Metropolis Monte Carlo Method Research Articles

Sol-gel hydrothermal synthesis of lead-free BT nanoparticles for enhanced dielectric properties in PVDF nanocomposites

In the present work BaTiO3 nanoparticles (NPs) with different sizes from 150 to 400 nm were prepared by sol–gel hydrothermal method at a temperature lower than 220 °C, and were used as nanofiller for PVDF composites with a loading from 10 to 25 vol%. The morphology of the BT NPs was analyzed by Scanning Electron Microscopy (SEM), and the structural composition was studied by Raman spectroscopy and X-ray diffraction (XRD). The hydrothermal temperature was found to control both the size as well as the phase composition of the BT NPs.The PVDF/BT nanocomposites exhibit enhanced dielectric permittivity and reduced loss tangent, especially with 20 vol% NPs, which contributes to the improvement of the ferroelectric properties. The inclusion of BT in PVDF matrix enhances also the crystallinity of PVDF by acting as a nucleating agent, which further increases the stiffness of the composite. However, at higher volume loading, the reverse tendency was observed with a huge decrease in the PVDF crystallinity at 25 vol%. The simulated PE loop was also investigated for the different loadings mentioned above using an Ising type model based on a 2D lattice and solved by monte-Carlo metropolis method. The results are in good agreement with the experimental results for the polarization hysteresis loops.

Local Ordering, Distortion, and Redox Activity in (La0.75Sr0.25)(Mn0.25Fe0.25Co0.25Al0.25)O3 Investigated by a Computational Workflow for Compositionally Complex Perovskite Oxides.

Mixing multiple cations can result in a significant configurational entropy, offer a new compositional space with vast tunability, and introduce new computational challenges. For applications such as the two-step solar thermochemical hydrogen (STCH) generation techniques, we demonstrate that using density functional theory (DFT) combined with Metropolis Monte Carlo method (DFT-MC) can efficiently sample the possible cation configurations in compositionally complex perovskite oxide (CCPO) materials, with (La0.75Sr0.25)(Mn0.25Fe0.25Co0.25Al0.25)O3 as an example. In the presence of oxygen vacancies (VO), DFT-MC simulations reveal a significant increase of the local site preference of the cations (short-range ordering), compared to a more random mixing without VO. Co is found to be the redox-active element and the VO is the preferentially generated next to Co due to the stretched Co-O bonds. A clear definition of the vacancy formation energy (Evf) is proposed for CCPO in an ensemble of structures evolved in parallel from independent DFT-MC paths. By combining the distribution of Evf with VO interactions into a statistical model, the oxygen nonstoichiometry (δ), under the STCH thermal reduction and oxidation conditions, is predicted and compared with the experiments. Similar to the experiments, the predicted δ can be used to extract the enthalpy and entropy of reduction using the van't Hoff method, providing direct comparisons with the experimental results. This procedure provides a full predictive workflow for using DFT-MC to obtain possible local ordering or fully random structures, understand the redox activity of each element, and predict the thermodynamic properties of CCPOs, for computational screening and design of these CCPO materials at STCH conditions.

Insights into thermally-induced disruption of magnetic-nanoparticle agglomerates

We investigated the temperature dependence of agglomeration systems consisting of interacting single-domain magnetic nanoparticles (MNPs). In our study, we utilized electron spin resonance (ESR) experiments to measure how temperature-induced change in agglomerate state affects the peak-to-peak width of ESR spectra (Hpp) and validated these observations through simulations. Micromagnetic simulations were conducted by combining the classical magnetic dipolar Metropolis Monte Carlo method with the semi-classical macro-spin Landau-Lifshitz-Gilbert finite element method, and the results were compared with experimental findings. Our research elucidates the behavior of thermally-induced disruption of MNP agglomerates. We discovered that the temperature at which MNPs are completely dispersed might correspond to one at which the temperature dependence of Hpp disappears.

Recent Advances in Automated Structure-Based De Novo Drug Design.

As the number of determined and predicted protein structures and the size of druglike 'make-on-demand' libraries soar, the time-consuming nature of structure-based computer-aided drug design calls for innovative computational algorithms. De novo drug design introduces in silico heuristics to accelerate searching in the vast chemical space. This review focuses on recent advances in structure-based de novo drug design, ranging from conventional fragment-based methods, evolutionary algorithms, and Metropolis Monte Carlo methods to deep generative models. Due to the historical limitation of de novo drug design generating readily available drug-like molecules, we highlight the synthetic accessibility efforts in each category and the benchmarking strategies taken to validate the proposed framework.

