Experimental Investigation of Lee–Yang Criticality Using Non-Hermitian Quantum System

Lee–Yang theory clearly demonstrates where the phase transition of many-body systems occurs and the asymptotic behavior near the phase transition using the partition function under complex parameters. The complex parameters make the direct investigation of Lee–Yang theory in practical systems challenging. Here we construct a non-Hermitian quantum system that can correspond to the one-dimensional Ising model with imaginary parameters through the equality of partition functions. By adjusting the non-Hermitian parameter,we successfully obtain the partition function under different imaginary magnetic fields and observe the Lee–Yang zeros. We also observe the critical behavior of free energy in vicinity of Lee–Yang zero that is consistent with theoretical prediction. Our work provides a protocol to study Lee–Yang zeros of the one-dimensional Ising model using a single-qubit non-Hermitian system.

Restraint effect of partition wall on the tunnel floor heave in layered rock mass

The presence of horizontal layered rocks in tunnel engineering significantly impacts the stability and strength of the surrounding rock mass,leading to floor heave in the tunnel.This study focused on preparing layered specimens of rock-like material with varying thickness to investigate the failure behaviors of tunnel floors.The results indicate that thin-layered rock mass exhibits weak interlayer bonding,causing rock layers near the surface to buckle and break upwards when subjected to horizontal squeezing.With an increase in the layer thickness,a transition in failure mode occurs from upward buckling to shear failure along the plane,leading to a noticeable reduction in floor heave deformation.The primary cause of significant deformation in floor heave is upward buckling failure.To address this issue,the study proposes the installation of a partition wall in the middle of the floor to mitigate heave deformation of the rock layers.The results demonstrate that the partition wall has a considerable stabilizing effect on the floor,reducing the zone of buckling failure and minimizing floor heave deformation.It is crucial for the partition wall to be sufficiently high to prevent buckling failure and ensure stability.Through simulation calculations on an engineering example,it is confirmed that implementing a partition wall can effectively reduce floor heave and enhance the stability of tunnel floor.

Long Duration Coverage Control of Multiple Robotic Surface Vehicles Under Battery Energy Constraints

Dear Editor,This letter addresses long duration coverage problem of multiple robotic surface vehicles(RSVs) subject to battery energy constraints,in addition to uncertainties and disturbances. An anti-disturbance energy-aware control method is proposed for performing coverage task of RSVs. Firstly, a centroidal Voronoi tessellation(CVT) is used to optimize the partition of the given coverage area.

The Weighted Basis for PHT-Splines

PHT-splines are defined as polynomial splines over hierarchical T-meshes with very efficient local refinement properties.The original PHT-spline basis functions constructed by the truncation mechanism have a decay phenomenon,resulting in numerical instability.The non-decay basis functions are constructed as the B-splines that are defined on the 2×2 tensor product meshes associated with basis vertices in Kang et al.,but at the cost of losing the partition of unity.In the field of finite element analysis and topology optimization,forming the partition of unity is the default ingredient for constructing basis functions of approximate spaces.In this paper,we will show that the non-decay PHT-spline basis functions proposed by Kang et al.can be appropriately modified to form a partition of unity.Each non-decay basis function is multiplied by a positive weight to form the weighted basis.The weights are solved such that the sum of weighted bases is equal to 1 on the domain.We provide two methods for calculatingweights,based on geometric information of basis functions and the subdivision of PHT-splines.Weights are given in the form of explicit formulas and can be efficiently calculated.We also prove that the weights on the admissible hierarchical T-meshes are positive.

