Application of computer algebra systems (CAS) to symbolic construction of coupled equations for magnetic susceptibility of amorphous systems with different coordination numbers

We present the application of computer algebra systems to symbolic construction of two coupled systems of equations obtained from the exact Callen equation for a set of magnetizations and relevant magnetic susceptibilities in the case of complex amorphous ternary and binary diluted alloys like (ApB1-p)xC1-x with concentrations p and x, and different coordination numbers. The present paper is an extension of our previous one (Annales UMCS Informatica AI 5, 2006, 93) where the systems of polynomial equations for spontaneous magnetizations without external magnetic field have been obtained. Now, we introduce the external magnetic field and determine with the use of CAS full system of equations for both local magnetic susceptibilities and local magnetizations concerning all components of the complex magnetic systems. Finally, the numerical solutions of constructed coupled equations are found and discussed. The special attention is paid to the ferromagnetic region where the existence of low-temperature ordering transition, below the usual Curie phase transition, is searched as an interesting phenomenon from the technical point of view. The presented CAS added description can be understood as automatic constructor-simulator of relevant properties of amorphous alloys when the parameters of the system in question form an input to the described CAS-package

The method of reduction of transfer matrix for modulated systems

We present a new method of calculation of partition function for the layered systems with the arbitrary spin-modulated structure in the linear cluster approximation. The thermodynamic description of the system in question is based on the Bogolyubov variational principle (inequality). The transfer matrix technique is used to determine the partition function, finally the free energy of the system, in terms of its largest eigenvalue. However, the compositional modulation introduces different types of transfer matrices related to different pure components of the system as well as the interface regions between them. The reduction of transfer matrices related to high-spin components obtained by a partial summation of the partition function gives us a simplified expression for the free energy in characteristic form already known for a low-spin component.In particular, we study two periodic magnetic superstructures ABAB with a strong perpendicular anisotropy, spin SA = XA and the large spin value SB = 1 or SB = 3/2. In each case, the method presented leads to a simple renormalized expression for the free energy of anisotropic homogeneous structure with only spins S = V2. Next, as a numerical result interesting discontinuous thermal transition between new stable ordered phases is obtained

Application of computer algebra systems (CAS) to formal expansion of exact Callen equations into the systems of algebraic equations

We present the application of computer algebra systems (CAS) to symbolic construction of algebraic equations describing different ordered as well as stochastic magnetic structures. We start with formal and exact, however non-tractable from the numerical point of view, Callen equations. Then, we apply the integral operator method (based on the integral representation of Dirac delta function) and use CAS to reformulate the related mathematical problem in terms of polynomial equations ready for numerical treatment. The complexity of the problem depends exponentially on coordination numbers of magnetic/nonmagnetic components, and by this, it makes the presented computer add approach the only possible method to treat complex multicomponent thin films and dilute multilayered structures. As two examples, we present the CAS add construction of related equations for binary alloys A^CB^1-C with structural disorder (Z^A = 2, Z^B = 4) and site-diluted thin film with n = 8 monatomic planes

Application of computer algebra systems (CAS) to symbolic construction of coupled equations for magnetic susceptibility of amorphous systems with different coordination numbers

We present the application of computer algebra systems to symbolic construction of two coupled systems of equations obtained from the exact Callen equation for a set of magnetizations and relevant magnetic susceptibilities in the case of complex amorphous ternary and binary diluted alloys like (ApB1-p)xC1-x with concentrations p and x, and different coordination numbers. The present paper is an extension of our previous one (Annales UMCS Informatica AI 5, 2006, 93) where the systems of polynomial equations for spontaneous magnetizations without external magnetic field have been obtained. Now, we introduce the external magnetic field and determine with the use of CAS full system of equations for both local magnetic susceptibilities and local magnetizations concerning all components of the complex magnetic systems. Finally, the numerical solutions of constructed coupled equations are found and discussed. The special attention is paid to the ferromagnetic region where the existence of low-temperature ordering transition, below the usual Curie phase transition, is searched as an interesting phenomenon from the technical point of view. The presented CAS added description can be understood as automatic constructor-simulator of relevant properties of amorphous alloys when the parameters of the system in question form an input to the described CAS-package

Multi-objective optimization of vehicle routing problem using evolutionary algorithm with memory

The idea of a new evolutionary algorithm with memory aspect included is proposed to find multiobjective optimized solution of vehicle routing problem with time windows. This algorithm uses population of agents that individually search for optimal solutions. The agent memory incorporates the process of learning from the experience of each individual agent as well as from the experience of the population. This algorithm uses crossover operation to define agents evolution. In the paper we choose as a base the Best Cost Route Crossover (BCRC) operator. This operator is well suited for VPRTW problems. However it does not treat both of parent symmetrically what is not natural for general evolutionary processes. The part of the paper is devoted to find an extension of the BCRC operator in order to improve inheritance of chromosomes from both of parents. Thus, the proposed evolutionary algorithm is implemented with use of two crossover operators: BCRC and its extended-modified version. We analyze the results obtained from both versions applied to Solomon’s and Gehring & Homberger instances. We conclude that the proposed method with modified version of BCRC operator gives statistically better results than those obtained using original BCRC. It seems that evolutionary algorithm with memory and modification of Best Cost Route Crossover Operator lead to very promising results when compared to the ones presented in the literature

Effect of pulsed magnetron sputtering process for the deposition of thin layers of nickel and nickel oxide

Magnetron sputtered nickel and nickel oxide films have been studied for various applications. We may find, among others, these films in electrochromic display devices, in resistive type gas sensors, as metal electrodes in electronic devices, in solar thermal absorbers. Pure nickel films deposited using PVD technique possess good corrosion and wear resistant properties. Magnetron sputtering has several advantages in film deposition (in comparison to other methods) such as relatively low heating temperature of the deposited substrate during sputtering process, high energy of sputtered atoms (about 10 eV) at the substrate, which influences positively the films adhesion. From application point of view, the most valuable feature of these films is the possibility of scaling target dimensions, which makes feasible the deposition on a several square meter surfaces. The improvement of magnetron sputtering devices design may influence positively the optimization of the deposition technology and its efficiency. The thin nickel and nickel oxide films were prepared by pulsed magnetron sputtering using original type WMK magnetron device. Ni (99.9 %) has been used as a sputtering target of 100 mm in diameter and different thicknesses (3 mm, 5 mm, and 6 mm). The distance between the substrate and target was the same in all experiments and equal to 120 mm. Argon and oxygen gases were introduced during the reactive process through needle gas valves at a total pressure of 0.4 Pa. The sputtering power, sputtering pressure and oxygen partial pressure have been used as technological knobs for deposition processes. The helpful tool for controlling the pulsed magnetron sputtering process was the original parameter of supply (so called circulating power). Results from our experiments showed that the deposition of Ni films is possible even from targets of 6 mm thickness. Deposition rate increased proportionally with the sputtering power. The aim of this work is to use the acquired expertise to develop an efficient technology of thin nickel oxide layers for electrochromic systems