Soft Interactions Research Articles

Enhancing versatility and adaptability in soft robotics: design and analysis of an adaptive gripping port

Abstract Currently, soft robots demonstrate the considerable promise for various applications. However, soft actuators tend to be damaged more easily compared to rigid mechanical components. The common practice of replacing soft actuators typically requires manual intervention and a longer duration. In this paper, we design an adaptive gripping port (AGP) for soft robotic interactions, which is used for fast switching and connectivity. Through a combination of theoretical modeling, fabrication, and experimental analysis, its gripping, releasing, and sealing capabilities are demonstrated. We present four types of the AGP with different internal bladder structures, demonstrating maximal enhancements in griping capability and sealing performance of up to 50% and 40%, respectively. Experiments show the AGP’s adaptability to connectors of various sizes, accommodating diameters from 0 mm to 15.76 mm under negative pressure driving. The relationship between gripping force, maximum sealing pressure, connector diameter, and driving pressure is studied. We also exhibit collaborations with a circular gripper and soft grippers incorporating the AGP to verify the possibility of their interactions.

All order factorization for virtual Compton scattering at next-to-leading power

We discuss all-order factorization for the virtual Compton process at next-to-leading power (NLP) in the ΛQCD/Q and −t\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{-t} $$\\end{document}/Q expansion (twist-3), both in the double-deeply-virtual case and the single-deeply-virtual case. We use the soft-collinear effective theory (SCET) as the main theoretical tool. We conclude that collinear factorization holds in the double-deeply virtual case, where both photons are far off-shell. The agreement is found with the known results for the hard matching coefficients at leading order αs0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\alpha}_s^0 $$\\end{document}, and we can therefore connect the traditional approach with SCET. In the single-deeply-virtual case, commonly called deeply virtual Compton scattering (DVCS), the contribution of non-target collinear regions complicates the factorization. These include momentum modes collinear to the real photon and (ultra)soft interactions between the photon-collinear and target-collinear modes. However, such contributions appear only for the transversely polarized virtual photon at the NLP accuracy and in fact it is the only NLP ~ (ΛQCD/Q)1 ~ (−t\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{-t} $$\\end{document}/Q)1 contribution in that case. We therefore conclude that the DVCS amplitude for a longitudinally polarized virtual photon, where the leading power ~ (ΛQCD/Q)0 ~ (−t\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{-t} $$\\end{document}/Q)0 contribution vanishes, is free of non-target collinear contributions and the collinear factorization in terms of twist-3 GPDs holds in that case as well.

Lifted TASEP: A Solvable Paradigm for Speeding up Many-Particle Markov Chains

Virtually all Markov-chain Monte Carlo algorithms used for sampling a given distribution are reversible, and they satisfy the detailed-balance condition. For local chains, this leads to a slow, diffusive exploration of sample space. Significant speedups can be achieved through nonreversible algorithms with the given distribution as a targeted steady state. However, nonreversible algorithms for sampling are difficult to set up and to analyze, and exact speedup results for interacting many-particle systems are very rare. Here, we introduce the “lifted” totally asymmetric simple exclusion process (TASEP) as an exactly solvable paradigm for nonreversible many-particle Markov chains. It samples the same hard-sphere distribution as the Metropolis algorithm for symmetrically diffusing hard-core particles on a one-dimensional lattice. We solve the lifted TASEP by an unusual kind of coordinate Bethe ansatz and show that it exhibits polynomial (in particle number) speedups in the relaxation time for the asymptotic approach of the steady state, as well as the nonasymptotic mixing time, compared to both Metropolis and Kardar-Parisi-Zhang-based dynamics. The lifted TASEP is the reduction onto the one-dimensional lattice of the successful hard-sphere event-chain Monte Carlo algorithm, and we discuss that it can likewise be generalized to soft interaction potentials. Published by the American Physical Society 2024

Triple-Layered Noncombustible PEO-Based Solid Electrolyte for Highly Safe Lithium-Metal Batteries.

