We consider two proposals for defining black hole entropy in spherical symmetry, where the horizon is defined locally as a trapping horizon. The first case, boundary terms in a dual-null form of the reduced action in two dimensions, gives a result that is proportional to the area. The second case, Wald’s Noether current method, is generalized to dynamic black holes, giving an entropy that is ju...

In this paper, a numerical solution of an inverse non-dimensional heat conduction problem by spline method will be considered. The given heat conduction equation, the boundary condition, and the initial condition are presented in a dimensionless form. A set of temperature measurements at a single sensor location inside the heat conduction body is required. The result show that the proposed meth...

We consider a reconstruction formula for the internal conductivity and uniqueness of conductivity in magnetic resonance electrical impedance tomography (MREIT) which aims to reconstruct the conductivity distribution using internal current distribution. We provide a counter-example of uniqueness for a single measurement of current density with Neumann boundary data and show that at least two mea...

The present work solves two-dimensional Advection-Dispersion Equation (ADE) in a semi-infinite domain. A variable source concentration is regarded as the monotonic decreasing function at the source boundary (x=0). Depth-dependent variables are considered to incorporate real life situations in this modeling study, with zero flux condition assumed to occur at the exit boundary of the domain, i.e....

Like other developing countries, Iranian cities are growing and expanding physically at a high speed. For about five decades, the only policy of the urban development plans in the field of urban growth management has been definition of the Urban Growth Boundary (U.G.B.) which is still used without any major modifications.Despite the slight evidences indicating the ineffectiveness of the current...

The present work solves two-dimensional Advection-Dispersion Equation (ADE) in a semi-infinite domain. A variable source concentration is regarded as the monotonic decreasing function at the source boundary (x=0). Depth-dependent variables are considered to incorporate real life situations in this modeling study, with zero flux condition assumed to occur at the exit boundary of the domain, i.e....

The present paper is devoted to the development of a kind of spectral meshless radial point interpolation (SMRPI) technique in order to obtain a reliable approximate solution for buckling of nano-actuators subject to different nonlinear forces. To end this aim, a general type of the governing equation for nano-actuators, containing integro-differential terms and nonlinear forces is considered. ...

analysis of aperture-coupled microstrip antennas with a superstrate using space domain closed form greens functions is presented. integral equations are derived from applying the boundary conditions on the radiating patch, across the aperture, and on the microstrip feedline. the computation of space domain greens functions is performed using the closed-form. the solution of the integral equatio...

This manuscript addresses trajectory tracking problem of autonomous underwater vehicles (AUVs) on the horizontal plane. Adaptive sliding mode control is employed in order to achieve a robust behavior against some uncertainty and ocean current disturbances, assuming that disturbance and its derivative are bounded by unknown boundary levels. The proposed approach is based on a dual layer adaptive...