Boundary Region Research Articles

A novel multi-source TWD model based on multi-granularity ball for multiple decision makers

Three-way incomplete multi-attribute decision-making model (TWIMADM) for multiple decision makers is an important topic in data science, which is an effective tool for decision making. However, calculation results of neighborhood blocks are still affected by neighborhood radius. In addition, most of the existing models without considering the information from the evaluations of multiple decision makers separately is difficult to obtain a comprehensive assessment. To address these problems, this paper builds a novel multi-source TWD model based on multi-granularity ball. First, the well-established granular ball is extended to multi-granularity, by which a weighted conditional probability is generated to divide the concerned region into three parts: positive, negative and boundary region. The calculation of the multi-granularity ball is independence of the neighborhood radius parameter. Subsequently, the joint entropy is developed by using the defined multi-granularity to obtain the optimal decision. Furthermore, the relative utility function is utilized to capture the preferences of decision makers, the classification and ranking of each object are determined by calculating the threshold value and expected utility value. Evaluation information from all decision makers are combined and fused. Finally, a novel TWD model is developed to address the challenges of incomplete multi-attribute decision-making problems involving multiple decision makers. The comparative case analyses and experimental evaluations have demonstrated the stability, validity, and feasibility of our model.

Long-term efficacy of liposomal nanocarriers of preassembled glycocalyx in restoring cerebral endothelial glycocalyx in sepsis

The endothelial glycocalyx (EG) undergoes early degradation in sepsis. Our recent work introduced a novel therapeutic approach involving liposomal nanocarriers of preassembled glycocalyx (LNPG) to restore EG in lipopolysaccharide (LPS)-induced sepsis model of mice. While short-term effects were promising, this study focuses on the long-term impact of LNPG on mouse cerebral microcirculation. Utilizing cranial window, we assessed the stability of vascular density (VD) and perfused boundary region (PBR), an index of EG thickness, over a five-day period in normal control mice. In septic groups (LPS, LPS + 1-dose LNPG, and LPS + 2-dose LNPG), the exposure of mice to LPS significantly reduced VD and increased PBR within 3 h. Without LNPG treatment, PBR returned to the normal control level by endogenous processes at 48 h, associated with the recovery of VD to the baseline level at 72 h. However, mice receiving LNPG treatment significantly reduced the increment of PBR at 3 h. The therapeutic effect of 1-dose LNPG persisted for 6 h while the 2-dose LNPG treatment further reduced PBR and significantly increased VD at 12 h compared to LPS group. This study provides valuable insights into the potential therapeutic benefits of LNPG in mitigating EG degradation in sepsis.

Boundary mixing. Part 2. The impact of ventilation

Through a combination of laboratory experiments and theoretical models, we investigate the interaction of a mean upwelling through a closed basin with a vertical buoyancy flux. The fluid is mixed by a horizontally oscillating rake, which either traverses the whole basin or which oscillates just near one vertical boundary. We first review the steady state and demonstrate that, in both mixing regimes, the vertical density profile across the basin is controlled by the steady-state balance between the upward advective and diffusive fluxes of salinity as described by the classical model introduced by Munk (Deep-Sea Res., vol. 13, issue 4, 1966, pp. 707–730). However, with boundary mixing, we show that both the upwelling and the buoyancy transport are localised to the mixing zone near the boundary, and the interior fluid is stagnant. We then develop a model to describe the transient evolution of the system if there is either a discrete increase or gradual decrease to the buoyancy flux. In the boundary mixing case, the change in the buoyancy flux at the lower boundary leads to a change in the buoyancy of the fluid in the boundary mixing region, and this induces a transient, buoyancy-driven flow in the boundary region in addition to the steady upwelling. In turn, an equal and opposite vertical flow develops in the interior, and this leads to a change in the density stratification of the interior fluid as the system adjusts to a new equilibrium. However, in our experiments, there is no vertical mixing in the interior and interior fluid may upwell or downwell dependent on the change to the buoyancy forcing. We discuss the implications of our results for the transport and mixing in the deep ocean, and the associated interpretation of field experiments.

