AREZKI BELDJENNA - Academia.edu (original) (raw)

Papers by AREZKI BELDJENNA

Research paper thumbnail of Continuous Displacement of “Lattice” Atoms

MRS Proceedings, 1992

In the existing CVM (cluster variation method) formulations, atoms are placed on lattice points. ... more In the existing CVM (cluster variation method) formulations, atoms are placed on lattice points. A new formulation is proposed in which atoms can be displaced from a lattice point. The displaced position is written by a vector r, which varies continuously. This model is treated in the CVM framework by regarding an atom at r as a species r. The probability of finding an atom displaced at r in dr is written as f(r) dr, and the corresponding pair probability is written as g(r,, r2) dr, dr,. We formulate using the pair approximation of the CVM in the present paper. The interatomic potential is assumed given, for example as the Lennard-Jones form. The entropy is written in terms of f(r) and g(r,, r2) using the CVM formula. The special feature of the present formulation, which is different from the prevailing no-displacement cases of the CVM, is that rotational symmetry of the lattice is to be satisfied by the f(r) and g(r,, rz) functions. After the general equations are written in the continuum vector form and in the integral equation formulation, examples of a single-component system are solved by changing integrals into summations over finite intervals. Further we construct simulations of displacement patterns in such a way that the pattern satisfies the pair probability distribution which has been calculated as the output of the CVM analysis. The simulated pattern shows the wavy behavior of phonons.

Research paper thumbnail of Theoretical investigation of the thermodynamic stability of nano-scale systems—II: Relaxation of a junction profile

Nanostructured Materials, Mar 1, 1995

Nonlinear relaxation of a sharp density profile typical of layered semiconductor junctions is stu... more Nonlinear relaxation of a sharp density profile typical of layered semiconductor junctions is studied using an irreversible statistical mechanical technique, the Path Probability Method, taking into account nearest neighbor correlations. The vacancy mechanism and the pair approximation are used. It isfound that atoms near a sharp density profile diffuse up against the density gradient. Our numerical examples demonstrate that in this range there is a possibility that the atom flux can go either down along or up against the local chemical potential #.) gradient. However, the calculations do not deny the possibility of modifying the definition of p in such a way that the atoms always flow toward the direction of decreasing 6~.

Research paper thumbnail of Continuous Displacement of “Lattice” Atoms

NATO advanced study institutes series, 1994

In the existing CVM (cluster variation method) formulations, atoms are placed on lattice points. ... more In the existing CVM (cluster variation method) formulations, atoms are placed on lattice points. A new formulation is proposed in which atoms can be displaced from a lattice point. The displaced position is written by a vector r, which varies continuously. This model is treated in the CVM framework by regarding an atom at r as a species r. The probability of finding an atom displaced at r in dr is written as f(r) dr, and the corresponding pair probability is written as g(r,, r2) dr, dr,. We formulate using the pair approximation of the CVM in the present paper. The interatomic potential is assumed given, for example as the Lennard-Jones form. The entropy is written in terms of f(r) and g(r,, r2) using the CVM formula. The special feature of the present formulation, which is different from the prevailing no-displacement cases of the CVM, is that rotational symmetry of the lattice is to be satisfied by the f(r) and g(r,, rz) functions. After the general equations are written in the continuum vector form and in the integral equation formulation, examples of a single-component system are solved by changing integrals into summations over finite intervals. Further we construct simulations of displacement patterns in such a way that the pattern satisfies the pair probability distribution which has been calculated as the output of the CVM analysis. The simulated pattern shows the wavy behavior of phonons.

Research paper thumbnail of Theoretical investigation of the thermodynamic structures and kinetic water-exchange reactions of aqueous Al(III)–salicylate complexes

