Relaxation Model Research Articles

An alternating direction multiplier method with variable neighborhood search for electric vehicle routing problem with time windows and battery swapping stations

This paper studies a real-world electric vehicle routing problem (EVRP). Specifically, it is an EVRP with time windows and battery swapping stations (EVRP_TWBSS). The EVRP_TWBSS considers the routing of electric vehicles (EVs), the determination of each electric vehicle’s battery level, and the selection of battery swapping stations. The criterion of EVRP_TWBSS is to minimize the operating costs. To simplify the structure of model, a time-discrete and multi-commodity flow model based on extended state-space-time network (TMFM_ESSTN) is established. Meanwhile, an alternating direction multiplier method with variable neighborhood search (ADMM_VNS) is presented to address the TMFM_ESSTN. In ADMM_VNS, the augmented lagrangian relaxation (ALR) model constructed from the TMFM_ESSTN is decomposed and linearized to a series of least cost vehicle routing subproblems through the linear augmented lagrangian relaxation (LALR) decomposed technique. Then, each subproblem is iteratively solved by using the dynamic programming and two special designed VNS strategies in ADMM_VNS iterative framework. The solution’s quality can be controlled to a certain extent through monitoring the gap between the lower and upper bounds obtained after each iteration. Test results on instances with different scales and a real-world instance based on partial road network in Kunming City demonstrate that ADMM_VNS can achieve smaller gaps and better solutions than several state-of-the-art algorithms. In which, ADMM_VNS can reduce the optimal gap by up to 2.27 % compared to the other state-of-the-art algorithms in small-scale instances. The gap of ADMM_VNS is calculated based on the lower bound and the upper bound in the large-scale instances and the real-world instance are 10.36 % and 1.57 %, respectively.

A molecular phylogeny of the Petaluridae (Odonata: Anisoptera): A 160-Million-Year-Old story of drift and extinction

Petaluridae (Odonata: Anisoptera) is a relict dragonfly family, having diverged from its sister family in the Jurassic, of eleven species that are notable among odonates (dragonflies and damselflies) for their exclusive use of fen and bog habitats, their burrowing behavior as nymphs, large body size as adults, and extended lifespans. To date, several nodes within this family remain unresolved, limiting the study of the evolution of this peculiar family. Using an anchored hybrid enrichment dataset of over 900 loci we reconstructed the species tree of Petaluridae. To estimate the temporal origin of the genera within this family, we used a set of well-vetted fossils and a relaxed molecular clock model in a divergence time estimation analysis. We estimate that Petaluridae originated in the early Cretaceous and confirm the existence of monophyletic Gondwanan and Laurasian clades within the family. Our relaxed molecular clock analysis estimated that these clades diverged from their MRCA approximately 160 mya. Extant lineages within this family were identified to have persisted from 6 (Uropetala) to 120 million years (Phenes). Our biogeographical analyses focusing on a set of key regions suggest that divergence within Petaluridae is largely correlated with continental drift, the exposure of land bridges, and the development of mountain ranges. Our results support the hypothesis that species within Petaluridae have persisted for tens of millions of years, with little fossil evidence to suggest widespread extinction in the family, despite optimal conditions for the fossilization of nymphs. Petaluridae appear to be a rare example of habitat specialists that have persisted for tens of millions of years.

A two-step framework integrating lasso and Relaxed Lasso for resolving multidimensional collinearity in Chinese baijiu aging research

The aging process is crucial for Chinese Baijiu production, significantly enhancing the spirit's flavor, aroma and quality. However, aging involves a complex interplay of numerous compounds, and the extensive duration required for aging leads to a scarcity of samples available for scientific research. These limitations pose a challenge in analyzing high-dimensional data with collinearity, complicating the understanding of the intricate chemical processes at play. In this article, a two-step framework was proposed that integrated Relaxed Lasso regression models with Lasso-selected predictors to address this issue. Baijiu samples subjected to various aging conditions were analyzed using direct GC-MS and HS-GC-MS, and the obtained data was processed by this approach. The results demonstrate significantly superior performance compared to other methods, including PLSR and Gradient Boosting. Analyses were also performed on a previously documented dataset, yielding enhanced results and underscoring the method's advantage in processing high dimensional data with multicollinearity. Moreover, this method proved effective in screening of potential indicative compounds, highlighting its utility in Baijiu aging research.