Optimizations of the Accelerated Axial Polynomial Method of Characteristics of the APOLLO3® Deterministic Neutron Transport Code

For some years now, the TDT (two- and three-dimensional transport) solver of the APOLLO3® deterministic neutron transport code has been able to perform lattice calculations on three-dimensional extruded and unstructured geometries. A polynomial expansion of the angular flux has been implemented to better describe the flux gradient axially to reduce the number of computational meshes required to reach a given accuracy. Then the polynomial approximation was extended to macroscopic cross sections to perform evolution calculations. Besides these transport schemes, synthetic acceleration has also been implemented, relying on double PN approximations of the angular flux on the boundaries of the spatial regions. The solver has already introduced several techniques to reduce the transport and memory footprint; for example, for the storage of the surfaces crossed by a trajectory or the classification of chords. In this paper, new optimizations are presented. One deals with how monomials of the polynomial basis are integrated along trajectories. Another one concerns the computation of the source term of the transmission equation in the case of polynomial cross sections. The last optimization exploits the fact that, along horizontal trajectories, the flux and the cross sections are constant to speed up the sweep algorithm. Calculations on 5 × 5 and 7 × 7 pressurized water reactor assemblies were performed to assess the gains of these recently developed strategies. The results show good improvements both in computing time and in memory footprint reductions.

Effect of chromatin structure modifiers on the trans-acting heterochromatin position effect in <i>Drosophila melanogaster</i>

The heterochromatin position effect is manifested in the inactivation of euchromatin genes transferred to heterochromatin. In chromosomal rearrangements, genes located near the new eu-heterochromatin boundary in the rearrangement (cis-inactivation) and, in rare cases, genes of a region of the normal chromosome homologous to the region of the eu-heterochromatin boundary of the chromosome with the rearrangement (trans-inactivation) are subject to inactivation. The In(2)A4 inversion is able to trans-inactivate the UAS-eGFP reporter gene located on the normal chromosome. We knockdown a number of chromatin proteins using temperature-controlled RNA interference and investigated the effect of knockdown on trans-inactivation of the reporter. We found suppression of trans-inactivation by knockdowns of Su(var)2-HP2, a protein that binds to the key heterochromatin protein HP1a, SAYP, a subunit of the chromatin remodelling complex, and Eggless histone methyltransferase (SETDB1), which introduces a H3K9me3 histone mark, recognized by the HP1a protein. The method of studying the effects of gene knockdown on heterochromatin position effects presented in this work is of independent methodological interest.

Damage evaluation of the austenitic heat-resistance steel subjected to creep by using Kikuchi pattern parameters

Abstract Austenitic heat-resistance steel is widely employed in ultra-supercritical power generation because of its superior performance. This article reports the evaluation of creep damage of a typical Super304H austenitic heat-resistance steel by using the Kikuchi pattern parameters, such as band contrast (BC), mean angular deviation (MAD), and band slope (BS). It was found that the mean BC and MAD values did not show a monotonic changing trend and then an in-depth research that distinguished grain boundary and grain interior regions of Super304H steel was studied, respectively. The results manifested that, with the increase of creep time, both the mean BC and BS values showed a monotonic decreasing trend, while the MAD did not. Besides, compared with the BC, the change amplitude of BS was larger. The results indicate that the BS could be a useful indicator, which can be utilized to evaluate the creep degree of Super304H steel in a quantitative way.