Geochimica et Cosmochimica Acta, 2013

Density functional theory (DFT) calculations were performed on the structures and water-exchange ... more Density functional theory (DFT) calculations were performed on the structures and water-exchange reactions of aqueous Al(III)-salicylate complexes. Based on the four models (gas phase (GP); polarizable continuum model (PCM), which estimates the bulk solvent effect; supermolecule model (SM), which considers the explicit solvent effect, and supermolecule-polarizable continuum model (SM-PCM), which accounts for both types of solvent effects), we systematically conducted this study by examining three different properties of the complexes. (1) The microscopic properties of the aqueous Al(III)-salicylate complexes were studied by optimizing their various structures (including the possible 1:1 mono-and bidentate complexes, cis and trans isomers of the 1:2 bidentate complexes and 1:3 bidentate complexes) at the B3LYP/6-311+G(d, p) level. (2) The 27 Al and 13 C NMR chemical shifts were calculated using the GIAO method at the HF/6-311+G(d, p) level. The calculation results show that the values obtained with the SM-PCM models are in good agreement with the experimental data available in the literature, indicating that the models we employed are appropriate for Al(III)-salicylate complexes. (3) The water-exchange reactions of 1:1 mono-and bidentate Al(III)-salicylate complexes were simulated using supermolecule models at the B3LYP/6-311+G(d, p) level. The logarithm of the water-exchange rate constant (log k ex) of the 1:1 bidentate complex predicted using the "log k ex-d Al-OH2 " correlation is 4.0, which is in good agreement with the experimental value of 3.7, whereas the calculated range of log k ex of the 1:1 monodentate complexes is 1.3-1.9. By effectively combining the results for the thermodynamic static structures with the simulations of the kinetic water-exchange reactions, this work promotes further understanding of the configurations and formation mechanism of Al(III)-salicylate complexes.

Research paper thumbnail of The Shapes of Random Walks: Development of 1/D Expansion

Research paper thumbnail of The Shapes of Random Walks with Fixed End-to-End Distance

Woodward Conference, 1990

Fixed length random walks embedded in d spatial dimensions are discussed. As a representation of ... more Fixed length random walks embedded in d spatial dimensions are discussed. As a representation of polymers, they correspond to long chain molecules whose heads and tails are fixed in space. An exact analytical expression for the asphericity is presented that is valid in arbitrary spatial dimensionality. We also present expressions for the average principal radii of gyration to order 0(1/d). These expressions recover the results for both unrestricted open and closed random walks.

Research paper thumbnail of Atomic Relaxation of a Junction Profile

MRS Proceedings, 1993

Nonlinear relaxation of a sharp concentration profile typical in layered semiconductor junctions ... more Nonlinear relaxation of a sharp concentration profile typical in layered semiconductor junctions is investigated using the Path Probability Method (PPM) of irreversible statistical mechanics. We employ the vacancy mechanism for atomic migration and the pair approximation for the statistical treatment. The PPM is a microscopic method, from which we can derive macroscopic parameters. Our results show that at the initial stage of the relaxation of a sharp concentration profile, atoms near the junction may diffuse up against the concentration gradient. More surprisingly, our numerical examples convincingly demonstrate that the atom flux goes up against the local chemical potential gradient near a sharp profile, indicating that in such highly nonlinear regime the usual linear diffusion theory in which the atom flux is linearly proportional to the chemical potential gradient breaks down. It is shown that the cause of the uphill diffusion is the repulsion among different species, which is also the physical origin of the square gradient term.

Research paper thumbnail of Shapes of random walks at order 1/d 2

Journal of Physics A: Mathematical and General, 1991

The authors calculate various parameters which characterize the size and shape of random walks ut... more The authors calculate various parameters which characterize the size and shape of random walks utilizing a recently developed 1/d expansion technique, where d is the spatial dimension in which the random walk takes place. A new procedure for extracting the averages of the principal radii of gyration is presented and the calculation is carried out to order 1/d2, which is one order higher than previous work. Comparison with the results of numerical simulations provides new insights regarding the accuracy of the 1/d expansion procedure.

Research paper thumbnail of The shapes and sizes of two-dimensional pressurized self-intersecting rings, as models for two-dimensional vesicles

Journal of Physics A: Mathematical and General, 1993

... self-intersecting rings, as models for two-dimensional vesicles George Gasparii, Joseph Rudni... more ... self-intersecting rings, as models for two-dimensional vesicles George Gasparii, Joseph Rudnickf and Arezki Beldjenna$ t Physics Department, University of California, Santa Cruz, Santa Cruz. CA 95064, USA I Department of Physics, UCLA. Los Angeles, CA 90024-1547, USA ...

Research paper thumbnail of The shapes of high-dimensional random walks

Journal of Physics A: Mathematical and General, 1987

The individual principal radii of gyration are computed for unrestricted random walks in a large ... more The individual principal radii of gyration are computed for unrestricted random walks in a large number of spatial dimensions. A low order expansion in one over the dimensionality yields useful information regarding the distribution and average of these measures of the extent and spatial anisotropy of high-dimensional random walks. Such an expansion may well prove useful in the study of the shapes of other random fractal objects.