Long-term relaxation analysis of steel cables based on viscoelastic model

Steel cables, renowned for their lightweight and high-strength properties, stand as ubiquitous building materials in large-span structures. Serving as crucial load-bearing elements, cables endure sustained tension throughout the structure's lifecycle. To further investigate the long-term relaxation characteristics of steel cables and provide more theoretical basis for structural relaxation calculations, this paper introduces a long-term relaxation constitutive model for steel cables, formulated through theoretical derivation, experimental validation, and data fitting techniques to establish time-dependent constitutive relationships. By employing the Bingham and Kelvin viscoelastic models, a relaxation model for steel cables is presented and optimized accordingly. Experimental investigations involve long-term tests on steel cables with three different sizes and detailed fitting analysis on collected internal force relaxation data. The findings emphasize the indispensability of structural relaxation behavior and the significance of altering internal forces, particularly in large-span cable-strut structures. The developed numerical model enables accurate simulation and prediction of long-term time-dependent performance in such structures, serving as a springboard for future studies in this domain.

MP2-Based Composite Extrapolation Schemes Can Predict Core-Ionization Energies for First-Row Elements with Coupled-Cluster Level Accuracy.

X-ray photoelectron spectroscopy (XPS) measures core-electron binding energies (CEBEs) to reveal element-specific insights into the chemical environment and bonding. Accurate theoretical CEBE prediction aids XPS interpretation but requires proper modeling of orbital relaxation and electron correlation upon core-ionization. This work systematically investigates basis set selection for extrapolation to the complete basis set limit of CEBEs from ΔMP2 and ΔCC energies across 94 K-edges in diverse organic molecules. We demonstrate that an alternative composite scheme using ΔMP2 in a large basis corrected by ΔCC-ΔMP2 difference in a small basis can quantitatively recover optimally extrapolated ΔCC CEBEs within 0.02 eV. Unlike ΔCC, MP2 calculations do not suffer from convergence issues and are computationally cheaper, and thus, the composite ΔMP2/ΔCC scheme balances accuracy and cost, overcoming limitations of solely using either method. We conclude by providing a comprehensive analysis of the choice of small and large basis sets for the composite schemes and provide practical recommendations for highly accurate (within 0.10-0.15 eV MAE) ab initio prediction of XPS data.

Specific line shape of the lowest frequency Raman scattering modes of triethylene glycol.

For both dielectric spectroscopy and light scattering spectra, the relaxation modes in the microwave region have been characterized by the Debye relaxation model, which is determined by the peak frequency, or by an empirically extended model (e.g., Cole-Davidson and Kohlrausch-Williams-Watts), which has the appropriate line shape. For light scattering from glass-forming liquids, the general line shape is a broader high frequency side in comparison with Debye relaxation. However, for triethylene glycol (TEG) in liquid form at room temperature, the lowest frequency Raman scattering (LFR) mode shows a peak at about 3.0GHz, which is narrower than that expected for the Debye relaxation. With increasing temperature, this peak exhibits a significant blueshift and begins to resemble the Debye relaxation shape, indicating that the LFR mode of TEG is also a relaxation mode. The narrowing of the LFR mode of TEG is suggested to be caused from the increased non-whiteness of the fluctuation correlations due to increased hydrogen bonding. This is a consequence of breaking the Debye relaxation model's approximation of the overdamping and narrowing limits in the GHz region, which was found in this study by analyzing the relaxation modes of Raman scattering using the multiple random telegraph model for evaluating thermal bath correlation. The analysis results show that the LFR relaxation times of TEG and the main dielectric relaxation overlap only by 333K. However, the second LFR mode and β-relaxation at higher frequencies coincide over a wide temperature range, suggesting that they are corresponding modes.

