Mechanical Theory Research Articles

Simulation of new waves in applied sciences via Schrödinger equations

The perturbed chiral nonlinear Schrö dinger equation (PCNLSE) reflects the quantum actions such as quantum pictures of Bohm potential and internal self-potential properties. Indeed, this equation introduces the basics of the hidden variable theory in quantum mechanics. Two unified solver methods and exp -expansion technique applied to PCNLSE to present many solitonic solutions in an explicit and effective way. The behaviour of these solutions is of qualitatively different structural natures, relying on physical coefficient parameters. The application of three mathematical techniques to our model system provides us with several possible physical property solutions that account for the majority of many phenomena the model under study attempts to depict. The reported bright explosive envelopes, explosive solitons, periodic blow up, bright periodic envelope and huge solitary waves are highly applicable in plasma and nuclear physics, optical communications, electro-magnetic propagations, superfluid and in a lot other applied sciences. The results of this system's solitary structures are consistent with the characteristics of the nonlinear Schrödinger equation systems used to study dispersive modes and higher-order perturbed systems. For more details about the physical dynamical representation of the presented solutions, we have illustrated them with profile pictures using Mathematica and Matlab 18, to obtain complete configurations. The proposed approach can be applied to several equations arising in all applied sciences.

Carbon nanotubes at the Graphene/hBN interface abnormally enhance its fracture toughness

Different from Van der Waals heterojunction, defects often appear at the interface of the planar heterostructures due to the low-dimensional structure characteristics. These defects lead to complex mechanical problems, and seriously affect application of planar heterostructures in flexible electronics devices. The most commonly used method to improve the toughness is to reduce/eliminate the interfacial structural defects. Using a defective Graphene/hBN interface, we show surprisingly that Carbon Nanotubes (CNTs) are able to enhance the toughness at the interface. It is found that interlayer stress transfer, bonding strain energies and energy release rate of the defective Graphene/hBN interface with CNTs are higher than those of free-defect Graphene/hBN interface, which is in strong contrast to the general view that interfacial defects reduce toughness. By combining the analysis of atomic mechanics and fracture mechanics theory, we find that the abnormal enhancement in interfacial toughness comes from the stress field localization arising from sp2 + sp3 hybrid state and out-of-plane deformation at the interface. In addition, the stress field at the distal end of the simulated models gradually decays with the CNTs height, resulting in the stress fields to be controlled at the interface. This abnormal mechanism provides a new dimension for enhancing toughness in two-dimensional heterostructures.

Analysis on crack propagation of CRTS III slab ballastless track under temperature loads and freeze–thaw deterioration

In seasonal frozen region, the Chinese Rail Track System (CRTS) III slab track is subject to temperature loads and freeze–thaw deterioration, which may lead to further expansion of microcracks in track slabs. Mechanical parameters of track structure materials after freeze–thaw cycles are obtained through the experimental tests in this study. A finite element model of CRTS III slab track on subgrade section is then established by ABAQUS. Based on fracture mechanics theory, the types of cracks generated in track slabs under temperature loads and freeze–thaw deterioration, and crack expansion law are analyzed by using extended finite element method. The results show that under temperature loads, the expanded cracks in track slab are mainly Mode Ⅰ - Opening mode. There is the possibility of expansion for transverse cracks with larger size on the upper surface of track slab under negative temperature gradient load. Vertical capillary cracks at the location where track slab is bonded to self-compacting concrete are more likely to expand. Freeze-thaw deterioration will reduce the difference between the SIFs of cracks and fracture toughness of track slab material, which has a certain promotion effect on crack expansion.

Helicopter transmission system anomaly detection in variable flight regimes with decoupling variational autoencoder

Condition monitoring of helicopter transmission system is the main focus of Health and Usage Monitoring System. Existing anomaly detection methods for transmission system ignore the challenges caused by variable flight regimes of helicopter, which greatly hinders their application in application scenarios. For the first time, we propose Decoupling Variational AutoEncoder (DVAE) as a pioneering solution for anomaly detection task under variable working conditions. It does not rely on any prior knowledge related to the task and greatly expands the application scenarios of anomaly monitoring tasks. With the purpose of decoupling original signals from regime information, we focus on three aspects: network mechanism, training strategy, and optimization theory, to extract domain-invariant latent features with regard to flight regimes. Specifically, domain shifting mechanism is built to train learnable transform index and implement cross-domain transformation adaptively. Domain adversarial regression strategy is proposed to alternately guide the decoupling process about regime information. Theoretical derivation guarantees that when algorithm converges, latent features would be independent of domain parameters. The effectiveness of DVAE is evaluated with three progressive experiments, including parts-level fault simulation, components-level fault simulation, and actual-level fault under practical scenarios of helicopter transmission system. Results show that it can timely and accurately detect actual failure of the helicopter transmission system under variable flight regimes and alert it before onboard Health and Usage Monitoring System.

