The quasi chemical approximation (QCA) which hitherto is used for the calculations of thermodynam... more The quasi chemical approximation (QCA) which hitherto is used for the calculations of thermodynamic properties of binary alloys have been applied to the study of Bi–As2Te3 and Tl–As2Te3 ternary systems by assuming a pseudo binary configuration for the systems. The calculated values of the activity (am) and free energy of mixing Gm/RT show good agreement with experiment. The concentration fluctuation in the long wavelength limit Scc(0) and the Warren-Cowley short range order parameter for the first neighbour shell (a1) have been studied as a function of composition in the ternary alloys. The results indicate that the Tl–As2Te3 ternary alloy is more stable than the Bi–As2Te3 alloys. Scc(0) computed from the model are in good agreement with experimental values for the systems investigated and for both systems indicate that they are compound forming. In addition for the Bi–As2Te3, the concentration dependence of the concentration-concentration fluctuations shows a regular solution behav...
The quasichemical approximation (QCA) has been applied to study the asymmetry observed in the con... more The quasichemical approximation (QCA) has been applied to study the asymmetry observed in the concentration dependence of the thermodynamic properties of Na-Bi liquid alloys. The formation of a complex of the form Na 3 Bi has been assumed to calculate the concentration dependence of some thermodynamic properties, the long wavelength limit of the structure factors S CC (0), S NN (0) and S NC (0) and the Warren-Cowley short-range order parameter α 1 . The calculations indicate that with decreasing percentage of the more electronegative Bi component, there is an increasing tendency for phase separation. Size effect is negligible and thus we ascribe observed compound formation to electronegativity (EN) difference between Na and Bi. We expect that K, Rb and Cs-Bi liquid alloys would tend to be systems for which heterocoordination would dominate since in all cases the EN difference is larger. This deduction is in agreement with experimental observations.
The Lebowitz’s solution of the direct correlation function for binary mixtures with a square well... more The Lebowitz’s solution of the direct correlation function for binary mixtures with a square well attractive tail has been used to model the structure factors of Cu–Si and Ni–Si molten alloys. The computed total structure factors compare favourably with experiment. Results from structural studies indicate a need for a study of ordering phenomena in the system. This has been done by evaluating the long wavelength limit of the concentration-concentration fluctuations Scc(0). The computed Scc(0) was used in evaluating the Warren-Cowley short range order parameter α1 for the two alloys. Our calculations indicate that the two systems manifest compound forming tendencies throughout the concentration range. Cu–Si, however, exhibits a greater tendency for compound formation than Ni–Si molten alloys.
Numerical simulations have been used to investigate the synchronization behavior of a unidirectio... more Numerical simulations have been used to investigate the synchronization behavior of a unidirectionally coupled pair of double-well duffing oscillators (DDOs). The DDOs were simulated in their structurally stable chaotic zone and their state variables were found to completely synchronized. The essential feature of the transition to the synchronous state is shown to correspond to a boundary crisis in which the cross-well chaotic attractor is destroyed.
The quasichemical approximation (QCA) has been applied to study the asymmetry observed in the con... more The quasichemical approximation (QCA) has been applied to study the asymmetry observed in the concentration dependence of the thermodynamic properties of Na-Bi liquid alloys. The formation of a complex of the form Na 3 Bi has been assumed to calculate the concentration dependence of some thermodynamic properties, the long wavelength limit of the structure factors S CC (0), S NN (0) and S NC (0) and the Warren-Cowley short-range order parameter α 1 . The calculations indicate that with decreasing percentage of the more electronegative Bi component, there is an increasing tendency for phase separation. Size effect is negligible and thus we ascribe observed compound formation to electronegativity (EN) difference between Na and Bi. We expect that K, Rb and Cs-Bi liquid alloys would tend to be systems for which heterocoordination would dominate since in all cases the EN difference is larger. This deduction is in agreement with experimental observations.
ABSTRACT An accurate, efficient and robust numerical method for the solution of the optimized ran... more ABSTRACT An accurate, efficient and robust numerical method for the solution of the optimized random phase approximation (ORPA) of classical liquids is presented. The uniqueness of the solution of the ORPA is proved rigorously. The method, hinging on the characterization of the generating functional, improves significantly on previous algorithms. Higher accuracy is obtained by using the values of the unknown functions on the grid points as independent variables instead of the usual coefficients of an expansion in orthogonal polynomials. It is shown that minimizing a suitably modified functional with a conjugate-gradient algorithm results in a very efficient and robust algorithm.
