Classical Monte Carlo Simulations Research Articles

Systematic evaluation of generative machine learning capability to simulate distributions of observables at the large hadron collider

Monte Carlo simulations are a crucial component when analysing the Standard Model and New physics processes at the Large Hadron Collider. This paper aims to explore the performance of generative models for complementing the statistics of classical Monte Carlo simulations in the final stage of data analysis by generating additional synthetic data that follows the same kinematic distributions for a limited set of analysis-specific observables to a high precision. Several deep generative models are adapted for this task and their performance is systematically evaluated using a well-known benchmark sample containing the Higgs boson production beyond the Standard Model and the corresponding irreducible background. The paper evaluates the autoregressive models and normalizing flows and the applicability of these models using different model configurations is investigated. The best performing model is chosen for a further evaluation using a set of statistical procedures and a simplified physics analysis. By implementing and performing a series of statistical tests and evaluations we show that a machine-learning-based generative procedure can be used to generate synthetic data that matches the original samples closely enough and that it can therefore be incorporated in the final stage of a physics analysis with some given systematic uncertainty.

Computing solubility and thermodynamic properties of H2O2 in water

Hydrogen peroxide plays a key role in many environmental and industrial chemical processes. We performed classical Molecular Dynamics and Continuous Fractional Component Monte Carlo simulations to calculate thermodynamic properties of H2O2 in aqueous solutions. The quality of the available force fields for H2O2 developed by Orabi and English (2018) [67], and by Cordeiro (2014) [69] was systematically evaluated. To assess which water force field is suitable for predicting properties of H2O2 in aqueous solutions, four widely used water force fields were used, namely the TIP3P, TIP4P/2005, TIP5P-E, and a modified TIP3P force field. While the computed densities of pure H2O2 in the temperature range of 253 - 353 K using the force field by Orabi & English are in excellent agreement with experimental results, the densities using the force field by Cordeiro are underestimated by 3%. The TIP4P/2005 force field in combination with the H2O2 force field developed by Orabi & English can predict the densities of H2O2 aqueous solution for the whole range of H2O2 mole fractions in very good agreement with experimental results. The TIP4P/2005 force field in combination with either of the H2O2 force fields can predict the viscosities of H2O2 aqueous solutions for the whole range of H2O2 mole fractions in reasonably good agreement with experimental results. The computed diffusion coefficients for H2O2 and water molecules using the TIP4P/2005 force field with either of the H2O2 force fields are almost constant for the whole range of H2O2 mole fractions. Hydrogen bond analysis showed a steady increase in the number of hydrogen bonds with the solute concentrations in H2O2 aqueous solutions for all combinations except for the Cordeiro-TIP5P-E and Orabi-TIP5P-E systems, which showed a minimum at intermediate concentrations. The Cordeiro force field for H2O2 in combination with either of the water force fields can predict the Henry coefficients of H2O2 in water in better agreement with experimental values than the force field by Orabi & English.

Zn/Ce-layered double hydroxide for adsorptive removal of doxycycline from water

Since antibiotic overuse created various environmental issues, antibiotic management and separation are critical in ecological research. In this regard, the main objective of this work was to design a simple and reliable solvothermal-synthesis-based sorbent for removing antibiotics such as doxycycline (DOX). The used sorbent was Zn/Ce-layered double hydroxide (Zn/Ce-LDH), and its layered structure was confirmed by the X-ray diffraction (XRD), field emission scanning electron microscopy (SEM), transmission electron microscopy (TEM) analysis. In addition, the Brunauer-Emmett-Teller (BET) test showed the specific surface area of the Zn/Ce-LDH achieved 45.17 m2 g−1. The sorbent was shown to have a high capability to remove DOX (the maximum experimental adsorption capacity of 1297 mg g−1) at the low equilibrium contact time of 15 min. Also, the obtained negative value of Gibbs free energy (ΔG°), the enthalpy (ΔH°), and the entropy (ΔS°) at the investigated temperatures reveal the fact that the involved adsorption process had spontaneous and exothermic features. Besides, the pseudo-second-order kinetic model favourably described DOX adsorption on the Zn/Ce LDH surface. Furthermore, a combination of classical molecular dynamics and Monte Carlo simulations were utilized to investigate the adsorption properties of DOX on the (001) and (010) Zn/Ce-LDH surfaces. The theoretical findings supported the possibility of DOX coordination with Zn/Ce atoms.

