Monopoles of the Dirac type and color confinement in QCD

We present results of SU(3) Monte-Carlo studies of a new color confinement scheme proposed recently due to Abelian-like monopoles of the Dirac type corresponding in the continuum limit to violation of the non-Abelian Bianchi identities (VNABI). The simulations are done without any additional gauge-fixing smoothing the vacuum. We get for the first time, in pure SU(3) simulations, (1) the perfect Abelian dominance with respect to the static potentials on (12 ~ 16)4 at β = 5.6 − 5.8 using the multilevel method, (2) the monopole as well as Abelian dominances with respect to the static potentials by evaluating the Polyakov-loop correlators on 243 × 4 at β = 5.6. The Abelian photon part gives zero string tension. The new SU(3) as well as the previous SU(2) results are consistent with the new Abelian picture of color confinement that each one of eight colored electric flux is squeezed by the corresponding colored Abelian-like monopole of the Dirac type corresponding to VNABI.

Accelerating the estimation of collisionless energetic particle confinement statistics in stellarators using multifidelity Monte Carlo

In the design of stellarators, energetic particle confinement is a critical point of concern which remains challenging to study from a numerical point of view. Standard Monte Carlo analyses are highly expensive because a large number of particle trajectories need to be integrated over long time scales, and small time steps must be taken to accurately capture the features of the wide variety of trajectories. Even when they are based on guiding center trajectories, as opposed to full-orbit trajectories, these standard Monte Carlo studies are too expensive to be included in most stellarator optimization codes. We present the first multifidelity Monte Carlo scheme for accelerating the estimation of energetic particle confinement in stellarators. Our approach relies on a two-level hierarchy, in which a guiding center model serves as the high-fidelity model, and a data-driven linear interpolant is leveraged as the low-fidelity surrogate model. We apply multifidelity Monte Carlo to the study of energetic particle confinement in a 4-period quasi-helically symmetric stellarator, assessing various metrics of confinement. Stemming from the very high computational efficiency of our surrogate model as well as its sufficient correlation to the high-fidelity model, we obtain speedups of up to 10 with multifidelity Monte Carlo compared to standard Monte Carlo.

A Spatial AMH Copula-Based Dissimilarity Measure to Cluster Variables in Panel Data

Investigating thermal energy demand is crucial for the development of sustainable cities and efficient use of renewable sources. Despite the advances made in this field, the analysis of energy data provided by smart grids is currently a demanding challenge. In this paper, we develop a clustering methodology based on a novel dissimilarity measure to analyze a high temporal resolution panel data for district heating demand in the Italian city Bozen-Bolzano. Starting from the characteristics of this data, we explore the usefulness of the Ali-Mikhail-Haq copula in defining a new dissimilarity measure to cluster variables in a hierarchical framework. We show that our proposal is particularly sensitive to small dissimilarities based on tiny differences in the dependence level. Therefore, the proposed measure is able to better distinguish between objects with low dissimilarity than classic rank-based dissimilarity measures. Moreover, our proposal is defined in a spatial version that is able to take into account the spatial location of the compared objects. We investigate the proposed measure through Monte Carlo studies and compare it with the corresponding spatial Kendall's correlation-based dissimilarity measure. Finally, the application to real data makes it possible to find clusters of buildings homogeneous with respect to their main characteristics, such as energy efficiency and heating surface, to support the design, expansion and management of district heating systems.

Optimized Weighted Nearest Neighbours Matching Algorithm for Control Group Selection

An essential criterion for the proper implementation of case-control studies is selecting appropriate case and control groups. In this article, a new simulated annealing-based control group selection method is proposed, which solves the problem of selecting individuals in the control group as a distance optimization task. The proposed algorithm pairs the individuals in the n-dimensional feature space by minimizing the weighted distances between them. The weights of the dimensions are based on the odds ratios calculated from the logistic regression model fitted on the variables describing the probability of membership of the treated group. For finding the optimal pairing of the individuals, simulated annealing is utilized. The effectiveness of the newly proposed Weighted Nearest Neighbours Control Group Selection with Simulated Annealing (WNNSA) algorithm is presented by two Monte Carlo studies. Results show that the WNNSA method can outperform the widely applied greedy propensity score matching method in feature spaces where only a few covariates characterize individuals and the covariates can only take a few values.

