In this paper, we present a new ultra fast detector called Low Gain Avalanche Detector (LGAD) with low internal gain. The LGAD is fabricated with conventional APD technology with a modified doping profile, in the multiplication region, which affects the device performance such as: breakdown, multiplication gain and noise factor. For this reason, a numerical method based on Newton-Raphson calculation is proposed to estimate the electrostatic potential and electric field models of low gain avalanche detectors (LGADs) in order to investigate their performances. These models have been validated by their agreement with TCAD numerical simulation results. The effect of Boron doping profile, with different doses in the multiplication region, on the LGAD electrical performance is studied for various device structures in order to extend the device capability to its limit. In addition, LGAD devices are simulated for different temperature considering the effect of the temperature on the multiplication gain.

Let E,F,G,D be infinite complex Banach spaces and B(F,E) the Banach space of all bounded linear operators from F into E. Consider A1,A2∈B(F,E), B1,B2∈B(D,G)B1,B2∈B(D,G). Let MA1,B1:X→A1XB1 be the multiplication operator on B(G,F) induced by A1,B1. In particular, LA1=MA1,I and RB1=MI,B1, where I is the identity operator are the left and the right multiplication operators, respectively. The elementary operator Ψ defined on B(G,F)B(G,F) is the sum of two multiplication operators Ψ=MA1,B1+MA2,B2. This paper gives necessary and sufficient conditions for the existence of a common solution of the operator equations MA1,B1(X)=C1 and MA2,B2(X)=C2 and derive a new representation of the general common solution via the inner inverse of the elementary operator Ψ; we apply this result to determine new necessary and sufficient conditions for the existence of a Hermitian solution and a representation of the general Hermitian solution to the operator equation MA,B(X)=C. As a consequence, we obtain well-known results of Dajic´ and Koliha.

Let E,F,G,D be infinite complex Banach spaces and B(F,E) the Banach space of all bounded linear operators from F into E. Consider A1,A2∈B(F,E), B1,B2∈B(D,G)B1,B2∈B(D,G). Let MA1,B1:X→A1XB1 be the multiplication operator on B(G,F) induced by A1,B1. In particular, LA1=MA1,I and RB1=MI,B1, where I is the identity operator are the left and the right multiplication operators, respectively. The elementary operator Ψ defined on B(G,F)B(G,F) is the sum of two multiplication operators Ψ=MA1,B1+MA2,B2. This paper gives necessary and sufficient conditions for the existence of a common solution of the operator equations MA1,B1(X)=C1 and MA2,B2(X)=C2 and derive a new representation of the general common solution via the inner inverse of the elementary operator Ψ; we apply this result to determine new necessary and sufficient conditions for the existence of a Hermitian solution and a representation of the general Hermitian solution to the operator equation MA,B(X)=C. As a consequence, we obtain well-known results of Dajic´ and Koliha.

The magnetohydrodynamics (MHD) is an important interdisciplinary field. It is the interaction between an electromagnetic field and an electrically conducting fluid. Electromagnetic pumps are widely used for the transportation of the fluids in a variety of technological processes. The advantage of these devices is that permits the pumping of liquids without moving parts. The design of the pump is considered as an optimization problem where the objective function is the minimum of the MHD pump mass with both geometrical and electromagnetic contraints type. The obtained optimization results using the finite volume method with Matlab software show the performances of the used stochastic simulated annealing method.

The magnetohydrodynamics (MHD) is an important interdisciplinary field. It is the interaction between an electromagnetic field and an electrically conducting fluid. Electromagnetic pumps are widely used for the transportation of the fluids in a variety of technological processes. The advantage of these devices is that permits the pumping of liquids without moving parts. The design of the pump is considered as an optimization problem where the objective function is the minimum of the MHD pump mass with both geometrical and electromagnetic contraints type. The obtained optimization results using the finite volume method with Matlab software show the performances of the used stochastic simulated annealing method.

The magnetohydrodynamics (MHD) is an important interdisciplinary field. It is the interaction between an electromagnetic field and an electrically conducting fluid. Electromagnetic pumps are widely used for the transportation of the fluids in a variety of technological processes. The advantage of these devices is that permits the pumping of liquids without moving parts. The design of the pump is considered as an optimization problem where the objective function is the minimum of the MHD pump mass with both geometrical and electromagnetic contraints type. The obtained optimization results using the finite volume method with Matlab software show the performances of the used stochastic simulated annealing method.

The magnetohydrodynamics (MHD) is an important interdisciplinary field. It is the interaction between an electromagnetic field and an electrically conducting fluid. Electromagnetic pumps are widely used for the transportation of the fluids in a variety of technological processes. The advantage of these devices is that permits the pumping of liquids without moving parts. The design of the pump is considered as an optimization problem where the objective function is the minimum of the MHD pump mass with both geometrical and electromagnetic contraints type. The obtained optimization results using the finite volume method with Matlab software show the performances of the used stochastic simulated annealing method.