Thermodynamic calculations using reverse Monte Carlo: Simultaneously tuning multiple short-range order parameters for 2D lattice adsorption problem.

Lattice simulations are an important class of problems in crystalline solids, surface science, alloys, adsorption, absorption, separation, catalysis, to name a few. We describe a fast computational method for performing lattice thermodynamic calculations that is based on the use of the reverse Monte Carlo (RMC) technique and multiple short-range order (SRO) parameters. The approach is comparable in accuracy to the Metropolis Monte Carlo (MC) method. The equilibrium configuration is determined in 5-10 Newton-Raphson iterations by solving a system of coupled nonlinear algebraic SRO growth rate equations. This makes the RMC-based method computationally more efficient than MC, given that MC typically requires sampling of millions of configurations. The technique is applied to the interacting 2D adsorption problem. Unlike grand canonical MC, RMC is found to be adept at tackling geometric frustration, as it is able to quickly and correctly provide the ordered c(2 × 2) adlayer configuration for Cl adsorbed on a Cu (100) surface.

Off-Lattice Coarse-Grained Model of Surface-Confined Metal–Organic Architectures

An off-lattice model of self-assembling surface-confined metal–organic nanostructures (SMONs) comprising tripod molecules has been developed. The model considers the directionality and saturability of coordination bonding. To parametrize the model, density functional theory methods have been used. Self-assembly of the SMONs has been simulated with Metropolis Monte Carlo method in the canonical ensemble. In this paper, we investigate how the directionality of metal–linker bonding and the linker/metal ratio affect the self-assembly of SMONs containing metal centers with different coordination numbers: M(II), M(III), and M(IV). The directionality of coordination bonding is determined by the functional group of the linker molecule and is defined in the model as the angular diameter of the interaction shell. Regardless of the preferred coordination number of the metal center, even a small change in the angular diameter significantly affects the structure of the SMONs. Depending on the angular diameter and composition of the metal–organic layer, various structures can appear. Using our model, we have simulated the self-assembly of the random porous (or defected honeycomb) and triangular structures, the set of hexagonal phases, amorphous structures of different densities, and metal–organic chains. Relative thermal stabilities of clusters of the main structures have been studied. The model reproduces correctly the main SMONs observed by scanning tunneling microscopy.

Non-ergodic fragmentation upon collision-induced activation of cysteine-water cluster cations.

Cysteine-water cluster cations Cys(H2O)3,6+ and Cys(H2O)3,6H+ are assembled in He droplets and probed by tandem mass spectrometry with collision-induced activation. Benchmark experimental data for this biologically important system are complemented with theory to elucidate the details of the collision-induced activation process. Experimental energy thresholds for successive release of water are compared to water dissociation energies from DFT calculations showing that clusters do not only fragment exclusively by sequential emission of single water molecules but also by the release of small water clusters. Release of clustered water is observed also in the ADMP (atom centered density matrix propagation) molecular dynamics model of small Cys(H2O)3+ and Cys(H2O)3H+ clusters. For large clusters Cys(H2O)6+ and Cys(H2O)6H+ the less computationally demanding statistical Microcanonical Metropolis Monte-Carlo method (M3C) is used to model the experimental fragmentation patterns. We are able to detail the energy redistribution in clusters upon collision activation. In the present case, about two thirds of the collision energy redistribute via an ergodic process, while the remaining one third is transferred into a non-ergodic channel leading to ejection of a single water molecule from the cluster. In contrast to molecular fragmentation, which can be well described by statistical models, modelling of collision-induced activation of weakly bound clusters requires inclusion of non-ergodic processes.

Training neural networks using Metropolis Monte Carlo and an adaptive variant

We examine the zero-temperature Metropolis Monte Carlo (MC) algorithm as a tool for training a neural network by minimizing a loss function. We find that, as expected on theoretical grounds and shown empirically by other authors, Metropolis MC can train a neural net with an accuracy comparable to that of gradient descent (GD), if not necessarily as quickly. The Metropolis algorithm does not fail automatically when the number of parameters of a neural network is large. It can fail when a neural network’s structure or neuron activations are strongly heterogenous, and we introduce an adaptive Monte Carlo algorithm (aMC) to overcome these limitations. The intrinsic stochasticity and numerical stability of the MC method allow aMC to train deep neural networks and recurrent neural networks in which the gradient is too small or too large to allow training by GD. MC methods offer a complement to gradient-based methods for training neural networks, allowing access to a distinct set of network architectures and principles.

