Engineering Mathematics

This paper discusses the numerical solutions of fourth order differential equation with initial value problem. The numerical methods consider to generate the sequence of improving approximate solution of the problems considered in both Adomian decomposition method (ADM) and Variational Iteration Method (VIM). The methods are applied on three differential examples of fourth order ordinary differential equation whose exact solutions are known. It is established that the VIM gives better solution as its series solution converges faster when compared to ADM.

Material flow simulation is in increasing need of multi-scale models. On the one hand, macroscopic flow models are used for large scale simulations with a large number of parts. On the other hand microscopic models are needed to describe the details of the production process. In this paper we present a hierarchy of models for material flow problems ranging from detailed microscopic, Discrete Element Method (DEM) type, models to macroscopic models using scalar conservation laws with nonlocal interaction terms. Numerical simulations are presented on all levels of the hierarchy and the results are compared to each other for several test cases.

Material flow simulation is in increasing need of multi-scale models. On the one hand, macroscopic flow models are used for large scale simulations with a large number of parts. On the other hand microscopic models are needed to describe the details of the production process. In this paper we present a hierarchy of models for material flow problems ranging from detailed microscopic, Discrete Element Method (DEM) type, models to macroscopic models using scalar conservation laws with nonlocal interaction terms. Numerical simulations are presented on all levels of the hierarchy and the results are compared to each other for several test cases.

Let C be a smooth simple curve contained in a complex region Ω . Let F be analytic in the region G \ Ω where G is a finite set. If no singularities are located on C, that is, if , ∅ = ∩ G C then the well-known residue formula from elementary complex variable courses,

A new model is proposed to characterize changes in traffic at transitions. These changes are affected by driver response. The distance headway between vehicles is considered as it affects driver behavior. Driver response is quick with a small distance headway and slow when the distance headway is large. The variations in traffic are greater with a slow driver while traffic is smooth with a quick driver. A model is developed which characterizes traffic based on driver response and distance headway. This model is compared with the well-known and widely employed Zhang and PW models. The Zhang model characterizes driver response at transitions using an equilibrium velocity distribution and ignores distance headway and driver response. Traffic flow in the PW model is characterized using only a velocity constant. Roe decomposition is employed to evaluate the Zhang, PW, and proposed models over a 270 m circular (ring) road. Results are presented which show that Zhang model provides unrealistic results. The corresponding behavior with the proposed model has large variations in flow with a slow driver but is smooth with a quick driver. The PW model provides smooth changes in flow according to the velocity constant, but the behavior is unrealistic because it is not based on traffic physics.

Cancer incidence and mortality are rapidly growing worldwide. The reasons are complex but reflect both aging and growth of the population, as well as changes in the prevalence and distribution of the main risk factors for cancer, several of which are associated with socioeconomic development. This study was analysed using Weibull distribution model on the survival of cancer patients. This study is inspired by Siegel R. L, et al (2017) .The main aim of this study was to analyse the survival of cancer patients using Weibull distribution model. The general objective of this study was to analyse the survival of cancer patients using Weibull parametric model. Analysis was performed using R and other mathematical modules were discussed. From the analysed data, age of diagnosis, Histologic grade, Cancer type, BMI, stages of infections and Gender were significant factors in the survival of Cancer patients. Family history and treatment administered did not show much significant effect. In fu...

An essential activity in curriculum design is to specify the topics of the curriculum and the courses where those topics will be taught. Disciplines, such as Computing present several challenges in this regard, since the topics that students must learn tend to be fine-grained and highly interconnected. First, one must ensure that the most important topics of the curriculum are taught in at least one course. Second, for every topic taught, their prerequisites must have been covered previously in the same course or in a previous one. Third, courses must include topics that are highly cohesive and with minimal dependencies to topics taught in previous courses. To address the above challenges, this paper proposes a graph-based approach to analyze and design a curriculum, which also includes some Backward Design elements. Learning goals (desired results), topics, and courses are modeled as nodes in a graph. Prerequisite dependencies are modeled as edges. The relation between courses and ...

