A Dugdale-Barenblatt model for elliptical orifice problem with asymmetric cracks in one-dimensional orthorhombic quasicrystals

By means of Muskhelishvili’s method and the technique of generalized conformal mapping,the physical plane problems are transformed into regular mathematical problems in quasicrystals(QCs).The analytical solution to an elliptical orifice problem with asymmetric cracks in one-dimensional(1D)orthorhombic QCs is obtained.By using the Dugdale-Barenblatt model,the plastic simulation at the crack tip of the elliptical orifice with asymmetric cracks in 1D orthorhombic QCs is performed.Finally,the size of the atomic cohesive force zone is determined precisely,and the size of the atomic cohesive force zone around the crack tip of an elliptical orifice with a single crack or two symmetric cracks is obtained.

A study on the numerical prediction method for the vertical thermal structure in the Bohai Sea and the Huanghai Sea-I.One-dimensional numerical prediction model

In this paper, on the basis of the heat conduction equation without consideration of the advection and turbulence effects, one-dimensional model for describing surface sea temperature ( T1), bottom sea temperature ( Tt ) and the thickness of the upper homogeneous layer ( h ) is developed in terms of the dimensionless temperature θT and depth η and self-simulation function θT - f(η) of vertical temperature profile by means of historical temperature data.The results of trial prediction with our one-dimensional model on T, Th, h , the thickness and gradient of thermocline are satisfactory to some extent.

Reconstructing the upper ocean thermal profiles using one-dimensional numerical model

The observation data for 5 d at a station in the South China Sea is presented. After brief anMysis of the wind speed, air temperature from the ship-borne meteorological instruments and temperature and salinity profiles from the CTD （conductivity, temperature, depth recorder） data, the authors find that the CTD casts are too sparse for us to understand the diurnal evolution of the thermal structure in the upper ocean. A one-dimensional （1D） numericM code based on Mellor-Yamada turbulence closure model is used to reconstruct the upper ocean thermal structure, utilizing the atmospheric forcing data from ship-borne weather station. The simulation results show good agreement with the observational data; the significance of breaking waves is also briefly discussed. The evolution of turbulence kinetic energy （TKE） and the contribution from shear production and buoy- ancy production are discussed respectively. Finally, several possible factors which might influence the numerical results are briefly analyzed.

Research on the Application of the Radiative Transfer Model Based on Deep Neural Network in One-dimensional Variational Algorithm

As a typical physical retrieval algorithm for retrieving atmospheric parameters,one-dimensional variational(1 DVAR)algorithm is widely used in various climate and meteorological communities and enjoys an important position in the field of microwave remote sensing.Among algorithm parameters affecting the performance of the 1 DVAR algorithm,the accuracy of the microwave radiative transfer model for calculating the simulated brightness temperature is the fundamental constraint on the retrieval accuracies of the 1 DVAR algorithm for retrieving atmospheric parameters.In this study,a deep neural network(DNN)is used to describe the nonlinear relationship between atmospheric parameters and satellite-based microwave radiometer observations,and a DNN-based radiative transfer model is developed and applied to the 1 DVAR algorithm to carry out retrieval experiments of the atmospheric temperature and humidity profiles.The retrieval results of the temperature and humidity profiles from the Microwave Humidity and Temperature Sounder(MWHTS)onboard the Feng-Yun-3(FY-3)satellite show that the DNN-based radiative transfer model can obtain higher accuracy for simulating MWHTS observations than that of the operational radiative transfer model RTTOV,and also enables the 1 DVAR algorithm to obtain higher retrieval accuracies of the temperature and humidity profiles.In this study,the DNN-based radiative transfer model applied to the 1 DVAR algorithm can fundamentally improve the retrieval accuracies of atmospheric parameters,which may provide important reference for various applied studies in atmospheric sciences.

Simulation of the Influence of Ion-Produced NO_X and HO_X Radicals on the Antarctic Ozone Depletion with a One-Dimensional Model

A one -dimensional time-dependent photochemical model is used to simulate the influence of ion-produced NOx and HOx radicals on the Antarctic ozone depletion in polar night and polar spring at a latitude of 73 degrees south.Vertical transport and nitrogen-oxygen (NOx). hydrogen-oxygen (HOx) production by ionic reactions have been introduced into the model.NOx and HOx produced by precipitating ions are transported into the lower stratosphere by vertical motion and have some effects in the development of the Antarctic ozone depletion.From winter through spring the calculated ozone column decreases to 269.4 DU. However, this value is significantly higher than the total ozone observed at several Antarctic ozone stations.