Research on the Secondary Motion of Engine Piston Considering the Transport of Lubricating Oil

<div>At present, it is generally considered in the analysis of the secondary motion of engine piston that the piston skirt–cylinder liner friction pair is fully lubricated in an engine operating cycle. However, in practice, when the piston moves upward, the amount of lubricating oil at the inlet may not ensure that the friction pair is fully lubricated. In this article, the secondary motion of piston is studied when the transport of lubricating oil is considered to determine the lubrication condition of piston skirt–cylinder liner friction pair. The secondary motion of piston is solved based on the combined piston motion model, hydrodynamic lubrication model, asperity contact model, and lubricating oil flow model. The secondary motion equation of piston is solved by the Broyden method. The hydrodynamic lubrication equation is solved by the finite difference method. The asperity contact between piston skirt and cylinder liner is calculated by the Greenwood model. The flow of lubricating oil is analyzed based on the theory of fluid mechanics. The results indicate that, when the actual transport of lubricating oil is considered to determine the lubrication condition of piston skirt–cylinder liner friction pair, the secondary motion of piston is remarkably different from that in which the flooded lubrication is assumed in an engine operating cycle. Therefore, it is helpful to improve the accuracy and make the analysis closer to the actual engine operating situation that the transport of lubricating oil is considered in the analysis of the secondary motion of engine piston.</div>

Refining one-class representation: A unified transformer for unsupervised time-series anomaly detection

The deep unsupervised time-series anomaly detector depends on the one-class representation, which is more effective by only formulating the normal samples. However, normal samples are always mixed with anomalies in the unlabeled training dataset. The learned one-class representation may be biased and violates the one-class setting. To address this problem, we refine the one-class representation and propose a unified AMFormer (Active Masked transFormer) framework, which integrates Transformer with the masked operation mechanism and cost-sensitive learning theory. Specifically, we first develop a network-driven masked operation with Hadamard product transformation to damage the initial input samples. The encoder and decoder representations rebuild the processed incomplete samples, which avoids identical shortcuts and further enhances robustness. Secondly, we exploit the active MSE (Mean Squared Error) loss function to purify the training samples. The different weights are dynamically added to different kinds of samples according to their rebuilding-errors-based pseudo labels. The pseudo anomalies with more significant rebuilding errors are removed by putting lower weights. Finally, extensive experiments are conducted on four benchmark datasets. The experimental results demonstrate that our AMFormer outperforms the nine relevant benchmark algorithms, boosting the mean f1-score from 0.851 to 0.937.

Efficiency and energy balance for substitution of CH4 in clathrate hydrates with CO2 under multiple-phase coexisting conditions.

Many experimental and theoretical studies on CH4-CO2 hydrates have been performed aiming at the extraction of CH4 as a relatively clean energy resource and concurrent sequestration of CO2. However, vague or insufficient characterization of the environmental conditions prevents us from a comprehensive understanding of even equilibrium properties of CH4-CO2 hydrates for this substitution. We propose possible reaction schemes for the substitution, paying special attention to the coexisting phases, the aqueous and/or the fluid, where CO2 is supplied from and CH4 is transferred to. We address the two schemes for the substitution operating in three-phase and two-phase coexistence. Advantages and efficiencies of extracting CH4 in the individual scheme are estimated from the chemical potentials of all the components in all the phases involved in the substitution on the basis of a statistical mechanical theory developed recently. It is found that although substitution is feasible in the three-phase coexistence, its working window in temperature-pressure space is much narrower compared to the two-phase coexistence condition. Despite that the substitution normally generates only a small amount of heat, a large endothermic substitution is suggested in the medium pressure range, caused by the vaporization of liquid CO2 due to mixing with a small amount of the released CH4. This study provides the first theoretical framework toward the practical use of hydrates replacing CH4 with CO2 and serves as a basis for quantitative planning.

