Search results for: Ordinary stone column

Authors: Ali H. Mahfouz, Hossam E. M.Sallam, Abdulwali Wazir, Hamod H. Kharezi

Abstract:

The soil profile at site of the bridge project includes soft fine grained soil layer located between 5.0 m to 11.0 m in depth, it has high water content, low SPT no., and low bearing capacity. The clay layer induces high settlement due to surcharge application of earth embankment at ramp T1, ramp T2, and ramp T3 especially at heights from 9m right 3m. Calculated settlement for embankment heights less than 3m may be accepted regarding Saudi Code for soil and foundation. The soil and groundwater at the project site comprise high contents of sulfates and chlorides of high aggressively on concrete and steel bars, respectively. Regarding results of the study, it has been recommended to use stone column piles or new technology named PCC piles as soil improvement to improve the bearing capacity of the weak layer. The new technology is cast in-situ thin wall concrete pipe piles (PCC piles), it has economically advantageous and high workability. The technology can save time of implementation and cost of application is almost 30% of other types of piles.

Keywords: Soft foundation soil, bearing capacity, bridge ramps, soil improvement, PCC piles.

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Authors: Mohsen Ebrahimi

Abstract:

In this paper, Steam Assisted Gravity Drainage (SAGD) is introduced and its advantages over ordinary steam injection is demonstrated. A simple simulation model is built and three scenarios of natural production, ordinary steam injection, and SAGD are compared in terms of their cumulative oil production and cumulative oil steam ratio. The results show that SAGD can significantly enhance oil production in quite a short period of time. However, since the distance between injection and production wells is short, the oil to steam ratio decreases gradually through time.

Keywords: Thermal recovery, Steam injection, SAGD, Enhanced oil recovery

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Authors: Mehmet Alpaslan Köroğlu, Musa Hakan Arslan, Muslu Kazım Körez

Abstract:

Basic objective of this study is to create a regression analysis method that can estimate the length of a plastic hinge which is an important design parameter, by making use of the outcomes of (lateral load-lateral displacement hysteretic curves) the experimental studies conducted for the reinforced square concrete columns. For this aim, 170 different square reinforced concrete column tests results have been collected from the existing literature. The parameters which are thought affecting the plastic hinge length such as crosssection properties, features of material used, axial loading level, confinement of the column, longitudinal reinforcement bars in the columns etc. have been obtained from these 170 different square reinforced concrete column tests. In the study, when determining the length of plastic hinge, using the experimental test results, a regression analysis have been separately tested and compared with each other. In addition, the outcome of mentioned methods on determination of plastic hinge length of the reinforced concrete columns has been compared to other methods available in the literature.

Keywords: Columns, plastic hinge length, regression analysis, reinforced concrete.

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Authors: R. Ziaie Moayed, E. Ghanbari Alamouty

Abstract:

Deep soil mixing is one of the improvement methods in geotechnical engineering which is widely used in soft soils. This article investigates the consolidation behavior of a soft clay soil which is improved by soil-cement column (SCC) by numerical modeling using Plaxis2D program. This behavior is simulated under vertical static and cyclic load which is applied on the soil surface. The static load problem is the simulation of a physical model test in an axisymmetric condition which uses a single SCC in the model center. The results of numerical modeling consist of settlement of soft soil composite, stress on soft soil and column, and excessive pore water pressure in the soil show a good correspondence with the test results. The response of soft soil composite to the cyclic load in vertical direction also compared with the static results. Also the effects of two variables namely the cement content used in a SCC and the area ratio (the ratio of the diameter of SCC to the diameter of composite soil model, a) is investigated. The results show that the stress on the column with the higher value of a, is lesser compared with the stress on other columns. Different rate of consolidation and excessive pore pressure distribution is observed in cyclic load problem. Also comparing the results of settlement of soil shows higher compressibility in the cyclic load problem.

Keywords: Area ratio, consolidation behavior, cyclic load, numerical modeling, soil-cement column.

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Authors: Ilqar Ramazanli

Abstract:

The matrix completion problem has been studied broadly under many underlying conditions. In many real-life scenarios, we could expect elements from distinct columns or distinct positions to have a different cost. In this paper, we explore this generalization under adaptive conditions. We approach the problem under two different cost models. The first one is that entries from different columns have different observation costs, but, within the same column, each entry has a uniform cost. The second one is any two entry has different observation cost, despite being the same or different columns. We provide complexity analysis of our algorithms and provide tightness guarantees.

