Search results for: finite time blow up

Authors: Xu Runzhang, Yang Yanbing, Niu Yi, Zhang Mingyou, Liu Yu

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For a class of semilinear parabolic equations with linear dynamical boundary conditions in a bounded domain, we obtain both global solutions and finite time blow-up solutions when the initial data varies in the phase space H1(Ω). Our main tools are the comparison principle, the potential well method and the concavity method. In particular, we discuss the behavior of the solutions with the initial data at critical and high energy level.

Keywords: high energy level, critical energy level, linear dynamical boundary condition, semilinear parabolic equation

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Authors: Ayaz Ahmad

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In this work, we present the effect of noise on the solution of a partial differential equation (PDE) in three different setting. We shall first consider random initial condition for two nonlinear dispersive PDE the non linear Schrodinger equation and the Kortteweg –de vries equation and analyse their effect on some special solution , the soliton solutions.The second case considered a linear partial differential equation , the wave equation with random initial conditions allow to substantially decrease the computational and data storage costs of an algorithm to solve the inverse problem based on the boundary measurements of the solution of this equation. Finally, the third example considered is that of the linear transport equation with a singular drift term, when we shall show that the addition of a multiplicative noise term forbids the blow up of solutions under a very weak hypothesis for which we have finite time blow up of a solution in the deterministic case. Here we consider the problem of wave propagation, which is modelled by a nonlinear dispersive equation with noisy initial condition .As observed noise can also be introduced directly in the equations.

Keywords: drift term, finite time blow up, inverse problem, soliton solution

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Authors: Vigen Arakelian

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This paper deals with the study of devices for displacement of the mould base of blow-molding machines. The displacement of the mould in the studied case is carried out by a linear actuator, which ensures the descent of the mould base and by extension springs, which return the letter in the initial position. The aim of this paper is to study the inverse dynamics of the device for displacement of the mould base of blow-molding machines and to determine its optimum parameters for higher rate of production. In the other words, it is necessary to solve the inverse dynamic problem to find the equation of motion linking applied forces with displacements. This makes it possible to determine the stiffness coefficient of the spring to turn the mold base back to the initial position for a given time. The obtained results are illustrated by a numerical example. It is shown that applying a spring with stiffness returns the mould base of the blow molding machine into the initial position in 0.1 sec.

Keywords: design, mechanisms, dynamics, blow-molding machines

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Authors: N. Ploysook, R. Rugsaj, C. Suvanjumrat

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The characteristic requirement for producing rectangular shape bottles was a uniform thickness of the plastic bottle wall. Die shaping was a good technique which controlled the wall thickness of bottles. An advance technology which was the finite element method (FEM) for blowing parison to be a rectangular shape bottle was conducted to reduce waste plastic from a trial and error method of a die shaping and parison control method. The artificial intelligent (AI) comprised of artificial neural network and genetic algorithm was selected to optimize the die gap shape from the FEM results. The application of AI technique could optimize the suitable die gap shape for the parison blow molding which did not depend on the parison control method to produce rectangular bottles with the uniform wall. Particularly, this application can be used with cheap blow molding machines without a parison controller therefore it will reduce cost of production in the bottle blow molding process.

Keywords: AI, bottle, die shaping, FEM

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Authors: Tanapon Suklim, Prachaya Intaphrom, Noppadol Poomvises, Anchalee Kongsuk

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The relationship between shear wave velocity (Vs30) and blow count Number from Standard Penetration Tests (NSPT) was investigated on specified embankment dam to find the solution which can be used to estimate the value of N. Shear wave velocity, Vs30 and blow count number, NSPT were performed at three specified dam sites. At each site, Vs30 measurement was recorded by using seismic survey of MASW technique and NSPT were measured by field Standard Penetration Test. Regression analysis was used to derive statistical relation. The relation is giving a final solution to applicable calculated N-value with other earthen dam. Dam engineer can use the statistical relation to convert field Vs30 to estimated N-value instead of absolute N-value from field Standard Penetration Test. It can be noted that the formulae can be applied only in the earthen dam of specified material.

