A hybrid method integrating Green's function Monte Carlo and projected entangled pair states

This paper introduces a hybrid approach combining Green’s function Monte Carlo(GFMC)method with projected entangled pair state(PEPS)ansatz.This hybrid method regards PEPS as a trial state and a guiding wave function in GFMC.By leveraging PEPS’s proficiency in capturing quantum state entanglement and GFMC’s efficient parallel architecture,the hybrid method is well-suited for the accurate and efficient treatment of frustrated quantum spin systems.As a benchmark,we applied this approach to study the frustrated J_(1)–J_(2) Heisenberg model on a square lattice with periodic boundary conditions(PBCs).Compared with other numerical methods,our approach integrating PEPS and GFMC shows competitive accuracy in the performance of ground-state energy.This paper provides systematic and comprehensive discussion of the approach of our previous work[Phys.Rev.B 109235133(2024)].

Future changes in precipitation and water availability over the Tibetan Plateau projected by CMIP6 models constrained by climate sensitivity

Precipitation projections over the Tibetan Plateau(TP)show diversity among existing studies,partly due to model uncertainty.How to develop a reliable projection remains inconclusive.Here,based on the IPCC AR6–assessed likely range of equilibrium climate sensitivity(ECS)and the climatological precipitation performance,the authors constrain the CMIP6(phase 6 of the Coupled Model Intercomparison Project)model projection of summer precipitation and water availability over the TP.The best estimates of precipitation changes are 0.24,0.25,and 0.45 mm d^(−1)(5.9%,6.1%,and 11.2%)under the Shared Socioeconomic Pathway(SSP)scenarios of SSP1–2.6,SSP2–4.5,and SSP5–8.5 from 2050–2099 relative to 1965–2014,respectively.The corresponding constrained projections of water availability measured by precipitation minus evaporation(P–E)are 0.10,0.09,and 0.22 mm d^(−1)(5.7%,4.9%,and 13.2%),respectively.The increase of precipitation and P–E projected by the high-ECS models,whose ECS values are higher than the upper limit of the likely range,are about 1.7 times larger than those estimated by constrained projections.Spatially,there is a larger increase in precipitation and P–E over the eastern TP,while the western part shows a relatively weak difference in precipitation and a drier trend in P–E.The wetter TP projected by the high-ECS models resulted from both an approximately 1.2–1.4 times stronger hydrological sensitivity and additional warming of 0.6℃–1.2℃ under all three scenarios during 2050–2099.This study emphasizes that selecting climate models with climate sensitivity within the likely range is crucial to reducing the uncertainty in the projection of TP precipitation and water availability changes.

Spatial Variation and Trend of Extreme Precipitation in Africa during 1981-2019 and Its Projected Changes at the End of 21st Century

This study comprehensively examines the patterns and regional variation of severe rainfall across the African continent, employing a suite of eight extreme precipitation indices. The analysis extends to the assessment of projected changes in precipitation extremes using five General Circulation Models (GCMs) from Coupled Model Intercomparison Project Phase 6 (CMIP6) under four Shared Socioeconomic Pathways (SSPs) scenarios at the long-term period (2081-2100) of the 21st century. Furthermore, the study investigates potential mechanisms influencing precipitation extremes by correlating extreme precipitation indices with oceanic system indices, specifically Ni?o 3.4 for El Ni?o-Southern Oscillation (ENSO) and Dipole Mode Index (DMI) for the Indian Ocean Dipole (IOD). The findings revealed distinct spatial distributions in mean trends of extreme precipitation indices, indicating a tendency toward decreased extreme precipitation in North Africa, Sahel region, Central Africa and the Western part of South Africa. Conversely, West Africa, East Africa and the Eastern part of South Africa exhibit an inclination toward increased extreme precipitation. The changes in precipitation extreme indices indicate a general rise in both the severity and occurrence of extreme precipitation events under all scenarios by the end of the 21st century. Notably, our analysis projects a decrease in consecutive wet days (CWD) in the far-future. Additionally, correlation analysis highlights significant correlation between above or below threshold rainfall fluctuation in East Africa and South Africa with oceanic systems, particularly ENSO and the IOD. Central Africa abnormal precipitation variability is also linked to ENSO with a significant negative correlation. These insights contribute valuable information for understanding and projecting the dynamics of precipitation extreme in Africa, providing a foundation for climate adaptation and mitigation efforts in the region.

