Terms Of Energy Research Articles

Predicting phase coexistence and adsorption isotherms of classical and quantum fluids using the microcanonical-ensemble perturbation theory (MEPT)

The Microcanonical-Ensemble Perturbation Theory (MEPT) of Sastre et al. (2018) [7] has been extended to study the vapor-liquid phase coexistence of binary and ternary mixtures of fluids. The attractive interactions between chains of molecules are represented as monomer segments interacting via a square-well pair potential. Calculations for the thermodynamic properties and phase behavior of square-well monomer chains are considered and compared with experimental data. Molecular parameters have been obtained to model the phase behavior of real fluids such as n-alkanes (from C1 to C12), nitrogen, perfluoromethane, carbon dioxide, i-butane, i-pentane, neon, and hydrogen. Furthermore, the capability of the MEPT approach in predicting critical and azeotropic lines of binary and ternary mixtures is explored. The results demonstrate that the MEPT approach provides a robust description of the phase behavior of mixtures containing chains of fluids. Additionally, we have integrated the MEPT approach with the two-dimensional Statistical Associating Fluid Theory for fluids interacting via variable range potentials (SAFT-VR-2D) to investigate the effect of quantum contributions on both phase behavior and adsorption. Remarkable improvements are observed when both higher order perturbation terms of the Helmholtz free energy and quantum contributions are included in the predictions of the phase behavior of quantum fluids such as neon and hydrogen. In all cases, the theoretical results exhibit favorable comparisons with experimental data in a wide range of compositions, pressures, and temperatures.

Evaluating Noncovalent Interactions in Halogenated Molecules with Double-Hybrid Functionals and a Dedicated Small Basis Set.

We present here an extension of our recently developed PBE-QIDH/DH-SVPD basis set to halogen atoms, with the aim of obtaining, for weakly interacting halogenated molecules, interaction energies close to those provided by a large basis set (def2-TZVPP) coupled to empirical dispersion potential. The core of our approach is the split-valence basis set, DH-SVPD, that has been developed for F, Cl, Br, and I atoms using a self-consistent formula, containing only energy terms computed for dimers and the corresponding monomers at the same level of theory. The basis set developed considering four systems, one for each halogen atoms, has been then tested on the X40, X4 × 10 benchmarks as well as on other two, less standard, data sets. Finally, a large system (380 atoms) has been also considered as a "crash" test. Our results show that the simple and nonempirical PBE-QIDH/DH-SVPD approach is able to provide accurate results for interaction energies of all the considered systems and can thus be considered as a cheaper alternative to DH functionals paired with empirical dispersion corrections and a large basis set of triple-ζ quality.

Governing of the piezoelectric effect by external fields and strains

Piezoelectricity in quantum rare-earth metallic boron oxides with the coupling between magnetic, electric and elastic subsystem is studied theoretically. It is proved that the change of piezoelectric modules of the considered crystals are proportional to components of the quadrupole susceptibility, which determines the external magnetic and electric fields, strain and temperature dependences of that change. We show why holmium compounds manifest the strongest renormalization among other rare-earth ions in this family of crystals. The reason is in the structure of the low energy term of the electron configuration, depending on spins and orbital moments of 4f electrons.

4+2]‐Cycloaddition Reactions to Corannulene Accelerated by η6‐Coordination of Ruthenium Complexes

The influence of different (LRu)nII (L = Cp– (n = 1, 2); C6H6) moieties η6‐coordinated to corannulene (CpRu+, (Benzene)Ru2+, and (CpRu)22+ has been explored by using the Activation Strain Model (ASM) of reactivity together with the Energy Decomposition Analysis (EDA) scheme. The results obtained have been compared with those obtained for the non‐coordinated corannulene counterpart. It has been observed that the presence of the ruthenium moiety favors, both kinetically and thermodynamically, the [4+2]‐cycloaddition reaction with cyclopentadiene. The factors governing these differences depend on the nature of the [Ru] complex. Whereas the interaction energy is solely responsible for the lower activation energy for the monocationic system (CpRu+), not only the higher interaction but also the lower strain energy explain the much higher reactivity observed for the dicationic systems ((C6H6)Ru2+ and (CpRu)22+). In this latter case, the Pauli repulsion energy term is the factor controlling the differences in the interaction energies, following the so‐called Pauli repulsion‐lowering concept. Finally, when η6‐coordinating mono‐ or dicationic ruthenium complexes, although although the [4+2]‐cycloaddition reaction in the external rim bonds remains thermodynamically and kinetically more favourable, the cycloaddition becomes also thermodynamically feasible in some internal bonds.

