Steady Configuration Research Articles

Prandtl-Meyer Reflection Configurations, Transonic Shocks, and Free Boundary Problems

We are concerned with the Prandtl-Meyer reflection configurations of unsteady global solutions for supersonic flow impinging upon a symmetric solid wedge. Prandtl (1936) first employed the shock polar analysis to show that there are two possible steady configurations: the steady weak shock solution and the steady strong shock solution, when a steady supersonic flow impinges upon the solid wedge – the half-angle of which is less than a critical angle (i.e., the detachment angle), and then conjectured that the steady weak shock solution is physically admissible since it is the one observed experimentally. The fundamental issue of whether one or both of the steady weak and strong shocks are physically admissible has been vigorously debated over the past eight decades and has not yet been settled in a definitive manner. On the other hand, the Prandtl-Meyer reflection configurations are core configurations in the structure of global entropy solutions of the two-dimensional Riemann problem, while the Riemann solutions themselves are local building blocks and determine local structures, global attractors, and large-time asymptotic states of general entropy solutions of multidimensional hyperbolic systems of conservation laws. In this sense, we have to understand the reflection configurations in order to understand fully the global entropy solutions of two-dimensional hyperbolic systems of conservation laws, including the admissibility issue for the entropy solutions. In this monograph, we address this longstanding open issue and present our analysis to establish the stability theorem for the steady weak shock solutions as the long-time asymptotics of the Prandtl-Meyer reflection configurations for unsteady potential flow for all the physical parameters up to the detachment angle. To achieve these, we first reformulate the problem as a free boundary problem involving transonic shocks and then obtain appropriate monotonicity properties and uniform a priori estimates for admissible solutions, which allow us to employ the Leray-Schauder degree argument to complete the theory for all the physical parameters up to the detachment angle.

Flow structure and heat transfer characteristics of sweeping and steady impingement jets with/without chevrons on a semi-circular concave surface

Striving for improved gas turbine performance requires operating at higher gas flow temperatures, posing challenges in preserving the structural integrity of the gas turbine. To respond to these challenges, gas turbine manufacturers have turned to internal cooling and jet impingement to provide an effective solution for cooling the leading edge of the gas turbine blades. Fluidic oscillator is known for its sweeping behavior and expansive coverage of targeted surface and, thus, it can efficiently remove heat. In this study, the author numerically simulated the cooling performance of the leading edge of the gas turbine blades under constant heat flux while using four different configurations of jet impingement: a sweeping jet, a sweeping jet with chevrons, a steady jet, and a steady jet with chevrons. The results showed that the sweeping jet configuration with chevrons outperformed the steady jet configurations owing to oscillating jet impingement and a higher intensity of turbulence that increased the entrainment of jet flow. Under the configuration of a sweeping jet with chevrons, the targeted surface recorded an average Nusselt number that is 19.2% higher than the one with a steady jet without chevrons, along with a more uniform distribution of the surface temperature. The outstanding behavior of the sweeping jet with chevrons is due to the its internal flow behavior, i.e., oscillating flow nature of the sweeping jet with augmented turbulence at the exit of the chevron's nozzle.

The intrinsic rarity of equilibrium response in stratigraphic processes

Conventional sequence stratigraphy is based, explicitly or implicitly, on the hypothesis that steady external forcing results in a steady stratigraphic configuration (equilibrium response), so that an unsteady stratigraphic configuration is usually believed to result from unsteady external forcing. Recent advances in autostratigraphy, on the other hand, have led to a significantly different notion that steady external forcing generally results in an unsteady stratigraphic configuration (non-equilibrium response). To advance this debate, it is necessary to clarify what exactly is meant by a steady stratigraphic configuration. Here, we propose a quantitative criterion for defining the latter concept in terms of the straightness of the shoreline trajectory, and specifically a straight shoreline trajectory or the shoreline being held still as a sign to express steady stratigraphic configurations. In such a definition, a steady stratigraphic configuration means that the ratio of the rate of aggradation and the rate of progradation is constant, or one of these two rates is zero. Based on this criterion, a total of 7 types of steady stratigraphic configurations can be clarified, most of which require unsteady external forcing and are thus realized by non-equilibrium response, although special cases exist. The reason that non-equilibrium responses dominate the stacking of strata is that it is common for a growing basin-margin depositional system to change its surface area. The size-changing system will easily change the stacking pattern (unsteady stratigraphic configuration) if the external forcing is steady, or, if the steady stratigraphic configuration is maintained, the rate of external forcing must change in a particular pattern (unsteady external forcing). Equilibrium responses can occur, but in very special cases. Conventional sequence stratigraphy should take into account the importance of non-equilibrium response.