Projected Changes in the Climate Zoning of Côte d’Ivoire

This study assesses the projected changes in the climate zoning of Côte d’Ivoire using the hierarchical classification of principal components (HCPC) method applied to the daily precipitation data of an ensemble of 14 CORDEX-AFRICA simulations under RCP4.5 and RCP8.5 scenarios. The results indicate the existence of three climate zones in Côte d’Ivoire (the coastal, the centre and the north) over the historical period (1981-2005). Moreover, CORDEX simulations project an extension of the surface area of drier climatic zones while a reduction of wetter zones, associated with the appearance of an intermediate climate zone with surface area varying from 77,560 km2 to 134,960 km2 depending on the period and the scenario. These results highlight the potential impacts of climate change on the delimitation of the climate zones of Côte d’Ivoire under the greenhouse gas emission scenarios. Thus, there is a reduction in the surface areas suitable for the production of cash crops such as cocoa and coffee. This could hinder the country’s economy and development, mainly based on these cash crops.

Relativistic Consistent Angular-Momentum Projected Shell-Model：Angular-Momentum Projection

The angular-momentum projection part of RECAPS is presented.Application of RECAPS to some deformed nuclei is also presented.

Relativistic Consistent Angular-Momentum Projected Shell-Model： Relativistic Mean Field

We develop a relativistic nuclear structure model, relativistic consistent angular-momentum projected shell-model (RECAPS), which combines the relativistic mean-field theory with the angular-momentum projection method. In this new model, nuclear ground-state properties are first calculated consistently using relativistic mean-field (RMF) theory. Then angular momentum projection method is used to project out states with good angular momentum from a few important configurations. By diagonalizing the hamiltonian, the energy levels and wave functions are obtained. This model is a new attempt for the understanding of nuclear structure of normal nuclei and for the prediction of nuclear properties of nuclei far from stability. In this paper, we will describe the treatment of the relativistic mean field. A computer code, RECAPS-RMF, is developed. It solves the relativistic mean field with axial-symmetric deformation in the spherical harmonic oscillator basis. Comparisons between our calculations and existing relativistic mean-field calculations are made to test the model. These include the ground-state properties of spherical nuclei 16O and 208Pb, the deformed nucleus 20Ne. Good agreement is obtained.

Consensus Control With a Constant Gain for Discrete-time Binary-valued Multi-agent Systems Based on a Projected Empirical Measure Method

This paper studies the consensus control of multiagent systems with binary-valued observations.An algorithm alternating estimation and control is proposed.Each agent estimates the states of its neighbors based on a projected empirical measure method for a holding time.Based on the estimates,each agent designs the consensus control with a constant gain at some skipping time.The states of the system are updated by the designed control,and the estimation and control design will be repeated.For the estimation,the projected empirical measure method is proposed for the binary-valued observations.The algorithm can ensure the uniform boundedness of the estimates and the mean square error of the estimation is proved to be at the order of the reciprocal of the holding time(the same order as that in the case of accurate outputs).For the consensus control,a constant gain is designed instead of the stochastic approximation based gain in the existing literature for binary-valued observations.And,there is no need to make modification for control since the uniform boundedness of the estimates ensures the uniform boundedness of the agents’states.Finally,the systems updated by the designed control are proved to achieve consensus and the consensus speed is faster than that in the existing literature.Simulations are given to demonstrate the theoretical results.

A SUBSPACE PROJECTED CONJUGATE GRADIENT ALGORITHM FOR LARGE BOUND CONSTRAINED QUADRATIC PROGRAMMING

A subspace projected conjugate gradient method is proposed for solving large bound constrained quadratic programming. The conjugate gradient method is used to update the variables with indices outside of the active set, while the projected gradient method is used to update the active variables. At every iterative level, the search direction consists of two parts, one of which is a subspace trumcated Newton direction, another is a modified gradient direction. With the projected search the algorithm is suitable to large problems. The convergence of the method is proved and same numerical tests with dimensions ranging from 5000 to 20000 are given.

