Study on Agro-meteorological Conditions for Film Mulching Planting in Autum

The agro-meteorological conditions for film mulching planting in autumn in Xiji, Ningxia was studied by using the meteorological data from the national basic stations over the years, including the mulching planting of corn in autumn in differ- ent stages from 1985 to 1986, the mulching planting in different stages after the appearance of effective precipitation in October, and the wind simulation experimen- tal data of blower. Precipitation suitability analysis model before autumn film mulching and crop growth period was simulated to analyze the effective precipitation weather before mulching planting in autumn, and simulations were also made to temperature suitability analysis model during soil preparation and film mulching peri- ods in autumn, the suitability function of optimal sowing time about the soil moisture dynamic changes in autumn in different times, the best water conservation effect in film mulching period at different time after the appearance of effective precipitation, the wind resistance function of film mulching in autumn. All the simulation work was of high referential value to carry out meteorological service and agricultural weather forecast about film mulching in autumn.

Genesis of LCT Pegmatites during Early Paleozoic Orogeny of the North Qinling Orogenic Belt,China:Emplacement Conditions and Structural Control

The Guanpo pegmatite field in the North Qinling orogenic belt(NQB),China,hosts the most abundant LCT pegmatites.However,their emplacement conditions and structural control remain unexplored.In this contribution,we investigated it combining pegmatite orientation measurement with oxygen isotope geothermometry and fluid inclusion study.The orientations of type A1 pegmatites(P_(f)<σ_(2))are predominantly influenced by P-and T-fractures due to simple shearing in Shiziping dextral thrust shear zone during D_(2)deformation,whereas type A2 pegmatites(contemporaneous with D_(4))are governed by hydraulic fractures aligned with S_(0)and S_(0+1)stemming from fluid pressure(P_(f)<σ_(2)).Additionally,type B pegmatites(P_(f)≤σ_(2))exhibit orientations shaped by en echelon extensional fractures in local ductile shear zones(contemporaneous with D_(3)).The albite-quartz oxygen isotope geothermometry and microthermometric analysis of fluid inclusions in elbaites from the latest pegmatites(including types B and A2)suggest that the crystallization P-T for late magmatic and hydrothermal stages are 527.5-559.2℃,320℃,3.1-3.6 kbar and 2.0 kbar,respectively.Our observations along with previous studies suggest that the genesis of the LCT pegmatites was a long-term,multi-stage event during early Paleozoic orogeny(including the collision stage)of the NQB,and was facilitated by various local fractures.

Oscillation properties of eigenfunctions for Sturm-Liouville problems with interface conditions via Prufer transformation

A class of Sturm-Liouville problems with discontinuity is studied in this paper.The oscillation properties of eigenfunctions for Sturm-Liouville problems with interface conditions are obtained.The main method used in this paper is based on Prufer transformation,which is different from the classical ones.Moreover,we give two examples to verify our main results.

Role of outdoor trees on pedestrian wind and thermal conditions around a pre-education building for sustainable energy management

Finding sustainable energy resources is essential to face the increasing energy demand.Trees are an important part of ancient architecture but are becoming rare in urban areas.Trees can control and tune the pedestrian-level wind velocity and thermal condition.In this study,a numerical investigation is employed to assess the role of trees planted in the windward direction of the building complex on the thermal and pedestrian wind velocity conditions around/inside a pre-education building located in the center of the complex.Compared to the previous studies(which considered only outside buildings),this work considers the effects of trees on microclimate change both inside/outside buildings.Effects of different parameters including the leaf area density and number of trees,number of rows,far-field velocity magnitude,and thermal condition around the main building are assessed.The results show that the flow velocity in the spacing between the first-row buildings is reduced by 30%-40% when the one-row trees with 2 m height are planted 15 m farther than the buildings.Furthermore,two rows of trees are more effective in higher velocities and reduce the maximum velocity by about 50%.The investigation shows that trees also could reduce the temperature by about 1℃around the building.