Entanglement in the Quantum Phase Transition of the Half-Integer Spin One-Dimensional Heisenberg Model

We use the Bethe’s ansatz method to study the entanglement of spinons in the quantum phase transition of half integer spin one-dimensional magnetic chains known as quantum wires. We calculate the entanglement in the limit of the number of particles . We obtain an abrupt change in the entanglement next the quantum phase transition point of the anisotropy parameter ?from the gapped phase ?to gapless phase .

Atmosphere-Ocean Coupling Schemes in a One-Dimensional Climate Model

In this paper, the coupling schemes of atmosphere-ocean climate models are discussed with one-dimensional advection equations. The convergence and stability for synchronous and asynchronous schemes are demonstrated and compared.Conclusions inferred from the analysis are given below. The synchronous scheme as well as the asynchronous-implicit scheme in this model are stable for arbitrary integrating time intervals. The asynchronous explicit scheme is unstable under certain conditions, which depend upon advection velocities and heat exchange parameters in the atmosphere and oceans. With both synchronous and asynchronous stable schemes the discrete solutions converge to their unique exact ones. Advections in the atmosphere and ocean accelerate the rate of convergence of the asynchronous-implicit scheme. It is suggusted that the asynchronous-implicit coupling scheme is a stable and efficient method for most climatic simulations.

A SOLVABLE ONE-DIMENSIONAL ALLOCATION DECISION MODEL OF RENEWABLE RESOURCES

In the paper, the determinate atlecation decision model and the probabilistic allocation decision model of a kind of renewable resource are separatly studied by means of dynamic programming, and the optimal allocation policy is given under some special conditions.

One-dimensional horizontal infiltration experiment for determining permeability coefficient of loamy sand

A knowledge of soil permeability is essential to evaluate hydrologic characteristics of soil, such as water storage and water movement, and soil permeability coefficient is an important parameter that reflects soil permeability. In order to confirm the acceptability of the one-dimensional horizontal infiltration method（one-D method） for simultaneously determining both the saturated and unsaturated permeability coefficients of loamy sand, we first measured the cumulative infiltration and the wetting front distance under various infiltration heads through a series of one-dimensional horizontal infiltration experiments, and then analyzed the relationships of the cumulative horizontal infiltration with the wetting front distance and the square root of infiltration time. We finally compared the permeability results from Gardner model based on the one-D method with the results from other two commonly-used methods（i.e., constant head method and van Genuchten model） to evaluate the acceptability and applicability of the one-D method. The results showed that there was a robust linear relationship between the cumulative horizontal infiltration and the wetting front distance, suggesting that it is more appropriate to take the soil moisture content after infiltration in the entire wetted zone as the average soil moisture content than as the saturated soil moisture content. The results also showed that there was a robust linear relationship between the cumulative horizontal infiltration and the square root of infiltration time, suggesting that the Philip infiltration formula can better reflect the characteristics of cumulative horizontal infiltration under different infiltration heads. The following two facts indicate that it is feasible to use the one-D method for simultaneously determining the saturated and unsaturated permeability coefficients of loamy sand. First, the saturated permeability coefficient（prescribed in the Gardner model） of loamy sand obtained from the one-D method well agreed with the value obtained from the constant head method. Second, the relationship of unsaturated permeability coefficient with soil water suction for loamy sand calculated using Gardner model based on the one-D method was nearly identical with the same relationship calculated using van Genuchten model.

Anomalous energy diffusion and heat conduction in one-dimensional system

We propose a new concept, the centre of energy, to study energy diffusion and heat conduction in a one-dimensional hard-point model. For the diatom model, we find an anomalous energy diffusion as （x2） - tβ with β = 1.33, which is independent of initial condition and mass rate. The present model can be viewed as the model composed by independent quasi-particles, the centre of energy. In this way, heat current can be calculated. Based on the theory of dynamic billiard, the divergent exponent of heat conductivity is estimated to be α = 0.33, which is confirmed by a simple numerical calculation.