Improved simulation of winter wheat yield in North China Plain by using PRYM-Wheat integrated dry matter distribution coefficient

The accurate simulation of regional-scale winter wheat yield is important for national food security and the balance of grain supply and demand in China.Presently,most remote sensing process models use the“biomass×harvest index(HI)”method to simulate regional-scale winter wheat yield.However,spatiotemporal differences in HI contribute to inaccuracies in yield simulation at the regional scale.Time-series dry matter partition coefficients(Fr)can dynamically reflect the dry matter partition of winter wheat.In this study,Fr equations were fitted for each organ of winter wheat using site-scale data.These equations were then coupled into a process-based and remote sensingdriven crop yield model for wheat(PRYM-Wheat)to improve the regional simulation of winter wheat yield over the North China Plain(NCP).The improved PRYM-Wheat model integrated with the fitted Fr equations(PRYM-Wheat-Fr)was validated using data obtained from provincial yearbooks.A 3-year(2000-2002)averaged validation showed that PRYM-Wheat-Fr had a higher coefficient of determination(R^(2)=0.55)and lower root mean square error(RMSE=0.94 t ha^(-1))than PRYM-Wheat with a stable HI(abbreviated as PRYM-Wheat-HI),which had R^(2) and RMSE values of 0.30 and 1.62 t ha^(-1),respectively.The PRYM-Wheat-Fr model also performed better than PRYM-Wheat-HI for simulating yield in verification years(2013-2015).In conclusion,the PRYM-Wheat-Fr model exhibited a better accuracy than the original PRYM-Wheat model,making it a useful tool for the simulation of regional winter wheat yield.

Displacement characteristics of CO_(2)flooding in extra-high water-cut reservoirs

Carbon dioxide(CO_(2))flooding is a widely applied recovery method during the tertiary recovery of oil and gas.A high water saturation condition in reservoirs could induce a‘water shielding’phenomenon after the injection of CO_(2).This would prevent contact between the injected gas and the residual oil,restricting the development of the miscible zone.A micro-visual experiment of dead-end models,used to observe the effect of a film of water on the miscibility process,indicates that CO_(2)can penetrate the water film and come into contact with the residual oil,although the mixing is significantly delayed.However,the dissolution loss of CO_(2)at high water-cut conditions is not negligible.The oil-water partition coefficient,defined as the ratio of CO_(2)solubility in an oil-brine/two-phase system,keeps constant for specific reservoir conditions and changes little with an injection gas.The NMR device shows that when CO_(2)flooding follows water flooding,the residual oil decreasesdnot only in medium and large pores but also in small and micro pores.At levels of higher water saturation,CO_(2)displacement is characterized initially by a low oil production rate and high water-cut.After the CO_(2)breakthrough,the water-cut decreases sharply and the oil production rate increases gradually.The response time of CO_(2)flooding at high watercut reservoirs is typically delayed and prolonged.These results were confirmed in a pilot test for CO_(2)flooding at the P1-1 well group of the Pucheng Oilfield.Observations from this pilot study also suggest that a larger injection gas pore volume available for CO_(2)injection is required to offset the dissolution loss in high water saturation conditions.

Partitioning Calculation Method of Short-Circuit Current for High Proportion DG Access to Distribution Network

Aiming at the problemthat the traditional short-circuit current calculationmethod is not applicable to Distributed Generation(DG)accessing the distribution network,the paper proposes a short-circuit current partitioning calculation method considering the degree of voltage drop at the grid-connected point of DG.Firstly,the output characteristics of DG in the process of low voltage ride through are analyzed,and the equivalent output model of DG in the fault state is obtained.Secondly,by studying the network voltage distribution law after fault in distribution networks under different DG penetration rates,the degree of voltage drop at the grid-connected point of DG is used as a partition index to partition the distribution network.Then,iterative computation is performed within each partition,and data are transferred between partitions through split nodes to realize the fast partition calculation of short-circuit current for high proportion DG access to distribution network,which solves the problems of long iteration time and large calculation error of traditional short-circuit current.Finally,a 62-node real distribution network model containing a high proportion of DG access is constructed onMATLAB/Simulink,and the simulation verifies the effectiveness of the short-circuit current partitioning calculation method proposed in the paper,and its calculation speed is improved by 48.35%compared with the global iteration method.

