Dynamic Boundary Research Articles

Uniform exponential stability approximations of semi‐discretization schemes for two hybrid systems

The uniform exponential stabilities (UESs) of two hybrid control systems comprised of a wave equation and a second‐order ordinary differential equation are investigated in this study. Linear feedback law and local viscosity are considered, as are nonlinear feedback law and internal anti‐damping. The hybrid system is first reduced to a first‐order port‐Hamiltonian system with dynamical boundary conditions, and the resulting system is discretized using the average central‐difference scheme. Second, the UES of the discrete system is obtained without prior knowledge of the exponential stability of the continuous system. The frequency domain characterization of UES for a family of contractive semigroups and the discrete multiplier approach are used to validate the main conclusions. Finally, the Trotter–Kato theorem is used to perform a convergence study on the numerical approximation approach. Most notably, the exponential stability of the continuous system is derived by the convergence of energy and UES, which is a novel approach to studying the exponential stability of some complex systems. Numerical simulation is used to validate the effectiveness of the numerical approximating strategy.

Integration of the wind and solar power for the dynamic economic emission dispatch with the charging and discharging of plug-in electric vehicles

Wind and solar power are incorporated into the dynamic economic emission dispatch with the plug-in electric vehicles (DEED-PEV) in this paper, seeking to reduce the generation cost and pollutant emission significantly. A Laplacian non-dominated sorting genetic algorithm-II (LNSGA-II) and a constraint handling method (CHM) are proposed for the DEED-PEV. The LNSGA-II applies the Laplace distribution to both the crossover and mutation. The Laplace-based crossover makes each individual carry out unidirectional search towards its partner and enhances the information exchange between each pair of individuals. The Laplace-based mutation makes each individual carry out bi-directional search surrounding itself and adjust the searching range adaptively. Therefore, the LNSGA-II is able to explore and exploit the decision space of the DEED-PEV sufficiently, contributing to the reductions of the generation cost and pollutant emission in the objective space. For the variables of every individual, the CHM limits them within the feasible operating zones. The CHM also limits them within the dynamic boundaries. It further adjusts them according to the power balances. The power generation constraints and up/down ramp rate constraints can be always satisfied while the elimination of the total violation of the other constraints can be expedited. Therefore, the CHM can transform infeasible individuals to feasible ones rapidly. Four strategies are investigated for six PEV charging/discharging scenarios. The first three strategies consider no more than one kind of renewable energy generation while the fourth strategy involves both the wind power and solar power. Experimental results suggest that the fourth strategy is more economical and environment-friendly than the other three strategies. Furthermore, the LNSGA-II outperforms the other three competitor algorithms for six DEED-PEV problems in the light of hypervolume, coverage rate and spacing.

The limit case in a nonlocal $p$-Laplacian equation with dynamical boundary conditions

The limit case in a nonlocal $p$-Laplacian equation with dynamical boundary conditions

Integral BLF-Based Adaptive Dynamic Event-Triggered Boundary Control for a Flexible Riser System.

For the flexible riser systems modeled with partial differential equations (PDEs), this article explores the boundary control problem in depth for the first time using a dynamic event-triggered mechanism (DETM). Given the intrinsic time-space coupling characteristic inherent in PDE computations, implementing a state-dependent DETM for PDE-based flexible risers presents a significant challenge. To overcome this difficulty, a novel dynamic event-triggered control method is introduced for flexible riser systems, focusing on optimizing available control inputs. In order to save computational costs from the controller to the actuator, a dynamic event-triggered adaptive boundary controller is designed to effectively reduce boundary position vibrations. Additionally, considering external disturbances, an adaptive bounded compensation term is incorporated to counteract the influence of external disturbances on the system. Addressing boundary position constraints, a new integral barrier Lyapunov function (iBLF) tailored specifically for flexible riser systems is introduced, thereby alleviating conservatism in the controller design of flexible risers modeled by PDEs. At last, the validity of the proposed method is demonstrated through a simulation example.