Keywords: Matrix completion, adaptive learning, heterogeneous cost, Matroid optimization.

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Authors: J.S.C. Prentice

Abstract:

The RK1GL2X3 method is a numerical method for solving initial value problems in ordinary differential equations, and is based on the RK1GL2 method which, in turn, is a particular case of the general RKrGLm method. The RK1GL2X3 method is a fourth-order method, even though its underlying Runge-Kutta method RK1 is the first-order Euler method, and hence, RK1GL2X3 is considerably more efficient than RK1. This enhancement is achieved through an implementation involving triple-nested two-point Gauss- Legendre quadrature.

Keywords: RK1GL2X3, RK1GL2, RKrGLm, Runge-Kutta, Gauss-Legendre, initial value problem, local error, global error.

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Authors: J. Fernandez de Canete, S. Gonzalez-Perez, P. del Saz-Orozco

Abstract:

LABVIEW is a graphical programming language that has its roots in automation control and data acquisition. In this paper we have utilized this platform to provide a powerful toolset for process identification and control of nonlinear systems based on artificial neural networks (ANN). This tool has been applied to the monitoring and control of a lab-scale distillation column DELTALAB DC-SP. The proposed control scheme offers high speed of response for changes in set points and null stationary error for dual composition control and shows robustness in presence of externally imposed disturbance.

Keywords: Distillation, neural networks, LABVIEW, monitoring, identification, control.

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Authors: Zarina Bibi Ibrahim, Mohamed Suleiman, Khairil Iskandar Othman

Abstract:

In this paper, a direct method based on variable step size Block Backward Differentiation Formula which is referred as BBDF2 for solving second order Ordinary Differential Equations (ODEs) is developed. The advantages of the BBDF2 method over the corresponding sequential variable step variable order Backward Differentiation Formula (BDFVS) when used to solve the same problem as a first order system are pointed out. Numerical results are given to validate the method.

Keywords: Backward Differentiation Formula, block, secondorder.

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Authors: Seyed Hamid Mirmohammad Sadeghi, Raffaella Sesana, Daniela Maffiodo

Abstract:

This study presents a procedure for friction calculation of column electric power steering (C-EPS) system which affects handling and comfort in driving. The friction losses estimation is obtained from experimental tests and mathematical calculation. Parts in C-EPS mainly involved in friction losses are bearings and worm gear. In the theoretical approach, the gear geometry and Hertz law were employed to measure the normal load and the sliding velocity and contact areas from the worm gears driving conditions. The viscous friction generated in the worm gear was obtained with a theoretical approach and the result was applied to model the friction in the steering system. Finally, by viscous friction coefficient and Coulomb friction coefficient, values of friction in worm gear were calculated. According to the Bearing Company and the characteristics of each bearing, the friction torques due to load and due to speed were calculated. A MATLAB Simulink model for calculating the friction in bearings and worm gear in C-EPS were done and the total friction value was estimated.

Keywords: Friction, worm gear, column electric power steering system, Simulink, bearing, electric power steering, EPS.

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Authors: Ali Y Al-Attraqchi, P. Rajeev, M. Javad Hashemi, Riadh Al-Mahaidi

Abstract:

This paper presents a probabilistic incremental dynamic analysis (IDA) of a full reinforced concrete building subjected to column loss scenario for the assessment of progressive collapse. The IDA is chosen to explicitly account for uncertainties in loads and system capacity. Fragility curves are developed to predict the probability of progressive collapse given the loss of one or more columns. At a broader scale, it will also provide critical information needed to support the development of a new generation of design codes that attempt to explicitly quantify structural robustness.

Keywords: Incremental dynamic analysis, progressive collapse, structural engineering, pushdown analysis.

