Search results for: Riccati differential equation

Authors: S. S. P. M. Isa, N. M. Arifin, R. Nazar, N. Bachok, F. M. Ali, I. Pop

Abstract:

A theoretical study has been presented to describe the boundary layer flow and heat transfer on an exponentially shrinking sheet with a variable wall temperature and suction, in the presence of magnetic field. The governing nonlinear partial differential equations are converted into ordinary differential equations by similarity transformation, which are then solved numerically using the shooting method. Results for the skin friction coefficient, local Nusselt number, velocity profiles as well as temperature profiles are presented through graphs and tables for several sets of values of the parameters. The effects of the governing parameters on the flow and heat transfer characteristics are thoroughly examined.

Keywords: Exponentially shrinking sheet, magnetic field, mixed convection, suction.

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Authors: Rampal Singh, S. Balasundaram

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In this paper, we study the application of Extreme Learning Machine (ELM) algorithm for single layered feedforward neural networks to non-linear chaotic time series problems. In this algorithm the input weights and the hidden layer bias are randomly chosen. The ELM formulation leads to solving a system of linear equations in terms of the unknown weights connecting the hidden layer to the output layer. The solution of this general system of linear equations will be obtained using Moore-Penrose generalized pseudo inverse. For the study of the application of the method we consider the time series generated by the Mackey Glass delay differential equation with different time delays, Santa Fe A and UCR heart beat rate ECG time series. For the choice of sigmoid, sin and hardlim activation functions the optimal values for the memory order and the number of hidden neurons which give the best prediction performance in terms of root mean square error are determined. It is observed that the results obtained are in close agreement with the exact solution of the problems considered which clearly shows that ELM is a very promising alternative method for time series prediction.

Keywords: Chaotic time series, Extreme learning machine, Generalization performance.

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Authors: Soumiya Bhattacharjee, P. K. Champati Ray, Shovan L. Chattoraj, Mrinmoy Dhara

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The entire Himalayan range is globally renowned for rainfall-induced landslides. The prime focus of the study is to determine rainfall based threshold for initiation of landslides that can be used as an important component of an early warning system for alerting stake holders. This research deals with temporal dimension of slope failures due to extreme rainfall events along the National Highway-58 from Karanprayag to Badrinath in the Garhwal Himalaya, India. Post processed 3-hourly rainfall intensity data and its corresponding duration from daily rainfall data available from Tropical Rainfall Measuring Mission (TRMM) were used as the prime source of rainfall data. Landslide event records from Border Road Organization (BRO) and some ancillary landslide inventory data for 2013 and 2014 have been used to determine Intensity Duration (ID) based rainfall threshold. The derived governing threshold equation, I= 4.738D^-0.025, has been considered for prediction of landslides of the study region. This equation was validated with an accuracy of 70% landslides during August and September 2014. The derived equation was considered for further prediction of landslides of the study region. From the obtained results and validation, it can be inferred that this equation can be used for initiation of landslides in the study area to work as a part of an early warning system. Results can significantly improve with ground based rainfall estimates and better database on landslide records. Thus, the study has demonstrated a very low cost method to get first-hand information on possibility of impending landslide in any region, thereby providing alert and better preparedness for landslide disaster mitigation.

Keywords: Landslide, intensity-duration, rainfall threshold, Tropical Rainfall Measuring Mission, slope, inventory, early warning system.

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Authors: Phool Singh, Ashok Jangid, N.S. Tomer, Deepa Sinha

Abstract:

The aim of this paper is to study the oblique stagnation point flow on vertical plate with uniform surface heat flux in presence of magnetic field. Using Stream function, partial differential equations corresponding to the momentum and energy equations are converted into non-linear ordinary differential equations. Numerical solutions of these equations are obtained using Runge-Kutta Fehlberg method with the help of shooting technique. In the present work the effects of striking angle, magnetic field parameter, Grashoff number, the Prandtl number on velocity and heat transfer characteristics have been discussed. Effect of above mentioned parameter on the position of stagnation point are also studied.