The dilute 3D and three site dimer Heisenberg antiferromagnet: review of some magnetic properties.

Many properties of the spin–½ kagome Heisenberg antiferromagnet remains controversial and receiving continuous attention from theorists and experimentalists due to their fascinating magnetic properties and high heterogeneity coax by the geometrical frustration. In this research we seek and compare the results obtained in our recent article [1] with that of Napel[2] where we elucidate some of the identified magnetic behaviour using the spin–½ Heisenbeg model with the application of Exact Diagonalization and classical Monte-Carlo simulation on three site dimer and 3D simple cubic lattice simulation. The results obtained shows excellent agreement in both papers reviewed with [1] establishing firmly the FM to AFM transition, having a clear transition point referred to mixed phased [2].

Kinetic Monte Carlo simulations of solute clustering during quenching and aging of Al–Mg–Zn alloys

The physical mechanisms behind cluster formation during quenching and aging of age-hardening metallic alloys are poorly understood based on classical nucleation and growth theories, especially in multicomponent alloys with supersaturated vacancies and fast-diffusing solute atoms. Here, solute clustering in an Al–Mg–Zn alloy during quenching immediately after high-temperature (800 K) solution treatment is modeled with a newly developed kinetic Monte Carlo (kMC) framework. This includes accurate surrogate models trained using first-principles-calculated data to predict vacancy migration energetics on the fly as functions of local lattice occupations. First, kMC simulations at constant aging temperatures revealed that temporal evolution of the number, sizes, and compositions of solute clusters change with aging temperature. Such changes are consistent with our analyses based on classical nucleation theory (CNT) and Monte Carlo simulations. Second, the kMC algorithm was revised for simulating quenching processes by iteratively updating the kMC temperature based on simulated cooling rate profiles. These quenching simulations show that rapid solute clustering mainly occurs from ∼600 to ∼400 K during cooling. Below ∼400 K, the clustering is suppressed to a steady state because vacancies are trapped by stable clusters with sizes of ∼2 nm and high magnitudes of formation energies. The configurations of these steady-state clusters closely resemble the solute clusters we observed experimentally in 7XXX series Al–Mg–Zn-based alloy samples immediately after quenching. A two-stage vacancy trapping mechanism revealed in our simulations can provide physical guidance to tune precipitation kinetics during natural and artificial aging.

Optical properties of InSb derived from reflection electron energy loss spectroscopy spectrum

The energy loss function (ELF) of the narrow bandgap semiconductor, InSb, was derived from the reflection electron energy loss spectroscopy (REELS) spectrum measured at 4 keV incident electron energy in an energy loss range of 1.6–200 eV using a high energy resolution electron spectrometer. The experimental spectrum was analyzed with the reverse Monte Carlo (RMC) method, which integrates the classical trajectory Monte Carlo simulation with the simulated annealing method for optimizing the trial ELF. Subsequently, the complex dielectric function ε(ω), refractive index and extinction coefficient were determined from the obtained ELF in the energy loss (i.e. photon energy) range of 1.6–200 eV. The validity of the obtained data was verified by the f-sum rule, ps-sum rule, inertial sum rule and dc-conductivity sum rule. We found that our calculated data of InSb fulfill the sum rules with very high accuracy; therefore, the use of these calculated optical data in material science and surface analysis is highly recommended for further applications.

Dissociative ionization and post-ionization alignment of aligned O2 in an intense femtosecond laser field.

We examined dissociative ionization of O2 in an intense femtosecond laser field (782 nm, 120 fs, 4 × 1014 W cm-2) by recording the kinetic energy distribution of O+ emitted along the laser polarization direction as a function of the delay time between the pump pulse (9 × 1013 W cm-2) for the molecular alignment and the probe pulse for the dissociative ionization. We found the two distinct rotational revival patterns which are out-of-phase by π with each other in the kinetic energy distribution of O+. One of the patterns shows the dissociative ionization is enhanced when the O2 axis is parallel to the laser polarization direction, suggesting that the ionization is induced by the electron emission from the 3σg orbital. On the other hand, the other pattern shows that the dissociative ionization is enhanced when the O2 axis is perpendicular to the laser polarization direction, suggesting that the ionization is induced by the electron emission from the 1πu orbital. Because of the collection efficiency of the time-of-flight mass spectrometer, the enhancement of the O+ yield at the anti-alignment time delay indicates that the electron emission from the 1πu orbital is followed by the molecular alignment of O2+ in the course of the dissociation. We performed classical trajectory Monte-Carlo simulation of O2+ with the dissociation and rotational coordinates in the light-dressed potential to evaluate the effect of the post-ionization alignment by the probe pulse.

