Stable Relaxation Research Articles

Preparation and Mechanical Properties Analysis of Rare Earth Filling Ethylene‐Allene Monomer Rubber Composite

AbstractEthylene propylene diene monomer (EPDM) rubber is used in critical sectors such as national defense, military, and aerospace. However, it has performance limitations under high temperatures, affecting its dynamic mechanical properties, creep, and stress relaxation. To overcome these limitations, rare earth cerium oxide (CeO2) was incorporated as a filler into EPDM in this study, which enhances its properties and makes it suitable for the demanding applications. It could be seen that the CeO2‐enriched EPDM has significantly improved mechanical characteristics at elevated temperatures. The Young's modulus of CeO2‐enriched EPDM increased by about 100 %, while the energy storage modulus reaches a maximum increase of around 140 % at 165 °C. The addition of CeO2 improves its damping properties, provides better creep and stress relaxation resistance, and results in greater residual strain recovery. At room temperature, the impact on the stress relaxation rate at 50 % strain is minimal for the material EPDM, and it is almost negligible for the material EPDM/CeO2.These findings demonstrate that CeO2‐enriched EPDM has enhanced performance under high‐temperature conditions. Under elevated temperature conditions, EPDM enriched with CeO2 exhibits enhanced mechanical properties, superior creep resistance, and stable stress relaxation behavior, rendering it more adept at withstanding the rigorous conditions encountered in aerospace applications.

Stress relaxation aging of 7050 aluminum alloy under elastic and plastic loadings: A perspective from the geometrically necessary dislocations

Aerospace integral panels with large curvature often experience not only elastic loading but also plastic loading during creep age forming. However, the stress relaxation aging behaviors and mechanisms under loading stresses ranging from elastic to plastic regions, especially from the perspective of geometrically necessary dislocations (GNDs), have not been fully explored. The stress relaxation aging (SRA) behavior of 7050 aluminum alloy under elastic (200/250/300 MPa) and plastic loadings (350/400 MPa) are studied by uniaxial SRA, hardness and tensile tests, and corresponding mechanisms are clarified by Electron Back Scatter Diffraction (EBSD) tests and transmission electron microscopy (TEM) observations. Regardless of the loading stress, the stress relaxation of 7050 alloy shows a typical two-stage behavior (rapid stress reduction and stable stress relaxation rate). The second stage of stress relaxation under elastic loading shows an abnormal stress rebound, while the stress continuously decreases under plastic loading, and hardness and yield strength at 350 MPa are lower than that at 200 MPa during SRA. These results are attributed to strong dislocation pinning from small and dense precipitates at elastic loading and dislocations shearing large and sparse precipitates at plastic loading, respectively. Furthermore, both the stress reduction and its ratio increase with the increase of initial stress. GNDs contribute to the formation of low-angle grain boundaries (LAGBs) and accumulate at the LAGBs intersection to coordinate grain orientation for creep deformation. Compared to elastic loading, plastic loading promotes global growth of intragranular precipitates by elastic stress field and local heterogeneous nucleation and coarsening of precipitates at subgrain boundaries by more GNDs.

State-of-health estimation for lithium-ion batteries using relaxation voltage under dynamic conditions

The data-driven approach accurately estimates the state-of-health of lithium-ion batteries using online data, aiding consumers in operational and maintenance decisions. However, the stochastic charging and discharging behavior in realistic scenarios leads to continuous transient processes that render conventional features undetectable or exacerbate fluctuations. Here, we use domain knowledge and equivalent circuit modeling to investigate the extraction of physical features of aging through a relatively stable relaxation process under dynamic conditions. Our study uses 16-cell data from the National Aeronautics and Space Administration randomized dataset and compares four basic data-driven models for validation. The results show that incorporating a limited set of previous discharge step information significantly enhances model robustness and accuracy. The best-performing model, auto-relevance determination gaussian process regression, achieves a low root mean square error of 1.94 %. Physically interpretable features do not rely on historical data, require a smaller sample size, and exhibit greater generalizability across different current scenarios. This method does not depend on a specific charging method, making it practical and adaptable. Therefore, the data-driven approach utilizing relaxation voltages and correlation features offers a viable solution for accurately estimating the health state of lithium-ion batteries under dynamic conditions.

