Mathematical modelling of nonlinear ring waves in a stratified fluid

Oceanic waves registered by satellite observations often have curvilinear fronts and propagate over various currents. In this thesis, we study long linear and weakly-nonlinear ring waves in a stratified fluid in the presence of a depth-dependent horizontal shear flow. It is shown that despite the clashing geometries of the waves and the shear flow, there exists a linear modal decomposition, which can be used to describe distortion of the wavefronts of surface and internal waves, and systematically derive a 2+1-dimensional cylindrical Korteweg-de Vries (cKdV)-type equation for the amplitudes of the waves. The general theory is applied to the case of the waves in a two-layer fluid with a piecewise-constant shear flow, with an emphasis on the effect of the shear flow on the geometry of the wavefronts. The distortion of the wavefronts is described by the singular solution (envelope of the general solution) of the nonlinear first order differential equation, constituting generalisation of the dispersion relation in this curvilinear geometry. There exists a striking difference in the shape of the wavefronts: the wavefront of the surface wave is elongated in the shear flow direction while the wavefront of the interfacial wave is squeezed in this direction. We solve the derived 2+1-dimensional cKdV-type equation numerically using a finite-difference scheme. The effects of nonlinearity and dispersion are studied by considering numerical results for surface and interfacial ring waves generated from a localised source with and without shear flow and the 2D dam break problem. In these examples, the linear and nonlinear surface waves are faster than interfacial waves, the wave height decreases faster at the surface, the shear flow leads to the wave height decreasing slower downstream and faster upstream, and the effect becomes more prominent as the shear flow strengthens

H∞ Robust T-S Fuzzy Design for Uncertain Nonlinear Systems with State Delays Based on Sliding Mode Control

This paper presents the fuzzy design of sliding mode control (SMC) for nonlinear systems with state delay, which can be represented by a Takagi-Sugeno (TS) model with uncertainties. There exist the parameter uncertainties in both the state and input matrices, as well as the unmatched external disturbance. The key feature of this work is the integration of SMC method with H∞ technique such that the robust asymptotically stability with a prescribed disturbance attenuation level γ can be achieved. A sufficient condition for the existence of the desired SMC is obtained by solving a set of linear matrix inequalities (LMIs). The reachability of the specified switching surface is proven. Simulation results show the validity of the proposed method

Nonlinear ring waves in a two-layer fluid

Surface and interfacial weakly-nonlinear ring waves in a two-layer fluid are modelled numerically, within the framework of the recently derived 2+1-dimensional cKdV-type equation. In a case study, we consider concentric waves from a localised initial condition and waves in a 2D version of the dam-break problem, as well as discussing the effect of a piecewise-constant shear flow. The modelling shows, in particular, the formation of 2D dispersive shock waves and oscillatory wave trains

Long ring waves in a stratified fluid over a shear flow

Oceanic waves registered by satellite observations often have curvilinear fronts and propagate over various currents. In this paper we study long linear and weakly nonlinear ring waves in a stratified fluid in the presence of a depth-dependent horizontal shear flow. It is shown that, despite the clashing geometries of the waves and the shear flow, there exists a linear modal decomposition (different from the known decomposition in Cartesian geometry), which can be used to describe distortion of the wavefronts of surface and internal waves, and systematically derive a $2+1$2+1-dimensional cylindrical Korteweg–de Vries-type equation for the amplitudes of the waves. The general theory is applied to the case of the waves in a two-layer fluid with a piecewise-constant current, with an emphasis on the effect of the shear flow on the geometry of the wavefronts. The distortion of the wavefronts is described by the singular solution (envelope of the general solution) of the nonlinear first-order differential equation, constituting generalisation of the dispersion relation in this curvilinear geometry. There exists a striking difference in the shapes of the wavefronts of surface and interfacial waves propagating over the same shear flow

