Large-scale Monte Carlo Simulations Research Articles

Comprehensive Assessment of the Health Risk of Cadmium Exposure from Soil-wheat System in Wheat Fields in Northern China

Accurately assessing the health risks of cadmium （Cd） exposure in the soil-wheat system is of great importance for the formulation of regional health risk prevention measures. Based on regional large-scale survey and Monte Carlo simulation methods, a case study on the health risk of Cd exposure in a soil-wheat system in a wheat production area of North China Plain was conducted by constructing a comprehensive health risk assessment （CHRA） model. The results showed that 73% of the soil samples in the study area exceeded the screening value of Cd for farmland soil （GB 15618-2018） and 57.8% of the wheat samples exceeded the national standard （GB 2762-2017） for Cd. The hand-mouth ingestion pathway was the main route of soil Cd exposure for adults and children in the region, and under this pathway, 34.7% of adults and 57.4% of children had a cancer risk higher than the safe threshold recommended by USEPA （1E-06）. The comprehensive non-carcinogenic and carcinogenic risks of cadmium exposure from the soil-wheat system in the region were higher than the safe domain values for both adults and children, with the probabilities of 26.4% and 100% for adults and 62.5% and 100% for children, respectively. The overall trends of the comprehensive risks showed that children had higher risks than those of adults. The combined application of the comprehensive health risk assessment model and the uncertainty random simulation method helps to improve the accuracy of risk decision-making.

A Novel Information Complexity Approach to Score Receiver Operating Characteristic (ROC) Curve Modeling.

Performance metrics are measures of success or performance that can be used to evaluate how well a model makes accurate predictions or classifications. However, there is no single measure since each performance metric emphasizes a different classification aspect. Model selection procedures based on information criteria offer a quantitative measure that balances model complexity with goodness of fit, providing a better alternative to classical approaches. In this paper, we introduce and develop a novel Information Complexity-Receiver Operating Characteristic, abbreviated as ICOMP-ROC, criterion approach to fit and study the performance of ROC curve models. We construct and derive the Universal ROC (UROC) for a combination of sixteen Bi-distributional ROC models to choose the best Bi-distributional ROC by minimizing the ICOMP-ROC criterion. We conduct large-scale Monte Carlo simulations using the sixteen Bi-distributional ROC models with the Normal-Normal and Weibull-Gamma pairs as the pseudo-true ROC models. We report the frequency of hits of the ICOMP-ROC criterion, showing its remarkable recovery rate. In addition to Bi-distributional fitting, we consider a high-dimensional real Magnetic Resonance Imaging (MRI) of the Brain dataset and Wisconsin Breast Cancer (WBC) dataset to study the performance of the common performance metrics and the ICOMP-ROC criterion using several machine learning (ML) classification algorithms. We use the genetic algorithm (GA) to reduce the dimensions of these two datasets to choose the best subset of the features to study and compare the performance of the newly proposed ICOMP-ROC criterion along with the traditional performance metrics. The choice of a suitable metric is not just contingent upon the ML model used, but it also depends upon the complexity and high dimensionality of the input datasets, since the traditional performance metrics give different results and have inherent limitations. Our numerical results show the consistency and reliability of the ICOMP-ROC criterion over the traditional performance metrics as a clever model selection criterion to choose the best fitting Bi-distributional ROC model and the best classification algorithm among the ones considered. This shows the utility and the versatility of our newly proposed approach in ROC curve modeling that integrates and robustifies currently used procedures.

Estimation of the Chances to Find New Phenomena at the LHC in a Model-Agnostic Combinatorial Analysis

In this paper, we estimate the number of event topologies that have the potential to be produced in pp collisions at the Large Hadron Collider (LHC) without violating kinematic and other constraints. We use numerical calculations and combinatorics, guided by large-scale Monte Carlo simulations of Standard Model (SM) processes. Then, we set the upper limit on the probability that new physics may escape detection, assuming a model-agnostic approach. The calculated probability is unexpectedly large, and the fact that LHC has not found new physics until now is not entirely surprising. Theoretical limitations and experimental challenges in observing new physics within the studied exclusive event classes are examined.

