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The Principles and Illustration of an Advantageous Method of Arranging the Differences of Logarithms, on Lines Graduated for the Purpose of Computation. By Mr. William Nicholson; Communicated by Sir Joseph Banks, Bart. P. R. S Nicholson, W.; Banks, J Philosophical Transactions of the Royal Society of London (1776-1886). 1787-01-01. 77:246–252

"The Principles and Illustration of an Advantageous Method of Arranging the Differences of Logarithms, on Lines Graduated for the Purpose of Computation. By Mr. William Nicholson; Communicated by Sir Joseph Banks, Bart. P. R. S." is an article from Philosophical Transactions of the Royal Society of London, Volume 77 . View more articles from Philosophical Transactions of the Royal Society of London . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-106724

"The Principles and Illustration of an Advantageous Method of Arranging the Differences of Logarithms, on Lines Graduated for the Purpose of Computation. By Mr. William Nicholson; Communicated by Sir Joseph Banks, Bart. P. R. S." is an article from Philosophical Transactions of the Royal Society of London, Volume 77 . View more articles from Philosophical Transactions of the Royal Society of London . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-106724

We investigate the electronic structure of the transition-metal oxide YVO3 by a hybrid first-principles scheme. The density-functional theory with the local-density-approximation by using the local muffin-tin orbital basis is applied to derive the whole band structure. The electron degrees of freedom far from the Fermi level are eliminated by a downfolding procedure leaving only the V 3d t2g Wannier band as the low-energy degrees of freedom, for which a low-energy effective model is constructed. This low-energy effective Hamiltonian is solved exactly by the path-integral renormalization group method. It is shown that the ground state has the G-type spin and the C-type orbital ordering in agreement with experimental indications. The indirect charge gap is estimated to be around 0.7 eV, which prominently improves the previous estimates by other conventional methods.

In this paper, we propose a first principles computation method for g-factor tensor, which not only gives comparable results with experiments but also establishes a clear physical picture of Zeeman effect in materials. In our method, the Hilbert space of the electronic states is treated as a direct product of "inner" space and "orbital" space, which are spanned by Bloch wave functions and envelope functions respectively. Correspondingly, vector-potential is divided into a periodic part acting only in inner space and a non-periodic part acting only in orbital space. With the above flamework we define the g-factors as coupling coefficients between inner space and magnetic field. By the method we developed, we have further computed the g-factors of bismuth and Bi$_2$Se$_3$ and got satisfactory results, which are in good agreement with the experimental data.

We present a perturbative treatment of the response properties of insulating crystals under a dc bias field, and use this to study the effects of such bias fields on the Born effective charge tensor and dielectric tensor of insulators. We start out by expanding a variational field-dependent total-energy functional with respect to the electric field within the framework of density-functional perturbation theory. The second-order term in the expansion of the total energy is then minimized with respect to the first-order wave functions, from which the Born effective charge tensor and dielectric tensor are easily computed. We demonstrate an implementation of the method and perform illustrative calculations for the III-V semiconductors AlAs and GaAs under finite bias field.

The high-performance potential of parallel and distributed computation can only be realized with significant computation speed-ups from the coordinated action of many processors. A basic problem that has to be addressed, in order to realize this potential, is the unreliability of the resulting (highly complex) systems of many processors. The research of N00014-91-J-1613 'Principles of Fault-Tolerant and Efficient Parallel Computation bas focused, primarily. on the algorithmic Principles of fault-tolerant and efficient parallel computing. The desirable combination of reliability and performance is nontrivial since efficiency implies removing redundancy, whereas fault-tolerance requires adding some redundancy to computations

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We present a perturbative method for calculating phonon properties of an insulator in the presence of a finite electric field. The starting point is a variational total-energy functional with a field-coupling term that represents the effect of the electric field. This total-energy functional is expanded in small atomic displacements within the framework of density-functional perturbation theory. The linear response of field-polarized Bloch functions to atomic displacements is obtained by minimizing the second-order derivatives of the total-energy functional. In the general case of nonzero phonon wavevector, there is a subtle interplay between the couplings between neighboring k-points introduced by the presence of the electric field in the reference state, and further-neighbor k-point couplings determined by the wavevector of the phonon perturbation. As a result, terms arise in the perturbation expansion that take the form of four-sided loops in k-space. We implement the method in the {\tt ABINIT} code and perform illustrative calculations of the field-dependent phonon frequencies for III-V semiconductors.

