Investigation of the high-spin rotational properties of the proton emitter ^113Cs using a particle-number conserving method

The recently observed two high-spin rotational bands in the proton emitter ^113Cs are investigated using the cranked shell model with pairing correlations treated by a particle-number conserving method, in which the Pauli blocking effects are taken into account exactly. By using the configuration assignments of band 1 [π3/2^＋[422]（g7/2）, α =-1/2] and band 2 [π1/2^＋[420]（d5/2）, α=1/2], the experimental moments of inertia and quasiparticle alignments can be reproduced much better by the present calculations than those using the configuration assginment of π1/2^-[550]（h11/2）, which in turn may support these configuration assignments. Furthermore, by analyzing the occupation probability nμ of each cranked Nilsson level near the Fermi surface and the contribution of each orbital to the angular momentum alignments, the backbending mechanism of these two bands is also investigated.

A Local Macroscopic Conservative(LoMaC)Low Rank Tensor Method with the Discontinuous Galerkin Method for the Vlasov Dynamics

In this paper,we propose a novel Local Macroscopic Conservative(LoMaC)low rank tensor method with discontinuous Galerkin(DG)discretization for the physical and phase spaces for simulating the Vlasov-Poisson(VP)system.The LoMaC property refers to the exact local conservation of macroscopic mass,momentum,and energy at the discrete level.The recently developed LoMaC low rank tensor algorithm(arXiv:2207.00518)simultaneously evolves the macroscopic conservation laws of mass,momentum,and energy using the kinetic flux vector splitting;then the LoMaC property is realized by projecting the low rank kinetic solution onto a subspace that shares the same macroscopic observables.This paper is a generalization of our previous work,but with DG discretization to take advantage of its compactness and flexibility in handling boundary conditions and its superior accuracy in the long term.The algorithm is developed in a similar fashion as that for a finite difference scheme,by observing that the DG method can be viewed equivalently in a nodal fashion.With the nodal DG method,assuming a tensorized computational grid,one will be able to(i)derive differentiation matrices for different nodal points based on a DG upwind discretization of transport terms,and(ii)define a weighted inner product space based on the nodal DG grid points.The algorithm can be extended to the high dimensional problems by hierarchical Tucker(HT)decomposition of solution tensors and a corresponding conservative projection algorithm.In a similar spirit,the algorithm can be extended to DG methods on nodal points of an unstructured mesh,or to other types of discretization,e.g.,the spectral method in velocity direction.Extensive numerical results are performed to showcase the efficacy of the method.

Construction of Conservative Numerical Fluxes for the Entropy Split Method

The entropy split method is based on the physical entropies of the thermally perfect gas Euler equations.The Euler flux derivatives are approximated as a sum of a conservative portion and a non-conservative portion in conjunction with summation-by-parts(SBP)difference boundary closure of(Gerritsen and Olsson in J Comput Phys 129:245-262,1996;Olsson and Oliger in RIACS Tech Rep 94.01,1994;Yee et al.in J Comp Phys 162:33-81,2000).Sj?green and Yee(J Sci Comput)recently proved that the entropy split method is entropy conservative and stable.Stand-ard high-order spatial central differencing as well as high order central spatial dispersion relation preserving(DRP)spatial differencing is part of the entropy stable split methodol-ogy framework.The current work is our first attempt to derive a high order conservative numerical flux for the non-conservative portion of the entropy splitting of the Euler flux derivatives.Due to the construction,this conservative numerical flux requires higher oper-ations count and is less stable than the original semi-conservative split method.However,the Tadmor entropy conservative(EC)method(Tadmor in Acta Numerica 12:451-512,2003)of the same order requires more operations count than the new construction.Since the entropy split method is a semi-conservative skew-symmetric splitting of the Euler flux derivative,a modified nonlinear filter approach of(Yee et al.in J Comput Phys 150:199-238,1999,J Comp Phys 162:3381,2000;Yee and Sj?green in J Comput Phys 225:910934,2007,High Order Filter Methods for Wide Range of Compressible flow Speeds.Proceedings of the ICOSAHOM09,June 22-26,Trondheim,Norway,2009)is proposed in conjunction with the entropy split method as the base method for problems containing shock waves.Long-time integration of 2D and 3D test cases is included to show the com-parison of these new approaches.