Wavelet Neural Network-Based Half-Period Predictive Roll-Reduction Control Using a Fin Stabilizer at Zero Speed

Among the commonly used ship-stabilizing devices, the fin stabilizer is the most effective. Since the lift force of the conventional fin stabilizer is proportional to the square of the incoming flow velocity, it has a better anti-rolling effect at higher speeds but a poor anti-rolling effect at low speeds and even no effect at zero speed. A combination of modelling analysis, simulation, and a model ship experiment is used in this paper to study the zero-speed roll-reduction control problem of the fin stabilizer. A simulation model of the rolling motion of a polar expedition ship is established. The lift model of the fin stabilizer at zero speed is established using the theory of fluid mechanics. The proportional–integral–differential (PID) controller is selected to control the fin to achieve zero-speed roll reduction. To obtain a better anti-rolling control effect under variable sea conditions, a wavelet neural network (WNN)-based half-period prediction algorithm is adopted to update and adjust PID control parameters in real time. A simulation was carried out, and the effectiveness of the proposed predictive control algorithm is proved. A reduced-scale ship model was established to carry out the water tank experiment, and the results verify the theoretical analysis and simulation. The results also verify the effectiveness of the proposed control strategy.

Risk-constrained stochastic scheduling for energy hub: Integrating renewables, demand response, and electric vehicles

This research introduces a stochastic scheduling approach that incorporates risk constraints for an energy hub (EH), considering uncertainties related to renewable generation and load demands. The proposed method utilizes the Conditional Value at Risk (CVaR) technique to assess and quantify risks. By striking a balance between reducing operational and emissions costs and increasing risk aversion, the approach presents a trade-off. The EH comprises various components such as a wind turbine (WT), photovoltaic (PV) cells, a fuel cell power plant (FCPP), a combined heat and power generation unit (CHP), and plug-in electric vehicles (PEVs). Uncertain variables encompass factors such as wind speed, solar irradiation, different demands, and market prices. To optimize profits and enhance the consumption curve, demand response programs (DRPs) for electrical, thermal, and cooling demands are implemented. To address the uncertainties associated with input random variables, the efficient k-means data clustering method is employed. A new slime mold algorithm, based on coughing and chaos theory, has been proposed to enhance the problem's solution. The algorithm incorporates innovative operators to improve its capabilities. By utilizing the coughing mechanism and chaos theory, the algorithm explores the solution space more effectively, resulting in improved outcomes for the problem at hand. The results demonstrate significant flexibility in EH management and are extensively discussed. Simulation results indicate that integrating PEVs, FCPP, and DRPs can lead to reductions of 2 %, 7 %, and 11 % in the EH's operating costs, respectively. Furthermore, considering PEVs, FCPP, and DRPs can improve the EH's risk cost by 1.98 %, 6.7 %, and 10.5 %, respectively. Based on the numerical results, in Case 4 led to a remarkable 12.65 % reduction in operational costs while simultaneously achieving a 15.43 % decrease in emission costs, showcasing the effectiveness of the proposed approach in optimizing energy management in an energy hub system.

Crankshaft High-Cycle Bending Fatigue Experiment Design Method Based on Unscented Kalman Filtering and the Theory of Crack Propagation.

The high-cycle bending fatigue experiment is one of the most important necessary steps in guiding the crankshaft manufacturing process, especially for high-power engines. In this paper, an accelerated method was proposed to shorten the time period of this experiment. First, the loading period was quickened through the prediction of the residual fatigue life based on the unscented Kalman filtering algorithm approach and the crack growth speed. Then, the accuracy of the predictions was improved obviously based on the modified training section based on the theory of fracture mechanics. Finally, the fatigue limit load analysis result was proposed based on the predicted fatigue life and the modified SAFL (statistical analysis for the fatigue limit) method. The main conclusion proposed from this paper is that compared with the conventional training sections, the modified training sections based on the theory of fracture mechanics can obviously improve the accuracy of the remaining fatigue life prediction results, which makes this approach more suitable for the application. In addition, compared with the system's inherent natural frequency, the fatigue crack can save the experiment time more effectively and thus is superior to the former factor as the failure criterion parameter.

Peristalsis prevents ureteral dilation.