Keywords: Heat flux, Oblique stagnation point, Mixedconvection, Magneto hydrodynamics

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Authors: Wei Jun-xia, Yuan Guang-wei, Yang Shu-lin, Shen Wei-dong

Abstract:

In order to make conventional implicit algorithm to be applicable in large scale parallel computers , an interface prediction and correction of discontinuous finite element method is presented to solve time-dependent neutron transport equations under 2-D cylindrical geometry. Domain decomposition is adopted in the computational domain.The numerical experiments show that our parallel algorithm with explicit prediction and implicit correction has good precision, parallelism and simplicity. Especially, it can reach perfect speedup even on hundreds of processors for large-scale problems.

Keywords: Transport Equation, Discontinuous Finite Element, Domain Decomposition, Interface Prediction And Correction

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Authors: Wen-liang Chen, Peng Wei, Yidong Bao

Abstract:

This paper presents a linear-elastic finite element method based flattening algorithm for three dimensional triangular surfaces. First, an intrinsic characteristic preserving method is used to obtain the initial developing graph, which preserves the angles and length ratios between two adjacent edges. Then, an iterative equation is established based on linear-elastic finite element method and the flattening result with an equilibrium state of internal force is obtained by solving this iterative equation. The results show that complex surfaces can be dealt with this proposed method, which is an efficient tool for the applications in computer aided design, such as mould design.

Keywords: Triangular mesh, surface flattening, finite elementmethod, linear-elastic deformation.

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Authors: Jihye Jeon

Abstract:

This paper analyzes the conceptual framework of three statistical methods, multiple regression, path analysis, and structural equation models. When establishing research model of the statistical modeling of complex social phenomenon, it is important to know the strengths and limitations of three statistical models. This study explored the character, strength, and limitation of each modeling and suggested some strategies for accurate explaining or predicting the causal relationships among variables. Especially, on the studying of depression or mental health, the common mistakes of research modeling were discussed.

Keywords: Multiple regression, path analysis, structural equation models, statistical modeling, social and psychological phenomenon.

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Authors: Peichen Zhao

Abstract:

In this paper, we extend the compound binomial model to the case where the premium income process, based on a binomial process, is no longer a linear function. First, a mathematically recursive formula is derived for non ruin probability, and then, we examine the expected discounted penalty function, satisfy a defect renewal equation. Third, the asymptotic estimate for the expected discounted penalty function is then given. Finally, we give two examples of ruin quantities to illustrate applications of the recursive formula and the asymptotic estimate for penalty function.

Keywords: Discounted penalty function, compound binomial process, recursive formula, discrete renewal equation, asymptotic estimate.

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Authors: R. Alipour, F.Najarian

Abstract:

Explosive welding is a process which uses explosive detonation to move the flyer plate material into the base material to produce a solid state joint. Experimental tests have been carried out by other researchers; have been considered to explosively welded aluminium 7039 and steel 4340 tubes in one step. The tests have been done using various stand-off distances and explosive ratios. Various interface geometries have been obtained from these experiments. In this paper, all the experiments carried out were simulated using the finite element method. The flyer plate and collision velocities obtained from the analysis were validated by the pin-measurement experiments. The numerical results showed that very high localized plastic deformation produced at the bond interface. The Ls_dyna_971 FEM has been used for all simulation process.

Keywords: Explosive Welding, Johnson-Cook Equation, Finite Element, JWL Equation.

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Authors: E.G. Bautista, F. Méndez, O. Bautista, J.C. Arcos

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In this work we study analytically and numerically the performance of the mean heave motion of an OWC coupled with the governing equation of the spreading ocean waves due to the wide variation in an open parabolic channel with constant depth. This paper considers that the ocean wave propagation is under the assumption of a shallow flow condition. In order to verify the effect of the waves in the OWC firstly we establish the analytical model in a non-dimensional form based on the energy equation. The proposed wave-power system has to aims: one is to perturb the ocean waves as a consequence of the channel shape in order to concentrate the maximum ocean wave amplitude in the neighborhood of the OWC and the second is to determine the pressure and volume oscillation of air inside the compression chamber.

Keywords: Oscillating water column, Shallow flow, Waveenergy.

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Authors: B. Tomczyk, R. Mania

Abstract:

Thin linear-elastic cylindrical circular shells having a micro-periodic structure along two directions tangent to the shell midsurface (biperiodic shells) are object of considerations. The aim of this paper is twofold. First, we formulate an averaged nonasymptotic model for the analysis of parametric vibrations or dynamical stability of periodic shells under consideration, which has constant coefficients and takes into account the effect of a cell size on the overall shell behavior (a length-scale effect). This model is derived employing the tolerance modeling procedure. Second we apply the obtained model to derivation of frequency equation being a starting point in the analysis of parametric vibrations. The effect of the microstructure length oh this frequency equation is discussed.

