Monte Carlo Computer Simulations Research Articles

Increase in Auxeticity Due to the Presence of a Disordered Crystalline Phase of Hard Dumbbells Within the Nanolayer-Nanochannel Inclusion Introduced to the f.c.c. Hard Sphere Crystal.

To obtain materials or metamaterials with desired elastic properties that are tailor-made for a particular application, it is necessary to design a new material or composite (which may be cumbersome) or to modify the structure of existing materials in order to change their properties in the desired direction. The latter approach, although also not easy, seems favourable with respect to parameters like costs and time-to-market. Despite the fact that elastic properties are one of the oldest studied physical parameters of matter, our understanding of the processes at the microstructural level, that are behind these properties, is still far from being complete. The present work, with the help of Monte Carlo computer simulations, aims to broaden this knowledge. The previously studied model crystal of hard spheres, containing a combined nanolayer and nanochannel inclusions, is revisited. This periodic model crystal has been extended to include a degree of disorder in the form of degenerate crystalline phase by introducing a degenerate crystalline phase within its structure. The inclusion has been transformed (without changes to its shape, size, or orientation) by randomly connecting the neighbouring spheres into di-atomic molecules (dumbbells). The impact of this modification on elastic properties has been investigated with the help of the Parrinello-Rahman approach in the isothermal-isobaric ensemble (NpT). It has been shown, that the presence of the degenerate crystalline phase of hard dumbbells in the system leads to a significant decrease in the Poisson's ratio in [110]-direction (ν=-0.235) and an overall enhancement of the auxetic properties.

Magnetic and magnetocaloric dynamics in [formula omitted] double perovskites: Impact of A and B site variations analyzed through Monte Carlo simulation and Ab initio calculations

We investigate the magnetic and magnetocaloric properties of the double perovskites Sr2FeOsO6,Sr2FeCoO6,Dy2FeOsO6 and Dy2FeCoO6 using a combination of Monte Carlo simulations and Density Functional Theory (DFT). The exchange couplings were calculated using DFT. Sr2FeOsO6 exhibits antiferromagnetic ordering with two transitions at 50 and 150 K, driven by strong antiferromagnetic exchange interactions between Fe³⁺ and Os⁵⁺ ions. In contrast, Sr2FeCoO6 shows ferrimagnetic behavior with a single transition around 75 K, attributed to ferromagnetic coupling between Co2⁺ and Fe³⁺ ions. For the rare-earth-containing compounds, Dy2FeOsO6 demonstrates complex magnetic ordering with transitions at approximately 20 K and 140 K, influenced by the strong spin-orbit coupling of Dy³⁺ ions. Similarly, Dy2FeCoO6 exhibits two transitions at around 60 K and 170 K, reflecting a mix of ferromagnetic and antiferromagnetic interactions involving Dy³⁺, Co2⁺, and Fe³⁺ ions. Sr2FeOsO6 shows a peak magnetic entropy change ΔSm of 0.22 J/kg.K under a 5 T field at 50 K, while Sr2FeCoO6 exhibits a broader peak at 75 K with ΔSm of 1.5 J/kg·K. Dy2FeOsO6 presents significant ΔSm peaks at 20 K and 140 K, reaching 1.9 J/kg·K under a 5 T field. Dy2FeCoO6 displays the highest ΔSm of 4.0 J/kg·K at 60 K.

Structural analysis of superparamagnetic colloid aggregates confined in spherical cavities under external magnetic field

In this study, we investigated the behaviour of aggregates composed of superparamagnetic colloids under the influence of an external magnetic field, confined within several spherical cavities. The study included systems of two and three cavities in contact, as well as two cavities separated by a distance d along the direction of the external field. Monte Carlo computer simulations employing a model of hard spheres with central dipoles were realised to explore the behaviour of the magnetic particles, constrained to move within pairs (and trios) of spherical cavities. The primary focus of this investigation was to elucidate the structures formed by magnetic particles within systems presented here. Chains or ribbons primarily form within the central region of the spherical cavities. The aggregates within each cavity are drawn towards one another until they make contact at the closest points of the cavities. This behaviour is replicated when there is a separation distance between the spherical cavities, including cases where three cavities are in contact. This phenomenon may explain the observed attraction between magnetoliposomes as reported in the literature [García-Jimeno et al. Nanoscale. 9 (39), 15131–15143 (2017)].