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Authors: I. Abuiziah, A. Oulhaj, K. Sebari, D. Ouazar, A. A. Saber

Abstract:

In water pipeline systems, the flow control is an integrated part of the operation, for instance, opening and closing the valves, starting and stopping the pumps, when these operations very quickly performed, they shall cause the hydraulic transient phenomena, which may cause pump and, valve failures and catastrophic pipe ruptures. Fluid transient analysis is one of the more challenging and complicated flow problems in the design and the operation of water pipeline systems. Transient control has become an essential requirement for ensuring safe operation of water pipeline systems. An accurate analysis and suitable protection devices should be used to protect water pipeline systems. The fourth-order Runge-Kutta method has been used to solve the dynamic and continuity equations in the rigid column method, while the characteristics method used to solve these equations in the full elastic methods. This paper presents the problem of modeling and simulating of transient phenomena in conveying pipeline systems based on the rigid column and full elastic methods. Also, it provides the influence of using the protection devices to protect the pipeline systems from damaging due to the gain pressure which occur in the transient state. The results obtained provide that the model is an efficient tool for flow transient analysis and provide approximately identical results by using these two methods. Moreover; using the closed surge tank reduces the unfavorable effects of transients.

Keywords: Flow transient, Pipeline, Air chamber, Numerical model, Protection devices, Elastic method, Rigid column method.

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Authors: Thomas Kampke

Abstract:

Equations with differentials relating to the inverse of an unknown function rather than to the unknown function itself are solved exactly for some special cases and numerically for the general case. Invertibility combined with differentiability over connected domains forces solutions always to be monotone. Numerical function inversion is key to all solution algorithms which either are of a forward type or a fixed point type considering whole approximate solution functions in each iteration. The given considerations are restricted to ordinary differential equations with inverted functions (ODEIs) of first order. Forward type computations, if applicable, admit consistency of order one and, under an additional accuracy condition, convergence of order one.

Keywords: Euler method, fixed points, golden section, multi-step procedures, Runge Kutta methods.

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Authors: Olusheye Akinfenwa

Abstract:

We consider the development of an eight order Adam-s type method, with A-stability property discussed by expressing them as a one-step method in higher dimension. This makes it suitable for solving variety of initial-value problems. The main method and additional methods are obtained from the same continuous scheme derived via interpolation and collocation procedures. The methods are then applied in block form as simultaneous numerical integrators over non-overlapping intervals. Numerical results obtained using the proposed block form reveals that it is highly competitive with existing methods in the literature.

Keywords: Block Adam's type Method; Periodic Ordinary Differential Equation; Stability.

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Authors: Umair Baig, Kohei Nagai

Abstract:

At highly congested reinforcement regions, which is common at beam-column joint area, clear spacing between parallel bars becomes less than maximum normal aggregate size (20mm) which has not been addressed in any design code and specifications. Limited clear spacing between parallel bars (herein after thin cover) is one of the causes which affect anchorage performance. In this study, an experimental investigation was carried out to understand anchorage performance of reinforcement in Self-Compacting Concrete (SCC) and Normal Concrete (NC) at highly congested regions under uni-axial tensile loading.  Column bar was pullout whereas; beam bars were offset from column reinforcement creating thin cover as per site condition. Two different sizes of coarse aggregate were used for NC (20mm and 10mm). Strain gauges were also installed along the bar in some specimens to understand the internal stress mechanism. Test results reveal that anchorage performance is affected at highly congested reinforcement region in NC with maximum aggregate size 20mm whereas; SCC and Small Aggregate (10mm) gives better structural performance. 

Keywords: Anchorage capacity, bond, Normal Concrete, self-compacting concrete.

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Authors: P. Wongmatar, C. Hansapinyo, C. Buachart

Abstract:

Failure of typical seismic frames has been found by plastic hinge occurring on beams section near column faces. On the other hand, the seismic capacity of the frames can be enhanced if the plastic hinges of the beams are shifted away from the column faces. This paper presents detailing of reinforcements in the interior beam– column connections aiming to relocate the plastic hinge of reinforced concrete and precast concrete frames. Four specimens were tested under quasi-static cyclic load including two monolithic specimens and two precast specimens. For one monolithic specimen, typical seismic reinforcement was provided and considered as a reference specimen named M1. The other reinforced concrete frame M2 contained additional intermediate steel in the connection area compared with the specimen M1. For the precast specimens, embedded T-section steels in joint were provided, with and without diagonal bars in the connection area for specimen P1 and P2, respectively. The test results indicated the ductile failure with beam flexural failure in monolithic specimen M1 and the intermediate steel increased strength and improved joint performance of specimen M2. For the precast specimens, cracks generated at the end of the steel inserts. However, slipping of reinforcing steel lapped in top of the beams was seen before yielding of the main bars leading to the brittle failure. The diagonal bars in precast specimens P2 improved the connection stiffness and the energy dissipation capacity.

