Determination of plutonium temperature using the special trans functions theory

Abstract

The problem of estimating plutonium temperature by an iterative procedure based on the special trans functions theory has been studied in some detail. In theory, the differential linear plutonium temperature equation can be effectively reduced to a non-linear functional transcendental equation solvable by special trans functions theory. This approach is practically invariant under the starting plutonium temperature value. This is significant, because the said iterative special trans functions theory does not depend on the password data of the plutonium cargo. Obtained numerical results and graphical simulations confirm the applicability of such approach

The Special Trans Functions Theory for the Degree of Nuclear Fuel Burn-Up Estimation

“…(3)) is solvable using the Special Tran Function Theory [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. Let us note that Perovich's Special Tran Functions Theory (STFT), has been proved to be a very powerful theory for solving transcendental equations, some integral and integro-differential equations, and, obtaining exact analytical closed-form solutions.…”

“…Let us note that Perovich's Special Tran Functions Theory (STFT), has been proved to be a very powerful theory for solving transcendental equations, some integral and integro-differential equations, and, obtaining exact analytical closed-form solutions. Examples of STFT application are shown in articles concerning the closed-form solution genesis in: the theory of neutron slowing down [ [6], [7], [16]], the nonlinear circuit theory [ [8], [16], [22]], the linear transport theory [ [9], [16], [20]], the Hopfield neuron analysis [11], some families of transcendental equations analysis [ [12], [16], [17]], the solar cell theoretical analysis [ [13], [18], [22]], the Plutonium temperature estimation [14], the ambient temperature estimation [ [15], [16]], the Lambert transcendental equations analysis [ [16], [17], [23]], as well as in the problem in the engineering materials [19], [21], [22]], etc.…”

On the exact analytical solution of some families of equilibrium critical thickness transcendental equations

“…In this section, as above mentioned, the problem of finding an exact analytical closed-form solution to the transcendental equation (6) using the Special Trans Functions Theory, [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] will be discussed in detail.…”

“…Let us note that Eq. (6) has two real solutions: z > (for z>1) and z < (for z<1), 19,21,26 which are presented in Fig. 1.…”

“…Mathematical form of the relationship between the equilibrium critical thickness and material parameters can be reduced to a transcendental equation (6). Perovich's Special Trans Functions Theory (STFT) has been proved to be a very powerful theory for solving transcendental equations and obtaining exact analytical closed-form solutions without any assumptions, hypotheses nor any additional proofs, [13][14][15][16][17][18][19][20][21][22][23] as opposed to the approaches presented in papers. 1,7 Examples of its application are shown in papers concerning the calculation of the closed-form solutions in some families of transcendental equations, 19 Lambert transcendental equation, 24 engineering materials, 26 theory of neutron slowing down, 13,14 linear transport theory, 17,23,27 Plutonium temperature estimation, 21 temperature estimation, 22 nonlinear circuit theory 15 and Hopfield neuron analysis, 18 as well as solar cell analysis 20,25 etc.…”