ON THE MONOTONE CONVERGENCE OF THE PROJECTED ITERATION METHODS FOR LINEAR COMPLEMENTARITY PROBLEMS

Under suitable conditions,the monotone convergence about the projected iteration method for solving linear complementarity problem is proved and the influence of the involved parameter matrix on the convergence rate of this method is investigated.

Projected Runge-Kutta methods for constrained Hamiltonian systems

Projected Runge-Kutta （R-K） methods for constrained Hamiltonian systems are proposed. Dynamic equations of the systems, which are index-3 differential-algebraic equations （DAEs） in the Heisenberg form, are established under the framework of Lagrangian multipliers. R-K methods combined with the technique of projections are then used to solve the DAEs. The basic idea of projections is to eliminate the constraint violations at the position, velocity, and acceleration levels, and to preserve the total energy of constrained Hamiltonian systems by correcting variables of the position, velocity, acceleration, and energy. Numerical results confirm the validity and show the high precision of the proposed method in preserving three levels of constraints and total energy compared with results reported in the literature.

Estimation of projected surface area of irregularly shaped fragments

The essence and the main contribution of this paper are consisted of the suggested novel method for estimation of a projected surface area of an irregularly shaped fragment, which represents a significant step toward a new method of an aerodynamic force estimation of a fragment motion through a resistive medium. The suggested method is to use a tri-axial ellipsoid that has a continuous surface(given as a mathematical function) to approximate an irregularly shaped fragment so that the fragment trajectory can be estimated faster taking into consideration that the aerodynamic force is proportional to a projected surface area of the fragment.During their motion, fragments can take any orientation relative to the velocity vector and aerodynamic force is proportional to a projected surface area of fragment perpendicular to the velocity vector,so it is necessary to have a method for correct estimation of the projected area in an arbitrary direction relatively to the fragment.The model was validated with analytical and CAD techniques, and verified using 3D model of a real fragment. The comparison of the projected surface area values for the fragment, obtained using the CAD tools and using our model, are generally in good agreement, This method represents a step toward modeling that does not require a CFD result for estimation of the aerodynamic force of irregularly shaped bodies.

Probability Distribution and Projected Trends of Daily Precipitation in China

Based on observed daily precipitation data of 540 stations and 3,839 gridded data from the high-resolution regional climate model COSMO-Climate Limited-area Modeling(CCLM)for 1961–2000,the simulation ability of CCLM on daily precipitation in China is examined,and the variation of daily precipitation distribution pattern is revealed.By applying the probability distribution and extreme value theory to the projected daily precipitation(2011–2050)under SRES A1B scenario with CCLM,trends of daily precipitation series and daily precipitation extremes are analyzed.Results show that except for the western Qinghai-Tibetan Plateau and South China,distribution patterns of the kurtosis and skewness calculated from the simulated and observed series are consistent with each other;their spatial correlation coefcients are above 0.75.The CCLM can well capture the distribution characteristics of daily precipitation over China.It is projected that in some parts of the Jianghuai region,central-eastern Northeast China and Inner Mongolia,the kurtosis and skewness will increase significantly,and precipitation extremes will increase during 2011–2050.The projected increase of maximum daily rainfall and longest non-precipitation period during flood season in the aforementioned regions,also show increasing trends of droughts and floods in the next 40 years.

PROJECTED GRADIENT DESCENT BASED ON SOFT THRESHOLDING IN MATRIX COMPLETION

Matrix completion is the extension of compressed sensing.In compressed sensing,we solve the underdetermined equations using sparsity prior of the unknown signals.However,in matrix completion,we solve the underdetermined equations based on sparsity prior in singular values set of the unknown matrix,which also calls low-rank prior of the unknown matrix.This paper firstly introduces basic concept of matrix completion,analyses the matrix suitably used in matrix completion,and shows that such matrix should satisfy two conditions:low rank and incoherence property.Then the paper provides three reconstruction algorithms commonly used in matrix completion:singular value thresholding algorithm,singular value projection,and atomic decomposition for minimum rank approximation,puts forward their shortcoming to know the rank of original matrix.The Projected Gradient Descent based on Soft Thresholding(STPGD),proposed in this paper predicts the rank of unknown matrix using soft thresholding,and iteratives based on projected gradient descent,thus it could estimate the rank of unknown matrix exactly with low computational complexity,this is verified by numerical experiments.We also analyze the convergence and computational complexity of the STPGD algorithm,point out this algorithm is guaranteed to converge,and analyse the number of iterations needed to reach reconstruction error.Compared the computational complexity of the STPGD algorithm to other algorithms,we draw the conclusion that the STPGD algorithm not only reduces the computational complexity,but also improves the precision of the reconstruction solution.