Keywords: blow count number, earthen dam, embankment, shear wave velocity

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Authors: Eva Savy, Anthony Ruiz

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In extrusion blow molding, there is great variability in product quality due to the sensitivity of the machine settings. These variations lead to unnecessary rejects and loss of time. Yet production control is a major challenge for companies in this sector to remain competitive within their market. Current quality control methods only apply to finished products (vision control, leak test...). It has been shown that material melt temperature, blowing pressure, and ambient temperature have a significant impact on the variability of product quality. Since blowing is a key step in the process, we have studied this parameter in this paper. The objective is to determine if airflow analysis allows the identification of quality problems before the full completion of the manufacturing process. We conducted tests to determine if it was possible to identify a leakage defect and an obstructed defect, two common defects on products. The results showed that it was possible to identify a leakage defect by airflow analysis.

Keywords: extrusion blow molding, signal, sensor, defects, detection

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Authors: Amir T. Payandeh Najafabadi

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This article considers the problem of evaluating infinite-time (or finite-time) ruin probability under a given compound Poisson surplus process by approximating the claim size distribution by a finite mixture exponential, say Hyperexponential, distribution. It restates the infinite-time (or finite-time) ruin probability as a solvable ordinary differential equation (or a partial differential equation). Application of our findings has been given through a simulation study.

Keywords: ruin probability, compound poisson processes, mixture exponential (hyperexponential) distribution, heavy-tailed distributions

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Authors: Maria Fonseca, Ana Branco, Joao Graca, Rui Mendes, Pedro Mimoso

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The present work is focused on the production of a carbon composite element for cycling through different techniques, namely, blow-molding and high-pressure resin transfer injection (HP-RTM). The main objective of this work is to compare both processes to produce carbon composite elements for the cycling industry. It is well known that the carbon composite components for cycling are produced mainly through blow-molding; however, this technique depends strongly on manual labour, resulting in a time-consuming production process. Comparatively, HP-RTM offers a more automated process which should lead to higher production rates. Nevertheless, a comparison of the elements produced through both techniques must be done, in order to assess if the final products comply with the required standards of the industry. The main difference between said techniques lies in the used material. Blow-moulding uses carbon prepreg (carbon fibres pre-impregnated with a resin system), and the material is laid up by hand, piece by piece, on a mould or on a hard male. After that, the material is cured at a high temperature. On the other hand, in the HP-RTM technique, dry carbon fibres are placed on a mould, and then resin is injected at high pressure. After some research regarding the best material systems (prepregs and braids) and suppliers, an element was designed (similar to a handlebar) to be constructed. The next step was to perform FEM simulations in order to determine what the best layup of the composite material was. The simulations were done for the prepreg material, and the obtained layup was transposed to the braids. The selected material was a prepreg with T700 carbon fibre (24K) and an epoxy resin system, for the blow-molding technique. For HP-RTM, carbon fibre elastic UD tubes and ± 45º braids were used, with both 3K and 6K filaments per tow, and the resin system was an epoxy as well. After the simulations for the prepreg material, the optimized layup was: [45°, -45°,45°, -45°,0°,0°]. For HP-RTM, the transposed layup was [ ± 45° (6k); 0° (6k); partial ± 45° (6k); partial ± 45° (6k); ± 45° (3k); ± 45° (3k)]. The mechanical tests showed that both elements can withstand the maximum load (in this case, 1000 N); however, the one produced through blow-molding can support higher loads (≈1300N against 1100N from HP-RTM). In what concerns to the fibre volume fraction (FVF), the HP-RTM element has a slightly higher value ( > 61% compared to 59% of the blow-molding technique). The optical microscopy has shown that both elements have a low void content. In conclusion, the elements produced using HP-RTM can compare to the ones produced through blow-molding, both in mechanical testing and in the visual aspect. Nevertheless, there is still space for improvement in the HP-RTM elements since the layup of the braids, and UD tubes could be optimized.