В работе рассматривается шаровой нейтронный спектрометр активационного типа [1][2][3][4]. Проанализированы данные, полученные при создании шарового нейтронного спектрометра Боннера активационного типа, состоящего из 5 полиэтиленовых шаров, содержащих цилиндрическую таблетку. В качестве активируемого материала использовался индий. Проведены измерения, в которых пучок электронов с энергией Е=12 МэВ преобразовывался в 100-микронном танталовом (е,γ)-конверторе в γ-излучение, которое попадало на свинцовый (γ,n)-конвертор. Нейтроны из конвертора падали на шары спектрометра, в каждом из них отеплялась неодинаковая их часть, и поэтому активация индиевых таблеток была разной. После облучения на ускорителе из шаров извлекались индиевые таблетки и помещались в γ-спектрометр, где определялась степень активации каждой таблетки. Таким образом, результатом измерений были 5 чисел, характеризующих активацию таблеток из 5 шаров. Предполагая некоторую функцию F(E,a j ), которая может описать спектр нейтронов и зависит от нескольких параметров a j , и, располагая функцией отклика i-ого шара φ i (E), активация может быть представлена как свёртка функций F(E,a j ) и φ i (E). Предложена модель математической обработки данных измерений наведенной в индии радиоактивности. Построена рекуррентная модель, основанная на минимизации функционала качества и нелинейных регрессионных уравнениях. С помощью стохастического рекуррентного алгоритма решена задача восстановления спектра нейтронов. Для использованной четырехпараметрической модели спектра типа распределения Максвелла получены оценки его параметров, а также оценки погрешностей оценок параметров. Таким образом, задача оценки характеристик нейтронного потока сведена к задаче оценки параметров энергетического спектра выбранного типа. Полученный в работе опыт может быть использован для оптимизации конструкции нейтронного спектрометра. Практика минимизации функций с помощью программ, базирующихся на принципе градиентного спуска, показывает их нередкое зависание или авосты, возникающие при произвольном выборе начальных значений варьируемых параметров. Как видно из полученных результатов, стохастический метод лишен этого недостатка. Это явилось преимуществом для практики применения этого метода.

Two, the most simple cases of special-relativistic flows of a viscous, incompressible fluid are considered: plane Couette flow and plane Poiseuille flow. Considering only the regular motion of the fluid we found the distribution of velocity in the fluid (velocity profiles) and the friction force, acting on immovable wall. The results are expressed through simple analytical functions for the Couette flow, while for the Poiseiulle flow they are expressed by higher transcendental functions (Jacobi's elliptic functions).

After a brief introduction to the theory and physical interpretation of Lagrangian force density in general sound fields, this article focuses on its stationary average property providing the general expression of the actionreaction law for acoustic fields. This fundamental property allows to define the tension field of sound, which turns out to be easily measured as the gradient of the average potential energy density. The acoustic tension field has been then analytically calculated and visualized for quasi-stationary wave fields and divergent spherical waves. Moreover 2-D graphics comparing the behaviors of sound energy trajectories and tension fields are here reported.

We consider the modified Emden equation (MEE) and introduce its most general solution, using the most general solution for the simple harmonic oscillator's linear dynamical equation (i.e., the initial conditions shall be identified by the PDM-MEE problem at hand) . We use a general nonlocal point transformation and show that modified Emden dynamical equation is transformed to describe position-dependent mass (PDM) classical particles. Two PDM-MEE-type classical particles are used as illustrative examples, and their exact solutions are reported. Under specific parametric considerations, the phase-space trajectories are reported for the MEE-type and for PDM-MEE-type classical particles.