Multi-soliton solutions of coupled Lakshmanan-Porsezian-Daniel equations with variable coefficients under nonzero boundary conditions

This paper aims to investigate the multi-soliton solutions of the coupled Lakshmanan–Porsezian–Daniel equations with variable coefficients under nonzero boundary conditions.These equations are utilized to model the phenomenon of nonlinear waves propagating simultaneously in non-uniform optical fibers.By analyzing the Lax pair and the Riemann–Hilbert problem,we aim to provide a comprehensive understanding of the dynamics and interactions of solitons of this system.Furthermore,we study the impacts of group velocity dispersion or the fourth-order dispersion on soliton behaviors.Through appropriate parameter selections,we observe various nonlinear phenomena,including the disappearance of solitons after interaction and their transformation into breather-like solitons,as well as the propagation of breathers with variable periodicity and interactions between solitons with variable periodicities.

Effects of Initial and Boundary Conditions on Heavy Rainfall Simulation over the Yellow Sea and the Korean Peninsula:Comparison of ECMWF and NCEP Analysis Data Effects and Verification with Dropsonde Observation

This study evaluated the simulation performance of mesoscale convective system(MCS)-induced precipitation,focusing on three selected cases that originated from the Yellow Sea and propagated toward the Korean Peninsula.The evaluation was conducted for the European Centre for Medium-Range Weather Forecasts(ECMWF)and National Centers for Environmental Prediction(NCEP)analysis data,as well as the simulation result using them as initial and lateral boundary conditions for the Weather Research and Forecasting model.Particularly,temperature and humidity profiles from 3D dropsonde observations from the National Center for Meteorological Science of the Korea Meteorological Administration served as validation data.Results showed that the ECMWF analysis consistently had smaller errors compared to the NCEP analysis,which exhibited a cold and dry bias in the lower levels below 850 hPa.The model,in terms of the precipitation simulations,particularly for high-intensity precipitation over the Yellow Sea,demonstrated higher accuracy when applying ECMWF analysis data as the initial condition.This advantage also positively influenced the simulation of rainfall events on the Korean Peninsula by reasonably inducing convective-favorable thermodynamic features(i.e.,warm and humid lower-level atmosphere)over the Yellow Sea.In conclusion,this study provides specific information about two global analysis datasets and their impacts on MCS-induced heavy rainfall simulation by employing dropsonde observation data.Furthermore,it suggests the need to enhance the initial field for MCS-induced heavy rainfall simulation and the applicability of assimilating dropsonde data for this purpose in the future.

Performance Analysis of Curved Track G2T-FSO(Ground-to-Train Free Space Optical)Model under Various Weather Conditions

The demand for broadband data services on high-speed trains is rapidly growing as more people commute between their homes and workplaces.However,current radio frequency(RF)technology cannot adequately meet this demand.In order to address the bandwidth constraint,a technique known as free space optics(FSO)has been proposed.This paper presents a mathematical derivation and formulation of curve track G2T-FSO(Ground-to-train Free Space Optical)model,where the track radius characteristics is 2667 m,divergence angle track is 1.5°for train velocity at V=250 km/h.Multiple transmitter configurations are proposed to maximize coverage range and enhance curve track G2T-FSO link performance under varying weather conditions.The curved track G2T-FSO model was evaluated in terms of received power,signal-to-noise ratio(SNR),bit error rate(BER),and eye diagrams.The results showed maximum coverage lengths of 618,505,365,and 240 m for 4Tx/1Rx,3Tx/1Rx,2Tx/1Rx,and 1Tx/1Rx configurations,respectively.The analyzed results demonstrate that the G2T-FSO link can be effectively implemented under various weather conditions.

Research on shell-side heat and mass transfer with multi-component in LNG spiral-wound heat exchanger under sloshing conditions

The spiral-wound heat exchanger(SWHE) is the primary low-temperature heat exchanger for large-scale LNG plants due to its high-pressure resistance, compact structure, and high heat exchange efficiency. This paper studied the shell-side heat and mass transfer characteristics of vapor-liquid two-phase mixed refrigerants in an SWHE by combining a multi-component model in FLUENT software with a customized multicomponent mass transfer model. Besides, the mathematical model under the sloshing condition was obtained through mathematical derivation, and the corresponding UDF code was loaded into FLUENT as the momentum source term. The results under the sloshing conditions were compared with the relevant parameters under the steady-state condition. The shell-side heat and mass transfer characteristics of the SWHE were investigated by adjusting the component ratio and other working conditions. It was found that the sloshing conditions enhance the heat transfer performance and sometimes have insignificant effects. The sloshing condition is beneficial to reduce the flow resistance. The comprehensive performance of multi-component refrigerants has been improved and the improvement is more significant under sloshing conditions, considering both the heat transfer and pressure drop.These results will provide theoretical support for the research and design of multi-component heat and mass transfer enhancement of LNG SWHE under ocean sloshing conditions.