Lithium-metal batteries are currently recognized as promising next-generation technologies owing to their high energy density. Solid polymer electrolytes, particularly those based on polyethylene oxide (PEO), are lauded for their leakage resistance, safety, and flexible design. Despite the ongoing fire safety- and ionic conductivity-related concerns, a novel noncombustible solid polymer electrolytes with superior ionic conductivities are introduced here with additive decabromodiphenyl ethane and zeolite. To enhance the mechanical strength and ensure soft interactions at the electrode interface, a triple-layer structure with self-extinguishing properties and robust ionic conductivity is proposed. Notably, the softness at the electrode interface intensifies as the LiTFSI concentration increases; this higher concentration negatively impacts PEO crystallinity, enhancing the ionic conductivity owing to the presence of free Li+ and TFSI- ions. This novel electrolyte can achieve a conductivity of 1.5 mS cm-1 at 60°C, maintain anodic stability up to 4.8V, and exhibit flame retardancy. Furthermore, adding LiTFSI at 60% relative to PEO is shown to reduce LiF formation on the surface, enhancing anode stability. The [LiFePO4/triple-layered electrolyte/Li] lithium-metal batteries are capable of an initial capacity of 153 mAh g-1, sustained superior capacity retention of 87.9%, and high Coulombic efficiency (99.6%) over 1000 cycles at a 1C rate.

Soft plant root structure-media flow interactions: Exploring the adverse effect of lead contamination in North-Eastern Indian rice

We experimentally investigate the effect of lead (Pb2+) contamination on the roots of an Assamese rice line variety Lachit using a heavy metal analyzing fluidic tool. To demonstrate the adverse effects of lead contamination on rice seedlings in a controlled environment, we have performed a number of multidisciplinary experiments. Also, we develop a numerical model in this endeavor to predict the Michaelis–Menten kinetics parameters, which are used to depict the lead transport phenomenon following soft root structure-media flow interactions. We show that increased inlet lead concentration of the media solution leads to a reduction in root growth exponentially in the developed fluidic device. As supported by the Raman spectra analysis, the drastic metabolic changes are visible under lead contamination. Our results revel that, in comparison to the control condition, lead accumulation results in a decrease in the uptake of nitrogen and also, the metallic nutritional components (K+, Na+, and Ca2+). Under lead contamination, the average osmotic pressure difference at the root surface is seen to be less than in the control situation. The inferences drawn from the current research shed light on the detrimental effects of lead contamination on rice roots, which have the potential to significantly lower agricultural yields and threaten food security in areas where rice is the primary food source.

Validation of a new road and contact model for vehicle–soft soil terrain interaction through an elaborate modelling of the FED-Alpha vehicle

Employing multibody dynamic simulations with semi-empirical tyre models is widely recognised as a cost-effective approach. A recent development introduces a novel road and tyre–soil contact model that is not only swift and memory-efficient but also addresses limitations in classical semi-empirical models. This study conducts a thorough validation of the new road and contact model by creating a detailed multibody model of the four-wheeled vehicle, Fuel Efficiency Demonstrator – Alpha, integral to NATO’s Next-Generation reference mobility model. The comprehensive model encompasses the chassis, suspension, tyres, engine, transmission and various other components. Through simulations of various driving scenarios, accounting for complex terrain geometries, spatially varying soil properties and multi-pass phenomena, the model’s performance is evaluated. The simulation results are compared with physical measurements, providing a detailed assessment of the tyre–soil model’s predictive accuracy for wheeled vehicle mobility on deformable terrains.

Recovery of precious metals from aqua regia leachate of e-wastes using dithiocarbamate-modified cellulose and development of a novel kinetic model