A steady two-dimensional free-surface flow in a channel of finite depth is considered. The channel ends abruptly with a barrier in the form of a vertical wall of finite height. Hence the stream, which is uniform far upstream, is forced to go upward and then falls under the effect of gravity. A configuration is examined where the rising stream splits into two jets, one falling backward and the other forward over the wall, in a fountain-like manner. The backward-going jet is assumed to be removed without disturbing the incident stream. This problem is solved numerically by an integral-equation method. Solutions are obtained for various values of a parameter measuring the fraction of the total incoming flux that goes into the forward jet. The limit where this fraction is one is also examined, the water then all passing over the wall, with a 120° corner stagnation point on the upper free surface.

In this paper, we investigate the existence and uniqueness of solutions for the Darboux problem of partial differential equations with Caputo-Katugampola fractional derivative. En este artículo investigamos la existencia y unicidad de soluciones para el problema de Darboux de ecuaciones diferenciales parciales con derivada fraccional de Caputo-Katugampola.

A system of linear equations, in general is solved in open literature for crisp unknowns, but in actual case the parameters (coefficients) of the system of linear equations contain uncertainty and are less crisp. The uncertainties may be considered in term of interval or fuzzy number. In this paper, a detail of study of linear simultaneous equations with interval and fuzzy parameter (triangular and trapezoidal) has been performed. New methods have been proposed for solving such systems. First, the methods have been tested for known problems viz. a circuit analysis solved in the literature and the results are found to be in good agreement with the present. Next more example problems are solved using the proposed methods to strengthen confidence on these new methods. The solutions of the example problems clearly show the efficacy and reliability of the proposed method(s).

He is an advocate of the active learning and teaching philosophy per ABET EC2000. Jenkins is a registered professional engineer in Washington and is actively involved through leadership roles in national/international committees such as ASTM, ASME and ISO. He is also an experienced ABET Program Evaluator (PEV) for general engineering and mechanical engineering. Jenkins received his B.S.M.E. from Marquette University, his M.S.M.E. from Purdue University, and his Ph.D. from the University of Washington. He worked at PACCAR Technical Center as an R&D engineer and at Oak Ridge National Laboratory as a development staff member. He was also faculty and associate chair at University of Washington, Seattle, and professor and chair at University of Detroit Mercy before starting his position as faculty and dean at CSU, Fresno. His research and teaching interests include characterization of advanced materials (e.g., ceramics), experimental mechanics, data base development, cumulative damage mechanics, and probabilistic design and reliability.

This contribution presents a numerical descent method for the identification of parameters in the flux function of a scalar nonlinear conservation law when the solution at a fixed time is known. This problem occurs in a model of batch sedimentation of an ideal suspension. We formulate the identification problem as a minimization problem of a suitable cost function and derive its formal gradient by means of a first-order perturbation of the solution of the direct problem, which yields a linear transport equation with source term and discontinuous coefficients. for the numerical approach, we assume that the direct problem is discretized by the Engquist-Osher scheme and obtain a discrete first order perturbation associated to this scheme. The discrete gradient is used in combination with the conjugate gradient and coordinate descent methods to find numerically the flux parameters.

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Arterial pressure and flow result from the interaction between the (actively) ejecting ventricle and the (passive) arterial circulation. The main objective was to construct a model, accounting for this interaction, that is simple enough so that (i) model parameters can be derived from data measured in experimental and/or clinical conditions, and (ii) the model can be applied to support the analysis and interpretation of these data. It is demonstrated how an established conceptual model of ventricular function (the time-varying elastance) can be coupled to a four-element windkessel model of the arterial system to yield an elegant model of heart-arterial interaction. The coupling leads to a set of three ordinary differential equations. The model allows the study of the effect of changes in cardiac and/or arterial properties on arterial pressure and flow. As an illustration, cardiac and arterial model parameters are derived from measured experimental data in the systemic circulation of a pig and in the pulmonary circulation of a dog. It is evaluated how well measured cardiac and arterial function actually adhere to their assumed theoretical models (time-varying elastance and four-element windkessel model). It is further assessed how well the simple model of heart-arterial interaction describes systemic and pulmonary hemodynamics by comparing simulated and measured experimental data. The limitations and pitfalls of the model, as well as possible applications in the clinical field, are discussed.