Tectona Grandis seed powder and Mangifera Indica leaf powder as bio adsorbents for removal of methylene blue from aqueous solution

This study intends to describe the use of modified Tectona Grandis seed powder (TG) and Mangifera Indica leaf powder (MI) as adsorbent materials in the process of removing Methylene Blue (MB) from the wastewater. Nitric acid (HNO3) was used to chemically modify the plant material. Thermogravimetric analysis (TGA), Fourier transform infrared spectroscopy (FTIR), scanning electron microscopy (SEM), and X-ray diffraction (XRD) were utilized to analyze the modified bio adsorbents (TG and MI). The adsorbents' ideal specific surface area and pore volume were measured using the N2 adsorption/desorption technique through detailed characterization. The efficiency of the adsorbents in eliminating the MB dye was investigated in relation to the effects of adsorbent dose (2–10 mg), pH (3, 7 and 10), exposure time (10–90 min), temperature (30 °C, 50 °C and 70 °C), and dye concentration (20–100 mg/L) through batch adsorption studies. The models proposed by Langmuir, Freundlich, and Dubinin Raduskevich (D-R) could explain the binding results for MB on TG and MI. The adsorption process were more in line with the Langmuir model than the other models. At neutral pH (7), TG showed maximum percentage removal of 73.12 % whereas, MI powder showed a maximum percentage removal of 50.5 %. Time and adsorbent dosage have both led to an increase in the percentage of methylene blue elimination. The experimental results were confirmed by density functional theory (DFT) calculations, which revealed energy gaps (ΔE) of 4.57 eV and 7.882 eV for MB and TG/MI, respectively. Following complexation, a change of 16.56 eV was observed, indicating a stronger MB adsorption tendency across the modified TG/MI surface. The primary components of the mechanism of MB adsorption include hydrogen bonds, n-π, π-π, and electrostatic interactions, as per the results of Monte Carlo(MC) simulation calculations. According to our findings, TG and MI are affordable biomaterials for treating wastewater in an ecologically responsible and green manner.

Constructing CO2 capture nanotraps via tentacle-like covalent organic frameworks towards efficient CO2 separation in mixed matrix membrane

The structure and morphology of fillers are crucial factors in the process of CO2 separation within mixed matrix membranes (MMMs). In this study, the tentacle-like covalent organic framework (COF) as a filler was incorporated into the Pebax matrix for CO2/CH4 separation. The COF has abundant Lewis base sites (O atom and N atom) and porous pores, thereby constructing efficient CO2 capture nanotraps in the MMMs. The CO2 capture nanotraps facilitate the CO2 transport in the MMMs, and this can be verified by the Grand Canonical Monte Carlo (GCMC) simulation and density functional theory (DFT) calculation. Simultaneously, the CO2 capture nanotraps are distributed on the surface of tentacle-like COF, which is conducive to strengthening CO2 capture ability. Therefore, Pebax/COF MMMs exhibited superior CO2 gas separation performance compared to the pure Pebax membrane. Among them, the MMM with 3 wt% COF loading displayed the highest CO2 gas separation performance, exhibiting permeability and selectivity that were 73.4% and 32.9% higher than the pure Pebax membrane, respectively. Thus, CO2 capture nanotraps constructed in the MMMs via tentacle-like COF showed a promising potential for CO2 separation.

Fingerprints of ordered self-assembled structures in the liquid phase of a hard-core, square-shoulder system.