Slow–Fast Dynamics of a Piecewise-Smooth Leslie–Gower Model with Holling Type-I Functional Response and Weak Allee Effect

The slow–fast Leslie–Gower model with piecewise-smooth Holling type-I functional response and weak Allee effect is studied in this paper. It is shown that the model undergoes singular Hopf bifurcation and nonsmooth Hopf bifurcation as the parameters vary. The theoretical analysis implies that the predator’s food quality and Allee effect play an important role and lead to richer dynamical phenomena such as the globally stable equilibria, canard explosion phenomenon, a hyperbolically stable relaxation oscillation cycle enclosing almost two canard cycles with different stabilities and so on. Moreover, the predator and prey will coexist as multiple steady states or periodic oscillations for different positive initial populations and positive parameter values. Finally, we present some numerical simulations to illustrate the theoretical analysis such as the existence of one, two or three limit cycles.

The Relationship between the Measured Blood Concentration of Rocuronium in Stable Muscle Relaxation with a Closed-Loop Control and the Estimated Blood Concentration from a Pharmacokinetic Simulation.

We developed a system to adjust the rate of a continuous rocuronium (Rb) infusion to achieve 3 ≤ %T1 ≤ 10 with a closed-loop control. Samples were collected from 15 patients, and Rb blood concentrations were measured at the following time points: (1) when %T1 recovered to 3% or more after the initial Rb infusion; (2) when %T1 stabilized within the target range; (3) at the cessation of the Rb infusion; (4) 5 min after the sugammadex administration. The predicted Rb blood concentration at each time point was calculated and recorded using the pharmacokinetic parameters of Wierda et al. At time points (1), (2), and (3), the predicted blood concentrations were in good agreement with the measured values, but after the administration of sugammadex, the blood concentrations were higher than the predicted values because the Rb distributed in the tissues migrated into the blood. From the above, it was confirmed that the predicted blood concentration of Rb can be a good indicator for the automatic Rb administration control.

Naturally biocompatible melanin based iron-complex nanoparticles for pH-responsive magnetic resonance imaging

The sensitivity and diagnostic accuracy of magnetic resonance imaging mainly depend on the relaxation capacity of contrast agents (CAs) and their accumulated amount at the pathological region. Due to the better biocompatibility and high-spin capacity, Fe-complexes have been studied widely as an alternative to replace popular Gd-based CAs associated with potential biotoxicity. Compared with a variety of Fe complex-based CAs, such as small molecular, macrocyclic, multinuclear complexes, the form of nanoparticle exhibits outstanding longitudinal relaxation, but the clinical transformation was still limited by the inconspicuous difference of contrast between tumor and normal tissue. The enhanced effect of contrast is a positive relation as relaxation of CAs and their concentration in desired region. To specifically improve the amount of CAs accumulated in the tumor, pH-responsive polymer poly(2-ethyl-2-oxazoline) (PEOz) was modified on melanin, a ubiquitous natural pigment providing much active sites for chelating with Fe(III). The Fe(III)-Mel-PEOz we prepared could raise the tumor cell endocytosis efficiency via switching surface charge from anion to cation with the stimuli of the decreasing pH of tumor microenvironment. The change of pH has negligible effect on the r 1 of Fe(III)-Mel-PEOz, which is always maintained at around 1.0 mM−1s−1 at 0.5 T. Moreover, Fe(III)-Mel-PEOz exhibited low cytotoxicity, and satisfactory enhancement of positive contrast effect in vivo. The excellent biocompatibility and stable relaxation demonstrate the high potential of Fe(III)-Mel-PEOz in the diagnosis of tumor.