Luo showed that the Fibonacci number U n is triangular if and only if n = ±1, 2, 4, 8, or 10. Over the course of his demonstration, he established a Jacobi symbol criterion. Moreover, he observed that this problem is equivalent to finding all integer points on two elliptic curves. In this paper, we shall prove a Jacobi symbol criterion for more general families of binary recurrences. In addition, applying the criterion and elementary methods, we shall determine all integer points on the elliptic curves y 2 = 5x 2 (x + 3) 2 + 4(-1) n .

We study the steady laminar advective transport of a diffusive passive scalar released at the base of narrow three-dimensional longitudinal open channels with nonabsorbing side walls and rectangular or truncated-wedge-shaped cross-sections. The scalar field in the advective-diffusive boundary layer at the base of the channels is fundamentally three-dimensional in the general case, owing to a three-dimensional velocity field and differing boundary conditions at the side walls. We utilise threedimensional numerical simulations and asymptotic analysis to understand how this inherent three-dimensionality influences the advective-diffusive transport as described by the normalised average flux, the Sherwood Sh or Nusselt numbers for mass or heat transfer, respectively. We show that Sh is well approximated by an appropriately formulated two-dimensional calculation, even when the boundary layer structure is itself far from two-dimensional. This is a key and novel results which can significantly simplify the modelling of many laminar advection-diffusion scalar transfer problems. The different transport regimes found depend on the channel geometry and a characteristic Péclet number Pe based on the ratio of the cross-channel diffusion time and the longitudinal advection time. We develop asymptotic expressions for Sh in the various limiting regimes, which mainly depend on the confinement of the boundary layer in the lateral and base-normal directions. For Pe 1 we recover the classical Lévêque solution with a cross-channel-averaged shear rate γ 1/3 , Sh ∝ γ 1/3 Pe 1/3 , for both geometries despite strongly curved boundary layers; for parallel walls a secondary regime with Sh ∝ Pe 1/2 is found for Pe 1. In the case of truncated wedge channels, further regimes are identified owing to curvature effects, which we capture through a curvature-rescaled Péclet number Pe β = β 2 Pe, with β the opening angle of the wedge. For Pe 1/2 β 1, the Sherwood number appears to follow Sh ∼ β 3/4 Pe 1/16 β . In all cases, we offer a comparison between our three-dimensional simulations, the asymptotic results and our two-dimensional simplifications, and can thus quantify the error in the flux from the simplified calculations. Our findings are relevant to heat and mass transfer applications in confined U-shaped or V-shaped channels such as for the decontamination and cleaning of narrow gaps or transport processes in chemical or biological microfluidic devices.

The failure pattern in slate tested under diametral compression is strongly influenced by the contact angle created in the loaded area. A small angle is created throughout the contact between the jaws (or platens) and the disc by adopting flat platens (ASTM standard) or curved jaws (suggested method by ISRM) load configurations, inducing failures due to shear stresses in the limit of the load rim. This causes failure patterns that do not exactly match the central diameter when the material is tested with the load direction parallel and perpendicular to foliation, which contradicts the failure by pure tensile typically assumed in the test for these orientations. In the present work, a new interpretation of the failure pattern in slate samples tested with the Brazilian method is established, playing the contact angle a significant role. Brazilian tests with the loading direction along and across foliation were carried out in the laboratory, by using the load configurations of ASTM standard and the ISRM recommendation. Furthermore, an analytical study allowed the estimation of the point in the whole of the disc in which a critical stress state is firstly reached by taking into account both the foliation and the intact rock failure criteria, hence justifying the experimental failure patterns. Finally, regarding the initial failure the influence of the strength properties in order to satisfy the classic hypothesis of the Brazilian test in rocks with multiple weak planes was analysed. An appropriate interpretation of the failure pattern can be an important indicator in order to reveal the true failure mechanism of rocks; this may help to improve the characterization and prediction of the initial failure of this material, which is widely used as an industrial rock or in dam foundations, underground excavations and slope engineering.

