scholarly journals Analytical Models for Gravitating Radiating Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
B. P. Brassel ◽  
S. D. Maharaj ◽  
G. Govender

We analyse the gravitational behaviour of a relativistic heat conducting fluid in a shear-free spherically symmetric spacetime. We show that the isotropy of pressure is a consistency condition which realises a second order nonlinear ordinary differential equation with variable coefficients in the gravitational potentials. Several new classes of solutions are found to the governing equation by imposing various forms on one of the potentials. Interestingly, a complex transformation leads to an exact solution with only real metric functions. All solutions are written in terms of elementary functions. We demonstrate graphically that the fluid pressure, energy density, and heat flux are well behaved for the model, and the model is consistent with a core-envelope framework.

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Fatima N. Ahmed ◽  
Rokiah Rozita Ahmad ◽  
Ummul Khair Salma Din ◽  
Mohd Salmi Md Noorani

We study the oscillatory behaviour of all solutions of first-order neutral equations with variable coefficients. The obtained results extend and improve some of the well-known results in the literature. Some examples are given to show the evidence of our new results.


2013 ◽  
Vol 80 (2) ◽  
Author(s):  
Minh H. Tran ◽  
Younane N. Abousleiman

The porochemoelectroelastic analytical models have been used to describe the response of chemically active and electrically charged saturated porous media such as clay soils, shales, and biological tissues. However, existing studies have ignored the anisotropic nature commonly observed on these porous media. In this work, the anisotropic porochemoelectroelastic theory is presented. Then, the solution for an inclined wellbore drilled in transversely isotropic shale formations subjected to anisotropic far-field stresses with time-dependent down-hole fluid pressure and fluid activity is derived. Numerical examples illustrating the combined effects of porochemoelectroelastic behavior and anisotropy on wellbore responses are also included. The analysis shows that ignoring either the porochemoelectroelastic effects or the formation anisotropy leads to inaccurate prediction of the near-wellbore pore pressure and effective stress distributions. Finally, wellbore responses during a leak-off test conducted soon after drilling are analyzed to demonstrate the versatility of the solution in simulating complex down-hole conditions.


1997 ◽  
Vol 27 (3) ◽  
pp. 257-265
Author(s):  
ZDZISLAW SZAFRANSKI ◽  
BLAZEJ SZMANDA

We obtain sufficient conditions for the oscillation of all solutions of some linear difference equations with variable coefficients.


2014 ◽  
Vol 548-549 ◽  
pp. 1196-1200
Author(s):  
Yong Mei Bao ◽  
Siqintana Bao

In order to construct exact soliton solutions of nonlinear evolution equations with variable coefficients. By using a transformation, the variable coefficient KdV equation with forced Term is reduced to nonlinear ordinary differential equation (NLODE), after that, a number of exact solitons solutions of variable coefficient KdV equation with forced Term are obtained by using the equation shorted in NLODE. As it showed above, this kind of method can be applied in solving a large number of nonlinear evolution equations.


Author(s):  
José J. García ◽  
Ana Belly Molano ◽  
Joshua H. Smith

An axisymmetric biphasic finite element model is proposed to simulate the backflow that develops around the external boundary of the catheter during flow-controlled infusions. The model includes both material and geometric nonlinearities and special treatments for the nonlinear boundary conditions used to represent the forward flow from the catheter tip and the axial backflow that occurs in the annular gap that develops as the porous medium detaches from the catheter. Specifically, a layer of elements with high hydraulic conductivity and low Young’s modulus was used to represent the nonlinear boundary condition for the forward flow, and another layer of elements with axial hydraulic conductivity consistent with Poiseuille flow was used to represent the backflow. Validation of the model was performed by modifying the elastic properties of the latter layer to fit published experimental values for the backflow length and maximum fluid pressure obtained during infusions into agarose gels undertaken with a 0.98-mm-radius catheter. Next, the finite element model predictions showed good agreement with independent experimental data obtained for 0.5-mm-radius and 0.33-mm-radius catheters. Compared to analytical models developed by others, this finite element model predicts a smaller backflow length, a larger fluid pressure, and a substantially larger percentage of forward flow. This latter difference can be explained by the important axial flow in the tissue that is not considered in the analytical models. These results may provide valuable guidelines to optimize protocols during future clinical studies. The model can be extended to describe infusions in brain tissue and in patient-specific geometries.