Oxide‐Based Electrolyte‐Gated Transistors with Stable and Tunable Relaxation Responses for Deep Time‐Delayed Reservoir Computing

AbstractTime‐delayed reservoir computing with marked strengths of friendly hardware implementation and low training cost is regarded as a promising solution to realize time and energy‐efficient time series information processing and thus receives growing attention. However, achieving a sufficient number of reproducible reservoir states remains a significant challenge, which severely limits its computing performance. Here, an electric‐double‐layer‐coupled oxide‐based electrolyte‐gated transistor with a shared gate and varying channel lengths is developed to construct a deep time‐delayed reservoir computing system. A variety of short‐term synaptic responses related to inherent ion‐electron‐coupled dynamics at the electrolyte/channel interface are demonstrated, reflecting a flexibly regulable channel current. Different stable and tunable relaxation responses corresponding to varying channel lengths are obtained to enrich reservoir states combined with virtual nodes ways. The spoken‐digit classification and Hénon map prediction tasks are implemented with high accuracy (≈92.2%) and ultralow normalized root mean square error (≈0.013), respectively, validating the significant improvement of the computing performance by introducing additional relaxation responses. This work opens a promising pathway in exploiting oxide‐based electrolyte‐gated transistors for realizing temporal information processing hardware systems.

Relaxation Oscillation in SEIR Epidemic Models with the Intrinsic Growth Rate

The periodic oscillation transmission of infectious diseases is widespread, deep understanding of this periodic pattern and exploring the generation mechanism, and identifying the specific factors that lead to such periodic outbreaks, which are of very importanceto predict and control the spread of infectious diseases. In this study, to further reveal the mathematical mechanism of spontaneous generation of periodic oscillation solution, we investigate a type of SEIR epidemic model with a small intrinsic growth rate. By utilizing the singular perturbation theory and center manifold theorem, we extend the relaxation oscillation of three‐dimensional SIR models to the four‐dimensional SEIR models and prove the existence of stable relaxation oscillation with a large amplitude in the model. Numerical simulations are performed to verify our theoretical results. The results presented in this study provide a new idea for the study of the intrinsic mechanism of periodic oscillation in epidemiology, enrich the dynamics of epidemic models, and deepen the understanding of the global dynamics of these models.

A class of unconditionally energy stable relaxation schemes for gradient flows

In this paper, a novel class of unconditionally energy stable schemes are constructed for solving gradient flow models by combining the relaxed scalar auxiliary variable (SAV) approach with the linear multistep technique. The main idea is first to rewrite the original model as an equivalent system, and then the linear multistep method in time, together with the relaxation strategy is employed to compute the solution of the reformulated system. The main benefit of the proposed schemes is that it can achieve second-order temporal accuracy and strictly unconditional energy stability, as well as a quite close to, and in many cases equal to, the original energy than the baseline SAV approaches. Finally, ample numerical experiments for the Allen–Cahn equation and Cahn–Hilliard equation are presented to confirm the efficiency, accuracy and strictly unconditional energy stability of the proposed schemes.

Quantitative Evaluation of Thermal Ageing State of Cross-Linked Polyethylene Insulation Based on Polarization and Depolarization Current

The widespread use of cross-linked polyethylene (XLPE) as insulation in cables may be attributed to its outstanding mechanical and dielectric properties. In order to quantitatively evaluate the insulation status of XLPE after thermal ageing, an accelerated thermal ageing experimental platform is established. Polarization and depolarization current (PDC) as well as elongation at break of XLPE insulation under different ageing durations are measured. XLPE insulation state is determined by the elongation at break retention rate (ER%). Based on the extended Debye model, the paper proposed the stable relaxation charge quantity and the dissipation factor at 0.1 Hz to evaluate the insulation state of XLPE. The results show that the ER% of XLPE insulation decreases with the growth of ageing degree. The polarization and depolarization current of XLPE insulation will increase obviously with thermal ageing. Conductivity and trap level density will also increase. The number of branches of the extended Debye model increases, and new polarization types appear. Stable relaxation charge quantity and dissipation factor at 0.1 Hz proposed in this paper have a good fitting relationship with ER% of XLPE insulation, which can evaluate the thermal ageing state of XLPE insulation effectively.