Machine Learning Meets Physics-based Modeling: A Mass-spring System to Predict Protein-ligand Binding Affinity.

Computational assessment of the energetics of protein-ligand complexes is a challenge in the early stages of drug discovery. Previous comparative studies on computational methods to calculate the binding affinity showed that targeted scoring functions outperform universal models. The goal here is to review the application of a simple physics-based model to estimate the binding. The focus is on a mass-spring system developed to predict binding affinity against cyclin-dependent kinase. Publications in PubMed were searched to find mass-spring models to predict binding affinity. Crystal structures of cyclin-dependent kinases found in the protein data bank and two web servers to calculate affinity based on the atomic coordinates were employed. One recent study showed how a simple physics-based scoring function (named Taba) could contribute to the analysis of protein-ligand interactions. Taba methodology outperforms robust physics-based models implemented in docking programs such as AutoDock4 and Molegro Virtual Docker. Predictive metrics of 27 scoring functions and energy terms highlight the superior performance of the Taba scoring function for cyclin- dependent kinase. The recent progress of machine learning methods and the availability of these techniques through free libraries boosted the development of more accurate models to address protein-ligand interactions. Combining a naïve mass-spring system with machine-learning techniques generated a targeted scoring function with superior predictive performance to estimate pKi.

Madelung mechanics and superoscillations

In single-particle Madelung mechanics, the single-particle quantum state Ψ(x→,t)=R(x→,t)eiS(x→,t)/ℏ is interpreted as comprising an entire conserved fluid of classical point particles, with local density R(x→,t)2 and local momentum ∇→S(x→,t) (where R and S are real). The Schrödinger equation gives rise to the continuity equation for the fluid, and the Hamilton–Jacobi equation for particles of the fluid, which includes an additional density-dependent quantum potential energy term Q(x→,t)=−ℏ22m∇→R(x→,t)R(x→,t) , which is all that makes the fluid behavior nonclassical. In particular, the quantum potential can become negative and create a nonclassical boost in the kinetic energy. This boost is related to superoscillations in the wavefunction, where the local frequency of Ψ exceeds its global band limit. Berry showed that for states of definite energy E, the regions of superoscillation are exactly the regions where Q(x→,t)<0 . For energy superposition states with band-limit E+ , the situation is slightly more complicated, and the bound is no longer Q(x→,t)<0 . However, the fluid model provides a definite local energy for each fluid particle which allows us to define a local band limit for superoscillation, and with this definition, all regions of superoscillation are again regions where Q(x→,t)<0 for general superpositions. An alternative interpretation of these quantities involving a reduced quantum potential is reviewed and advanced, and a parallel discussion of superoscillation in this picture is given. Detailed examples are given which illustrate the role of the quantum potential and superoscillations in a range of scenarios.

ExoMol line lists – LX. Molecular line list for the ammonia isotopologue 15NH3

Abstract A theoretical line list for 15NH3 CoYuTe-15 is presented based on the empirical potential energy and ab initio dipole moments surfaces developed and used for the production of the ExoMol line list CoYuTe for 14NH3. The ro-vibrational energy levels and wavefunctions are computed using the variational program TROVE. The line list ranges up to 10 000 cm−1 (λ ≥ 1 μm) and contains 929 795 249 transitions between 1 269 961 states with J ≤ 30. The line list should be applicable for temperatures up to ∼1000 K. To improve the accuracy of the line positions, a set of experimentally-derived energy levels of 15NH3 is produced using the Marvel procedure. To this end, 37 experimental sources of the line positions of 15NH3 available in the literature are collected, combined and systematised to produce a self-consistent spectroscopic network of 21 095 15NH3 transitions covering 40 vibrational bands ranging up to 6818 cm−1 and resulting in 2777 energy term values. These Marvel energies are then used to replace the theoretical values in the CoYuTe-15 line list and also complemented by pseudo-Marvel energies obtained by an isotopologue extrapolation using the previously reported Marvel energies of the 14NH3 parent isotopologue of ammonia. A list of 53 856 high resolution transitions between Marvel states and theoretical intensities is provided in the HITRAN format. Comparison with the recent experimental spectra of 15NH3 illustrate the potential of the line list for detections and as an efficient assistant in spectroscopic assignments. The line list is available from www.exomol.com.