Keywords: Relocation, Plastic hinge, Intermediate bar, Tsection steel, Precast concrete frame.

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Authors: Arash Esmaeili, Omid Ghabouli

Abstract:

The production and consumption of natural gas is on the rise throughout the world as a result of its wide availability, ease of transportation, use and clean-burning characteristics. The chief use of ethane is in the chemical industry in the production of Ethene (ethylene) by steam cracking. In this simulation, obtained ethane recovery percent based on Gas sub-cooled process (GSP) is 99.9 by mole that is included 32.1% by using de-methanizer column and 67.8% by de-ethanizer tower. The outstanding feature of this process is the novel split-vapor concept that employs to generate reflux for de-methanizer column. Remain amount of ethane in export gas cause rise in gross heating value up to 36.66 MJ/Nm3 in order to use in industrial and household consumptions.

Keywords: Ethane recovery, Hydrocarbon dew point, Simulation, Water dew point

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Authors: O. A. Akinfenwa, N.M. Yao, S. N. Jator

Abstract:

In this paper, a self starting two step continuous block hybrid formulae (CBHF) with four Off-step points is developed using collocation and interpolation procedures. The CBHF is then used to produce multiple numerical integrators which are of uniform order and are assembled into a single block matrix equation. These equations are simultaneously applied to provide the approximate solution for the stiff ordinary differential equations. The order of accuracy and stability of the block method is discussed and its accuracy is established numerically.

Keywords: Collocation and Interpolation, Continuous HybridBlock Formulae, Off-Step Points, Stability, Stiff ODEs.

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Authors: Abdulkarim Mohammed Iliyasu, Mahmud Abba Tahir

Abstract:

Freezing and thawing are considered to be one of the major causes of concrete deterioration in the cold regions. This study aimed at assessing the freezing and thawing of concrete within the cover zone by monitoring the formation of ice and melting at different temperatures using electrical measurement technique. A multi-electrode array system was used to obtain the resistivity of ice formation and melting at discrete depths within the cover zone of the concrete. A total number of four concrete specimens (250 mm x 250 mm x 150 mm) made of ordinary Portland cement concrete and ordinary Portland cement replaced by 65% ground granulated blast furnace slag (GGBS) is investigated. Water/binder ratios of 0.35 and 0.65 were produced and ponded with water to ensure full saturation and then subjected to freezing and thawing process in a refrigerator within a temperature range of -30 ⁰C and 20 ⁰C over a period of time 24 hours. The data were collected and analysed. The obtained results show that the addition of GGBS changed the pore structure of the concrete which resulted in the decrease in conductance. It was recommended among others that, the surface of the concrete structure should be protected as this will help to prevent the instantaneous propagation of ice trough the rebar and to avoid corrosion and subsequent damage.

Keywords: Concrete, conductance, deterioration, freezing and thawing, ordinary Portland cement.

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Authors: A. A. Azemati, H. Hosseini, B. Shirkavand Hadavand

Abstract:

By using an adequate thermal barrier coating in buildings the energy saving will be happened. In this study, a range of wall paints with different absorption coefficient in different climates has been investigated. In order to study these effects, heating and cooling loads of a common building with different ordinary paints and paint with mineral coating have been calculated. The effect of building paint in different climatic condition was studied and comparison was done between ordinary paints and paint with mineral insulators in temperate climate to obtain optimized energy consumption. The results have been shown that coatings with inorganic micro particles as insulation reduce the energy consumption of buildings around 14%.

Keywords: Insulator, coating, climate, energy consumption.

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Authors: Shyam Kumar, Nannuri Srinivasulu, Ashok Khanna

Abstract:

Bubble columns have a variety of applications in absorption, bio-reactions, catalytic slurry reactions, and coal liquefaction; because they are simple to operate, provide good heat and mass transfer, having less operational cost. The use of Computational Fluid Dynamics (CFD) for bubble column becomes important, since it can describe the fluid hydrodynamics on both local and global scale. Euler- Euler two-phase fluid model has been used to simulate two-phase (air and water) transient up-flow in bubble column (15cm diameter) using FLUENT6.3. These simulations and experiments were operated over a range of superficial gas velocities in the bubbly flow and churn turbulent regime (1 to16 cm/s) at ambient conditions. Liquid velocity was varied from 0 to 16cm/s. The turbulence in the liquid phase is described using the standard k-ε model. The interactions between the two phases are described through drag coefficient formulations (Schiller Neumann). The objectives are to validate CFD simulations with experimental data, and to obtain grid-independent numerical solutions. Quantitatively good agreements are obtained between experimental data for hold-up and simulation values. Axial liquid velocity profiles and gas holdup profiles were also obtained for the simulation.