A time-domain SGFD-FK hybrid method for 2D teleseismic elastic wave modeling and inversion

AbstractFull waveform inversion (FWI) has proved to be a reliable tool for high-resolution imaging of lithospheric structures at various depths down to the upper mantle. However, when the size of the model is large, the computational burden is significative and applications are restricted to low frequencies. To tackle this issue, we developed a new 2D time-domain hybrid method to simulate high-frequency teleseismic body waves propagating through a local heterogeneous elastic Earth model: The frequency-wavenumber (FK) integration method is coupled with the staggered grid finite difference method (SGFD). The FK method is used to compute the wavefield due to obliquely incident plane P and SV waves in a 1D multilayered half space that excites a local heterogeneous region. Inside this region, the velocity-stress staggered grid FD method (SGFD) is used to accurately deal with wave propagation in heterogeneous media. Spurious waves that might be generated at the boundaries of the local region are avoided using convolutional perfectly matched layers (CPML). This new hybrid method inherits the low-memory requirements of the FK method and the accuracy, efficiency and easy implementation of the SGFD. The new hybrid method is benchmarked against the analytical FK method for some canonical models and shows good agreement with analytical solutions. Subsequently, our modeling tool is incorporated into a full waveform inversion algorithm adapted for teleseismic configurations to invert the incident P wave and its coda. The inversion is carried out using a gradient approach that is efficiently implemented via the adjoint-state method. The results suggest that our hybrid method and FWI algorithm represent a valuable tool for 2D forward and inverse regional applications using teleseismic data sets.

Role of dietary interventions on microvascular health in South-Asian Surinamese people with type 2 diabetes in the Netherlands: A randomized controlled trial

Background/objectivesWe investigated whether dietary interventions, i.e. a fasting mimicking diet (FMD, Prolon®) or glycocalyx mimetic supplementation (EndocalyxTM) could stabilize microvascular function in Surinamese South-Asian patients with type 2 diabetes (SA-T2DM) in the Netherlands, a patient population more prone to develop vascular complications.Subjects/methodsA randomized, placebo controlled, 3-arm intervention study was conducted in 56 SA-T2DM patients between 18 and 75 years old, for 3 consecutive months, with one additional follow up measurement 3 months after the last intervention. Sublingual microcirculation was assessed with SDF-imaging coupled to the GlycoCheckTM software, detecting red blood cell velocity, capillary density, static and dynamic perfused boundary region (PBR), and the overall microvascular health score (MVHS). Linear mixed models and interaction analysis were used to investigate the effects the interventions had on microvascular function.ResultsDespite a temporal improvement in BMI and HbA1c after FMD the major treatment effect on microvascular health was worsening for RBC-velocity independent PBRdynamic, especially at follow-up. Glycocalyx supplementation, however, reduced urinary MCP-1 presence and improved both PBRdynamic and MVHSdynamic, which persisted at follow-up.ConclusionsWe showed that despite temporal beneficial changes in BMI and HbA1c after FMD, this intervention is not able to preserve microvascular endothelial health in Dutch South-Asian patients with T2DM. In contrast, glycocalyx mimetics preserves the microvascular endothelial health and reduces the inflammatory cytokine MCP-1.Clinical study registrationNCT03889236.

A 2-Stable Family of Triple Systems

For many well-known families of triple systems $\mathcal{M}$, there are perhaps many near-extremal $\mathcal{M}$-free configurations that are far from each other in edit-distance. Such a property is called non-stable and is a fundamental barrier to determining the Turán number of $\mathcal{M}$. Liu and Mubayi gave the first finite example that is non-stable. In this paper, we construct another finite family of triple systems $\mathcal{M}$ such that there are two near-extremal $\mathcal{M}$-free configurations that are far from each other in edit-distance. We also prove its Andrásfai-Erdős-Sós type stability theorem: Every $\mathcal{M}$-free triple system whose minimum degree is close to the average degree of the extremal configurations is a subgraph of one of these two near-extremal configurations. As a corollary, our main result shows that the boundary of the feasible region of $\mathcal{M}$ has exactly two global maxima.

Cancellative hypergraphs and Steiner triple systems

A triple system is cancellative if it does not contain three distinct sets A,B,C such that the symmetric difference of A and B is contained in C. We show that every cancellative triple system H that satisfies a particular inequality between the sizes of H and its shadow must be structurally close to the balanced blowup of some Steiner triple system. Our result contains a stability theorem for cancellative triple systems due to Keevash and Mubayi as a special case. It also implies that the boundary of the feasible region of cancellative triple systems has infinitely many local maxima, thus giving the first example showing this phenomenon.