Impact of wetting-drying cycles and acidic conditions on the soil aggregate stability of yellow‒brown soil

Soil aggregate is the basic structural unit of soil,which is the foundation for supporting ecosystem functions,while its composition and stability is significantly affected by the external environment.This study was conducted to explore the effect of external environment(wetting-drying cycles and acidic conditions)on the soil aggregate distribution and stability and identify the key soil physicochemical factors that affect the soil aggregate stability.The yellow‒brown soil from the Three Gorges Reservoir area(TGRA)was used,and 8 wetting-drying conditions(0,1,2,3,4,5,10 and 15 cycles)were simulated under 4 acidic conditions(pH=3,4,5 and 7).The particle size distribution and soil aggregate stability were determined by wet sieving method,the contribution of environmental factors(acid condition,wetting-drying cycle and their combined action)to the soil aggregate stability was clarified and the key soil physicochemical factors that affect the soil aggregate stability under wetting-drying cycles and acidic conditions were determined by using the Pearson’s correlation analysis,Partial least squares path modeling(PLS‒PM)and multiple linear regression analysis.The results indicate that wetting-drying cycles and acidic conditions have significant effects on the stability of soil aggregates,the soil aggregate stability gradually decreases with increasing number of wetting-drying cycles and it obviously decreases with the increase of acidity.Moreover,the combination of wetting-drying cycles and acidic conditions aggravate the reduction in the soil aggregate stability.The wetting-drying cycles,acidic conditions and their combined effect imposes significant impact on the soil aggregate stability,and the wetting-drying cycles exert the greatest influence.The soil aggregate stability is significantly correlated with the pH,Ca^(2+),Mg^(2+),maximum disintegration index(MDI)and soil bulk density(SBD).The PLS‒PM and multiple linear regression analysis further reveal that the soil aggregate stability is primarily influenced by SBD,Ca^(2+),and MDI.These results offer a scientific basis for understanding the soil aggregate breakdown mechanism and are helpful for clarifying the coupled effect of wetting-drying cycles and acid rain on terrestrial ecosystems in the TGRA.

Improving autoencoder-based unsupervised damage detection in uncontrolled structural health monitoring under noisy conditions

Structural health monitoring is widely utilized in outdoor environments,especially under harsh conditions,which can introduce noise into the monitoring system.Therefore,designing an effective denoising strategy to enhance the performance of guided wave damage detection in noisy environments is crucial.This paper introduces a local temporal principal component analysis(PCA)reconstruction approach for denoising guided waves prior to implementing unsupervised damage detection,achieved through novel autoencoder-based reconstruction.Experimental results demonstrate that the proposed denoising method significantly enhances damage detection performance when guided waves are contaminated by noise,with SNR values ranging from 10 to-5 dB.Following the implementation of the proposed denoising approach,the AUC score can elevate from 0.65 to 0.96 when dealing with guided waves corrputed by noise at a level of-5 dB.Additionally,the paper provides guidance on selecting the appropriate number of components used in the denoising PCA reconstruction,aiding in the optimization of the damage detection in noisy conditions.

Impact of Initial Soil Conditions on Soil Hydrothermal and Surface Energy Fluxes in the Permafrost Region of the Tibetan Plateau

Accurate initial soil conditions play a crucial role in simulating soil hydrothermal and surface energy fluxes in land surface process modeling.This study emphasized the influence of the initial soil temperature(ST)and soil moisture(SM)conditions on a land surface energy and water simulation in the permafrost region in the Tibetan Plateau(TP)using the Community Land Model version 5.0(CLM5.0).The results indicate that the default initial schemes for ST and SM in CLM5.0 were simplistic,and inaccurately represented the soil characteristics of permafrost in the TP which led to underestimating ST during the freezing period while overestimating ST and underestimating SLW during the thawing period at the XDT site.Applying the long-term spin-up method to obtain initial soil conditions has only led to limited improvement in simulating soil hydrothermal and surface energy fluxes.The modified initial soil schemes proposed in this study comprehensively incorporate the characteristics of permafrost,which coexists with soil liquid water(SLW),and soil ice(SI)when the ST is below freezing temperature,effectively enhancing the accuracy of the simulated soil hydrothermal and surface energy fluxes.Consequently,the modified initial soil schemes greatly improved upon the results achieved through the long-term spin-up method.Three modified initial soil schemes experiments resulted in a 64%,88%,and 77%reduction in the average mean bias error(MBE)of ST,and a 13%,21%,and 19%reduction in the average root-mean-square error(RMSE)of SLW compared to the default simulation results.Also,the average MBE of net radiation was reduced by 7%,22%,and 21%.