Keywords: Bubble column, Computational fluid dynamics, Gas holdup profile, k-ε model.

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Authors: Sophia C. Alih, Mohammadreza Vafaei, Farnoud Rahimi Mansour, Nur Hajarul Falahi Abdul Halim

Abstract:

Built-up columns have been widely employed by practice engineers in the design and construction of buildings and bridges. However, failures have been observed in this type of columns in previous seismic events. This study analyses the performance of built-up columns with different configurations of battens when it is subjected to seismic loads. Four columns with different size of battens were simulated and subjected to three different intensities of axial load along with a lateral cyclic load. Results indicate that the size of battens influences significantly the seismic behavior of columns. Lower shear capacity of battens results in higher ultimate strength and ductility for built-up columns. It is observed that intensity of axial load has a significant effect on the ultimate strength of columns, but it is less influential on the yield strength. For a given drift value, the stress level in the centroid of smaller size battens is significantly more than that of larger size battens signifying damage concentration in battens rather than chords. It is concluded that design of battens for shear demand lower than code specified values only slightly reduces initial stiffness of columns; however, it improves seismic performance of battened columns.

Keywords: Battened column, built-up column, cyclic behavior, seismic design, steel column.

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Authors: A. Djafer, S. Kouadri Moustefai, A. Idou, M. Douani

Abstract:

The removal of chromium by living yeast biomass immobilized onto pozzolana was studied. The results obtained in batch experiments indicate that the immobilized yeast on to pozzolana is a excellent biosorbent of Cr(V) with a good removal rates of 85–90%. The initial concentration solution and agitation speed affected Cr(V) removal. The batch studies data were described using the Freundlich and Langmuir models, but the best fit was obtained with Langmuir model. The breakthrough curve from the continuous flow studies shows that immobilized yeast in the fixed-bed column is capable of decreasing Cr(VI) concentration from 15mg/l to a adequate level. 

Keywords: Biosorption, yeast, chromium, kinetic biosorption, fixed biomass

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Authors: Jain-Shing Liu

Abstract:

In this work, we study the problem of determining the minimum scheduling length that can satisfy end-to-end (ETE) traffic demand in scheduling-based multihop WSNs with cooperative multiple-input multiple-output (MIMO) transmission scheme. Specifically, we present a cross-layer formulation for the joint routing, scheduling and stream control problem by incorporating various power and rate adaptation schemes, and taking into account an antenna beam pattern model and the signal-to-interference-and-noise (SINR) constraint at the receiver. In the context, we also propose column generation (CG) solutions to get rid of the complexity requiring the enumeration of all possible sets of scheduling links.

Keywords: Wireless Sensor Networks, Cross-Layer Design, CooperativeMIMO System, Column Generation.

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Authors: Khairil Iskandar Othman, Zarina Bibi Ibrahim, Mohamed Suleiman

Abstract:

A parallel block method based on Backward Differentiation Formulas (BDF) is developed for the parallel solution of stiff Ordinary Differential Equations (ODEs). Most common methods for solving stiff systems of ODEs are based on implicit formulae and solved using Newton iteration which requires repeated solution of systems of linear equations with coefficient matrix, I - hβJ . Here, J is the Jacobian matrix of the problem. In this paper, the matrix operations is paralleled in order to reduce the cost of the iterations. Numerical results are given to compare the speedup and efficiency of parallel algorithm and that of sequential algorithm.

Keywords: Backward Differentiation Formula, block, ordinarydifferential equations.

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Authors: N. Hachemi, A. Nouani, A. Benchabane

Abstract:

The influence of cultivation factors such as content of ammonium sulfate, glucose and water in the culture medium and particle size of dry orange waste, on their bioconversion for pectinase production was studied using complete factorial design. A polygalacturonase (PG) was isolated using ion exchange chromatography under gradient elution 0-0,5 m/l NaCl (column equilibrate with acetate buffer pH 4,5), subsequently by sephadex G75 column chromatography was applied and the molecular weight was obtained about 51,28 KDa. Purified PG enzyme exhibits a pH and temperature optima of activity at 5 and 35°C respectively. Treatment of apple juice by purified enzyme extract yielded a clear juice, which was competitive with juice yielded by pure Sigma Aldrich Aspergillus niger enzyme.