Nonlinear three-dimensional modeling for encapsulated microbubble dynamics subject to ultrasound

Encapsulated microbubbles (EMBs) stabilized by thin coatings have been used as contrast agents for ultrasound sonography as well as having been demonstrated as a promising new technology for targeted drug delivery. The dynamics of EMBs is three-dimensional (3D) because EMBs within micro-vessels inevitably interact with boundaries, but the theoretical and numerical studies are limited to spherical, weakly non-spherical, and/or axisymmetric EMBs. Here, we have developed physical, mathematical, and numerical models for nonlinear 3D EMB dynamics. The liquid flow is evaluated using the boundary integral method. The EMB coating is modeled as a thin viscoelastic shell including stretching, bending, and shear effects and simulated using the finite element method. These models are coupled through the kinematic and dynamic boundary conditions at the interface. The model is in good agreement with the Hoff equation for spherical EMBs and the asymptotic theory for weakly non-spherical deformation of EMBs. Using this model, a numerical study for EMB dynamics near a rigid boundary subject to an ultrasonic wave is performed. The migration, non-spherical oscillation, resonant oscillation, and jetting of EMBs are displayed and analyzed systematically. If the ultrasound wave is strong, a high-speed liquid jet forms at the final stage of the collapse, orientated between the directions of the wave and toward the wall. The EMB jet is weaker and slower and has less momentum, as the non-spherical deformation of the coating and the jetting are suppressed by the viscoelastic property of the coating. If the ultrasound is not strong, the EMB remains spherical for many cycles of oscillation but the EMB undergoes resonant oscillation and becomes significantly non-spherical after several oscillation cycles, when the wave frequency is equal to its natural frequency. The numerical capability has the potential to be developed for the optimization of sonography or drug delivery.

Logic-Based Fixed-Time Control for Uncertain Nonlinear Systems With Unknown Control Directions.

The fixed-time control problem is investigated for a class of uncertain nonlinear systems subjected to multiple unknown control directions. The control coefficients of nonlinear systems under consideration are time varying and their signs are not required to be identical. To tackle this challenge, a switching mechanism along with a novel dynamic boundary function is proposed. Utilizing the devised dynamic boundary function, adaptive parameters are introduced into the controller to effectively handle system uncertainties. It is proved that the system output converges to a small neighborhood of the origin in fixed time and the boundedness of all system signals is maintained. Finally, two simulation examples are used to show the validity of the presented switching control strategy.

Simulation Study on Rock Crack Expansion in CO2 Directional Fracturing

In underground construction projects, traversing hard rock layers demands concentrated CO2 fracturing energy and precise directional crack expansion. Due to the discontinuity of the rock mass at the tip of prefabricated directional fractures in CO2 fracturing, traditional simulations assuming continuous media are limited. It is challenging to set boundary conditions for high strain rate and large deformation processes. The dynamic expansion mechanism of the 3D fracture network in CO2 directional fracturing is not yet fully understood. By treating CO2 fracturing stress waves as hemispherical resonance waves and using a particle expansion loading method along with dynamic boundary condition processing, a 3D numerical model of CO2 fracturing is constructed. This model analyzes the dynamic propagation mechanism of 3D spatial fractures network in CO2 directional fracturing rock materials. The results show that in undirected fracturing, the fracture network relies on the weak structures near the rock borehole, whereas in directional fracturing, the crack propagation is guided, extending the fracture’s range. Additionally, the tip of the directional crack is vital for the re-expansion of the rock mass by high-pressure CO2 gas, leading to the formation of a symmetrical, umbrella-shaped structure with evenly developed fractures. The findings also demonstrate that the discrete element method (DEM) effectively reproduces the dynamic fracture network expansion at each stage of fracturing, providing a basis for studying the CO2 directional rock cracking mechanism.

Local existence and blow up for the wave equation with nonlinear logarithmic source term and nonlinear dynamical boundary conditions combined with distributed delay

Local existence and blow up for the wave equation with nonlinear logarithmic source term and nonlinear dynamical boundary conditions combined with distributed delay

Patient-specific compliant simulation framework informed by 4DMRI-extracted pulse wave Velocity: Application post-TEVAR