Combining the Fragment Molecular Orbital and GRID Approaches for the Prediction of Ligand-Metalloenzyme Binding Affinity: The Case Study of hCA II Inhibitors.

Polarization and charge-transfer interactions play an important role in ligand-receptor complexes containing metals, and only quantum mechanics methods can adequately describe their contribution to the binding energy. In this work, we selected a set of benzenesulfonamide ligands of human Carbonic Anhydrase II (hCA II)-an important druggable target containing a Zn2+ ion in the active site-as a case study to predict the binding free energy in metalloprotein-ligand complexes and designed specialized computational methods that combine the ab initio fragment molecular orbital (FMO) method and GRID approach. To reproduce the experimental binding free energy in these systems, we adopted a machine-learning approach, here named formula generator (FG), considering different FMO energy terms, the hydrophobic interaction energy (computed by GRID) and logP. The main advantage of the FG approach is that it can find nonlinear relations between the energy terms used to predict the binding free energy, explicitly showing their mathematical relation. This work showed the effectiveness of the FG approach, and therefore, it might represent an important tool for the development of new scoring functions. Indeed, our scoring function showed a high correlation with the experimental binding free energy (R2 = 0.76-0.95, RMSE = 0.34-0.18), revealing a nonlinear relation between energy terms and highlighting the relevant role played by hydrophobic contacts. These results, along with the FMO characterization of ligand-receptor interactions, represent important information to support the design of new and potent hCA II inhibitors.

Energy and Structure of the Terbium Domain Wall

The domain wall energy is calculated by the balance between exchange, magnetocrystalline anisotropy and magnetoelastic energy contributions. The described method is theoretical and is based on experimental measurements of neutron inelastic scattering. The domain wall energy is determined by both finding the minimum of energy and deriving the energy and setting it to zero. The determination was undertaken for the discrete case, and this means that the calculation was performed for each plane or atomic layer. This is in contrast with the Bloch wall, which assumes continuum mean. The energy of the Lilley domain wall was discussed. Most of the energy of the Bloch wall was comprised inside the Lilley distance (above 99.9% of the energy). Antiferromagnetic interactions strongly decreased the domain wall energy. The negative terms due to antiferromagnetism must be considered in the Hamiltonian describing the exchange energy terms. The domain wall energy and width of terbium were reassessed. The values varied between 83.7 and 95.2 Kelvin (10.3 to 11.2 ergs/cm2). The domain width was estimated to be 57 Angstroms. It was found that a significant part of the total domain wall energy was concentrated on the planes at the center of the domain wall.

Ligand Gaussian Accelerated Molecular Dynamics 3 (LiGaMD3): Improved Calculations of Binding Thermodynamics and Kinetics of Both Small Molecules and Flexible Peptides.

Binding thermodynamics and kinetics play critical roles in drug design. However, it has proven challenging to efficiently predict ligand binding thermodynamics and kinetics of small molecules and flexible peptides using conventional molecular dynamics (cMD), due to limited simulation time scales. Based on our previously developed ligand Gaussian accelerated molecular dynamics (LiGaMD) method, we present a new approach, termed "LiGaMD3″, in which we introduce triple boosts into three individual energy terms that play important roles in small-molecule/peptide dissociation, rebinding, and system conformational changes to improve the sampling efficiency of small-molecule/peptide interactions with target proteins. To validate the performance of LiGaMD3, MDM2 bound by a small molecule (Nutlin 3) and two highly flexible peptides (PMI and P53) were chosen as the model systems. LiGaMD3 could efficiently capture repetitive small-molecule/peptide dissociation and binding events within 2 μs simulations. The predicted binding kinetic constant rates and free energies from LiGaMD3 were in agreement with the available experimental values and previous simulation results. Therefore, LiGaMD3 provides a more general and efficient approach to capture dissociation and binding of both small-molecule ligands and flexible peptides, allowing for accurate prediction of their binding thermodynamics and kinetics.

