Contribution to the Analytical Study of Barrier Surface Waves: Decomposition of the Solution

When a partially or completely immersed solid moves in a liquid such as water, it undergoes a force called hydrodynamic drag. Reducing this force has always been the objective of hydrodynamic engineers to make water slide better on submerged bodies. This paper deals with the examination of the different terms composing the analytical solution of the flow over an obstacle embedded at the bottom of a hydraulic channel. We have chosen to use a linear method to study a two-dimensional flow over an obstacle, in order to understand the evolution of the drag. We set the following assumptions: incompressible inviscid fluid, irrotational flow, low obstacle height compared to the water height. Those assumptions allow overcoming the difficulties associated with modelling these waves. We will mathematically formulate the equations that allow the determination of the stream function, and then the free surface equation. A similar method is used to determine the exact analytical solution for an obstacle in the shape of a sinusoidal arch.

Utilization of Industrial Byproducts in Concrete Applications by Adopting Grey Taguchi Method for Optimization

This paper presents the results of an experimental investigation carried out to evaluate the effects of partial replacement of cement and fine aggregate with industrial waste by-products on concrete strength properties. The Grey Taguchi approach has been used to optimize the mix proportions for desired properties. In this research work, a ternary combination of industrial waste by-products has been used. The experiments have been designed using Taguchi's L9 orthogonal array with four factors having three levels each. The cement was partially replaced by ladle furnace slag (LFS), fly ash (FA) and copper slag (CS) at 10%, 25% and 40% level and fine aggregate (sand) was partially replaced with electric arc furnace slag (EAFS), iron slag (IS) and glass powder (GP) at 20%, 30% and 40% level. Three water to binder ratios, fixed at 0.40, 0.44 and 0.48, were used, and the curing age was fixed at 7, 28 and 90 days. Thus, a series of nine experiments was conducted on the specimens for water to binder ratios of 0.40, 0.44 and 0.48 at 7, 28 and 90 days of the water curing regime. It is evident from the investigations that Grey Taguchi approach for optimization helps in identifying the factors affecting the final outcomes, i.e. compressive strength and split tensile strength of concrete. For the materials and a range of parameters used in this research, the present study has established optimum mixes in terms of strength properties. The best possible levels of mix proportions were determined for maximization through compressive and splitting tensile strength. To verify the results, the optimal mix was produced and tested. The mixture results in higher compressive strength and split tensile strength than other mixes. The compressive strength and split tensile strength of optimal mixtures are also compared with the control concrete mixtures. The results show that compressive strength and split tensile strength of concrete made with partial replacement of cement and fine aggregate is more than control concrete at all ages and w/c ratios. Based on the overall observations, it can be recommended that industrial waste by-products in ternary combinations can effectively be utilized as partial replacements of cement and fine aggregates in all concrete applications.

Adomian’s Decomposition Method to Generalized Magneto-Thermoelasticity

Due to many applications and problems in the fields of plasma physics, geophysics, and other many topics, the interaction between the strain field and the magnetic field has to be considered. Adomian introduced the decomposition method for solving linear and nonlinear functional equations. This method leads to accurate, computable, approximately convergent solutions of linear and nonlinear partial and ordinary differential equations even the equations with variable coefficients. This paper is dealing with a mathematical model of generalized thermoelasticity of a half-space conducting medium. A magnetic field with constant intensity acts normal to the bounding plane has been assumed. Adomian’s decomposition method has been used to solve the model when the bounding plane is taken to be traction free and thermally loaded by harmonic heating. The numerical results for the temperature increment, the stress, the strain, the displacement, the induced magnetic, and the electric fields have been represented in figures. The magnetic field, the relaxation time, and the angular thermal load have significant effects on all the studied fields.

An Efficient Collocation Method for Solving the Variable-Order Time-Fractional Partial Differential Equations Arising from the Physical Phenomenon

In this work, we present an efficient approach for solving variable-order time-fractional partial differential equations, which are based on Legendre and Laguerre polynomials. First, we introduced the pseudo-operational matrices of integer and variable fractional order of integration by use of some properties of Riemann-Liouville fractional integral. Then, applied together with collocation method and Legendre-Laguerre functions for solving variable-order time-fractional partial differential equations. Also, an estimation of the error is presented. At last, we investigate numerical examples which arise in physics to demonstrate the accuracy of the present method. In comparison results obtained by the present method with the exact solution and the other methods reveals that the method is very effective.

