Separated Boundary Research Articles

Finite Spectrum of 2nth Order Boundary Value Problems with Transmission Conditions

For any positive integer 2n and any positive integer m, l, a class of regular self-adjoint and non-self-adjoint boundary value problems whose spectrum consists of at most eigenvalues is constructed. The key to this analysis is the division of intervals and an iterative construction of the characteristic function. In the self-adjoint case with separated boundary conditions this upper bound can be improved to

Densities and momentum distributions in A≤12 nuclei from chiral effective field theory interactions

This study presents calculations of one- and two-body densities in both coordinate and momentum space for various nuclei up to ${}^{12}$C, using the phenomenological AV18+UX and various Norfolk $N\phantom{\rule{0}{0ex}}N$ + $N\phantom{\rule{0}{0ex}}N\phantom{\rule{0}{0ex}}N$ $\ensuremath{\chi}$EFT interactions. It features new calculations of the pair density as a function of both pair separation and center-of-mass, as well as the two-body momentum distribution for short- and long-range pairs differentiated by a pair separation boundary. The full set of results are available online for general use by the nuclear physics community and are intended to provide useful insights into the short-range structure of nuclei and various reaction processes.

Stability analysis for a maximum principle preserving explicit scheme of the Allen–Cahn equation

In this study, we present the stability analysis of a fully explicit finite difference method (FDM) for solving the Allen–Cahn (AC) equation. The AC equation is a second-order nonlinear partial differential equation (PDE), which describes the antiphase boundaries of the binary phase separation. In the presented stability analysis, we consider the explicit Euler method for the temporal derivative and second-order finite difference in the space direction. The explicit scheme is fast and accurate because it uses a small time step, however, it has a temporal step constraint. We analyze and compute that the explicit time step constraint formula guarantees the discrete maximum principle for the numerical solutions of the AC equation. The numerical stability of the explicit scheme automatically holds when we use the time satisfying the discrete maximum principle. The computational numerical experiments demonstrate the stability, discrete maximum principle, and accuracy of the explicit scheme for the constrained time step. Furthermore, it is shown that the time step obtained is not severe restriction when we consider the temporal accuracy.

EXPERIMENTAL AND NUMERICAL ANALYSIS FOR MODIFICATION OF SEPARATED BOUNDARY LAYERS OVER NREL'S S822 USING BLOWING/SUCTION TECHNIQUES

The majority of wind turbine models are built to work in areas with high wind speeds. Such turbines would waste a lot of the energy available in low-speed zones. The performance of these turbines should be improved using sophisticated techniques in order to match the locations' available wind energy. Therefore, in the current study, active flow control (AFC) was applied over the NREL S822 profile (small horizontal wind turbine) using blowing/suction techniques to determine where these methods will be most effective. At a constant speed of 15.8 m/s and an angle of attack of 18 deg, blowing and suction techniques have been used either together or individually. The results showed that the use of the NREL S822 aerofoil with AFC enhances the wind turbine performance by an average of 15% compared to using no AFC. It was discovered that the technique at the B3 (x/c = 0.54) slot was the best blowing technique, and the technique at the S1 (x/c = 0.18) slot was the best suction case and the maximum lift-to-drag ratio (C<sub>L</sub>/C<sub>D</sub>) when S1B3 was activated, indicating that S1B3 is the best technique with an 87% improvement rate.

Modeling the wall shear stress in large-eddy simulation using graph neural networks

AbstractAs the Reynolds number increases, the large-eddy simulation (LES) of complex flows becomes increasingly intractable because near-wall turbulent structures become increasingly small. Wall modeling reduces the computational requirements of LES by enabling the use of coarser cells at the walls. This paper presents a machine-learning methodology to develop data-driven wall-shear-stress models that can directly operate, a posteriori, on the unstructured grid of the simulation. The model architecture is based on graph neural networks. The model is trained on a database which includes fully developed boundary layers, adverse pressure gradients, separated boundary layers, and laminar–turbulent transition. The relevance of the trained model is verified a posteriori for the simulation of a channel flow, a backward-facing step and a linear blade cascade.