High-Frequency Pulsed Coaxial Injectors for High-Speed Flow Mixing and Control

Efficient and controlled mixing of fuel with fast-moving air is a challenging physical problem relevant to hypersonic systems. Although mixing happens at the molecular level through diffusion, the macroscopic phenomenon such as entrainment and vorticity dynamics resulting from the shear layer instabilities of the mixing fluids play a significant role in the overall efficiency of the process. With a focus on improving mixing at extreme flow conditions, this paper presents a fundamental study of a novel, high-speed, pulsed coflow system integrated with ultrahigh-frequency actuators (11–20 kHz). This injection system consists of a supersonic actuation air jet at the inner core that provides large mean and fluctuating velocity profiles in the shear layers of a fluid stream injected surrounding the core through an annular nozzle, with pulsing occurring at a designated frequency. The high-frequency streamwise vortices and shockwaves tailored to the mean flow significantly enhanced supersonic flow mixing between the fluids compared to a steady coaxial configuration operating at the same input pressure. Experiments also indicate a strong connection between the frequency and unsteady amplitude of the actuation jet to the supersonic flow mixing phenomenon. This paper reports the design details of the injector assembly and flow mixing characteristics captured using phase-locked microschlieren and planar laser-induced fluorescence techniques.

Hole-driven dynamics of a three-dimensional gravitational liquid curtain

It is known that the disintegration of vertical liquid curtains (sheets) is affected crucially by the amplification of free edge holes forming inside the curtain. This paper aims to investigate the influence of the hole expansion dynamics, driven by the so-called rim retraction, on the breakup of a liquid curtain, in both supercritical (Weber number $We > 1$ ) and subcritical ( $We < 1$ ) conditions. The analysis is based on three-dimensional direct numerical simulations. For a selected supercritical configuration, the steady flow topology is first analysed. The investigation reveals the classic triangular shape regime of the steady curtain, due to the surface-tension-induced borders retraction towards its centre plane. The unsteady dynamics is then investigated as the curtain response to a hole perturbation introduced artificially in the steady flow configuration. The hole evolution determines a rim retraction phenomenon inside the curtain, which is influenced by both capillary and gravity forces. In supercritical conditions, the hole does not influence the curtain flow dynamics in the long-time limit. By reducing the Weber number slightly under the critical threshold ( $We=1$ ), the initial amplification rate of the hole area increases, due to the stronger retraction effect of surface tension acting on the hole rims. The free hole expansion in fully subcritical conditions ( $We < 1$ ) is investigated finally by simulating an edge-free curtain flow. As $We$ decreases progressively, the hole expands while it is convected downstream by gravity acceleration. In the range $0.4< We<1$ , the subcritical curtain returns to the intact unperturbed configuration after the hole expulsion at the downstream outflow. For $We<0.4$ , the surface tension force becomes strong enough to reverse the gravitational motion of the hole top point, which retracts upstream towards the sheet inlet section while expanding along the lateral directions. This last phenomenon causes finally the breakup of the curtain, which results in a columnar regime strictly resembling similar experimental findings of the literature.

Aggregation of biochar nanoparticles and the impact on bisphenol A sorption: Experiments and molecular dynamics simulations