Keywords: HP-RTM, carbon composites, cycling, FEM

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Authors: Behbood Maashkar

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One of the principles for societies’ development is the requirement to consider past experiences. Man should always take advantage of the predecessor’s experiences and analyze their works and methods. The predecessors have had a more friendly relationship with nature and their lives less damaged the nature, and it is one of the elements of green building. One of the things the ancients have observed in regard to green building in their houses, stores, sacred places, etc. was using wind-catchers as an air conditioning and cooling system which can be considered as the first foundations of green building. In designing houses Iranian architects have paid a great attention to the factor of making use of more shaded area in hot season and insulation of wall and ceiling against influence of hot weather and also air circulation inside the building. In order to circulate the air inside closed spaces and decrease the temperature, they have considered different winds which blow in Iran and its effective power, and in order to make use of it they invented wind catcher. Direction of wind blow and its height from the earth as well as the time and duration of wind blow and other factors have been effective in making different types of wind catchers. Using wind catchers has been and is prevalent mainly in central and south regions of Iran, coastal areas of Persian Gulf, and Khorasan, especially in cities like Yazd, Kashan, Bam, Abarghoo, Jahrom, and Tabas.

Keywords: environment pollution, green building, Iran, wind catchers

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Authors: Khyati Sharma, A. Satyanarayana Reddy

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The topic of how many subgroups exist within a certain finite group naturally arises in the study of finite groups. Over the years, different researchers have investigated this issue from a variety of angles. The significant contributions of the key mathematicians over the time have been summarized in this article. To this end, we classify finite groups into three categories viz. (a) Groups for which the number of subgroups is less than |G|, (b) equals to |G|, and finally, (c) greater than |G|. Because every element of a finite group generates a cyclic subgroup, counting cyclic subgroups is the most important task in this endeavor. A brief survey on the number of cyclic subgroups of finite groups is also conducted by us. Furthermore, we also covered certain arithmetic relations between the order of a finite group |G| and the number of its distinct cyclic subgroups |C(G)|. In order to provide pertinent context and possibly reveal new novel areas of potential research within the field of research on finite groups, we finally pose and solicit a few open questions.

Keywords: abstract algebra, cyclic subgroup, finite group, subgroup

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Authors: Z. Bouchama, N. Essounbouli, A. Hamzaoui, M. N. Harmas

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A new robust finite time synergetic controller is presented based on recently developed synergetic control methodology and a terminal attractor technique. A Fast Terminal Synergetic Control (FTSC) is proposed for controlling DC-DC buck converter. Unlike Synergetic Control (SC) and sliding mode control, the proposed control scheme has the characteristics of finite time convergence and chattering free phenomena. Simulation of stabilization and reference tracking for buck converter systems illustrates the approach effectiveness while stability is assured in the Lyapunov sense and converse Lyapunov results involving scalar differential inequalities are given for finite-time stability.

Keywords: dc-dc buck converter, synergetic control, finite time convergence, terminal synergetic control, fast terminal synergetic control, Lyapunov

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Authors: Ying Yi Wu

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In this paper, we present a proof of the fact that a finite morphism is proper. We show that a finite morphism is universally closed and of finite type, which are the conditions for properness. Our proof is based on the theory of schemes and involves the use of the projection formula and the base change theorem. We first show that a finite morphism is of finite type and then proceed to show that it is universally closed. We use the fact that a finite morphism is also an affine morphism, which allows us to use the theory of coherent sheaves and their modules. We then show that the map induced by a finite morphism is flat and that the module it induces is of finite type. We use these facts to show that a finite morphism is universally closed. Our proof is constructive, and we provide details for each step of the argument.

Keywords: finite, morphism, schemes, projection.

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Authors: Sule Sahin, Basak Bulut Karageyik

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This paper introduces a hazard rate function for the time of ruin to calculate the conditional probability of ruin for very small intervals. We call this function the force of ruin (FoR). We obtain the expected time of ruin and conditional expected time of ruin from the exact finite time ruin probability with exponential claim amounts. Then we introduce the FoR which gives the conditional probability of ruin and the condition is that ruin has not occurred at time t. We analyse the behavior of the FoR function for different initial surpluses over a specific time interval. We also obtain FoR under the excess of loss reinsurance arrangement and examine the effect of reinsurance on the FoR.

