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Coherent phase transformations in interstitial solid solutions or intercalation compounds with a miscibility gap are of practical relevance for energy storage materials and specifically for metal hydride or lithium-ion compound nanoparticles. Different conclusions on the size-dependence of the transformation conditions are reached by modeling or theory focusing on the impact of either one (internal, solid-state-) critical-point wetting of the nanoparticle surface or coherency constraints from solute-saturated surface layers. We report a hybrid numerical approach, combining atomistic grand canonical Monte Carlo simulation with a continuum mechanics analysis of coherency stress and modeling simultaneously wetting and mechanical constraints. When the ratio between chemical and misfit-strain-related contributions to the solute-solute interaction energy takes values realistic for interstitial solutions—which are typical for energy storage materials—we find that the impact of solid-state wetting is weak and that of coherency stress is dominant. Specifically, mechanical interaction can act to reduce the phase transformation hysteresis at small system size, and it can make the solid more binding for solute, thereby reducing the "plateau" chemical potential at phase coexistence. We present equations for the impact of coherency stress on the size-dependence of upper consolute temperature, plateau chemical potential, and charging/discharging hysteresis. [ABSTRACT FROM AUTHOR]

A comprehensive set of single-component and binary isotherms were collected for ethanol/water adsorption into the siliceous forms of 185 known zeolites using grand-canonical Monte Carlo simulations. Using these data, a systematic analysis of ideal/real adsorbed-solution theory (IAST/RAST) was conducted and activity coefficients were derived for ethanol/water mixtures adsorbed in different zeolites based on RAST. It was found that activity coefficients of ethanol are close to unity while activity coefficients of water are larger in most zeolites, indicating a positive excess free energy of the mixture. This observation can be attributed to water/ethanol interactions being less favorable than water/water interactions in the single-component adsorption of water at comparable loadings. The deviation from ideal behavior can be highly structure-dependent but no clear correlation with pore diameters was identified. Our analysis also demonstrates the following: (1) accurate unary isotherms in the low-loading regime are critical for obtaining physically sensible activity coefficients; (2) the global regression scheme to solve for activity model parameters performs better than fitting activity models to activity coefficients calculated locally at each binary state point; and (3) including the dependence on adsorption potential offers only a minor benefit for describing binary adsorption at the lowest fugacities. Finally, the Margules activity model was found incapable of capturing the non-ideal adsorption behavior over the entire range of fugacities and compositions in all zeolites, but for conditions typical of solution-phase adsorption, RAST predictions using zeolite-specific or even bulk Margules parameters provide an improved description compared to IAST. [ABSTRACT FROM AUTHOR]

Quantum Monte Carlo (QMC) methods represent a powerful family of computational techniques for tackling complex quantum many-body problems and performing calculations of stationary state properties. QMC is among the most accurate and powerful approaches to the study of electronic structure, but its application is often hindered by a steep learning curve; hence it is rarely addressed in undergraduate and postgraduate classes. This tutorial is a step toward filling this gap. We offer an introduction to the diffusion Monte Carlo (DMC) method, which aims to solve the imaginary time Schrödinger equation through stochastic sampling of the configuration space. Starting from the theoretical foundations, the discussion leads naturally to the formulation of a step-by-step algorithm. To illustrate how the method works in simplified scenarios, examples such as the harmonic oscillator and the hydrogen atom are provided. The discussion extends to the fixed-node approximation, a crucial approach for addressing the fermionic sign problem in multi-electron systems. In particular, we examine the influence of trial wave function nodal surfaces on the accuracy of DMC energy by evaluating results from a non-interacting two-fermion system. Extending the method to excited states is feasible in principle, but some additional considerations are needed, supported by practical insights. By addressing the fundamental concepts from a hands-on perspective, we hope this tutorial will serve as a valuable guide for researchers and students approaching DMC for the first time. [ABSTRACT FROM AUTHOR]

We report a model to predict equilibrium density profiles for different shaped colloids in two-dimensional liquid, nematic, and crystal states in nonuniform external fields. The model predictions are validated against Monte Carlo simulations and optical microscopy experiments for circular, square, elliptical, and rectangular colloidal particles in AC electric fields between parallel electrodes. The model to predict the densities of all states of different shaped particles is based on a balance of the local quasi-2D osmotic pressure against a compressive force due to induced dipole-field interactions. The osmotic force balance employs equations of state for hard ellipse liquid, nematic, and crystal state osmotic pressures, which are extended to additional particle shapes. The resulting simple analytical model is shown to accurately predict particle densities within liquid, liquid crystal, and crystal states for a broad range of particle shapes, system sizes, and field conditions. These findings provide a basis for quantitative design and control of fields to assemble and reconfigure colloidal particles in interfacial materials and devices. [ABSTRACT FROM AUTHOR]

