GLOBAL SOLUTIONS TO A HYDRODYNAMIC MODEL FOR SEMICONDUCTORS WITH VELOCITY RELAXATION

In this paper,we apply the method given in the paper“Zero relaxation time limits to a hydrodynamic model of two carrier types for semiconductors”(Mathematische Annalen,2022,382:1031–1046)to study the Cauchy problem for a one dimensional inhomogeneous hydrodynamic model of two-carrier types for semiconductors with the velocity relaxation.

Full 2D Hydrodynamic Modelling of Rainfall-induced Flash Floods

Mountain catchments are prone to flash flooding due to heavy rainfall. Enhanced understanding of the generation and evolution processes of flash floods is essential for effective flood risk management. However, traditional distributed hydrological models based on kinematic and diffusion wave approximations ignore certain physical mechanisms of flash floods and thus bear excessive uncertainty. Here a hydrodynamic model is presented for flash floods based on the full two-dimensional shallow water equations incorporating rainfall and infiltration. Laboratory experiments of overland flows were modelled to illustrate the capability of the model. Then the model was applied to resolve two observed flash floods of distinct magnitudes in the Lengkou catchment in Shanxi Province, China. The present model is shown to be able to reproduce the flood flows fairly well compared to the observed data. The spatial distribution of rainfall is shown to be crucial for the modelling of flash floods. Sensitivity analyses of the model parameters reveal that the stage and discharge hydrographs are more sensitive to the Manning roughness and initial water content in the catchment than to the Green-Ampt head. Most notably, as the flash flood augments due to heavier rainfall, the modelling results agree with observed data better, which clearly characterizes the paramount role of rainfall in dictating the floods. From practical perspectives, the proposed model is more appropriate for modelling large flash floods.

RELAXATION TIME LIMITS PROBLEM FOR HYDRODYNAMIC MODELS IN SEMICONDUCTOR SCIENCE

In this article, two relaxation time limits, namely, the momentum relaxation time limit and the energy relaxation time limit are considered. By the compactness argument, it is obtained that the smooth solutions of the multidimensional nonisentropic Euler-Poisson problem converge to the solutions of an energy transport model or a drift diffusion model, respectively, with respect to different time scales.

Flow difference effect in the lattice hydrodynamic model

In this paper, a new lattice hydrodynamic model based on Nagatani＇s model INagatani T 1998 Physica A 261 5991 is presented by introducing the flow difference effect. The stability condition for the new model is obtained by using the linear stability theory. The result shows that considering the flow difference effect leads to stabilization of the system compared with the original lattice hydrodynamic model. The jamming transitions among the freely moving phase, the coexisting phase, and the uniform congested phase are studied by nonlinear analysis. The modified KdV equation near the critical point is derived to describe the traffic jam, and kink -antikink soliton solutions related to the traffic density waves are obtained. The simulation results are consistent with the theoretical analysis for the new model.

STEADY-STATE SOLUTIONS FOR A ONE-DIMENSIONAL NONISENTROPIC HYDRODYNAMIC MODEL WITH NON-CONSTANT LATTICE TEMPERATURE

A one-dimensional stationary nonisentropic hydrodynamic model for semiconductor devices with non-constant lattice temperature is studied. This model consists of the equations for the electron density, the electron current density and electron temperature, coupled with the Poisson equation of the electrostatic potential in a bounded interval supplemented with proper boundary conditions. The existence and uniqueness of a strong subsonic steady-state solution with positive particle density and positive temperature is established. The proof is based on the fixed-point arguments, the Stampacchia truncation methods, and the basic energy estimates.

A BLOW-UP CRITERION OF STRONG SOLUTIONS TO THE QUANTUM HYDRODYNAMIC MODEL

In this article,we focus on the short time strong solution to a compressible quantum hydrodynamic model.We establish a blow-up criterion about the solutions of the compressible quantum hydrodynamic model in terms of the gradient of the velocity,the second spacial derivative of the square root of the density,and the first order time derivative and first order spacial derivative of the square root of the density.