Effect of boundary conditions on shakedown analysis of heterogeneous materials

The determination of the ultimate load-bearing capacity of structures made of elastoplastic heterogeneous materials under varying loads is of great importance for engineering analysis and design. Therefore, it is necessary to accurately predict the shakedown domains of these materials. The static shakedown theorem, also known as Melan's theorem, is a fundamental method used to predict the shakedown domains of structures and materials. Within this method, a key aspect lies in the construction and application of an appropriate self-equilibrium stress field(SSF). In the structural shakedown analysis, the SSF is typically constructed by governing equations that satisfy no external force(NEF) boundary conditions. However, we discover that directly applying these governing equations is not suitable for the shakedown analysis of heterogeneous materials. Researchers must consider the requirements imposed by the Hill-Mandel condition for boundary conditions and the physical significance of representative volume elements(RVEs). This paper addresses this issue and demonstrates that the sizes of SSFs vary under different boundary conditions, such as uniform displacement boundary conditions(DBCs), uniform traction boundary conditions(TBCs), and periodic boundary conditions(PBCs). As a result, significant discrepancies arise in the predicted shakedown domain sizes of heterogeneous materials. Built on the demonstrated relationship between SSFs under different boundary conditions, this study explores the conservative relationships among different shakedown domains, and provides proof of the relationship between the elastic limit(EL) factors and the shakedown loading factors under the loading domain of two load vertices. By utilizing numerical examples, we highlight the conservatism present in certain results reported in the existing literature. Among the investigated boundary conditions, the obtained shakedown domain is the most conservative under TBCs.Conversely, utilizing PBCs to construct an SSF for the shakedown analysis leads to less conservative lower bounds, indicating that PBCs should be employed as the preferred boundary conditions for the shakedown analysis of heterogeneous materials.

Consideration of the influence of supports in modeling the electromagnetic fields of 25 kV traction networks under emergency conditions

Single-phase 25 kV traction networks of electrified alternating current(AC)railways create electromagnetic fields(EMFs)with significant levels of intensity.The most intense magnetic fields occur when short circuits exist between the contact wire and rails or ground.Despite the short duration of exposure,they can adversely affect electronic devices and induce significant voltages in adjacent power lines,which is dangerous for operating personnel.Although numerous investigations have focused on modeling the EMF of traction networks and power lines,the challenge of determining the three-dimensional electromagnetic fields near metal supports during the flow of a short-circuit current through them is yet to be resolved.In this case,the field has a complex spatial structure that significantly complicates the calculations of intensities.This study proposes a methodology,algorithms,software,and digital models for determining the EMF in the described emergency scenarios.During the modeling process,the objects being studied were represented by segments of thin wires to analyze the distribution of the electric charge and calculate the intensities of the electric and magnetic fields.This approach was implemented in the Fazonord software,and the modeling results show a substantial increase in EMF levels close to the support,with a noticeable decrease in the levels as the distance from it increases.The procedure implemented in the commercial software Fazonord is universal and can be used to determine electromagnetic fields at any electrical power facility that includes live parts of limited length.Based on the proposed procedure,the EMF near the supports of overhead power lines and traction networks of various designs could be determined,the EMF levels at substations can be calculated,and the influence of metal structures located near traction networks,such as pedestrian crossings at railway stations,can be considered.