We have performed a data science study of Monte Carlo (MC) simulation trajectories to understand factors that can accelerate the formation of zeolite nanoporous crystals, a process that can take days or even weeks. In previous work, MC simulations predicted and experiments confirmed that using a secondary organic structure-directing agent (OSDA) accelerates the crystallization of all-silica LTA zeolite, with experiments finding a three-fold speedup [Bores et al., Phys. Chem. Chem. Phys. 24, 142–148 (2022)]. However, it remains unclear what physical factors cause the speed-up. Here, we apply data science to analyze the simulation trajectories to discover what drives accelerated zeolite crystallization in MC simulations going from a one-OSDA synthesis (1OSDA) to a two-OSDA version (2OSDA). We encoded simulation snapshots using the smooth overlap of atomic positions approach, which represents all two- and three-body correlations within a given cutoff distance. Principal component analyses failed to discriminate datasets of structures from 1OSDA and 2OSDA simulations, while the Support Vector Machine (SVM) approach succeeded at classifying such structures with an area-under-curve (AUC) score of 0.99 (where AUC = 1 is a perfect classification) with all three-body correlations and as high as 0.94 with only two-body correlations. SVM decision functions reveal relatively broad/narrow histograms for 1OSDA/2OSDA datasets, suggesting that the two simulations differ strongly in information heterogeneity. Informed by these results, we performed pair (2-body) entropy calculations during crystallization, resulting in entropy differences that semi-quantitatively account for the speedup observed in the previous MC simulations. We conclude that altering synthesis conditions in ways that substantially change the entropy of labile silica networks may accelerate zeolite crystallization, and we discuss possible approaches for achieving such acceleration. [ABSTRACT FROM AUTHOR]

A kinetic Monte Carlo (KMC) simulation tool for modeling the pattern formation process in photoresist materials for extreme ultraviolet (photon energy 92 eV) nanolithography is presented. The availability of such a tool should support the progress toward novel materials and experimental procedures that lead to an improved pattern resolution. The molecular-scale simulations describe the process in a stochastic and mechanistic manner and include the excitation of high-energy electrons upon light absorption, the creation of a charged-particle cloud, electron-induced chemical degradation of the photoresist molecules, the resulting bond formation between neighboring degraded molecules, and a chemical development step after which a pattern of the remaining non-dissolved molecules is obtained. The method is applied to the application-relevant class of Sn-oxocore photoresist materials and uses their known electronic structure and optical electron energy loss function. The validity of the approach is tested by comparing measured and simulated total electron yield spectra and photoelectron spectra. A demonstration of the method is given by calculating the dose and pitch dependent average shape and stochastic variability (line edge roughness) of line patterns that are obtained for rectangular and sine-wave illumination, assuming various scenarios that determine how molecular-scale degradation will lead to bond creation. We show how from these simulations the ultimate pattern resolution can be deduced. The findings are analyzed systematically using results of KMC simulations that reveal the size of the cloud of degraded molecules around a point of absorption (blur length) and that further reveal the sensitivity to uniform illumination (contrast curves), and using percolation theory. We find that KMC modeling captures the consequences of the strong gradients in the density of degraded molecules and of the stochasticity of the patterning process that simplified models do not include, leading to a significantly improved view of the final pattern quality. [ABSTRACT FROM AUTHOR]

Many ternary mixtures composed of saturated and unsaturated lipids with cholesterol (Chol) exhibit a region of coexistence between liquid-disordered (Ld) and liquid-ordered (Lo) domains, bearing some similarities to lipid rafts in biological membranes. However, biological rafts also contain many proteins that interact with the lipids and modify the distribution of lipids. Here, we extend a previously published lattice model of ternary DPPC/DOPC/Chol mixtures by introducing a small amount of small proteins (peptides). We use Monte Carlo simulations to explore the mixing phase behavior of the components as a function of the interaction parameter representing the affinity between the proteins and the saturated DPPC chains and for different mixture compositions. At moderate fractions of DPPC, the system is in a two-phase Ld + Lo coexistence, and the proteins exhibit a simple partition behavior between the phases that depends on the protein–lipid affinity parameter. At low DPPC compositions, the mixture is in Ld phase with local nanoscopic ordered domains. The addition of proteins with sufficiently strong attraction to the saturated lipids can induce the separation of a distinct Lo large domain with tightly packed gel-like clusters of proteins and saturated lipids. Consistent with the theory of phase transitions, we observe that the domain sizes grow when the mixture composition is in the vicinity of the critical point. Our simulations show that the addition of a small amount of proteins to such mixtures can cause their size to grow even further and lead to the formation of metastable dynamic Lo domains with sizes comparable to biological rafts. [ABSTRACT FROM AUTHOR]