The escalating demand and dwindling natural supplies of precious metals (PMs) necessitate innovative hydrometallurgical recovery approaches with rapid kinetics and reduced environmental impact. The current study investigated the sorption and recovery of PMs from electronic waste (e-waste) utilizing dithiocarbamate-modified cellulose (DMC) and its proline derivative with epoxy cross-linkage (DMC-Pro-Epo-6) in aqua regia (AR). The effects of various sorption parameters, such as sorbent dose in feed, HCl:HNO3 ratio, AR dilution times, etc., on PM recovery were explored. Equilibrium for AuIII and PtIV sorption by DMC and DMC-Pro-Epo6 was reached in less than an hour, which is significantly faster than most reported sorbents. The maximum sorption capacities in AR settings, calculated using the Langmuir equation, were 348.0 mg g−1 for AuIII and 34.7 mg g−1 for PtIV for DMC, while DMC-Pro-Epo6 achieved 350.3 mg g−1 for AuIII and 31.1 mg g−1 for PtIV. These capacities, particularly for the higher sorption capacity of AuIII by DMCs, are attributed to the relativistic effects of gold, soft–soft interactions, and strong sulfur binding. FT-IR, FE-SEM, and EDX analyses elucidated the chelation bonding and mechanisms involved in PM sorption onto DMCs. By utilizing AR-DMC integrated techniques, step-by-step protocols were established for Au recovery from diverse e-waste sources, such as smartphones and smart chip cards. The study also highlighted the importance of chemical pre-concentration of e-waste to remove base metals, facilitating efficient PM recovery. Finally, a key innovation of this work is introducing a new pseudo-mix order fractional model, based on the preference of active sites with fractional assumptions, which more accurately correlates the sorption kinetics observed in complex systems.

Development of Specialized PDC Drill Bits for the Interaction of Soft and Hard Strata in Igneous Rocks

In response to the technical challenges of low mechanical drilling speed and severe drill bit wear caused by the development of some igneous rocks in the Dongying and Shahejie formations of the Bozhong 34-9 oilfield, it is urgent to develop a specialized PDC drill bit suitable for the soft hard interaction formation of the BZ-34-9 oilfield. The PDC drill bit is required to have strong aggressiveness, as well as good impact resistance and abrasion resistance, in order to meet the drilling requirements of the soft hard interaction formation of the BZ34-9 oilfield. Through on-site use, the mechanical drilling speed has been significantly improved.

Polyurethanes Synthesized with Blends of Polyester and Polycarbonate Polyols—New Evidence Supporting the Dynamic Non-Covalent Exchange Mechanism of Intrinsic Self-Healing at 20 °C

Polyurethanes (PUs) synthesized with blends of polycarbonate and polyester polyols (CD+PEs) showed intrinsic self-healing at 20 °C. The decrease in the polycarbonate soft segments content increased the self-healing time and reduced the kinetics of self-healing of the PUs. The percentage of C-O species decreased and the ones of C-N and C=O species increased by increasing the polyester soft segments in the PUs, due to higher micro-phase separation. All PUs synthetized with CD+PE blends exhibited free carbonate species and interactions between the polycarbonate and polyester soft segments to a somewhat similar extent in all PUs. By increasing the polyester soft segments content, the storage moduli of the PUs decreased and the tan delta values increased, which resulted in favored polycarbonate soft segments interactions, and this was related to slower kinetics of self-healing at 20 °C. Although the PU made with a mixture of 20 wt.% CD and 80 wt.% PE showed cold crystallization and important crystallinity of the soft segments, as well as high storage moduli, the intercalation of a small amount of polycarbonate soft segments disturbed the interactions between the polyester soft segments, so it exhibited self-healing at 20 °C. The self-healing of the PUs was attributed to the physical interactions between polycarbonate soft segments themselves and with polyester soft segments, and, to a minor extent, to the mobility of the polymeric chains. Finally, the PUs made with 40 wt.% or more polyester polyol showed acceptable mechanical properties.

Leveraging Soft Acid-Base Interactions Alters the Pathway for Electrochemical Nitrogen Oxidation to Nitrate with High Faradaic Efficiency.

Electrocatalytic nitrogen oxidation reaction (N2OR) offers a sustainable alternative to the conventional methods such as the Haber-Bosch and Ostwald oxidation processes for converting nitrogen (N2) into high-value-added nitrate (NO3 -) under mild conditions. However, the concurrent oxygen evolution reaction (OER) and inefficient N2 absorption/activation led to slow N2OR kinetics, resulting in low Faradaic efficiencies and NO3 - yield rates. This study explored oxygen-vacancy induced tin oxide (SnO2-Ov) as an efficient N2OR electrocatalyst, achieving an impressive Faradaic efficiency (FE) of 54.2% and a notable NO3 - yield rate (22.05µg h-1 mgcat -1) at 1.7V versus reversible hydrogen electrode (RHE) in 0.1m Na2SO4. Experimental results indicate that SnO2-Ov possesses substantially more oxygen vacancies than SnO2, correlating with enhanced N2OR performance. Computational findings suggest that the superior performance of SnO2-Ov at a relatively low overpotential is due to reduced thermodynamic barrier for the oxidation of *N2 to *N2OH during the rate-determining step, making this step energetically favorable than the oxygen adsorption step for OER. This work demonstrates the feasibility of ambient nitrate synthesis on the soft acidic Sn active site and introduces a new approach for rational catalyst design.