Structural, optical and heat transfer characteristics of rotating [MgO+ ZrO2/PEG-H2O]h Hybrid nanofluid flow over an expanding surfaces with activation energy

SignificanceHybrid nanofluids have garnered significant interest due to their potential for enhanced thermal and optical properties compared to their individual counterparts. AimThe aim of this research is to examine the structural, optical, and heat transfer properties of a hybrid nanofluid [MgO+ZrO2/PEG-H2O]h within a rotating system. This research integrated variable viscosity, MHD, convection, and activation energy terms into the momentum, energy, and concentration equations. A comprehensive experimental analysis, including Fourier-transform infrared and ultraviolet visible spectroscopy, elucidates the structural arrangement, optical behavior, and thermal transport properties of the nanofluids. MethodologyThe partial differential equations that govern the system are converted into nonlinear ordinary differential equations through similarity transformations. Then, these ODEs are numerically solved by employing the Runge-Kutta-Fehlberg method in combination with a shooting procedure. FindingsThe research findings demonstrate that the rotational factor impacts skin friction differently by 2 % on x and y axes, while skin friction surges by 3.63 % in [MgO+ZrO2/PEG-H2O]h hybrid nanofluid with higher magnetic field intensity. The heat transmission rates of the [MgO+ZrO2/PEG-H2O]h hybrid nanofluid are significantly higher by 4.58 % compared to the [ZrO2/PEG-H2O]n nanofluid. The mass transfer rate of [ZrO2/PEG-H2O]n declines by 3.57 % with the rise of the activation energy factor. Utilizing spin coating, thin films of nanostructures [ZrO2/PEG-H2O]n, [MgO/PEG-H2O]n and [MgO+ZrO2/PEG-H2O]h are fabricated, resulting in films with a consistent thickness of ∼200 nm at a temperature of 25 °C. A reduction in the difference in energy bandgap values from 4.5 eV for [ZrO2/PEG-H2O]s to 5.3 eV for [MgO/PEG-H2O]n and 4.8 eV for [MgO+ZrO2/PEG-H2O]h is observed. This indicates that the [MgO+ZrO2/PEG-H2O]h hybrid nanofluid yields an appropriate bandgap compared to individual nanofluids because hybrid nanofluids can lead to synergistic mechanisms that elevate their electronic attributes.

The velocity studies in the pure viscoelastic liquid core in displacement flow with interfacial instabilities

The velocity profiles in the core of a pure viscoelastic liquid displacing a Newtonian oil in a 500 µm microchannel were measured with micro-particle image velocimetry (µPIV) to investigate the onset of elastic turbulence. During displacement, a film of the displaced phase remains on the channel wall while interfacial instabilities develop upstream of the displacing core. Two displacing phase flow rates were investigated at 0.1 ml/min and 0.2 ml/min, corresponding to elastic Mach numbers, Ma, of 0.43 and 0.86 respectively. It was found that the velocity profiles in the streamwise and wall-normal directions are almost symmetric with respect to the centre of the core phase, apart from the case at high Ma and at the position of maximum interface deformation. Velocity fluctuations are present for the 0.2 ml/min while they are almost zero for the 0.1 ml/min, indicating the presence of elastic turbulence at large flow rate. Similarly, the calculated turbulence strengths at different directions (which make up the turbulent kinetic energy) and the Reynolds stresses have significant values at 0.2 ml/min but are almost zero at the low flow rate. In both flow rates, a circulation pattern is formed below the interfacial instability.

CWF: Consolidating Weak Features in High-quality Mesh Simplification

In mesh simplification, common requirements like accuracy, triangle quality, and feature alignment are often considered as a trade-off. Existing algorithms concentrate on just one or a few specific aspects of these requirements. For example, the well-known Quadric Error Metrics (QEM) approach [Garland and Heckbert 1997] prioritizes accuracy and can preserve strong feature lines/points as well, but falls short in ensuring high triangle quality and may degrade weak features that are not as distinctive as strong ones. In this paper, we propose a smooth functional that simultaneously considers all of these requirements. The functional comprises a normal anisotropy term and a Centroidal Voronoi Tessellation (CVT) [Du et al. 1999] energy term, with the variables being a set of movable points lying on the surface. The former inherits the spirit of QEM but operates in a continuous setting, while the latter encourages even point distribution, allowing various surface metrics. We further introduce a decaying weight to automatically balance the two terms. We selected 100 CAD models from the ABC dataset [Koch et al. 2019], along with 21 organic models, to compare the existing mesh simplification algorithms with ours. Experimental results reveal an important observation: the introduction of a decaying weight effectively reduces the conflict between the two terms and enables the alignment of weak features. This distinctive feature sets our approach apart from most existing mesh simplification methods and demonstrates significant potential in shape understanding. Please refer to the teaser figure for illustration.