We apply the methodology of Lustig, with which rigorous expressions for all thermodynamic properties can be derived in any statistical ensemble, to derive expressions for the calculation of thermodynamic properties in the path integral formulation of the quantum-mechanical isobaric–isothermal (NpT) ensemble. With the derived expressions, thermodynamic properties such as the density, speed of sound, or Joule–Thomson coefficient can be calculated in path integral Monte Carlo simulations, fully incorporating quantum effects without uncontrolled approximations within the well-known isomorphism between the quantum-mechanical partition function and a classical system of ring polymers. The derived expressions are verified by simulations of supercritical helium above the vapor–liquid critical point at selected state points using recent highly accurate ab initio potentials for pairwise and nonadditive three-body interactions. We observe excellent agreement of our results with the most accurate experimental data for the density and speed of sound and a reference virial equation of state for helium in the region where the virial equation of state is converged. Moreover, our results agree closer with the experimental data and virial equation of state than the results of semiclassical simulations using the Feynman–Hibbs correction for quantum effects, which demonstrates the necessity to fully include quantum effects by path integral simulations. Our results also show that nonadditive three-body interactions must be accounted for when accurately predicting thermodynamic properties of helium by solely theoretical means. [ABSTRACT FROM AUTHOR]

In this study, we present a novel orientation discretization approach based on the rhombic triacontahedron for Monte Carlo simulations of semiflexible polymer chains, aiming at enhancing structural analysis through rheo-small-angle scattering (rheo-SAS). Our approach provides a more accurate representation of the geometric features of semiflexible chains under deformation, surpassing the capabilities of traditional lattice structures. Validation against the Kratky–Porod chain system demonstrated superior consistency, underscoring its potential to significantly improve the precision of uncovering geometric details from rheo-SAS data. This approach opens new avenues for investigating the conformations of semiflexible polymers and mechanically induced phase transitions in more complex polymer structures, offering deeper insights into their behavior under various conditions. [ABSTRACT FROM AUTHOR]

I studied the ground state properties and phase behavior of a two-dimensional lattice gas in which hard-core particles can have at most one nearest neighboring occupied site on the square lattice. Monte Carlo simulations in the grand-canonical ensemble showed no apparent signature of singular thermodynamic behavior when the chemical potential was increased. The absence of an ordering phase transition is traced to the large number of ground state configurations the model is endowed, which is due to the impossibility of satisfying simultaneously closest packing around a vacancy and around a particle. Numerical simulations confirm that the ground state entropy is proportional to the square root of system size. [ABSTRACT FROM AUTHOR]

This paper investigates the influence of Co addition and atomic ordering on the magnetic and magnetocaloric properties of all-d-metal Heusler alloys Ni 2 − x Co x Mn 1.25 Ti 0.75 , which exhibit a second-order magnetic phase transition. The modeling approach employed is based on the density functional theory and Monte Carlo method. The atomic ordering is considered with reference to the fully ordered structure, L2 1 , and the partially ordered structure, B2. It is demonstrated that in both structures, the predominant magnetic state within the cubic austenitic phase is characterized by ferromagnetic ordering. An increase in the Co content results in the strengthening of the ferromagnetic exchange interactions between Mn, Ni, and Co, as well as an increase in the Curie temperature. For the ground state L2 1 structure, the largest Curie temperature values are observed, exceeding those of the B2 structure by almost 100 K. The temperature dependencies of the magnetization and magnetocaloric effect (Δ S m a g ) in magnetic fields up to 2 T are calculated using the Heisenberg Hamiltonian by the Monte Carlo method. The largest effect (Δ S m a g ≈ 1.4 J/kg K) is observed for the compound with x = 0.375 and B2 structure at temperature ≈ 150 K, whereas for L2 1 -Ni 1.5 Co 0.5 Mn 1.25 Ti 0.75 and B2-Ni 1.25 Co 0.75 Mn 1.25 Ti 0.75 , Δ S m a g of 1.05 J/kg K appears in the vicinity of room temperature. [ABSTRACT FROM AUTHOR]

