Relaxation Function Research Articles

A Comparative View of Becker, Lomnitz, and Lambert Linear Viscoelastic Models

We compare the classical viscoelastic models due to Becker and Lomnitz with respect to a recent viscoelastic model based on the Lambert W function. We take advantage of this comparison to derive new analytical expressions for the relaxation spectrum in the Becker and Lomnitz models, as well as novel integral representations for the retardation and relaxation spectra in the Lambert model. In order to derive these analytical expressions, we have used the analytical properties of the exponential integral and the Lambert W function, as well as the Titchmarsh’s inversion formula of the Stieltjes transform. In addition, we prove some interesting inequalities by comparing the different models considered, as well as the non-negativity of the retardation and relaxation spectral functions. This means that the complete monotonicity of the rate of creep and the relaxation functions is satisfied, as required by the classical theory of linear viscoelasticity.

Acute kidney disease in mice is associated with early cardiovascular dysfunction

Acute kidney injury (AKI) and chronic kidney disease (CKD) are major health concerns due to their increasing incidence and high mortality. They are interconnected syndromes; AKI without recovery evolves into acute kidney disease (AKD), which can indicate an AKI-to-CKD transition. Both AKI and CKD are associated with a risk of long-term cardiovascular complications, but whether vascular and cardiac dysfunctions can occur as early as the AKD period has not been studied extensively. In a mouse model of kidney injury (KI) with non-recovery, we performed vasoreactivity and echocardiography analyses on days 15 (D15) and 45 (D45) after KI. We determined the concentrations of two major gut-derived protein-bound uremic toxins known to induce cardiovascular toxicity—indoxyl sulfate (IS) and para-cresyl sulfate (PCS)—and the levels of inflammation and contraction markers on D7, D15, and D45. Mice with KI showed acute tubular and interstitial kidney lesions on D7 and D15 and chronic glomerulosclerosis on D45. They showed significant impairment of aorta relaxation and systolic-diastolic heart function, both on D15 and D45. Such dysfunction was associated with downregulation of the expression of two contractile proteins, αSMA and SERCA2a, with a more pronounced effect on D15 than on D45. KI was also followed by a rapid increase in IS and PCS serum concentrations and the expression induction of pro-inflammatory cytokines and endothelial adhesion molecules in serum and cardiovascular tissues. Therefore, these results highlight that AKD leads to early cardiac and vascular dysfunctions. How these dysfunctions could be managed to prevent cardiovascular events deserves further study.

Are pelvic floor muscle function, quadriceps femorismuscle, gluteus mediusmuscle, hand grip strength and functional performance affected by incontinence types in elderly people with urinary incontinence?

The aim of this study is to examine the relationship between incontinence type and pelvic floor muscle function, gluteus mediusmuscle, quadriceps femorismuscle, hand grip strength, functional performance and balance in elderly people with incontinence. This cross-sectional study was conducted in a nursing home with 78 elderly people with stress (SUI, n: 20), urgency (UUI, n: 27) and mixed (MUI, n: 31) urinary incontinence. "Urogenital Distress Inventory-6, Incontinence Impact Questionnaire Form-7, Overactive Bladder-8" were used to evaluate incontinence symptoms and severity. Superficial electromyography was used to evaluate the function of the PFM. A hand dynamometer was used to evaluate hand grip strength, and a digital manual muscle tester was used to evaluate quadriceps femoris (QF) and gluteus medius muscle strength. Short Physical Performance Battery and Time Up and Go Test were performed for functional performance. There was no significant difference between PFM contraction and relaxation functions, gluteus medius, QF muscle strength, functional performance (p > 0.05) but hand grip strength was highest in the group with UUI (ptotal: 0.022).The group with the highest rate of low hand grip strength is MUI (38.7%). A weak positive correlation was found between QF muscle strength and PFM Work Average value in the MUI group (r: 0.370, p: 0.048). In the MUI group, a moderate positive correlation was found between hand grip strength and gluteus medius muscle strength (r: 0.499, p: 0.005). Our findings show that hand grip strength is related to the type of incontinence in the elderly people. The average hand grip strength was highest in the elderly people with UUI. Additionally, there was a positive relationship between gluteus medius and hang grip strength in MUI. It may provide guidance for evaluation and risk factors in elderly people with incontinence.

