scholarly journals Vibration of the Biomass Boiler Tube Excited with Impact of the Cleaning Device

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1519
Author(s):  
Dragan Cveticanin ◽  
Nicolae Herisanu ◽  
Istvan Biro ◽  
Miodrag Zukovic ◽  
Livija Cveticanin
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Initial Conditions ◽  
Nonlinear Differential Equations ◽  
Nonlinear Partial Differential Equation ◽  
Mode Shapes ◽  
Straight Beam ◽  
Special Cases ◽  
Cleaning Device ◽  
The Impact

In boilers with biomass fuel, a significant problem is caused due to the slag layer formed from the unburned particles during combustion. In the paper, a tube cleaning method from slag is proposed. The method is based on the impact effect of the end of the tube with the aim to produce vibration for slag elimination. The tube is modeled as a clamped-free nonlinear oscillatory system. The initial impact of the tube causes vibrations. The mathematical model of the system is a nonlinear partial differential equation with zero initial deflection. To obtain the ordinary differential equations, the Galerkin method is applied. By discretizing the equation into a finite degree of freedom system, using the undamped linear mode shapes of the straight beam as basic functions, the reduced order model, consisting of ordinary differential equations in time, is obtained. The ordinary time equations are analytically solved by adopting the Krylov–Bogoliubov procedure. Special cases of nonlinear differential equations are investigated. In the paper, the influence of the nonlinear parameters and initial conditions on the vibration properties of the tube is obtained. We use the procedure developed in the paper and the analytical results for computation of the impact parameters of the cleaning device.

Plumes Above Line Fires in a Cross-Wind

1994 ◽  
Vol 4 (4) ◽  
pp. 201 ◽  
Author(s):  
GN Mercer ◽  
RO Weber
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Initial Conditions ◽  
Velocity Profiles ◽  
Ambient Wind ◽  
Leaf Scorch ◽  
Wind Velocities ◽  
Wind Profiles ◽  
Fire Characteristics ◽  
Temperature Time

A model for the plume above a line fire in a cross wind is constructed. This problem is shown to reduce to numerically solving a system of 6 coupled ordinary differential equations for given initial conditions that depend upon the fire characteristics. The model is valid above the flaming zone and takes inputs such as the width, velocity and temperature of the plume at a given height above the flaming zone, Different horizontal ambient wind velocities are allowed for and a comparison is made between some of these representative wind profiles. The plume trajectory, width, velocity and temperature are calculated for these different representative velocity profiles. This model has application to the calculation of temperature-time exposures of vegetation above line fires and hence can be used in models that predict effects such as leaf scorch and canopy stored seed death. On a larger scale it has application to the problem of tracking burning brands which can cause spotting ahead of the fire.

scholarly journals Nonlinear translational symmetric equilibria relevant to the L–H transition

2012 ◽  
Vol 79 (3) ◽  
pp. 257-265 ◽  
Author(s):  
Ap. KUIROUKIDIS ◽  
G. N. THROUMOULOPOULOS
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Plasma Flow ◽  
Sufficient Condition ◽  
Sheared Flow ◽  
Equilibrium Configurations ◽  
Shafranov Equation ◽  
The Impact ◽  
The Magnetic Field

AbstractNonlinear z-independent solutions to a generalized Grad–Shafranov equation (GSE) with up to quartic flux terms in the free functions and incompressible plasma flow non-parallel to the magnetic field are constructed quasi-analytically. Through an ansatz, the GSE is transformed to a set of three ordinary differential equations and a constraint for three functions of the coordinate x, in Cartesian coordinates (x,y), which then are solved numerically. Equilibrium configurations for certain values of the integration constants are displayed. Examination of their characteristics in connection with the impact of nonlinearity and sheared flow indicates that these equilibria are consistent with the L–H transition phenomenology. For flows parallel to the magnetic field, one equilibrium corresponding to the H state is potentially stable in the sense that a sufficient condition for linear stability is satisfied in an appreciable part of the plasma while another solution corresponding to the L state does not satisfy the condition. The results indicate that the sheared flow in conjunction with the equilibrium nonlinearity plays a stabilizing role.

scholarly journals Integral averaging techniques for the oscillation of second order sublinear ordinarry differential equations

1986 ◽  
Vol 40 (1) ◽  
pp. 111-130 ◽  
Author(s):  
Ch. G. Philos
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Second Order ◽  
Averaging Technique ◽  
Oscillation Criteria ◽  
Integral Averaging Technique ◽  
Special Cases ◽  
Averaging Techniques

AbstractNew oscillation criteria are established for second order sublinear ordinary differential equations with alternating coefficients. These criteria are obtained by using an integral averaging technique and can be applied in some special cases in which other classical oscillation results are no applicable.

scholarly journals Quasi–additive solutions of nonlinear differential equations II

1988 ◽  
Vol 38 (1) ◽  
pp. 19-21 ◽  
Author(s):  
A.S. Jones
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Nonlinear Differential Equations ◽  
Second Order ◽  
Nonlinear Ordinary Differential Equations

In a previous paper, the author sought to classify those solutions of second order nonlinear ordinary differential equations which can be expressed as sums of solutions of related equations. In that paper one sub-class of solutions was overlooked. This paper is to remedy that defect.