Threshold displacement in the tungsten-carbon system

ABSTRACT Threshold displacement energies (Ed) of carbon and tungsten in tungsten carbide (WC), W2C, tungsten and diamond are predicted using molecular dynamics. The spatial dependence of Ed is probed by considering a geodesic projection of a symmetrically distinct arc of crystallographic directions for each lattice site. Further, the definition of threshold displacement is explored by making the distinction between atomic displacement ( E ¯ d disp ) and defect formation ( E ¯ d def ). Predicted values of E ¯ d def compare favourably to experimental observations for tungsten and tungsten carbide. Results confirm that E ¯ d def and E ¯ d disp are strongly structure dependent. Differences between E ¯ d disp and E ¯ d def are commensurate with rapid defect recombination within the timeframe of the simulations for some species and structures but not universally. The probability of displacement and defect formation as a function of primary knock-on energy is also reported. Previously developed models for the average displacement of the primary knock-on atom based on kinetic energy and momentum-dependent drag terms are generally found to provide a useful level of approximation. Anisotropy is investigated and results highlight differences due to structures.

The fractal structure of high-energy era of the universe

This study examines the structure of the universe during its high-energy era. In this context, we examine Barrow’s proposal of entropy, which forecasts a fractal configuration for the geometric properties of the black hole’s horizon. By applying the principles of thermodynamics, we get the equation of motion using the Barrow entropic consideration. A quasi-de Sitter phase, in which fractal and non-fractal states may coexist, is determined. This is an uncertainty state (coexistence of fractal and non-fractal states), and so a deformation for de Sitter spacetime, which contains a high-energy scale in the framework of the COBE normalization. With the kinetic energy term of the inflation field, we remove this ambiguity owing to the field oscillations. However, the oscillatory behavior of the inflation field continues and causes the universe to enter a new phase state. At this point, in which the inflation field oscillations are over, we obtain a solution that provides the universe transition to the radiation and dust phases.

Entanglement in Quantum Dots: Insights from Dynamic Susceptibility and Quantum Fisher Information

AbstractThis study investigates the entanglement properties of quantum dots (QDs) under a universal Hamiltonian where the Coulomb interaction between particles (electrons or holes) decouples into charging energy and exchange coupling terms. Although this formalism typically decouples the charge and spin components, confinement‐induced energy splitting can induce unexpected entanglement within the system. By analyzing the dynamic susceptibility and quantum Fisher information (QFI), significant behaviors are uncovered influenced by exchange constants, temperature variations, and confinement effects. In QDs with Ising exchange interactions, far below the Stoner instability (SI) point, where the QD is in a disordered paramagnetic phase, temperature reductions lead to decreased entanglement, challenging conventional expectations. These findings demonstrate that for QDs with small exchange interactions, the responses of easy‐plane () and easy‐axis () configurations are similar, with increased anisotropy broadening susceptibility and shifting its maximum to higher frequencies. For large exchange interactions, the susceptibility differences between easy‐plane and easy‐axis QDs become significant, with easy‐plane QDs exhibiting a higher susceptibility magnitude. Additionally, the study reveals that temperature variations affect the dynamic response functions differently in easy‐axis and easy‐plane QDs. In easy‐plane QDs, QFI consistently decreases with increasing temperature, whereas in easy‐axis QDs, QFI behavior is highly dependent on the strengths of and , showing either an increase or decrease with temperature based on specific coupling conditions. Conversely, at low temperatures, anisotropic Heisenberg models exhibit enhanced entanglement near isotropic points. Overall, this work contributes to advancing the understanding of entanglement in QDs and its potential applications in quantum technologies.