Rational design of a two-dimensional high-temperature ferromagnet from HCP cobalt.

Cobalt has the highest Curie temperature (Tc) among the elemental ferromagnetic metals and has a hexagonal close-packed (HCP) structure at room temperature. In this study, HCP Co was thinned to the thickness of several (n) unit cells along the c-axis and then passivated by halogen atoms, thus being named Co2nX2 (X = F, Cl, Br and I). For Co2X2 and Co3X2, all of them are not only kinetically but also thermodynamically stable from the viewpoint of the phonon spectra and molecular dynamics. Similar to HCP Co, two-dimensional (2D) Co2F2, Co2Cl2 and Co3X2 (X = Cl, Br and I) are still ferromagnetic metals within the Stoner model but Co2X2 (X = Br and I) is a ferromagnetic half-metal with the coexistence of the metallic behavior for one spin and the insulating behavior for the other spin. Taking into account the spin-orbital coupling (SOC), the easy-magnetization axis is within the plane where the magnetization is isotropic, making it look like a 2D XY magnet. Applying a critical biaxial strain could lead to an easy-magnetization axis changing from the in-plane to the out-of-plane direction. Finally, we use classical Monte Carlo simulations to estimate the Curie temperature (Tc) which is as high as 957 and 510 K for Co2F2 and Co2Cl2, respectively, because of the strong direct exchange interaction. Different from being obtained by mechanical or liquid exfoliation from van der Waals layered structures, our study opens up new possibilities to search for novel 2D ferromagnets from the elemental ferromagnets and provides opportunities for realizing realistic ultra-thin spintronic devices.

The base versus tip growth mode of carbon nanotubes by catalytic hydrocarbon cracking: Review, challenges and opportunities

Hydrogen gas production using catalytic hydrocarbon cracking on metal nanoparticles has become a vital bridge technology, as this process, unlike the traditional methane-based reforming process, does not co-produce carbon gasses (e.g., CO, CO2). The major benefit of direct catalytic methane cracking using a nanostructured catalyst is the formation of solid carbon in high-value products, such as carbon nanotubes (CNTs) or filaments. This solid carbon can then be removed physically and valorized. However, it is challenging to design a catalyst capable of sustaining its activity after solid carbon has started to deposit and grow, meanwhile preventing the formation of coke. For CNTs, in particular, the base growth mode of CNTs is the desired pathway, as the catalyst can then be regenerated and re-used. If the CNTs are formed under the tip-growth mode, the catalyst particle will be lifted off the support of the regeneration and reusability is lost. Therefore, the study of CNTs growth modes is a vital topic, both experimentally and theoretically, of designing appropriate catalysts. To date, enormous efforts have been made to investigate conditions where the CNTs base growth mode can be maintained during the carbon deposition process. Several possible correlations and mechanisms regarding the base growth mode have been explored and established. Theoretical calculations and numerical simulations across length scales were conducted to investigate the nucleation mechanism and growth of CNTs. Density functional theory (DFT), classical and quantum-based molecular dynamics (MD) and Monte Carlo (MC) simulations were also carried out to study the initial CNT cap formation and its encapsulation during the catalytic hydrocarbon cracking process. A thermodynamics-based nucleation formula of CNTs for both the base and tip growth modes was also established. However, there is still no consensus on what determines the CNT growth modes and what the roles are of the various influencing factors such as the nanoparticle size, the oxidation state of the catalyst, the mechanical properties of CNT, and the catalyst-support interaction. This paper reviews the current status of CNT's growth mechanism development. The benefits and limitations of theory and modeling approaches concerning CNT growth modes are discussed.