Interplay of the complete-graph and Gaussian fixed-point asymptotics in finite-size scaling of percolation above the upper critical dimension.

For statistical mechanical systems with continuous phase transitions, there are two closely related but subtly different mean-field treatments, the Gaussian fixed point (GFP) in the renormalization group framework and the Landau mean-field theory or the complete-graph (CG) asymptotics. By large-scale Monte Carlo simulations, we systematically study the interplay of the GFP and CG effects to the finite-size scaling of percolation above the upper critical dimension d_{c}=6 with periodic and cylindrical boundary conditions. Our results suggest that, with periodic boundaries, the unwrapped correlation length scales as L^{d/6} at the critical point, diverging faster than L above d_{c}. As a consequence, the scaling behaviors of macroscopic quantities with respect to the linear system size L follow the CG asymptotics. The distance-dependent properties, such as the short-distance behavior of the two-point correlation function and the Fourier transformed quantities with nonzero modes, are still controlled by the GFP. With cylindrical boundaries, due to the interplay of the GFP and CG effects, the correlation length along the axial direction of the cylinder scales as ξ_{L}∼L^{(d-1)/5} within the critical window of size O(L^{-2(d-1)/5}), distinct from periodic boundary. A field-theoretical calculation for deriving the scaling of ξ_{L} is also presented. Moreover, the one-point surface correlation function along the axial direction of the cylinder is observed to scale as τ^{(1-d)/2} when the distance τ is short, but then enter a plateau of order L^{-3(d-1)/5} before it decays significantly fast.

Adaptive location and scale estimation with kernel-weighted averages

A wide variety of location and scale estimators have been developed for light-tailed distributions. Despite indisputable importance in business, finance, cybersecurity, etc., statistical estimation and inference in the presence of heavy tails have received less attention in the literature. We adopt the Kernel-Weighted Average (KWA) approach to location and scale estimation and present a set of extensive comparisons with five prominent competitors. Unlike nonparametric kernel density estimation, the optimally tuned bandwidth for KWA estimators does not necessarily converge to zero as sample size grows. We also perform a large-scale Monte Carlo simulation to search for the optimal bandwidth that minimizes the mean squared error (MSE) of KWA location and scale estimators with simulated samples from Student’s t-distribution with degrees of freedom (df) 1 , 2 , … , 30 . We further develop an adaptive technique to estimate the df that best match the observed samples using Cramér-von Mises test of goodness-of-fit. Unlike many existing methodologies, our approach is data-driven and exhibits excellent statistical performance. To illustrate this, we apply it to three real-world financial datasets containing daily closing prices of AMC Entertainment (AMC), GameStop (GME) and Meta Platforms (META) stocks to calibrate a geometric random walk model with Student’s t log-increments.

Quantum-critical properties of the one- and two-dimensional random transverse-field Ising model from large-scale quantum Monte Carlo simulations

We study the ferromagnetic transverse-field Ising model with quenched disorder at T = 0T=0 in one and two dimensions by means of stochastic series expansion quantum Monte Carlo simulations using a rigorous zero-temperature scheme. Using a sample-replication method and averaged Binder ratios, we determine the critical shift and width exponents \nu_\mathrm{s}νs and \nu_\mathrm{w}νw as well as unbiased critical points by finite-size scaling. Further, scaling of the disorder-averaged magnetisation at the critical point is used to determine the order-parameter critical exponent \betaβ and the critical exponent \nu_{\mathrm{av}}νav of the average correlation length. The dynamic scaling in the Griffiths phase is investigated by measuring the local susceptibility in the disordered phase and the dynamic exponent z'z′ is extracted. By applying various finite-size scaling protocols, we provide an extensive and comprehensive comparison between the different approaches on equal footing. The emphasis on effective zero-temperature simulations resolves several inconsistencies in existing literature.

