A numerical research on magnetohydrodynamic mixed convection flow in a lid-driven trapezoidal enclosure at non-uniform heating of bottom wall has been studied numerically. The enclosure consists of insulated top wall ...A numerical research on magnetohydrodynamic mixed convection flow in a lid-driven trapezoidal enclosure at non-uniform heating of bottom wall has been studied numerically. The enclosure consists of insulated top wall and cold side walls, too. It also contains a heated triangular block (<em>Rot</em> = 0<span style="font-family:Verdana, Helvetica, Arial;white-space:normal;background-color:#FFFFFF;">°</span> - 90<span style="font-family:Verdana, Helvetica, Arial;white-space:normal;background-color:#FFFFFF;">°</span>) located somewhere inside the enclosure. The boundary top wall of the enclosure is moving through uniform speed <em>U</em><sub>0</sub>. The geometry of the model has been represented mathematically by coupled governing equations in accordance with proper boundary conditions and then a two-dimensional Galerkin finite element based numerical approach has been adopted to solve this paper. The numerical computations have been carried out for the wide range of parameters Prandtl number (0.5 ≤ <em>Pr</em> ≤ 2), Reynolds number (60 ≤ <em>Re</em> ≤ 120), Rayleigh number (<em>Ra</em> = 10<sup>3</sup>) and Hartmann number (<em>Ha</em> = 20) taking with different rotations of heated triangular block. The results have been shown in the form of streamlines, temperature patterns or isotherms, average Nusselt number and average bulk temperature of the fluid in the enclosure at non-uniform heating of bottom wall. It is also indicated that both the streamlines, isotherm patterns strongly depend on the aforesaid governing parameters and location of the triangular block but the thermal conductivity of the triangular block has a noteworthy role on the isotherm pattern lines. Moreover, the variation of <em>Nu</em><sub>av</sub> of hot bottom wall and <em>θ</em><sub>av</sub> in the enclosure is demonstrated here to show the characteristics of heat transfer in the enclosure.展开更多
This paper proposes a two-parameter block triangular splitting(TPTS)preconditioner for the general block two-by-two linear systems.The eigenvalues of the corresponding preconditioned matrix are proved to cluster aroun...This paper proposes a two-parameter block triangular splitting(TPTS)preconditioner for the general block two-by-two linear systems.The eigenvalues of the corresponding preconditioned matrix are proved to cluster around 0 or 1 under mild conditions.The limited numerical results show that the TPTS preconditioner is more efficient than the classic block-diagonal and block-triangular preconditioners when applied to the flexible generalized minimal residual(FGMRES)method.展开更多
The rapid advancement of data in web-based communication has created one of the biggest issues concerning the security of data carried over the internet from unauthorized access.To improve data security,modern cryptos...The rapid advancement of data in web-based communication has created one of the biggest issues concerning the security of data carried over the internet from unauthorized access.To improve data security,modern cryptosystems use substitution-boxes.Nowadays,data privacy has become a key concern for consumers who transfer sensitive data from one place to another.To address these problems,many companies rely on cryptographic techniques to secure data from illegal activities and assaults.Among these cryptographic approaches,AES is a well-known algorithm that transforms plain text into cipher text by employing substitution box(S-box).The S-box disguises the relationship between cipher text and the key to guard against cipher attacks.The security of a cipher using an S-box depends on the cryptographic strength of the respective S-box.Therefore,various researchers have employed different techniques to construct high order non-linear S-box.This paper provides a novel approach for evolving S-boxes using coset graphs for the action of the alternating group A5 over the finite field and the symmetric group S256.The motivation for this work is to study the symmetric group and coset graphs.The authors have performed various analyses against conventional security criteria such as nonlinearity,differential uniformity,linear probability,the bit independence criterion,and the strict avalanche criterion to determine its high cryptographic strength.To evaluate its image application performance,the proposed S-box is also used to encrypt digital images.The performance and comparison analyses show that the suggested S-box can secure data against cyber-attacks.展开更多