The unique properties and environmental implications of biochar nanoparticles (BNPs) have attracted increasing attention. The abundant functional groups and aromatic structures in BNPs may promote the aggregation of BNPs, but the mechanism and implications of this aggregation process remain unclear. Thus, this study investigated the aggregation of BNPs and the sorption of bisphenol A (BPA) on BNPs by combining experimental investigations with molecular dynamics simulations. As the concentration of BNP increased from 100 mg/L to 500 mg/L, the particle size increased from approximately 200 nm to 500 nm, and the exposed surface area ratio in the aqueous phase decreased from 0.46 to 0.05, which confirmed the aggregation of BNPs. The sorption of BPA on BNPs decreased with increasing BNP concentration in both the experiments and molecular dynamics simulations because of BNP aggregation. According to a detailed analysis of the BPA molecules adsorbed on BNP aggregates, the sorption mechanisms were hydrogen bonding, hydrophobic effect, and π-π interactions, which were driven by aromatic rings and O- and N-containing functional groups. The aggregation of BNPs embedded some functional groups in the aggregates and thus inhibited sorption. Interestingly, the steady configuration of the BNP aggregates in the molecular dynamics simulations (2000 ps relaxation) also determined the apparent BPA sorption. BPA molecules were adsorbed in the V-shaped interlayers of the BNP aggregates that acted as semi-closed pores, but could not be adsorbed in the parallel interlayers because of their small layer spacing. This study can provide theoretical guidance for the application of BNPs in pollution control and remediation.

Frictional contact analysis in a spherical roller bearing

Abstract Numerical analyses of the roller–raceway contact have been carried out in a spherical roller bearing using frictional contact models of different complexity. The models used in the study include an implementation of Kalker’s exact contact theory named CECT (Conformal Exact Contact Theory) and detailed Finite Element models. The adequacy of the more simplified contact solutions is assessed by contrasting them with the solutions obtained with the more comprehensive models. Additionally, the use of the exact contact theory, well known in the wheel–rail application, is demonstrated in contact mechanics analyses in rolling bearings, describing relevant details of its implementation for this application. Situations with different normal loads and friction levels have been analysed, and two distinct steady equilibrium configurations of the roller have been identified.

Multipole Vortex Patch Equilibria for Active Scalar Equations

We study how a general steady configuration of finitely many point vortices, with Newtonian interaction or generalized surface quasi-geostrophic interactions, can be desingularized into a steady configuration of vortex patches. The configurations can be uniformly rotating, uniformly translating, or completely stationary. Using a technique first introduced by Hmidi and Mateu [Comm. Math. Phys., 350 (2017), pp. 699--747] for vortex pairs, we reformulate the problem for the patch boundaries so that it no longer appears singular in the point vortex limit. Provided the point vortex equilibrium is nondegenerate in a natural sense, solutions can then be constructed directly using the implicit function theorem, yielding asymptotics for the shape of the patch boundaries. As an application, we construct new families of asymmetric translating and rotating pairs, as well as stationary tripoles. We also show how the techniques can be adapted for highly symmetric configurations such as regular polygons, body-centered polygons, and nested regular polygons by integrating the appropriate symmetries into the formulation of the problem.

Approaches and Challenges in Internet of Robotic Things

The Internet of robotic things (IoRT) is the combination of different technologies including cloud computing, robots, Internet of things (IoT), artificial intelligence (AI), and machine learning (ML). IoRT plays a major role in manufacturing, healthcare, security, and transport. IoRT can speed up human development by a very significant percentage. IoRT allows robots to transmit and receive data to and from other devices and users. In this paper, IoRT is reviewed in terms of the related techniques, architectures, and abilities. Consequently, the related research challenges are presented. IoRT architectures are vital in the design of robotic systems and robotic things. The existing 3–7-tier IoRT architectures are studied. Subsequently, a detailed IoRT architecture is proposed. Robotic technologies provide the means to increase the performance and capabilities of the user, product, or process. However, robotic technologies are vulnerable to attacks on data security. Trust-based and encryption-based mechanisms can be used for secure communication among robotic things. A security method is recommended to provide a secure and trustworthy data-sharing mechanism in IoRT. Significant security challenges are also discussed. Several known attacks on ad hoc networks are illustrated. Threat models ensure integrity confidentiality and availability of the data. In a network, trust models are used to boost a system’s security. Trust models and IoRT networks play a key role in obtaining a steady and nonvulnerable configuration in the network. In IoRT, remote server access results in remote software updates of robotic things. To study navigation strategies, navigation using fuzzy logic, probabilistic roadmap algorithms, laser scan matching algorithms, heuristic functions, bumper events, and vision-based navigation techniques are considered. Using the given research challenges, future researchers can get contemporary ideas of IoRT implementation in the real world.