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Materials with characteristic structures at nanoscale sizes exhibit significantly different mechanical responses from those predicted by conventional, macroscopic continuum theory. For example, nanocrystalline metals display an inverse Hall-Petch effect whereby the strength of the material decreases with decreasing grain size. The origin of this effect is believed to be a change in deformation mechanisms from dislocation motion across grains and pileup at grain boundaries at microscopic grain sizes to rotation of grains and deformation within grain boundary interface regions for nanostructured materials. These rotational defects are represented by the mathematical concept of disclinations. The ability to capture these effects within continuum theory, thereby connecting nanoscale materials phenomena and macroscale behavior, has eluded the research community. The goal of our project was to develop a consistent theory to model both the evolution of disclinations and their kinetics. Additionally, we sought to develop approaches to extract continuum mechanical information from nanoscale structure to verify any developed continuum theory that includes dislocation and disclination behavior. These approaches yield engineering-scale expressions to quantify elastic and inelastic deformation in all varieties of materials, even those that possess highly directional bonding within their molecular structures such as liquid crystals, covalent ceramics, polymers and biological materials. This level of accuracy is critical for engineering design and thermo-mechanical analysis is performed in micro-and nanosystems. The research proposed here innovates on how these nanoscale deformation mechanisms should be incorporated into a continuum mechanical formulation, and provides the foundation upon which to develop a means for predicting the performance of advanced engineering materials.

For the iterative solution of the Schur complement system associated with the discretization of an elliptic problem by means of a triangular spectral element method (TSEM), Neumann-Neumann (NN) type preconditioners are constructed and studied. The TSEM approximation, based on Fekete nodes, is a generalization to non-tensorial elements of the classical Gauss-Lobatto-Legendre quadrilateral spectral elements. Numerical experiments show that the TSEM Schur complement condition number grows linearly with the polynomial approximation degree, N, and quadratically with the inverse of the mesh size, h. NN preconditioners for the Schur complement allow to reduce the N-dependence of the condition number, by solving local Neumann problems on each spectral element, and to eliminate the h-dependence if an additional coarse solver is employed. Numerical results indicate that, in spite of the more severe ill-conditioning, the condition number of the TSEM preconditioned operator satisfies the same bound as that of the standard SEM, i.e., Ch -2 (1 + log N) 2 for one-level NN preconditioning and C(1 + log N) 2 for two-level Balancing Neumann-Neumann (BNN) preconditioning.

Описано структуру спеціалізованого програмного комплексу моделювання на основі ітераційних алгоритмів методу групового урахування аргументів (МГУА) з можливістю мультидоступу через Інтернет або локальну мережу. В програмному комплексі процес моделювання реалізовано у трьох режимах діалогу – два автоматичних (стандартний та плановий) та один інтерактивний, коли можна втручатися в процес самоорганізації моделей. Програмне забезпечення працює з різними наборами даних у форматі Excel та текстовому редакторі Блокнот. Будуються моделі різної складності та структури з різним розбиттям вибірки. Найкращі моделі представляються системою для графічного і змістового аналізу та зберігаються в базі даних разом із проміжними розрахунками і результатами експериментів для подальшого застосування. Система одночасно працює з трьома базами даних: початковою, базою даних проміжних розрахунків та базою даних результатів.The structure of specialized modeling software based on iterative algorithms of the g...