Teaching Translation in Brazilian Universities: A Study about the Possible Impacts of Translators’ Comments on the Cyberspace about Translator Education

The objective of this paper is to discuss relevant points about teaching translation in Brazilian universities and the possible impacts of blogs and social networks to translator education today. It is intended to analyze the curricula of Brazilian translation courses, contrasting them to information obtained from two social networking groups of great visibility in the area concerning essential characteristics to become a successful profession. Therefore, research has, as its main corpus, a few undergraduate translation programs’ syllabuses, as well as a few postings on social networks groups that specifically share professional opinions regarding the necessity for a translator to obtain a degree in translation to practice the profession. To a certain extent, such comments and their corresponding responses lead to the propagation of discourses which influence the ideas that aspiring translators and recent graduates end up having towards themselves and their undergraduate courses. The postings also show that many professionals do not have a clear position regarding the translator education; while refuting it, they also encourage “free” courses. It is thus observed that cyberspace constitutes, on the one hand, a place of mobilization of people in defense of similar ideas. However, on the other hand, it embodies a place of tension and conflict, in view of the fact that there are many participants and, as in any other situation of interlocution, disagreements may arise. From the postings, aspects related to professionalism were analyzed (including discussions about regulation), as well as questions about the classic dichotomies: theory/practice; art/technique; self-education/academic training. As partial result, the common interest regarding the valorization of the profession could be mentioned, although there is no consensus on the essential characteristics to be a good translator. It was also possible to observe that the set of socially constructed representations in the group reflects characteristics of the world situation of the translation courses (especially in some European countries and in the United States), which, in the first instance, does not accurately reflect the Brazilian idiosyncrasies of the area.

Influence of Sr(BO2)2 Doping on Superconducting Properties of (Bi,Pb)-2223 Phase

Chemical doping with different elements and compounds at various amounts represents the most suitable approach to improve the superconducting properties of bismuth-based superconductors for technological applications. In this paper, the influence of partial substitution of Sr(BO2)2 for SrO on the phase formation kinetics and transport properties of (Bi,Pb)-2223 HTS has been studied for the first time. Samples with nominal composition Bi1.7Pb0.3Sr2-xCa2Cu3Oy[Sr(BO2)2]x, x=0, 0.0375, 0.075, 0.15, 0.25, were prepared by the standard solid state processing. The appropriate mixtures were calcined at 845 oC for 40 h. The resulting materials were pressed into pellets and annealed at 837 oC for 30 h in air. Superconducting properties of undoped (reference) and Sr(BO2)2-doped (Bi,Pb)-2223 compounds were investigated through X-ray diffraction (XRD), resistivity (ρ) and transport critical current density (Jc) measurements. The surface morphology changes in the prepared samples were examined by scanning electron microscope (SEM). XRD and Jc studies have shown that the low level Sr(BO2)2 doping (x=0.0375-0.075) to the Sr-site promotes the formation of high-Tc phase and leads to the enhancement of current carrying capacity in (Bi,Pb)-2223 HTS. The doped sample with x=0.0375 has the best performance compared to other prepared samples. The estimated volume fraction of (Bi,Pb)-2223 phase increases from ~25 % for reference specimen to ~70 % for x=0.0375. Moreover, strong increase in the self-field Jc value was observed for this dopant amount (Jc=340 A/cm2), compared to an undoped sample (Jc=110 A/cm2). Pronounced enhancement of superconducting properties of (Bi,Pb)-2223 superconductor can be attributed to the acceleration of high-Tc phase formation as well as the improvement of inter-grain connectivity by small amounts of Sr(BO2)2 dopant.