The etiology of ureteral dilation in primary nonrefluxing, nonobstructing megaureters is still not well understood. Impaired ureteral peristalsis has been theorized as one of the contributing factors. However, ureteral peristalsis and its "normal" function is not well defined. In this study, using mathematical modeling techniques, we aim to better understand how ureteral peristalsis works. This is the first model to consider clinically observed, back-and-forth, cyclic wall longitudinal motion during peristalsis. We hypothesize that dysfunctional ureteral peristalsis, caused by insufficient peristaltic amplitudes (e.g., circular muscle dysfunction) and/or lack of ureteral wall longitudinal motion (e.g., longitudinal muscle dysfunction), promotes peristaltic reflux (i.e., retrograde flow of urine during an episode of peristalsis) and may result in urinary stasis, urine accumulation, and consequent dilation. Based on lubrication theory in fluid mechanics, we developed a two-dimensional(planar) model of ureteral peristalsis. In doing so, we treated ureteral peristalsis as an infinite train of sinusoidal waves. We then analyzed antegrade and retrograde flows in the ureter under different bladder-kidney differential pressure and peristalsis conditions. There is a minimum peristaltic amplitude required to prevent peristaltic reflux. Ureteral wall longitudinal motion decreases this minimum required amplitude, increasing the nonrefluxing range of peristaltic amplitudes. As an example, for a normal bladder-kidney differential pressure of 5 cmH2 O, ureteral wall longitudinal motion increases nonrefluxing range of peristaltic amplitude by 65%. Additionally, ureteral wall longitudinal motion decreases refluxing volumetric flow rates. For a similar normal bladder pressure example of 5 cmH2 O, refluxing volumetric flow rate decreases by a factor of 18. Finally, elevated bladder pressure, not only increases the required peristaltic amplitude for reflux prevention but it increases maximum refluxing volumetric flow rates. For the case without wall longitudinal motion, as bladder-kidney differential pressure increases from 5 to 40 cmH2 O, minimum required peristaltic amplitude to prevent reflux increases by 40% while the maximum refluxing volumetric flow rate increases by approximately 100%. The results presented in this study show how abnormal ureteral peristalsis, caused by the absence of wall longitudinal motion and/or lack of sufficient peristaltic amplitudes, facilitates peristaltic reflux and retrograde flow. We theorize that this retrograde flow can lead to urinary stasis and urine accumulation in the ureters, resulting in ureteral dilation seen on imaging studies and elevated infection risk. Our results also show how chronically elevated bladder pressures are more susceptible to such refluxing conditions that could lead to ureteral dilation.

Multi-scale numerical simulation of fracture behavior for the gadolinia-doped ceria (GDC) under mechano-electrochemical coupling fields at high temperature

The fracture toughness of gadolinia-doped ceria (GDC) solid oxide fuel cells (SOFCs) electrolyte with a central crack is significantly reduced under the mechano-electrochemical coupling fields at high temperature. In this work, an atom-to-continuum (AtC) multi-scale method combining the finite element method (FEM) and the molecular dynamics (MD) simulation is developed. Firstly, the AtC multi-scale method is validated by investigating the uniaxial tensile stress–strain curves of GDC with a central crack at different temperatures. Then, based on the theory of fracture mechanics, the macrostructure of GDC is transformed into a microscopic intermediate transition model, and a detailed computational procedure for analyzing the fracture toughness of the macrostructure of the GDC is given by the AtC multi-scale method. Finally, the fracture toughness of GDC macrostructure under the mechano-electrochemical coupling fields is studied by the proposed approach. The simulation results show that the fracture toughness of 10GDC and 20GDC under the mechano-electrochemical coupling fields is clearly reduced compared to the uniaxial tensile loading. Among them, the fracture toughness of 10GDC under the mechano-electrochemical coupling fields is decreased by 12.28% and 30.67% at 800℃ and 900℃, and the fracture toughness of 20GDC under the mechano-electrochemical coupling fields is decreased by 17.25% and 29.52% at 800℃ and 900℃. These findings are critical in predicting the fracture behavior of GDC electrolyte under real working conditions.

Space-time is doomed! Introducing Planck scale physics in the classroom

This article provides an overview of some tentative ideas relating to Planck scale physics at a level suitable for advanced high school students, beginning undergraduate students, and teachers. After discussing the ratio of the electric and gravitational forces, Heisenberg’s uncertainty principle is combined with Einstein’s theory of special relativity to estimate the scale at which the strength of gravity becomes comparable to the electrostatic force. It is shown that the energy required to probe a region of space smaller than the Planck length may lead to the formation of a black hole, placing a fundamental lower limit on the distances that can be meaningfully probed in Nature. The Planck length, mass and time are then obtained using a combination of dimensional analysis and the fundamental constants appearing in theories of quantum mechanics, relativity and gravity. Finally, a heuristic derivation of the generalised uncertainty principle is provided.