Molecular Modes Elucidate the Nuclear Magnetic Resonance Relaxation of Viscous Fluids.

The Bloembergen, Purcell, and Pound (BPP) theory of nuclear magnetic resonance (NMR) relaxation in fluids dating back to 1948 continues to be the linchpin in interpreting NMR relaxation data in applications ranging from characterizing fluids in porous media to medical imaging (MRI). The BPP theory is founded on assuming molecules are hard spheres with 1H-1H dipole pairs reorienting randomly; assumptions that are severe in light of modern understanding of liquids. Nevertheless, it is intriguing to this day that the BPP theory was consistent with the original experimental data for glycerol, a hydrogen-bonding molecular fluid for which the hard-sphere-rigid-dipole assumption is inapplicable. To better understand this incongruity, atomistic molecular simulations are used to compute 1H NMR T1 relaxation dispersion (i.e., frequency dependence) in two contrasting cases: glycerol, and a (non hydrogen-bonding) viscosity standard. At high viscosities, simulations predict distinct functional forms of T1 for glycerol compared to the viscosity standard, in agreement with modern measurements, yet both in contrast to BPP theory. The cause of these departures from BPP theory is elucidated, without assuming any relaxation models and without any free parameters, by decomposing the simulated T1 response into dynamic molecular modes for both intramolecular and intermolecular interactions. The decomposition into dynamic molecular modes provides an alternative framework to understand the physics of NMR relaxation for viscous fluids.

Towards dynamical low-rank approximation for neutrino kinetic equations. Part I: Analysis of an idealized relaxation model

Dynamical low-rank approximation (DLRA) is an emerging tool for reducing computational costs and provides memory savings when solving high-dimensional problems. In this work, we propose and analyze a semi-implicit dynamical low-rank discontinuous Galerkin (DLR-DG) method for the space homogeneous kinetic equation with a relaxation operator, modeling the emission and absorption of particles by a background medium. Both DLRA and the discontinuous Galerkin (DG) scheme can be formulated as Galerkin equations. To ensure their consistency, a weighted DLRA is introduced so that the resulting DLR-DG solution is a solution to the fully discrete DG scheme in a subspace of the standard DG solution space. Similar to the standard DG method, we show that the proposed DLR-DG method is well-posed. We also identify conditions such that the DLR-DG solution converges to the equilibrium. Numerical results are presented to demonstrate the theoretical findings.

Pulsed MPI Relaxometry of Brownian and Néel Field-Dependent Relaxation in Superparamagnetic Magnetite Nanoparticles Confirm Theory and Simulations.

Superparamagnetic iron oxide nanoparticles (SPIOs) are used as tracers in Magnetic Particle Imaging (MPI). It is crucial to understand the magnetic properties of SPIOs for optimizing MPI imaging contrast, resolution, and sensitivity. Brownian and Néel relaxation theory developed in the early 1950s posits that relaxation times can vary with particle size, shell thickness, medium viscosity, and the applied field strength. Magnetic relaxation can soon provide a unique imaging capability, the ability to distinguish bound from unbound MPI tracers in vivo. Yet experimental validation of these theories has not been completed. In this paper, a novel method of pulsed magnetic field relaxometry is used to directly probe the relaxation behavior of superparamagnetic magnetite nanoparticles over a spectrum of magnetic field amplitudes, providing the first experimental validation of theoretical relaxation models. It is also shown that closed-form approximations generated in the early 1970s accurately match both data and numerical Fokker Planck computational models, which are computationally burdensome. This means researchers can trust these approximations for future modeling. All the findings can be translated to sinusoidal excitations used in conventional MPI scanningtrajectories.

