Abstract: This study offers a comprehensive review of the
research papers published in the field of cooling towers and gives an
insight into the latest developments of the natural draught cooling
towers. Different modeling, analysis and design techniques are
summarized and the challenges are discussed. The 118 references
included in this paper are mostly concentrated on the review of the
published papers after 2005. The present paper represents a complete
collection of the studies done for cooling towers and would give an
updated material for the researchers and design engineers in the field
of hyperbolic cooling towers.
Abstract: In this paper analysis of an infinite beam resting on tensionless extensible geosynthetic reinforced granular bed overlying soft soil strata under moving load with constant velocity is presented. The beam is subjected to a concentrated load moving with constant velocity. The upper reinforced granular bed is modeled by a rough elastic membrane embedded in Pasternak shear layer overlying a series of compressible nonlinear Winkler springs representing the under-lied very poor soil. The tensionless extensible geosynthetic layer has been assumed to deform such that at interface the geosynthetic and the soil have some deformation. Nonlinear behavior of granular fill and the very poor soil has been considered in the analysis by means of hyperbolic constitutive relationships. Detailed parametric study has been conducted to study the influence of various parameters on the response of soil foundation system under consideration by means of deflection and bending moment in the beam and tension mobilized in the geosynthetic layer. This study clearly observed that the comparisons of tension and tensionless foundation and magnitude of applied load, relative compressibility of granular fill and ultimate resistance of poor soil has significant influence on the response of soil foundation system.
Abstract: In this article, we propose a new approximate procedure
based on He’s variational iteration method for solving nonlinear
hyperbolic equations. We introduce two transformations q = ut and
σ = ux and formulate a first-order system of equations. We can
obtain the approximation solution for the scalar unknown u, time
derivative q = ut and space derivative σ = ux, simultaneously.
Finally, some examples are provided to illustrate the effectiveness of
our method.
Abstract: Utilizing echoic intension and distribution from different organs and local details of human body, ultrasonic image can catch important medical pathological changes, which unfortunately may be affected by ultrasonic speckle noise. A feature preserving ultrasonic image denoising and edge enhancement scheme is put forth, which includes two terms: anisotropic diffusion and edge enhancement, controlled by the optimum smoothing time. In this scheme, the anisotropic diffusion is governed by the local coordinate transformation and the first and the second order normal derivatives of the image, while the edge enhancement is done by the hyperbolic tangent function. Experiments on real ultrasonic images indicate effective preservation of edges, local details and ultrasonic echoic bright strips on denoising by our scheme.
Abstract: This paper deals with a high-order accurate Runge
Kutta Discontinuous Galerkin (RKDG) method for the numerical
solution of the wave equation, which is one of the simple case of a
linear hyperbolic partial differential equation. Nodal DG method is
used for a finite element space discretization in 'x' by discontinuous
approximations. This method combines mainly two key ideas which
are based on the finite volume and finite element methods. The
physics of wave propagation being accounted for by means of
Riemann problems and accuracy is obtained by means of high-order
polynomial approximations within the elements. High order accurate
Low Storage Explicit Runge Kutta (LSERK) method is used for
temporal discretization in 't' that allows the method to be nonlinearly
stable regardless of its accuracy. The resulting RKDG
methods are stable and high-order accurate. The L1 ,L2 and L∞ error
norm analysis shows that the scheme is highly accurate and effective.
Hence, the method is well suited to achieve high order accurate
solution for the scalar wave equation and other hyperbolic equations.
Abstract: In this paper, we study on finite projective Hjelmslev planes M(Zq) coordinatized by Hjelmslev ring Zq (where prime power q = pk). We obtain finite hyperbolic Klingenberg planes from these planes under certain conditions. Also, we give a combinatorical result on M(Zq), related by deleting a line from lines in same neighbour.
Abstract: This paper presents a new function expansion method for finding traveling wave solution of a non-linear equation and calls it the (G'/G)-expansion method. The shallow water wave equation is reduced to a non linear ordinary differential equation by using a simple transformation. As a result the traveling wave solutions of shallow water wave equation are expressed in three forms: hyperbolic solutions, trigonometric solutions and rational solutions.
Abstract: In this paper, we study a new modified Novikov equation for its classical and nonclassical symmetries and use the symmetries to reduce it to a nonlinear ordinary differential equation (ODE). With the aid of solutions of the nonlinear ODE by using the modified (G/G)-expansion method proposed recently, multiple exact traveling wave solutions are obtained and the traveling wave solutions are expressed by the hyperbolic functions, trigonometric functions and rational functions.