Effect of microstructural heterogeneity on fatigue strength predicted by reinforcement machine learning

AbstractThe posterior statistical distributions of fatigue strength are determined using Bayesian inferential statistics and the Metropolis Monte Carlo method. This study explores how structural heterogeneity affects ultrahigh cycle fatigue strength in additive manufacturing. Monte Carlo methods and procedures may assist estimate fatigue strength posteriors and scatter. The acceptable probability in Metropolis Monte Carlo relies on the Markov chain's random microstructure state. In addition to commonly studied variables, the proportion of chemical composition was demonstrated to substantially impact fatigue strength if fatigue lifetime in crack propagation did not prevail due to high threshold internal notches. The study utilizes an algorithm typically used for quantum mechanics to solve the complicated multifactorial fatigue problem. The inputs and outputs are modified by fitting the microstructural heterogeneities into the Metropolis Monte Carlo algorithm. The main advantage here is applying a general‐purpose nonphenomenological model that can be applied to multiple influencing factors without high numerical penalty.

Langevin dynamics/Monte Carlo simulations method for calculating nanoscale dielectric functions of materials

We have developed a simulational methodology for calculating the nanoscale frequency-dependent complex dielectric function of a wide range of materials using a combination of Langevin dynamics and Metropolis Monte Carlo methods. The premise of such a scheme is to use the atomistic structure of materials and designate appropriate interatomic interactions as well as internal field couplings to accommodate correlated materials. We validate our model by recreating the dielectric functions of well-studied representative materials including insulator ${\text{SiO}}_{2}$ thin film that has phonon resonances in the midinfrared, and semiconductor monolayer ${\text{MoS}}_{2}$ that exhibits strong excitonic resonances in the visible frequency range. To further showcase the capability of the model in calculating nanoscale dielectric modulation of complex materials, we simulate the dielectric response of ${\text{SmNiO}}_{3}$, a correlated perovskite oxide, with respect to differing levels of hydrogenation, oxygen vacancy formation, and external fields. This is accomplished by inserting and tracking the movement of dopants at the nanoscale using Metropolis Monte Carlo methods that explicitly include interactions with each other as well as external fields. Simulated nanoscale dielectric spectra agree very well with high-resolution near-field experimental measurements based on scattering type scanning near-field microscopy. We find that this modeling scheme carries a broad utility in describing and predicting the nanoscale dielectric behavior of a broad range of materials exposed to changing local environments.

Extraction of kinetics from equilibrium distributions of states using the Metropolis Monte Carlo method.

The Metropolis Monte Carlo (MMC) method is used to extract reaction kinetics from a given equilibrium distribution of states of a complex system. The approach is illustrated by the folding/unfolding reaction for two proteins: a model β-hairpin and α-helical protein α_{3}D. For the β-hairpin, the free energy surfaces (FESs) and free energy profiles (FEPs) are employed as the equilibrium distributions of states, playing a role of the potentials of mean force to determine the acceptance probabilities of new states in the MMC simulations. Based on the FESs and PESs for a set of temperatures that were simulated with the molecular dynamics (MD) method, the MMC simulations are performed to extract folding/unfolding rates. It has been found that the rate constants and first-passage time (FPT) distributions obtained in the MMC simulations change with temperature in good agreement with those from the MD simulations. For α_{3}D protein, whose equilibrium folding/unfolding was studied with the single-molecule FRET method [Chung etal., J. Phys. Chem. A 115, 3642 (2011)1089-563910.1021/jp1009669], the FRET-efficiency histograms at different denaturant concentrations were used as the equilibrium distributions of protein states. It has been found that the rate constants for folding and unfolding obtained in the MMC simulations change with denaturant concentration in reasonable agreement with the constants that were extracted from the photon trajectories on the basis of theoretical models. The simulated FPT distributions are single-exponential, which is consistent with the assumption of two-state kinetics that was made in the theoretical models. The promising feature of the present approach is that it is based solely on the equilibrium distributions of states, without introducing any additional parameters to perform simulations, which suggests its applicability to other complex systems.

Randomly aperiodically poled LiNbO3 crystal design by Monte Carlo–Metropolis with simulated annealing optimization for ultrabroadband photon pair generation

We report a scheme for generating ultrabroadband two-photon states by spontaneous parametric downconversion (SPDC) using randomly aperiodically poled crystals designed with an optimization algorithm based on the Monte Carlo-Metropolis method with simulated annealing. A particular SPDC source is discussed, showing results of the spectral and temporal properties of the emitted two-photon states, obtaining almost transform-limited SPDC biphoton wave packets. We also analyze the effect of fabrication errors on the SPDC.