Integrated gravity and magnetic study on patterns of petroleum basin occurrence in the China seas and adjacent areas

The China seas and adjacent areas contain numerous petroleum basins.One of the main challenges for future oil and gas exploration is to identify the inherent patterns of petroleum basin distribution.The formation and evolution of petroleum basins along with the migration and accumulation of oil and gas are often closely related to the tectonic environment.The gravity and magnetic fields with high lateral resolution and wide coverage provide important data for regional tectonic research.Based on the gravity data in the Global Satellite Gravity Anomaly Database(V31.1)and magnetic data from the Earth Magnetic Anomaly Grid(2-arc-minute resolution)(V2),this study uses integrated gravity and magnetic field technique to obtain integrated gravity and magnetic field result for the China seas and adjacent areas,and then adopts the normalized vertical derivative of the total horizontal derivative technique to conduct partition.Finally,it identifies the relationship between the partition characteristics and tectonics as well as the patterns of petroleum basin occurrence.The research shows that the partition of gravity and magnetic field integrated result has a good correlation with the Neo-Cathaysian tectonic system and tectonic units.The petroleum basins are characterized according to three blocks arranged from north to south and four zones arranged from east to west.The north-south block structure causes the uneven distribution of oil and gas resources in the mainland area and the differences in the hydrocarbon-bearing strata.Petroleum basins are more abundant in the north than in the south.The ages of the main oil-and gas-bearing strata are“Paleozoic–Mesozoic,Paleozoic–Mesozoic–Cenozoic,and Paleozoic–Mesozoic”,in order from north to south.The difference in the overall type of oil and gas resources in all basins is controlled by the east–west zonation.From east to west,the oil and gas resource type exhibits a wave-like pattern of“oil and gas,gas,oil and gas,gas”.The vertical distribution is characterized by an upper oil(Mesozoic–Cenozoic)and lower gas(Mesozoic–Paleozoic)structure.Within the study area,the Paleozoic marine strata should be the main strata of future natural gas exploration.

Allocation patterns of nonstructural carbohydrates in response to CO_(2)elevation and nitrogen deposition in Cunninghamia lanceolata saplings

Stored nonstructural carbohydrates(NSC)indicate a balance between photosynthetic carbon(C)assimilation and growth investment or loss through respiration and root exudation.They play an important role in plant function and whole-plant level C cycling.CO_(2)elevation and nitrogen(N)deposition,which are two major environmental issues worldwide,aff ect plant photosynthetic C assimilation and C release in forest ecosystems.However,information regarding the eff ect of CO_(2)elevation and N deposition on NSC storage in diff erent organs remains limited,especially regarding the trade-off between growth and NSC reserves.Therefore,here we analyzed the variations in the NSC storage in diff erent organs of Chinese fi r(Cunninghamia lanceolata)under CO_(2)elevation and N addition and found that NSC concentrations and contents in all organs of Chinese fi r saplings increased remarkably under CO_(2)elevation.However,N addition induced diff erential accumulation of NSC among various organs.Specifi cally,N addition decreased the NSC concentrations of needles,branches,stems,and fi ne roots,but increased the NSC contents of branches and coarse roots.The increase in the NSC contents of roots was more pronounced than that in the NSC content of aboveground organs under CO_(2)elevation.The role of N addition in the increase in the structural biomass of aboveground organs was greater than that in the increase in the structural biomass of roots.This result indicated that a diff erent tradeoff between growth and NSC storage occurred to alleviate resource limitations under CO_(2)elevation and N addition and highlights the importance of separating biomass into structural biomass and NSC reserves when investigating the eff ects of environmental change on biomass allocation.

CD4^(+)CD25^(+) regulatory T cells decreased future liver remnant after associating liver partition and portal vein ligation for staged hepatectomy