Keywords: Micro-periodic shells, mathematical modeling, length-scale effect, parametric vibrations

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Authors: Mandana Kariminejad, Ali Ghaffari

Abstract:

Today, the treatment of cancer, in a relatively short period, with minimum adverse effects is a great concern for oncologists. In this paper, based on a recently used mathematical model for cancer, a guideline has been proposed for the amount and duration of drug doses for cancer treatment by immunotherapy. Dynamically speaking, the mathematical ordinary differential equation (ODE) model of cancer has different equilibrium points; one of them is unstable, which is called the no tumor equilibrium point. In this paper, based on the number of tumor cells an intelligent soft computing controller (a combination of fuzzy logic controller and genetic algorithm), decides regarding the amount and duration of drug doses, to eliminate the tumor cells and stabilize the unstable point in a relatively short time. Two different immunotherapy approaches; active and adoptive, have been studied and presented. It is shown that the rate of decay of tumor cells is faster and the doses of drug are lower in comparison with the result of some other literatures. It is also shown that the period of treatment and the doses of drug in adoptive immunotherapy are significantly less than the active method. A recommendation to oncologists has also been presented.

Keywords: Tumor, immunotherapy, fuzzy controller, Genetic algorithm, mathematical model.

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Authors: Hsian Ming Goo

Abstract:

The paper concerns a special approximate algorithm of the square root of the specific positive integer, which is built by the use of the property of positive integer solution of the Pell’s equation, together with using some elementary theorems of matrices, and then takes it to compare with general used the Newton’s method and give a practical numerical example and error analysis; it is unexpected to find its special property: the significant figure of the approximation value of the square root of positive integer will increase one digit by one. It is well useful in some occasions.

Keywords: Special approximate algorithm, square root, Pell’s equation, Newton’s method, error analysis.

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Authors: A. Soltani, M. Karimi Demneh

Abstract:

In this paper, modeling of an acoustic enclosed vehicle cabin has been carried out by using boundary element method. Also, the second purpose of this study is analyzing of linear wave equation in an acoustic field. The resultants of this modeling consist of natural frequencies that have been compared with resultants derived from finite element method. By using numerical method (boundary element method) and after solution of wave equation inside an acoustic enclosed cabin, this method has been progressed to simulate noise inside a simple vehicle cabin.

Keywords: Boundary element method, natural frequency, noise, vehicle cabin.

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Authors: Arpita Soni, Sapna Mittal

Abstract:

Austenite and Martensite indicate the phases of solids undergoing phase transformation which we usually associate with materials and not with living organisms. This article provides an overview of bacterial proteins and structures that are undergoing phase transformation and suggests its probable effect on mechanical behavior. The context is mainly within the role of phase transformations occurring in the flagellum of bacteria. The current knowledge of molecular mechanism leading to phase variation in living organisms is reviewed. Since in bacteria, each flagellum is driven by a separate motor, similarity to a Differential drive in case of four-wheeled vehicles is suggested. It also suggests the application of the mechanism in which bacteria changes its direction of movement to facilitate single point turning of a multi-wheeled vehicle. Finally, examples are presented to illustrate that the motion due to phase transformation of flagella in bacteria can start a whole new research on motion mechanisms.

Keywords: Flagella, Phase Transformation, Nanobots, Differential Drive, Single point turn, Biomimetics

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Authors: Arup K. George, Wai Pan Chan, Zhi Hui Kong, Minkyu Je

Abstract:

This paper describes a low-power second-order filter for a continuous-time chopper stabilized capacitive sensor interface, integrated with a fully differential post-CMOS surface-micromachined MEMS pressure sensor. The circuit uses a single-ended folded-cascode operational amplifier and two GM-C filters connected in cascade. The circuit is realized in a 0.18 μm CMOS process and offers differential to single-ended conversion. The novelty of the scheme is the cascade of two GM-C filters to achieve a second-order filter while minimizing power dissipation. The simulated filter cutoff frequency is 1.14 kHz at common-mode voltage 1.65 V, operating from a 3.3 V supply while dissipating 172μW of power. The filter achieves an operating range of 1V for an output load of 1MOhm and 10pF.