The origin of interparticle aggregation: Probing the long-range hydrophobic forces between particles induced by nanobubbles in aqueous solutions

The processes of particle–particle collision, adhesion, and detachment are omnipresent in the solid particle separation and purification processes. Nanobubbles, serving as a critical medium for interactions between particles, play a pivotal role in numerous fields of separation and purification such as mineral flotation, hydrometallurgy, chemical engineering, materials, and more. The elucidation of the principles governing nanobubbles’ involvement in interparticle interactions holds significant implications for enhancing and controlling separation and purification processes. The impact of nanobubbles on interparticle interactions between calcite particles was investigated in this study by measuring the forces between particles with and without nanobubbles and analysing them using DLVO and EDLVO theories. The experimental results demonstrate the occurrence of long-range attractive forces and significant adhesion between particles in the presence of nanobubbles under natural pH and ultrapure water conditions, phenomena that cannot be explained by classical DLVO theory. The generation of long-range hydrophobic attraction at the particle interface due to nanobubbles was confirmed through further EDLVO calculations and modifications, enhancing the stability of particle flocculation. Additionally, for the first time, the entire process from contact to detachment between the “particle-nanobubble” system in atomic force microscopy (AFM) simulations was described by combining experimental force curves with stepwise graphical interpretation. This approach provides valuable guidance for the analysis of bubble and soft matter interactions under AFM. The results of this study indicate that nanobubbles can indirectly alter the hydrophilicity and hydrophobicity of particles, increasing the probability of particle adhesion and reducing the probability of desorption, thereby enhancing the stability of particle flocculation.

Understanding the Effect of Ionic Liquid-Mediated Solvent Engineering on the Kinetics and Thermodynamic Stability of Phenylalanine Ammonia-Lyase.

Phenylalanine ammonia-lyase (PAL) plays a central role in the phenylpropanoid pathway and in the treatment of phenylketonuria. However, the integration of PAL into sustainable industrial biocatalysis is hampered by its instability under harsh conditions. This study demonstrates that ionic liquid (IL)-assisted solvent (Tris-HCl buffer) engineering enables improvement of the reaction kinetics and thermodynamic stability of Rhodotorula glutinisPAL (RgPAL) under various stresses. Under optimized conditions, a 66.2% higher Kcat value, >60% remaining activity after 5 weeks of storage at room temperature, and >80% activity of RgPAL after incubation at 60 °C for 1 h were obtained in the [Ch][Ac]-blended Tris-HCl solvent compared to pristine Tris-HCl. The spectroscopic and molecular docking results suggest that the higher extent of hydration and the soft interactions complemented by the ILs with the D-chain residues of RgPAL jointly contributed to achieving more stable and active conformations of RgPAL. The enzyme showed a higher melting temperature (Tm) in ILs+Tris-HCl compared to that in pristine Tris-HCl, with less change in enthalpy (ΔHfu) and entropy (ΔSfu) of unfolding. Overall, IL-mediated solvent engineering alters the microenvironment of RgPAL and allows the development of a robust PAL-based biocatalytic system.

A Deep Recurrent Neural Network for Predicting Subject-specific Facial Soft Tissue Interaction

Predicting biological soft tissue interaction is of great interest for developing computer-aided decision systems. This study aims to develop and evaluate a novel deep-learning approach based on the recurrent neural network for predicting facial soft tissue impact with a rubber ball. A computational workflow was established including a subject-specific finite element model of the facial soft tissue under interaction with the rubber ball. A series of simulations under different ball velocities was performed to build the learning database. We implemented a long-short-term memory (LSTM) model and then evaluated its performance using root mean square error (RMSE) and regression coefficient metrics. The obtained results showed a RMSE of 3.13 mm and a Pearson correlation coefficient of 0.98 for soft tissue displacement prediction. A RMSE of 0.001 MPa and a Pearson correlation coefficient of 0.94 was also obtained for soft tissue von Mises stress prediction. The present study showed the robustness and accuracy of the recurrent neural network for predicting complex soft tissue interaction behaviours. Our findings open new avenues for deploying novel deep learning workflow for human-facial softtissue interaction. As perspective, this workflow will be integrated into our interactive facial analysis and rehabilitation system.