Molecular dynamics simulation of the Ni – FLiNaK interface: adsorption layers as origin of metal passivity

The method of classical molecular dynamics was used to study the Ni (solid) – FliNaK (melt) phase separation boundary at temperatures of 800 K, 1000K , and 1200 K. An ab initio-based pairwise model is developed to describe the interactions that take place at the Ni – FLiNaK interface. It was shown that at temperatures of 800 K and 1000 K, lithium and fluorine ions are predominantly adsorbed on the nickel surface in the form of a two-dimensional ordered structure. Such a dense layer prevents the dissolution of nickel and the metal solid has no defects in the surface layer. However, at a temperature of 1200 K the structure of the adsorption layer is noticeably disturbed with the partial replacement of lithium ions by sodium ones. Along with higher temperature, this leads to the formation of point defects and degradation of the surface layers of the nickel crystal lattice.

Verification, calibration, and validation of stall delay models using NREL phase VI and MEXICO data

An accurate estimation of rotational effects is critical during the preliminary design of wind turbines. For this purpose, different stall delay models were developed based on the centrifugal pumping mechanism. However, their generality is not yet thoroughly evaluated. In this work, we investigated the causal relationship between the radial flow, the pressure reduction, and forces augmentation. Three stall delay models, which represent different solutions of the centrifugal pumping mechanism, were verified and modified to accurately predict the radial flow, the pressure coefficient, and normal and tangential force coefficients. Then, the three modified stall delay models were calibrated using radial flow data available from the literature. Finally, they were validated against the experimental data of the NREL phase VI and MEXICO rotors. The results showed that the centrifugal pumping produces a small chordwise pressure gradient in the separated boundary layer, which produces a small augmentation in the normal and tangential force coefficients. In contrast, the measured pressure coefficient and the normal and tangential force coefficients showed a large augmentation compared to the three modified stall delay models. Consequently, the lack of generality of current stall delay models is mainly due to the centrifugal pumping assumption. Furthermore, the verification and calibration of these stall delay models allowed us to isolate large errors in the model's output due to the model's assumptions. Thus, the importance of a rigorous verification and calibration before performing the validation.

Чи деградують термоелектричні генераторні модулі внаслідок дифузії нікелю

The author builds a strict diffusion theory of electrical contact resistance by studying the process of non-stationary diffusion of metal into the thermoelectric material, as a result of which a transition contact layer is formed. The distribution of metal atoms in the transition layer and the law of its growth are strictly determined from the condition of the balance of the substance quantity. It is shown that the relative distribution of nickel in the transition layer is described by a function erfc(6,771x), where erfc(…) is the so-called complementary error integral, and x is the normalized depth measured from the metal-thermoelectric material separation boundary. At the same time, the transition contact layer grows with time t according to the law x0 = 13,552(Dt)1/2, where D is the diffusion coefficient of the metal in the thermoelectric material, and its thickness is related to the thickness of the spent metal layer by the ratio x0 = 12h, where h the thickness of the spent nickel layer. Based on the obtained regularities, the temperature dependence of the electrical contact resistance of the transition layer and its time dependence (degradation law) were strictly calculated for the first time. It is shown that for the thickness of the spent nickel layer in the range of 5–20 μm and in the temperature range of 300–500 K, the electrical contact resistance varies in the range from 3,8•10–6 to 3,4•10–5 Ω•cm2 and increases over time according to the square root law. It is also shown that there is no reason to fear a significant decrease in the thermoelectric figure of merit of the generator material as a result of nickel concentration leveling through the thickness of the thermoelectric leg after its surface layer is depleted.

Inverse Sturm–Liouville problems with polynomials in nonseparated boundary conditions

An nonself-adjoint Sturm–Liouville problem with two polynomials in nonseparated boundary conditions are considered. It is shown that this problem have an infinite countable spectrum. The corresponding inverse problems is solved. Criterions for unique reconstruction of the nonself-adjoint Sturm-Liouville problem by eigenvalues of this problem and the spectral data of an additional problem with separated boundary conditions are proved. Schemes for unique reconstruction of the Sturm-Liouville problems with polynomials in nonseparated boundary conditions and corresponding examples are given

Intracellular phase separation of globular proteins facilitated by short cationic peptides

Phase separation provides intracellular organization and underlies a variety of cellular processes. These biomolecular condensates exhibit distinct physical and material properties. Current strategies for engineering condensate formation include using intrinsically disordered domains and altering protein surface charge by chemical supercharging or site-specific mutagenesis. We propose adding to this toolbox designer peptide tags that provide several potential advantages for engineering protein phase separation in bacteria. Herein, we demonstrate the use of short cationic peptide tags for sequestration of proteins of interest into bacterial condensates and provide a foundational study for their development as tools for condensate engineering. Using a panel of GFP variants, we demonstrate how cationic tag and globular domain charge contribute to intracellular phase separation in E. coli and observe that the tag can affect condensate disassembly at a given net charge near the phase separation boundary. We showcase the broad applicability of these tags by appending them onto enzymes and demonstrating that the sequestered enzymes remain catalytically active.