Performance Analysis of Ferrocement Retrofitted Masonry Wall Units under Cyclic Loading

A huge portion of old masonry buildings in Bangladesh are vulnerable to earthquake. In most of the cases these buildings contain unreinforced masonry wall which are most likely to be subjected to earthquake damages. Due to deterioration of mortar joint and aging, shear resistance of these unreinforced masonry walls dwindle. So, retrofitting of these old buildings has become an important issue. Among many researched and experimented techniques, ferrocement retrofitting can be a low cost technique in context of the economic condition of Bangladesh. This study aims at investigating the behavior of ferrocement retrofitted unconfined URM walls under different types of cyclic loading. Four 725 mm × 725 mm masonry wall units were prepared with bricks jointed by stretcher bond with 12.5 mm mortar between two adjacent layers of bricks. To compare the effectiveness of ferrocement retrofitting a particular type wire mesh was used in this experiment which is 20 gauge woven wire mesh with 12.5 mm × 12.5 mm square opening. After retrofitting with ferrocement these wall units were tested by applying cyclic deformation along the diagonals of the specimens. Then a comparative study was performed between the retrofitted specimens and control specimens for both partially reversed cyclic load condition and cyclic compression load condition. The experiment results show that ultimate load carrying capacities of ferrocement retrofitted specimens are 35% and 27% greater than the control specimen under partially reversed cyclic loading and cyclic compression respectively. And before failure the deformations of ferrocement retrofitted specimens are 43% and 33% greater than the control specimen under reversed cyclic loading and cyclic compression respectively. Therefore, the test results show that the ultimate load carrying capacity and ductility of ferrocement retrofitted specimens have improved.

Application of Stochastic Models to Annual Extreme Streamflow Data

This study was designed to find the best stochastic model (using of time series analysis) for annual extreme streamflow (peak and maximum streamflow) of Karkheh River at Iran. The Auto-regressive Integrated Moving Average (ARIMA) model used to simulate these series and forecast those in future. For the analysis, annual extreme streamflow data of Jelogir Majin station (above of Karkheh dam reservoir) for the years 1958–2005 were used. A visual inspection of the time plot gives a little increasing trend; therefore, series is not stationary. The stationarity observed in Auto-Correlation Function (ACF) and Partial Auto-Correlation Function (PACF) plots of annual extreme streamflow was removed using first order differencing (d=1) in order to the development of the ARIMA model. Interestingly, the ARIMA(4,1,1) model developed was found to be most suitable for simulating annual extreme streamflow for Karkheh River. The model was found to be appropriate to forecast ten years of annual extreme streamflow and assist decision makers to establish priorities for water demand. The Statistical Analysis System (SAS) and Statistical Package for the Social Sciences (SPSS) codes were used to determinate of the best model for this series.

A Neuron Model of Facial Recognition and Detection of an Authorized Entity Using Machine Learning System

This paper has critically examined the use of Machine Learning procedures in curbing unauthorized access into valuable areas of an organization. The use of passwords, pin codes, user’s identification in recent times has been partially successful in curbing crimes involving identities, hence the need for the design of a system which incorporates biometric characteristics such as DNA and pattern recognition of variations in facial expressions. The facial model used is the OpenCV library which is based on the use of certain physiological features, the Raspberry Pi 3 module is used to compile the OpenCV library, which extracts and stores the detected faces into the datasets directory through the use of camera. The model is trained with 50 epoch run in the database and recognized by the Local Binary Pattern Histogram (LBPH) recognizer contained in the OpenCV. The training algorithm used by the neural network is back propagation coded using python algorithmic language with 200 epoch runs to identify specific resemblance in the exclusive OR (XOR) output neurons. The research however confirmed that physiological parameters are better effective measures to curb crimes relating to identities.

The Problem of Reconciling the Principle of Confidentiality in Foreign Investment Arbitration with the Public Interest

The economical globalization through the liberalization of the markets and capitals boosted the economical development of the nations and the needs for sorting out the disputes arising from the foreign investment. The arbitration, for all the inherent advantages, such as swiftness, arbitrators’ specialise skills and impartiality sets a pacifier tool for the interest in account. Safeguarded the public interest, we face the problem of the confidentiality in the arbitration. The urgent development of impelling mechanisms concerning transparency, guaranty and protection of the interest in account, reveals itself urgent. Through a bibliography review, we will dense the state of art, by going through the several solutions concerning, and pointing out the most suitable. Through the jurisprudential analysis we will point out the solution for the conflict confidentiality/public interest. The transparency, inextricable from the public interest, imposes the arbitration process can be open to all citizens. Transparency rules have been considered at the UNCITRAL in attempting to conciliate the necessity of publicity and the public interest, however still insufficient. The arbitration of foreign investment carries consequences to the citizens of the State. Articulating mechanisms between the arbitral procedures secrecy and the public interest should be adopted. The arbitration of foreign investment, being a tertius genius between the international arbitration and the administrative arbitration would claim its own regulation in each and every States where the confidentiality rules and its exceptions could be identified. One should enquiry where the limit of the citizens’ individual rights protection and the public interest should give way to the principle of transparency