Surface hydrogenation of oxygen terminated MXenes M2CO2 (M = Ti, V, Nb)

We have investigated reduction of MXenes M2CO2 (M = Ti, V, Nb) surface by hydrogen using density functional theory and statistical physics methods. We have approximated lateral interactions between adsorbed hydrogen with simple pairwise potential. We have confirmed model stability via cross-validation. Adsorption isotherms are calculated using Metropolis Monte Carlo method. We have built analytical Langmuir-like approximation of calculated isotherms. Ordered phases with 1/3 and 2/3 ML coverage are visually observed at low temperatures. At temperatures above 300 K no obvious plateau is observed, and intermediate phases does not exist. We compared adsorptive properties of MXenes at the same external conditions.

Symmetry Energy and the Pauli Exclusion Principle

In this article we present a classical potential that respects the Pauli exclusion principle and can be used to describe nucleon-nucleon interactions at intermediate energies. The potential depends on the relative momentum of the colliding nucleons and reduces interactions at low momentum transfer mimicking the Pauli exclusion principle. We use the potential with Metropolis Monte Carlo methods and study the formation of finite nuclei and infinite systems. We find good agreement in terms of the binding energies, radii, and internal nucleon distribution of finite nuclei, and the binding energy in nuclear matter and neutron star matter, as well as the formation of nuclear pastas, and the symmetry energy of neutron star matter.

A universal framework for metropolis Monte Carlo simulation of magnetic Curie temperature

Recent research of two-dimensional magnetism intrigues rapidly growing attention and broadens the prospects for utility in nano-devices. However, understanding the new magnetic phenomena and the behavior of magnetic centers is still one of the challenges. The Heisenberg model with the Metropolis Monte Carlo method provides an accurate description with continuous degrees of freedom while effective and universal spin update algorithms remain highly desirable. In this study, we propose algorithms for the magnetization switching in the classical Heisenberg model based on the concept of Euler angles and quaternion, which update the spins simply by a rotation matrix and convert to sphere and Cartesian coordinates in a very convenient way. The proposed methods are fully tested and validated by comparisons with the benchmarks of both the two-dimensional square lattice Ising model and the three-dimensional cubic lattice Heisenberg model. As an application example of the two-dimensional ferromagnetic material of CrI3, the simulated Curie temperature is about 42 K, which is in good agreement with the experimental value of 45 K. The update algorithms together with other configuration schemes are compiled into an easy-to-operate program named SEU-mtc, aiming to execute post-processing analysis of the spin microstates and greatly improve the efficiency of Curie temperature simulations based on ab initio methods.

3D Bioprinting of Model Tissues That Mimic the Tumor Microenvironment.

The tumor microenvironment (TME) influences cancer progression. Therefore, engineered TME models are being developed for fundamental research and anti-cancer drug screening. This paper reports the biofabrication of 3D-printed avascular structures that recapitulate several features of the TME. The tumor is represented by a hydrogel droplet uniformly loaded with breast cancer cells (106 cells/mL); it is embedded in the same type of hydrogel containing primary cells—tumor-associated fibroblasts isolated from the peritumoral environment and peripheral blood mononuclear cells. Hoechst staining of cryosectioned tissue constructs demonstrated that cells remodeled the hydrogel and remained viable for weeks. Histological sections revealed heterotypic aggregates of malignant and peritumoral cells; moreover, the constituent cells proliferated in vitro. To investigate the interactions responsible for the experimentally observed cellular rearrangements, we built lattice models of the bioprinted constructs and simulated their evolution using Metropolis Monte Carlo methods. Although unable to replicate the complexity of the TME, the approach presented here enables the self-assembly and co-culture of several cell types of the TME. Further studies will evaluate whether the bioprinted constructs can evolve in vivo in animal models. If they become connected to the host vasculature, they may turn into a fully organized TME.