Large Eddy Simulation of Transitional Separated Flow Over a Low Reynolds Number Cambered Airfoil

Abstract The accurate simulation of the aerodynamic behavior of low Reynolds number (Re) cambered airfoils requires the ability to capture the transitional separated boundary layer (BL) that occurs naturally on the surface of the airfoil. In this study, simulations are performed using a modern cambered airfoil designed for use in low Re applications, which are an advancement from previous studies using flat plate geometries or symmetric NACA airfoils. The cambered SD 7037 airfoil is simulated using wall-resolved large eddy simulation (LES) at a modest Re of 4.1×104 and at 1 deg, 5 deg, and 7 deg angles of attack (AOAs), with results validated against experimental data. Simulated predictions of pressure and skin friction coefficients clearly capture the correct location of the laminar separated bubble (LSB) which forms during the natural BL transition process. Sensitivity to elevated inflow turbulence is found to cause early BL reattachment at higher AOAs without impacting the location of BL separation. An integral BL analysis verifies the accuracy of the simulated velocity profiles against experimental values. The scale of horseshoe structures visualized in the transitional BL is larger in comparison to airfoil chord length than what is seen in previous simulations at Re of the order of 105, which highlights the importance of investigating cambered airfoils at a modest Re.

A study on the effect of driver section length on the flow field inside a two-dimensional closed-ended viscous shock tube: A numerical investigation

The interaction of a reflected shock wave with the boundary layer inside a closed-ended shock tube is studied by many researchers using different numerical schemes. However, the interaction of a reflected shock wave having a decaying pressure profile ahead of the reflected shock is lacking in the literature. It is essential to quantify the deviation in flow characteristics experienced in tests performed inside the shock tube compared to field tests while studying blast wave attenuation and mitigation. In the present study, the effect of transient upstream pressure on the shock wave reflecting from a solid wall and the associated flow separation inside the boundary layer is examined in detail through numerical simulations using the viscous shock tube problem for Re = 1000. Simulations were performed using an in-house 13th-order high-resolution hybrid solver with 50 million grid points. The transient pressure profile behind the incident shock wave is achieved by varying the non-dimensional driver section length from 0.5 to 0.02 while keeping the overall shock tube length as 1. The flow field is scrutinized through numerical schlieren and vorticity plots. It is observed that the decaying pressure profiles behind the incident shock wave have an immense impact on the dynamics of shockwave-boundary layer interaction and the vortices emanating from the shear layer due to Kelvin–Helmholtz Instability. The secondary vortices inside the boundary layer, vortices at the shear layer, and compression waves in the separated boundary layer region reduce with a decrease in driver section length. The triple point height increases as driver section length decreases due to the weakening of upstream velocity. The Kelvin–Helmholtz vortices originating from the triple point moves back into the separated boundary layer rather than interacting with the end wall. It suggests that the decaying pressure behind the incident shock wave minimizes the secondary effects on the solid wall during shock wave impingement.

Artificial neural network-based wall-modeled large-eddy simulations of turbulent channel and separated boundary layer flows

Wall-models in a large-eddy simulation (LES) are essential to alleviate the large near-wall resolution requirements for high-Reynolds-number turbulent flow simulations. Among the existing wall-models for a LES, an equilibrium wall-stress model has the highest computational efficiency. Because this model has limitations, such as a lack of non-equilibrium effects and the assumption of a particular law of the wall in the mean velocity, we propose artificial neural network-based wall-stress models (AWMs). The input variables for the AWMs are extracted from the decomposition of the skin-friction coefficient proposed by Fukagata et al. [1], and the AWMs are shown to be able to predict the wall-shear stress in complex flows accurately. The performance of the AWMs is tested for two types of flows, a fully developed turbulent channel flow and a separated turbulent boundary layer flow. A direct comparison of the turbulence statistics with those obtained by previous wall-models (i.e., a log-law-based wall-stress model and a non-equilibrium wall-stress model) shows that better predictions are achieved using the AWMs for both flows, even with untrained Reynolds numbers. When using a coarse grid along the wall-normal direction in wall-modeled LESs (WMLESs) with the AWMs, an upward shift of the mean velocity profile (positive log-layer mismatch, LLM) compared to direct numerical simulation data is found, consistent with previous studies. However, this LLM problem can be overcome by imposing a filtered wall-normal velocity at the wall that is dynamically determined based on the continuity equation and the Taylor series expansion within wall-adjacent cells.