This paper investigates the influence of Co addition and atomic ordering on the magnetic and magnetocaloric properties of all-d-metal Heusler alloys Ni 2 − x Co x Mn 1.25 Ti 0.75 , which exhibit a second-order magnetic phase transition. The modeling approach employed is based on the density functional theory and Monte Carlo method. The atomic ordering is considered with reference to the fully ordered structure, L2 1 , and the partially ordered structure, B2. It is demonstrated that in both structures, the predominant magnetic state within the cubic austenitic phase is characterized by ferromagnetic ordering. An increase in the Co content results in the strengthening of the ferromagnetic exchange interactions between Mn, Ni, and Co, as well as an increase in the Curie temperature. For the ground state L2 1 structure, the largest Curie temperature values are observed, exceeding those of the B2 structure by almost 100 K. The temperature dependencies of the magnetization and magnetocaloric effect (Δ S m a g ) in magnetic fields up to 2 T are calculated using the Heisenberg Hamiltonian by the Monte Carlo method. The largest effect (Δ S m a g ≈ 1.4 J/kg K) is observed for the compound with x = 0.375 and B2 structure at temperature ≈ 150 K, whereas for L2 1 -Ni 1.5 Co 0.5 Mn 1.25 Ti 0.75 and B2-Ni 1.25 Co 0.75 Mn 1.25 Ti 0.75 , Δ S m a g of 1.05 J/kg K appears in the vicinity of room temperature. [ABSTRACT FROM AUTHOR]

Spontaneous self-assembly of hard convex polyhedra is known to form orientationally disordered crystalline phases, where particle orientations do not follow the same pattern as the positional arrangement of the crystal. A distinct type of orientational phase with discrete rotational mobility has been reported in hard particle systems. In this paper, we present a new analysis method for characterizing the orientational phase of a crystal, which is based on algorithmic detection of unique orientations. Using this method, we collected complete statistics of discrete orientations along the Monte Carlo simulation trajectories and observed that particles were equally partitioned among them, with specific values of pairwise orientational differences. These features remained constant across the pressure range and did not depend on rotational mobility. The discrete mobility was characteristic of a distinct equilibrium thermodynamic phase, qualitatively different from the freely rotating plastic phase with continuous orientations. The high pressure behavior with frozen particle orientations was part of that same description and not a non-equilibrium arrested state. We introduced a precise notion of orientational order and demonstrated that the system was maximally disordered at the level of a unit cell, even though individual particles could only take a few discrete orientations. We report the existence of this phase in five polyhedral shapes and in systematically curated shape families constructed around two of them. The symmetry mismatch between the particle and the crystallographic point groups was found to be a predictive indicator for the occurrence of this phase. [ABSTRACT FROM AUTHOR]

The introduction of machine learned potentials (MLPs) has greatly expanded the space available for studying Nuclear Quantum Effects computationally with ab initio path integral (PI) accuracy, with the MLPs' promise of an accuracy comparable to that of ab initio at a fraction of the cost. One of the challenges in development of MLPs is the need for a large and diverse training set calculated by ab initio methods. This dataset should ideally cover the entire phase space, while not searching this space using ab initio methods, as this would be counterproductive and generally intractable with respect to computational time. In this paper, we present the self-learning PI hybrid Monte Carlo Method using a mixed ab initio and ML potential (SL-PIHMC-MIX), where the mixed potential allows for the study of larger systems and the extension of the original SL-HMC method [Nagai et al., Phys. Rev. B 102, 041124 (2020)] to PI methods and larger systems. While the MLPs generated by this method can be directly applied to run long-time ML-PIMD simulations, we demonstrate that using PIHMC-MIX with the trained MLPs allows for an exact reproduction of the structure obtained from ab initio PIMD. Specifically, we find that the PIHMC-MIX simulations require only 5000 evaluations of the 32-bead structure, compared to the 100 000 evaluations needed for the ab initio PIMD result. [ABSTRACT FROM AUTHOR]