Imbalances in Two-Level Hierarchical Linear Modeling of Single-Case Data: A Monte Carlo Simulation Study

Hierarchical linear modeling (HLM) is a promising approach that can be applied to explain variability in intervention effectiveness between participants in single-case experimental design (SCED) research. This approach allows the inclusion of participant characteristics as moderators to account for variability in intervention effectiveness. However, little is known about the performance of HLM for analysis with the inclusion of imbalanced intervention starting points and imbalanced moderators. Therefore, the goal of this study is to empirically evaluate the statistical properties of this model through a large-scale Monte Carlo simulation study under these scenarios. The results indicate that imbalanced intervention starting points have no impact on the statistical properties of estimating intervention effects. On the other hand, imbalanced moderators have an impact on estimating the intervention and moderator. How the conditions of imbalanced moderators influence the performance of two-level HLM depends on how the moderators are coded. Two general conclusions can be made. The model results in more favorable statistical properties when (i) a larger number of participants are included and (ii) the variability in continuous moderators is larger. Practical implications for the design and analysis of SCEDs are discussed.

Mirror symmetry breakdown in the Kardar-Parisi-Zhang universality class.

The current/height fluctuation statistics of Kardar-Parisi-Zhang (KPZ) universality in 1+1 dimensions are sensitive to the initial state. We find that the averages over the initial states exhibit universal and scale-invariant patterns when conditioning on fluctuations. To establish universality of our findings, we demonstrate scale invariance at different times and heights using large-scale Monte Carlo simulations of the totally asymmetric simple exclusion process, which belongs to the KPZ universality class. Here we focus on current (or height) fluctuations in the steady-state regime described by the Baik-Rains distribution. The conditioned probability distribution of an initial-state order parameter shows a transition from uni- to bimodal. Bimodality occurs for negative current/height fluctuations that are dominated by superdiffusive shock dynamics. It is caused by two possible point-symmetric shock profiles and the KPZ mirror symmetry breakdown. Similar surprising relations between initial states and fluctuations might exist in other universality classes as well.

Effective model for superconductivity in magic-angle graphene

We carry out large-scale quantum Monte Carlo simulations of a candidate field theory for the onset of superconductivity in magic-angle twisted bilayer graphene. The correlated insulating state at charge neutrality spontaneously breaks U(1) Moiré valley symmetry. Owing to the topological nature of the bands, skyrmion defects of the order parameter carry charge 2e and condense upon doping. In our calculations we encode the U(1) symmetry by an internal degree of freedom such that it is not broken upon lattice regularization. Furthermore, the skyrmion carries the same charge. The nature of the doping-induced phase transitions depends on the strength of the easy-plane anisotropy that reduces the SU(2) valley symmetry to U(1)×Z2. For large anisotropy, we observe two distinct transitions separated by phase coexistence. While the insulator to superconducting transition is of mean-field character, the U(1) transition is consistent with three-dimensional XY criticality. Hence, the coupling between the gapless charge excitations of the superconducting phase and the XY order parameter is irrelevant. At small anisotropy, we observe a first-order transition characterized by phase separation. Published by the American Physical Society 2024

Emergent Macroscopic Bistability Induced by a Single Superconducting Qubit

The photon blockade breakdown in a continuously driven cavity QED system has been proposed as a prime example for a first-order driven-dissipative quantum phase transition. However, the predicted scaling from a microscopic behavior—dominated by quantum fluctuations—to a macroscopic one—characterized by stable phases—and the associated exponents and phase diagram have not been observed so far. In this work we couple a single transmon qubit with a fixed coupling strength g to a superconducting cavity that is bandwidth κ tunable to controllably approach this thermodynamic limit. Even though the system remains microscopic, we observe its behavior becoming increasingly macroscopic as a function of g/κ. For the highest realized g/κ of approximately 287, the system switches with a characteristic timescale as long as 6 s between a bright coherent state with approximately 8×103 intracavity photons and the vacuum state. This exceeds the microscopic timescales by 6 orders of magnitude and approaches the perfect hysteresis expected between two macroscopic attractors in the thermodynamic limit. These findings and interpretation are qualitatively supported by neoclassical theory and large-scale quantum-jump Monte Carlo simulations. Besides shedding more light on driven-dissipative physics in the limit of strong light-matter coupling, this system might also find applications in quantum sensing and metrology. Published by the American Physical Society 2024