Transfer learning relaxation, electronic structure and continuum model for twisted bilayer MoTe2

Large-scale moiré systems are extraordinarily sensitive, with even minute atomic shifts leading to significant changes in electronic structures. Here, we investigate the lattice relaxation effect on moiré band structures in twisted bilayer MoTe2 with two approaches: (a) large-scale plane-wave basis first principle calculation down to 2.88°, (b) transfer learning structure relaxation + local-basis first principles calculation down to 1.1°. We use two types of van der Waals corrections: the D2 method of Grimme and the density-dependent energy correction, and find that the density-dependent energy correction yields a continuous evolution of bandwidth with twist angles. Based on the above results. we develop a complete continuum model with a single set of parameters for a wide range of twist angles, and perform many-body simulations at ν = −1, −2/3, −1/3.

A Review of the Relaxation Models for Phase Transition Flows Centered on the Topological Aspects of the Nonequilibrium Mass Transfer Modelling

A Review of the Relaxation Models for Phase Transition Flows Centered on the Topological Aspects of the Nonequilibrium Mass Transfer Modelling

Relaxed Model Predictive Control of T-S Fuzzy Systems via a New Switching-Type Homogeneous Polynomial Technique

Relaxed Model Predictive Control of T-S Fuzzy Systems via a New Switching-Type Homogeneous Polynomial Technique

Quantitative MRI post-processing algorithm and visualization research based on moisture status detection of winter jujube

Quantitative Magnetic Resonance Imaging (qMRI) offers precise measurements of the relaxation characteristics of microstructures, representing a cutting-edge method in non-destructive fruit analysis. This study aims to visualize information on changes in moisture status and distribution at the subcellular level of winter jujube. The 0.5 T nuclear magnetic imaging equipment was utilized to rapidly, non-invasively, and accurately capture the internal relaxation status of the sample with multiple-echo-imaging. By examining the signal and noise data, a simulated dataset was developed to tackle the optimization challenge of estimating parameters for the discrete relaxation model from the multiple-echo-imaging data, especially under conditions of low signal-to-noise ratio (SNR) and in the context of heteroscedastic noise. An optimal weighting factor and the T2NR truncation model have been identified to establish an effective experimental inversion strategy. Subsequently, multiple-echo-imaging can rapidly and stably yielded voxel-level maps under conditions of low signal-to-noise ratio. Utilizing this experimental approach, data from winter jujube was collected and analyzed, facilitating an exploration of water activity (T2 mapping) and associated water content (A2 mapping). Through analyzing winter jujube fruits across two maturity stages, this study elucidates the role of precise quantification and voxel-wise visualization in moisture status detection. The methodology presents an innovative approach for assessing internal moisture distribution in fruits.

Design and analysis of a metamaterial based biosensor to determine blood glucose concentration

In this paper, a biosensor utilizing metamaterials is designed and simulated to detect blood glucose concentration. The proposed sensor comprised of a microstrip patch antenna designed on a Rogers RT5880 substrate. A circular-shaped complementary split ring resonator (CSRR) cell is integrated onto the patch of the antenna which acts as the sensing region. The sensor is analyzed in order to ascertain the blood glucose concentration ranging from 50-300 mg/dL in a human finger model. The sensing parameter is amplitude of reflection coefficient, which exhibits variation in response to alterations in the dielectric characteristics of the sample being tested. The Cole-Cole relaxation model is employed to predict the dielectric properties of different finger tissues. An analysis of the characteristics of the CSRR was conducted to illustrate its significance in the realm of glucose detection. The glucose level is determined through the utilization of a linear regression model that describes the relationship between the reflection coefficient of the sensor and glucose level. The sensor demonstrates an impressive sensitivity of 1.792 dB per (mgdL<sup>-1</sup>) and has the ability of determining glucose levels with a good accuracy, as verified by the application of Clarke error grid. This sensor exhibits enhanced performance compared to some other recent glucose sensors.