A modified discrete element method for concave granular materials based on energy-conserving contact model

The development of a general discrete element method for irregularly shaped particles is the core issue of the simulation of the dynamic behavior of granular materials.The general energy-conserving contact theory is used to establish a universal discrete element method suitable for particle contact of arbitrary shape.In this study,three dimentional(3D)modeling and scanning techniques are used to obtain a triangular mesh representation of the true particles containing typical concave particles.The contact volumebased energy-conserving model is used to realize the contact detection between irregularly shaped particles,and the contact force model is refined and modified to describe the contact under real conditions.The inelastic collision processes between the particles and boundaries are simulated to verify the robustness of the modified contact force model and its applicability to the multi-point contact mode.In addition,the packing process and the flow process of a large number of irregular particles are simulated with the modified discrete element method(DEM)to illustrate the applicability of the method of complex problems.

A local pseudo arc-length method for hyperbolic conservation laws

A local pseudo arc-length method（LPALM）for solving hyperbolic conservation laws is presented in this paper.The key idea of this method comes from the original arc-length method,through which the critical points are bypassed by transforming the computational space.The method is based on local changes of physical variables to choose the discontinuous stencil and introduce the pseudo arc-length parameter,and then transform the governing equations from physical space to arc-length space.In order to solve these equations in arc-length coordinate,it is necessary to combine the velocity of mesh points in the moving mesh method,and then convert the physical variable in arclength space back to physical space.Numerical examples have proved the effectiveness and generality of the new approach for linear equation,nonlinear equation and system of equations with discontinuous initial values.Non-oscillation solution can be obtained by adjusting the parameter and the mesh refinement number for problems containing both shock and rarefaction waves.

Estimation of conservation value of myrtle(Myrtus communis)using a contingent valuation method:a case study in a Dooreh forest area,Lorestan Province,Iran

Background： Around 2000 plant species occur naturally in Lorestan Province of which 250 species are medicinal and myrtle is one of them. Myrtle is a shrub whose leaves and fruits have medicinal value and thus, if managed and harvested properly, could produce sustained economic benefits. In recent years, however, over half of the myrtle site areas was destroyed, due to inappropriate management and excessive harvesting practices. Thus, coming up with a practical harvesting approach along with identifying those factors damaging the sites, seems to be very crucial. Methods： In our investigation, we calculated the conservation value per hectare of myrtle in the Dooreh forest area in Lorestan Province. Using the Contingent Valuation （CV） and Double Bounded Dichotomous Choice （DBDC） methods, we determined the willingness to pay （VVTP） for myrtle conservation. The VVTP was estimated with a Iogit model for which indices were obtained based on a maximum precision criterion. Results： The results showed that 86.67 per cent of people were willing to pay for the conservation of these myrtle sites. Average monthly WTP per family was calculated as $0.79. The annual conservation value in terms of WTP for the preservation of the myrtle sites in Dooreh was estimated as $102,525. Among the variables of the model presented, education had a positive impact, while the amount proposed for payment and family size had a negative impact on the WTP. Conclusions： Our estimate of the value of myrtle conservation should provide justification for policy makers and decision making bodies of natural resources to implement policies in order to conserve the natural sites of this species more effectively.

Non-invasive glucose measuring apparatus based on conservation of energy method

A new non-invasive blood glucose measuring apparatus (NBGMA) made up of MSP430F149 SCM (single chip micyoco) was developed,which can measure blood glucose level (BGL) frequently,conveniently and painlessly. The hardware and software of this apparatus were designed,and detecting algorithms based on conservation of energy method (COEM) were presented. According to the law of conservation of energy that the energy derived by human body equals energy consumed by metabolism,and the relationship between convection,evaporation,radiation and the BGL was established. The sensor module was designed. 20 healthy volunteers were involved in the clinical experiment. The BGL measured by an automatic biochemical analyzer (ABA) was set as the reference. Regression analysis was performed to compare the conservation of energy method with the biochemical method,using the 20 data points with blood glucose concentrations ranging from 680 to 1 100 mg/L. Reproducibility was measured for healthy fasting volunteers. The results show that the means of BGL detected by NBGMA and ANA are very close to each other,and the difference of standard deviation (SD) is 24.7 mg/L. The correlative coefficient is 0.807. The coefficient of variation (CV) is 4% at 921.6 mg/L. The resultant regression is evaluated by the Clarke error grid analysis (EGA) and all data points are included in the clinically acceptable regions (region A:100%,region B:0%). Accordingly,it is feasible to measure BGL with COEM.