BACKGROUND Associating liver partition and portal vein ligation for staged hepatectomy(ALPPS)is an innovative surgical approach for the treatment of massive hepatocellular carcinoma(HCC),the key to successful planned stage 2 ALPPS is future liver remnant(FLR)volume growth,but the exact mechanism has not been elucidated.The correlation between regulatory T cells(Tregs)and postoperative FLR regeneration has not been reported.AIM To investigate the effect of CD4^(+)CD25^(+)Tregs on FLR regeneration after ALPPS.METHODS Clinical data and specimens were collected from 37 patients who developed massive HCC treated with ALPPS.Flow cytometry was performed to detect changes in the proportion of CD4^(+)CD25^(+)Tregs to CD4^(+)T cells in peripheral blood before and after ALPPS.To analyze the relationship between peripheral blood CD4^(+)CD25^(+)Treg proportion and clinicopathological information and liver volume.RESULTS The postoperative CD4^(+)CD25^(+)Treg proportion in stage 1 ALPPS was negatively correlated with the amount of proliferation volume,proliferation rate,and kinetic growth rate(KGR)of the FLR after stage 1 ALPPS.Patients with low Treg proportion had significantly higher KGR than those with high Treg proportion(P=0.006);patients with high Treg proportion had more severe postoperative pathological liver fibrosis than those with low Treg proportion(P=0.043).The area under the receiver operating characteristic curve between the percentage of Tregs and proliferation volume,proliferation rate,and KGR were all greater than 0.70.CONCLUSION CD4^(+)CD25^(+)Tregs in the peripheral blood of patients with massive HCC at stage 1 ALPPS were negatively correlated with indicators of FLR regeneration after stage 1 ALPPS and may influence the degree of fibrosis in patients’livers.Treg percentage was highly accurate in predicting the FLR regeneration after stage 1 ALPPS.

2D Minimum Compliance Topology Optimization Based on a Region Partitioning Strategy

This paper presents an extended sequential element rejection and admission(SERA)topology optimizationmethod with a region partitioning strategy.Based on the partitioning of a design domain into solid regions and weak regions,the proposed optimizationmethod sequentially implements finite element analysis(FEA)in these regions.After standard FEA in the solid regions,the boundary displacement of the weak regions is constrained using the numerical solution of the solid regions as Dirichlet boundary conditions.This treatment can alleviate the negative effect of the material interpolation model of the topology optimization method in the weak regions,such as the condition number of the structural global stiffness matrix.For optimization,in which the forward problem requires nonlinear structural analysis,a linear solver can be applied in weak regions to avoid numerical singularities caused by the over-deformedmesh.To enhance the robustness of the proposedmethod,the nonmanifold point and island are identified and handled separately.The performance of the proposed method is verified by three 2D minimum compliance examples.

Numerical Study of Natural Convective Heat Transfer in an Air Filled Square Cavity Heated from Below and Symmetrically Cooled from the Sides with a Partition in the Hot Wall

A two-dimensional numerical study of laminar natural convection in a square enclosure filled with air with a wall partially heated on the bottom is presented.The heat source is located on the lower wall with different heated widths varied from 20 to 80%(ε=0.2–0.8)of the total width of the lower wall and different heights h=H/4 and H/2 of the partition.The effect of the partition height on the main system dynamics is investigated through solution of the two-dimensional Navier-Stokes equations and the energy equation by means of a finite volume method based on the SIMPLE algorithm.The influence of the Rayleigh number(Ra=10^(3) to 10^(6))and the hot wall length is also examined.It is shown that the average Nusselt number grows whenεincreases and when h decreases.For a given value ofεand h,the average Nusselt number increases as Ra increases.It is concluded that the partition height causes a decrease in the average Nusselt number.

A Novel Incremental Attribute Reduction Algorithm Based on Intuitionistic Fuzzy Partition Distance

Attribute reduction,also known as feature selection,for decision information systems is one of the most pivotal issues in machine learning and data mining.Approaches based on the rough set theory and some extensions were proved to be efficient for dealing with the problemof attribute reduction.Unfortunately,the intuitionistic fuzzy sets based methods have not received much interest,while these methods are well-known as a very powerful approach to noisy decision tables,i.e.,data tables with the low initial classification accuracy.Therefore,this paper provides a novel incremental attribute reductionmethod to dealmore effectivelywith noisy decision tables,especially for highdimensional ones.In particular,we define a new reduct and then design an original attribute reduction method based on the distance measure between two intuitionistic fuzzy partitions.It should be noted that the intuitionistic fuzzypartitiondistance iswell-knownas aneffectivemeasure todetermine important attributes.More interestingly,an incremental formula is also developed to quickly compute the intuitionistic fuzzy partition distance in case when the decision table increases in the number of objects.This formula is then applied to construct an incremental attribute reduction algorithm for handling such dynamic tables.Besides,some experiments are conducted on real datasets to show that our method is far superior to the fuzzy rough set based methods in terms of the size of reduct and the classification accuracy.