Magneto-viscoelastic rod model for hard-magnetic soft rods under 3D large deformation: Theory and numerical implementation

The main purpose of this work is to develop a three-dimensional (3D) viscoelastic rod model for hard-magnetic soft (HMS) rods under large deformation which are widely used active structures in soft robotics. To do so, the Simo’s viscoelasticity theory has been rationally incorporated into the geometrically exact 3D curved rod model. The proposed model includes the deformation modes of axial tension, shear, bending, and torsion, which is applicable to the HMS rods with arbitrarily initial curved and twisted geometries under 3D large deformation. The viscoelastic constitutive equations of the HMS rod in the present formulation are formulated, which include the general relaxation functions. To obtain the expression for the magnetic load, the rotation-based magnetic free energy density is introduced, and the governing equations of the HMS rod with magnetic load and body force are presented. To obtain the numerical implementation, an implicit time integration algorithm that simply extends the generalized-α method for the rotation group, and the corresponding variational formulation and its linearization of the rod model are derived. To validate the model, five numerical examples, including 2D dynamic buckling, 3D static, and 3D dynamic problem are presented. The dynamic problems include the dynamic snap-through behavior of a bistable HMS arch and damped oscillation of a quarter arc cantilever under 3D deformation. The simulation results show good agreement with the results reported in the literature.

A hybrid SPH model of the Navier-Stokes and Boussinesq equations for simulating wave propagation and deformation

A two-way hybrid model based on the smoothed particle hydrodynamics (SPH) method is proposed in this paper to simulate wave propagation and deformation effectively. The hybrid model is composed of two submodels: the first submodel is based on the Boussinesq equations (B-SPH) for simulating wave propagation, and the second submodel is based on the Navier-Stokes (N-S) equations (NS-SPH) for simulating wave deformation caused by interactions with structures. The exchange of information between the two submodels is realized through an open-boundary method: the results derived from the B-SPH submodel are transferred to the open boundaries of the NS-SPH submodel through a relaxation function; the information derived from the NS-SPH submodel is matched to the open boundaries of the B-SPH submodel through the continuity equation. To obtain a stable pressure field in the NS-SPH submodel, the particle shifting technique (PST) is implemented. The subsequent validation of the hybrid model includes four typical numerical examples related to solitary and regular waves. The agreement between the numerical results and the experimental data indicates that the proposed hybrid model is suitable for simulating the propagation and deformation of shallow water waves. Compared with the traditional NS-SPH model, which uses N-S equations to describe the whole fluid domain, the hybrid model has greater computational efficiency.

Relaxed Control Barrier Function Based Control for Closest Approach by Underactuated USVs

Relaxed Control Barrier Function Based Control for Closest Approach by Underactuated USVs

Human induced pluripotent stem cell-derived cardiomyocytes to study inflammation-induced aberrant calcium transient.

Heart failure with preserved ejection fraction (HFpEF) is commonly found in persons living with HIV (PLWH) even when antiretroviral therapy suppresses HIV viremia. However, studying this condition has been challenging because an appropriate animal model is not available. In this article, we studied calcium transient in human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs) in culture to simulate the cardiomyocyte relaxation defect noted in PLWH and HFpEF and assess whether various drugs have an effect. We show that treatment of hiPSC-CMs with inflammatory cytokines (such as interferon-γ or TNF-α) impairs their Ca2+ uptake into sarcoplasmic reticulum and that SGLT2 inhibitors, clinically proven as effective for HFpEF, reverse this effect. Additionally, treatment with mitochondrial antioxidants (like mito-Tempo) and certain antiretrovirals resulted in the reversal of the effects of these cytokines on calcium transient. Finally, incubation of hiPSC-CMs with serum from HIV patients with and without diastolic dysfunction did not alter their Ca2+-decay time, indicating that the exposure to the serum of these patients is not sufficient to induce the decrease in Ca2+ uptake in vitro. Together, our results indicate that hiPSC-CMs can be used as a model to study molecular mechanisms of inflammation-mediated abnormal cardiomyocyte relaxation and screen for potential new interventions.