Grain-selective growth makes Al0.1CoCrFeNi high entropy alloys strong and ultra-ductile

The trade-off between strength and ductility of structural materials has always been a concern, and the pursuit of higher strength often comes with the inevitable sacrifice of ductility, which poses challenges for the design and manufacture of high-performance engineering materials. In this study, we introduce a novel concept called grain-selective growth (GSG) to address the strength-ductility trade-off by effectively triggering the strain hardening capacity of the single-phase FCC HEAs. Specifically, we prepared an Al0.1CoCrFeNi high-entropy alloy with a heterogeneous grain structure using cyclic rolling and annealing. By employing this approach, our GSG HEA achieves an ultra-ductility with ∼53% uniform elongation and an ultimate tensile strength of 1165 MPa. Rapidly accumulating geometrically necessary dislocations in the domain boundary region, as revealed through electron backscatter diffraction analysis, have led to the development of high-level heterogeneous deformation-induced (HDI) stress. In addition, we also observed synergistic strain hardening effects generated by various deformation mechanisms, such as dislocation pile-ups, stacking faults (SFs), deformation twinning, dislocation walls, and SF networks. This study provides valuable insights for the manufacturing of high-performance heterostructure materials, making it possible to develop advanced alloys with higher strength and ductility, suitable for a wide range of engineering applications.

Defining the Cortical Purchase Zone in New Minimally Invasive Bunion Surgery. A Retrospective Study of 638 Cases.

Introduction The stability of the screws in the cortical purchase zone (CPZ) with new minimally invasive bunion surgery (MIBS) is of utmost importance in creating a stable construct for maintaining position and providing a scaffold for bone healing. The distance between the osteotomy and where the screw(s) exit the lateral cortex (a distance we herein coin the “Cortical Runway”) within the CPZ has yet to be studied, and is the focus of this retrospective study. Methods A retrospective review was preformed of a single surgeons first and consecutive cases of patients who had undergone MIBS from January 2018 to November 2022. The CPZ measurement was obtained on early postoperative radiographs. The CPZ was divided into five stability regions using the statistical empirical rule to define the boundaries of each of the regions. Results We included 427 patients and 638 feet in this study. Radiographic measurements were performed at an average 20.7±24.2 days (95% CI, 15.3–15.8 days) from surgery. The mean age of the patients was 46.5±15.0 years (95% CI, 45.3–47.6 years). There were 330 (51.7%) right feet and 308 (48.3%) left feet. Of the 427 patients, 211 (49.4%) had surgery on both feet, with 97 (46%) having both feet operated on the same day. A 1-screw construct was performed in 526 feet (82.4%) and a 2-screw construct in 112 feet (17.6%) of the total 638 feet. The mean anchor screw (primary screw) distance was 10.4±3.7mm (95% CI, 10.1-10.7mm). The mean collateral screw (secondary screw) distance was 1.2±2.0mm (95% CI, 0.8-1.5) and the mean cortical bridge (distance between the two screws) was 10.3±3.2mm (95% CI, 9.7-10.9), in 112 feet. We were able to define the CPZ stability region boundaries, which are: danger (< 2.9mm), vulnerable (3.0 - 6.6mm), standard (6.6 - 14.1mm), safety (14.2 - 17.8mm) and the security (> 17.9mm). Conclusion These CPZ boundaries and newly delineated stability regions will serve not only as an intraoperative visual tool for surgeons to perform MIBS successfully, but will also provide a much more stable and safer construct, thus minimizing risks and complications.

Parallel Computation of Piecewise Linear Morse-Smale Segmentations.