Keywords: Chopper Stabilization, MEMS, Pressure Sensors, Low Pass Filter

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Authors: Simon Brown

Abstract:

Glomerular filtration rate (GFR) is a measure of kidney function. It is usually estimated from serum concentrations of cystatin C or creatinine although there has been considerable debate in the literature about (i) the best equation to use and (ii) the variability in the correlation between the concentrations of creatinine and cystatin C. The equations for GFR can be written in a general form and from these I calculate the error of the GFR estimates associated with analyte measurement error. These show that the error of the GFR estimates is such that it is not possible to distinguish between the equations over much of the concentration range of either analyte. The general forms of the equations are also used to derive an expression for the concentration of cystatin C as a function of the concentration of creatinine. This equation shows that these analyte concentrations are not linearly related. Clinical reports of cystatin C and creatinine concentration are consistent with the expression derived.

Keywords: creatinine, cystatin C, error analysis, glomerularfiltration rate, measurement error.

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Authors: Ravi V. Joat, Pravin S. Bodke, Shradha S. Binani, S. S. Wasnik

Abstract:

A phase diagram of the Ag₂SO₄ - CaSO₄ (Silver sulphate – Calcium Sulphate) binaries system using conductivity, XRD (X-Ray Diffraction Technique) and DTA (Differential Thermal Analysis) data is constructed. The eutectic reaction (liquid -» a-Ag₂SO₄ + CaSO₄) is observed at 10 mole% CaSO₄ and 645°C. Room temperature solid solubility limit up to 5.27 mole % of Ca ²⁺ in Ag₂SO₄ is set using X-ray powder diffraction and scanning electron microscopy results. All compositions beyond this limit are two-phase mixtures below and above the transition temperature (≈ 416°C). The bulk conductivity, obtained following complex impedance spectroscopy, is found decreasing with increase in CaSO₄ content. Amongst other binary compositions, the 80AgSO₄-20CaSO₄ gave improved sinterability/packing density.

Keywords: Ag2SO4-CaSO4 (Silver sulphate–Calcium Sulphate) binaries system, XRD (X-Ray Diffraction Technique) and DTA (Differential Thermal Analysis).

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Authors: Zanariah Abdul Majid, Mohamed Suleiman

Abstract:

The aim of this paper is to investigate the performance of the developed two point block method designed for two processors for solving directly non stiff large systems of higher order ordinary differential equations (ODEs). The method calculates the numerical solution at two points simultaneously and produces two new equally spaced solution values within a block and it is possible to assign the computational tasks at each time step to a single processor. The algorithm of the method was developed in C language and the parallel computation was done on a parallel shared memory environment. Numerical results are given to compare the efficiency of the developed method to the sequential timing. For large problems, the parallel implementation produced 1.95 speed-up and 98% efficiency for the two processors.

Keywords: Numerical methods, parallel method, block method, higher order ODEs.

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Authors: M. Chitsazi, B. Maraghechi, M. H. Rouhani

Abstract:

Three-dimensional simulation of harmonic up generation in free electron laser amplifier operating simultaneously with a cold and relativistic electron beam is presented in steady-state regime where the slippage of the electromagnetic wave with respect to the electron beam is ignored. By using slowly varying envelope approximation and applying the source-dependent expansion to wave equations, electromagnetic fields are represented in terms of the Hermit Gaussian modes which are well suited for the planar wiggler configuration. The electron dynamics is described by the fully threedimensional Lorentz force equation in presence of the realistic planar magnetostatic wiggler and electromagnetic fields. A set of coupled nonlinear first-order differential equations is derived and solved numerically. The fundamental and third harmonic radiation of the beam is considered. In addition to uniform beam, prebunched electron beam has also been studied. For this effect of sinusoidal distribution of entry times for the electron beam on the evolution of radiation is compared with uniform distribution. It is shown that prebunching reduces the saturation length substantially. For efficiency enhancement the wiggler is set to decrease linearly when the radiation of the third harmonic saturates. The optimum starting point of tapering and the slope of radiation in the amplitude of wiggler are found by successive run of the code.

Keywords: Free electron laser, Prebunching, Undulator, Wiggler.