Hydrodynamic modeling of ferrofluid flow in magnetic targeting drug delivery

Among the proposed techniques for delivering drugs to specific locations within human body, magnetic drug targeting prevails due to its non-invasive character and its high targeting efficiency. Magnetic targeting drug delivery is a method of carrying drug-loaded magnetic nanoparticles to a target tissue target under the applied magnetic field. This method increases the drug concentration in the target while reducing the adverse side-effects. Although there have been some theoretical analyses for magnetic drug targeting, very few researchers have addressed the hydrodynamic models of magnetic fluids in the blood vessel. A mathematical model is presented to describe the hydrodynamics of ferrofiuids as drug carriers flowing in a blood vessel under the applied magnetic field. In this model, magnetic force and asymmetrical force are added, and an angular momentum equation of magnetic nanoparticles in the applied magnetic field is modeled. Engineering approximations are achieved by retaining the physically most significant items in the model due to the mathematical complexity of the motion equations. Numerical simulations are performed to obtain better insight into the theoretical model with computational fluid dynamics. Simulation results demonstrate the important parameters leading to adequate drug delivery to the target site depending on the magnetic field intensity, which coincident with those of animal experiments. Results of the analysis provide important information and suggest strategies for improving delivery in clinical application.

Stability analysis of multiple-lattice self-anticipative density integration effect based on lattice hydrodynamic model in V2V environment

Under the environment of vehicle-to-vehicle(V2V)communication,the traffic information on a large scale can be obtained and used to coordinate the operation of road traffic system.In this paper,a new traffic lattice hydrodynamic model is proposed which considers the influence of multiple-lattice self-anticipative density integration on traffic flow in the V2V environment.Through theoretical analysis,the linear stability condition of the new model is derived and the stable condition can be enhanced when more-preceding-lattice self-anticipative density integration effect is taken into account.The property of the unstable traffic density wave in the unstable region is also studied according to the nonlinear analysis.It is shown that the unstable traffic density wave can be described by solving the modified Korteweg-de-Vries(mKdV)equation.Finally,the simulation results demonstrate the validity of the theoretical results.Both theoretical analysis and numerical simulations demonstrate that multiple-lattice self-anticipative density integration effect can enhance the stability of traffic flow system in the V2V environment.

Dynamic simulation of hydrodynamic model of drum level wave action and sloshing

In order to build the model of the drum level wave action and sloshing, based on the method of modularization modeling, the hydrodynamic model of drum level wave action and sloshing was developed, and dynamic simulation researches were carried out based on the model. The results indicate that both drum level and drum length have functional relations with period of drum level wave action and sloshing. When the drum level decreases or drum length increases, the period of drum level wave action and sloshing increases, density of liquid and number of sub-module division have little influence on the period of drum level wave action and sloshing. The model was validated by the analytical solution theory of liquid’s wave action and sloshing in cuboid container, and the 3D graphics of drum level wave action and sloshing was also obtained. The model can dynamically reflect the rules of wave action and sloshing of water in the container exactly.

Multiple flux difference effect in the lattice hydrodynamic model

Considering the effect of multiple flux difference, an extended lattice model is proposed to improve the stability of traffic flow. The stability condition of the new model is obtained by using linear stability theory. The theoretical analysis result shows that considering the flux difference effect ahead can stabilize traffic flow. The nonlinear analysis is also conducted by using a reduetive perturbation method. The modified KdV （mKdV） equation near the critical point is derived and the kink antikink solution is obtained from the mKdV equation. Numerical simulation results show that the multiple flux difference effect can suppress the traffic jam considerably, which is in line with the analytical result.

A new control method based on the lattice hydrodynamic model considering the double flux difference

A new feedback control method is derived based on the lattice hydrodynamic model in a single lane. A signal based on the double flux difference is designed in the lattice hydrodynamic model to suppress the traffic jam. The stability of the model is analyzed by using the new control method. The advantage of the new model with and without the effect of double flux difference is explored by the numerical simulation. The numerical simulations demonstrate that the traffic jam can be alleviated by the control signal.

Asymptotic Behavior of the Solutions to the One-Dimensional Nonisentropic Hydrodynamic Model for Semiconductors

In this paper, the asymptotic behavior of the global smooth solutions to the Cauchy problem for the one-dimensional nonisentropic Euler-Poisson （or full hydrodynamic） model for semiconductors, where the energy equation with non-zero thermal conductivity coefficient are contained, is discussed. The global existence of smooth solutions for the Cauchy problem with small perturbed initial data is proved. In particular, that the solutions converge to the corresponding stationary solutions exponentially fast as t → ∞ is showed.

Flow difference effect in the two-lane lattice hydrodynamic model

By introducing a flow difference effect, a modified lattice two-lane traffic flow model is proposed, which is proved to be capable of improving the stability of traffic flow. Both the linear stability condition and the kink-antikink solution derived from the modified Korteweg-de Vries （mKdV） equation are analyzed. Numerical simulations verify the theoretical analysis. Futhermore, the evolution laws under different disturbances in the metastable region are studied.