Conservative high precision pseudo arc-length method for strong discontinuity of detonation wave

A hyperbolic conservation equation can easily generate strong discontinuous solutions such as shock waves and contact discontinuity.By introducing the arc-length parameter,the pseudo arc-length method(PALM)smoothens the discontinuous solution in the arc-length space.This in turn weakens the singularity of the equation.To avoid constructing a high-order scheme directly in the deformed physical space,the entire calculation process is conducted in a uniform orthogonal arc-length space.Furthermore,to ensure the stability of the equation,the time step is reduced by limiting the moving speed of the mesh.Given that the calculation does not involve the interpolation process of physical quantities after the mesh moves,it maintains a high computational efficiency.The numerical examples show that the algorithm can effectively reduce numerical oscillations while maintaining excellent characteristics such as high precision and high resolution.

Big-M based MILP method for SCUC considering allowable wind power output interval and its adjustable conservativeness

In contrast to most existing works on robust unit commitment(UC),this study proposes a novel big-M-based mixed-integer linear programming(MILP)method to solve security-constrained UC problems considering the allowable wind power output interval and its adjustable conservativeness.The wind power accommodation capability is usually limited by spinning reserve requirements and transmission line capacity in power systems with large-scale wind power integration.Therefore,by employing the big-M method and adding auxiliary 0-1 binary variables to describe the allowable wind power output interval,a bilinear programming problem meeting the security constraints of system operation is presented.Furthermore,an adjustable confidence level was introduced into the proposed robust optimization model to decrease the level of conservatism of the robust solutions.This can establish a trade-off between economy and security.To develop an MILP problem that can be solved by commercial solvers such as CPLEX,the big-M method is utilized again to represent the bilinear formulation as a series of linear inequality constraints and approximately address the nonlinear formulation caused by the adjustable conservativeness.Simulation studies on a modified IEEE 26-generator reliability test system connected to wind farms were performed to confirm the effectiveness and advantages of the proposed method.

Using modified Soil Conservation Service curve number method to simulate the role of forest in flood control in the upper reach of the Tingjiang River in China

To improve flood control efficiency and increase urban resilience to flooding,the impacts of forest type change on flood control in the upper reach of the Tingjiang River(URTR) were evaluated by a modified model based on the Soil Conservation Service curve number(SCS-CN) method. Parameters of the model were selected and determined according to the comprehensive analysis of model evaluation indexes. The first simulation of forest reconstruction scenario,namely a coniferous forest covering 59.35km^2 is replaced by a broad-leaved forest showed no significant impact on the flood reduction in the URTR. The second simulation was added with 61.75km^2 bamboo forest replaced by broad-leaved forest,the reduction of flood peak discharge and flood volume could be improved significantly. Specifically,flood peak discharge of 10-year return period event was reduced to 7-year event,and the reduction rate of small flood was 21%-28%. Moreover,the flood volume was reduced by 9%-14% and 18%-35% for moderate floods and small floods,respectively. The resultssuggest that the bamboo forest reconstruction is an effective control solution for small to moderate flood in the URTR,the effect of forest conversion on flood volume is increasingly reduced as the rainfall amount increases to more extreme magnitude. Using a hydrological model with scenarios analysis is an effective simulation approach in investigating the relationship between forest type change and flood control. This method would provide reliable support for flood control and disaster mitigation in mountainous cities.