Experimental study of laminar-to-turbulent transition in an adverse pressure gradient flow

Experimental results on laminar-to-turbulent transition in a separated laminar boundary layer formed over a flat plate in an adverse pressure gradient are provided. Experiments have been performed for a range of Reynolds numbers (1.4 − 2.4 · 105) and for two freestream turbulence levels (Tu =3.6 and 5.3%). The measurements of mean and fluctuating velocity profiles have been carried out at inlet to the test section using Constant Temperature Anemometry (CTA). The data might be useful for validation and development of transition models. In order to characterize the dynamics leading to the transition process in the separated boundary layer on the plate surface, the Particle Image Velocimetry (PIV) measurements have been performed. The results show that the transition process in the separated boundary layer is influenced by breakdown of the Klebanoff streaks.

Experimental analysis of the impact of an acoustic excitation on a separated boundary layer behaviour

The paper examines the effect of acoustic excitation at broadband frequency range (100 - 650 Hz) on separated boundary layer developing on a flat plate subjected to an adverse pressure gradient. The experiment was conducted with a low inlet turbulence intensity level (Tu < 1%) in order to provide a cleaner environment that magnifies the effects of the excitation frequency. It was shown that acoustic excitation at sound pressure levels: SPL=125 and 135 dB, can lead to a more rapid increase in flow instability followed by an earlier laminar-turbulent (l-t) transition. The boundary layer reattachment point was shifted upstream and the size of the separation bubble was reduced in the flow with the acoustic excitation active.

Comparative Modal Study of the Two-Dimensional and Three-Dimensional Transonic Shock Buffet

A computational comparative study of the shock buffet phenomenon is presented. A comparison between the two-dimensional airfoil buffet and the three-dimensional swept-wing buffet is made at pre-buffet and developed buffet flow conditions to shed further light on the distinct mechanisms that characterize the phenomena. We perform modal analysis using dynamic mode decomposition and compare the dominant modal shapes and time-space evolution of the wing’s full flow field to the airfoil. This allows to characterize their distinct dominant driving mechanisms. While the airfoil buffet involves a strong interaction between the shock wave and the separated boundary layer behind it, we show that the finite-wing buffet exhibits mainly spanwise traveling perturbations that induce only small chordwise shock travel, with only weak interaction between the shock wave and boundary layer. The finite-wing shock excursion distance is significantly smaller than the airfoil’s, while the average chordwise shock wave velocities are shown to be comparable, providing a physical explanation for the swept-wing buffet frequencies that are higher than those of an airfoil.

Enhanced Hemolytic Activity of Mesophilic Aeromonas salmonicida SRW-OG1 Is Brought about by Elevated Temperatures.

Aeromonas salmonicida is a well-known cold-water pathogenic bacterium. Previously, we reported the first isolation of pathogenic A. salmonicida from diseased Epinephelus coioides, a kind of warm-water fish, and it was proved to be a putative mesophilic strain with potent pathogenicity to humans. In order to investigate the mechanisms underlying mesophilic growth ability and virulence, the transcriptome of A. salmonicida SRW-OG1 at 18, 28, and 37 °C was analyzed. The transcriptome of A. salmonicida SRW-OG1 at different temperatures showed a clear separation boundary, which might provide valuable information for the temperature adaptation and virulence regulation of A. salmonicida SRW-OG1. Interestingly, aerA and hlyA, the hemolytic genes encoding aerolysin and hemolysin, were found to be significantly up-regulated at 28 and 37 °C. Since aerolysin and hemolysin are the most well-known and -characterized virulence factors of pathogenic Aeromonas strains, the induction of aerA and hlyA was associated with the mesophilic virulence. Further study proved that the extracellular products (ECPs) purchased from A. salmonicida SRW-OG1 cultured at 28 and 37 °C showed elevated hemolytic activity and virulence than those at 18 °C. Moreover, the silence of aerA and hlyA led to significantly decreased hemolysis and virulence. Taken together, our results revealed that the mesophilic virulence of A. salmonicida SRW-OG1 might be due to the enhanced expression of aerA and hlyA induced by elevated temperatures.