Influence of Discretization on the Speed Gradient Synchronization Control

Increasing the productivity of technological operations is a current task of modern science. The introduction of modern industrial equipment control systems is associated with the digitalization and computerization of enterprises. Vibration technology is one of the common types of industrial equipment used for screening, crushing, vibratory movement, etc. The energy approach for the vibration setups control makes it possible to keep a constant level of total energy of vibration setup oscillations, which makes it possible to develop intelligent control system under conditions of uncertainty in the parameter space. This paper is devoted to the study of the influence of digitalization and discretization on the speed gradient algorithm operation for the multiple synchronization control of vibration setup rotors and evaluation of the critical sensor signals sampling steps. The paper presents the results of numerical simulation based on the system dynamics equations and approximate values of vibration setup parameters. The simulation results present that an increase of the discretization sampling step leads to a disruption of the multiple synchronization mode up to the stability loss. The results of an experimental study on a mechatronic vibration setup SV-2M demonstrate in normal operation mode the low-frequency oscillations of the rotors speeds and the total system energy, which frequency is determined by the control signal limit. When the discretization step increase, the motion with stops is observed, which has a similar nature with the stable relaxation self-oscillations. The practical relevance of the obtained results is a detection of possible effects that occur in the system with significant discretization steps. Further development of adaptive control systems can be aimed to compensating of the discretization effect on the operation of the speed gradient control of the vibration setup rotors synchronization.

A New Approach to Capacitive Sensor Measurements Based on a Microcontroller and a Three-Gate Stable RC Oscillator

A complete smart capacitive sensor solution based on a microcontroller was developed. This approach includes the development of both the hardware and software. The hardware part comprises an 8-bit microcontroller equipped with two timers/counters and a three-gate stable RC relaxation oscillator. The software part handles system configuration, measurement control, communication control, and data processing. Hence, the microcontroller acts as a frequency meter with an adaptive measuring time, and the relaxation oscillator generates a square wave with a frequency depending on the value of the capacitance of the sensor. The paper also proposes a calibration method that reduces the measurement range to 1 pF. The experimentally proven relative measurement errors of sensor capacitance are less than 0.012% for values smaller than 12 pF, and less than 0.0084% for values from 12 pF to 300 pF.

Coupled bond dynamics alters relaxation in polymers with multiple intrinsic dissociation rates.

Dynamic networks containing multiple bond types within a continuous network grant engineers another design parameter - relative bond fraction - by which to tune storage and dissipation of mechanical energy. However, the mechanisms governing emergent properties are difficult to deduce experimentally. Therefore, we here employ a network model with prescribed fractions of dynamic and stable bonds to predict relaxation characteristics of hybrid networks. We find that during stress relaxation, predominantly dynamic networks can exhibit long-term moduli through conformationally inhibited relaxation of stable bonds due to exclusion interactions with neighboring chains. Meanwhile, predominantly stable networks exhibit minor relaxation through non-affine reconfiguration of dynamic bonds. Given this, we introduce a single fitting parameter, ξ, to Transient Network Theory via a coupled rule of mixture, that characterizes the extent of stable bond relaxation. Treating ξ as a fitting parameter, the coupled rule of mixture's predicted stress response not only agrees with the network model's, but also unveils likely micromechanical traits of gels hosting multiple bond dissociation timescales.

Entropy–Preserving and Entropy–Stable Relaxation IMEX and Multirate Time–Stepping Methods

We propose entropy-preserving and entropy-stable partitioned Runge–Kutta (RK) methods. In particular, we extend the explicit relaxation Runge–Kutta methods to IMEX–RK methods and a class of explicit second-order multirate methods for stiff problems arising from scale-separable or grid-induced stiffness in a system. The proposed approaches not only mitigate system stiffness but also fully support entropy-preserving and entropy-stability properties at a discrete level. The key idea of the relaxation approach is to adjust the step completion with a relaxation parameter so that the time-adjusted solution satisfies the entropy condition at a discrete level. The relaxation parameter is computed by solving a scalar nonlinear equation at each timestep in general; however, as for a quadratic entropy function, we theoretically derive the explicit form of the relaxation parameter and numerically confirm that the relaxation parameter works the Burgers equation. Several numerical results for ordinary differential equations and the Burgers equation are presented to demonstrate the entropy-conserving/stable behavior of these methods. We also compare the relaxation approach and the incremental direction technique for the Burgers equation with and without a limiter in the presence of shocks.