In this paper, we provide new preconditioner for saddle point linear systems with (1,1) blocks that have a high nullity. The preconditioner is block triangular diagonal with two variable relaxation paremeters and it i...In this paper, we provide new preconditioner for saddle point linear systems with (1,1) blocks that have a high nullity. The preconditioner is block triangular diagonal with two variable relaxation paremeters and it is extension of results in [1] and [2]. Theoretical analysis shows that all eigenvalues of preconditioned matrix is strongly clustered. Finally, numerical tests confirm our analysis.展开更多
文摘A numerical research on magnetohydrodynamic mixed convection flow in a lid-driven trapezoidal enclosure at non-uniform heating of bottom wall has been studied numerically. The enclosure consists of insulated top wall and cold side walls, too. It also contains a heated triangular block (<em>Rot</em> = 0<span style="font-family:Verdana, Helvetica, Arial;white-space:normal;background-color:#FFFFFF;">°</span> - 90<span style="font-family:Verdana, Helvetica, Arial;white-space:normal;background-color:#FFFFFF;">°</span>) located somewhere inside the enclosure. The boundary top wall of the enclosure is moving through uniform speed <em>U</em><sub>0</sub>. The geometry of the model has been represented mathematically by coupled governing equations in accordance with proper boundary conditions and then a two-dimensional Galerkin finite element based numerical approach has been adopted to solve this paper. The numerical computations have been carried out for the wide range of parameters Prandtl number (0.5 ≤ <em>Pr</em> ≤ 2), Reynolds number (60 ≤ <em>Re</em> ≤ 120), Rayleigh number (<em>Ra</em> = 10<sup>3</sup>) and Hartmann number (<em>Ha</em> = 20) taking with different rotations of heated triangular block. The results have been shown in the form of streamlines, temperature patterns or isotherms, average Nusselt number and average bulk temperature of the fluid in the enclosure at non-uniform heating of bottom wall. It is also indicated that both the streamlines, isotherm patterns strongly depend on the aforesaid governing parameters and location of the triangular block but the thermal conductivity of the triangular block has a noteworthy role on the isotherm pattern lines. Moreover, the variation of <em>Nu</em><sub>av</sub> of hot bottom wall and <em>θ</em><sub>av</sub> in the enclosure is demonstrated here to show the characteristics of heat transfer in the enclosure.
基金the National Natural Science Foundation of China under Grant Nos.61273311 and 61803247.
文摘This paper proposes a two-parameter block triangular splitting(TPTS)preconditioner for the general block two-by-two linear systems.The eigenvalues of the corresponding preconditioned matrix are proved to cluster around 0 or 1 under mild conditions.The limited numerical results show that the TPTS preconditioner is more efficient than the classic block-diagonal and block-triangular preconditioners when applied to the flexible generalized minimal residual(FGMRES)method.
文摘The rapid advancement of data in web-based communication has created one of the biggest issues concerning the security of data carried over the internet from unauthorized access.To improve data security,modern cryptosystems use substitution-boxes.Nowadays,data privacy has become a key concern for consumers who transfer sensitive data from one place to another.To address these problems,many companies rely on cryptographic techniques to secure data from illegal activities and assaults.Among these cryptographic approaches,AES is a well-known algorithm that transforms plain text into cipher text by employing substitution box(S-box).The S-box disguises the relationship between cipher text and the key to guard against cipher attacks.The security of a cipher using an S-box depends on the cryptographic strength of the respective S-box.Therefore,various researchers have employed different techniques to construct high order non-linear S-box.This paper provides a novel approach for evolving S-boxes using coset graphs for the action of the alternating group A5 over the finite field and the symmetric group S256.The motivation for this work is to study the symmetric group and coset graphs.The authors have performed various analyses against conventional security criteria such as nonlinearity,differential uniformity,linear probability,the bit independence criterion,and the strict avalanche criterion to determine its high cryptographic strength.To evaluate its image application performance,the proposed S-box is also used to encrypt digital images.The performance and comparison analyses show that the suggested S-box can secure data against cyber-attacks.
文摘In this paper, we provide new preconditioner for saddle point linear systems with (1,1) blocks that have a high nullity. The preconditioner is block triangular diagonal with two variable relaxation paremeters and it is extension of results in [1] and [2]. Theoretical analysis shows that all eigenvalues of preconditioned matrix is strongly clustered. Finally, numerical tests confirm our analysis.