Influence of magnetic anisotropy on the vortex stability in circular Permalloy nanodots using energy analysis

We thoroughly investigated the stability of vortex magnetization in Permalloy (Py) circular nanodots with and without magnetocrystalline anisotropy using micromagnetic simulations. This study explores a wide-ranging understanding of influence of anisotropy on hysteresis loops, and spin-configurations, and provides a detailed analysis of the energy profile. The ground state vortex configuration considered of size 64 × 20-nm2 Py-nanodot at zero out-of-plane anisotropy had been modulated till the anisotropy 250 kJ/m3. We analyzed different energy terms at nucleation field, annihilation field and remanent states to gain deeper insights into the magnetization reversal mechanism. The energy analysis revealed an interplay between exchange and demagnetization energies, resulting in the stability of vortex up to a critical anisotropy (CK) 170 kJ/m3. Beyond this CK, the vortex destabilizes, switching the magnetization to a single-domain state. Additionally, we estimated the energy barrier involved in single domain to vortex state transformation. These findings provide valuable insights for designing vortex-based magnetic data storage and memory devices.

Crease instability in Gent-Gent hyperelastic materials

We study the crease instability of an incompressible Gent-Gent elastomer under general loading conditions. The Gent-Gent model has two distinct characteristics: the logarithmic nonlinearity triggered by I2 energy term and the strain hardening due to limiting chain extensibility. By performing finite element analysis combined with an evaluation of surface tension, we investigate the effects of the two characteristics on the critical creasing onset and the creasing onset delayed by surface tension. The results show that uniaxial compression induces logarithmic nonlinearity that accelerates the critical creasing onset, whereas equibiaxial compression hastens the initiation of strain hardening that delays the critical creasing onset. In addition, logarithmic nonlinearity mitigates the delay in creasing onset caused by surface tension under the uniaxial condition, and strain hardening suppresses creasing in cooperation with surface tension under the equibiaxial condition. Conversely, under the plane strain condition, two characteristics have little effect on the creasing onset delayed by surface tension.

Signature flips in time-varying Λ(t)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda (t)$$\\end{document} cosmological models with observational data

In this study, we investigate signature flips within the framework of cosmological models featuring a time-varying vacuum energy term Λ(t)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda (t)$$\\end{document}. Specifically, we consider the power-law form of Λ=αHn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda =\\alpha H^n$$\\end{document}, where α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} and n are constants. To constrain the model parameters, we use the MCMC technique, allowing for effective exploration of the model’s parameters. We apply this approach to analyze 31 points of observational Hubble Data (OHD), 1048 points from the Pantheon data, and additional CMB data. We consider three scenarios: when n is a free parameter (Case I), when n=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n=0$$\\end{document} (Case II), and when n=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n=1$$\\end{document} (Case III). In our analysis across all three cases, we observe that our model portrays the universe’s evolution from a matter-dominated decelerated epoch to an accelerated epoch, as indicated by the corresponding deceleration parameter. In addition, we investigate the physical behavior of total energy density, total EoS parameter, and jerk parameter. Our findings consistently indicate that all cosmological parameters predict an accelerated expansion phase of the universe for all three cases (q0<0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$q_0<0$$\\end{document}, ω0<-13\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega _0<-\\frac{1}{3}$$\\end{document}, j0>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$j_0>0$$\\end{document}). Furthermore, our analysis reveals that the Om(z) diagnostics for Cases I and III align with the quintessence region, while Case II corresponds to the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}CDM model.

Motion analysis of and experimental research on a magnetic and elastic coupling oscillation system

To analyze the motion laws of a magnetic and elastic coupling system under the influence of various factors, this paper proposes a magnetic coupling pendulum based on spring pieces and magnets—a magnetic–mechanical oscillator. By fixing spring pieces onto two non-magnetic bases and attaching magnets to their upper ends, which repel each other, the potential energy during oscillation is expanded using Fourier series. Subsequently, Lagrange equations are solved to study the effects of the first two terms of potential energy. spring piece Using algebraic simplification and transformation, as well as model experiments, its dynamic behaviors, such as its motion frequency and phase characteristics, were explored according to different influencing factors, including the magnetic potential energy, the elastic modulus of the spring, and the external environment. We analyzed the impact of the simplified system's main parameters on its vibration modes, deriving the model formulas and the experimental results. The conclusions from the formula derivation indicate that the motion frequency of the simplified system is a superposition of two frequency. Under certain conditions, these frequencies can be separated, simplifying the system's dynamics. Equally, the experimental results corroborated the findings from the formula derivation, providing a reference for the design and study of dynamic behaviors in magnetic coupling systems.