This article presents a well-scaling parallel algorithm for the computation of Morse-Smale (MS) segmentations, including the region separators and region boundaries. The segmentation of the domain into ascending and descending manifolds, solely defined on the vertices, improves the computational time using path compression and fully segments the border region. Region boundaries and region separators are generated using a multi-label marching tetrahedra algorithm. This enables a fast and simple solution to find optimal parameter settings in preliminary exploration steps by generating an MS complex preview. It also poses a rapid option to generate a fast visual representation of the region geometries for immediate utilization. Two experiments demonstrate the performance of our approach with speedups of over an order of magnitude in comparison to two publicly available implementations. The example section shows the similarity to the MS complex, the useability of the approach, and the benefits of this method with respect to the presented datasets. We provide our implementation with the paper.

Downscaling grain size toward the nanometre range – A key-factor for tuning the crystalline structure, phase transitions, dielectric and ferroelectric behaviour in Ba0·8Sr0·2TiO3 ceramics

The present study aims to describe the role of the grain size on the properties of submicron- and nano-structured Ba0·8Sr0·2TiO3 (BST) ceramics. Dense (1 − 2% porosity) ceramics with average grain sizes in the range of (77 − 234) nm were consolidated under different spark plasma sintering conditions starting from nanopowders with a mean particle size of 70 nm, synthesized via the acetate variant of the sol-gel method. The structural analysis based on XRD data revealed a mixture of cubic and tetragonal modifications at room temperature for the precursor powders and for all the investigated ceramics. The structural heterogeneity of the individual ceramic grains with coexistence of cubic and tetragonal polymorphs was confirmed by HR-TEM investigations. Accordingly, a “brick-wall" model with cubic grain boundary regions and tetragonal grain cores is proposed. By increasing the grain size, from 77 to 234 nm, a decrease of the phase transitions diffuseness accompanied by an increase of the permittivity maxima (from 650 to 4500) and dielectric losses (from 5 to 7.5%, at 100 Hz), was detected by broadband dielectric spectroscopy. No variation of the Curie temperature in the investigated Ba0·8Sr0·2TiO3 ceramics was detected, unlike typically reported for BaTiO3 ceramics with similar grain sizes. The Curie-Weiss temperature and the Curie constant decrease when grain size is diminished, indicating an overall reduction of the ferroelectric active volume, as a scaling effect. The ferroelectric switching was demonstrated for all the selected fine-grained BST ceramics, either at nanoscale or macroscopically, with an increased ferroelectric character for the coarser submicron-structured ceramics, with respect to the nanocrystalline one. The observed properties of the fine-grained Ba0·8Sr0·2TiO3 ceramics are explained in the frame of multiphase coexistence and ferroelectricity “dilution” due to the increasing role of non-ferroelectric grain boundaries when reducing grain size and complete the knowledge on the scale-dependent properties of dense fine-grained BaTiO3-based ceramics.

Persistent Upflows and Downflows at Active Region Boundaries Observed by SUTRI and AIA

Upflows and downflows at active region (AR) boundaries have been frequently observed with spectroscopic observations at extreme ultraviolet passbands. In this paper, we report the coexistence of upflows and downflows at the AR boundaries with imaging observations from the Solar Upper Transition Region Imager (SUTRI) and the Atmospheric Imaging Assembly (AIA). With their observations from 2022 September 21 to 2022 September 30, we find 17 persistent opposite flows occurring along the AR coronal loops. The upflows are prominent in the AIA 193 Å images with a velocity of 50–200 km s−1, while the downflows are best seen in the SUTRI 465 Å and AIA 131 Å images with a slower velocity of tens of kilometers per second (characteristic temperatures (log T(K)) for 193, 465, and 131 Å are 6.2, 5.7, and 5.6, respectively). We also analyze the center-to-limb variation of the velocities for both upflows and downflows. The simultaneous observations of downflows and upflows can be explained by the chromosphere–corona mass-cycling process, in which the localized chromospheric plasma is impulsively heated to coronal temperature forming a upflow and then these upflows experience radiative cooling producing a downflow with the previously heated plasma returning to the lower atmosphere. In particular, the persistent downflows seen by SUTRI provide strong evidence of the cooling process in the mass cycle. For upflows associated with open loops, part of the plasma is able to escape outward and into the heliosphere as solar wind.