Keywords: conditional time of ruin, finite time ruin probability, force of ruin, reinsurance

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Authors: Hyun-Ho Lee, Kee-Won Kim

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The arithmetic operations over GF(2m) have been extensively used in error correcting codes and public-key cryptography schemes. Finite field arithmetic includes addition, multiplication, division and inversion operations. Addition is very simple and can be implemented with an extremely simple circuit. The other operations are much more complex. The multiplication is the most important for cryptosystems, such as the elliptic curve cryptosystem, since computing exponentiation, division, and computing multiplicative inverse can be performed by computing multiplication iteratively. In this paper, we present a parallel computation algorithm that operates Montgomery multiplication over finite field using redundant basis. Also, based on the multiplication algorithm, we present an efficient semi-systolic multiplier over finite field. The multiplier has less space and time complexities compared to related multipliers. As compared to the corresponding existing structures, the multiplier saves at least 5% area, 50% time, and 53% area-time (AT) complexity. Accordingly, it is well suited for VLSI implementation and can be easily applied as a basic component for computing complex operations over finite field, such as inversion and division operation.

Keywords: finite field, Montgomery multiplication, systolic array, cryptography

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Authors: Raphael Zanella

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This works deals with the finite element approximation of axisymmetric problems. The weak formulation of the heat equation under the axisymmetry assumption is established for continuous finite elements. The weak formulation is implemented in a C++ solver with implicit march-in-time. The code is verified by space and time convergence tests using a manufactured solution. The solving of an example problem with an axisymmetric formulation is compared to that with a full-3D formulation. Both formulations lead to the same result, but the code based on the axisymmetric formulation is much faster due to the lower number of degrees of freedom. This confirms the correctness of our approach and the interest in using an axisymmetric formulation when it is possible.

Keywords: axisymmetric problem, continuous finite elements, heat equation, weak formulation

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Authors: Ayan Chakraborty, BV. Rathish Kumar

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Off-late many models in viscoelasticity, signal processing or anomalous diffusion equations are formulated in fractional calculus. Tempered fractional calculus is the generalization of fractional calculus and in the last few years several important partial differential equations occurring in the different field of science have been reconsidered in this term like diffusion wave equations, Schr$\ddot{o}$dinger equation and so on. In the present paper, a time-dependent tempered fractional diffusion equation of order $\gamma \in (0,1)$ with forcing function is considered. Existence, uniqueness, stability, and regularity of the solution has been proved. Crank-Nicolson discretization is used in the time direction. B spline finite element approximation is implemented. Generally, B-splines basis are useful for representing the geometry of a finite element model, interfacing a finite element analysis program. By utilizing this technique a priori space-time estimate in finite element analysis has been derived and we proved that the convergent order is $\mathcal{O}(h²+T²)$ where $h$ is the space step size and $T$ is the time. A couple of numerical examples have been presented to confirm the accuracy of theoretical results. Finally, we conclude that the studied method is useful for solving tempered fractional diffusion equations.

Keywords: B-spline finite element, error estimates, Gronwall's lemma, stability, tempered fractional

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Authors: Pyung Soo Kim, Eung Hyuk Lee, Mun Suck Jang

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In the current paper, a residual generation filter with finite memory structure is proposed for fault detection. The proposed finite memory residual generation filter provides the residual by real-time filtering of fault vector using only the most recent finite observations and inputs on the window. It is shown that the residual given by the proposed residual generation filter provides the exact fault for noise-free systems. Finally, to illustrate the capability of the proposed residual generation filter, numerical examples are performed for the discretized DC motor system having the multiple sensor faults.

Keywords: residual generation filter, finite memory structure, kalman filter, fast detection

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Authors: Alena Zemanová, Jan Zeman, Michal Šejnoha

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The polymer foil used for manufacturing of laminated glass members behaves in a viscoelastic manner with temperature dependence. This contribution aims at incorporating the time/temperature-dependent behavior of interlayer to our earlier elastic finite element model for laminated glass beams. The model is based on a refined beam theory: each layer behaves according to the finite-strain shear deformable formulation by Reissner and the adjacent layers are connected via the Lagrange multipliers ensuring the inter-layer compatibility of a laminated unit. The time/temperature-dependent behavior of the interlayer is accounted for by the generalized Maxwell model and by the time-temperature superposition principle due to the Williams, Landel, and Ferry. The resulting system is solved by the Newton method with consistent linearization and the viscoelastic response is determined incrementally by the exponential algorithm. By comparing the model predictions against available experimental data, we demonstrate that the proposed formulation is reliable and accurately reproduces the behavior of the laminated glass units.