Ceratonia Siliqua L seeds extract as eco-friendly corrosion inhibitor for carbon steel in 1 M HCl: Characterization, electrochemical, surface analysis, and theoretical studies

Electrochemical and theoretical behaviors of the carbon steel was investigated in 1 M HCl solution using the Ceratonia Siliqua L seeds (CFE) extract. This extract was analyzed using GC–MS technique; it was found that the extract contains 18 compounds on which the main constituents represent 27.78 wt.% vanillin (VN), 25.69 wt.% α-tumerone (AT), 11.68 wt.% 2-heptanal (HP), 9.49 wt.% mome-inositol (MI), 4.94 wt.% 1-dotiacontanol(DT), and 2.92 wt.% linoleic acid (LA). The corrosion inhibition and adsorption (CIA) behavior were investigated using the electrochemical measurements (open circuit potential (OCP), polarization curves (PC) and impedance spectroscopy (IS)), and both thermodynamic and kinetic parameters (ΔHa, ΔSa and Ea). The outcomes show that CFE extract exhibits a worthy anti-corrosion action with an inhibition efficiency (η%) of 95% at 100 mg/l at 298 °K. This result could be attributed probably to the adsorption of CFE extract matrix on carbon steel surface, and this was confirmed by surface visualization using SEM-EDS technique. The adsorption of CFE extract onto carbon steel surface is controlled by a Langmuir adsorption isotherm, which suggests that there are no interactions between molecules of the CFE during adsorption. The computational chemistry calculations by density functional theory (DFT), natural bond orbital (NBO), molecular electrostatic potential surface (MESP) and Metropolis Monte Carlo (MC) methods were performed to better understand the inhibition and adsorption behavior of the main constituents of CFE extract on the Fe (110) surface.

Optimization and Computational Approach to Understand the Adsorption Behavior of Alizarine Red S on the Surface of Fish Scales

The key components of fish scales are hydroxyapatite and collagen, which form a natural composite. In this present study, fish scales were used as biosorbent to uptake Alizarine Red S dyes from the wastewaters. Here, dye concentration, adsorbent amount, pH, and temperature were optimized using complete factorial design analysis. Sixteen experiments were required, and a linear mathematical model representing the influence of the different variables and their interactions was obtained. The discussion covered analysis of variance (ANOVA), normal probability plots of residuals, and surface plots. Theoretical calculations by Metropolis Monte Carlo (MC) methods, the density functional theory (DFT), and the electrostatic potential surface (ESP) analysis were achieved to obtain a more understanding of the dyes adsorption mechanism on both collagen and hydroxyapatite (HDA) surfaces. The findings results exhibited that the ARS dye presents more tendency of adsorption on the collagen than on the HDA surface.

Melting in two-dimensional systems: Characterizing continuous and first-order transitions

The mechanisms underlying the melting process in bidimensional systems have been widely studied by means of experiments, theory, and simulations since Kosterlitz, Thouless, Halperin, Nelson, and Young elaborated the KTHNY theory. In the framework of this theory, melting is produced by two continuous transitions mediated by the unbinding of local defects and the appearance of an intermediate phase between solid and liquid, called ``hexatic.'' There are also other competing theories that could explain this process, as, e.g., the formation of grain boundaries (lines of defects), which lead to a first-order transition. In this paper, simulations of systems interacting via the Lennard Jones 6--12 and Morse potentials using the Metropolis Monte Carlo method in the NVT ensemble have been performed to study the effect of the potential shape in the melting process. Additionally, truncated Morse potentials (with only a repulsive part) have been used to investigate the effect of the long-range interactions. Transitions from solid to hexatic phases were found to be continuous for all potentials studied, but transitions from hexatic to liquid phases were found to be either continuous or first order, depending on the thermodynamic conditions and the potential interaction selected, suggesting that melting can be triggered by different mechanisms, like grain boundary formation or defect unbinding. We find that the ratio of defects at the liquid-hexatic or liquid-coexistence phase transitions could determine the nature of these transitions and the mechanism underlying the melting process. The effect of the interaction of particles with their first- and second-nearest neighbors is also discussed.

Superstatistical two-temperature Ising model.

The previous approach of the nonequilibrium Ising model was based on the local temperature in which each site or part of the system has its own specific temperature. We introduce an approach of the two-temperature Ising model as a prototype of the superstatistic critical phenomena. The model is described by two temperatures (T_{1},T_{2}) in a zero magnetic field. To predict the phase diagram and numerically estimate the exponents, we develop the Metropolis and Swendsen-Wang Monte Carlo method. We observe that there is a nontrivial critical line, separating ordered and disordered phases. We propose an analytic equation for the critical line in the phase diagram. Our numerical estimation of the critical exponents illustrates that all points on the critical line belong to the ordinary Ising universality class.