Nested mixed-mode oscillations in a canard-generating driven Bonhoeffer–van der Pol oscillator

In previous works (Inaba and Kousaka, 2020; Inaba and Tsubone, 2020), the existence of nested mixed-mode oscillation (MMO) bifurcation structures, generated by a driven slow–fast Bonhoeffer–van der Pol (BVP) oscillator, was confirmed. This oscillator has a stable focus and a stable relaxation oscillation caused by a subcritical Hopf bifurcation in the absence of perturbation. In this study, we assert that nested MMOs in this circuit can occur regardless of whether the oscillation is caused by a supercritical or subcritical Hopf bifurcation when no perturbation is applied, and that therefore, this phenomenon could be widespread. We show that MMOs that occur under weak periodic perturbations, generated in a classical BVP oscillator, where the oscillation is caused by a supercritical Hopf bifurcation, can be at least doubly nested. To show that nested MMOs can be at least doubly nested, we utilize first return plots, which are approximated one-dimensional maps and well explain mixed-mode oscillation-incrementing bifurcations.

Correlation of Relaxation Modeling Parameters of the Studied Polymer Blends at the Air/Water Interface

The main studied mixed monolayers consisting of polyethylene-block-polycaprolactone ( PEO-b-PCL) and its component polymers with poly( vinyl phenol). It was shown previously that most of the area relaxation process of mixed monolayers could be well represented by a model considering the nucleation and growth mechanisms. The characteristic exponent x values were found to be slightly temperature dependent. The kx values were detected to decrease with increasing temperature. When PVPh was added into the most unstable PEO, the mixed monolayer films exhibited a remarkably improved stable relaxation behavior than PCL (or PEO-b-PCL). The characteristic exponent x and kx values were plotted vesus the A∞/A0 values. Mostly increasing characteristic exponent x and kx values with increasing A∞/A0 values were observed. For the PCL and PVPh monolayers, the xkx values were detected to increase with increasing A∞/A0 values. The xkx values of previously published stereoregular and different molecular weight PMMAs were also demonstrated to become larger with the increasing A∞/A0 values.

Process-Oriented Geometric Singular Perturbation Theory and Calcium Dynamics

Phenomena in chemistry, biology and neuroscience are often modelled using ordinary differential equations (ODEs) in which the right-hand-side is comprised of terms which correspond to individual 'processes' or 'fluxes'. Frequently, these ODEs are characterised by multiple time-scale phenomena due to order of magnitude differences between contributing processes and the presence of switching, i.e., dominance or sub-dominance of particular terms as a function of state variables. We outline a heuristic procedure for the identification of small parameters in ODE models of this kind, with a particular emphasis on the identification of small parameters relating to switching behaviours. This procedure is outlined informally in generality, and applied in detail to a model for intracellular calcium dynamics characterised by switching and multiple (more than two) time-scale dynamics. A total of five small parameters are identified, and related to a single perturbation parameter by a polynomial scaling law based on order of magnitude comparisons. The resulting singular perturbation problem has a time-scale separation which depends on the region of state space. We prove the existence and uniqueness of stable relaxation oscillations with three distinct time-scales using a coordinate-independent formulation of GSPT in combination with the blow-up method. We also provide an estimate for the period of the oscillations, and consider a number of possibilities for their onset under parameter variation.

Leading edge maintenance in migrating cells is an emergent property of branched actin network growth.