Least Square Finite Element Model for Analysis of Multilayered Composite Plates under Arbitrary Boundary Conditions

Laminated composites are widely used in many engineering industries such as aircraft, spacecraft, boat hulls, racing car bodies, and storage tanks. We analyze the 3D deformations of a multilayered, linear elastic, anisotropic rectangular plate subjected to arbitrary boundary conditions on one edge and simply supported on other edge. The rectangular laminate consists of anisotropic and homogeneous laminae of arbitrary thicknesses. This study presents the elastic analysis of laminated composite plates subjected to sinusoidal mechanical loading under arbitrary boundary conditions. Least square finite element solutions for displacements and stresses are investigated using a mathematical model, called a state-space model, which allows us to simultaneously solve for these field variables in the composite structure’s domain and ensure that continuity conditions are satisfied at layer interfaces. The governing equations are derived from this model using a numerical technique called the least-squares finite element method (LSFEM). These LSFEMs seek to minimize the squares of the governing equations and the associated side conditions residuals over the computational domain. The model is comprised of layerwise variables such as displacements, out-of-plane stresses, and in- plane strains, treated as independent variables. Numerical results are presented to demonstrate the response of the laminated composite plates under various arbitrary boundary conditions using LSFEM and compared with the 3D elasticity solution available in the literature.

The Impact of Physiotherapy Interventions on the Elderly Population with Mental Health Conditions at Chainama Hills College Hospital in Zambia. A Pre-Post Single Sample Study Design

Background: Physical functional decline is common among elderly individuals with mental disorders, worsening their symptoms. Physiotherapy interventions have shown some evidence in improving physical function and mental health outcomes in this population. This study aimed to assess the impact of physiotherapy interventions on the elderly with mental health conditions at Chainama Hills College Hospital in Zambia. Methods: A pre-post single sample design was used to track patient progress over six weeks, with 10 physiotherapy sessions. The study population (N = 30) comprised of all elderly individuals with mental health conditions, encompassing both men and women, who were hospitalized during the research period. The Katz Index of Activities of Daily Living and the six-minute walk test were evaluated before and after the intervention. The IBM SPSS version 26 was used to analyze data and results were presented as mean ± SD with a 95% confidence interval. The variables were described in terms of their mean, SD, and range. A significance level of 0.05 was used for a paired T-test to detect changes and multiple logistic regression was used to identify factors associated with mental health. Results: Following the intervention, the percentage of participants achieving full function and independence increased significantly to 96.7% from the initial 73.3%, supported by a 95% CI = [0.82 - 0.99]. There was also a notable decrease in the proportion of individuals experiencing moderate impairment, dropping from 26.7% to just 3.3%, with a corresponding 95% CI = [0.00 - 0.17]. Conclusion: The findings derived from this study illustrate an enhancement in the aspects of participants’ overall health and functional condition, including blood pressure, heart rate, and respiratory rate. Consequently, physiotherapy exercises can be employed as a tactic to ameliorate the functional status and physical well-being of older individuals afflicted with mental disorders in Zambia.

Probabilistic Global Maximum Power Point Tracking Algorithm for Continuously Varying Partial Shading Conditions on Autonomous PV Systems

A photovoltaic (PV) string with multiple modules with bypass diodes frequently deployed on a variety of autonomous PV systems may present multiple power peaks under uneven shading. For optimal solar harvesting, there is a need for a control schema to force the PV string to operate at global maximum power point (GMPP). While a lot of tracking methods have been proposed in the literature, they are usually complex and do not fully take advantage of the available characteristics of the PV array. This work highlights how the voltage at operating point and the forward voltage of the bypass diode are considered to design a global maximum power point tracking (GMPPT) algorithm with a very limited global search phase called Fast GMPPT. This algorithm successfully tracks GMPP between 94% and 98% of the time under a theoretical evaluation. It is then compared against Perturb and Observe, Deterministic Particle Swarm Optimization, and Grey Wolf Optimization under a sequence of irradiance steps as well as a power-over-voltage characteristics profile that mimics the electrical characteristics of a PV string under varying partial shading conditions. Overall, the simulation with the sequence of irradiance steps shows that while Fast GMPPT does not have the best convergence time, it has an excellent convergence rate as well as causes the least amount of power loss during the global search phase. Experimental test under varying partial shading conditions shows that while the GMPPT proposal is simple and lightweight, it is very performant under a wide range of dynamically varying partial shading conditions and boasts the best energy efficiency (94.74%) out of the 4 tested algorithms.