We investigate the phase ordering (pattern formation) of systems of two-dimensional core-shell particles using Monte Carlo (MC) computer simulations and classical density functional theory (DFT). The particles interact via a pair potential having a hard core and a repulsive square shoulder. Our simulations show that on cooling, the liquid state structure becomes increasingly characterized by long wavelength density modulations and on further cooling forms a variety of other phases, including clustered, striped, and other patterned phases. In DFT, the hard core part of the potential is treated using either fundamental measure theory or a simple local density approximation, whereas the soft shoulder is treated using the random phase approximation. The different DFTs are benchmarked using large-scale grand-canonical-MC and Gibbs-ensemble-MC simulations, demonstrating their predictive capabilities and shortcomings. We find that having the liquid state static structure factor S(k) for wavenumber k is sufficient to identify the Fourier modes governing both the liquid and solid phases. This allows us to identify from easier-to-obtain liquid state data the wavenumbers relevant to the periodic phases and to predict roughly where in the phase diagram these patterned phases arise.

Life cycle assessment of tomato biomass residue anaerobic digestion preceded by ethanol-based organosolv and choline chloride-based deep eutectic solvent

Anaerobic digestion (AD) of lignocellulosic wastes (LW) has garnered substantial interest because of its notable energy and nutrient recovery, along with its potential for reducing greenhouse gas emissions. However, the LW is resistant to degradation, and its hydrolysis typically requires harsh conditions, hence the need for a pretreatment. Conducting a life cycle assessment (LCA) to evaluate the pretreatment of LW is an effective way to assess the environmental impacts associated with various pretreatment methods. This work evaluates and compares three scenarios for handling lignified tomato green waste (TGW), generated in the Greater of Agadir in Morocco, in terms of their environmental impacts and energy demand, using the LCA approach, performed with OpenLCA software. To achieve this aim, the impact of these scenarios on 11 indicators is studied. The analyzed management options include a base case scenario S0 where TGW undergoes a direct anaerobic digestion (AD), organosolv pretreatment of TGW followed by AD of the free-lignin fraction (S1), and choline chloride-based deep eutectic solvent (DES) delignification followed by AD of the free-lignin fraction (S2). The data used for the analysis comes from the Tamelast landfill, laboratory tests, literature, CML-IA baseline and Monte Carlo simulation calculations. The results obtained showed that the introduction of pretreatments in S1 and S2 mitigates significantly the environmental impact in different categories compared to S0. Scenario S2, with its enhanced recovery processes, shows the highest positive environmental contributions, despite its reliance on additional external electricity. S1 and S0 both respect energy circularity. Through this study, it has been demonstrated that chemical pretreatment of LW is energy, water and solvent-intensive and requires a large investment. It opens up perspectives for further works on pretreatment using natural DES technology, its development and its applications in the delignification of ligneous biomass on an industrial scale.

How Transcription Factors Binding Stimulates Transcriptional Bursting.

Transcription is a fundamental biological process of transferring genetic information which often occurs in stochastic bursts when periods of intense activity alternate with quiescent phases. Recent experiments identified strong correlations between the association of transcription factors (TFs) to gene promoters on DNA and transcriptional activity. However, the underlying molecular mechanisms of this phenomenon remain not well understood. Here, we present a theoretical framework that allowed us to investigate how binding dynamics of TF influences transcriptional bursting. Our minimal theoretical model incorporates the most relevant physical-chemical features, including TF exchange among multiple binding sites at gene promoters and TF association/dissociation dynamics. Using analytical calculations supported by Monte Carlo computer simulations, it is demonstrated that transcriptional bursting dynamics depends on the strength of TF binding and the number of binding sites. Stronger TF binding affinity prolongs burst duration but reduces variability, while an optimal number of binding sites maximizes transcriptional noise, facilitating cellular adaptation. Our theoretical method explains available experimental observations quantitatively, confirming the model's predictive accuracy. This study provides important insights into molecular mechanisms of gene expression and regulation, offering a new theoretical tool for understanding complex biological processes.