Regional pooling in extreme event attribution studies: an approach based on multiple statistical testing

Statistical methods are proposed to select homogeneous regions when analyzing spatial block maxima data, such as in extreme event attribution studies. Here, homogeneitity refers to the fact that marginal model parameters are the same at different locations from the region. The methods are based on classical hypothesis testing using Wald-type test statistics, with critical values obtained from suitable parametric bootstrap procedures and corrected for multiplicity. A large-scale Monte Carlo simulation study finds that the methods are able to accurately identify homogeneous locations, and that pooling the selected locations improves the accuracy of subsequent statistical analyses. The approach is illustrated with a case study on precipitation extremes in Western Europe. The methods are implemented in an R package that allows for easy application in future extreme event attribution studies.

Extraordinary-log Universality of Critical Phenomena in Plane Defects.

The recent discovery of the extraordinary-log (E-Log) criticality is a celebrated achievement in modern critical theory and calls for generalization. Using large-scale MonteCarlo simulations, we study the critical phenomena of plane defects in three- and four-dimensional O(n) critical systems. In three dimensions, we provide the first numerical proof for the E-Log criticality of plane defects. In particular, for n=2, the critical exponent q[over ^] of two-point correlation and the renormalization-group parameter α of helicity modulus conform to the scaling relation q[over ^]=(n-1)/(2πα), whereas the results for n≥3 violate this scaling relation. In four dimensions, it is strikingly found that the E-Log criticality also emerges in the plane defect. These findings have numerous potential realizations and would boost the ongoing advancement of conformal field theory.

Finite-temperature critical behaviors in 2D long-range quantum Heisenberg model

The Mermin-Wagner theorem states that spontaneous continuous symmetry breaking is prohibited in systems with short-range interactions at spatial dimension D ≤ 2. For long-range interactions with a power-law form (1/rα), the theorem further forbids ferromagnetic or antiferromagnetic order at finite temperature when α ≥ 2D. However, the situation for α ∈ (2, 4) at D = 2 is not covered by the theorem. To address this, we conduct large-scale quantum Monte Carlo simulations and field theoretical analysis. Our findings show spontaneous breaking of SU(2) symmetry in the ferromagnetic Heisenberg model with 1/rα-form long-range interactions at D = 2. We determine critical exponents through finite-size analysis for α < 3 (above the upper critical dimension with Gaussian fixed point) and 3 ≤ α < 4 (below the upper critical dimension with non-Gaussian fixed point). These results reveal new critical behaviors in 2D long-range Heisenberg models, encouraging further experimental studies of quantum materials with long-range interactions beyond the Mermin-Wagner theorem’s scope.

Superdiffusion-like behavior in zero-temperature coarsening of the d=3 Ising model

One key aspect of coarsening following a quench below the critical temperature is domain growth. For the non-conserved Ising model a power-law growth of domains of like spins with exponent alpha = 1/2 is predicted. Including recent work, it was not possible to clearly observe this growth law in the special case of a zero-temperature quench in the three-dimensional model. Instead a slower growth with alpha <1/2 was reported. We attempt to clarify this discrepancy by running large-scale Monte Carlo simulations on simple-cubic lattices with linear lattice sizes up to L=2048 employing an efficient GPU implementation. Indeed, at late times we measure domain sizes compatible with the expected growth law—but surprisingly, at still later times domains even grow superdiffusively, i.e., with alpha > 1/2. We argue that this new problem is possibly caused by sponge-like structures emerging at early times.

Study of the de Almeida-Thouless line in the one-dimensional diluted power-law XY spin glass.