Calculation and prediction of divertor detachment via impurity seeding by using one-dimensional model

Achieving the detachment of divertor can help to alleviate excessive heat load and sputtering problems on the target plates,thereby extending the lifetime of divertor components for fusion devices.In order to provide a fast but relatively reliable prediction of plasma parameters along the flux tube for future device design,a one-dimensional(1D)modeling code for the operating point of impurity seeded detached divertor is developed based on Python language,which is a fluid model based on previous work(Plasma Phys.Control.Fusion 58045013(2016)).The experimental observation of the onset of divertor detachment by neon(Ne)and argon(Ar)seeding in EAST is well reproduced by using the 1D modeling code.The comparison between the 1D modeling and two-dimensional(2D)simulation by the SOLPS-ITER code for CFETR detachment operation with Ne and Ar seeding also shows that they are in good agreement.We also predict the radiative power loss and corresponding impurity concentration requirement for achieving divertor detachment via different impurity seeding under high heating power conditions in EAST and CFETR phase II by using the 1D model.Based on the predictions,the optimized parameter space for divertor detachment operation on EAST and CFETR is also determined.Such a simple but reliable 1D model can provide a reasonable parameter input for a detailed and accurate analysis by 2D or three-dimensional(3D)modeling tools through rapid parameter scanning.

Analysis of piezoelectric semiconductor fibers under gradient temperature changes

Piezoelectric semiconductors(PSs)possess both semiconducting properties and piezoelectric coupling effects,making them optimal building blocks for semiconductor devices.PS fiber-like structures have wide applications in multi-functional semiconductor devices.In this paper,a one-dimensional(1D)theoretical model is established to describe the piezotronic responses of a PS fiber under gradient temperature changes.The theoretical model aims to explain the mechanism behind the resistance change caused by such gradient temperature changes.Numerical results demonstrate that a gradient temperature change significantly affects the physical fields within the PS fiber,and can induce changes in its surface resistance.It provides important theoretical guidance on the development of piezotronic devices that are sensitive to temperature effects.

Effects of gravel on the water absorption characteristics and hydraulic parameters of stony soil

The eastern foothills of the Helan Mountains in China are a typical mountainous region of soil and gravel,where gravel could affect the water movement process in the soil.This study focused on the effects of different gravel contents on the water absorption characteristics and hydraulic parameters of stony soil.The stony soil samples were collected from the eastern foothills of the Helan Mountains in April 2023 and used as the experimental materials to conduct a one-dimensional horizontal soil column absorption experiment.Six experimental groups with gravel contents of 0%,10%,20%,30%,40%,and 50%were established to determine the saturated hydraulic conductivity(K_(s)),saturated water content(θ_(s)),initial water content(θ_(i)),and retention water content(θ_(r)),and explore the changes in the wetting front depth and cumulative absorption volume during the absorption experiment.The Philip model was used to fit the soil absorption process and determine the soil water absorption rate.Then the length of the characteristic wetting front depth,shape coefficient,empirical parameter,inverse intake suction and soil water suction were derived from the van Genuchten model.Finally,the hydraulic parameters mentioned above were used to fit the soil water characteristic curves,unsaturated hydraulic conductivity(K_(θ))and specific water capacity(C(h)).The results showed that the wetting front depth and cumulative absorption volume of each treatment gradually decreased with increasing gravel content.Compared with control check treatment with gravel content of 0%,soil water absorption rates in the treatments with gravel contents of 10%,20%,30%,40%,and 50%decreased by 11.47%,17.97%,25.24%,29.83%,and 42.45%,respectively.As the gravel content increased,inverse intake suction gradually increased,and shape coefficient,K_(s),θ_(s),andθ_(r)gradually decreased.For the same soil water content,soil water suction and K_(θ)gradually decreased with increasing gravel content.At the same soil water suction,C(h)decreased with increasing gravel content,and the water use efficiency worsened.Overall,the water holding capacity,hydraulic conductivity,and water use efficiency of stony soil in the eastern foothills of the Helan Mountains decreased with increasing gravel content.This study could provide data support for improving soil water use efficiency in the eastern foothills of the Helan Mountains and other similar rocky mountainous areas.

Numerical Simulation for One Dimensional Steady Quasineutral Hybrid Model of Stationary Plasma Thruster

Based on the analysis of the physical mechanism of the Stationary Plasma Thruster （SPT）, an integral equation describing the ion density of the steady SPT and the ion velocity distribution function at an arbitrary axial position of the steady SPT channel are derived. The integral equation is equivalent to the Vlasov equation, but the former is simpler than the latter. A one dimensional steady quasineutral hybrid model is established. In this model, ions are described by the above integral equation, and neutrals and electrons are described by hydrodynamic equations. The transferred equivalency to the differential equation and the integral equation, together with other equations, are solved by an ordinary differential equation （ODE） solver in the Matlab. The numerical simulation results show that under various circumstances, the ion average velocity would be different and needs to be deduced separately.