Research paper thumbnail of The shapes of open and closed random walks: a 1/d expansion

Journal of Physics A: Mathematical and General, 1987

A new technique for calculating the shapes of random walks is presented. The method is used to de... more A new technique for calculating the shapes of random walks is presented. The method is used to derive an exact analytical expression for the asphericity of an unrestricted closed or ring walk embedded in d spatial dimensions. A graphical procedure is developed to systematise a 1/d series expansion for the individual principal radii of gyration and their respective probability distribution functions P(R2i)(1<or=i<or=d). The average principal radii of gyration are calculated to O(1/d2) for both open and closed walks and selected terms in the 1/d expansion are summed to all orders in 1/d in the determination of P(R2i). This leads to an explicit analytical form for P(R2i) for open walks. The distribution of the largest eigenvalue is compared with a distribution obtained from numerical simulations of walks in three dimensions. The agreement between the two is extremely good. Other predictions for various parameters that characterise the average shape of open and closed walks in three dimensions are also found to agree remarkably well with the results of simulations, the error being of the order of 5%.

Research paper thumbnail of Continuous displacement of “lattice” atoms

Physica A: Statistical Mechanics and its Applications, 1992

In the existing CVM (cluster variation method) formulations, atoms are placed on lattice points. ... more In the existing CVM (cluster variation method) formulations, atoms are placed on lattice points. A new formulation is proposed in which atoms can be displaced from a lattice point. The displaced position is written by a vector r, which varies continuously. This model is treated in the CVM framework by regarding an atom at r as a species r. The probability of finding an atom displaced at r in dr is written as f(r) dr, and the corresponding pair probability is written as g(r,, r2) dr, dr,. We formulate using the pair approximation of the CVM in the present paper. The interatomic potential is assumed given, for example as the Lennard-Jones form. The entropy is written in terms of f(r) and g(r,, r2) using the CVM formula. The special feature of the present formulation, which is different from the prevailing no-displacement cases of the CVM, is that rotational symmetry of the lattice is to be satisfied by the f(r) and g(r,, rz) functions. After the general equations are written in the continuum vector form and in the integral equation formulation, examples of a single-component system are solved by changing integrals into summations over finite intervals. Further we construct simulations of displacement patterns in such a way that the pattern satisfies the pair probability distribution which has been calculated as the output of the CVM analysis. The simulated pattern shows the wavy behavior of phonons.

Research paper thumbnail of Continuous Displacement of “Lattice” Atoms

MRS Proceedings, 1992

In the existing CVM (cluster variation method) formulations, atoms are placed on lattice points. ... more In the existing CVM (cluster variation method) formulations, atoms are placed on lattice points. A new formulation is proposed in which atoms can be displaced from a lattice point. The displaced position is written by a vector r, which varies continuously. This model is treated in the CVM framework by regarding an atom at r as a species r. The probability of finding an atom displaced at r in dr is written as f(r) dr, and the corresponding pair probability is written as g(r,, r2) dr, dr,. We formulate using the pair approximation of the CVM in the present paper. The interatomic potential is assumed given, for example as the Lennard-Jones form. The entropy is written in terms of f(r) and g(r,, r2) using the CVM formula. The special feature of the present formulation, which is different from the prevailing no-displacement cases of the CVM, is that rotational symmetry of the lattice is to be satisfied by the f(r) and g(r,, rz) functions. After the general equations are written in the continuum vector form and in the integral equation formulation, examples of a single-component system are solved by changing integrals into summations over finite intervals. Further we construct simulations of displacement patterns in such a way that the pattern satisfies the pair probability distribution which has been calculated as the output of the CVM analysis. The simulated pattern shows the wavy behavior of phonons.

Research paper thumbnail of Theoretical investigation of the thermodynamic stability of nano-scale systems—II: Relaxation of a junction profile

Nanostructured Materials, Mar 1, 1995

Nonlinear relaxation of a sharp density profile typical of layered semiconductor junctions is stu... more Nonlinear relaxation of a sharp density profile typical of layered semiconductor junctions is studied using an irreversible statistical mechanical technique, the Path Probability Method, taking into account nearest neighbor correlations. The vacancy mechanism and the pair approximation are used. It isfound that atoms near a sharp density profile diffuse up against the density gradient. Our numerical examples demonstrate that in this range there is a possibility that the atom flux can go either down along or up against the local chemical potential #.) gradient. However, the calculations do not deny the possibility of modifying the definition of p in such a way that the atoms always flow toward the direction of decreasing 6~.