Aerothermal Loads on a Representative Porous Mesostructure at Flight Conditions Using Direct Simulation Monte Carlo

Spacecraft require thermal protection systems (TPS) in order to survive the extreme conditions present during atmospheric entry missions. Porous ablators are a class of TPS materials that have been used successfully on several entry missions, although they can be difficult to model because of their complex nature at the micro- and mesoscales. Specifically, the processes that lead to mechanical erosion (spallation) of these materials are poorly understood. In order to gain insight into the spallation process, the current work computes aerothermal loads on a mesostructure representative of FiberForm (the substrate of phenolic impregnated carbon ablator) by leveraging a simulation framework involving loosely coupled Computational Fluid Dynamics-Direct Simulation Monte Carlo (CFD-DSMC) simulations of hypersonic boundary layers. CFD boundary layers are extracted from two altitudes, 68.9 and 81 km, along the Stardust entry trajectory and are imposed as boundary conditions on a DSMC simulation over an artificially generated mesostructure, which is representative of the charred layer of the TPS material. In order to produce high-quality results, the DSMC boundary conditions require careful consideration; specifically, Chapman–Enskog distributions are needed to account for large velocity and temperature gradients. Visualizations of the DSMC flowfield indicate excellent agreement with the original CFD data, and the aerothermal loads (heat flux and traction force) on the surface were examined using probability density functions. Additionally, the effects of pyrolysis blowing through the mesostructure on the surface properties are also determined.

Defect and dopant complex mediated high power factor in transparent selenium-doped copper iodide thin films

Copper iodide (CuI) is a promising p-type transparent thermoelectric material for near-room temperature energy harvesting. We report a high-power factor for selenium (Se)-doped CuI films. Ion beam-sputtered CuI films were doped using 30 keV 80Se+ implantation with Se concentration varying between 0.50% and 6.50%. Hall effect measurements showed a ∼34% increase in electrical conductivity (σ ≈ 36.1 Ω−1cm−1) due to a ∼54% increase in carrier density (pH ≈ 5.4 × 1019 cm−3) in the p-type γ-CuI film implanted with 5.0 × 1014 Se.cm−2. A high Seebeck coefficient, α ≈ 388.9 μVK−1−1, and moderate electrical conductivity, σ ≈ 29.1 Ω−1cm−1, yield a nearly 85% increase in the power factor, α2σ ≈ 439.7 μWm−1K−2, for a 1.0 × 1015 Se.cm−2 implanted film compared to the unimplanted film (α2σ ≈ 236.4 μWm−1K−2). Monte Carlo simulation and ab initio density functional theory calculations revealed that the increased displacement per atom values and the {SeI−VCu} defect complex-induced shallow acceptor could be attributed to the observed increase in hole density. Our results highlight that native defects and defect complexes are beneficial for enhancing the power factor in transparent CuI for thermoelectric applications.

Measurement of Naturally-Occurring Radioactive Materials (NORM) using a scintillator-based alpha detector

It is important to differentiate between natural and artificial radioactive materials such as plutonium in nuclear facilities. In this study, a scintillator-based alpha-particle detector was developed using YAP:Ce scintillator and Multi-Anode PhotoMultiplier Tube. The detector was used to measure various naturally occurring radioactive materials (NORM) samples including radon progeny, lead plate, lantern mantle, and radium ceramic ball. The measurement results were compared with Monte Carlo simulation calculations and were found to be in agreement. The energy resolution of the detector is 8.6%FWHM. In the measurement results of radon progeny, peaks of 212Bi (6.1 MeV), 214Po (7.7 MeV), and 212Po (8.8 MeV) can be observed. The lead plate contains 210Po and emits 5.3 MeV alpha particle. The simulation with the same energy was able to reproduce the actual measurement. The results showed the energy and distribution of the alpha particles emitted by the NORM samples. The study successfully demonstrated the capability of the developed alpha-particle detector in identifying NORM.