Picture-Neutrosophic Trusted Safe Semi-Supervised Fuzzy Clustering for Noisy Data

Clustering is a crucial method for deciphering data structure and producing new information.Due to its significance in revealing fundamental connections between the human brain and events,it is essential to utilize clustering for cognitive research.Dealing with noisy data caused by inaccurate synthesis from several sources or misleading data production processes is one of the most intriguing clustering difficulties.Noisy data can lead to incorrect object recognition and inference.This research aims to innovate a novel clustering approach,named Picture-Neutrosophic Trusted Safe Semi-Supervised Fuzzy Clustering(PNTS3FCM),to solve the clustering problem with noisy data using neutral and refusal degrees in the definition of Picture Fuzzy Set(PFS)and Neutrosophic Set(NS).Our contribution is to propose a new optimization model with four essential components:clustering,outlier removal,safe semi-supervised fuzzy clustering and partitioning with labeled and unlabeled data.The effectiveness and flexibility of the proposed technique are estimated and compared with the state-of-art methods,standard Picture fuzzy clustering(FC-PFS)and Confidence-weighted safe semi-supervised clustering(CS3FCM)on benchmark UCI datasets.The experimental results show that our method is better at least 10/15 datasets than the compared methods in terms of clustering quality and computational time.

Using “Particle Density” of “Graviton Gas”, to Obtain Value of Cosmological Constant

We use the work of de Vega, Sanchez, and Comes (1997), to approximate the “particle density” of a “graviton gas”. This “particle density” derivation is compared with Dolgov’s (1997) expression of the Vacuum energy in terms of a phase transition. The idea is to have a quartic potential, and then to utilize the Bogomol’nyi inequality to refine what the phase transition states. We utilize Ng, Infinite quantum information procedures to link our work with initial entropy and other issues and close with a variation in the HUP: at the start of the expansion of the universe.

The Method and Practice of Constructing 3D Geological Model from Coalfield Exploration 2D Maps

3D geological modeling is an inevitable choice for coal exploration to adapt to the transformation of coal mining for green, fine, transparent and Intelligent mining. In the traditional Coalfield exploration geological reports, the spatial expression form for the coal seams and their surrounding rocks are 2D maps. These 2D maps are excellent data sources for constructing 3D geological models of coal field exploration areas. How to construct 3D models from these 2D maps has been studying in coal exploration industry for a long time, and still no breakthrough has been achieved so far. This paper discusses the principle, method and software design idea of constructing 3D geological model of an exploration area with 2D maps made by AutoCAD/MapGIS. At first, the paper analyzes 3D geological surface expression mode in 3D geological modeling software. It is pointed out that although contour method has unique advantages in coal field exploration, TIN (Triangular Irregular Network) is still the standard configuration of 3D modeling software for coal field. Then, the paper discusses the method of 2D line features obtaining elevation and upgrading 2D curve to 3D curve. Next, the method of semi-automatic partition is introduced to build the boundary ring of the surface patch, that is, the user clicks and selects the line feature to build the outer boundary ring of the surface patch. Then, Auto-process method for fault line inside of the outer boundary ring is discussed, it including construction of fault ring, determining fault ring being normal fault ring or reverse fault ring and an algorithm of dealing with normal fault ring. An algorithm of dealing with reverse fault ring is discussed detailly, the method of expanding reverse fault ring and dividing the duplicate area in reverse fault into two portions is introduced. The paper also discusses the method of extraction ridge line/valley line, the construction of fault plane, the construction of stratum and coal body. The above ideas and methods have been initially implemented in the “3D modeling platform for coal field exploration” software, and applied to the 3D modeling practice of data from several coal field exploration areas in Ningxia, Shanxi, Qinghai, etc.