We study the de Almeida-Thouless (AT) line in the one-dimensional power-law diluted XY spin-glass model, in which the probability that two spins separated by a distance r interact with each other, decays as 1/r^{2σ}. Tuning the exponent σ is equivalent to changing the space dimension of a short-range model. We develop a heat bath algorithm to equilibrate XY spins; using this in conjunction with the standard parallel tempering and overrelaxation sweeps, we carry out large-scale Monte Carlo simulations. For σ=0.6, which is in the mean-field regime above six dimensions-it is similar to being in 10 dimensions-we find clear evidence for an AT line. For σ=0.75 and σ=0.85, which are in the non-mean-field regime and similar to four and three dimensions, respectively, our data is like that found in previous studies of the Ising and Heisenberg spin glasses when reducing the temperature at fixed field. For σ=0.75, there is evidence from finite-size-scaling studies for an AT transition but for σ=0.85, the evidence for a transition is nonexistent. We have also studied these systems at fixed temperature varying the field and discovered that at both σ=0.75 and at σ=0.85 there is evidence of an AT transition! Confusingly, the correlation length and spin-glass susceptibility as a function of the field are both entirely consistent with the predictions of the droplet picture and hence the nonexistence of an AT line. In the usual finite-size critical point scaling studies used to provide evidence for an AT transition, there is seemingly good evidence for an AT line at σ=0.75 for small values of the system size N, which is strengthening as N is increased, but for N>2048 the trend changes and the evidence then weakens as N is further increased. We have also studied with fewer bond realizations the system at σ=0.70, which is the analog of a system with short-range interactions just below six dimensions, and found that it is similar in its behavior to the system at σ=0.75 but with larger finite-size corrections. The evidence from our simulations points to the complete absence of the AT line in dimensions outside the mean-field region and to the correctness of the droplet picture. Previous simulations which suggested there was an AT line can be attributed to the consequences of studying systems which are just too small. The collapse of our data to the droplet scaling form is poor for σ=0.75 and to some extent also for σ=0.85, when the correlation length becomes of the order of the length of the system, due to the existence of excitations which only cost a free energy of O(1), just as envisaged in the TNT picture of the ordered state of spin glasses. However, for the case of σ=0.85 we can provide evidence that for larger system sizes, droplet scaling will prevail even when the correlation length is comparable to the system size.

Nonsteady dynamics at the dynamic depinning transition in the two-dimensional Gaussian random-field Ising model.

With large-scale Monte Carlo simulations, we investigate the nonsteady relaxation at the dynamic depinning transition in the two-dimensional Gaussian random-field Ising model. The dynamic scaling behavior is carefully analyzed, and the transition fields as well as static and dynamic exponents are accurately determined based on the short-time dynamic scaling form. Different from the usual assumption, two distinguished growth processes of spatial correlation lengths for the velocity and height of the domain wall are found. Thus, the universality class of the depinning transition is established, which significantly differs from that of the quenched disorder equationbut agrees with that of the recent experiment as well as other simulations works. Under the influence of the mesoscopic time regime, the crossover from the second-order phase transition to the first-order one is confirmed in the weak-disorder regime, yielding an abnormal disorder-dependent nature of the criticality.

Co-segregation of Y and Zr in W-Cr-Y-Zr alloys: First-principles modeling at finite temperature and application to SMART materials