Keywords: Bioconversion, orange wastes, optimization, pectinase.

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Authors: Kahil Amar, Nekmouche Aghiles, Titouche Billal, Hamizi Mohand, Hannachi Naceur Eddine

Abstract:

The ductility is an important parameter in the nonlinear behavior of portal structures reinforced concrete. It may be explained by the ability of the structure to deform in the plastic range, or the geometric characteristics in the map may influence the overall ductility. Our study is based on the influence of geometric slenderness (Lx / Ly) on the overall ductility of these structures, a study is made on a structure has 05 floors with varying the column section of 900 cm², 1600 cm² and 1225 cm². A slight variation in global ductility is noticed as (Lx/Ly) varies; however, column sections can control satisfactorily the plastic behavior of buildings.

Keywords: Ductility, nonlinear behavior, pushover analysis, geometric slenderness, structural behavior.

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Authors: Dhruba Das

Abstract:

In this paper, a method has been developed to construct the membership surfaces of row and column vectors and arithmetic operations of imprecise matrix. A matrix with imprecise elements would be called an imprecise matrix. The membership surface of imprecise vector has been already shown based on Randomness-Impreciseness Consistency Principle. The Randomness- Impreciseness Consistency Principle leads to defining a normal law of impreciseness using two different laws of randomness. In this paper, the author has shown row and column membership surfaces and arithmetic operations of imprecise matrix and demonstrated with the help of numerical example.

Keywords: Imprecise number, Imprecise vector, Membership surface, Imprecise matrix.

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Authors: F. Kharchi, M. Benhadji, O. Bouksani

Abstract:

The objective of this work is to study the influence of the properties of the substrate on the retrofit (thin repair) of damaged concrete elements, with the SCC. Fluidity, principal characteristic of the SCC, would enable it to cover and adhere to the concrete to be repaired. Two aspects of repair are considered, the bond (Adhesion) and the tensile strength and the cracking. The investigation is experimental; It was conducted over test specimens made up of ordinary concrete prepared and hardened in advance (the material to be repaired) over which a self compacting concrete layer is cast. Three alternatives of SC concrete and one ordinary concrete (comparison) were tested. It appears that the self-compacting concrete constitutes a good material for repairing. It follows perfectly the surfaces- forms to be repaired and allows a perfect bond. Fracture tests made on specimens of self-compacting concrete show a brittle behaviour. However when a small percentage of fibres is added, the resistance to cracking is very much improve.

Keywords: Adhesion, concrete, experimental, repair, self-compacting.

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Authors: Sadegh Papari, Mohammad Kazemeini, Moslem Fattahi

Abstract:

In the present study, a heterogeneous and homogeneous gas flow dispersion model for simulation and optimisation of a large-scale catalytic slurry reactor for the direct synthesis of dimethyl ether (DME) from syngas and CO2, using a churn-turbulent regime was developed. In the heterogeneous gas flow model the gas phase was distributed into two bubble phases: small and large, however in the homogeneous one, the gas phase was distributed into only one large bubble phase. The results indicated that the heterogeneous gas flow model was in more agreement with experimental pilot plant data than the homogeneous one.

Keywords: Modelling, Slurry bubble column, Dimethyl ether synthesis, Homogeneous gas flow, Heterogeneous gas flow

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Authors: Gabofetswe Malema, Michael Liebelt

Abstract:

LDPC codes could be used in magnetic storage devices because of their better decoding performance compared to other error correction codes. However, their hardware implementation results in large and complex decoders. This one of the main obstacles the decoders to be incorporated in magnetic storage devices. We construct small high girth and rate 2 columnweight codes from cage graphs. Though these codes have low performance compared to higher column weight codes, they are easier to implement. The ease of implementation makes them more suitable for applications such as magnetic recording. Cages are the smallest known regular distance graphs, which give us the smallest known column-weight 2 codes given the size, girth and rate of the code.

Keywords: Structured LDPC codes, cage graphs.

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