Flicker noise in two-dimensional electron gas

Using the method developed in a recent paper (Euro. Phys. J. B 92.8 (2019): 1-28) we consider 1/f noise in two-dimensional electron gas (2DEG). The electron coherence length of the system is considered as a basic parameter for discretizing the space, inside which the dynamics of electrons is described by quantum mechanics, while for length scales much larger than it the dynamics is semi-classical. For our model, which is based on the Thomas-Fermi-Dirac approximation, there are two control parameters: temperature T and the disorder strength (∆). Our Monte Carlo studies show that the system exhibits 1/f noise related to the electronic avalanche size, which can serve as a model for describing the experimentally observed flicker noise in 2DEG. The power spectrum of our model scales with frequency with an exponent in the interval 0.3 < αPS < 0.6. We numerically show that the electronic avalanches are scale invariant with power-law behaviors in and out of the metal-insulator transition line.

Monte Carlo studies on shape deformation and stability of 3D skyrmions under mechanical stresses

We study the stability/instability of skyrmions under mechanical stresses by Monte Carlo simulations in a 3D disk composed of tetrahedrons. Skyrmions emerge in chiral magnetic materials, such as FeGe and MnSi, under the competition of ferromagnetic interaction (FMI) and Dzyaloshinskii-Moriya interaction (DMI) and are stabilized by the external magnetic field. Recent experimental studies show that skyrmions are also stabilized/destabilized by uniaxial compressive stress perpendicular to or along the magnetic field direction. These phenomena are studied by using a 3D Finsler geometry (FG) model. In this 3D FG model, the DMI coefficient is automatically anisotropic by a geometrically implemented coupling of strains and electronic spins. We find that skyrmions are stabilized (destabilized) by extension (compression) stress along the direction of the applied magnetic field consistent with reported experimental data. This consistency implies that the 3D FG model successfully implements the magnetostrictive or magneto-elastic effect of external mechanical stresses on chiral magnetic orders, including the skyrmion configuration.

Improving reproducibility of proton MRST by optimally averaging temperatures measured from multiple references: theoretical and empirical approaches

Purpose: In 1H MRS-based thermometry of brain, averaging temperatures measured from more than one reference peak offers several advantages including improving the reproducibility, i.e. precision, of the measurement. This paper proposes theoretically and empirically optimal weighting factors to improve the weighted average of temperatures measured from three references. Methods: We first proposed concepts of equivalent noise and equivalent signal-to-noise ratio in terms of frequency measurement and a concept of relative frequency that allows the combination of different peaks in a spectrum for improving the accuracy of frequency measurement. Based on these, we then developed a theoretically optimal weighting factor and suggested an empirical weighting factor for weighted average of temperatures measured from three references in 1H MRS-based thermometry. We assessed the two new weighting factors, together with other two previously proposed weighting factors, by comparing the errors of temperatures measured from individual references and the errors of averaged temperatures using these differing weighting factors. These errors were defined as the standard deviations in repeated measurements and in Monte Carlo studies. We also performed computer simulations to aid error analyses in temperature averaging. Results: Both the proposed theoretical and empirical weighting factors outperformed the other two previously proposed weighting factors as well as the three individual references in all phantom and in vivo experiments. In phantom experiments with 4 Hz or 10 Hz line broadening, the theoretical weighting outperformed the empirical one, but the latter was superior in all other repeated and Monte Carlo tests performed on phantom and in vivo data. Computer simulations offered explanations for the performances of the two new proposed weightings. Conclusion: The proposed two new weighting factors are superior to the two previously proposed weighting factors and can improve the measurement of temperature using 1H MRS-based thermometry.