SPECTRAL DATA ASYMPTOTICS FOR THE HIGHER-ORDER DIFFERENTIAL OPERATORS WITH DISTRIBUTION COEFFICIENTS

In this paper, the asymptotics of the spectral data (eigenvalues and weight numbers) are obtained for the higher-order differential operators with distribution coefficients and separated boundary conditions. Additionally, we consider the case when, for the two boundary value problems, some coefficients of the differential expressions and of the boundary conditions coincide. We estimate the difference of their spectral data in this case. Although the asymptotic behaviour of spectral data is well-studied for differential operators with regular (integrable) coefficients, to the best of the author’s knowledge, there were no results in this direction for the higher-order differential operators with distribution coefficients (generalized functions) in a general form. The technique of this paper relies on the recently obtained regularization and the Birkhoff-type solutions for differential operators with distribution coefficients. Our results have applications to the theory of inverse spectral problems as well as a separate significance.

Building a mathematical model to prevent hydrate formation in gas pipelines

Development of mathematical models of laminar gas flow in certainty and uncertainty conditions were considered. All factors that influence to character of flow of gas in pipeline and conditions of arising of hydrate inside of pipeline wall are analyzed. Results of analyze were used for development mathematical model of gas flow in pipeline that allow to calculate main parameters of hydrate deposition process. Model of gas flow consist of three non-linear differential equations that can be solved by exist soft wares. Two and three-dimension characteristic obtained, that describe of quantity of hydrate deposited at given process depending on time.&#x0D; Besides, the effectiveness of using DELPHI 7 software to determine the preparation of gas for transportation and the hydrates formed during transportation and its prevention based on the results of the application software was discussed. As a result, the change in cross-sectional area of the pipeline of hydrates formed on the inner surface of the pipeline is shown in 3D. Hydrate formation and elimination are visually represented by graphs. The results of theoretical and practical studies of changes in the inner surface of the pipeline depending on temperature and pressure have been identified. All this was investigated during quasi-stationary gas flow in the pipelines and the results were obtained.&#x0D; The assumes regarding calculation of parameters of gas flow were determined and necessary recommendations for applying of developed model in different conditions with taking account of temperature and pressure variation and depending on time of hydrate deposition were presented. The diagram of gas-hydrate separation boundary considered for detailed analysis of process

Towards Predicting Partitioning of Enzymes between Macromolecular Phases: Effects of Polydispersity on the Phase Behavior of Nonadditive Hard Spheres in Solution.

The ability to separate enzymes, or cells or viruses, from a mixture is important and can be realized by the incorporation of the mixture into a macromolecular solution. This incorporation may lead to a spontaneous phase separation, with one phase containing the majority of one of the species of interest. Inspired by this phenomenon, we studied the theoretical phase behavior of a model system composed of an asymmetric binary mixture of hard spheres, of which the smaller component was monodisperse and the larger component was polydisperse. The interactions were modeled in terms of the second virial coefficient and could be additive hard sphere (HS) or nonadditive hard sphere (NAHS) interactions. The polydisperse component was subdivided into two subcomponents and had an average size ten or three times the size of the monodisperse component. We gave the set of equations that defined the phase diagram for mixtures with more than two components in a solvent. We calculated the theoretical liquid–liquid phase separation boundary for the two-phase separation (the binodal) and three-phase separation, the plait point, and the spinodal. We varied the distribution of the polydisperse component in skewness and polydispersity, and we varied the nonadditivity between the subcomponents as well as between the main components. We compared the phase behavior of the polydisperse mixtures with binary monodisperse mixtures for the same average size and binary monodisperse mixtures for the same effective interaction. We found that when the compatibility between the polydisperse subcomponents decreased, the three-phase separation became possible. The shape and position of the phase boundary was dependent on the nonadditivity between the subcomponents as well as their size distribution. We conclude that it is the phase enriched in the polydisperse component that demixes into an additional phase when the incompatibility between the subcomponents increases.