Understanding and characterizing very low-energy (∼ eV) background sources is a must in rare-event searches. Oscura, an experiment aiming to probe electron recoils from sub-GeV dark matter using a 10 kg skipper-CCD detector, has recently fabricated its first two batches of sensors. In this work, we present the characterization of defects/contaminants identified in the buried-channel region of these newly fabricated skipper-CCDs. These defects/contaminants produce deferred charge from trap emission in the images next to particle tracks, which can be spatially resolved due to the sub-electron resolution achieved with these sensors. Using the trap-pumping technique, we measured the energy and cross section associated with these traps in three Oscura prototype sensors from different fabrication batches which underwent different gettering methods during fabrication. Results suggest that the type of defects/contaminants is more closely linked to the fabrication batch rather than to the gettering method used. The exposure-dependent single-electron rate (SER) of one of these sensors was measured ∼ 100 m underground, yielding (1.8 ± 0.3) × 10 − 3 e − /pix/day at 131 K. The impact of the identified traps on the measured exposure-dependent SER is evaluated via a Monte Carlo simulation. Results suggest that the exposure-dependent SER of Oscura prototype sensors would be lower in lower background environments as expected. [ABSTRACT FROM AUTHOR]

The critical adsorption conditions of polyelectrolytes (PEs) onto planar, cylindrical, and spherical surfaces were obtained by solving the Edwards equation using the Wentzel–Kramers–Brillouin (WKB) method. It demonstrated to provide a suitable analytical approach for all three geometries, in conformity with some experimental results for weakly charged micelles. However, our Monte Carlo simulations implementing approximate solutions of the nonlinear Poisson–Boltzmann equation for highly charged surfaces indicated recently the emergence of a limiting value of ionic strength due to a nonlinear dependence of the electrostatic (ES) potential on the surface-charge density σ. Beyond this limiting ionic strength, the PE adsorption no longer occurs, shifting the standard paradigm. In this work, we employ the concept of a renormalized charge and use the WKB method to study the effects of this nonlinearity on the critical adsorption conditions, density profile, and adsorbed layer of PE segments, all in comparison with the results of the linear Debye–Hückel (DH) approach. Charge renormalization makes it possible to use the known WKB solutions in the DH regime also for surfaces with high σ, introducing a saturation effect observed in the nonlinear case. The larger ES screening affects the density profile and the adsorbed layer of PEs, promoting a more dispersed distribution of PEs at higher surface-charge densities. Our analytical results for the critical adsorption curve reproduce the limiting ionic strength for high σ and also recover the DH regime at low σ. [ABSTRACT FROM AUTHOR]

Two-molecule theory refers to a class of microscopic, self-consistent field theories for the radial distribution function in classical molecular liquids. The version examined here can be considered as one of the very few formally derived closures to the reference interaction site model (RISM) equation. The theory is applied to polyethylene liquids, computing their equilibrium structural and thermodynamic properties at melt densities. The equation for the radial distribution function, which is represented as an average over the accessible states of two molecules in an external field that mimics the effects of the other molecules in the liquid, is computed by Monte Carlo simulation along with the intramolecular structure function. An improved direct sampling algorithm is utilized to speed the equilibration. Polyethylene chains of 24 and 66 united atom CH2 units are studied. The results are compared to full, many-chain molecular dynamics (MD) simulations and self-consistent polymer-RISM (PRISM) theory with the atomic Percus–Yevick (PY) closure under the same conditions. It is shown that the two-molecule theory produces results that are close to those of MD and is thus able to overcome defects of PRISM-PY theory and predict more accurate liquid structure at both short and long ranges. Predictions for the equation of state are also discussed. [ABSTRACT FROM AUTHOR]

Vibrational strong coupling (VSC), the strong coupling between a Fabry–Perrot cavity and molecular vibrations at mid-infrared frequencies, has received important attention in the last years due to its capacity of modifying both vibrational spectra and chemical reactivity. VSC is a collective effect, and in this work, we introduce Path Integral Monte Carlo (PIMC) simulations that not only take into account the quantum character of the molecular vibrations and of the optical resonance of the cavity but also reproduce this collective behavior by considering multiple replicas of the molecular system. Moreover, we show that it is possible to extract from the PIMC simulations the decomposition of the hybrid optical and molecular states in terms of the bare molecular modes. On a model system of an ensemble of disordered Morse oscillators coupled to a single cavity through the Pauli–Fierz Hamiltonian, PIMC can retrieve known features obtained from analytical modes such as the Tavis–Cummings model and obtain a very close agreement with exact diagonalization for a small number of Morse oscillators. We also find that notwithstanding the anhamonic character of the Morse oscillators, the collective mode coupled to the cavity behaves as a harmonic oscillator, following the quantum central limit theorem. [ABSTRACT FROM AUTHOR]