High order symplectic conservative perturbation method for time-varying Hamiltonian system

This paper presents a high order symplectic con- servative perturbation method for linear time-varying Hamil- tonian system. Firstly, the dynamic equation of Hamilto- nian system is gradually changed into a high order pertur- bation equation, which is solved approximately by resolv- ing the Hamiltonian coefficient matrix into a ＂major compo- nent＂ and a ＂high order small quantity＂ and using perturba- tion transformation technique, then the solution to the orig- inal equation of Hamiltonian system is determined through a series of inverse transform. Because the transfer matrix determined by the method in this paper is the product of a series of exponential matrixes, the transfer matrix is a sym- plectic matrix; furthermore, the exponential matrices can be calculated accurately by the precise time integration method, so the method presented in this paper has fine accuracy, ef- ficiency and stability. The examples show that the proposed method can also give good results even though a large time step is selected, and with the increase of the perturbation or- der, the perturbation solutions tend to exact solutions rapidly.

EXPLICIT SQUARE CONSERVING SCHEMES OF LANDAU-LIFSHITZ EQUATIONWITH GILBERT COMPONENT

A kind of explicit square-conserving scheme is proposed for the Landau-Lifshitz equation with Gilbert component. The basic idea was to semidiscrete the Landau-Lifshitz equation into the ordinary differential equations. Then the Lie group method and the Runge-Kutta (RK) method were applied to the ordinary differential equations. The square conserving property and the accuracy of the two methods were compared. Numerical experiment results show the Lie group method has the good accuracy and the square conserving property than the RK method.

A mass-conserved multiphase lattice Boltzmann method based on high-order difference

The Z–S–C multiphase lattice Boltzmann model [Zheng, Shu, and Chew(ZSC), J. Comput. Phys. 218, 353(2006)]is favored due to its good stability, high efficiency, and large density ratio. However, in terms of mass conservation, this model is not satisfactory during the simulation computations. In this paper, a mass correction is introduced into the ZSC model to make up the mass leakage, while a high-order difference is used to calculate the gradient of the order parameter to improve the accuracy. To verify the improved model, several three-dimensional multiphase flow simulations are carried out,including a bubble in a stationary flow, the merging of two bubbles, and the bubble rising under buoyancy. The numerical simulations show that the results from the present model are in good agreement with those from previous experiments and simulations. The present model not only retains the good properties of the original ZSC model, but also achieves the mass conservation and higher accuracy.

Conservative method for simulation of a high-order nonlinear Schrdinger equation with a trapped term

We propose a new scheme for simulation of a high-order nonlinear Schrodinger equation with a trapped term by using the mid-point rule and Fourier pseudospectral method to approximate time and space derivatives, respectively. The method is proved to be both charge- and energy-conserved. Various numerical experiments for the equation in different cases are conducted. From the numerical evidence, we see the present method provides an accurate solution and conserves the discrete charge and energy invariants to machine accuracy which are consistent with the theoretical analysis.

SPACE-TIME FINITE ELEMENT METHOD FOR SCHRDINGER EQUATION AND ITS CONSERVATION

Energy conservation of nonlinear Schrodinger ordinary differential equation was proved through using continuous finite element methods of ordinary differential equation; Energy integration conservation was proved through using space-time continuous fully discrete finite element methods and the electron nearly conservation with higher order error was obtained through using time discontinuous only space continuous finite element methods of nonlinear Schrodinger partial equation. The numerical results are in accordance with the theory.

SPECTRAL/HP ELEMENT METHOD WITH HIERARCHICAL RECONSTRUCTION FOR SOLVING NONLINEAR HYPERBOLIC CONSERVATION LAWS

The hierarchical reconstruction （HR） [Liu, Shu, Tadmor and Zhang, SINUM ＇07] has been successfully applied to prevent oscillations in solutions computed by finite volume, Runge-Kutta discontinuous Galerkin, spectral volume schemes for solving hyperbolic conservation laws. In this paper, we demonstrate that HR can also be combined with spectral/hp element method for solving hyperbolic conservation laws. An orthogonal spectral basis written in terms of Jacobi polynomials is applied. High computational efficiency is obtained due to such matrix-free algorithm. The formulation is conservative, and essential nomoscillation is enforced by the HR limiter. We show that HR preserves the order of accuracy of the spectral/hp element method for smooth solution problems and generate essentially non-oscillatory solutions profiles for capturing discontinuous solutions without local characteristic decomposition. In addition, we introduce a postprocessing technique to improve HR for limiting high degree numerical solutions.