Numerical Investigation of the Evolving Inelastic Deformation Path of a Solder Ball Joint under Various Loading Conditions

Solder joints of ball grid arrays (BGA) have been widely used to connect electronic components to printed circuit boards (PCBs) and are often subjected to mechanical stress. Several studies have been conducted on the mechanical reliability of solder joints. While these studies have been useful in the industry, detailed studies on how the inelastic deformation path of the solder ball joints evolves under specific loading conditions have not been sufficiently reported. This study aims to understand how the inelastic deformation path evolves when a solder joint is subjected to a constant external force by utilizing the theory of mechanics. It has also been found that the mechanical failure is strongly influenced by the evolution history of the deformation modes in materials. For this study, an elastoplastic constitutive model and a ductile fracture criterion were implemented into the vectorized user-defined material (VUMAT) subroutine of the ABAQUS program for finite element (FE) analysis. With the model, the evolution of the inelastic deformation path of a single solder ball under different loading conditions was numerically analyzed. Three loadings (shear, compression, and bending) were chosen as the basic loading conditions. In addition, combinations of the basic loadings resulted in three dual loadings and one complex loading. The simulation results showed that the shear and bending caused the fracture for both single and dual loadings, but when combined with compression, the fracture was suppressed. The results indicate that fracture is not solely determined by the magnitude of equivalent plastic strain but also by the evolution of inelastic deformation mode. This research offers an improved understanding of the significance of the inelastic deformation path and fracture.

Fracture prediction of solder joints using two-parameter fracture mechanics

Two-parameter fracture mechanics theory is a novel approach to investigate the fracture behavior of solder joints. The present study showed that the single-parameter fracture mechanics was not valid for evaluating the fracture behavior of these joints. Therefore, the ability of the two-parameter (J-Q) fracture mechanics method was assessed. J (critical strain energy release rate) and Q (The constraint parameter) parameters were calculated for the double cantilever beam (DCB) specimens. The two-parameter fracture mechanics theory was observed to be valid for the DCB specimens examined in this research. The J-Q loci extracted from two distinct experimental data sets (adherend thickness and loading arm variation) were coincident. The overlap of two J-Q locus curves indicates the uniqueness of the J-Q locus and capability to predict fracture load.

Abstract 11663: T Wave Alternans: A Clue in Plain Sight

Introduction: T-wave alternans (TWA) refers to the beat-to-beat variability in T-wave amplitudes or polarity on surface ECGs, and can signify susceptibility to malignant ventricular arrhythmias (VA). Aims: We present a case to emphasize the pathophysiology and clinical significance of this ECG finding. Case description: A 52 year-old female with history of HIV presents with shortness of breath and is treated for heart failure. In the ED, she has witnessed syncope and is found to have VT that progresses to VF. Resuscitation efforts are successful and include amiodarone loading. Figure 1A demonstrates baseline ECG on admission with a QTc of 495 ms. A few days later, an ECG reveals QTc of 696 ms with TWA (figure 1B). Shortly after, she develops polymorphic VT in the setting of long-short sequences and an R on T trigger (figure 1C) that is terminated with cardioversion. Review of pre-admission ECGs reveals that QTc prolongation occurred after initiation of a retroviral regimen that included rilpivirine and worsened with amiodarone. Both medications are discontinued, and she is eventually discharged with a QTc of 450 ms. Early theories for TWA's mechanism hypothesized that dispersion of refractoriness resulted in depolarization through alternating pathways and thus this phenomenon. Recent understanding further suggests that TWA occurs as a result of cellular alternans and variation in action potential duration due to dysregulation of repolarization. If discordant repolarization alternans ensues, whereby neighboring cells repolarize in opposite phases (long-short, short-long), the resultant repolarization gradient and heterogeneity in cellular repolarization serves as the substrate for VA; if a premature beat encounters refractory myocardium and unidirectional block occurs, a re-entrant excitation tachycardia can be initiated. Conclusions: TWA on ECG suggests myocardial electrical instability as a result of cellular repolarization inhomogeneity.

Algebraic Techniques for Canonical Forms and Applications in Split Quaternionic Mechanics

The algebra of split quaternions is a recently increasing topic in the study of theory and numerical computation in split quaternionic mechanics. This paper, by means of a real representation of a split quaternion matrix, studies the problem of canonical forms of a split quaternion matrix and derives algebraic techniques for finding the canonical forms of a split quaternion matrix. This paper also gives two applications for the right eigenvalue and diagonalization in split quaternionic mechanics.