The Type and Function of Floor Area Ratio Relaxation in South Korea

We live in a world where floor area ratio(“FAR”) dominate. Floor area ratio is expressed as a percentage and is regarded as technical, but the difference in that percentage determines the price of the land, the height and shape of the building that can be built, and the success or failure of various construction projects. However, it is difficult for us to grasp the meaning of relaxing floor area ratio to 400%, and how far it can be relaxed. Large cities with limited land area have reached the limits of their horizontal expansion. High-rise buildings have become a low-cost solution to housing problems by vertically expanding scarce land. The method of solving housing problems through high-rise buildings has been used worldwide and is welcomed as a way to accommodate large-scale populations at low cost. The policy of easing floor area ratio in South Korea played an important role in solving housing problems. The government have been utilizing the policy of relaxing FAR to supply high-quality housing to the metropolitan area, stimulate the construction economy, and improve outdated urban infrastructure. Relaxing FAR is widely used in Korea because the interests of the major players in the dynamics surrounding FAR are consistent. Ordinary people without a house have the opportunity to obtain a new house in the space created through an increase in FAR. In addition, landowners can benefit from increase land prices by increasing their FAR. For business operators in reconstruction or redevelopment, FAR increase works as a factor that determines the profitability of the project. While the government uses FAR as a tool to realize a comfortable residential space, it is possible to balanced development and sustainable growth. Local governments can revive the economy in their jurisdiction by raising FAR and securing the necessary facilities, such as expanding infrastructure. This paper aims to examine the history of laws and regulations on how the relaxation of FAR has been introduced and developed in our legal system. The types of FAR relaxation were classified into four types; under the Building Act and the Urban Planning Act, district unit planning type, Zoning type, and other legislative type. The function of FAR relaxation for each type is to provide a clue for inferring the legal nature of FAR and predicting the future of FAR. This paper makes a contribution to understanding urban planning by providing a new case study of relaxing FAR focused in South Korea.

Comparison of energy conservation strategies for 5G NR RedCap service in industrial environment

The recently standardized reduced capability (RedCap) type of user equipment (UE) for 5G New Radio (NR) systems offers a useful option for energy-constrained devices. By utilizing a combination of discontinuous reception (DRX), wake-up signal (WUS), and radio resource management (RRM) relaxation functions, RedCap UE may provide excellent power efficiency for a large set of applications. In this study, we investigate power efficiency and battery lifetime for RedCap UEs for different types of applications and various combinations of energy conservation mechanisms. We utilize extended virtual reality (X-VR) and web browsing as applications of interest. To this aim, we develop a versatile mathematical framework representing the sought metrics as a function of time, accounting for specifics of millimeter wave (mmWave) propagation, micro- and macro-mobility of UEs, human body blockage, and type of application. Numerically, we show that higher micro- and macro-mobility speeds lead to worse power efficiency and the loss can be quite substantial amounting up to 30%. Antenna arrays with worse directivity show better performance in the presence of micro- and macro-mobilities when RRM Relaxation is utilized, with a difference between 15×15 and 4×4 arrays reaching 1.5 bit/J/KHz, which is approximately 40%. The energy conservation mechanisms produce no noticeable impact on the power efficiency and battery lifetime for rate-greedy applications such as X-VR. Low-data-rate applications with long pauses between transmission cycles, such as web browsing, may benefit from utilizing WUS and RRM Relaxation in addition to conventional DRX. However, their impact is rather small at a scale of 5%–10%.

Finite-time property of a mechanical viscoelastic system with nonlinear boundary conditions on corner-Sobolev spaces

In this article, we deal with the initial boundary value problem for a viscoelastic system related to the quasilinear parabolic equation with nonlinear boundary source term on a manifold $\mathbb{M}$ with corner singularities. We prove that, under certain conditions on relaxation function $g$, any solution $u$ in the corner-Sobolev space $\mathcal{H}^{1,(\frac{N-1}{2},\frac{N}{2})}_{\partial^{0}\mathbb{M}}(\mathbb{M})$ blows up in finite time. The estimates of the life-span of solutions are also given.