Removal of boron from metallurgical grade silicon by electromagnetic induction slag melting

A new purification process was developed to remove impurities in metallurgical grade silicon （MG-Si） by electromagnetic induction slag melting （EISM）. Vacuum melting furnace was used to purify boron in different slag systems. The results show that the removal effect in SiO2-CaO-Al2O3 systems is better than that in other slag systems by EISM. The boron content in MG-Si is successfully reduced from 1.5× 10^-5 to 0.2× 10^-5 during EISM at 1 823 K for 2 h. Meanwhile, Al, Ca and Mg elements in MG-Si are also well removed and their removal efficiencies reach 85.0%, 50.2% and 66.7%, respectively, which indicates that EISM is very effective to remove boron and metal impurities in silicon.

Boron removal from metallurgical silicon using CaO-SiO_2-CaF_2 slags

The removal of boron from metallurgical silicon in slag system of CaO-SiO2-10%CaF2 was investigated. The partition coefficient of boron （LB） between slag and silicon phase was studied under different conditions of slag basicity （CaO/SiO2 ratio）, temperature, mass ratio of slag to silicon and gas blowing. The results show that LB has a maximum value of 4.61 when the CaO/SiO2 mass ratio is around 2 at l 873 K. The logarithm of LB is linear to the reciprocal of temperatures in the range of 1 773-1 973 K. LB increases with the increase of mass ratio of slag to silicon, but it does not increase markedly when the ratio excesses 3. Gas blowing can sionificantlv increase the removal of boron, and LR increases with the increase of water vapor content.

Alloy gene Gibbs energy partition function and equilibrium holographic network phase diagrams of AuCu_3-type sublattice system

Taking AuCu3-type sublattice system as an example, three discoveries have been presented: First, the third barrier hindering the progress in metal materials science is that researchers have got used to recognizing experimental phenomena of alloy phase transitions during extremely slow variation in temperature by equilibrium thinking mode and then taking erroneous knowledge of experimental phenomena as selected information for establishing Gibbs energy function and so-called equilibrium phase diagram. Second, the equilibrium holographic network phase diagrams of AuCu3-type sublattice system may be used to describe systematic correlativity of the composition?temperature-dependent alloy gene arranging structures and complete thermodynamic properties, and to be a standard for studying experimental subequilibrium order-disorder transition. Third, the equilibrium transition of each alloy is a homogeneous single-phase rather than a heterogeneous two-phase, and there exists a single-phase boundary curve without two-phase region of the ordered and disordered phases; the composition and temperature of the top point on the phase-boundary curve are far away from the ones of the critical point of the AuCu3 compound.

Alloy gene Gibbs energy partition function and equilibrium holographic network phase diagrams of Au_3Cu-type sublattice system

Taking Au3Cu-type sublattice system as an example, three discoveries have been presented. First, the fourth barrier to hinder the progress of metal materials science is that today’s researchers do not understand that the Gibbs energy function of an alloy phase should be derived from Gibbs energy partition function constructed of alloy gene sequence and their Gibbs energy sequence. Second, the six rules for establishing alloy gene Gibbs energy partition function have been discovered, and it has been specially proved that the probabilities of structure units occupied at the Gibbs energy levels in the degeneracy factor for calculating configuration entropy should be degenerated as ones of component atoms occupied at the lattice points. Third, the main characteristics unexpected by today’s researchers are as follows. There exists a single-phase boundary curve without two-phase region coexisting by the ordered and disordered phases. The composition and temperature of the top point on the phase-boundary curve are far away from those of the critical point of the Au3Cu compound; At 0 K, the composition of the lowest point on the composition-dependent Gibbs energy curve is notably deviated from that of the Au3Cu compounds. The theoretical limit composition range of long range ordered Au3Cu-type alloys is determined by the first jumping order degree.