Keywords: finite element method, finite-strain Reissner model, Lagrange multipliers, generalized Maxwell model, laminated glass, Newton method, Williams-Landel-Ferry equation

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Authors: Haowen Xi

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We propose and solve exactly a class of non-linear generalization of the Black-Scholes process of stochastic differential equations describing price bubble and crashes dynamics. As a result of nonlinear positive feedback, the faster-than-exponential price positive growth (bubble forming) and negative price growth (crash forming) are found to be the power-law finite-time singularity in which bubbles and crashes price formation ending at finite critical time tc. While most literature on the market bubble and crash process focuses on the nonlinear positive feedback mechanism aspect, very few studies concern the noise level on the same process. The present work adds to the market bubble and crashes literature by studying the external sources noise influence on the critical time tc of the bubble forming and crashes forming. Two main results will be discussed: (1) the analytical expression of expected value of the critical time is found and unexpected critical slowing down due to the coupling external noise is predicted; (2) numerical simulations of the nonlinear stochastic equation is presented, and the probability distribution of Prob(tc) is found to be the inverse gamma function.

Keywords: bubble, crash, finite-time-singular, numerical simulation, price dynamics, stochastic differential equations

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Authors: N. R. Mohamad, H. Ono, H. Haroon, A. Salleh, N. M. Z. Hashim

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In this research, we have studied and analyzed the modulation of light and liquid crystal in HPDLCs using Finite Domain Time Difference (FDTD) method. HPDLCs are modeled as a mixture of polymer and liquid crystals (LCs) that categorized as an anisotropic medium. FDTD method is directly solves Maxwell’s equation with less approximation, so this method can analyze more flexible and general approach for the arbitrary anisotropic media. As the results from FDTD simulation, the highest diffraction efficiency occurred at ±19 degrees (Bragg angle) using p polarization incident beam to Bragg grating, Q > 10 when the pitch is 1µm. Therefore, the liquid crystal is assumed to be aligned parallel to the grating constant vector during these parameters.

Keywords: birefringence, diffraction efficiency, finite domain time difference, nematic liquid crystals

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Authors: R. K. Apalowo, D. Chronopoulos

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A Finite Element (FE) based scheme is presented for quantifying guided wave interaction with Localised Nonlinear Structural Damage (LNSD) within structures of arbitrary layering and geometric complexity. The through-thickness mode-shape of the structure is obtained through a wave and finite element method. This is applied in a time domain FE simulation in order to generate time harmonic excitation for a specific wave mode. Interaction of the wave with LNSD within the system is computed through an element activation and deactivation iteration. The scheme is validated against experimental measurements and a WFE-FE methodology for calculating wave interaction with damage. Case studies for guided wave interaction with crack and delamination are presented to verify the robustness of the proposed method in classifying and identifying damage.

Keywords: layered structures, nonlinear ultrasound, wave interaction with nonlinear damage, wave finite element, finite element

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Authors: Jerzy Ejsmont, Beata Świeczko-Żurek, Grzegorz Ronowski

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Gas cylinders in general and particularly cylinders containing acetylene constitute a great potential danger for fire and rescue services involved in salvage operations. Experiments show that gas cylinders with acetylene, oxygen, hydrogen, CNG, LPG or CO2 may blow after short exposition to heat with very destructive effect as fragments of blown cylinder may fly even several hundred meters. In the case of acetylene, the explosion may occur also several hours after the cylinder is cooled down. One of the possible neutralization procedures that in many cases may be used to prevent explosions is shooting dangerous cylinders by rifle bullets. This technique is used to neutralize acetylene cylinders in a few European countries with great success. In Poland research project 'BLOW' was launched in 2014 with the aim to investigate phenomena related to fire influence on industrial and home used cylinders and to evaluate usefulness of the shooting technique. All together over 100 gas cylinders with different gases were experimentally tested at the military blasting grounds and in shelters. During the experiments cylinder temperature and pressure were recorded. In the case of acetylene that is subjected to thermal decomposition also concentration of hydrogen was monitored. Some of the cylinders were allowed to blow and others were shot by snipers. It was observed that shooting hot cylinders has never created more dangerous situations than letting the cylinders to explode spontaneously. In a great majority of cases cylinders that were punctured by bullets released gas in a more or less violent but relatively safe way. The paper presents detailed information about experiments and presents particularities of behavior of cylinders containing different gases. Extensive research was also done in order to select bullets that may be safely and efficiently used to puncture different cylinders. The paper shows also results of those experiments as well as gives practical information related to techniques that should be used during shooting.