Molecular Simulation Studies of Pharmaceutical Pollutant Removal (Rosuvastatin and Simvastatin) Using Novel Modified-MOF Nanostructures (UIO-66, UIO-66/Chitosan, and UIO-66/Oxidized Chitosan).

The ubiquitous presence of pharmaceutical pollutants in the environment significantly threatens human health and aquatic ecosystems. Conventional wastewater treatment processes often fall short of effectively removing these emerging contaminants. Therefore, the development of high-performance adsorbents is crucial for environmental remediation. This research utilizes molecular simulation to explore the potential of novel modified metal-organic frameworks (MOFs) in pharmaceutical pollutant removal, paving the way for the design of efficient wastewater treatment strategies. Utilizing UIO-66, a robust MOF, as the base material, we developed UIO-66 functionalized with chitosan (CHI) and oxidized chitosan (OCHI). These modified MOFs' physical and chemical properties were first investigated through various characterization techniques. Subsequently, molecular dynamics simulation (MDS) and Monte Carlo simulation (MCS) were employed to elucidate the adsorption mechanisms of rosuvastatin (ROSU) and simvastatin (SIMV), two prevalent pharmaceutical pollutants, onto these nanostructures. MCS calculations demonstrated a significant enhancement in the adsorption energy by incorporating CHI and OCHI into UIO-66. This increased ROSU from -14,522 to -16,459 kcal/mol and SIMV from -17,652 to -21,207 kcal/mol. Moreover, MDS reveals ROSU rejection rates in neat UIO-66 to be at 40%, rising to 60 and 70% with CHI and OCHI. Accumulation rates increase from 4 Å in UIO-66 to 6 and 9 Å in UIO-CHI and UIO-OCHI. Concentration analysis shows SIMV rejection surges from 50 to 90%, with accumulation rates increasing from 6 to 11 Å with CHI and OCHI in UIO-66. Functionalizing UIO-66 with CHI and OCHI significantly enhanced the adsorption capacity and selectivity for ROSU and SIMV. Abundant hydroxyl and amino groups facilitated strong interactions, improving performance over that of unmodified UIO-66. Surface functionalization plays a vital role in customizing the MOFs for pharmaceutical pollutant removal. These insights guide next-gen adsorbent development, offering high efficiency and selectivity for wastewater treatment.

A method of calculating weighted values of objective traits for BLUP of breeding values to achieve relative desired changes.

A method of calculating weighted values for objective traits from the phenotypic records of all animals in a population was devised as an alternative to the conventional method of calculating weighted values from a family selection index. The genetic improvement of this method was verified by Monte Carlo computer simulation. A base population consisting of 10 males and 50 females, and five separate generations, other than the base population that had been randomly selected, was bred for two traits with different heritabilities. The breeding values of animals in generation five were estimated using the bivariate BLUP method. The three different weighted values obtained from this method and two conventional methods for estimated breeding values of the objective traits were used to estimate aggregate breeding values for selection. The results showed that selection using weighted values calculated from all animals in a population resulted in a greater response to selection, especially when the genetic correlation between the two traits was positive, than selection using other conventional methods. The use of the method devised in this study was expected to result in a greater genetic improvement than the conventional family selection index method for pig breeding programs applied in closed herds in Japan.

Prediction of response to truncated selection based on BLUP of breeding values and its prediction accuracy.