Different aspects of blow-up property for a nonlinear wave equation

In this work, we are concerned with a nonlinear wave equation with variable exponents. In the presence of the logarithmic nonlinear source, we established a global nonexistence result with negative initial data and without imposing the Sobolev Logarithmic Inequality. The blow-up time is established with upper bound and lower bound. In addition, under some conditions on the initial data and for a specific class of relaxation functions, we established an infinite time blow-up result.

General Relations between Stress Fluctuations and Viscoelasticity in Amorphous Polymer and Glass-Forming Systems.

Mechanical stress governs the dynamics of viscoelastic polymer systems and supercooled glass-forming fluids. It was recently established that liquids with long terminal relaxation times are characterized by transiently frozen stress fields, which, moreover, exhibit long-range correlations contributing to the dynamically heterogeneous nature of such systems. Recent studies show that stress correlations and relaxation elastic moduli are intimately related in isotropic viscoelastic systems. However, the origin of these relations (involving spatially resolved material relaxation functions) is non-trivial: some relations are based on the fluctuation-dissipation theorem (FDT), while others involve approximations. Generalizing our recent results on 2D systems, we here rigorously derive three exact FDT relations (already established in our recent investigations and, partially, in classical studies) between spatio-temporal stress correlations and generalized relaxation moduli, and a couple of new exact relations. We also derive several new approximate relations valid in the hydrodynamic regime, taking into account the effects of thermal conductivity and composition fluctuations for arbitrary space dimension. One approximate relation was heuristically obtained in our previous studies and verified using our extended simulation data on two-dimensional (2D) glass-forming systems. As a result, we provide the means to obtain, in any spatial dimension, all stress-correlation functions in terms of relaxation moduli and vice versa. The new approximate relations are tested using simulation data on 2D systems of polydisperse Lennard-Jones particles.

Generalized Linear Response Theory for the Full Quantum Work Statistics.

We consider a quantum system driven out of equilibrium via a small Hamiltonian perturbation. Building on the paradigmatic framework of linear response theory (LRT), we derive an expression for the full generating function of the dissipated work. Remarkably, we find that all information about the distribution can be encoded in a single quantity, the standard relaxation function in LRT, thus opening up new ways to use phenomenological models to study nonequilibrium fluctuations in complex quantum systems. Our results establish a number of refined quantum thermodynamic constraints on the work statistics that apply to regimes of perturbative but arbitrarily fast protocols, and do not rely on assumptions such as slow driving or weak coupling. Finally, our approach uncovers a distinctly quantum signature in the work statistics that originates from underlying zero-point energy fluctuations. This causes an increased dispersion of the probability distribution at short driving times, a feature that can be probed in efforts to witness nonclassical effects in quantum thermodynamics.

Low Calcium-High Magnesium Krebs-Henseleit Solution Combined with Adenosine and Lidocaine Improved Rat Aortic Function and Structure Following Cold Preservation.

Background and objectives: The main problem of vascular preservation is the maintenance of vessel graft quality and function following extended storage. Conventional preservation solutions such as histidine-tryptophan-ketoglutarate (HTK) solution, Phosphate-Buffer Solution (PBS), or sodium chloride 0.9% has been shown to be inadequate in preserving vascular physiological function after 3 days of cold storage. This study aimed to evaluate whether adenosine and lidocaine (AL) in a modified Krebs-Henseleit (KH) solution can preserve the function and histological structure of rat aortic rings after 6 days. Materials and Methods: Thirty-five aortic rings from male Wistar rats (200-300 g) were harvested and immediately immersed in one of the assigned cold preservation solutions: standard KH, modified KH (mod KH) with lower calcium (Ca2+) and higher magnesium content (Mg2+) with or without adenosine and lidocaine (mod KH-AL), and modified KH with AL, insulin, and melatonin (Mod KH-ALMI). The contraction and relaxation function of the aortic rings were examined using an isometric force transducer after 6 days of cold preservation. Hematoxylin and eosin staining were used to analyze the rings' histological structure. Results: Vascular contraction and relaxation functions were severely affected after a 6-day cold storage period in standard KH. Modifying the KH solution by reducing the Ca2+ and increasing the Mg2+ levels greatly recovered the vessel functions. The addition of AL or ALMI to the modified KH did not further recover vascular contractility. However, only the addition of AL to the modified KH increased the ACh-induced relaxation at 6 days when compared to the conventional KH, suggesting that endothelium preservation is improved. From histological analysis, it was found that the addition of AL but not ALMI further improved the endothelial lining and the structure of the elastic membrane layers of the preserved vessels after 6 days of cold preservation. Conclusions: The addition of AL to low calcium-high magnesium KH solution significantly enhanced endothelial preservation and improved endothelial-induced relaxation of preserved vessels after 6 days of cold storage.