Evolutionary timeline of a modeled cell

A theoretical study of cell evolution is presented here. By using a toolbox containing an intracellular catalytic reaction network model and a mutation–selection process, four distinct phases of self-organization were unveiled. First, the nutrients prevail as the central substrate of the chemical reactions. Second, the cell becomes a small-world. Third, a highly connected core component emerges, concurrently with the nutrient carriers becoming the central product of reactions. Finally, the cell reaches a steady configuration where the concentrations of the core chemical species are described by Zipf’s law.

Superfluid vortex multipoles and soliton stripes on a torus

We study the existence, stability, and dynamics of vortex dipole and quadrupole configurations in the nonlinear Schr\"odinger (NLS) equation on the surface of a torus. For this purpose we use, in addition to the full two-dimensional NLS on the torus, a recently derived [Phys. Rev. A 101, 053606 (2021)] reduced point-vortex particle model which is shown to be in excellent agreement with the full NLS evolution. Horizontal, vertical, and diagonal stationary vortex dipoles are identified and continued along the torus aspect ratio and the chemical potential of the solution. Windows of stability for these solutions are identified. We also investigate stationary vortex quadrupole configurations. After eliminating similar solutions induced by invariances and symmetries, we find a total of 16 distinct configurations ranging from horizontal and vertical aligned quadrupoles, to rectangular and rhomboidal quadrupoles, to trapezoidal and irregular quadrupoles. The stability for the least unstable and, potentially, stable quadrapole solutions is monitored both at the NLS and the reduced model levels. Two quadrupole configurations are found to be stable on small windows of the torus aspect ratio and a handful of quadrupoles are found to be very weakly unstable for relatively large parameter windows. Finally, we briefly study the dark soliton stripes and their connection, through a series of bifurcation cascades, with steady state vortex configurations.

Settling dynamics of Brownian chains in viscous fluids

We investigate the dynamics of sedimenting Brownian filaments using experimental, computational, and theoretical approaches. The filaments under consideration are composed of linked colloidal particles that form bead-spring-like chains. Under the action of gravitational forces, the nonlocal hydrodynamic interactions cause the filaments to bend and rotate to get their end-to-end direction perpendicular to gravity. Different reorientation mechanisms are verified for different regimes of flexibility, characterized by the elastogravitational number. The thermal forces promote shape and orientation fluctuations around the steady configurations of the reciprocal non-Brownian chains. The competition between the reorientation mechanisms and the Brownian effects results in normal distributions of the orientation of the chains. In the stiff regime, these fluctuations cause the chains to fall faster than their reciprocal non-Brownian cases. With increasing flexibility, thermal fluctuations lead to more compact configurations of the chains and higher average settling velocity. Nonetheless, chain flexibility plays an important role on lateral migration. The interplay between elastic, gravitational, and thermal forces leads to important secondary influences on the filament settling dynamics.3 MoreReceived 11 May 2021Accepted 11 March 2022DOI:https://doi.org/10.1103/PhysRevFluids.7.034303©2022 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasBrownian motionConfinementElastic deformationFluctuation mediated interactionsPolymers & Soft Matter

Marine outlet glacier dynamics, steady states and steady-state stability

Abstract Laterally confined marine outlet glaciers exhibit a diverse range of behaviours. This study investigates time-evolving and steady configurations of such glaciers. Using simplified analytic models, it determines conditions for steady states, their stability and expressions for the rate of the calving-front migration for three widely used calving rules. It also investigates the effects of ice mélange when it is present. The results show that ice flux at the terminus is an implicit function of ice thickness that depends on the glacier geometric and dynamic parameters. As a consequence, stability of steady-state configurations is determined by a complex combination of these parameters, specifics of the calving rule and the details of mélange stress conditions. The derived expressions of the rate of terminus migration suggest a non-linear feedback between the migration rate and the calving-front position. A close agreement between the obtained analytic expressions and numerical simulations suggests that these expressions can be used to gain insights into the observed behaviour of the glaciers and also to use observations to improve understanding of calving conditions.