An adaptation model for trabecular bone at different mechanical levels

<p>Abstract</p> <p>Background</p> <p>Bone has the ability to adapt to mechanical usage or other biophysical stimuli in terms of its mass and architecture, indicating that a certain mechanism exists for monitoring mechanical usage and controlling the bone's adaptation behaviors. There are four zones describing different bone adaptation behaviors: the disuse, adaptation, overload, and pathologic overload zones. In different zones, the changes of bone mass, as calculated by the difference between the amount of bone formed and what is resorbed, should be different.</p> <p>Methods</p> <p>An adaptation model for the trabecular bone at different mechanical levels was presented in this study based on a number of experimental observations and numerical algorithms in the literature. In the proposed model, the amount of bone formation and the probability of bone remodeling activation were proposed in accordance with the mechanical levels. Seven numerical simulation cases under different mechanical conditions were analyzed as examples by incorporating the adaptation model presented in this paper with the finite element method.</p> <p>Results</p> <p>The proposed bone adaptation model describes the well-known bone adaptation behaviors in different zones. The bone mass and architecture of the bone tissue within the adaptation zone almost remained unchanged. Although the probability of osteoclastic activation is enhanced in the overload zone, the potential of osteoblasts to form bones compensate for the osteoclastic resorption, eventually strengthening the bones. In the disuse zone, the disuse-mode remodeling removes bone tissue in disuse zone.</p> <p>Conclusions</p> <p>The study seeks to provide better understanding of the relationships between bone morphology and the mechanical, as well as biological environments. Furthermore, this paper provides a computational model and methodology for the numerical simulation of changes of bone structural morphology that are caused by changes of mechanical and biological environments.</p

The active aging level of the rural older adults with disability in China: a cross-sectional study

BackgroundActive aging has been listed as an important indicator to measure the quality of life of the older adults and the construction of the senior care system. There is an imbalance between the supply and demand of senior care services for the disabled older adults in rural areas, and the quality of life needs to be improved.ObjectivesWe aimed to analyze the current situation of active aging and the influencing factors of the rural disabled older adults, in order to provide a reference basis for improving the quality of life of the rural disabled older adults.MethodsWe conducted a multicenter and cross-sectional study, using the Barthel Index Scale and Chinese version of the Active Aging Scale, to facilitate the selection of 304 rural older adults with disability in 26 villages under Henan Province for a questionnaire survey.ResultsThe mean score for the level of active aging of rural older adults with disability was 1.87 (SD 0.36), with the highest score for the dimension of being self-reliant (Mean2.29, SD 0.61) and lower scores for the dimension of active contribution to society (Mean 1.37, SD 0.55) and building up financial security (Mean 1.37, SD 0.57). The results of the multiple regression analysis showed higher levels of active aging among the disabled older adults with retirement pay, mild disability, and longer time per activity/rehabilitation exercise (p &lt; 0.05).ConclusionActive aging of the rural disabled older adults is at a low level, with insufficient economic security and social participation. The national government should help improve the quality of primary health care in rural areas, build a friendly environment for senior communities, and improve policies to protect the welfare of the older adults, so as to collaboratively empower the disabled older adults in rural areas at three levels: health, participation, and protection

Traditional Chinese medicine health literacy among rural older adults: a cross-sectional study

BackgroundThe purpose of this study was to understand the current status of traditional Chinese medicine (TCM) health literacy among rural older adults people and its influencing factors.MethodsThis study used a random number table method to select one prefecture from Henan Province, China and used a convenience sampling method to select 200 rural older adults who met the inclusion criteria in a township in northern Henan from March to April 2023. A cross-sectional survey was conducted using a general information questionnaire and a traditional Chinese medicine health literacy questionnaire, and the influencing factors of rural older adults were analyzed using univariate analysis of variance (ANOVA) and multiple linear regression.ResultsThe total TCM health literacy score of 200 rural older adults people was 84.14 ± 6.709. One-way ANOVA revealed that six factors, including education level, marital status, type of occupation, presence of family members engaged in medical-related work, main economic sources, and monthly income, influenced the TCM health literacy score of rural older adults people (p &lt; 0.05). Multiple linear regression analysis revealed that education level, occupation type, and the presence of family members engaged in medical-related work were the factors influencing the TCM health literacy of rural older adults.ConclusionThe TCM health literacy level of rural older adults people is at the lower to middle level, and health educators should strengthen the publicity and education of TCM healthcare knowledge for rural older adults people to improve their TCM health literacy level and thus enhance their quality of life