Supramolecular Hybrids of Proteins from Habu Snake Venom with Discrete [Pt(CN)4]2- Complex.

The venom of the Habu snake Protobothrops flavoviridis (P. flavoviridis) is known to contain a diverse array of proteins and peptides, with a notable presence of phospholipase A2 (PLA2) enzymes. These PLA2 enzymes have been extensively studied for their function and molecular evolution. Nevertheless, several aspects, such as the physical properties and the self-assembly mechanism of hierarchical structure from the nanoscale to the microscale with different chemical compounds, remain poorly understood. This study aims to fill this knowledge gap by investigating the behavior of enzyme components purified from P. flavoviridis venom in the presence of anionic [Pt(CN)4]2- complexes, which have the potential for soft metallophilic interactions and interesting optical properties. The purified PLA2 isozymes were diluted in Dulbecco's phosphate buffered saline (D-PBS (-)) and combined with the anionic metal complex, resulting in the formation of microstructures several micrometers in size, which further grew to form fibrous structures. This novel approach of combining PLA2 enzymes with discrete functional metal complexes opens up exciting possibilities for designing flexible and functional supramolecular and biomolecular hybrid systems in aqueous environments. These findings shed light on the potential applications of snake venom enzymes in nanotechnology and bioengineering.

Study of B→PP decays in the modified perturbative QCD approach

We study the nonleptonic decays of B→PP in the modified perturbative QCD approach, where P stands for pseudoscalar mesons. Transverse momenta of partons and the Sudakov factor are included, which help to suppress the contributions of soft interactions. The wave function of the B meson obtained from the relativistic potential model is used, and then the contributions in the infrared region cannot be suppressed completely. So a soft cutoff scale and soft form factors are introduced. The contributions with the scale higher than the soft cutoff scale are calculated with perturbative QCD, while the contributions lower than the cutoff scale are replaced by the soft form factors. To explain experimental data, we find that contributions of color-octet operators for the quark-antiquarks in the mesons in the final state need to be considered. The contributions of the color-octet operators are parametrized by a few parameters with the help of SU(3) flavor symmetry and symmetry breaking. These parameters for color-octet contributions are universal for all the nonleptonic decay modes of the B meson, where the mesons in the final state belong to the same flavor SU(3) nonet. Both the branching ratios and CP violations are studied. We find that the theoretical calculation can well explain the experimental data of B factories. Published by the American Physical Society 2024

Cyano-determined mercury (II) ion selective fluorescence assay over polymeric carbon nitride

Selective response is the key index to evaluate the performance of polymeric carbon nitride (PCN)-based heavy metal ion fluorescence sensors. Herein, to explore the role of cyano groups on selectivity, four kinds of PCN, including PCN-Cl, PCN-Ac, PCN-B and PCN-K were prepared by the molten salt method of sodium chloride and sodium acetate, the reduction method of sodium borohydride and the etching method of potassium hydroxide, respectively. These PCNs exhibited different surface cyano characteristics, but all of them had significant blue emission under ultraviolet excitation. It is proved that the assistant of sodium chloride or potassium hydroxide is an effective method to prepare PCNs with abundant surface cyano group. A series of fluorescence quenching experiments of metal ions showed that the cyano-rich degree of PCN is closely related to its selective response to mercury (II) ions. PCN-Cl and PCN-K emerged good selective quenching of mercury (II) ions, which may be related to the soft acid-soft base strong interaction between mercury (II) ions and cyano groups. Both PCN-Cl and PCN-K fluorescent probes for mercury (II) ions had a linear range of 5 ∼ 50 μmol L−1, and PCN-Cl exhibited a lower detection limit of 0.38 μmol L−1. This work confirmed the selective fluorescence response of cyano-rich PCN to mercury (II) ions, proposed the mechanism of selective fluorescence quenching response of mercury (II) ions, and provided a new idea for the design of efficient and accurate PCN-based fluorescence probes.