Undescribed Meroterpenoids from Hypericum japonicum with Neuroprotective Effects on H2O2 Insult SH‐SY5Y Cells Targeting Keap1‐Nrf2

Comprehensive SummaryUnreported tautomeric/enantiomeric meroterpenoids, (±)‐hyperjaponols I—K (1—3), were discovered from Hypericum japonicum. Comprehensive chemical investigations established the absolute characteristics of these stereoisomers. The TS calculation demonstrated that 1a and 2a easily occur enol‐keto tautomerism with steady configurations individually. Amongst isolates, 1b showed the strongest neuroprotective activity with the concentration at 25 μmol/L on H2O2 insult SH‐SY5Y cells. In vitro molecular biological experiments manifested that 1b activated the Keap1‐Nrf2‐ARE pathway, leading to the promotion of Nrf2 nuclear translocation, downregulation of the expression level of Keap1, and upregulation of the levels of Nrf2, NQO‐1, and HO‐1. The results of in silico simulation showed that 1b possessed good binding features with Keap1 (5FNQ) via forming multiple typical hydrogen and hydrophobic bonds as well as less fluctuation of RMSD and RMSF during a natural physiological condition.

Modeling Open Channel Flows of a Viscous Fluid: Critical Transition and Apparent Bottom

The Shallow Water model (SWM) provides a simplification of the Navier–Stokes model (NSM) for stratified flows over a topography when the depth of the fluid layer is small compared to the horizontal scale of the flow. Nevertheless, the application of SWM is limited to the case of slowly variable bottoms and fails in describing the fluid flow over steep obstacles. In this work, we propose to extend the applicability of SWM when the topography is no longer slowly variable with space, by replacing the topography with an “apparent bottom”. This methodology is tested for the laminar flow of a two-layer fluid over a semi-circular cylinder. Sixteen different steady configurations are investigated in order to assess the influence of the Froude number and the blocking factor corresponding to the ratio between the obstacle height and the fluid layer normal height. Here, the apparent bottom required for SWM is obtained by enforcing the liquid height profile to be the one obtained from full resolution (NSM).

Asymmetric games on networks: Towards an Ising-model representation

We here study the Battle of the Sexes game, a textbook case of asymmetric games, on small networks. Due to the conflicting preferences of the players, analytical approaches are scarce and most often update strategies are employed in numerical simulations of repeated games on networks until convergence is reached. As a result, correlations between the choices of the players emerge. Our approach is to study these correlations with a generalized Ising model. First, we show that these correlations emerge in simulations and can have an Ising-like form. Then, using the response strategy framework, we describe how the actions of the players can bring the network into a steady configuration, starting from an out-of-equilibrium one. We obtain these configurations using game-theoretic tools, and describe the results using Ising parameters. We exhaust the two-player case, giving a detailed account of all the equilibrium possibilities. Going to three players, we generalize the Ising model and compare the equilibrium solutions of three representative types of networks. We find that players that are not directly linked retain a degree of correlation that is proportional to their initial correlation. We also find that the local network structure is the most relevant for small values of the magnetic field and the interaction strength of the Ising model. Finally, we conclude that certain parameters of the equilibrium states are network independent, which opens up the possibility of an analytical description of asymmetric games played on networks.

Global stability analysis of flexible channel flow with a hyperelastic wall

We consider the stability of flux-driven flow through a long planar rigid channel, where a segment of one wall is replaced by a pre-tensioned hyperelastic (neo-Hookean) solid of finite thickness and subject to a uniform external pressure. We construct the steady configuration of the nonlinear system using Newton's method with spectral collocation and high-order finite differences. In agreement with previous studies, which use an asymptotically thin wall, we show that the thick-walled system always has at least one stable steady configuration, while for large Reynolds numbers the system exhibits three co-existing steady states for a range of external pressures. Two of these steady configurations are stable to non-oscillatory perturbations, one where the flexible wall is inflated (the upper branch) and one where the flexible wall is collapsed (the lower branch), connected by an unstable intermediate branch. We test the stability of these steady configurations to oscillatory perturbations using both a global eigensolver (constructed based on an analytical domain mapping technique) and also fully nonlinear simulations. We find that both the lower and upper branches of steady solutions can become unstable to self-excited oscillations, where the oscillating wall profile has two extrema. In the absence of wall inertia, increasing wall thickness partially stabilises the onset of oscillations, but the effect remains weak until the wall thickness becomes comparable to the width of the undeformed channel. However, with finite wall inertia and a relatively thick wall, higher-frequency modes of oscillation dominate the primary global instability for large Reynolds numbers.