General solution of the modified Korteweg-de-Vries equation in the lattice hydrodynamic model

Traffic congestion is related to various density waves, which might be described by the nonlinear wave equations, such as the Burgers, Korteweg-de-Vries （KdV） and modified Korteweg-de-Vries （mKdV） equations. In this paper, the mKdV equations of four different versions of lattice hydrodynamic models, which describe the kink-antikink soliton waves are derived by nonlinear analysis. Furthermore, the general solution is given, which is applied to solving a new model -- the lattice hydrodynamic model with bidirectional pedestrian flow. The result shows that this general solution is consistent with that given by previous work.

Asymptotic Convergence to Steady-State Solutions for Solutions of the Initial Boundary Problem to a Simplified Hydrodynamic Model for Semiconductor

We studied the asymptotic behavior of solutions to the initial boundary value problem on the spatial interval [0,1] for a one-dimensional simplified gydrodynamic model for semiconductors wheng(t)→b *, and proved the unique global existence of smooth solutions to the initial boundary problem. We also show that the solutions converge to the corresponding steady-state solutions time-asymptotically by introducing the suitable shift functions.

Time-dependent Ginzburg-Landau equation for lattice hydrodynamic model describing pedestrian flow

A thermodynamic theory is formulated to describe the phase transition and critical phenomena in pedestrian flow. Based on the extended lattice hydrodynamic pedestrian model taking the interaction of the next-nearest-neighbor persons into account, the time-dependent Ginzburg-Landau （TDGL） equation is derived to describe the pedestrian flow near the critical point through the nonlinear analysis method. The corresponding two solutions, the uniform and the kink solutions, are given. The coexisting curve, spinodal line, and critical point are obtained by the first and second derivatives of the thermodynamic potential.

Asymptotic stability of solutions to the nonisentropic hydrodynamic model for semiconductors

In this paper, the asymptotic stability of smooth solutions to the multidimensional nonisentropic hydrodynamic model for semiconductors is established, under the assumption that the initial data are a small perturbation of the stationary solutions for the thermal equilibrium state, whose proofs mainly depend on the basic energy methods.

Application of River Network Hydrodynamic Model in Determining Water Distribution Scale of Haishu Plain

The water distribution network is an important part of the plain water environment improvement system. To make efficient use of the regional water diversion source, scientifically distribute the water diversion flow and improve the water environment carrying capacity of Haishu Plain, the river network hydrodynamic model is used in this paper to simulate the water intake location, reasonable water quantity and influence range of water transfer in Haishu Plain. The simulation results have high accuracy, which can provide a scientific basis for the scale, water transfer mechanism and project layout of water transfer construction in Haishu Plain and show a strong reference value for the study of water diversion and distribution scheme of coastal plain river network.

The Time Asymptotic Expansion of the Bipolar Hydrodynamic Model for Semiconductors

In 2003, Gasser-Hsiao-Li [JDE(2003)] showed that the solution to the bipolar hydrodynamic model for semiconductors(HD model) without doping function time-asymptotically converges to the diffusion wave of the porous media equation(PME) for the switch-off case. Motivated by the work of Huang-Wu[arXiv:2210.13157], we will confirm that the time-asymptotic expansion proposed by Geng-Huang-Jin-Wu [arXiv:2202.13385] around the diffusion wave is a better asymptotic profile for the HD model in this paper, where we mainly adopt the approximate Green function method and the energy method.

Numerical simulation of typhoon- induced storm surge on the coast of Jiangsu Province,China,based on coupled hydrodynamic and wave models

In order to facilitate engineering design and coastal flooding protection, the potential storm surge induced by a typhoon is studied.Using an unstructured mesh, a coupled model which combines the advanced circulation （ ADCIRC ） hydrodynamic model and simulating waves nearshore （ SWAN ） model is applied to analyze the storm surge and waves on the coast of Jiangsu Province.The verifications of wind velocity, tidal levels and wave height show that this coupling model performs well to reflect the characteristics of the water levels and waves in the studied region.Results show that the effect of radiation stress on storm surge is significant, especially in shallow areas such as the coast of Jiangsu Province and the Yangtze estuary.By running the coupled model, the simulated potential flooding results can be employed in coastal engineering applications in the Jiangsu coastal area, such as storm surge warnings and extreme water level predictions.