Three methods of predicting the response to truncated selection based on BLUP of breeding values (BVs) were compared under conditions in which the phenotypic values for the progenies of selected animals were not available. The following methods were used to predict the response to selection: (1) based on the mean of estimated breeding values (EBV) in the candidate population for selection ( ), (2) based on the variance of EBV in the candidate population for selection ( ), and (3) based on diagonal elements of the inverse matrix on the left-hand side of the mixed model equation ( ). The deviation of the average BV of the selected animals from the average BV of the candidate population for selection was taken as the true response to selection. The pedigree information and phenotypic values used for comparison were generated by Monte Carlo computer simulation. The results showed that had the smallest absolute mean error and had the smallest root-mean-square error. We concluded that it is desirable to use or to predict the response to truncated selection based on BLUP of BVs. However, in the population where selection is ongoing, the prediction accuracy of selection response is likely to be affected by the distortion of the distribution and the Bulmer effect for .

Pulling on grafted flexible polymers can cause twisted bundles.

Bundles of semiflexible polymers can twist at low temperatures to balance energy gain from attraction and energy cost from bending. This raises the question whether twisting can be also observed for bundles of rather flexible grafted polymers stretched out by pulling force. Here, we address this question using Monte Carlo computer simulations of small bundles. Our data show that for weak forces F < Fl, intertwined globular conformations are favored, whereas for strong forces F > Fu, rod-like bundles emerge. In the intermediate force window Fl < F < Fu, bundles with a helical twist can be clearly identified. Applying a field to all monomers yields qualitatively the same effect. This suggests the conclusion that rather flexible polymers under pulling force or field behave effectively like semiflexible polymers without external pull.

Thermodynamic properties of fluids with Mie n − m potentials and application to tune effective Mie potentials for simple real fluids

ABSTRACT Monte Carlo computer simulations have been performed to obtain the equation of state and internal energy of fluids with Mie n − m potentials, with m = 6 and n = 9, 12 and 15, for different supercritical temperatures and densities covering most of the fluid phase. These data have been used to test the performance of a third-order perturbation theory with the first three perturbation terms determined from computer simulation, giving rise to a very good agreement between theory and simulation. Next, the theory has been used to tune effective two-body Mie n − 6 potentials for the real fluids Ne, Ar, Kr, Xe and C H 4 at supercritical temperatures for wide range of densities and pressures. It has been shown that the theory is able to accurately fit the experimental data for the energy and pressure of these fluids within the temperature and density ranges considered. This theory might be useful to obtain the equation of state and the internal energy of real molecular fluids within the context of the SAFT-VR Mie theory.

Monte Carlo Simulation of Percolation Phenomena for Direct Current in Large Square Matrices

In this study, an in-depth analysis of the percolation phenomenon for square matrices with dimensions from L = 50 to 600 for a sample number of 5 × 104 was performed using Monte Carlo computer simulations. The percolation threshold value was defined as the number of conductive nodes remaining in the matrix before drawing the node interrupting the last percolation channel, in connection with the overall count of nodes within the matrix. The distributions of percolation threshold values were found to be normal distributions. The dependencies of the expected value (mean) of the percolation threshold and the standard deviation of the dimensions of the matrix were determined. It was established that the standard deviation decreased with the increase in matrix dimensions, ranging from 0.0262253 for a matrix with L = 50 to 0.0044160 for L = 600, which is almost six-fold lower. The mean value of the percolation threshold was practically constant and amounted to approximately 0.5927. The analysis involved not only the spatial distributions of nodes interrupting the percolation channels but also the overall patterns of node interruption in the matrix. The distributions revealed an edge phenomenon within the matrices, characterized by the maximum concentration of nodes interrupting the final percolation channel occurring at the center of the matrix. As they approached the edge of the matrix, their concentration decreased. It was established that increasing the dimensions of the matrix slowed down the rate of decrease in the number of nodes towards the edge. In doing so, the area in which values close to the maximum occurred was expanded. Based on the approximation of the experimental results, formulas were determined describing the spatial distributions of the nodes interrupting the last percolation channel and the values of the standard deviation from the matrix dimensions. The relationships obtained showed that with increasing matrix dimensions, the edge phenomenon should gradually disappear, and the percolation threshold standard deviation values caused by it will tend towards zero.