Application of particle trajectory model in 1D planar ejection

A simple one-dimensional planar model for ejection was set up based on experiments.And numerical simulation was performed on this model with particle trajectory model method.An Eulerian finite volume method was conducted to resolve gas field.And Lagrangian method was imposed to track each particle.The interaction between gas and particles was responded as source terms in governing equations which were induced by forces.The effects of total spraying mass,particle size and other factors on the mixture of particles and gas were investigated.The spatial distributions of particle mass and velocity at different time were presented.The result shows that the numerical results are qualitatively consistent to those of experiments.

Calogero Model with Different Masses

We study a multispecies one-dimensional Calogero model with two- and three-body interactions. Here, we factorize the ground stateout of the Hamiltonian H in order to get the new operatorwhich preserves some spaces of polynomialsin the case of equal masses, i.e. (the usual Calogero model) and in the case with different masses. The spectrum of these both cases is found easily.

Investigation on One-Dimensional Loss Models for Predicting Performance of Multistage Centrifugal Compressors in Supercritical CO Brayton Cycle

The main compressor in a supercritical carbon dioxide(SCO2)Brayton cycle works near the critical point where the physical properties of CO_(2)are far away from the ideal gas.To investigate the effectiveness of the conventional one-dimensional(1D)loss models for predicting the performance of compressors working in such nontraditional conditions,detailed comparisons of 1D predicted performance,experimental data and threedimensional CFD results are made.A 1D analysis method with enthalpy and total pressure based loss system is developed for multistage SCO2 centrifugal compressors,and it is firstly validated against the experimental results of a single stage SCO2 centrifugal compressor from the Sandia National Laboratory.A good agreement of pressure ratios with experiments can be achieved by the 1D method.But the efficiency deviations reveal the potential deficiencies of the parasitic loss models.On the basis of the validation,a two-stage SCO2 centrifugal compressor is employed to do the evaluation.Three-dimensional CFD simulations are performed.Detailed comparisons are made between the CFD and the 1D results at different stations located in the compressor.The features of the deviations are analyzed in detail,as well as the reasons that might cause these deviations.

Uniform Asymptotics for Finite-Time Ruin Probabilities of Risk Models with Non-Stationary Arrivals and Strongly Subexponential Claim Sizes

This paper considers the one-and two-dimensional risk models with a non-stationary claim-number process.Under the assumption that the claim-number process satisfies the large deviations principle,the uniform asymptotics for the finite-time ruin probability of a one-dimensional risk model are obtained for the strongly subexponential claim sizes.Further,as an application of the result of onedimensional risk model,we derive the uniform asymptotics for a kind of finite-time ruin probability in a two dimensional risk model sharing a common claim-number process which satisfies the large deviations principle.

Computing equations of water hammer in pseudo-homogeneous solid-liquid flow and their verification

In engineering practice, single-phase water hammer models are still employed to analyze the water hammer of solid-liquid flow. According to the characteristics of solid-liquid flow, continuity equations and momentum equations of pseudo-homogeneous flows are deduced, and a pseudo-homogeneous water hammer model is thus built and verified with experiment results. The characteristics of solid-liquid flow’s viscosity, resistance and wave velocity are considered in the model. Therefore, it has higher precision than a single-phase model.

Method of coupling 1-D unsaturated flow with 3-D saturated flow on large scale

A coupled unsaturated-saturated water flow numerical model was developed. The water flow in the unsaturated zone is considered the one-dimensional vertical flow, which changes in the horizontal direction according to the groundwater table and the atmospheric boundary conditions. The groundwater flow is treated as the three-dimensional water flow. The recharge flux to groundwater from soil water is considered the bottom flux for the numerical simulation in the unsaturated zone, and the upper flux for the groundwater simulation. It connects and unites the two separated water flow systems. The soil water equation is solved based on the assumed groundwater table.and the subsequent predicted recharge flux. Then, the groundwater equation is solved with the predicted recharge flux as the upper boundary condition. Iteration continues until the discrepancy between the assumed and calculated groundwater nodal heads have a certain accuracy. Illustrative examples with different water flow scenarios regar.ding the Dirichlet boundary condition, the Neumann boundary condition, the a.tmospheric boundary condition, and the source or sink term were calculated by the coupled model. The results are compared with those of other models, including Hydrus-lD, SWMS-2D, and FEFLOW, which demonstrate that the coupled model is effective and accurate and can significantly reduce the computational time for the large number of nodes in saturated-unsaturated water flow simulation.