Research paper thumbnail of Continuous Displacement of “Lattice” Atoms

NATO advanced study institutes series, 1994

In the existing CVM (cluster variation method) formulations, atoms are placed on lattice points. ... more In the existing CVM (cluster variation method) formulations, atoms are placed on lattice points. A new formulation is proposed in which atoms can be displaced from a lattice point. The displaced position is written by a vector r, which varies continuously. This model is treated in the CVM framework by regarding an atom at r as a species r. The probability of finding an atom displaced at r in dr is written as f(r) dr, and the corresponding pair probability is written as g(r,, r2) dr, dr,. We formulate using the pair approximation of the CVM in the present paper. The interatomic potential is assumed given, for example as the Lennard-Jones form. The entropy is written in terms of f(r) and g(r,, r2) using the CVM formula. The special feature of the present formulation, which is different from the prevailing no-displacement cases of the CVM, is that rotational symmetry of the lattice is to be satisfied by the f(r) and g(r,, rz) functions. After the general equations are written in the continuum vector form and in the integral equation formulation, examples of a single-component system are solved by changing integrals into summations over finite intervals. Further we construct simulations of displacement patterns in such a way that the pattern satisfies the pair probability distribution which has been calculated as the output of the CVM analysis. The simulated pattern shows the wavy behavior of phonons.

Research paper thumbnail of Theoretical investigation of the thermodynamic structures and kinetic water-exchange reactions of aqueous Al(III)–salicylate complexes

Geochimica et Cosmochimica Acta, 2013

Density functional theory (DFT) calculations were performed on the structures and water-exchange ... more Density functional theory (DFT) calculations were performed on the structures and water-exchange reactions of aqueous Al(III)-salicylate complexes. Based on the four models (gas phase (GP); polarizable continuum model (PCM), which estimates the bulk solvent effect; supermolecule model (SM), which considers the explicit solvent effect, and supermolecule-polarizable continuum model (SM-PCM), which accounts for both types of solvent effects), we systematically conducted this study by examining three different properties of the complexes. (1) The microscopic properties of the aqueous Al(III)-salicylate complexes were studied by optimizing their various structures (including the possible 1:1 mono-and bidentate complexes, cis and trans isomers of the 1:2 bidentate complexes and 1:3 bidentate complexes) at the B3LYP/6-311+G(d, p) level. (2) The 27 Al and 13 C NMR chemical shifts were calculated using the GIAO method at the HF/6-311+G(d, p) level. The calculation results show that the values obtained with the SM-PCM models are in good agreement with the experimental data available in the literature, indicating that the models we employed are appropriate for Al(III)-salicylate complexes. (3) The water-exchange reactions of 1:1 mono-and bidentate Al(III)-salicylate complexes were simulated using supermolecule models at the B3LYP/6-311+G(d, p) level. The logarithm of the water-exchange rate constant (log k ex) of the 1:1 bidentate complex predicted using the "log k ex-d Al-OH2 " correlation is 4.0, which is in good agreement with the experimental value of 3.7, whereas the calculated range of log k ex of the 1:1 monodentate complexes is 1.3-1.9. By effectively combining the results for the thermodynamic static structures with the simulations of the kinetic water-exchange reactions, this work promotes further understanding of the configurations and formation mechanism of Al(III)-salicylate complexes.

Research paper thumbnail of The Shapes of Random Walks: Development of 1/D Expansion

Research paper thumbnail of The Shapes of Random Walks with Fixed End-to-End Distance

Woodward Conference, 1990

Fixed length random walks embedded in d spatial dimensions are discussed. As a representation of ... more Fixed length random walks embedded in d spatial dimensions are discussed. As a representation of polymers, they correspond to long chain molecules whose heads and tails are fixed in space. An exact analytical expression for the asphericity is presented that is valid in arbitrary spatial dimensionality. We also present expressions for the average principal radii of gyration to order 0(1/d). These expressions recover the results for both unrestricted open and closed random walks.

Research paper thumbnail of Atomic Relaxation of a Junction Profile

MRS Proceedings, 1993

Nonlinear relaxation of a sharp concentration profile typical in layered semiconductor junctions ... more Nonlinear relaxation of a sharp concentration profile typical in layered semiconductor junctions is investigated using the Path Probability Method (PPM) of irreversible statistical mechanics. We employ the vacancy mechanism for atomic migration and the pair approximation for the statistical treatment. The PPM is a microscopic method, from which we can derive macroscopic parameters. Our results show that at the initial stage of the relaxation of a sharp concentration profile, atoms near the junction may diffuse up against the concentration gradient. More surprisingly, our numerical examples convincingly demonstrate that the atom flux goes up against the local chemical potential gradient near a sharp profile, indicating that in such highly nonlinear regime the usual linear diffusion theory in which the atom flux is linearly proportional to the chemical potential gradient breaks down. It is shown that the cause of the uphill diffusion is the repulsion among different species, which is also the physical origin of the square gradient term.