We present a perturbative method for calculating phonon properties of an insulator in the presence of a finite electric field. The starting point is a variational total-energy functional with a field-coupling term that represents the effect of the electric field. This total-energy functional is expanded in small atomic displacements within the framework of density-functional perturbation theory. The linear response of field-polarized Bloch functions to atomic displacements is obtained by minimizing the second-order derivatives of the total-energy functional. In the general case of nonzero phonon wavevector, there is a subtle interplay between the couplings between neighboring k-points introduced by the presence of the electric field in the reference state, and further-neighbor k-point couplings determined by the wavevector of the phonon perturbation. As a result, terms arise in the perturbation expansion that take the form of four-sided loops in k-space. We implement the method in the {\tt ABINIT} code and perform illustrative calculations of the field-dependent phonon frequencies for III-V semiconductors.

We present a perturbative method for calculating phonon properties of an insulator in the presence of a finite electric field. The starting point is a variational total-energy functional with a field-coupling term that represents the effect of the electric field. This total-energy functional is expanded in small atomic displacements within the framework of density-functional perturbation theory. The linear response of field-polarized Bloch functions to atomic displacements is obtained by minimizing the second-order derivatives of the total-energy functional. In the general case of nonzero phonon wavevector, there is a subtle interplay between the couplings between neighboring k-points introduced by the presence of the electric field in the reference state, and further-neighbor k-point couplings determined by the wavevector of the phonon perturbation. As a result, terms arise in the perturbation expansion that take the form of four-sided loops in k-space. We implement the method in the {\tt ABINIT} code and perform illustrative calculations of the field-dependent phonon frequencies for III-V semiconductors.

We present a perturbative method for calculating phonon properties of an insulator in the presence of a finite electric field. The starting point is a variational total-energy functional with a field-coupling term that represents the effect of the electric field. This total-energy functional is expanded in small atomic displacements within the framework of density-functional perturbation theory. The linear response of field-polarized Bloch functions to atomic displacements is obtained by minimizing the second-order derivatives of the total-energy functional. In the general case of nonzero phonon wavevector, there is a subtle interplay between the couplings between neighboring k-points introduced by the presence of the electric field in the reference state, and further-neighbor k-point couplings determined by the wavevector of the phonon perturbation. As a result, terms arise in the perturbation expansion that take the form of four-sided loops in k-space. We implement the method in the {\tt ABINIT} code and perform illustrative calculations of the field-dependent phonon frequencies for III-V semiconductors.

We present a perturbative method for calculating phonon properties of an insulator in the presence of a finite electric field. The starting point is a variational total-energy functional with a field-coupling term that represents the effect of the electric field. This total-energy functional is expanded in small atomic displacements within the framework of density-functional perturbation theory. The linear response of field-polarized Bloch functions to atomic displacements is obtained by minimizing the second-order derivatives of the total-energy functional. In the general case of nonzero phonon wavevector, there is a subtle interplay between the couplings between neighboring k-points introduced by the presence of the electric field in the reference state, and further-neighbor k-point couplings determined by the wavevector of the phonon perturbation. As a result, terms arise in the perturbation expansion that take the form of four-sided loops in k-space. We implement the method in the {\tt ABINIT} code and perform illustrative calculations of the field-dependent phonon frequencies for III-V semiconductors.