Current status and influencing factors of activation of older patients with chronic disease

ObjectiveWe aimed to investigate the status and influencing factors of activation of older patients with chronic disease.MethodsWe conducted a cross-sectional study, using the general information questionnaire, Patient Activation Measure, the Chinese version of the e-Health Literacy Scale, and the Health Empowerment Scale for the Elderly with Chronic Disease. By the convenience sampling method, 289 older patients with chronic disease were selected from January to April 2023 in a Class A tertiary hospital in Zhengzhou.ResultsThe mean score of the Patient Activation Measure for older patients with chronic disease was 65.94 ± 13.35. The association of influencing factors such as religion, family income, health empowerment, e-health literacy, and patient activation was investigated.ConclusionThe patient activation of older patients with chronic disease was at a middle level. Patients without religion and from high-income families tended to have a higher level of patient activation. Improving health empowerment and e-health literacy levels promotes patient activation and enhances their self-health management ability

Novel Zinc Finger Transcription Factor ZFP580 Facilitates All-Trans Retinoic Acid -Induced Vascular Smooth Muscle Cells Differentiation by Rarα-Mediated PI3K/Akt and ERK Signaling

Background/Aims: Phenotypic switching of vascular smooth muscle cells (VSMC) plays a vital role in the development of vascular diseases. All-trans retinoic acid (ATRA) is known to regulate VSMC phenotypes. However, the underlying mechanisms remain completely unknown. Here, we have investigated the probable roles and underlying mechanisms of the novel C2H2 zinc finger transcription factor ZFP580 on ATRA-induced VSMC differentiation. Methods: VSMCs were isolated, cultured, and identified. VSMCs were infected with an adenovirus encoding ZFP580 or Ad-siRNA to silence ZFP580. The expression levels of ZFP580, SMα-actin, SM22α, SMemb, RARα, RARβ, and RARγ were assayed by Q-PCR and western blot. A rat carotid artery injury model and morphometric analysis of intimal thickening were also used in this study. Results: ATRA caused a significant reduction of VSMC proliferation and migration in a doseand time-dependent manner. Moreover, it promoted VSMC differentiation by enhancing expression of differentiation markers and reducing expression of dedifferentiation markers. This ATRA activity was accompanied by up-regulation of ZFP580, with concomitant increases in RARα expression. In contrast, silencing of the RARα gene or inhibiting RARα with its antagonist Ro41-5253 abrogated the ATRA-induced ZFP580 expression. Furthermore, ATRA binding to RARα induced ZFP580 expression via the PI3K/Akt and ERK pathways. Adenovirusmediated overexpression of ZFP580 promoted VSMC differentiation by enhancing expression of SM22α and SMα-actin and reducing expression of SMemb. In contrast, silencing ZFP580 dramatically reduced the expression of differentiation markers and increased expression of dedifferentiation markers. The classic rat carotid artery balloon injury model demonstrated that ZFP580 inhibited proliferation and intimal hyperplasia in vivo. Conclusion: The novel zinc finger transcription factor ZFP580 facilitates ATRA-induced VSMC differentiation by the RARα-mediated PI3K/Akt and ERK signaling pathways. This might represent a novel mechanism of regulation of ZFP580 by ATRA and RARα, which is critical for understanding the biological functions of retinoids during VSMC phenotypic modulation