Abstract 14751: A Rare Presentation of 5-Fluorouracil-Induced Cardiotoxicity

Background: 5-fluorouracil (5-FU) is associated with numerous cardiotoxic effects, most commonly chest pain and acute coronary syndrome. Less common effects include arrhythmias, myocarditis, pericarditis, and heart failure. We present a rare case of 5-FU causing cardiogenic shock. Case: A 54-year-old man with metastatic esophageal adenocarcinoma presented at 3:50 with chest pain that began the day before at 16:00, shortly after starting a 5-FU pump. Electrocardiogram (EKG) showed normal sinus rhythm with no ST or T wave changes. High sensitivity troponin T was 18 ng/L, followed by 24 ng/L at 1 hour and 81 ng/L at 6 hours. Computed tomography angiography (CTA) ruled out pulmonary embolism. Transthoracic echocardiogram (TTE) showed a globally reduced left ventricular ejection fraction (LVEF) of 35-40%. The patient received metoprolol and was scheduled for coronary CTA to investigate for coronary disease. Over the next few hours, he continued to report chest pain. Repeat troponin at 18:12 was 235 ng/L. Repeat EKG showed new anterior ST depressions. Posterior EKG did not show ST elevations. Repeat TTE revealed LVEF of 15%. The patient underwent left and right heart catheterization at 21:14, which showed normal coronary arteries, pulmonary artery pressure 50/31 mmHg (mean 38 mmHg), pulmonary capillary wedge pressure 36 mmHg, and cardiac index 1.1 L/min/m 2 . An Impella device was placed for circulatory support. He was treated with vasopressors and milrinone. Given concern for 5-FU toxicity, he received the antidote uridine triacetate 10 g IV every 6 hours for 5 days. LVEF improved to 70%. He was treated with nifedipine for possible coronary vasospasm. He was discharged 8 days later with heart failure medications. Conclusion: The incidence of cardiotoxicity from 5-FU ranges from 1.2-18%. Mechanistic theories include coronary vasospasm and direct cellular injury. Symptoms usually present within 12 hours of initiation but may present up to 2 days later. Management includes stopping the offending agent and starting anti-anginal drugs and uridine triacetate. Uridine triacetate is deacetylated to uridine, which prevents cell damage and death via competitive inhibition of 5-FU.

Accretion–ablation mechanics

In this paper, we formulate a geometric nonlinear theory of the mechanics of accreting–ablating bodies. This is a generalization of the theory of accretion mechanics of Sozio & Yavari (Sozio & Yavari 2019 J. Nonlinear Sci. 29 , 1813–1863 (doi:10.1007/s00332-019-09531-w)). More specifically, we are interested in large deformation analysis of bodies that undergo a continuous and simultaneous accretion and ablation on their boundaries while under external loads. In this formulation, the natural configuration of an accreting–ablating body is a time-dependent Riemannian 3 -manifold with a metric that is an unknown a priori and is determined after solving the accretion–ablation initial-boundary-value problem. In addition to the time of attachment map, we introduce a time of detachment map that along with the time of attachment map, and the accretion and ablation velocities, describes the time-dependent reference configuration of the body. The kinematics, material manifold, material metric, constitutive equations and the balance laws are discussed in detail. As a concrete example and application of the geometric theory, we analyse a thick hollow circular cylinder made of an arbitrary incompressible isotropic material that is under a finite time-dependent extension while undergoing continuous ablation on its inner cylinder boundary and accretion on its outer cylinder boundary. The state of deformation and stress during the accretion–ablation process, and the residual stretch and stress after the completion of the accretion–ablation process, are computed. This article is part of the theme issue ‘Foundational issues, analysis and geometry in continuum mechanics’.

Microscopic quantum mechanical Marcus theory for chemical reactions and its relationship to theButler‐Volmerequation used in redox flow battery analysis

AbstractThe vanadium redox flow battery has been intensively examined since the 1970s. What is missing is a connection between the current‐overpotential Butler‐Volmer equation, which provides an extremely helpful starting point for analytical and numerical studies, and microscopic quantum mechanical behavior at the atomic level. Such a connection will allow further advancements beyond the macroscopic, though very useful and insightful, modeling already done in the literature. Here we show rigorously the connection between the Butler‐Volmer transfer coefficients, and the Marcus Gibbs free energy quantum mechanical parameters, and develop the equation directly in terms of the quantum mechanical parameters.