A boundary value problem on the half-line for higher-order nonlinear differential equations

2009 ◽  
Vol 139 (5) ◽  
pp. 1017-1035 ◽  
Author(s):  
Ch. G. Philos
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Ordinary Differential Equations ◽  
Existence And Uniqueness ◽  
Nonlinear Differential Equations ◽  
Boundary Value ◽  
Higher Order ◽  
Half Line ◽  
Nonlinear Ordinary Differential Equations ◽  
Specific Class

This article is devoted to the study of the existence of solutions as well as the existence and uniqueness of solutions to a boundary-value problem on the half-line for higher-order nonlinear ordinary differential equations. An existence result is obtained by the use of the Schauder–Tikhonov theorem. Furthermore, an existence and uniqueness criterion is established using the Banach contraction principle. These two results are applied, in particular, to the specific class of higher-order nonlinear ordinary differential equations of Emden–Fowler type and to the special case of higher-order linear ordinary differential equations, respectively. Moreover, some (general or specific) examples demonstrating the applicability of our results are given.

Application of GDQ method in nonlinear analysis of a flexible manipulator undergoing large deformation

2013 ◽  
Vol 227 (12) ◽  
pp. 2671-2685 ◽  
Author(s):  
Mohammad R Fazel ◽  
Majid M Moghaddam ◽  
Javad Poshtan
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Nonlinear Partial Differential Equation ◽  
Flexible Manipulator ◽  
Runge Kutta Method ◽  
Highly Nonlinear ◽  
Frechet Derivatives ◽  
Fréchet Derivatives ◽  
Generalized Differential

Analysis of a flexible manipulator as an initial value problem, due to its large deformations, involves nonlinear ordinary differential equations of motion. In the present work, these equations are solved through the general Frechet derivatives and the generalized differential quadrature (GDQ) method directly. The results so obtained are compared with those of the fourth-order Runge–Kutta method. It is seen that both the results match each other well. Further considering the same manipulator as a boundary value problem, its governing equation is a highly nonlinear partial differential equation. Again applying the general Frechet derivatives and the GDQ method, it is seen that the results are in good match with the linear theory. In both cases, the general Frechet derivatives are introduced and successfully used for linearization. The results of the present study indicate that the GDQ method combined with the general Frechet derivatives can be successfully used for the solution of nonlinear differential equations.

scholarly journals A hybrid three-scale model of tumor growth

2017 ◽  
Vol 28 (01) ◽  
pp. 61-93 ◽  
Author(s):  
H. L. Rocha ◽  
R. C. Almeida ◽  
E. A. B. F. Lima ◽  
A. C. M. Resende ◽  
J. T. Oden ◽  
...  
Keyword(s):  
Tumor Microenvironment ◽  
Differential Equations ◽  
Tumor Growth ◽  
Nonlinear Differential Equations ◽  
Reaction Diffusion Equations ◽  
Scale Model ◽  
Wide Range ◽  
Induced Stresses ◽  
The Impact

Cancer results from a complex interplay of different biological, chemical, and physical phenomena that span a wide range of time and length scales. Computational modeling may help to unfold the role of multiple evolving factors that exist and interact in the tumor microenvironment. Understanding these complex multiscale interactions is a crucial step toward predicting cancer growth and in developing effective therapies. We integrate different modeling approaches in a multiscale, avascular, hybrid tumor growth model encompassing tissue, cell, and sub-cell scales. At the tissue level, we consider the dispersion of nutrients and growth factors in the tumor microenvironment, which are modeled through reaction–diffusion equations. At the cell level, we use an agent-based model (ABM) to describe normal and tumor cell dynamics, with normal cells kept in homeostasis and cancer cells differentiated into quiescent, proliferative, migratory, apoptotic, hypoxic, and necrotic states. Cell movement is driven by the balance of a variety of forces according to Newton’s second law, including those related to growth-induced stresses. Phenotypic transitions are defined by specific rule of behaviors that depend on microenvironment stimuli. We integrate in each cell/agent a branch of the epidermal growth factor receptor (EGFR) pathway. This pathway is modeled by a system of coupled nonlinear differential equations involving the mass laws of 20 molecules. The rates of change in the concentration of some key molecules trigger proliferation or migration advantage response. The bridge between cell and tissue scales is built through the reaction and source terms of the partial differential equations. Our hybrid model is built in a modular way, enabling the investigation of the role of different mechanisms at multiple scales on tumor progression. This strategy allows representing both the collective behavior due to cell assembly as well as microscopic intracellular phenomena described by signal transduction pathways. Here, we investigate the impact of some mechanisms associated with sustained proliferation on cancer progression. Speci- fically, we focus on the intracellular proliferation/migration-advantage-response driven by the EGFR pathway and on proliferation inhibition due to accumulation of growth-induced stresses. Simulations demonstrate that the model can adequately describe some complex mechanisms of tumor dynamics, including growth arrest in avascular tumors. Both the sub-cell model and growth-induced stresses give rise to heterogeneity in the tumor expansion and a rich variety of tumor behaviors.

Application of Ambarzumian’s Method to Radiant Interchange in a Rectangular Cavity

1974 ◽  
Vol 96 (2) ◽  
pp. 191-196 ◽  
Author(s):  
A. L. Crosbie ◽  
T. R. Sawheny
Keyword(s):  
Differential Equation ◽  
Heat Flux ◽  
Integral Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Nonlinear Integral Equation ◽  
Initial Conditions ◽  
Rectangular Cavity ◽  
Wide Range ◽  
First Time

Ambarzumian’s method had been used for the first time to solve a radiant interchange problem. A rectangular cavity is defined by two semi-infinite parallel gray surfaces which are subject to an exponentially varying heat flux, i.e., q = q0 exp(−mx). Instead of solving the integral equation for the radiosity for each value of m, solutions for all values of m are obtained simultaneously. Using Ambarzumian’s method, the integral equation for the radiosity is first transformed into an integro-differential equation and then into a system of ordinary differential equations. Initial conditions required to solve the differential equations are the H functions which represent the radiosity at the edge of the cavity for various values of m. This H function is shown to satisfy a nonlinear integral equation which is easily solved by iteration. Numerical results for the H function and radiosity distribution within the cavity are presented for a wide range of m values.

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