Research paper thumbnail of Shapes of random walks at order 1/d 2

Journal of Physics A: Mathematical and General, 1991

The authors calculate various parameters which characterize the size and shape of random walks ut... more The authors calculate various parameters which characterize the size and shape of random walks utilizing a recently developed 1/d expansion technique, where d is the spatial dimension in which the random walk takes place. A new procedure for extracting the averages of the principal radii of gyration is presented and the calculation is carried out to order 1/d2, which is one order higher than previous work. Comparison with the results of numerical simulations provides new insights regarding the accuracy of the 1/d expansion procedure.

Research paper thumbnail of The shapes and sizes of two-dimensional pressurized self-intersecting rings, as models for two-dimensional vesicles

Journal of Physics A: Mathematical and General, 1993

... self-intersecting rings, as models for two-dimensional vesicles George Gasparii, Joseph Rudni... more ... self-intersecting rings, as models for two-dimensional vesicles George Gasparii, Joseph Rudnickf and Arezki Beldjenna$ t Physics Department, University of California, Santa Cruz, Santa Cruz. CA 95064, USA I Department of Physics, UCLA. Los Angeles, CA 90024-1547, USA ...

Research paper thumbnail of The shapes of high-dimensional random walks

Journal of Physics A: Mathematical and General, 1987

The individual principal radii of gyration are computed for unrestricted random walks in a large ... more The individual principal radii of gyration are computed for unrestricted random walks in a large number of spatial dimensions. A low order expansion in one over the dimensionality yields useful information regarding the distribution and average of these measures of the extent and spatial anisotropy of high-dimensional random walks. Such an expansion may well prove useful in the study of the shapes of other random fractal objects.

Research paper thumbnail of The shapes of open and closed random walks: a 1/d expansion

Journal of Physics A: Mathematical and General, 1987

A new technique for calculating the shapes of random walks is presented. The method is used to de... more A new technique for calculating the shapes of random walks is presented. The method is used to derive an exact analytical expression for the asphericity of an unrestricted closed or ring walk embedded in d spatial dimensions. A graphical procedure is developed to systematise a 1/d series expansion for the individual principal radii of gyration and their respective probability distribution functions P(R2i)(1<or=i<or=d). The average principal radii of gyration are calculated to O(1/d2) for both open and closed walks and selected terms in the 1/d expansion are summed to all orders in 1/d in the determination of P(R2i). This leads to an explicit analytical form for P(R2i) for open walks. The distribution of the largest eigenvalue is compared with a distribution obtained from numerical simulations of walks in three dimensions. The agreement between the two is extremely good. Other predictions for various parameters that characterise the average shape of open and closed walks in three dimensions are also found to agree remarkably well with the results of simulations, the error being of the order of 5%.

Research paper thumbnail of Continuous displacement of “lattice” atoms

Physica A: Statistical Mechanics and its Applications, 1992

In the existing CVM (cluster variation method) formulations, atoms are placed on lattice points. ... more In the existing CVM (cluster variation method) formulations, atoms are placed on lattice points. A new formulation is proposed in which atoms can be displaced from a lattice point. The displaced position is written by a vector r, which varies continuously. This model is treated in the CVM framework by regarding an atom at r as a species r. The probability of finding an atom displaced at r in dr is written as f(r) dr, and the corresponding pair probability is written as g(r,, r2) dr, dr,. We formulate using the pair approximation of the CVM in the present paper. The interatomic potential is assumed given, for example as the Lennard-Jones form. The entropy is written in terms of f(r) and g(r,, r2) using the CVM formula. The special feature of the present formulation, which is different from the prevailing no-displacement cases of the CVM, is that rotational symmetry of the lattice is to be satisfied by the f(r) and g(r,, rz) functions. After the general equations are written in the continuum vector form and in the integral equation formulation, examples of a single-component system are solved by changing integrals into summations over finite intervals. Further we construct simulations of displacement patterns in such a way that the pattern satisfies the pair probability distribution which has been calculated as the output of the CVM analysis. The simulated pattern shows the wavy behavior of phonons.