We introduce a new computational framework that utilises Pulse Wave Velocity (PWV) extracted directly from 4D flow MRI (4DMRI) to inform patient-specific compliant computational fluid dynamics (CFD) simulations of a Type-B aortic dissection (TBAD), post-thoracic endovascular aortic repair (TEVAR). The thoracic aortic geometry, a 3D inlet velocity profile (IVP) and dynamic outlet boundary conditions are derived from 4DMRI and brachial pressure patient data. A moving boundary method (MBM) is applied to simulate aortic wall displacement. The aortic wall stiffness is estimated through two methods: one relying on area-based distensibility and the other utilising regional pulse wave velocity (RPWV) distensibility, further fine-tuned to align with in vivo values. Predicted pressures and outlet flow rates were within 2.3 % of target values. RPWV-based simulations were more accurate in replicating in vivo hemodynamics than the area-based ones. RPWVs were closely predicted in most regions, except the endograft. Systolic flow reversal ratios (SFRR) were accurately captured, while differences above 60 % in in-plane rotational flow (IRF) between the simulations were observed. Significant disparities in predicted wall shear stress (WSS)-based indices were observed between the two approaches, especially the endothelial cell activation potential (ECAP). At the isthmus, the RPWV-driven simulation indicated a mean ECAP>1.4 Pa-1 (critical threshold), indicating areas potentially prone to thrombosis, not captured by the area-based simulation.RPWV-driven simulation results agree well with 4DMRI measurements, validating the proposed pipeline and facilitating a comprehensive assessment of surgical decision-making scenarios and potential complications, such as thrombosis and aortic growth.

Impact of double diffusion on solid particle dispersion in rotated cylinders with nano-enhanced phase change materials

This study introduces an innovative approach that combines the Incompressible Smoothed Particle Hydrodynamics method with Artificial Neural Networks to examine the dispersion of solid particles within rotated circular cylinders filled with nano-enhanced phase change materials. This method addresses the limitations of traditional numerical techniques by improving accuracy in complex geometries and dynamic boundary conditions. The various parameters are examined, including the lengths of low sources in boundary walls Lb, dimensionless time τ, Hartmann number (Ha), Darcy number (Da), thermal radiation parameter (Rd), and Rayleigh number (Ra). The solid particles are initially situated at the center gate between the two circular cylinders, maintained at elevated temperature Th and concentration Ch. Due to the upward direction of convection flow, the solid particles are consistently dispersed into the top circular cylinder. The findings offer valuable insights into the system's behavior. The dispersion of solid particles within the NEPCM is influenced by both τ and Lb, showcasing minimal dispersion for τ≤0.1 and intensified dispersion for τ≥0.2, particularly augmented by larger Lb. The heat capacity ratio (Cr) exhibits a decrease with increasing Lb at multiple time points. A decrease in the Darcy number significantly slows down the dispersion of solid particles because of the substantial resistance posed by the porous medium. As the Rayleigh number increases, there is an enhanced dispersion of solid particles into the upper circular cylinder and heightened temperature distributions. Additionally, the average Nusselt number Nu¯ and Sherwood number Sh¯ decrease with the increase in Lb due to the expansion of low-temperature and concentration source. When the length Lb was increased from 0.25 to 1, Nu¯ and Sh¯ decreased by approximately 76% and 67%, respectively, underscoring the impact of geometric configuration on heat and mass transfer efficiency. The study highlights the effectiveness of the MLP model in predicting Nu¯ and Sh¯ values through graphical analysis, showing significant agreement with the target values. The results demonstrated notable improvements in managing particle dispersion and heat/mass transfer, emphasizing the potential of this integrated approach for applications in thermal management and energy optimization.

Analysis of energy dissipation in hyperbolic problems influenced by internal and boundary control mechanisms

ABSTRACT This article primarily focuses on the rational stabilisation of the wave equation, supplied with a second-order dynamical boundary condition of hyperbolic type, while considering an additional internal damping mechanism within the specified ring. To achieve rational decay rates of the associated energy, it is imperative to exponentially stabilise a portion of the domain using a global Ingham's-type estimate. This paper will subsequently illustrate how this partially localised exponential stabilisation, combined with a Bessel analysis, leads to a rational decrease in the overall energy of the system considered.

An investigation of vibration responses for bolted composite flanged-cylindrical shells considering material and joint nonlinearity

In this paper, a thorough investigation into the vibration response of bolted composite flanged-cylindrical shell structures, considering the material nonlinearity of carbon fiber-reinforced polymer composites (CFRP) and the joint nonlinearity of bolt connections, is presented. Firstly, a general semi-analytical modeling method for bolted composite flanged-cylindrical shell is developed based on the first-order shear deformation theory (FSDT) and the energy method. In this method, material nonlinearity is introduced by accounting for the frequency-strain dependency of material parameters. A joint model with non-uniform distribution parameters and dynamic boundaries is proposed to simulate the interface pressure distribution and nonlinear mechanical behavior of bolted joints. Then, for the general numerical model that incorporates both types of nonlinearities, the ability to accurately predict the nonlinear vibration behavior of a bolted composite flanged-cylindrical shell is demonstrated through experimental testing. Finally, an in-depth discussion is conducted on the influence of fiber layup patterns and bolt numbers on the nonlinear vibration response of the bolted composite flanged-cylindrical shells. The conducted analysis indicates that the proposed method can offer utility to designers, empowering them with the insights necessary for the dynamic optimization of such structures.