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Authors: R. F. B. Gonçalves, E. N. Iwama, J. A. F. F. Rocco, K. Iha

Abstract:

Propellants based on Hydroxyl Terminated Polybutadiene/Ammonium Perchlorate (HTPB/AP) are the most commonly used in most of the rocket engines used by the Brazilian Armed Forces. This work aimed at the possibility of extending its useful life (currently in 10 years) by performing kinetic-chemical analyzes of its energetic material via Differential Scanning Calorimetry (DSC) and also performing computer simulation of aging process using the software Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). Thermal analysis via DSC was performed in triplicates and in three heating ratios (5 ºC, 10 ºC, and 15 ºC) of rocket motor with 11 years shelf-life, using the Arrhenius equation to obtain its activation energy, using Ozawa and Kissinger kinetic methods, allowing comparison with manufacturing period data (standard motor). In addition, the kinetic parameters of internal pressure of the combustion chamber in 08 rocket engines with 11 years of shelf-life were also acquired, for comparison purposes with the engine start-up data.

Keywords: Shelf-life, thermal analysis, Ozawa method, Kissinger method, LAMMPS software, thrust.

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Authors: A.R. Ismail, M. R. A. Rani, Z. K. M. Makhbul, M. J. M. Nor, M. N. A. Rahman

Abstract:

The environmental factors such as temperature and relative humidity are very contribute to the effect of comfort, health, performance and worker productivity. To ensure an ergonomics work environment, it is possible to require a specific attention especially in industries. The aim of this study is to show the effect of temperature and relative humidity on worker productivity in automotive industry by taking a workstation in an automotive plant as the location to conduct the study. From the analysis of the data, there were relationship between temperature and relative humidity on worker productivity. Mathematical equation to represent the relationship between temperatures and relative humidity on the production rate is modelled. From the equation model, the production rate for the workstation can be predicted base on the value of temperature and relative humidity.

Keywords: WBGT, Relative Humidity, Comfort, Productivity.

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Authors: Abdurrahim Dal, Tuncay Karaçay

Abstract:

Dynamics of a rotor supported by air bearings is strongly depends on the pressure distribution between the rotor and the bearing. In this study, internal pressure in air bearings is numerical and experimental analyzed for different radial clearances. Firstly the pressure distribution between rotor and bearing is modeled using Reynold's equation and this model is solved numerically. The rotor-bearing system is also modeled in four degree of freedom and it is simulated for different radial clearances. Then, in order to validate numerical results, a test rig is designed and the rotor bearing system is run under the same operational conditions. Pressure signals of left and right bearings are recorded. Internal pressure variations are compared for numerical and experimental results for different radial clearances.

Keywords: Air bearing, internal pressure, Reynold’s equation, rotor.

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Authors: Mehrdad Mahmudizad, Roya Ahmadi Ahangar

Abstract:

This paper presents the method of designing the type 2 fuzzy PID controllers in order to solve the problem of Load Frequency Control (LFC). The Harmony Search (HS) algorithm is used to regulate the measurement factors and the effect of uncertainty of membership functions of Interval Type 2 Fuzzy Proportional Integral Differential (IT2FPID) controllers in order to reduce the frequency deviation resulted from the load oscillations. The simulation results implicitly show that the performance of the proposed IT2FPID LFC in terms of error, settling time and resistance against different load oscillations is more appropriate and preferred than PID and Type 1 Fuzzy Proportional Integral Differential (T1FPID) controllers.

Keywords: Load Frequency Control, Fuzzy-PID controller, Type 2 fuzzy system, Harmony Search algorithm.

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Authors: Xin Luo, Jin Huang, Chuan-Long Wang

Abstract:

The mechanical quadrature methods for solving the boundary integral equations of the anisotropic Darcy-s equations with Dirichlet conditions in smooth domains are presented. By applying the collectively compact theory, we prove the convergence and stability of approximate solutions. The asymptotic expansions for the error show that the methods converge with the order O (h3), where h is the mesh size. Based on these analysis, extrapolation methods can be introduced to achieve a higher convergence rate O (h5). An a posterior asymptotic error representation is derived in order to construct self-adaptive algorithms. Finally, the numerical experiments show the efficiency of our methods.

Keywords: Darcy's equation, anisotropic, mechanical quadrature methods, extrapolation methods, a posteriori error estimate.