Adaptive unified gas-kinetic scheme for diatomic gases with rotational and vibrational nonequilibrium

Multiscale nonequilibrium physics at large variations of local Knudsen number are encountered in applications of aerospace engineering and micro-electro-mechanical systems, such as high-speed flying vehicles and low pressure of the encapsulation. An accurate description of flow physics in all flow regimes within a single computation requires a genuinely multiscale method. The adaptive unified gas-kinetic scheme (AUGKS) is developed for such multiscale flow simulation. The AUGKS applies discretized velocity space to accurately capture the non-equilibrium physics in the multiscale UGKS, and adaptively employs continuous distribution functions following Chapman–Enskog expansion to efficiently recover near-equilibrium flow region in GKS. The UGKS and GKS are dynamically connected at the cell interface through the fluxes from the discretized and continuous gas distribution functions, which avoids any buffer zone between them. In this study, the AUGKS with rotation and vibration non-equilibrium is developed based on a multiple temperature relaxation model. The real gas effect in different flow regimes has been properly captured. To capture aerodynamic heating accurately, the heat flux modifications from the rotation and vibration modes are also included in the current scheme. Unstructured discrete particle velocity space is adopted to further improve the computational performance of the AUGKS. Numerical tests, including Sod tube, normal shock structure, high-speed flow around the two-dimensional cylinder and three-dimensional sphere and space vehicles, and an unsteady nozzle plume flow from the continuum flow to the background vacuum, have been conducted to validate the current scheme. In comparison with the original UGKS, the current scheme speeds up the computation, reduces the memory requirement, and maintains the equivalent accuracy for multiscale flow simulation, which provides an effective tool for nonequilibrium flow simulations, especially for the flows at low and medium speed.

Prediction on the time-varying behavior of tunnel segment gaskets under compression

The compression force is a critical indicator for assessing the waterproofing capability of ethylene propylene diene monomer (EPDM) rubber gaskets, and the relaxation of EPDM gaskets under compression is a key factor contributing to water leakage in shield tunnels. In this study, detailed accelerated aging tests of gaskets with different precompression openings were conducted. Analytical method and simulation method for predicting the long-term performance of EPDM gaskets considering their different compression states were proposed. First, the compression curve of the gasket was divided into three stages to analyze the mechanism of compression force degradation in depth. Under the action of a compression force, the unrecoverable deformation caused by open holes shortened stage III of the compression curve, which constituted the primary factor influencing gasket compression force relaxation. In addition, the Arrhenius equation was used to establish a conversion relationship between the accelerated aging test conditions and actual service time, and an analytical expression (AE) method for predicting the compression force degradation pattern of gaskets was proposed. Finally, a finite element (FE) method based on the relaxation constitutive model was proposed, enabling simulation of deteriorating tunnel segment gasket performance under complex compression states. Then, the effectiveness and accuracy of the proposed relaxation model were validated by comparing the compression force curves and deformation states obtained from experiments and simulations. Based on the time-varying relaxation constitutive parameters, the variation in the compression force of EPDM gaskets with different joint openings over time was simulated. The results show that the minimum compression force retention rates of gaskets after 100 years of service predicted by the AE method and FE method are 28.5 % and 30.6 %, respectively. This study provides two effective means for predicting the long-term mechanical performance of compressed EPDM gaskets, offering pivotal insights for long-term waterproofing design of shield tunnel joints.

Modeling of direct AC/AC hybrid distribution transformer based on relaxed two port network theory

Traditional distribution transformers have shortcomings such as poor dynamic characteristics and unreasonable voltage compensation. It is difficult for them to meet the demand for power quality with the large-scale integration of new energy into the grid. Hybrid distribution transformers (HDTs) are an important means of addressing these issues. They have good flexibility in voltage regulation and huge development potential. To analyze the operating status and losses of an HDT, this study constructs a simplified equivalent impedance model for an HDT. First, the operating principle, characteristics, and voltage regulation range of a direct AC/AC HDT were analyzed. Second, based on the state–space averaging method, we obtain the HDT single-phase average circuit topology and construct an HDT relaxed two-port network model. Third, considering the operating losses of the transformer, Thevenin equivalent parameters of an HDT were derived. Then, a simplified equivalent impedance model for an HDT and the corresponding control strategies are presented. Finally, we verify the correctness and rationality of the proposed theory by constructing an HDT simulation model.