The Performance of Natural Light by Roof Systems in Cultural Buildings

This paper presents an approach to the performance of the natural lighting, when the use of appropriated solar lighting systems on the roof is applied in cultural buildings such as museums and foundations. The roofs, as a part of contact between the building and the external environment, require special attention in projects that aim at energy efficiency, being an important element for the capture of natural light in greater quantity, but also for being the most important point of generation of photovoltaic solar energy, even semitransparent, allowing the partial passage of light. Transparent elements in roofs, as well as superior protection of the building, can also play other roles, such as: meeting the needs of natural light for the accomplishment of the internal tasks, attending to the visual comfort; to bring benefits to the human perception and about the interior experience in a building. When these resources are well dimensioned, they also contribute to the energy efficiency and consequent character of sustainability of the building. Therefore, when properly designed and executed, a roof light system can bring higher quality natural light to the interior of the building, which is related to the human health and well-being dimension. Furthermore, it can meet the technologic, economic and environmental yearnings, making possible the more efficient use of that primordial resource, which is the light of the Sun. The article presents the analysis of buildings that used zenith light systems in search of better lighting performance in museums and foundations: the Solomon R. Guggenheim Museum in the United States, the Iberê Camargo Foundation in Brazil, the Museum of Fine Arts in Castellón in Spain and the Pinacoteca of São Paulo.

Design of Multiband Microstrip Antenna Using Stepped Cut Method for WLAN/WiMAX and C/Ku-Band Applications

In this paper, a planar monopole antenna for multi band applications is proposed. The antenna structure operates at three operating frequencies at 3.7, 6.2, and 13.5 GHz which cover different communication frequency ranges. The antenna consists of a quasi-modified rectangular radiating patch with a partial ground plane and two parasitic elements (open-loop-ring resonators) to serve as coupling-bridges. A stepped cut at lower corners of the radiating patch and the partial ground plane are used, to achieve the multiband features. The proposed antenna is manufactured on the FR4 substrate and is simulated and optimized using High Frequency Simulation System (HFSS). The antenna topology possesses an area of 30.5 x 30 x 1.6 mm3. The measured results demonstrate that the candidate antenna has impedance bandwidths for 10 dB return loss and operates from 3.80 – 3.90 GHz, 4.10 – 5.20 GHz, 11.2 – 11.5 GHz and from 12.5 – 14.0 GHz, which meet the requirements of the wireless local area network (WLAN), worldwide interoperability for microwave access (WiMAX), C- (Uplink) and Ku- (Uplink) band applications. Acceptable agreement is obtained between measurement and simulation results. Experimental results show that the antenna is successfully simulated and measured, and the tri-band antenna can be achieved by adjusting the lengths of the three elements and it gives good gains across all the operation bands.

A Review on Comparative Analysis of Path Planning and Collision Avoidance Algorithms

Autonomous mobile robots (AMR) are expected as smart tools for operations in every automation industry. Path planning and obstacle avoidance is the backbone of AMR as robots have to reach their goal location avoiding obstacles while traversing through optimized path defined according to some criteria such as distance, time or energy. Path planning can be classified into global and local path planning where environmental information is known and unknown/partially known, respectively. A number of sensors are used for data collection. A number of algorithms such as artificial potential field (APF), rapidly exploring random trees (RRT), bidirectional RRT, Fuzzy approach, Purepursuit, A* algorithm, vector field histogram (VFH) and modified local path planning algorithm, etc. have been used in the last three decades for path planning and obstacle avoidance for AMR. This paper makes an attempt to review some of the path planning and obstacle avoidance algorithms used in the field of AMR. The review includes comparative analysis of simulation and mathematical computations of path planning and obstacle avoidance algorithms using MATLAB 2018a. From the review, it could be concluded that different algorithms may complete the same task (i.e. with a different set of instructions) in less or more time, space, effort, etc.