Initial Experience of NIR-II Fluorescence Imaging-Guided Surgery in Foot and Ankle Surgery

Optical imaging in the second near-infrared (NIR-II; 900–1880 nm) window is currently a popular research topic in the field of biomedical imaging. This study aimed to explore the application value of NIR-II fluorescence imaging in footandankle surgeries. A lab-established NIR-II fluorescence surgical navigation system was developed and used to navigate foot and ankle surgeries which enabled obtaining more high-spatial-frequency information and a higher signal-to-background ratio (SBR) in NIR-II fluorescence images compared to NIR-I fluorescence images; our result demonstrates that NIR-II imaging could provide higher-contrast and larger-depth images to surgeons. Three types of clinical applicationscenarios (diabetic foot, calcaneal fracture, and lower extremity trauma) were included in this study. Using the NIR-II fluorescence imaging technique, we observed the ischemic region in the diabetic foot before morphologicalalterations, accurately determined the boundary of the ischemic region in the surgical incision, and fully assessed the blood supply condition of the flap. NIR-II fluorescence imaging can help surgeons precisely judge surgical margins, detect ischemic lesions early, and dynamically trace the perfusion process. We believe that portable and reliable NIR-II fluorescence imaging equipment and additional functional fluorescent probes can play crucial roles in precision surgery.

The Subcortical Atlas of the Marmoset ("SAM") monkey based on high-resolution MRI and histology.

A comprehensive three-dimensional digital brain atlas of cortical and subcortical regions based on MRI and histology has a broad array of applications in anatomical, functional, and clinical studies. We first generated a Subcortical Atlas of the Marmoset, called the "SAM," from 251 delineated subcortical regions (e.g. thalamic subregions, etc.) derived from high-resolution Mean Apparent Propagator-MRI, T2W, and magnetization transfer ratio images ex vivo. We then confirmed the location and borders of these segmented regions in the MRI data using matched histological sections with multiple stains obtained from the same specimen. Finally, we estimated and confirmed the atlas-based areal boundaries of subcortical regions by registering this ex vivo atlas template to in vivo T1- or T2W MRI datasets of different age groups (single vs. multisubject population-based marmoset control adults) using a novel pipeline developed within Analysis of Functional NeuroImages software. Tracing and validating these important deep brain structures in 3D will improve neurosurgical planning, anatomical tract tracer injections, navigation of deep brain stimulation probes, functional MRI and brain connectivity studies, and our understanding of brain structure-function relationships. This new ex vivo template and atlas are available as volumes in standard NIFTI and GIFTI file formats and are intended for use as a reference standard for marmoset brain research.

The Effect of Bi0.5Li0.5ZrO3-SrSnO3 Composite Doping on the Construction of Polymorphic Phase Boundaries and Enhanced Electrical Properties of K0.45Na0.55Nb0.965Sb0.035O3 Piezoelectric Ceramics

In this experiment, a new lead-free piezoelectric ceramics (1−x)K0.45Na0.55Nb0.965Sb0.035O3−x(0.9Bi0.5Li0.5ZrO3−0.1SrSnO3) were prepared by the conventional solid-phase method, and the effects of the doping amount of 0.9Bi0.5Li0.5ZrO3−0.1SrSnO3 on the K0.45Na0.55Nb0.965Sb0.035O3 ceramics on the crystal structure, microstructure, microscopic structure and electrical properties. All the doping ions entered the KNN lattice and formed a dense solid solution with a single-phase structure, and the phase structure of the ceramics coexisted from orthorhombic (O) to orthorhombic-tetragonal (O-T) phases in the range of 0 ≤ x ≤ 0.03, and transitioned to rhombohedral-tetragonal (R-T) phase coexistence when 0.035 ≤ x ≤ 0.05. The electrical properties of the ceramics were analyzed and the polymorphic phase boundary (PPB) region was obtained at x = 0.035 and had the best overall properties: d 33 = 324pC/N, k p = 49%, ε r = 1479, tanδ = 3.21%, P r = 31.98 μC/cm2, E c = 16.83 kV cm−1 and T C = 293°C. By The microstructural analysis of the ceramics showed that the appropriate amount of compound doping of the second element enhances the denseness of the ceramics as well as makes the grains uniformly distributed. These results indicate that the ceramics of this system have great prospects for future applications in the field of lead-free piezoelectric ceramics.