Keywords: fire, gas cylinders, neutralization, shooting

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Authors: Xiaofei Hu, Zhiyu Cai, Weian Yao

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V-notch problem under dynamic loading condition is considered in this paper. In the time domain, the precise time domain expanding algorithm is employed, in which a self-adaptive technique is carried out to improve computing accuracy. By expanding variables in each time interval, the recursive finite element formulas are derived. In the space domain, a Symplectic Analytical Singular Element (SASE) for V-notch problem is constructed addressing the stress singularity of the notch tip. Combining with the conventional finite elements, the proposed SASE can be used to solve the dynamic stress intensity factors (DSIFs) in a simple way. Numerical results show that the proposed SASE for V-notch problem subjected to dynamic loading condition is effective and efficient.

Keywords: V-notch, dynamic stress intensity factor, finite element method, precise time domain expanding algorithm

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Authors: Pyung Soo Kim, Eung Hyuk Lee, Mun Suck Jang

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A packet loss probability (PLP) estimation filter with finite memory structure is proposed to estimate the packet rate mean and variance of the input traffic process in real-time while removing undesired system and measurement noises. The proposed PLP estimation filter is developed under a weighted least square criterion using only the finite traffic measurements on the most recent window. The proposed PLP estimation filter is shown to have several inherent properties such as unbiasedness, deadbeat, robustness. A guideline for choosing appropriate window length is described since it can affect significantly the estimation performance. Using computer simulations, the proposed PLP estimation filter is shown to be superior to the Kalman filter for the temporarily uncertain system. One possible explanation for this is that the proposed PLP estimation filter can have greater convergence time of a filtered estimate as the window length M decreases.

Keywords: packet loss probability estimation, finite memory filter, infinite memory filter, Kalman filter

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Authors: Tribhuvan N. Soorya

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Charging and discharging of a capacitor through a resistor can be shown as exponential curve. Theoretically, it takes infinite time to fully charge or discharge a capacitor. The flow of charge is due to electrons having finite and fixed value of charge. If we carefully examine the charging and discharging process after several time constants, the points on q vs t graph become discrete and curve become discontinuous. Moreover for all practical purposes capacitor with charge (q0-e) can be taken as fully charged, as it introduces an error less than one part per million. Similar is the case for discharge of a capacitor, where the capacitor with the last electron (charge e) can be taken as fully discharged. With this, we can estimate the finite value of time for fully charging and discharging a capacitor.

Keywords: charging, discharging, RC Circuit, capacitor

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Authors: Abhijeet Kumar, Palaniswamy N. K.

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Heavy metal contamination in water sources endangers both the environment and human health. Various water filtration techniques have been employed till now for purification and removal of hazardous metals from water. Among all the existing methods, nanofibres have emerged as a viable alternative for effective heavy metal removal in recent years because of their unique qualities, such as large surface area, interconnected porous structure, and customizable surface chemistry. Among the numerous manufacturing techniques, solution blow spinning has gained popularity as a versatile process for producing nanofibers with customized properties. This paper seeks to offer a complete overview of the use of nanofibers for heavy metal filtration, particularly those produced using solution blow spinning. The review discusses current advances in nanofiber materials, production processes, and heavy metal removal performance. Furthermore, the field's difficulties and future opportunities are examined in order to direct future research and development activities.