Cooker's sloshing experiment is a prototype for studying the dynamic coupling between fluid sloshing and vessel motion. It involves a container, partially filled with fluid, suspended by two cables and constrained to remain horizontal while undergoing a pendulum-like motion. In this paper the fully-nonlinear equations are taken as a starting point, including a new derivation of the coupled equation for vessel motion, which is a forced nonlinear pendulum equation. The equations are then linearized and the natural frequencies studied. The coupling leads to a highly nonlinear transcendental characteristic equation for the frequencies. Two derivations of the characteristic equation are given, one based on a cosine expansion and the other based on a class of vertical eigenfunctions. These two characteristic equations are compared with previous results in the literature. Although the two derivations lead to dramatically different forms for the characteristic equation, we prove that they are equivalent. The most important observation is the discovery of an internal 1 : 1 resonance in the fully two-dimensional finite depth model, where symmetric fluid modes are coupled to the vessel motion. Numerical evaluation of the resonant and nonresonant modes are presented. The implications of the resonance for the fluid dynamics, and for the nonlinear coupled dynamics near the resonance are also briefly discussed.

A novel method is presented to calculate the deformation of a simple elastic aerofoil with a view to determining its aerodynamic viability. The aerofoil is modelled as a thin two-dimensional elastic sheet whose ends are joined together to form a corner of prescribed angle, with a simple support included to constrain the shape to resemble that of a classical aerofoil. The weight of the aerofoil is counterbalanced exactly by the lift force due to a circulation set according to the Kutta condition. An iterative process based on a boundary integral method is used to compute the deformation of the aerofoil in response to an inviscid fluid flow, and a range of flow speeds is determined for which the aerofoil maintains an aerodynamic shape. As the flow speed is increased the aerofoil deforms significantly around its trailing edge, resulting in a negative camber and a loss of lift. The loss of lift is ameliorated by increasing the inflation pressure but at the expense of an increase in drag...

The characteristics of flow and heat transfer of a fluid in a channel with oscillatory stretching walls in the presence of an externally applied magnetic field are investigated. The fluid considered is a second-grade viscoelastic electrically conducting fluid. The partial differential equations that govern the flow are solved by developing a suitable numerical technique. The computational results for the velocity, temperature and the wall shear stress are presented graphically. The study reveals that flow reversal takes place near the central line of the channel. This flow reversal can be reduced to a considerable extent by applying a strong external magnetic field. The results are found to be in good agreement with those of earlier investigations.

• The surface gravity wave interaction with a floating flexible circular porous membrane in a two-layer fluid is studied using the linearized theory of water waves. • The boundary value problem is solved using the matched eigenfunction expansion method, and Darcy's law is used for wave past porous structure. • The vertical wave force acting on the membrane, surface and interface elevations, deflection of the membrane and flow distribution around the structure in a two-layer fluid are computed and analyzed for various structural and wave parameters. • The study reveals that the density ratio, porous-effect parameter, radius of the membrane and depth ratio are the major parameters for reducing wave force on the structure and creating calm region in the lee side of the structure. Thus, a floating circular flexible porous membrane can be used as a cost-effective coastal structure to protect marine facilities.

For the study of transients in gas-liquid flows, the equations of the so-called separated flow model are inadequate, because they possess, in the general case where gas and liquid move at different velocities, complex characteristics. This paper is concerned with the equations of motion for bubbly flow. The equations are discussed with emphasis on the aspects of relative motion and the characteristics are calculated. It is found that all characteristics are real. The results are used to establish a relation between gas velocity, liquid velocity, void fraction and sound velocity at critical flow. This relation agrees very well with experimental data for these quantities as measured by Muir and Eichhorn in the throat of a converging-diverging nozzle.

For the study of transients in gas-liquid flows, the equations of the so-called separated flow model are inadequate, because they possess, in the general case where gas and liquid move at different velocities, complex characteristics. This paper is concerned with the equations of motion for bubbly flow. The equations are discussed with emphasis on the aspects of relative motion and the characteristics are calculated. It is found that all characteristics are real. The results are used to establish a relation between gas velocity, liquid velocity, void fraction and sound velocity at critical flow. This relation agrees very well with experimental data for these quantities as measured by Muir and Eichhorn in the throat of a converging-diverging nozzle.