Acridine-Isoxazole and Acridine-Azirine Hybrids: Synthesis, Photochemical Transformations in the UV/Visible Radiation Boundary Region, and Anticancer Activity.

Easy-to-handle N-hydroxyacridinecarbimidoyl chloride hydrochlorides were synthesized as convenient nitrile oxide precursors in the preparation of 3-(acridin-9/2-yl)isoxazole derivatives via 1,3-dipolar cycloaddition with terminal alkynes, 1,1-dichloroethene, and acrylonitrile. Azirines with an acridin-9/2-yl substituent attached directly or via the 1,2,3-triazole linker to the azirine C2 were also synthesized. The three-membered rings of the acridine-azirine hybrids were found to be resistant to irradiation in the UV/visible boundary region, despite their long-wave absorption at 320-420 nm, indicating that the acridine moiety cannot be used as an antenna to transfer light energy to generate nitrile ylides from azirines for photoclick cycloaddition. The acridine-isoxazole hybrids linked at the C9-C3 or C2-C3 atoms under blue light irradiation underwent the addition of such hydrogen donor solvents, such as, toluene, o-xylene, mesitylene, 4-chlorotoluene, THF, 1,4-dioxane, or methyl tert-butyl ether (MTBE), to the acridine system to give the corresponding 9-substituted acridanes in good yields. The synthesized acridine-azirine, acridine-isoxazole, and acridane-isoxazole hybrids exhibited cytotoxicity toward both all tested cancer cell lines (HCT 116, MCF7, and A704) and normal cells (WI-26 VA4).

Стационарное протекание несжимаемой вязкой жидкости сквозь двухмерный разветвленный канал

The results of a numerical experiment for the problem of an incompressible viscous fluid stationary flow through a branched planar (two-dimensional) channel are presented. The region in which the flow occurs simulates either blood vessels or a river delta. The finite element method and a modification of the penalty method, as well as the splitting method, are used for calculations. The implementation of the calculation algorithm is using with the help the package FreeFem++. The main goal, in addition, of course, to study the properties and structure of the stationary flow, is to demonstrate the effectiveness of the proposed modification of the penalty method. It is assumed that the region has one input boundary section through which the liquid flows into the region, and several (five) boundary sections through which the liquid flows out of the region. The remaining sections of the region boundary are considered impermeable to liquid. The boundary condition corresponding to the Poiseuille flow in a plane rectilinear channel is set at the input section. Three types of boundary conditions are considered on the output boundary secctions. 1. The boundary conditions correspond to the conditions of conservation of motion of luid particles i. e. the material derivative of the velocity is zero. 2. The boundary conditions correspond to the setting of the flow velocity. 3. The boundary conditions correspond to the setting of the same pressure. The stationary solution is constructed by the relaxation method. In fact, a non-stationary problem is solved over a sufficiently large time interval. As an initial condition for a non-stationary problem, a flow is chosen that is a Poiseuille flow in some region near the input boundary. The dependence of the convergence rate of the relaxation method on the initial data is investigated. It is found that the Poiseuille flow, given at the input section of the boundary of the region, induces similar Poiseuille flows at the output boundaries sections of the region in all these cases of boundary conditions. For a region with five sections of the output boundaries for some configuration of the region, the presence of stationary vortex flows (‘maelstorm’) is found.