The anisotropic potential energy surface of the (H2)2 dimer represents a challenging problem for many-body methods. Here, we determine the potential energy curves of five different dimer configurations (T, Z, X, H, and L) using the lattice regularized diffusion Monte Carlo method and a number of approximate functionals within density functional theory (DFT), including advanced orbital-dependent functionals based on the random phase approximation (RPA). We assess their performance in describing the potential wells, bond distances, and relative energies. The repulsive potential wall is studied by looking at the relative stability of the different dimer configurations as a function of an applied force acting along the intermolecular axis. It is shown that most functionals within DFT break down at finite compression, even those that give an accurate description around the potential well minima. Only by including exchange within RPA, a qualitatively correct description along the entire potential energy curve is obtained. Finally, we discuss these results in the context of solid molecular hydrogen at finite pressures. [ABSTRACT FROM AUTHOR]

We report on the construction of the SiRO—SiPM ReadOut muon detector, a detection system based on plastic scintillator bars designed for muography applications. Using six 1 m 2 layers of active medium, grouped two by two into three rectangular matrices of pixels, each separated by a variable distance, the spatial coordinates of the muon's impact point on every matrice are obtained and used for trajectory reconstruction. Validation studies have been performed using Monte Carlo simulations and later confirmed by preliminary measurements in our laboratory and in underground, in the Slănic Prahova salt mine, in Romania. [ABSTRACT FROM AUTHOR]

Non-additive mixing plays a key role in the properties of molecular fluids and solids. In this work, the potential for athermal order–disorder phase transitions is explored in non-additive binary colloidal nanoparticles that form substitutionally ordered compounds, namely, for equimolar mixtures of octahedra + spheres, which form a CsCl lattice compound, and cubes + spheres, which form a NaCl crystal. Monte Carlo simulations that target phase coexistence conditions were used to examine the effect on compound formation of varying degrees of negative non-additivity created by component size asymmetry and by size-tunable indentations in the polyhedra's facets, intended to allow the nestling of neighboring spheres. Our results indicate that the stabilization of the compound crystal requires a relatively large degree of negative non-additivity, which depends on particle geometry and the packing of the relevant phases. It is found that negative non-additivity can be achieved in mixtures of large spheres and small cubes having no indentations and lead to the athermal crystallization of the NaCl lattice. For similarly sized components, athermal congruent transitions are attainable and non-additivity can be generated through indentations, especially for the cubes + spheres system. Increasing indentation leads to lower phase coexistence free energy and pressure in the cubes + spheres system but has the opposite effect in the octahedra + spheres system. These results indicate a stronger stabilizing effect on the athermal compound phase by the cubes' indentations, where a deeper nestling of the spheres leads to a denser compound phase and a larger reduction in the associated pressure-volume free-energy term. [ABSTRACT FROM AUTHOR]

The cross section of options holds great promise for identifying return distributions and risk premia, but estimating dynamic option valuation models with latent state variables is challenging when using large option panels. We propose a particle Markov Chain Monte Carlo framework with a novel filtering approach and illustrate our method by estimating index option pricing models. Estimates of variance risk premiums, variance mean reversion, and higher moments differ from the literature. We show that these differences are due to the composition of the option sample. Restricting the option sample's maturity dimension has the strongest impact on parameter inference and option fit in these models. [ABSTRACT FROM AUTHOR]

Signaling in cells is full of noise and, hence, described with stochastic biochemical models. Thus, an efficient computation algorithm for these fluctuating reactions is much needed. Apart from the very popular Monte Carlo simulation, methods based on probability distributions are frequently desired due to their analytical tractability and possible numerical advantages in diverse circumstances, among which the variational approach is the most notable. In this paper, new basis functions are proposed to better depict possibly complex distribution profiles, and an extra regularization scheme is supplied to the variational equation to remove occasional degeneracy-induced singularities during the evolution. The new extension is applied to four typical biochemical reaction models and restores the Gillespie results accurately but with greatly reduced simulation time. This modified variational approach is expected to work in a wide range of cell signaling networks. [ABSTRACT FROM AUTHOR]

Inelastic n-changing collisions play an important role in the evolution of Rydberg atoms into ultracold plasmas. However, for the initially intermediate n (n ∼ 40) Rydberg states, these collisions can hardly be observed due to the low electron temperature in ultracold plasmas. In this work, we designed an experimental scheme to facilitate collisions between free electrons at 1.5 eV and intermediate n Rydberg atoms. Using the field ionization technique, we measured the state distributions resulting from the evolution of initially cold rubidium atoms in the 45P3/2 Rydberg state. The experimentally obtained probability of inelastic collisions excitation agrees well with the Monte Carlo simulation results. In addition, our experimental results indicate that the n-changing population induced by hot electrons is significant for lower nP Rydberg states. Our work plays a significant role in calculating the rates of electron–ion three-body recombination in ultracold plasmas. [ABSTRACT FROM AUTHOR]