The evaluation and assessment of the design of large wireless networks is an important problem in numerous applications. Direct simulation is a traditional approach for studying such networks but is severely limited in its utility as the size of the network increases. This necessitates other means for studying large networks, one of which is the modeling of large networks with continuum models. In this paper, we introduce nonlinear partial differential equations whose solutions approximate the expected behavior of large networks governed by probabilistic communication rules. The relative speed at which solutions can be obtained from the continuum models allows for the investigation of routing protocols and communication limitations due to interference-a feat that is not feasible via simulation methods. Specifically, we investigate the effects of a directed diffusion routing protocol and explore communication limitations in an interference-sensitive network. Network design studies using the approximating continuum models are then presented.

This research presents a new mathematical framework for the optimal design of elliptical isolated footings under vertical load and two orthogonal moments. The suggested method considers the spatial variation of contact pressure between the footing and the supporting soil, facilitating an accurate representation of structural requirements. New formulations for bending moment, unidirectional shear, and punching shear are generated using volume integration, accurately representing the complex stress distribution beneath elliptical foundations. Lagrange multipliers are utilized to identify the crucial points of maximum and minimum contact stresses for elliptical and circular footing shapes. A thorough numerical analysis illustrates the benefits of the suggested strategy by contrasting its results with those of a conventional design methodology. The findings demonstrate that the newly created model produces more cost-effective designs while maintaining structural integrity and performance, underscoring its potential as a significant asset in engineering practice. A MATLAB code for design using new formulas is programmed and results obtained compared to those from literature and were more efficient and economic.

The control of a mobile robot using a linear model with uncertainty for design purposes is investigated. The uncertainty arises from the variation of the operation point of the mobile robot. Robust Control Theory is used for the controller design, which allows dealing with systems whose parameters may vary between certain bounds. The proposed controller has shown, in experimentation tests, an acceptable performance and an easy and simple practical implementation. Also, an application of the proposed controller to a leader-following problem is shown; in it, the relative position between robots is obtained through a laser.

In this article, we extend the Laplace transform method to obtain analytic solutions for linear RDDEs and NDDEs which have real and complex poles of higher order. Furthermore, we present first-order linear DDEs that feature resonance phenomena. The procedure is similar to the one where all of the poles are order one, but requires one to use the appropriate modifications when using Cauchy’s residue theorem for the poles of higher order. The process for obtaining the solution relies on computing the relevant infinite sequence of poles and then determining the Laplace inverse, via the Cauchy residue theorem. For RDDEs, the poles can be obtained in terms of the Lambert W function, but for NDDEs,the complex poles, in most cases, must be computed numerically. We found that an important feature of first-order linear RDDES and NDDES with poles of higher order is that it is possible to incite the resonance phenomena, which in the counterpart ordinary differential equation cannot occur. We sh...

A model is presented for polish-rate decay in chemical-mechanical polishing based on the Greenwood-Williamson theory of contact between a smooth surface (a wafer) and a rough surface (the polishing pad). The model assumes that polishing causes pad asperities to wear, with high asperities wearing faster than low asperities. Model predictions of the time dependence of polish-rate decay compare favorably with experiments.

Statistical models are presented to describe the evolution of the surface roughness of polishing pads during the pad-conditioning process in chemical-mechanical polishing. The models describe the evolution of the surface-height probability-density function of solid pads during fixed height or fixed cut-rate conditioning. An integral equation is derived for the effect of conditioning on a foamed pad in terms of a model for a solid pad. The models that combine wear and conditioning are then discussed for both solid and foamed pads. Models include the dependence of the surface roughness on the shape and density of the cutting tips used in the conditioner and on other operating parameters. Good agreement is found between the model, Monte Carlo simulations and with experimental data.