Abstract: In this paper, the melting of a semi-infinite body as a
result of a moving laser beam has been studied. Because the Fourier
heat transfer equation at short times and large dimensions does not
have sufficient accuracy; a non-Fourier form of heat transfer
equation has been used. Due to the fact that the beam is moving in x
direction, the temperature distribution and the melting pool shape are
not asymmetric. As a result, the problem is a transient threedimensional
problem. Therefore, thermophysical properties such as
heat conductivity coefficient, density and heat capacity are functions
of temperature and material states. The enthalpy technique, used for
the solution of phase change problems, has been used in an explicit
finite volume form for the hyperbolic heat transfer equation. This
technique has been used to calculate the transient temperature
distribution in the semi-infinite body and the growth rate of the melt
pool. In order to validate the numerical results, comparisons were
made with experimental data. Finally, the results of this paper were
compared with similar problem that has used the Fourier theory. The
comparison shows the influence of infinite speed of heat propagation
in Fourier theory on the temperature distribution and the melt pool
size.
Abstract: A Picard-Newton iteration method is studied to accelerate the numerical solution procedure of a class of two-dimensional nonlinear coupled parabolic-hyperbolic system. The Picard-Newton iteration is designed by adding higher-order terms of small quantity to an existing Picard iteration. The discrete functional analysis and inductive hypothesis reasoning techniques are used to overcome difficulties coming from nonlinearity and coupling, and theoretical analysis is made for the convergence and approximation properties of the iteration scheme. The Picard-Newton iteration has a quadratic convergent ratio, and its solution has second order spatial approximation and first order temporal approximation to the exact solution of the original problem. Numerical tests verify the results of the theoretical analysis, and show the Picard-Newton iteration is more efficient than the Picard iteration.
Abstract: In this work, a radial basis function (RBF) neural network is developed for the identification of hyperbolic distributed parameter systems (DPSs). This empirical model is based only on process input-output data and used for the estimation of the controlled variables at specific locations, without the need of online solution of partial differential equations (PDEs). The nonlinear model that is obtained is suitably transformed to a nonlinear state space formulation that also takes into account the model mismatch. A stable robust control law is implemented for the attenuation of external disturbances. The proposed identification and control methodology is applied on a long duct, a common component of thermal systems, for a flow based control of temperature distribution. The closed loop performance is significantly improved in comparison to existing control methodologies.
Abstract: In this paper, a nonconforming mixed finite element method is studied for semilinear pseudo-hyperbolic partial integrodifferential equations. By use of the interpolation technique instead of the generalized elliptic projection, the optimal error estimates of the corresponding unknown function are given.
Abstract: A new numerical scheme based on the H1-Galerkin mixed finite element method for a class of second-order pseudohyperbolic equations is constructed. The proposed procedures can be split into three independent differential sub-schemes and does not need to solve a coupled system of equations. Optimal error estimates are derived for both semidiscrete and fully discrete schemes for problems in one space dimension. And the proposed method dose not requires the LBB consistency condition. Finally, some numerical results are provided to illustrate the efficacy of our method.
Abstract: In this paper we present, propose and examine
additional membership functions for the Smoothing Transition
Autoregressive (STAR) models. More specifically, we present the
tangent hyperbolic, Gaussian and Generalized bell functions.
Because Smoothing Transition Autoregressive (STAR) models
follow fuzzy logic approach, more fuzzy membership functions
should be tested. Furthermore, fuzzy rules can be incorporated or
other training or computational methods can be applied as the error
backpropagation or genetic algorithm instead to nonlinear squares.
We examine two macroeconomic variables of US economy, the
inflation rate and the 6-monthly treasury bills interest rates.
Abstract: The Goursat partial differential equation arises in
linear and non linear partial differential equations with mixed
derivatives. This equation is a second order hyperbolic partial
differential equation which occurs in various fields of study such as
in engineering, physics, and applied mathematics. There are many
approaches that have been suggested to approximate the solution of
the Goursat partial differential equation. However, all of the
suggested methods traditionally focused on numerical differentiation
approaches including forward and central differences in deriving the
scheme. An innovation has been done in deriving the Goursat partial
differential equation scheme which involves numerical integration
techniques. In this paper we have developed a new scheme to solve
the Goursat partial differential equation based on the Adomian
decomposition (ADM) and associated with Boole-s integration rule to
approximate the integration terms. The new scheme can easily be
applied to many linear and non linear Goursat partial differential
equations and is capable to reduce the size of computational work.