Interaction between two overall neutral charged microscopically patterned surfaces.

We study the interaction between heterogeneously charged surfaces in an electrolyte solution by employing classical Density Functional Theory (cDFT) and Monte Carlo simulations. We observe a consistent behavior between cDFT and Monte Carlo simulations regarding force curves and two-dimensional density profiles. Armed with the validated cDFT, we explore the system's behavior under parameters that are challenging to simulate directly. Our findings include the impacts of domain size, domain charge, domain charge configuration, and bulk electrolyte concentration on the osmotic pressure. Remarkably, the force curve is more sensitive to the domain size for an asymmetric configuration than a symmetry configuration; the bulk concentration weakly influences the force curve independent of the system configurations.

Biotransformation of 1-nitro-2-phenylethane [Formula: see text] 2-phenylethanol from fungi species of the Amazon biome: an experimental and theoretical analysis.

Natural products and their biotransformation procedures are a powerful source of new chromophores with potential applications in fields like biology, pharmacology and materials science. Thus, this work discusses about the extraction procedure of 1-nitro-2-phenylethane (1N2PE) from Aniba canelilla, its biotransformation setup into 2-phenylethanol (2PE) using four fungi, Lasiodiplodia caatinguensis (phytopathogenic fungus from Citrus sinensis), Colletotrichum sp. (phytopathogenic fungus from Euterpe oleracea), Aspergillus flavus and Rigidoporus lineatus isolated from copper mining waste located in the interior of the Brazilian Amazon. A detailed experimental and theoretical vibrational analysis (IR and Raman) have allowed us to perform some charge transfer effects on the title compounds (push-pull effect) by monitoring specific vibrational modes of their electrophilic and nucleophilic molecular sites. The solvent interactions promote molecular conformations that affect the vibrational spectra of the donor and acceptor groups, as can be seen comparatively in the gas and aqueous solution spectra, an effect possibly related to the bathochromic shift in the calculated optical spectrum of the compounds. The nonlinear optical behavior shows that while the solvent reduces the response of 1N2PE, the response of 2PE increases the optical parameters, which presents low refractive index (n) and first hyperpolarizability. ([Formula: see text]) is almost eight times that reported for urea (42.79 a.u.), a common nonlinear optical material. Furthermore, the bioconversion goes from an electrophilic to a nucleophilic compound, affecting its molecular reactivity. 1N2PE was obtained from Aniba canelilla, whose essential oil is constituted of [Formula: see text] of 2PE. The A. canelilla essential oil was extracted under hydrodistillation. The biotransformation reactions were performed in autoclaved liquid media (100mL) composed of malt extract (2%) in 250mL Erlenmeyer flask. Each culture was incubated in an orbital shaker (130 rpm) at [Formula: see text]C during 7 days and after that, 50mg of 1N2PE (80%) were diluted in 100 [Formula: see text]L of dimethylsulfoxide (DMSO) and added to the reactions flasks. Aliquots (2mL) were removed using ethyl acetate (2mL) and analyzed by GC-MS (fused silica capillary col1umn, Rtx -5MS 30m [Formula: see text] 0.25 mm [Formula: see text] 0.25 [Formula: see text]m) in order to determine the amount of 1N2PE biotransformation. FTIR 1N2PE and 2PE spectra were obtained by attenuated total reflectance (ATR), using a Agilent CARY 630 spectrometer, in the spectral region 4000-650cm[Formula: see text]. The quantum chemical calculations were carried out in the Gaussian 09 program while the DICE code was used to perform the classical Monte Carlo simulations and generate the liquid environment using the classical All-Atom Optimized parameters for Liquid Simulations (AA-OPLS). All nonlinear optical properties, reactive parameters, and electronic excitations were calculated using the Density Functional Theory framework coupled to the standard 6-311++G(d,p) basis set.