The Lebowitz’s solution of the direct correlation function for binary mixtures with a square well... more The Lebowitz’s solution of the direct correlation function for binary mixtures with a square well attractive tail has been used to model the structure factors of Cu–Si and Ni–Si molten alloys. The computed total structure factors compare favourably with experiment. Results from structural studies indicate a need for a study of ordering phenomena in the system. This has been done by evaluating the long wavelength limit of the concentration-concentration fluctuations Scc(0). The computed Scc(0) was used in evaluating the Warren-Cowley short range order parameter α1 for the two alloys. Our calculations indicate that the two systems manifest compound forming tendencies throughout the concentration range. Cu–Si, however, exhibits a greater tendency for compound formation than Ni–Si molten alloys.
Numerical simulations have been used to investigate the synchronization behavior of a unidirectio... more Numerical simulations have been used to investigate the synchronization behavior of a unidirectionally coupled pair of double-well duffing oscillators (DDOs). The DDOs were simulated in their structurally stable chaotic zone and their state variables were found to completely synchronized. The essential feature of the transition to the synchronous state is shown to correspond to a boundary crisis in which the cross-well chaotic attractor is destroyed.
ABSTRACT The authors calculate the Helmholtz free energies of the liquid alkali metals at various... more ABSTRACT The authors calculate the Helmholtz free energies of the liquid alkali metals at various temperatures and those of several polyvalent metals (Mg, Cd, Al, In, Tl and Pb) near freezing, using the variational approach based on the Gibbs-Bogoliubov inequality in conjunction with the charged-hard-sphere reference fluid and with ab initio non-local pseudopotentials for the electron-ion interactions. The reference fluid introduces two variational parameters, i.e. the plasma coupling strength Gamma and the packing fraction eta , and is treated by a thermodynamically self-consistent approach which reduces to a highly accurate description of the one-component classical plasma for eta =0 and of the neutral-hard-sphere fluid for Gamma =0.
ABSTRACT An accurate, efficient and robust numerical method for the solution of the optimized ran... more ABSTRACT An accurate, efficient and robust numerical method for the solution of the optimized random phase approximation (ORPA) of classical liquids is presented. The uniqueness of the solution of the ORPA is proved rigorously. The method, hinging on the characterization of the generating functional, improves significantly on previous algorithms. Higher accuracy is obtained by using the values of the unknown functions on the grid points as independent variables instead of the usual coefficients of an expansion in orthogonal polynomials. It is shown that minimizing a suitably modified functional with a conjugate-gradient algorithm results in a very efficient and robust algorithm.
ABSTRACT The authors calculate the Helmholtz free energies of the liquid alkali metals at various... more ABSTRACT The authors calculate the Helmholtz free energies of the liquid alkali metals at various temperatures and those of several polyvalent metals (Mg, Cd, Al, In, Tl and Pb) near freezing, using the variational approach based on the Gibbs-Bogoliubov inequality in conjunction with the charged-hard-sphere reference fluid and with ab initio non-local pseudopotentials for the electron-ion interactions. The reference fluid introduces two variational parameters, i.e. the plasma coupling strength Gamma and the packing fraction eta , and is treated by a thermodynamically self-consistent approach which reduces to a highly accurate description of the one-component classical plasma for eta =0 and of the neutral-hard-sphere fluid for Gamma =0.
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2004
We study chaotic phase synchronization of unidirectionally coupled deterministic chaotic ratchets... more We study chaotic phase synchronization of unidirectionally coupled deterministic chaotic ratchets. The coupled ratchets were simulated in their chaotic states and perfect phase locking was observed as the coupling was gradually increased. We identified the region of phase synchronization for the ratchets and show that the transition to chaotic phase synchronization is via an interior crisis transition to strange attractor in the phase space.