Atomic Metal–Support Interaction Enables Reconstruction-Free Dual-Site Electrocatalyst

Real bifunctional electrocatalysts for hydrogen evolution reaction and oxygen evolution reaction have to be the ones that exhibit a steady configuration during/after reaction without irreversible structural transformation or surface reconstruction. Otherwise, they can be termed as "precatalysts" rather than real catalysts. Herein, through a strongly atomic metal-support interaction, single-atom dispersed catalysts decorating atomically dispersed Ru onto a nickel-vanadium layered double hydroxide (LDH) scaffold can exhibit excellent HER and OER activities. Both in situ X-ray absorption spectroscopy and operando Raman spectroscopic investigation clarify that the presence of atomic Ru on the surface of nickel-vanadium LDH is playing an imperative role in stabilizing the dangling bond-rich surface and further leads to a reconstruction-free surface. Through strong metal-support interaction provided by nickel-vanadium LDH, the significant interplay can stabilize the reactive atomic Ru site to reach a small fluctuation in oxidation state toward cathodic HER without reconstruction, while the atomic Ru site can stabilize the Ni site to have a greater structural tolerance toward both the bond constriction and structural distortion caused by oxidizing the Ni site during anodic OER and boost the oxidation state increase in the Ni site that contributes to its superior OER performance. Unlike numerous bifunctional catalysts that have suffered from the structural reconstruction/transformation for adapting the HER/OER cycles, the proposed Ru/Ni3V-LDH is characteristic of steady dual reactive sites with the presence of a strong metal-support interaction (i.e., Ru and Ni sites) for individual catalysis in water splitting and is revealed to be termed as a real bifunctional electrocatalyst.

Critical effective radius for holes in thin films: Energetic and dynamic considerations

Questions regarding the stability of holes and arrays of holes in solid thin films have attracted much attention over the past few decades since an absence of holes is necessary for certain devices to operate properly and a presence of holes is needed in various industrial applications. Here, we study the energetic and dynamic stability of a single axisymmetric grain with a hole at its center, under the assumption that the exterior surface evolves by surface diffusion. Our energetic considerations enable us to formulate a criterion in terms of a critical effective hole radius, which distinguishes between energetically stable and unstable steady state hole configurations and which, somewhat surprisingly, is independent of the contact angle at the substrate and should be readily measurable in experiments. The set of steady states for the system is characterized in terms of admissible nodoidal surfaces, whose dynamic stability is studied via numerical simulation of the full non-linear dynamic problem for zero-volume perturbations. Our dynamic stability study confirms and extends our conclusions based on energetic considerations. Our results, moreover, confirm and extend the classical results of Srolovitz and Safran [J. Appl. Phys. 60, 247–254 (1986); J. Appl. Phys. 60, 255–260 (1986)] and Wong et al. [J. Appl. Phys. 81, 6091–6099 (1997); Acta Mater. 45, 2477–2484 (1997)]. Furthermore, our studies of the steady states and their stability contribute to our understanding of various phenomena observed in experiments: void formation, hillock formation, hole induction and propagation, ligament formation and evolution, blistering prior to film rupture, etc. Importantly, our study shows that in order to relate theory with experiments, careful monitoring of spatial variations in the mean curvature in experiments is required.

Rotor imbalance suppression by optimal control

AbstractAn imbalanced rotor is considered. A system of moving balancing masses is given. We determine the optimal movement of the balancing masses to minimize the imbalance on the rotor. The optimal movement is given by an open‐loop control solving an optimal control problem posed in infinite time. By methods of the Calculus of Variations, the existence of the optimum is proved and the corresponding optimality conditions have been derived. Asymptotic behavior of the control system is studied rigorously. By Łojasiewicz inequality, convergence of the optima as time towards a steady configuration is ensured. An explicit estimate of the convergence rate is given. This guarantees that the optimal control stabilizes the system. In case the imbalance is below a computed threshold, the convergence occurs exponentially fast. This is proved by the Stable Manifold Theorem applied to the Pontryagin optimality system. Moreover, a closed‐loop control strategy based on Reinforcement Learning is proposed. Numerical simulations have been performed, validating the theoretical results.