Investigating the Increased CO2 Capture Performance of Amino Acid Functionalized Nanoporous Materials from First-Principles and Grand Canonical Monte Carlo Simulations

Nanoporous materials such as metal-organic frameworks (MOFs) and covalent-organic frameworks (COFs) have been identified as key candidates for environmental remediation through catalytic reduction and sequestration of pollutants. Given the prevalence of CO2 as a target molecule for capture, MOFs and COFs have seen a long history of application in the field. More recently, functionalized nanoporous materials have been demonstrated to improve performance metrics associated with the capture of CO2. We employ a multiscale computational approach including ab initio density functional theory (DFT) calculations and classical grand canonical Monte Carlo (GCMC) simulations, to investigate the impact of amino acid (AA) functionalization in three such nanoporous materials. Our results demonstrate a nearly universal improvement of CO2 uptake metrics such as adsorption capacity, accessible surface area, and CO2/N2 selectivity for six AAs. In this work, we elucidate the key geometric and electronic properties associated with improving the CO2 capture performance of functionalized nanoporous materials.

An intermolecular potential for hydrogen: Classical molecular simulation of pressure-density-temperature behavior, vapor-liquid equilibria, and critical and triple point properties.

An intermolecular potential is reported for molecular hydrogen that combines two-body interactions from abinitio data with three-body interactions. The accuracy of the two-body potential is validated by comparison with experimental second virial coefficient data. Experimental pressure-density-temperature data are used to validate the addition of three-body interactions, often yielding very accurate predictions. Classical Monte Carlo simulations that neglect quantum effects are reported for the vapor-liquid equilibria (VLE), critical properties, and the triple point. A comparison with experimental data indicates that the effect of quantum interactions is to narrow the VLE phase envelope and to lower the critical temperature. The three-body interactions have a considerable influence on the phase behavior, resulting in good agreement with the experimental density. The critical properties of the two-body + three-body potential for hydrogen provide an alternative set of input parameters to improve the accuracy of theoretical predictions at temperatures above 100K. In the vicinity of the critical point, the coexistence densities do not obey the law of rectilinear diameters, which is a feature that has largely been overlooked in both experimental data and reference equations of state.

Isotopic effect on thermal physical properties of cubic SiC

Using path-integral Monte Carlo (PIMC) and classical Monte Carlo (CMC) simulations in the isothermal–isobaric (NPT) ensemble, we investigate the isotope effect on the thermal properties of the cubic silicon carbide (c-SiC) crystal. At T=50 K, the calculations show that the isotopic substitutions shift up the average vibrational energy and root-mean-square displacements (RMSD) values, with a more significant impact on carbon isotope substitution than the silicon ones. However, the total kinetic to total potential energy ratio suggests that the system behaves harmonically and insensitive to isotopic changes. We also calculated the effect of the quantum contribution on c-SiC crystal, considering the most abundant isotopes. At low temperatures, the c-SiC crystal behaves harmonically, although the C and Si atoms behave anharmonically. The quantum effects increase the lattice constant by almost 0.3%, the average RMSD by 0.0703(4) Å and are responsible for reducing the linear thermal expansion coefficient by about 5.8×10−6 K. The zero-point energy is found about 0.1225(3) eV/atom. A satisfactory agreement between the PIMC values and available theoretical and experimental results are found and discussed.

Electron Impact Ionization Cross-Section Maxima of Atoms

Using measured cross-sections and polarizability data, an empirical scaling law is extracted for the electron collision single-ionization cross-section maxima of neutral atoms. We found that the cross sections scale linearly with the target’s static polarizability. We confirm this observation using our present three-body classical trajectory Monte Carlo simulations.

Monte Carlo investigation for an Ising model with competitive magnetic interactions in the dominant ferromagnetic-interaction regime

We apply classical Monte Carlo simulation to examine the thermodynamic properties of perovskites described by the Ising model with competitive magnetic interactions. By correspondingly adjusting the ferromagnetic-interaction and antiferromagnetic-interaction probabilities, $p$ and $(1-p)$, in the regime $p \ge 0.5$, the temperature dependence of magnetization, total energy, spin susceptibility, and specific heat consistently show a ferromagnetic to paramagnetic (FM-PM) phase transition at a critical temperature $T_c$. Besides, the inverse susceptibility is confirmed to follow Curie-Weiss's law above another critical temperature $T_{CW}$. By increasing the FM interaction probability, we have observed the FM-PM critical temperature $T_c$ shifted to the higher value while the Curie-Weiss critical temperature $T_{CW}$ moves to the lower. The different values between these two critical temperatures imply the inhomogeneity of the systems having phase separation, thus in agreement with the increased homogeneity with increasing $p$.