Designing a Socio-Technical System for Groundwater Resources Management, Applying Smart Energy and Water Meter

World, nowadays, encounters serious water scarcity problem. During the past few years, by advent of Smart Energy and Water Meter (SEWM) and its installation at the electro-pumps of the water wells, one had believed that it could be the golden key to address the groundwater resources over-pumping issue. In fact, implementation of these Smart Meters managed to control the water table drawdown for short; but it was not a sustainable approach. SEWM has been considered as law enforcement facility at first; however, for solving a complex socioeconomic problem like shared groundwater resources management, more than just enforcement is required: participation to conserve common resources. The well owners or farmers, as water consumers, are the main and direct stakeholders of this system and other stakeholders could be government sectors, investors, technology providers, privet sectors or ordinary people. Designing a socio-technical system not only defines the role of each stakeholder but also can lubricate the communication to reach the system goals while benefits of each are considered and provided. Farmers, as the key participators for solving groundwater problem, do not trust governments but they would trust a fair system in which responsibilities, privileges and benefits are clear. Technology could help this system remained impartial and productive. Social aspects provide rules, regulations, social objects and etc. for the system and help it to be more human-centered. As the design methodology, Design Thinking provides probable solutions for the challenging problems and ongoing conflicts; it could enlighten the way in which the final system could be designed. Using Human Centered Design approach of IDEO helps to keep farmers in the center of the solution and provides a vision by which stakeholders’ requirements and needs are addressed effectively. Farmers would be considered to trust the system and participate in their groundwater resources management if they find the rules and tools of the system fair and effective. Besides, implementation of the socio-technical system could change farmers’ behavior in order that they concern more about their valuable shared water resources as well as their farm profit. This socio-technical system contains nine main subsystems: 1) Measurement and Monitoring system, 2) Legislation and Governmental system, 3) Information Sharing system, 4) Knowledge based NGOs, 5) Integrated Farm Management system (using IoT), 6) Water Market and Water Banking system, 7) Gamification, 8) Agribusiness ecosystem, 9) Investment system.

Model-Driven and Data-Driven Approaches for Crop Yield Prediction: Analysis and Comparison

Crop yield prediction is a paramount issue in agriculture. The main idea of this paper is to find out efficient way to predict the yield of corn based meteorological records. The prediction models used in this paper can be classified into model-driven approaches and data-driven approaches, according to the different modeling methodologies. The model-driven approaches are based on crop mechanistic modeling. They describe crop growth in interaction with their environment as dynamical systems. But the calibration process of the dynamic system comes up with much difficulty, because it turns out to be a multidimensional non-convex optimization problem. An original contribution of this paper is to propose a statistical methodology, Multi-Scenarios Parameters Estimation (MSPE), for the parametrization of potentially complex mechanistic models from a new type of datasets (climatic data, final yield in many situations). It is tested with CORNFLO, a crop model for maize growth. On the other hand, the data-driven approach for yield prediction is free of the complex biophysical process. But it has some strict requirements about the dataset. A second contribution of the paper is the comparison of these model-driven methods with classical data-driven methods. For this purpose, we consider two classes of regression methods, methods derived from linear regression (Ridge and Lasso Regression, Principal Components Regression or Partial Least Squares Regression) and machine learning methods (Random Forest, k-Nearest Neighbor, Artificial Neural Network and SVM regression). The dataset consists of 720 records of corn yield at county scale provided by the United States Department of Agriculture (USDA) and the associated climatic data. A 5-folds cross-validation process and two accuracy metrics: root mean square error of prediction(RMSEP), mean absolute error of prediction(MAEP) were used to evaluate the crop prediction capacity. The results show that among the data-driven approaches, Random Forest is the most robust and generally achieves the best prediction error (MAEP 4.27%). It also outperforms our model-driven approach (MAEP 6.11%). However, the method to calibrate the mechanistic model from dataset easy to access offers several side-perspectives. The mechanistic model can potentially help to underline the stresses suffered by the crop or to identify the biological parameters of interest for breeding purposes. For this reason, an interesting perspective is to combine these two types of approaches.