We present a perturbative method for calculating phonon properties of an insulator in the presence of a finite electric field. The starting point is a variational total-energy functional with a field-coupling term that represents the effect of the electric field. This total-energy functional is expanded in small atomic displacements within the framework of density-functional perturbation theory. The linear response of field-polarized Bloch functions to atomic displacements is obtained by minimizing the second-order derivatives of the total-energy functional. In the general case of nonzero phonon wavevector, there is a subtle interplay between the couplings between neighboring k-points introduced by the presence of the electric field in the reference state, and further-neighbor k-point couplings determined by the wavevector of the phonon perturbation. As a result, terms arise in the perturbation expansion that take the form of four-sided loops in k-space. We implement the method in the {\tt ABINIT} code and perform illustrative calculations of the field-dependent phonon frequencies for III-V semiconductors.

We present a perturbative method for calculating phonon properties of an insulator in the presence of a finite electric field. The starting point is a variational total-energy functional with a field-coupling term that represents the effect of the electric field. This total-energy functional is expanded in small atomic displacements within the framework of density-functional perturbation theory. The linear response of field-polarized Bloch functions to atomic displacements is obtained by minimizing the second-order derivatives of the total-energy functional. In the general case of nonzero phonon wavevector, there is a subtle interplay between the couplings between neighboring k-points introduced by the presence of the electric field in the reference state, and further-neighbor k-point couplings determined by the wavevector of the phonon perturbation. As a result, terms arise in the perturbation expansion that take the form of four-sided loops in k-space. We implement the method in the {\tt ABINIT} code and perform illustrative calculations of the field-dependent phonon frequencies for III-V semiconductors.

We present a perturbative method for calculating phonon properties of an insulator in the presence of a finite electric field. The starting point is a variational total-energy functional with a field-coupling term that represents the effect of the electric field. This total-energy functional is expanded in small atomic displacements within the framework of density-functional perturbation theory. The linear response of field-polarized Bloch functions to atomic displacements is obtained by minimizing the second-order derivatives of the total-energy functional. In the general case of nonzero phonon wavevector, there is a subtle interplay between the couplings between neighboring k-points introduced by the presence of the electric field in the reference state, and further-neighbor k-point couplings determined by the wavevector of the phonon perturbation. As a result, terms arise in the perturbation expansion that take the form of four-sided loops in k-space. We implement the method in the {\tt ABINIT} code and perform illustrative calculations of the field-dependent phonon frequencies for III-V semiconductors.

viii, 200 p. 25 cm

viii, 200 p. 25 cm

viii, 200 p. 25 cm

The Born effective charge, Z*, that describes the polarization created by collective atomic displacements, can be computed from first-principles by different techniques. Its band-by-band decomposition appeared recently as a powerful tool for the microscopic characterisation of the bonding in solids. We describe the connections between the different expressions used for the computation of Z*, and analyze the possible associated band-by-band decompositions. We show that unlike for the full Z*, the different band-by-band values are not equal, and emphasize that one of them has an interesting physical meaning.

The Born effective charge, Z*, that describes the polarization created by collective atomic displacements, can be computed from first-principles by different techniques. Its band-by-band decomposition appeared recently as a powerful tool for the microscopic characterisation of the bonding in solids. We describe the connections between the different expressions used for the computation of Z*, and analyze the possible associated band-by-band decompositions. We show that unlike for the full Z*, the different band-by-band values are not equal, and emphasize that one of them has an interesting physical meaning.

In order to promote public education and public safety, equal justice for all, a better informed citizenry, the rule of law, world trade and world peace, this legal document is hereby made available on a noncommercial basis, as it is the right of all humans to know and speak the laws that govern them. (For more information: 12 Tables of Code ) Name of Standards Organization: Bureau of Indian Standards (BIS) Division Name: Mechanical Engineering Section Name: Mining Techniques and Equipment (MED 8) Designator of Legally Binding Document: IS 12450-1 Title of Legally Binding Document: Steel headframes for mines, Part 1: Principles of load computation and applicable factors of safety Number of Amendments: Equivalence: Superceding: Superceded by: LEGALLY BINDING DOCUMENT Step Out From the Old to the New --Jawaharlal Nehru Invent a new India using knowledge. --Satyanarayan Gangaram Pitroda