Animal cell migration is predominantly driven by the coordinated, yet stochastic, polymerization of thousands of nanometer-scale actin filaments across micron-scale cell leading edges. It remains unclear how such inherently noisy processes generate robust cellular behavior. We employed high-speed imaging of migrating neutrophil-like HL-60 cells to explore the fine-scale shape fluctuations that emerge and relax throughout the process of leading edge maintenance. We then developed a minimal stochastic model of the leading edge that reproduces this stable relaxation behavior. Remarkably, we find lamellipodial stability naturally emerges from the interplay between branched actin network growth and leading edge shape - with no additional feedback required - based on a synergy between membrane-proximal branching and lateral spreading of filaments. These results thus demonstrate a novel biological noise-suppression mechanism based entirely on system geometry. Furthermore, our model suggests that the Arp2/3-mediated ~70-80° branching angle optimally smooths lamellipodial shape, addressing its long-mysterious conservation from protists to mammals.

An abdominal phantom with anthropomorphic organ motion and multimodal imaging contrast for MR-guided radiotherapy

Purpose. Improvements in image-guided radiotherapy (IGRT) enable accurate and precise treatment of moving tumors in the abdomen while simultaneously sparing healthy tissue. However, the lack of validation tools for newly developed MR-guided radiotherapy hybrid devices such as the MR-Linac is an open issue. This study presents a custom developed abdominal phantom with respiratory organ motion and multimodal imaging contrast to perform end-to-end tests for IGRT treatment planning scenarios. Methods. The abdominal phantom contains deformable and anatomically shaped liver and kidney models made of Ni-DTPA and KCl-doped agarose mixtures that can be reproducibly positioned within the phantom. Organ models are wrapped in foil to avoid ion exchange with the surrounding agarose and to provide stable T1 and T2 relaxation times as well as HU numbers. Breathing motion is realized by a diaphragm connected to an actuator that is hydraulically controlled via a programmable logic controller. With this system, artificial and patient-specific breathing patterns can be carried out. In 1.5 T magnetic resonance imaging (MRI), diaphragm, liver and kidney motion was measured and compared to the breathing motion of a healthy male volunteer for different breathing amplitudes including shallow, normal and deep breathing. Results. The constructed abdominal phantom demonstrated organ-equivalent intensity values in CT as well as in MRI. T1-weighted (T1w) and T2-weighted (T2w) relaxation times for 1.5 T and CT numbers were 552.9 ms, 48.2 ms and 48.8 HU (liver) as well as 950.42 ms, 79 ms and 28.2 HU (kidney), respectively. These values were stable for more than six months. Extracted breathing motion from a healthy volunteer revealed a liver to diaphragm motion ratio (LDMR) of 64.4% and a kidney to diaphragm motion ratio (KDMR) of 30.7%. Well-comparable values were obtained for the phantom (LDMR: 65.5%, KDMR: 27.5%). Conclusions. The abdominal phantom demonstrated anthropomorphic T1 and T2 relaxation times as well as HU numbers and physiological motion pattern in MRI and CT. This allows for wide use in the validation of IGRT including MRgRT.

Canards and homoclinic orbits in a slow-fast modified May-Holling-Tanner predator-prey model with weak multiple Allee effect

<p style='text-indent:20px;'>This paper studies bifurcations of canards and homoclinic orbits in a slow-fast modified May-Holling-Tanner predator-prey model with weak multiple Allee effect. Based on geometric singular perturbation theory (GSPT) and canard theory, canard explosion is observed and the associated bifurcation curve is determined. Due to the canard point, a homoclinic orbit with slow and fast segments and homoclinic to a saddle can also exist, in which, the stable and unstable manifolds of the saddle are connected under certain parameter value. By analyzing the slow divergence integral, it is proved that the cyclicity of canard cycles in this model is at most four. Finally, by calculating the entry-exit function explicitly, a unique, orbitally stable canard relaxation oscillation passing through a transcritical bifurcation point is detected. All these theoretical predictions on the birth of canard explosion, canard limit cycles and homoclinic orbits are verified by numerical simulations.</p>