Existing methods to compute theoretical spectra are restricted to the use of time-correlation functions evaluated from accurate atomistic molecular dynamics simulations, often at the ab initio level. The molecular interpretation of the computed spectra requires additional steps to deconvolve the spectroscopic contributions from local water and surface structural populations at the interface. The lack of a standard procedure to do this often hampers rationalization. To overcome these challenges, we rewrite the equations for spectra calculation into a sum of partial contributions from interfacial populations, weighted by their abundance at the interface. We show that SFG signatures from each population can be parameterized into a minimum dataset of reference partial spectra. Accurate spectra can then be predicted by just evaluating the statistics of interfacial populations, which can be done even with force field simulations as well as with analytic models. This approach broadens the range of simulation techniques from which theoretical spectra can be calculated, opening toward non-atomistic and Monte Carlo simulation approaches. Most notably, it allows constructing accurate theoretical spectra for interfacial conditions that cannot even be simulated, as we demonstrate for the pH-dependent SFG spectra of silica/water interfaces. [ABSTRACT FROM AUTHOR]

Recent experiments have demonstrated the self-assembly and long-range ordering of concentrated aqueous solutions of DNA and RNA mononucleotides. These are found to form Watson–Crick pairs that stack into columns that become spatially organized into a columnar liquid-crystalline phase. In this work, we numerically investigate this phase behavior by adopting an extremely coarse-grained model in which nucleotides are represented as semi-disk-like polyhedra decorated with attractive (patchy) sites that mimic the stacking and pairing interactions. We carry out Monte Carlo simulations of these patchy polyhedra by adapting algorithms borrowed from computer graphics. This model reproduces the features of the experimental phase behavior, which essentially depends on the combination of pairing and stacking interactions. [ABSTRACT FROM AUTHOR]

The interplay between densification and positional ordering during the process of crystal nucleation is a greatly investigated topic. Even for the simplest colloidal model—hard spheres—there has been much debate regarding the potential foreshadowing of nucleation by significant fluctuations in either local density or local structure. Considering anisotropic particles instead of spheres adds a third degree of freedom to the self-organization process of crystal nucleation: orientational ordering. Here, we investigate the crystal nucleation of hard triangular prisms. Using Monte Carlo simulations, we first carefully determine the crystal–fluid coexistence values and calculate the nucleation barriers for two degrees of supersaturation. Next, we use brute force simulations to obtain a large set of spontaneous nucleation events. By studying the time evolution of the local density, positional ordering, and orientational ordering in the region in which the nucleus first arises, we demonstrate that all local order parameters increase simultaneously from the very start of the nucleation process. We thus conclude that we observe no precursor for the crystal nucleation of hard triangular prisms. [ABSTRACT FROM AUTHOR]

We explore the possibility of implementing random walks in the manifold of Hartree–Fock–Bogoliubov wave functions. The goal is to extend state-of-the-art quantum Monte Carlo approaches, in particular the constrained-path auxiliary-field quantum Monte Carlo technique, to systems where finite pairing order parameters or complex pairing mechanisms, e.g., Fulde–Ferrell–Larkin–Ovchinnikov pairing or triplet pairing, may be expected. Leveraging the flexibility to define a vacuum state tailored to the physical problem, we discuss a method to use imaginary-time evolution of Hartree–Fock–Bogoliubov states to compute ground state correlations, extending beyond situations spanned by current formalisms. Illustrative examples are provided. [ABSTRACT FROM AUTHOR]

Finite size scaling for a first order phase transition, where a continuous symmetry is broken, is tested using an approximation of Gaussian probability distributions with a phenomenological "degeneracy" factor. Predictions are compared to the data from Monte Carlo simulations of the Lebwohl–Lasher model on L × L × L simple cubic lattices. The data show that the intersection of the fourth-order cumulant of the order parameter for different lattice sizes can be expressed in terms of the relative degeneracy q = 4π of the ordered and disordered phases. This result further supports the concept of universality at first order transitions developed recently. [ABSTRACT FROM AUTHOR]