Entropy of strongly coupled Yukawa fluids.

The entropy of strongly coupled Yukawa fluids is discussed from several perspectives. First, it is demonstrated that a vibrational paradigm of atomic dynamics in dense fluids can be used to obtain a simple and accurate estimate of the entropy without any adjustable parameters. Second, it is explained why a quasiuniversal value of the excess entropy of simple fluids at the freezing point should be expected, and it is demonstrated that a remaining very weak dependence of the freezing point entropy on the screening parameter in the Yukawa fluid can be described by a simple linear function. Third, a scaling of the excess entropy with the freezing temperature is examined, a modified form of the Rosenfeld-Tarazona scaling is put forward, and some consequences are briefly discussed. Fourth, the location of the Frenkel line on the phase diagram of Yukawa systems is discussed in terms of the excess entropy and compared with some predictions made in the literature. Fifth, the excess entropy scaling of the transport coefficients (self-diffusion, viscosity, and thermal conductivity) is reexamined using the contemporary datasets for the transport properties of Yukawa fluids. The results could be of particular interest in the context of complex (dusty) plasmas, colloidal suspensions, electrolytes, and other related systems with soft pairwise interactions.

Selective sensing of dopamine using copper hollow tube-integrated conjugated poly(arylene-ethynylene)-4 in the presence of epinephrine and norepinephrine

The Sonagashira-Hagihara coupling reaction was employed to prepare the conjugated Poly(arylene-ethynylene)-4 (CMP-4), into which copper hollow tubes (Cu-HT) were incorporated. This incorporation significantly enhanced the electrical conductivity and the selectivity of CMP-4 for dopamine (DA). The resulting composite exhibited high selectivity for DA over norepinephrine (NE) and epinephrine (EP) in a PBS-urine electrolyte. The peak current displayed a linear relationship with DA concentrations ranging from 100 to 900 nM, with limits of detection (LODs) of 17.84 and 16.03 nanomolar (R2 = 0.9906). This selective DA sensing is attributed to the adsorption of the analyte on the CMP-Cu-4-GCE surface, facilitated by aromatic functionality, soft–soft interactions, Lewis basicity, and steric hindrance. Additionally, the CMP-Cu-4-GCE demonstrated remarkable sensitivity, stability, selectivity, and reproducibility in DA detection. Voltammetric results from the screen-printed electrode (SPE) using CMP-Cu-4-SPE suggest that it is a promising electrochemical probe for detecting DA in a PBS-urine solvent.

Comparative Study of Methods for Robot Control with Flexible Joints

Robots with flexible joints are gaining importance in areas such as collaborative robots (cobots), exoskeletons, and prostheses. They are meant to directly interact with humans, and the emphasis in their construction is not on precision but rather on weight reduction and soft interaction with humans. Well-known rigid robot control strategies are not valid in this area, so new control methods have been proposed to deal with the complexity introduced by elasticity. Some of these methods are seldom used and are unknown to most of the academic community. After selecting the methods, we carried out a comprehensive comparative study of algorithms: simple gravity compensation (Sgc), the singular perturbation method (Spm), the passivity-based approach (Pba), backstepping control design (Bcd), and exact gravity cancellation (Egc). We modeled these algorithms using MATLAB and simulated them for different stiffness levels. Furthermore, their practical implementation was analyzed from the perspective of the magnitudes to be measured and the computational costs of their implementation. In conclusion, the Sgc method is a fast and affordable solution if joint stiffness is relatively high. If good performance is necessary, the Pba is the best option.

On the Identification of Solid-Like Clusters in a Crystallizing Yukawa System

The crystallization of systems with soft interaction potentials is analyzed for a Yukawa system as an example. The crystallization pathway in the plane of rotational invariants q4 and q6 is studied in detail. The recently proposed invariants bcc1 and bcc2, calculated using 12 nearest neighbors, are applied for the first time to study the crystallization. It is shown that the combination of the rotational invariant technique and the method of Voronoi polyhedra allows us to identify quite simply all types of solid-like clusters formed during the solidification of the system, including bcc-like clusters, which are hardly identified by conventional methods.