Fractional boundary value problems and elastic sticky brownian motions

AbstractWe extend the results obtained in [14] by introducing a new class of boundary value problems involving non-local dynamic boundary conditions. We focus on the problem to find a solution to a local problem on a domain $$\varOmega $$ Ω with non-local dynamic conditions on the boundary $$\partial \varOmega $$ ∂ Ω . Due to the pioneering nature of the present research, we propose here the apparently simple case of $$\varOmega =(0, \infty )$$ Ω = ( 0 , ∞ ) with boundary $$\{0\}$$ { 0 } of zero Lebesgue measure. Our results turn out to be instructive for the general case of boundary with positive (finite) Borel measures. Moreover, in our view, we bring new light to dynamic boundary value problems and the probabilistic description of the associated models.

Short-Term Groundwater Level Fluctuations Drive Subsurface Redox Variability.

As global change processes modify the extent and functions of terrestrial-aquatic interfaces, the variability of critical and dynamic transitional zones between wetlands and uplands increases. However, it is still unclear how fluctuating water levels at these dynamic boundaries alter groundwater biogeochemical cycling. Here, we used high-temporal resolution data along gradients from wetlands to uplands and during fluctuating water levels at freshwater coastal areas to capture spatiotemporal patterns of groundwater redox potential (Eh). We observed that topography influences groundwater Eh that is higher in uplands than in wetlands; however, the high variability within TAI zones challenged the establishment of distinct redox zonation. Declining water levels generally decreased Eh, but most locations exhibited significant Eh variability, which is associated with rare instances of short-term water level fluctuations, introducing oxygen. The Eh-oxygen relationship showed distinct hysteresis patterns, reflecting redox poising capacity at higher Eh, maintaining more oxidizing states longer than the dissolved oxygen presence. Surprisingly, we observed more frequent oxidizing states in transitional areas and wetlands than in uplands. We infer that occasional oxygen entering specific wetland-upland boundaries acts as critical biogeochemical control points. High-resolution data can capture such rare yet significant biogeochemical instances, supporting redox-informed models and advancing the predictability of climate change feedback.

Discordance between taxonomy and population genomic data: An avian example relevant to the United States Endangered Species Act.

Population genomics can reveal cryptic biological diversity that may impact fitness while simultaneously serving to delineate relevant conservation units. Here, we leverage the power of whole-genome resequencing for conservation by studying 433 individual lesser prairie-chicken (Tympanuchus pallidicinctus; LEPC, a federally endangered species of conservation concern in the United States) and greater prairie-chicken (Tympanuchus cupido; GRPC, a legally huntable species throughout much of its range). The genomic diversity of two formally recognized distinct population segments (DPSs) of LEPCs is similar, but they are genetically distinct. Neither DPS is depleted of its genomic diversity, neither is especially inbred, and temporal diversity is relatively stable in both conservation units. Interspecific differentiation between the two species was only slightly higher than that observed between LEPC DPSs, due largely to bidirectional introgression. The high resolution provided by our dataset identified a genomic continuum between the two species such that individuals sampled from the hybrid zone were imperfectly assigned to their presumptive species when considering only their physical characteristics. The admixture between the two species is reflected in the spectrum of individual ancestry coefficients, which has legal implications for the "take" of individuals under the Endangered Species Act. Overall, our data highlight the recurring dissonance between static policies and dynamic species boundaries that are increasingly obvious in the population genomic era.

Null controllability of a volume-surface reaction-diffusion equation with dynamic boundary conditions

This article focuses on investigating the null controllability of a volume-surface reaction-diffusion equation with dynamic boundary conditions. Notably, the reaction and diffusion coefficients depend on the state variable in the bulk and on its surface. Our main result establishes the local null controllability of the quasi-linear equation under certain conditions on the regularity of diffusion and reaction coefficients as well as initial data. To this end, we approach the problem by first addressing the question of null controllability in the framework of a inhomogeneous linearized equation. Next, we derive new estimates of both control and state, allowing us to apply a local inversion theorem to obtain the local null controllability of the quasi-linear equation.