Implementation of State-Space and Super-Element Techniques for the Modeling and Control of Smart Structures with Damping Characteristics

Minimizing the weight in flexible structures means reducing material and costs as well. However, these structures could become prone to vibrations. Attenuating these vibrations has become a pivotal engineering problem that shifted the focus of many research endeavors. One technique to do that is to design and implement an active control system. This system is mainly composed of a vibrating structure, a sensor to perceive the vibrations, an actuator to counteract the influence of disturbances, and finally a controller to generate the appropriate control signals. In this work, two different techniques are explored to create two different mathematical models of an active control system. The first model is a finite element model with a reduced number of nodes and it is called a super-element. The second model is in the form of state-space representation, i.e. a set of partial differential equations. The damping coefficients are calculated and incorporated into both models. The effectiveness of these models is demonstrated when the system is excited by its first natural frequency and an active control strategy is developed and implemented to attenuate the resulting vibrations. Results from both modeling techniques are presented and compared.

Resistance to Chloride Penetration of High Strength Self-Compacting Concretes: Pumice and Zeolite Effect

This paper aims to contribute to the characterization and the understanding of fresh state, compressive strength and chloride penetration tendency of high strength self-compacting concretes (HSSCCs) where Portland cement type II is partially substituted by 10% and 15% of natural pumice and zeolite. First, five concrete mixtures with a control mixture without any pozzolan are prepared and tested in both fresh and hardened states. Then, resistance to chloride penetration for all formulation is investigated in non-steady state and steady state by measurement of chloride penetration and diffusion coefficient. In non-steady state, the correlation between initial current and chloride penetration with diffusion coefficient is studied. Moreover, the relationship between diffusion coefficient in non-steady state and electrical resistivity is determined. The concentration of free chloride ions is also measured in steady state. Finally, chloride penetration for all formulation is studied in immersion and tidal condition. The result shows that, the resistance to chloride penetration for HSSCC in immersion and tidal condition increases by incorporating pumice and zeolite. However, concrete with zeolite displays a better resistance. This paper shows that the HSSCC with 15% pumice and 10% zeolite is suitable in fresh, hardened, and durability characteristics.

Microstructure, Compressive Strength and Transport Properties of High Strength Self-Compacting Concretes Containing Natural Pumice and Zeolite

Due to the difficult placement and vibration between reinforcements of reinforced concrete and the defects that it may cause, the use of self-compacting concrete (SCC) is becoming more widespread. Ordinary Portland Cement (OPC) is the most widely used binder in the construction industry. However, the manufacture of this cement results in a significant amount of CO2 being released, which is detrimental to the environment. Thus, an alternative to reduce the cost of SCC is the use of more economical and environmental mineral additives in partial or total substitution of Portland cement. Our study is in this context and aims to develop SCCs both economic and ecological. Two natural pozzolans such as pumice and zeolite are chosen in this research. This research tries to answer questions including the microstructure of the two types of natural pozzolan and their influence on the mechanical properties as well as on the transport property of SCC. Based on the findings of this study, the studied zeolite is a clinoptilolite that presents higher pozzolan activity compared to pumice. However, the use of zeolite decreases the compressive strength of SCC composites. On the contrary, the compressive strength in SCC containing of pumice increases at both early and long term ages with a remarkable increase at long term. A correlation is obtained between the compressive strength with permeable pore and capillary absorption. Also, the results concerning compressive strength and transport property are well justified by evaporable and non-evaporable water content measurement. This paper shows that the substitution of Portland cement by 15% of pumice or 10% of zeolite in HSSCC is suitable in all aspects. 

Comparison of CPW Fed Microstrip Patch Antennas with Varied Ground Structures for Fixed Satellite Applications

This paper draws a comparison between two microstrip patch antennas having different ground structures. The designs utilize 45 mm x 40 mm x 1.6 mm FR4 epoxy substrate (relative permittivity of 4.4 and dielectric loss tangent of 0.02) and CPW feeding technique. The design 1 uses conducting partial ground plates along the two sides of the radiating X’mas tree shaped patch. The design 2 utilizes an X’mas tree shaped slotted ground structure that features a circular radiating patch. A comparative analysis of results of both designs has been carried. The two designs are intended to serve the fixed satellite applications in X and Ku band respectively.

Hypersonic Flow of CO2-N2 Mixture around a Spacecraft during the Atmospheric Reentry

The aim of this work is to analyze a flow around the axisymmetric blunt body taken into account the chemical and vibrational nonequilibrium flow. This work concerns the entry of spacecraft in the atmosphere of the planet Mars. Since the equations involved are non-linear partial derivatives, the volume method is the only way to solve this problem. The choice of the mesh and the CFL is a condition for the convergence to have the stationary solution.