Empirical Light-soaking and Relaxation Model of Perovskite Solar Cells in an Indoor Environment

Empirical Light-soaking and Relaxation Model of Perovskite Solar Cells in an Indoor Environment

Dynamic Compressive Stress Relaxation Model of Tomato Fruit Based on Long Short-Term Memory Model.

Tomatoes are prone to mechanical damage due to improper gripping forces during automated harvest and postharvest processes. To reduce this damage, a dynamic viscoelastic model based on long short-term memory (LSTM) is proposed to fit the dynamic compression stress relaxation characteristics of the individual fruit. Furthermore, the classical stress relaxation models involved, the triple-element Maxwell and Caputo fractional derivative models, are compared with the LSTM model to validate its performance. Meanwhile, the LSTM and classical stress relaxation models are used to predict the stress relaxation characteristics of tomato fruit with different fruit sizes and compression positions. The results for the whole test dataset show that the LSTM model achieves a RMSE of 2.829×10-5 Mpa and a MAPE of 0.228%. It significantly outperforms the Caputo fractional derivative model by demonstrating a substantial enhancement with a 37% decrease in RMSE and a 36% reduction in MAPE. Further analysis of individual tomato fruit reveals the LSTM model's performance, with the minimum RMSE recorded at the septum position being 3.438×10-5 Mpa, 31% higher than the maximum RMSE at the locule position. Similarly, the lowest MAPE at the septum stands at 0.375%, outperforming the highest MAPE at the locule position by a significant margin of 90%. Moreover, the LSTM model consistently reports the smallest discrepancies between the predicted and observed values compared to classical stress relaxation models. This accuracy suggests that the LSTM model could effectively supplant classical stress relaxation models for predicting stress relaxation changes in individual tomato fruit.

Effect of compound treatments on mouse lens viscoelasticity

Previous studies have shown that pharmaceutical agents such as lipoic acid have the ability to soften the lens, presenting a promising avenue for treating presbyopia. One obstacle encountered in the preclinical stage of such agents is the need for precise measurements of lens elasticity in experimental models. This study aimed to evaluate the effects of 25-hydroxycholesterol, lipoic acid, and obeticholic acid on the viscoelastic properties of mouse lenses using a custom-built elastometer system. Data were acquired on lenses from C57BL/6J female mice from two age groups: young (age: 8–10 weeks) and old (age: 32–43 weeks). OD lenses were used as the control and OS lenses were treated. Control lenses were immersed in Dulbecco's Modified Eagle Medium (DMEM) and treatment lenses were immersed in a compound solution containing 25-hydroxycholesterol (5 young and 5 old), lipoic acid at 2.35 mM (5 young and 5 old), lipoic acid at 0.66 mM (5 old), or obeticholic acid (5 old) at 37 °C for 18 h. After treatment, the mouse lenses were placed in a DMEM-filled chamber within a custom-built elastometer system that recorded the load and lens shape as the lens was compressed by 600 μm at a speed of 50 μm/s. The load was continuously recorded during compression and during stress-relaxation. The compression phase was fit with a linear function to quantify lens stiffness. The stress-relaxation phase was fit with a 3-term exponential relaxation model providing relaxation time constants (t1, t2, t3), and equilibrium load. The lens stiffness, time constants and equilibrium load were compared for the control and treated groups. Results revealed an increase in stiffness with age for the control group (young: 1.16 ± 0.11 g/mm, old: 1.29 ± 0.14 g/mm) and relaxation time constants decreased with age (young: t1 = 221.9 ± 29.0 s, t2 = 24.7 ± 3.8 s, t3 = 3.12 ± 0.87 s, old: t1 = 183.0 ± 22.0 s, t2 = 20.6 ± 2.6 s and t3 = 2.24 ± 0.43 s). Among the compounds tested, only 25-hydroxycholesterol produced statistically significant changes in the lens stiffness, relaxation time constants, and equilibrium load. In conclusion, older mouse lenses are stiffer and less viscous than young mouse lenses. Notably, no significant change in lens stiffness was observed following treatment with lipoic acid, contrary to previous findings.