Factors influencing airway smooth muscle tone: a comprehensive review with a special emphasis on pulmonary surfactant.

A thin film of pulmonary surfactant lines the surface of the airways and alveoli, where it lowers the surface tension in the peripheral lungs, preventing collapse of the bronchioles and alveoli and reducing the work of breathing. It also possesses a barrier function for maintaining the blood-gas interface of the lungs and plays an important role in innate immunity. The surfactant film covers the epithelium lining both large and small airways, forming the first line of defense between toxic airborne particles/pathogens and the lungs. Furthermore, surfactant has been shown to relax airway smooth muscle (ASM) after exposure to ASM agonists, suggesting a more subtle function. Whether surfactant masks irritant sensory receptors or interacts with one of them is not known. The relaxant effect of surfactant on ASM is absent in bronchial tissues denuded of an epithelial layer. Blocking of prostanoid synthesis inhibits the relaxant function of surfactant, indicating that prostanoids might be involved. Another possibility for surfactant to be active, namely through ATP-dependent potassium channels and the cAMP-regulated epithelial chloride channels [cystic fibrosis transmembrane conductance regulators (CFTRs)], was tested but could not be confirmed. Hence, this review discusses the mechanisms of known and potential relaxant effects of pulmonary surfactant on ASM. This review summarizes what is known about the role of surfactant in smooth muscle physiology and explores the scientific questions and studies needed to fully understand how surfactant helps maintain the delicate balance between relaxant and constrictor needs.

Dimethyl Fumarate Prevents the Development of Chronic Social Stress-Induced Hypertension in Borderline Hypertensive Rats.

This study investigated the effects of chronic crowding-induced social stress and dimethyl fumarate (DMF) on borderline hypertensive rats, focusing on the transcription nuclear factor (erythroid-derived 2)-like 2 (NRF2) gene Nfe2l2, on the expression of selected NFR2-mediated gene expressions in the heart, and on vascular function. Rats were exposed to chronic crowding, DMF treatment (30 mg/kg/day, p.o.), or a combination of both for six weeks. Blood pressure (BP) was measured non-invasively, gene expressions were analysed using RT-qPCR, and vascular function was assessed by measuring noradrenaline (NA)-induced vasoconstriction and endothelium-dependent and -independent relaxations in the femoral arteries using a wire myograph. Chronic stress increased BP, Nfe2l2 expression, and NA-induced vasoconstriction, though it did not affect relaxation responses nor the left heart ventricle-to-body weight (LHV/BW) ratio. DMF elevated Nfe2l2 expression (as the main effect) in the heart but did not alter BP and vascular functions vs. control when administered alone. Interestingly, DMF increased the LHV/BW ratio, supposedly due to reductive stress induced by continuous NRF2 activation. When combined with stress, DMF treatment prevented stress-induced hypertension and mitigated NA-induced vasoconstriction without altering relaxation functions. In addition, the combination of stress and DMF increased Tnf and Nos2 expression and the expressions of several genes involved in iron metabolism. In conclusion, these findings suggest that DMF can prevent chronic stress-induced hypertension by reducing vascular contractility. Moreover, DMF itself may produce reductive stress in the heart and induce inflammation when combined with stress. This indicates a need for the careful consideration of long-term DMF treatment considering its impact on the heart.