The inherent flexibility of two-dimensional (2D) materials allows for efficient manipulation of their physical properties through strain application, which is essential for the development of advanced nanoscale devices. This study aimed to understand the impact of mechanical strain on the magnetic properties of two-dimensional (2D) materials using Monte Carlo simulations. The effects of several strain states on the magnetic properties were investigated using the Lennard-Jones potential and bond length-dependent exchange interactions. The key parameters analyzed include the Lindemann coefficient, radial distribution function, and magnetization in relation to temperature and magnetic field. The results indicate that applying biaxial tensile strain generally reduces the critical temperature (Tc). In contrast, the biaxial compressive strain increased Tc within the elastic range, but decreased at higher strain levels. Both compressive and tensile strains significantly influence the ferromagnetic properties and structural ordering, as evidenced by magnetization hysteresis. Notably, pure shear strain did not induce disorder, leaving the magnetization unaffected. In addition, our findings suggest the potential of domain-formation mechanisms. This study provides comprehensive insights into the influence of mechanical strain on the magnetic behavior and structural integrity of 2D materials, offering valuable guidance for future research and advanced material design applications. [ABSTRACT FROM AUTHOR]

The configuration of a high-quality security system or computer using a Monte Carlo simulation high-quality random-number generator has been expected. The high-quality random-number generators are obtained using physical randomness phenomena. In particular, chaos is an appropriate random-number generator. First, we investigate the chaotic behavior in the Josephson junction (JJ) under irradiation with external radio frequency (RF) at 77 K using an equivalent circuit of the JJ. JJ is assumed to be an intrinsic JJ in a Bi 2 Sr 2 CaCu 2 O 8 + δ single crystal. The output voltages of the JJ behave chaotic under some conditions and are evaluated using the Lyapunov exponent, Poincaré section, and attractors. Next, random numbers were generated from the chaotic output voltage in rgw JJ under irradiation with RF and evaluated by a verification test. Thus, random-number generators can be applied using the output voltage of theJJ under irradiation with external RF. [ABSTRACT FROM AUTHOR]

The structures of metal nanoparticles (NPs) significantly influence their catalytic reactivities. Recent in situ experimental observations of dramatic structural changes in NPs underscore the need to establish a dynamic structure–property relationship that accounts for the reconstruction of NPs in reactive environments. Here, we present the MOSP, a free and open-source graphical user interface (GUI) package designed to simulate the structure and reactivity of metal NPs under operando conditions. MOSP integrates two models: the multiscale structure reconstruction model predicting equilibrium metal NP structures under specific reaction conditions and the kinetic Monte Carlo model simulating the reaction dynamics. This combination allows for the exploration of the dynamic structure–property relationships of NPs. MOSP enhances user accessibility through its intuitive GUI, facilitating easy input, post-processing, and visualization of simulation data. This article is the release note of MOSP, focusing on its implementation and functionality. [ABSTRACT FROM AUTHOR]

A novel statistical mechanical methodology is applied to clusters of N ≤ 7 atoms. Exact statistical analogs for any energy derivative of entropy ∂mS/∂Em are used in rigorous microcanonical Monte Carlo simulations to vastly enlarge the pool of measurable thermodynamic properties relative to previous work. All analogs are given for two alternative partition functions of the microcanonical ensemble. Coarse grained energy distributions are used to establish the existence of melting transitions. LJ7, LJ5, and LJ4 are found to exhibit trimodal distributions, a feature not being reported before. Varieties of combinations of entropy derivatives are tested for a direct detection of the melting region. It is shown that for such a purpose, derivatives of at least fourth order are necessary. [ABSTRACT FROM AUTHOR]

Monte Carlo simulations are widely employed to measure the physical properties of glass-forming liquids in thermal equilibrium. Combined with local Monte Carlo moves, the Metropolis algorithm can also be used to simulate the relaxation dynamics, thus offering an efficient alternative to molecular dynamics. Monte Carlo simulations are, however, more versatile because carefully designed Monte Carlo algorithms can more efficiently sample the rugged free energy landscape characteristic of glassy systems. After a brief overview of Monte Carlo studies of glass-formers, we define and implement a series of Monte Carlo algorithms in a three-dimensional model of polydisperse hard spheres. We show that the standard local Metropolis algorithm is the slowest and that implementing collective moves or breaking detailed balance enhances the efficiency of the Monte Carlo sampling. We use time correlation functions to provide a microscopic interpretation of these observations. Seventy years after its invention, the Monte Carlo method remains the most efficient and versatile tool to compute low-temperature properties in supercooled liquids. [ABSTRACT FROM AUTHOR]