1 Department of Mechanical, Aerospace and Nuclear Engineering, 2 Center for Multiphase Research, Rensselaer Polytechnic Institute, Troy, NY 12180, USA (*) Tel: 518-276-4000, Fax: 518-276-3055 Email: podowm@ rpi. edu Key words: Membrane filtration; Dean ...

In this paper, a mathematical model is proposed with three classes of population namely, susceptible, incubated and infected. The incubation period is defined as the time from exposure to onset of viral disease, and when limited to infectious viral disease, corresponds to the time from infection with a microorganism to symptom development. Immunity(natural or caused by vaccination) plays an important role in recovery of a disease, due to strong immunity a portion of incubated class rejoins susceptible class without being infected. The stability behavior of the trivial, disease free and endemic steady states are studied, it is found that the instability of disease free state leads to the existence of the endemic state. The possibility of Hopf-bifurcation of the endemic equilibrium is studied, considering the transfer rate from susceptible to incubated population as bifurcation parameter. Finally, a threshold value of bifurcation parameter is determined numerically for a particular se...

TO DETERMINE cardiac performance, a comparison between the whole heart and isolated (skeletal) muscle often has been made. Otto Frank (1895) designed his beautiful experiments on the frog heart following "the same pattern which Fick and Von Kries used in their studies of skeletal muscle...." A similar comparison between heart and muscle can be found in Starling's formulation of, his "law of the heart" (Patterson et al., 1914): "The law of the heart is therefore the same as that of skeletal muscle that the mechanical energy set free on passage from the resting to the contracted state depends ... on the length of the muscle fibers." Presently, the same line of thinking prevails, since variables derived from studies on isolated muscle are determined for the whole heart to establish its performance . The task of the heart is to transport arterial blood to the various organs and venous blood to the lungs. It does this by ejecting a sufficient amount of blood at a given pressure against the resistance of the arterial system. Although this pump function of the heart has been fully recognized since Harvey wrote his "de motu cordis" (1628), it is still not clear how to quantify it. Cardiac output, stroke volume, left ventricular function curves, peak systolic pressure, stroke work, peak wall stress, rate of rise of left ventricular pressure, maximum velocity of shortening, and many other variables all have been put forward as a measure of the function or per-

The purpose of this study is the derivation of a closed-form formula for Green's function in elliptic coordinates that could be used for achieving an analytic solution for the second-order diffraction problem by elliptical cylinders subjected to monochromatic incident waves. In fact, Green's function represents the solution of the so-called locked wave component of the second-order velocity potential. The mathematical analysis starts with a proper analytic formulation of the second-order diffraction potential that results in the inhomogeneous Helmholtz equation. The associated boundary-value problem is treated by applying Green's theorem to obtain a closed-form solution for Green's function. Green's function is initially expressed in polar coordinates while its final elliptic form is produced through the proper employment of addition theorems.

We analyze the hydrodynamics of a rotating disk in a two-dimensional compressible fluid layer with odd viscosity. Unlike conventional fluids, odd viscosity introduces a radial flow component that can be directed either inward or outward, depending on its sign. This phenomenon is expected to significantly impact the hydrodynamic interactions between two rotating disks, potentially causing effective attraction or repulsion depending on the sign of the odd viscosity and the direction of rotation. Furthermore, we calculate the rotational resistance coefficient and find that odd viscosity increases this coefficient, regardless of its sign.

Sedimentation and suspension flows play an important role in modern technology. This special issue joins nine recent contributions to the mathematics of these processes. The Guest Editors provide a concise account of the contributions to research in sedimentation and thickening that were made during the 20th century with a focus on the different steps of progress that were made in

In one space dimension, the phenomenological sedimentation-consolidation model reduces to an initial-boundary value problem (IBVP) for a nonlinear strongly degenerate convection-diffusion equation with a non-convex, time-dependent flux function. The frequent assumption that the effective stress of the sediment layer is a function of the local solids concentration only which vanishes below a critical concentration value causes the model to be