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Authors: V. Ghadamyari, F. Samadi, F. Kowsary

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An inverse geometry problem is solved to predict an unknown irregular boundary profile. The aim is to minimize the objective function, which is the difference between real and computed temperatures, using three different versions of Conjugate Gradient Method. The gradient of the objective function, considered necessary in this method, obtained as a result of solving the adjoint equation. The abilities of three versions of Conjugate Gradient Method in predicting the boundary profile are compared using a numerical algorithm based on the method. The predicted shapes show that due to its convergence rate and accuracy of predicted values, the Powell-Beale version of the method is more effective than the Fletcher-Reeves and Polak –Ribiere versions.

Keywords: Boundary elements, Conjugate Gradient Method, Inverse Geometry Problem, Sensitivity equation.

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Authors: M. Akbari, S. Sadodin

Abstract:

In this paper, the melting of a semi-infinite body as a result of a moving laser beam has been studied. Because the Fourier heat transfer equation at short times and large dimensions does not have sufficient accuracy; a non-Fourier form of heat transfer equation has been used. Due to the fact that the beam is moving in x direction, the temperature distribution and the melting pool shape are not asymmetric. As a result, the problem is a transient threedimensional problem. Therefore, thermophysical properties such as heat conductivity coefficient, density and heat capacity are functions of temperature and material states. The enthalpy technique, used for the solution of phase change problems, has been used in an explicit finite volume form for the hyperbolic heat transfer equation. This technique has been used to calculate the transient temperature distribution in the semi-infinite body and the growth rate of the melt pool. In order to validate the numerical results, comparisons were made with experimental data. Finally, the results of this paper were compared with similar problem that has used the Fourier theory. The comparison shows the influence of infinite speed of heat propagation in Fourier theory on the temperature distribution and the melt pool size.

Keywords: Non-Fourier, Enthalpy technique, Melt pool, Radiational boundary condition

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Authors: Yiqin Lin, Liang Bao, Yimin Wei

Abstract:

In this paper we study numerical methods for solving Sylvester matrix equations of the form AX +XBT +CDT = 0. A new projection method is proposed. The union of Krylov subspaces in A and its inverse and the union of Krylov subspaces in B and its inverse are used as the right and left projection subspaces, respectively. The Arnoldi-like process for constructing the orthonormal basis of the projection subspaces is outlined. We show that the approximate solution is an exact solution of a perturbed Sylvester matrix equation. Moreover, exact expression for the norm of residual is derived and results on finite termination and convergence are presented. Some numerical examples are presented to illustrate the effectiveness of the proposed method.

Keywords: Arnoldi process, Krylov subspace, Iterative method, Sylvester equation, Dissipative matrix.

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Authors: YaoAn Lu, QingZhen Bi, BaoRui Du, ShuLin Chen, LiMin Zhu, Kai Huang

Abstract:

Taking the design tolerance into account, this paper presents a novel efficient approach to generate iso-scallop tool path for five-axis strip machining with a barrel cutter. The cutter location is first determined on the scallop surface instead of the design surface, and then the cutter is adjusted to locate the optimal tool position based on the differential rotation of the tool axis and satisfies the design tolerance simultaneously. The machining strip width and error are calculated with the aid of the grazing curve of the cutter. Based on the proposed tool positioning algorithm, the tool paths are generated by keeping the scallop height formed by adjacent tool paths constant. An example is conducted to confirm the validity of the proposed method.

Keywords: Strip machining, barrel cutter, iso-scallop tool path, sculptured surfaces, differential motion.

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Authors: Aurora Cerri, Niko Pullojani

Abstract:

Long-term differential settlement between the bridge structure and the bridge embankment typically results in an abrupt grade change, causing driver discomfort, impairing driver safety, and exerting a potentially excessive impact traffic loading on the abutment. This paper has analysed a case of study showing the effect of an approaching slab realized in a bridge constructed at Tirane-Elbasan Motorway. The layer thickness under the slab is modeled as homogenous, the slab is a reinforced concrete structure and over that the asphaltic layers take place. Analysis indicates that reinforced concrete approaching slab distributes the stresses quite uniformly into the road fill layers and settlements varies in a range less than 2.50 cm in the total slab length of 6.00 m with a maximum slope of 1/240. Results taken from analytical analysis are compared with topographic measurements done on field and they carry great similarities.

Keywords: Approach slab, bridge, road pavement, differential settlement.

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