First-order quasi-chemical theory has been used to explain the concentration dependence of the co... more First-order quasi-chemical theory has been used to explain the concentration dependence of the concentration-concentration fluctuations S CC (0), number-number fluctuations S NN (0) and number-concentration fluctuations S NC (0). To gain further insight into the nature of ordering in the alloy, the Warren-Cowley short range order parameter α 1 , and the chemical diffusion D have also been computed and their essential features explained. The assumption of a complex of the form In 4 Na enables to calculate these parameters and to reproduce the important features of compound formation and phase separation observed experimentally at different compositions in the alloy
The quasi chemical approximation (QCA) which hitherto is used for the calculations of thermodynam... more The quasi chemical approximation (QCA) which hitherto is used for the calculations of thermodynamic properties of binary alloys have been applied to the study of Bi–As2Te3 and Tl–As2Te3 ternary systems by assuming a pseudo binary configuration for the systems. The calculated values of the activity (am) and free energy of mixing Gm/RT show good agreement with experiment. The concentration fluctuation in the long wavelength limit Scc(0) and the Warren-Cowley short range order parameter for the first neighbour shell (a1) have been studied as a function of composition in the ternary alloys. The results indicate that the Tl–As2Te3 ternary alloy is more stable than the Bi–As2Te3 alloys. Scc(0) computed from the model are in good agreement with experimental values for the systems investigated and for both systems indicate that they are compound forming. In addition for the Bi–As2Te3, the concentration dependence of the concentration-concentration fluctuations shows a regular solution behav...
The quasichemical approximation (QCA) has been applied to study the asymmetry observed in the con... more The quasichemical approximation (QCA) has been applied to study the asymmetry observed in the concentration dependence of the thermodynamic properties of Na-Bi liquid alloys. The formation of a complex of the form Na 3 Bi has been assumed to calculate the concentration dependence of some thermodynamic properties, the long wavelength limit of the structure factors S CC (0), S NN (0) and S NC (0) and the Warren-Cowley short-range order parameter α 1 . The calculations indicate that with decreasing percentage of the more electronegative Bi component, there is an increasing tendency for phase separation. Size effect is negligible and thus we ascribe observed compound formation to electronegativity (EN) difference between Na and Bi. We expect that K, Rb and Cs-Bi liquid alloys would tend to be systems for which heterocoordination would dominate since in all cases the EN difference is larger. This deduction is in agreement with experimental observations.
The Lebowitz’s solution of the direct correlation function for binary mixtures with a square well... more The Lebowitz’s solution of the direct correlation function for binary mixtures with a square well attractive tail has been used to model the structure factors of Cu–Si and Ni–Si molten alloys. The computed total structure factors compare favourably with experiment. Results from structural studies indicate a need for a study of ordering phenomena in the system. This has been done by evaluating the long wavelength limit of the concentration-concentration fluctuations Scc(0). The computed Scc(0) was used in evaluating the Warren-Cowley short range order parameter α1 for the two alloys. Our calculations indicate that the two systems manifest compound forming tendencies throughout the concentration range. Cu–Si, however, exhibits a greater tendency for compound formation than Ni–Si molten alloys.
Numerical simulations have been used to investigate the synchronization behavior of a unidirectio... more Numerical simulations have been used to investigate the synchronization behavior of a unidirectionally coupled pair of double-well duffing oscillators (DDOs). The DDOs were simulated in their structurally stable chaotic zone and their state variables were found to completely synchronized. The essential feature of the transition to the synchronous state is shown to correspond to a boundary crisis in which the cross-well chaotic attractor is destroyed.
The quasichemical approximation (QCA) has been applied to study the asymmetry observed in the con... more The quasichemical approximation (QCA) has been applied to study the asymmetry observed in the concentration dependence of the thermodynamic properties of Na-Bi liquid alloys. The formation of a complex of the form Na 3 Bi has been assumed to calculate the concentration dependence of some thermodynamic properties, the long wavelength limit of the structure factors S CC (0), S NN (0) and S NC (0) and the Warren-Cowley short-range order parameter α 1 . The calculations indicate that with decreasing percentage of the more electronegative Bi component, there is an increasing tendency for phase separation. Size effect is negligible and thus we ascribe observed compound formation to electronegativity (EN) difference between Na and Bi. We expect that K, Rb and Cs-Bi liquid alloys would tend to be systems for which heterocoordination would dominate since in all cases the EN difference is larger. This deduction is in agreement with experimental observations.
ABSTRACT An accurate, efficient and robust numerical method for the solution of the optimized ran... more ABSTRACT An accurate, efficient and robust numerical method for the solution of the optimized random phase approximation (ORPA) of classical liquids is presented. The uniqueness of the solution of the ORPA is proved rigorously. The method, hinging on the characterization of the generating functional, improves significantly on previous algorithms. Higher accuracy is obtained by using the values of the unknown functions on the grid points as independent variables instead of the usual coefficients of an expansion in orthogonal polynomials. It is shown that minimizing a suitably modified functional with a conjugate-gradient algorithm results in a very efficient and robust algorithm.