The accuracy of the results reveals the advantage of this new scheme
over existing numerical method.
Abstract: Super-quadrics can represent a set of implicit surfaces,
which can be used furthermore as primitive surfaces to construct a
complex object via Boolean set operations in implicit surface
modeling. In fact, super-quadrics were developed to create a
parametric surface by performing spherical product on two parametric
curves and some of the resulting parametric surfaces were also
represented as implicit surfaces. However, because not every
parametric curve can be redefined implicitly, this causes only implicit
super-elliptic and super-hyperbolic curves are applied to perform
spherical product and so only implicit super-ellipsoids and
hyperboloids are developed in super-quadrics. To create implicit
surfaces with more diverse shapes than super-quadrics, this paper
proposes an implicit representation of spherical product, which
performs spherical product on two implicit curves like super-quadrics
do. By means of the implicit representation, many new implicit curves
such as polygonal, star-shaped and rose-shaped curves can be used to
develop new implicit surfaces with a greater variety of shapes than
super-quadrics, such as polyhedrons, hyper-ellipsoids, superhyperboloids
and hyper-toroids containing star-shaped and roseshaped
major and minor circles. Besides, the newly developed implicit
surfaces can also be used to define new primitive implicit surfaces for
constructing a more complex implicit surface in implicit surface
modeling.
Abstract: In this paper we study the transformation of Euler equations 1 , u u u Pf t (ρ ∂) + ⋅∇ = − ∇ + ∂ G G G G ∇⋅ = u 0, G where (ux, t) G G is the velocity of a fluid, P(x, t) G is the pressure of a fluid andρ (x, t) G is density. First of all, we rewrite the Euler equations in terms of new unknown functions. Then, we introduce new independent variables and transform it to a new curvilinear coordinate system. We obtain the Euler equations in the new dependent and independent variables. The governing equations into two subsystems, one is hyperbolic and another is elliptic.
Abstract: This research paper deals with the implementation of face recognition using neural network (recognition classifier) on low-resolution images. The proposed system contains two parts, preprocessing and face classification. The preprocessing part converts original images into blurry image using average filter and equalizes the histogram of those image (lighting normalization). The bi-cubic interpolation function is applied onto equalized image to get resized image. The resized image is actually low-resolution image providing faster processing for training and testing. The preprocessed image becomes the input to neural network classifier, which uses back-propagation algorithm to recognize the familiar faces. The crux of proposed algorithm is its beauty to use single neural network as classifier, which produces straightforward approach towards face recognition. The single neural network consists of three layers with Log sigmoid, Hyperbolic tangent sigmoid and Linear transfer function respectively. The training function, which is incorporated in our work, is Gradient descent with momentum (adaptive learning rate) back propagation. The proposed algorithm was trained on ORL (Olivetti Research Laboratory) database with 5 training images. The empirical results provide the accuracy of 94.50%, 93.00% and 90.25% for 20, 30 and 40 subjects respectively, with time delay of 0.0934 sec per image.
Abstract: This paper adopted the hybrid differential transform approach for studying heat transfer problems in a gold/chromium thin film with an ultra-short-pulsed laser beam projecting on the gold side. The physical system, formulated based on the hyperbolic two-step heat transfer model, covers three characteristics: (i) coupling effects between the electron/lattice systems, (ii) thermal wave propagation in metals, and (iii) radiation effects along the interface. The differential transform method is used to transfer the governing equations in the time domain into the spectrum equations, which is further discretized in the space domain by the finite difference method. The results, obtained through a recursive process, show that the electron temperature in the gold film can rise up to several thousand degrees before its electron/lattice systems reach equilibrium at only several hundred degrees. The electron and lattice temperatures in the chromium film are much lower than those in the gold film.
Abstract: The aim of the current study is to develop a numerical
tool that is capable of achieving an optimum shape and design of
hyperbolic cooling towers based on coupling a non-linear finite
element model developed in-house and a genetic algorithm
optimization technique. The objective function is set to be the
minimum weight of the tower. The geometric modeling of the tower
is represented by means of B-spline curves. The finite element
method is applied to model the elastic buckling behaviour of a tower
subjected to wind pressure and dead load. The study is divided into
two main parts. The first part investigates the optimum shape of the
tower corresponding to minimum weight assuming constant
thickness. The study is extended in the second part by introducing the
shell thickness as one of the design variables in order to achieve an
optimum shape and design. Design, functionality and practicality
constraints are applied.