Godunov＇s method for initial-boundary value problem of scalar conservation laws

This paper is concerned with Godunov＇s scheme for the initial-boundary value problem of scalar conservation laws. A kind of Godunov＇s scheme, which satisfies the boundary entropy condition, was given. By use of the scheme, numerical simulation for the weak entropy solution to the initial-boundary value problem of scalar conservation laws is conducted.

Effect of Moisture Conservation Methods and Plant Density on the Productivity of Two Maize (<i>Zea mays</i>L.) Varieties under Semi-Arid Tropics of Hamelmalo, Eritrea

The productivity of maize in Eritrea in general and under semi-arid tropics of Hamelmalo in particular is low because of moisture stress. The low moisture content is ascribed to the low and erratic distribution of rainfall, high temperature, lack of suitable varieties, and competition by weeds and low soil fertility. To overcome some of these problems, a field experiment was carried out to assess the effect of moisture conservation methods (MCM) and plant density on the productivity of two maize (Zea mays L.) varieties under semi-arid tropics of Hamelmalo, Eritrea. The experiment was conducted in split-split plot design with three MCM viz tied ridge, ridge and furrow and flat-bed in main plots;two maize varieties viz early local and 04sadve hybrid in sub plots and three plant densities by manipulating the plant to plant distance viz 35 cm, 25 cm and 15 cm at a fixed 75 cm row spacing in sub-sub plots, each replicated thrice. The experiment was focused in addressing the effective moisture conservation techniques, optimum plant density to each variety thus to improve productivity. The crop experienced 10°C to 34.8°C minimum and maximum temperature, respectively and received 429.1 mm total rainfall. The results of the experiment indicated that among all the combinations, 04sadve hybrid variety sown at 75 cm × 25 cm spacing in ridge and furrow method or at 75 cm × 15 cm spacing in tied ridge or flat-bed method and early local variety sown at 75 cm × 15 cm spacing in flat-bed being statistically at par resulted in significantly higher moisture conservation and consequently higher grain yield (4509 kg·ha-1) and higher water use efficiency. It is, therefore, recommended that tied ridge or flat-bed of moisture conservation method at 15 cm plant spacing and 04sadve is preferable to optimize productivity in Hamelmalo area, Eritrea.

A New Application of the Flux Approximation Method on Hyperbolic Conservation Systems

In this paper, we first summarize several applications of the flux approximation method on hyperbolic conservation systems. Then, we introduce two hyperbolic conservation systems (2.1) and (2.2) of Temple’s type, and prove that the global weak solutions of each system could be obtained by the limit of the linear combination of two systems.

High-Order Bound-Preserving Finite Difference Methods for Multispecies and Multireaction Detonations

In this paper,we apply high-order finite difference(FD)schemes for multispecies and multireaction detonations(MMD).In MMD,the density and pressure are positive and the mass fraction of the ith species in the chemical reaction,say zi,is between 0 and 1,withΣz_(i)=1.Due to the lack of maximum-principle,most of the previous bound-preserving technique cannot be applied directly.To preserve those bounds,we will use the positivity-preserving technique to all the zi'is and enforceΣz_(i)=1 by constructing conservative schemes,thanks to conservative time integrations and consistent numerical fluxes in the system.Moreover,detonation is an extreme singular mode of flame propagation in premixed gas,and the model contains a significant stiff source.It is well known that for hyperbolic equations with stiff source,the transition points in the numerical approximations near the shocks may trigger spurious shock speed,leading to wrong shock position.Intuitively,the high-order weighted essentially non-oscillatory(WENO)scheme,which can suppress oscillations near the discontinuities,would be a good choice for spatial discretization.However,with the nonlinear weights,the numerical fluxes are no longer“consistent”,leading to nonconservative numerical schemes and the bound-preserving technique does not work.Numerical experiments demonstrate that,without further numerical techniques such as subcell resolutions,the conservative FD method with linear weights can yield better numerical approximations than the nonconservative WENO scheme.