The Lebowitz’s solution of the direct correlation function for binary mixtures with a square well... more The Lebowitz’s solution of the direct correlation function for binary mixtures with a square well attractive tail has been used to model the structure factors of Cu–Si and Ni–Si molten alloys. The computed total structure factors compare favourably with experiment. Results from structural studies indicate a need for a study of ordering phenomena in the system. This has been done by evaluating the long wavelength limit of the concentration-concentration fluctuations Scc(0). The computed Scc(0) was used in evaluating the Warren-Cowley short range order parameter α1 for the two alloys. Our calculations indicate that the two systems manifest compound forming tendencies throughout the concentration range. Cu–Si, however, exhibits a greater tendency for compound formation than Ni–Si molten alloys.
Numerical simulations have been used to investigate the synchronization behavior of a unidirectio... more Numerical simulations have been used to investigate the synchronization behavior of a unidirectionally coupled pair of double-well duffing oscillators (DDOs). The DDOs were simulated in their structurally stable chaotic zone and their state variables were found to completely synchronized. The essential feature of the transition to the synchronous state is shown to correspond to a boundary crisis in which the cross-well chaotic attractor is destroyed.
ABSTRACT The authors calculate the Helmholtz free energies of the liquid alkali metals at various... more ABSTRACT The authors calculate the Helmholtz free energies of the liquid alkali metals at various temperatures and those of several polyvalent metals (Mg, Cd, Al, In, Tl and Pb) near freezing, using the variational approach based on the Gibbs-Bogoliubov inequality in conjunction with the charged-hard-sphere reference fluid and with ab initio non-local pseudopotentials for the electron-ion interactions. The reference fluid introduces two variational parameters, i.e. the plasma coupling strength Gamma and the packing fraction eta , and is treated by a thermodynamically self-consistent approach which reduces to a highly accurate description of the one-component classical plasma for eta =0 and of the neutral-hard-sphere fluid for Gamma =0.
ABSTRACT An accurate, efficient and robust numerical method for the solution of the optimized ran... more ABSTRACT An accurate, efficient and robust numerical method for the solution of the optimized random phase approximation (ORPA) of classical liquids is presented. The uniqueness of the solution of the ORPA is proved rigorously. The method, hinging on the characterization of the generating functional, improves significantly on previous algorithms. Higher accuracy is obtained by using the values of the unknown functions on the grid points as independent variables instead of the usual coefficients of an expansion in orthogonal polynomials. It is shown that minimizing a suitably modified functional with a conjugate-gradient algorithm results in a very efficient and robust algorithm.
ABSTRACT The authors calculate the Helmholtz free energies of the liquid alkali metals at various... more ABSTRACT The authors calculate the Helmholtz free energies of the liquid alkali metals at various temperatures and those of several polyvalent metals (Mg, Cd, Al, In, Tl and Pb) near freezing, using the variational approach based on the Gibbs-Bogoliubov inequality in conjunction with the charged-hard-sphere reference fluid and with ab initio non-local pseudopotentials for the electron-ion interactions. The reference fluid introduces two variational parameters, i.e. the plasma coupling strength Gamma and the packing fraction eta , and is treated by a thermodynamically self-consistent approach which reduces to a highly accurate description of the one-component classical plasma for eta =0 and of the neutral-hard-sphere fluid for Gamma =0.
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2004
We study chaotic phase synchronization of unidirectionally coupled deterministic chaotic ratchets... more We study chaotic phase synchronization of unidirectionally coupled deterministic chaotic ratchets. The coupled ratchets were simulated in their chaotic states and perfect phase locking was observed as the coupling was gradually increased. We identified the region of phase synchronization for the ratchets and show that the transition to chaotic phase synchronization is via an interior crisis transition to strange attractor in the phase space.
First-order quasi-chemical theory has been used to explain the concentration dependence of the co... more First-order quasi-chemical theory has been used to explain the concentration dependence of the concentration-concentration fluctuations S CC (0), number-number fluctuations S NN (0) and number-concentration fluctuations S NC (0). To gain further insight into the nature of ordering in the alloy, the Warren-Cowley short range order parameter α 1 , and the chemical diffusion D have also been computed and their essential features explained. The assumption of a complex of the form In 4 Na enables to calculate these parameters and to reproduce the important features of compound formation and phase separation observed experimentally at different compositions in the alloy
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