Finite element model to investigate the dynamic instability of ring stiffened conical shells subjected to flowing fluid

In this study, the vibration stability (i.e., static divergence) and critical velocity of fluid-conveying, ring-stiffened, truncated conical shells are investigated under various boundary conditions. The shell is characterized using Sanders’ theory, while the fluid is modeled using a velocity potential approach with the impermeability condition at the fluid-shell interface. Using linear superposition, the natural frequencies corresponding to each flow velocity are determined by satisfying the dynamic characteristic equation and boundary conditions. Critical velocities are identified where the natural frequencies vanish, indicating static divergence. Parametric studies are conducted to investigate the effect of ring stiffeners on the critical velocities with respect to the semi-cone angle, number of rings, and boundary conditions. The proposed model is validated through comparison with published data. It is found that the rings significantly affect the stability of the cone under different boundary conditions. Instability in stiffened shells occurs at higher critical fluid velocities than in unstiffened shells across all boundary conditions. An increase in the vertex angle leads to a decrease in critical flow discharge.

Population Dynamics, Economic Growth and Planetary Boundaries

Population Dynamics, Economic Growth and Planetary Boundaries

Beyond wrecking a wall: revisiting the concept of blood-brain barrier breakdown in ischemic stroke.

The blood-brain barrier constitutes a dynamic and interactive boundary separating the central nervous system and the peripheral circulation. It tightly modulates the ion transport and nutrient influx, while restricting the entry of harmful factors, and selectively limiting the migration of immune cells, thereby maintaining brain homeostasis. Despite the well-established association between blood-brain barrier disruption and most neurodegenerative/neuroinflammatory diseases, much remains unknown about the factors influencing its physiology and the mechanisms underlying its breakdown. Moreover, the role of blood-brain barrier breakdown in the translational failure underlying therapies for brain disorders is just starting to be understood. This review aims to revisit this concept of "blood-brain barrier breakdown," delving into the most controversial aspects, prevalent challenges, and knowledge gaps concerning the lack of blood-brain barrier integrity. By moving beyond the oversimplistic dichotomy of an "open"/"bad" or a "closed"/"good" barrier, our objective is to provide a more comprehensive insight into blood-brain barrier dynamics, to identify novel targets and/or therapeutic approaches aimed at mitigating blood-brain barrier dysfunction. Furthermore, in this review, we advocate for considering the diverse time- and location-dependent alterations in the blood-brain barrier, which go beyond tight-junction disruption or brain endothelial cell breakdown, illustrated through the dynamics of ischemic stroke as a case study. Through this exploration, we seek to underscore the complexity of blood-brain barrier dysfunction and its implications for the pathogenesis and therapy of brain diseases.

The Influence of Dynamical Downscaling and Boundary Layer Selection on Egypt’s Potential Evapotranspiration using a Calibrated Version of the Hargreaves-samani Equation: RegCM4 Approach

Potential Evapotranspiration (PET) is an important variable for monitoring daily agricultural activity as well as meteorological drought. Therefore, it is necessary to investigate the influence of different options of the physical dynamical downscaling and boundary layer schemes on the simulated PET. Using the RegCM4 regional climate model, four simulations were conducted (two for each case) in the period 1997 to 2017. In all simulations, the RegCM4 was configured with 25 km resolution and downscaled by the ERA-Interim reanalysis dataset. To ensure a reliable estimation of the PET, a calibrated version of the Hargreaves-Samani equation was adopted. A high-resolution product of the ERA5 was used as the observational dataset. Results showed that the simulated PET is insensitive either to the dynamical downscaling or the boundary layer options. Concerning the annual climatological cycle, the RegCM4’s performance varies with month and location. Quantitatively, a root mean square error lies between 1 mm and 1.6 mm day-1, the Nash-Sutcliffe efficiency between 0.2 and 0.6, and the coefficient of determination between 0.5 and 0.75. Additionally, the Linear Scaling (LS) method showed its added value in the evaluation/validation periods. In conclusion, the RegCM4 can be used to develop a regional PET map of Egypt using the LS either in the present climate or under different future scenarios.