2011 ◽  
Vol 26 (17) ◽  
pp. 2927-2950
Author(s):  
A. M. GHEZELBASH ◽  
R. ORAJI

We present analytic solutions for membrane metric function based on transverse k-center instanton geometries. The membrane metric functions depend on more than two transverse coordinates and the solutions provide realizations of fully localized type IIA D2/D6 and NS5/D6 brane intersections. All solutions have partial preserved supersymmetries.


2021 ◽  
Author(s):  
Vai Yee Hon ◽  
M Faizzudin Mat Piah ◽  
Noor 'Aliaa M Fauzi ◽  
Peter Schutjens ◽  
Binayak Agarwal ◽  
...  

Abstract An integrated 3D dynamic reservoir geomechanics model can provide a diverse 3D view of depletion-injection-induced field stress changes and the resulting deformation of both reservoir and overburden formations at various field locations. It enables the assessment of reservoir compaction, platform site subsidence, fault reactivation and caprock integrity associated with multiple production and injection reservoirs of the field. We demonstrated this integrated approach for a study field located in the South China Sea, Malaysia, which is planned for water injection for pressure support and EOR scheme thereafter. Reservoir fluid containment during water injection is an important concern because of the intensive geologic faulting and fracturing in the collapsed anticlinal structure, with some faults extending from the reservoirs to shallow depths at or close to the seafloor. Over 30 simulations were done, and most input parameters were systematically varied to gain insight in their effect on result that was of most interest to us: The tendency of fault slip as a function of our operation-induced variations in pore pressure in the reservoir rocks bounding the fault, both during depletion and injection. The results showed that depletion actually reduces the risk of fault slip and of the overburden, while injection-induced increase in pore fluid pressure will lead to a significant increase in the risk of fault slip. Overall, while depletion appears to stabilize the fault and injection appears to destabilize the fault, no fault slip is predicted to occur, not even after a 900psi increase in pore pressure above the pore pressure levels at maximum depletion. We present the model results to demonstrate why depletion and injection have such different effects on fault slip tendency. The interpretation of these geomechanical model results have potential applications beyond the study field, especially for fields with a similar geology and development plan. This is a novel application of 3D dynamic reservoir geomechanics model that cannot be obtained from 1D analytical models alone.


2015 ◽  
Vol 2 (5) ◽  
pp. 140348 ◽  
Author(s):  
Matthew J. Simpson ◽  
Liam C. Morrow

Analytical solutions of partial differential equation (PDE) models describing reactive transport phenomena in saturated porous media are often used as screening tools to provide insight into contaminant fate and transport processes. While many practical modelling scenarios involve spatially variable coefficients, such as spatially variable flow velocity, v ( x ), or spatially variable decay rate, k ( x ), most analytical models deal with constant coefficients. Here we present a framework for constructing exact solutions of PDE models of reactive transport. Our approach is relevant for advection-dominant problems, and is based on a regular perturbation technique. We present a description of the solution technique for a range of one-dimensional scenarios involving constant and variable coefficients, and we show that the solutions compare well with numerical approximations. Our general approach applies to a range of initial conditions and various forms of v ( x ) and k ( x ). Instead of simply documenting specific solutions for particular cases, we present a symbolic worksheet, as supplementary material, which enables the solution to be evaluated for different choices of the initial condition, v ( x ) and k ( x ). We also discuss how the technique generalizes to apply to models of coupled multispecies reactive transport as well as higher dimensional problems.


1992 ◽  
Vol 46 (1) ◽  
pp. 149-157 ◽  
Author(s):  
Jianshe Yu ◽  
Zhicheng Wang

We obtain new sufficient conditions for the oscillation of all solutions of the neutral differential equation with variable coefficientswhere P, Q, R ∈ C([t0, ∞), R+), r ∈ (0, ∞) and τ, σ ∈ [0, ∞). Our results improve several known results in papers by: Chuanxi and Ladas; Lalli and Zhang; Wei; Ruan.


2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Fatima N. Ahmed ◽  
Rokiah R. Ahmad ◽  
Ummul K. S. Din ◽  
Mohd S. M. Noorani

A class of nonlinear neutral delay differential equations is considered. Some new oscillation criteria of all solutions are derived. The obtained results generalize and extend some of well known previous results in the literature.


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