gradually degrade and the dissociation occurs.

The relationship between different magnetic structures and energies of NpO₂ with a series of U values (3~7 eV) is first calculated by DFT+U method, and then the influence of different point defects in NpO₂ on its architecture and energy properties is studied according to reliable U (4.0 eV). In the calculated results of three different magnetic orders of NpO₂, the structural results of 3 k AFM are in good agreement with the experimental values and obtained a lower energy of formation. Compared with the perfect structure of NpO₂, the energy of formation of single O vacancy system increase by about 0.06 eV, while the energy of formation of the single Np vacancy system increase by 1.4 eV. In addition, we also study the changes in the volume and energy of the system as O and Np vacancies increase.

The rapid solidification process of liquid Ag-Cu alloy at different solute concentrations are simulated by molecular dynamics method. The microstructure evolution characteristic of Ag-Cu alloy is analyzed by two-body distribution function, Honeycutt-Andersen bond type index and extended cluster type index method (CTIM). The results show that the main bond type of Ag-Cu quick setting glass alloy is 1551, and the local quintic symmetry are obvious. The main atomic configuration is icosahedral clusters, in which the regular icosahedral cluster (12 12/1551) is dominant. The highest heritable fraction f of Ag-Cu corresponds to the transition temperature of reduced glass, which proves that Ag₆₀Cu₄₀ has the best amorphous forming ability.

Based on the improved electromagnetic induction neuron model, the coherent resonance (CR) phenomenon of the Memristor Hindmarsh-Rose (HR) network is studied. In addition to electrical coupling connecting gaps between adjacent neurons, magnetic coupling is used to describe the effect of field coupling between neurons. The dynamic analysis of the stable point is performed using the bifurcation diagram and phase diagram, and the potential dynamic mechanism of the emergence of CR and the change of discharge mode are explained. It is found that white Gaussian noise can induce CR in the resting state near the subcritical Hopf bifurcation of memristor neurons, and the occurrence of CR is related to the change of firing mode caused by the increase of noise amplitude.

A phototube is connected to a simple neural circuit for developing a light-sensitive neural circuit, which can be regulated to trigger suitable firing modes by taming the frequency or amplitude of external stimulus. Furthermore, the photoelectric neuron and its Hamilton energy are obtained through scale transformation. It is discerned that the firing modes of neuron is dependent on the energy level of the neuron. Chaotic signals are filtered and encoded to excite the neuron, then chaotic firing modes are obtained and the modes transition and energy value are changed significantly by increasing the intensity of the filtered signals from chaotic system. Considering the complexity and plasticity of the synapse, a nonlinear resistor is used to couple two photosensitive neural circuits. The synchronization stability and energy exchange between two coupled neurons presenting with different initial firing modes are investigated by applying periodic and filtered signals on the neurons. Furthermore, additive noise is applied to investigate the synchronization stability and energy propagation between the two neurons. When photocurrent is selected in periodic type, two coupled neurons are blocked to reach complete synchronization, the coupling intensity is fluctuated with time and energy balance is broken between two neurons. By taming the noise intensity, two bursting neurons can reach complete synchronization while two chaotic neurons seldom reach synchronization when the neurons are driven by peridic currents. When filtered signals are used to excite the two coupled neurons, intermittent phase lock and phase synchronization can be realized between two neurons.

A high-dimensional multi-objective differential evolution algorithm based on global ranking is developed to identify the resistance coefficient of heat supply network, and the multi-objective algorithm is applied to the resistance identification of heat supply network, and the calculation process of resistance identification is improved. The fuzzy mathematics method is applied to the process of resistance identification, a set of optimal solution is generated by identifying each pipe segment, and the optimal solution is selected from the optimal solution set according to the fuzzy membership degree. The results show that compared with the single objective algorithm, the optimal solution set generated by the high-dimensional multi-objective differential evolution algorithm based on global ranking is uniformly distributed and concentrated, and the optimal solution obtained is more accurate.