A deep investigation of NiO and MnO through the first principle calculations and Monte Carlo simulations

In this study, we use Hubbard-corrected density functional theory (DFT+U) to derive spin model Hamiltonians consisting of Heisenberg exchange interactions up to the fourth nearest neighbors and bi-quadratic interactions. We map the DFT+U results of several magnetic configurations to the Heisenberg spin model Hamiltonian to estimate Heisenberg exchanges. We demonstrate that the number of magnetic configurations should be at least twice the number of exchange parameters to estimate exchange parameters correctly. To calculate biquadratic interaction, we propose specific non-collinear magnetic configurations that do not change the energy of the Heisenberg spin model. We use classical Monte Carlo (MC) simulations to evaluate DFT+U results. We obtain the temperature dependence of magnetic susceptibility and specific heat to determine the Curie–Weiss and Néel temperatures. The MC simulations reveal that although the biquadratic interaction can not change the Néel temperature, it modifies the order parameter. We indicate that for a fair comparison between classical MC simulations and experiments, we need to consider the quantum effect by applying correction in classical MC simulations.

Deep Curve-Dependent PDEs for Affine Rough Volatility

We introduce a new deep learning–based algorithm to evaluate options in affine rough stochastic volatility models. Viewing the pricing function as the solution to a curve-dependent PDE, depending on forward curves rather than the whole path of the process, we develop a numerical scheme based on deep learning techniques. Numerical simulations suggest that the latter is a promising alternative to classical Monte Carlo simulations.

Simulation of random fields on random domains

This paper focuses on the simulation of random fields on random domains. This is an important class of problems in fields such as topology optimization and multiphase material analysis. However, there is still a lack of effective methods to simulate this kind of random fields. To this end, we extend the classical Karhunen–Loève expansion (KLE) to this class of problems, and we denote this extension as stochastic Karhunen–Loève expansion (SKLE). We present three numerical algorithms for solving the stochastic integral equations arising in the SKLE. The first algorithm is an extension of the classical Monte Carlo simulation (MCS), which is used to solve the stochastic integral equation on each sampled domain. However, such approach demands remeshing each sampled domain and solving the corresponding integral equation, which can become computationally very demanding. In the second algorithm, a domain transformation is used to map the random domain into a reference domain, and only one mesh for the reference domain is required. In this way, remeshing different sample realizations of the random domain is avoided and much computational effort is thus saved. MCS is then adopted to solve the corresponding stochastic integral equation. Further, to avoid the computational effort of MCS, the third algorithm proposed in this contribution involves a reduced-order method to solve the stochastic integral equation efficiently. In this third algorithm, stochastic eigenvectors are represented as a sum of products of unknown random variables and deterministic vectors, where the deterministic vectors are efficiently computed by solving deterministic eigenvalue problems. The random variables and stochastic eigenvalues that appear in this third algorithm are calculated by a reduced-order stochastic eigenvalue problem constructed by the obtained deterministic vectors. Based on the obtained stochastic eigenvectors, the target random field is then simulated and reformulated as a classical KLE-like representation. Finally, three numerical examples are presented to demonstrate the performance of the proposed methods.

Thermal first-order phase transitions, Ising critical points, and reentrance in the Ising-Heisenberg model on the diamond-decorated square lattice in a magnetic field

The thermal phase transitions of a spin-1/2 Ising-Heisenberg model on the diamond-decorated square lattice in a magnetic field are investigated using a decoration-iteration transformation and classical Monte Carlo simulations. A generalized decoration-iteration transformation maps this model exactly onto an effective classical Ising model on the square lattice with temperature-dependent effective nearest-neighbor interactions and magnetic field strength. The effective field vanishes along a ground-state phase boundary of the original model, separating a ferrimagnetic and a quantum monomer-dimer phase. At finite temperatures this phase boundary gives rise to an exactly solvable surface of discontinuous (first-order) phase transitions, which terminates in a line of Ising critical points. The existence of discontinuous reentrant phase transitions within a narrow parameter regime is reported and explained in terms of the low-energy excitations from both phases. These exact results, obtained from the mapping to the zero-field effective Ising model are corroborated by classical Monte Carlo simulations of the effective model.