Geological conditions and reservoir characteristics of various shales in major shalehosted regions of China

China is home to shales of three facies:Marine shale,continental shale,and marine-continental transitional shale.Different types of shale gas are associated with significantly different formation conditions and major controlling factors.This study compared the geological characteristics of various shales and analyzed the influences of different parameters on the formation and accumulation of shale gas.In general,shales in China’s several regions exhibit high total organic carbon(TOC)contents,which lays a sound material basis for shale gas generation.Marine strata generally show high degrees of thermal evolution.In contrast,continental shales manifest low degrees of thermal evolution,necessitating focusing on areas with relatively high degrees of thermal evolution in the process of shale gas surveys for these shales.The shales of the Wufeng and Silurian formations constitute the most favorable shale gas reservoirs since they exhibit the highest porosity among the three types of shales.These shales are followed by those in the Niutitang and Longtan formations.In contrast,the shales of the Doushantuo,Yanchang,and Qingshankou formations manifest low porosities.Furthermore,the shales of the Wufeng and Longmaxi formations exhibit high brittle mineral contents.Despite a low siliceous mineral content,the shales of the Doushantuo Formation feature a high carbonate mineral content,which can increase the shales’brittleness to some extent.For marine-continental transitional shales,where thin interbeds of tight sandstone with unequal thicknesses are generally found,it is recommended that fracturing combined with drainage of multiple sets of lithologic strata should be employed to enhance their shale gas production.

On the Relationship between Chinese Language Education in Malaysia and Indonesia with Their National Conditions

Chinese language education exists in both Malaysia and Indonesia. The commonalities and individualities of the national conditions of both countries have an impact on their Chinese language education. The official languages scripts, and major beliefs of the two countries are quite similar, and under their influence, local Chinese have special expectations for Chinese language education. Compared to Indonesia, Malaysian Chinese have a larger proportion of the population and a tendency towards marriage, which to some extent is more conducive to the Chinese language education of local Chinese. Both countries’ national conditions and personalities have unfavorable factors for local Chinese language education.

Modelling of the variation of granular base materials resilient modulus with material characteristics and humidity conditions

This study aims to quantify the susceptibility of granular materials used in pavements to changes in moisture content and propose a correlation model to incorporate this susceptibility into seasonal analyses.The fines content and the percentage of fractured coarse aggregates were identified as direct indicators of the resilient modulus susceptibility to changes in water content.The results showed that the percentage of fractured coarse aggregates particles(FR)has a more significant impact on the resilient modulus(Er)of crushed granular materials used in pavement construction than the combined indicator of the fines content and sample volumetrics(nf).Crushed granular materials with a higher percentage of fractured coarse aggregates are relatively insensitive to changes in the degree of saturation,but become more sensitive as the fine fraction porosity decreases.An adjusted model was proposed based on the existing formulation,but considers a complex parameter to describe and adjust the sensitivity of base granular materials to variations in moisture content with respect to fabrication charac-teristics,fines content and volumetric properties.The model shows that the variation of Er values is below10%for fully crushed granular materials.However,it reaches approximately±12%for materials with 75%of crushed coarse aggregates andþ40%and-25%for materials with FR=50%.This model could help select good ag-gregates characteristics and adjust grain-size distribution for environments where significant moisture content variations can occur in the pavement system,such as in the Province of Quebec(Canada).As it is based on pa-rameters that can be easily determined or estimated,it also represents a valuable tool for detailed design and analysis that can consider material characteristics.

Boundary Conditions for Momentum and Vorticity at an Interface between Two Fluids

Boundary conditions for momentum and vorticity have been precisely derived, paying attention to the physical meaning of each mathematical expression of terms rigorously obtained from the basic equations: Navier-Stokes equation and the equation of vorticity transport. It has been shown first that a contribution of fluid molecules crossing over a conceptual surface moving with fluid velocity due to their fluctuating motion is essentially important to understanding transport phenomena of momentum and vorticity. A notion of surface layers, which are thin layers at both sides of an interface, has been introduced next to elucidate the transporting mechanism of momentum and vorticity from one phase to the other at an interface through which no fluid molecules are crossing over. A fact that a size of δV, in which reliable values of density, momentum, and velocity of fluid are respectively defined as a volume-averaged mass of fluid molecules, a volume-averaged momentum of fluid molecules and a mass-averaged velocity of fluid molecules, is not infinitesimal but finite has been one of the key factors leading to the boundary conditions for vorticity at an interface between two fluids. The most distinguished characteristics of the boundary conditions derived here are the zero-value conditions for a normal component of momentum flux and tangential components of vorticity flux, at an interface.