Level Structure of 83Rb in the Projected Shell Model

The projected shell model is applied to the odd-proton nucleus 83 Rb. The results of theoretical calculationsabout the excited positive-parity yrast states and the negative-parity ground-state band are compared with experimentaldata, and the best reproduction of the experiment has been given by this model. In addition, a band diagram calculatedfor the negative-parity g.s. band is also shown in order to extract physics out of the numerical results.

Autonomous Control Strategy of a Swarm System Under Attack Based on Projected View and Light Transmittance

In the study of a visual projection field with swarm movements,an autonomous control strategy is presented in this paper for a swarm system under attack.To ensure a fast swarm dynamic response and stable spatial cohesion in a complex environment,a new hybrid swarm motion model is proposed by introducing global visual projection information to a traditional local interaction mechanism.In the face of attackers,individuals move towards the largest free space according to the projected view of the environment,rather than directly in the opposite direction of the attacker.Moreover,swarm individuals can certainly regroup without dispersion after the attacker leaves.On the other hand,the light transmittance of each individual is defined based on global visual projection information to represent its spatial freedom and relative position in the swarm.Then,an autonomous control strategy with adaptive parameters is proposed according to light transmittance to guide the movement of swarm individuals.The simulation results demonstrate in detail how individuals can avoid attackers safely and reconstruct ordered states of swarm motion.

Projected gradient trust-region method for solving nonlinear systems with convex constraints

In this paper, a projected gradient trust region algorithm for solving nonlinear equality systems with convex constraints is considered. The global convergence results are developed in a very general setting of computing trial directions by this method combining with the line search technique. Close to the solution set this method is locally Q-superlinearly convergent under an error bound assumption which is much weaker than the standard nonsingularity condition.

Projected subgradient method for non-Lipschitz set-valued mixed variational inequalities

A projected subgradient method for solving a class of set-valued mixed variational inequalities （SMVIs） is proposed when the mapping is not necessarily Lipschitz. Under some suitable conditions, it can be proven that the sequence generated by the method can strongly converge to the unique solution to the problem in the Hilbert spaces.

A projected gradient method with nonmonotonic backtracking technique for solving convex constrained monotone variational inequality problem

Based on a differentiable merit function proposed by Taji, et al in “Mathematical Programming, 1993, 58： 369-383”, a projected gradient trust region method for the monotone variational inequality problem with convex constraints is presented. Theoretical analysis is given which proves that the proposed algorithm is globally convergent and has a local quadratic convergence rate under some reasonable conditions. The results of numerical experiments are reported to show the effectiveness of the proposed algorithm.

Angular Momentum Projected Potential-Energy-Surface Calculation:Application to ^(178)Hf

An angular momentum projected potential-energy-surface （PES） calculation, which takes both rotational symmetry restoration and multi-quasiparticle excitation into account, is developed by using the macroscopic-microscopic model and the projected shell model （PSM）. Within this method, it may become possible to modify the excitation spectra which are influenced by shape-softness of nuclei, including high-K states. As our first example, this method is adopted to study the collective and multi-quasiparticle excitations of 178Hf~ and the results are in good agreement with the existing experimental data. In addition, as for the dominant structure of non- collective 6＋ bands, the conflict between experimental result and the previous PSM calculation is clarified.

Energy model of projected transfer with additional mechanical force in the welding process

Based on the theory of electrodynamics and other relational subjects,through introducing “Surface Evolver” as the means of FEM analysis, by computing and describing the energy (electromagnetic, gravity, and so on) in the droplet transfer system, an energy model was accomplished for studying the mechanism of projected transfer mode.Furthermore, the behavior of droplet transfer was studied by analyzing its menisci with FEM, and the theoretical results coincide well with the experiment results.