Spinodal phase separation in SMART (Self-passivating Metal Alloys with Reduced Thermo-oxidation) materials based on binary W-Cr with alloying elements Y and Zr is systematically investigated by a combination of Density Functional Theory with Cluster Expansion Hamiltonian and large-scale Monte Carlo simulations with thermodynamic integration. Comparing alloys of Zr with those of Y in ternary compositions with W and Cr, it is shown that there is a significant difference in the average short-range order between W and Zr, which changes from positive to negative from 500 K to higher temperatures in W70Cr29Zr1 alloys compared with the positive SRO (Short-Range Order) between W and Y in W70Cr29Y1 alloys at all temperatures. This change, however, does not affect the segregation behavior between W and Cr in the whole range of temperature between these alloys. Importantly, it is found that co-segregation of Y and Zr due to the negative SRO between them, in W70Cr29Y0.5Zr0.5 and W70Cr28Y1Zr1 considered alloys, increases the W-Cr positive SRO closer to the binary W70Cr30. Our modeling results reveal a significant impact on spinodal phase segregation of W and Cr in designing SMART materials for DEMO devices of future fusion power plants. Findings from recent experimental studies validate the modeling results, particularly the high-temperature behavior of the W-Cr-Zr alloys and the microstructure evolution of the W-Cr-Y-Zr alloys. The results provide a fundamental understanding of the radiation resistance phenomena observed in recent experiments on neutron-irradiated self-passivating alloys.

Decision support algorithm for intermodal transport networks: Urban aerial cableway systems

We propose a decision support algorithm to solve the service policy of urban cableway systems, which are used as a transport mode to address the First-Last Mile problem for intermodal urban public transport networks. Our work develops a stochastic discrete-event model for computing the queuing performance of the public transport networks and evaluates the effects on the passenger waiting time over a commercial working day, considering different service policies: (i) previous policy; (ii) current policy; and (iii) proposed policy. We provide an embarking procedure for urban cableway lines to aid transport operators in managing queues on platforms during rush hours. Finally, a set of large-scale Monte-Carlo simulations was conducted using a real multimodal network of a large-size metropolitan city (3.8 million inhabitants) to evaluate the effectiveness of different service policies.

Development of a hybrid parallelism Monte Carlo transport middleware on mesh geometry

Mesh-based Monte Carlo particle transport is suitable for complex geometry modeling and for multi-physics coupling calculations. Performing large-scale mesh-based Monte Carlo simulations requires a quite large amount of computation and memory space. Therefore, parallel Monte Carlo computing is crucial. In this study, a hybrid parallelism Monte Carlo transport middleware on mesh geometry was developed. The middleware can provide the following algorithms and functions: 1. hybrid parallelism of domain decomposition and particle parallelism; 2. particle data structure, which manages particle information and automatically performs asynchronous communication between decomposed domains; 3. subset data structure, which provides an efficient management strategy for materials and tally data; 4. particle tracking method on structured/unstructured mesh and k-dimensional tree (KD-Tree) acceleration algorithm; 5. condensed application programming interface for the rapid development of Monte Carlo code based on the middleware. We transplanted the fixed source module of the J Monte Carlo transport code (JMCT) which was based on constructive solid geometry (CSG) to the middleware for verification. The results indicated that the serial particle tracking efficiency of an unstructured mesh model was 6.56 times as high as that of MCNP6 and the serial simulation efficiency of the corresponding structured mesh model was basically equivalent to that of JMCT. The parallel efficiency of domain decomposition was higher than that of JMCT. We also calculated the shielding problem of the Qinshan No. 1 reactor through hybrid parallelism. The results were in good agreement with the experimental data, and the hybrid parallel efficiencies were higher than 65% on 4000 CPU cores.

Anisotropic Melting of Frustrated Ising Antiferromagnets.

Magnetic frustrations and dimensionality play an important role in determining the nature of the magnetic long-range order and how it melts at temperatures above the ordering transition T_{N}. In this Letter, we use large-scale MonteCarlo simulations to study these phenomena in a class of frustrated Ising spin models in two spatial dimensions. We find that the melting of the magnetic long-range order into an isotropic gaslike paramagnet proceeds via an intermediate stage where the classical spins remain anisotropically correlated. This correlated paramagnet exists in a temperature range T_{N}<T<T^{*}, whose width increases as magnetic frustrations grow. This intermediate phase is typically characterized by short-range correlations; however, the two-dimensional nature of the model allows for an additional exotic feature-formation of an incommensurate liquidlike phase with algebraically decaying spin correlations. The two-stage melting of magnetic order is generic and pertinent to many frustrated quasi-2D magnets with large (essentially classical) spins.