Analysis of Uneven Distribution of Nodes Creating a Percolation Channel in Matrices with Translational Symmetry for Direct Current

In this study, the phenomenon of node percolation was tested using the Monte Carlo computer simulation method for square matrices with dimensions L = 55, 101 and 151. The number of samples for each matrix was 5 × 106. The spatial distributions of the coordinates of the nodes creating the percolation channel were determined, and maps of the density distribution of these nodes were created. It has been established that in matrices with finite dimensions, an edge phenomenon occurs, consisting of a decrease in the concentration of nodes creating a percolation channel as one approaches the edge of the matrix. As the matrix dimensions increase, the intensity of this phenomenon decreases. This expands the area in which values close to the maximum occur. The length distributions of the left and right clusters of non-conducting nodes were determined for the situation when the next randomly selected node connects them and thus reaches the percolation threshold. It was found that clusters whose dimensions are close to half of the matrix dimensions are most likely to occur. The research shows that both the values of the standard deviation of the percolation threshold and the intensity of the edge phenomenon are clearly related to the dimensions of the matrices and decrease as they increase.

Investigations into the Influence of Matrix Dimensions and Number of Iterations on the Percolation Phenomenon for Direct Current

The paper presents studies of the site percolation phenomenon for square matrixes with dimensions L = 55, 101 and 151 using the Monte Carlo computer simulation method. The number of iterations for each matrix was 5 × 106. An in-depth analysis of the test results using the metrological approach consisting of determining the uncertainty of estimating the results of iterations with statistical methods was performed. It was established that the statistical distribution of the percolation threshold value is a normal distribution. The coefficients of determination for the simulation results in approximations of the percolation threshold using the normal distribution for the number of iterations 5 × 106 are 0.9984, 0.9990 and 0.9993 for matrixes with dimensions 55, 101 and 151, respectively. The average value of the percolation threshold for relatively small numbers of iterations varies in a small range. For large numbers of iterations, this value stabilises and practically does not depend on the dimensions of the matrix. The value of the standard deviation of the percolation threshold for small numbers of iterations also fluctuates to a small extent. For a large number of iterations, the standard deviation values reach a steady state. Along with the increase in the dimensions of the matrix, there is a clear decrease in the value of the standard deviation. Its value is about 0.0243, about 0.01 and about 0.012 for matrixes with dimensions 55, 101 and 151 for the number of iterations 5 × 106. The mean values of the percolation threshold and the uncertainty of its determination are (0.5927046 ± 1.1 × 10−5), (0.5927072 ± 7.13 × 10−6) and (0.5927135 ± 5.33 × 10−6), respectively. It was found that the application of the metrological approach to the analysis of the percolation phenomenon simulation results allowed for the development of a new method of optimizing the determination and reducing the uncertainty of the percolation threshold estimation. It consists in selecting the dimensions of the matrix and the number of iterations in order to obtain the assumed uncertainty in determining the percolation threshold. Such a procedure can be used to simulate the percolation phenomenon and to estimate the value of the percolation threshold and its uncertainty in matrices with other matrix shapes than square ones.

Phase behaviour of semiflexible lattice polymers in poor-solvent solution: Mean-field theory and Monte Carlo simulations.

We study a solution of interacting semiflexible polymers with curvature energy in poor-solvent conditions on the d-dimensional cubic lattice using mean-field theory and Monte Carlo computer simulations. Building upon past studies on a single chain, we construct a field-theory representation of the system and solve it within a mean-field approximation supported by Monte Carlo simulations in d = 3. A gas-liquid transition is found in the temperature-density plane that is then interpreted in terms of real systems. Interestingly, we find this transition to be independent of the bending rigidity. Past classical Flory-Huggins and Flory mean-field results are shown to be particular cases of this more general framework. Perspectives in terms of guiding experimental results towards optimal conditions are also proposed.