Method of splitting polarization coordinates for description of ultrafast multistage electron transfer in a non-debye medium

A method for constructing the space of medium states in reactions of ultrafast multistage intramolecular electron transfer in media with several relaxation times is developed. The method uses the splitting of polarization coordinates into relaxation components, and is a generalization of two previously developed approaches used (1) to describe multistage reactions, and (2) to consider multicomponent relaxation. Within the suggested generalized scheme, a model of charge transfer in a three-center molecular system in the environment with a two-component relaxation function is considered, an algorithm for constructing the diabatic free energy surfaces of electronic states is described, a system of equations for the evolution of the distribution functions is written. The results of the general model are shown to reproduce well-known solutions in particular cases.

Sodium tanshinone IIA sulfonate protects vascular relaxation in ApoE-knockout mice by inhibiting the SYK-NLRP3 inflammasome-MMP2/9 pathway

BackgroundHyperlipidemia damages vascular wall and serves as a foundation for diseases such as atherosclerosis, hypertension and stiffness. The NOD-like receptor family pyrin domain-containing 3 (NLRP3) inflammasome is implicated in vascular dysfunction associated with hyperlipidemia-induced vascular injury. Sodium tanshinone IIA sulfonate (STS), a well-established cardiovascular protective drug with recognized anti-inflammatory, antioxidant, and vasodilatory properties, is yet to be thoroughly investigated for its impact on vascular relaxant imbalance induced by hyperlipidemia.MethodsIn this study, we treated ApoE-knockout (ApoE-/-) mouse with STS and assessed the activation of the NLRP3 inflammasome, expression of MMP2/9, integrity of elastic fibers, and vascular constriction and relaxation.ResultsOur findings reveal that STS intervention effectively preserves elastic fibers, significantly restores aortic relaxation function in ApoE-/- mice, and reduces their excessive constriction. Furthermore, STS inhibits the phosphorylation of spleen tyrosine kinase (SYK), suppresses NLRP3 inflammasome activation, and reduces MMP2/9 expression.ConclusionsThese results demonstrate that STS protects vascular relaxation against hyperlipidemia-induced damage through modulation of the SYK-NLRP3 inflammasome-MMP2/9 pathway. This research provides novel insights into the mechanisms underlying vascular relaxation impairment in a hyperlipidemic environment and uncovers a unique mechanism by which STS preserves vascular relaxation, offering valuable foundational research evidence for its clinical application in promoting vascular health.

Klotho enhances diastolic function in aged hearts through Sirt1-mediated pathways.

Aging leads to a progressive decline in cardiac function, increasing the risk of heart failure with preserved ejection fraction (HFpEF). This study elucidates the impact of α-Klotho, an anti-aging hormone, on cardiac diastolic dysfunction and explore its downstream mechanisms. Aged wild-type and heterozygous Klotho-deficient mice received daily injection of soluble α-Klotho (sKL) for 10weeks, followed by a comprehensive assessment of heart function by echocardiography, intracardiac pressure catheter, exercise tolerance, and cardiac pathology. Our findings show that klotho deficiency accentuated cardiac hypertrophy, diastolic dysfunction, and exercise intolerance, while sKL treatment ameliorates these abnormalities and improves cardiac capillary densities. Downstream of klotho, we focused on the Sirtuin1 (Sirt1) signaling pathway to elucidate the potential underlying mechanism by which Klotho improves diastolic function. We found that decreased Klotho levels were linked with Sirt1 deficiency, whereas sKL treatment restored Sirt1 expression in aged hearts and mitigated the DNA damage response pathway activation. Through tandem mass tag proteomics and unbiased acetylomics analysis, we identified 220 significantly hyperacetylated lysine sites in critical cardiac proteins of aged hearts. We found that sKL supplementation attenuated age-dependent DNA damage and cardiac diastolic dysfunction. In contrast, Klotho deficiency significantly increased hyperacetylation of several crucial cardiac contractile proteins, potentially impairing ventricular relaxation and diastolic function, thus predisposing to HFpEF. These results suggest the potential benefit of sKL supplementation as a promising therapeutic strategy for combating HFpEF in aging.

Stability of a fractional heat equation with memory

Of concern is a fractional differential problem of order between zero and one. The model generalizes an existing well-known problem in heat conduction theory with memory. First, we justify the replacement of the first order derivative by a fractional one. Then, we establish a Mittag-Leffler stability result for a class of heat flux relaxation functions. We will combine the energy method with some properties from fractional calculus.