Keywords: heavy metals, nanofiber composite, filter membranes, adsorption, impaction

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Authors: S. A. Tabatabaei, S. Aarabi

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Predicting the hot mix asphalt (HMA) response and performance is a challenging task because of the subjectivity of HMA under the complex loading and environmental condition. The behavior of HMA is a function of temperature of loading and also shows the time and rate-dependent behavior directly affecting design criteria of mixture. Velocity of load passing make the time and rate. The viscoelasticity illustrates the reaction of HMA under loading and environmental conditions such as temperature and moisture effect. The behavior has direct effect on design criteria such as tensional strain and vertical deflection. In this paper, the computational framework for viscoelasticity and implementation in 3D dimensional HMA model is introduced to use in finite element method. The model was lied under various repeated loading conditions at constant temperature. The response of HMA viscoelastic behavior is investigated in loading condition under speed vehicle and sensitivity of behavior to the range of speed and compared to HMA which is supposed to have elastic behavior as in conventional design methods. The results show the importance of loading time pulse, unloading time and various speeds on design criteria. Also the importance of memory fading of material to storing the strain and stress due to repeated loading was shown. The model was simulated by ABAQUS finite element package

Keywords: viscoelasticity, finite element method, repeated loading, HMA

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Authors: Raoul Ouambo Tobou, Alexis Kuitche, Marcel Edoun

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The FWM (Finite Window Method) is a new numerical meshfree technique for solving problems defined either in terms of PDEs (Partial Differential Equation) or by a set of conservation/equilibrium laws. The principle behind the FWM is that in such problem each element of the concerned domain is interacting with its neighbors and will always try to adapt to keep in equilibrium with respect to those neighbors. This leads to a very simple and robust problem solving scheme, well suited for transfer problems. In this work, we have applied the FWM to an unsteady scalar convection-diffusion equation. Despite its simplicity, it is well known that convection-diffusion problems can be challenging to be solved numerically, especially when convection is highly dominant. This has led researchers to set the scalar convection-diffusion equation as a benchmark one used to analyze and derive the required conditions or artifacts needed to numerically solve problems where convection and diffusion occur simultaneously. We have shown here that the standard FWM can be used to solve convection-diffusion equations in a robust manner as no adjustments (Upwinding or Artificial Diffusion addition) were required to obtain good results even for high Peclet numbers and coarse space and time steps. A comparison was performed between the FWM scheme and both a first order implicit Finite Volume Scheme (Upwind scheme) and a third order implicit Finite Volume Scheme (QUICK Scheme). The results of the comparison was that for equal space and time grid spacing, the FWM yields a much better precision than the used Finite Volume schemes, all having similar computational cost and conditioning number.

Keywords: Finite Window Method, Convection-Diffusion, Numerical Technique, Convergence

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Authors: Khaled R. Khater

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The weight of the SPT hammer is standard (0.623kN). The locally manufacturer drilling rigs use hammers, sometimes deviating off the standard weight. This affects the field measured blow counts (Nf) consequentially, affecting most of correlations previously obtained, as they were obtained based on standard hammer weight. The literature presents energy corrections factor (η2) to be applied to the SPT total input energy. This research investigates the effect of the hammer weight variation, as a single parameter, on the field measured blow counts (Nf). The outcome is a correction factor (ηk), equation, and correction chart. They are recommended to adjust back the measured misleading (Nf) to the standard one as if the standard hammer is used. This correction is very important to be done in such cases where a non-standard hammer is being used because the bore logs in any geotechnical report should contain true and representative values (Nf), let alone the long records of correlations, already in hand. The study here-in is achieved by using laboratory physical model to simulate the SPT dripping hammer mechanism. It is designed to allow different hammer weights to be used. Also, it is manufactured to avoid and eliminate the energy loss sources. This produces a transmitted efficiency up to 100%.

Keywords: correction factors, hammer weight, physical model, standard penetration test

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Authors: Hassan J. Al Salman, Ahmed A. Al Ghafli

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In this study, we consider a nonlinear in time finite element approximation of a reaction diffusion system of lambda-omega type. We use a fixed-point theorem to prove existence of the approximations at each time level. Then, we derive some essential stability estimates and discuss the uniqueness of the approximations. In addition, we employ Nochetto mathematical framework to prove an optimal error bound in time for d= 1, 2 and 3 space dimensions. Finally, we present some numerical experiments to verify the obtained theoretical results.

Keywords: reaction diffusion system, finite element approximation, stability estimates, error bound

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