A comment on the consistency of truncated nonlinear integral equation based theories of freezing

We report the results of two studies of aspects of the consistency of truncated nonlinear integral equation based theories of freezing: (i) We show that the self-consistent solutions to these nonlinear equations are unfortunately sensitive to the level of truncation. For the hard sphere system, if the Wertheim–Thiele representation of the pair direct correlation function is used, the inclusion of part but not all of the triplet direct correlation function contribution, as has been common, worsens the predictions considerably. We also show that the convergence of the solutions found, with respect to number of reciprocal lattice vectors kept in the Fourier expansion of the crystal singlet density, is slow. These conclusions imply great sensitivity to the quality of the pair direct correlation function employed in the theory. (ii) We show the direct correlation function based and the pair correlation function based theories of freezing can be cast into a form which requires solution of isomorphous nonlinear integral equations. However, in the pair correlation function theory the usual neglect of the influence of inhomogeneity of the density distribution on the pair correlation function is shown to be inconsistent to the lowest order in the change of density on freezing, and to lead to erroneous predictions. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.

A comment on the consistency of truncated nonlinear integral equation based theories of freezing

We report the results of two studies of aspects of the consistency of truncated nonlinear integral equation based theories of freezing: (i) We show that the self-consistent solutions to these nonlinear equations are unfortunately sensitive to the level of truncation. For the hard sphere system, if the Wertheim–Thiele representation of the pair direct correlation function is used, the inclusion of part but not all of the triplet direct correlation function contribution, as has been common, worsens the predictions considerably. We also show that the convergence of the solutions found, with respect to number of reciprocal lattice vectors kept in the Fourier expansion of the crystal singlet density, is slow. These conclusions imply great sensitivity to the quality of the pair direct correlation function employed in the theory. (ii) We show the direct correlation function based and the pair correlation function based theories of freezing can be cast into a form which requires solution of isomorphous nonlinear integral equations. However, in the pair correlation function theory the usual neglect of the influence of inhomogeneity of the density distribution on the pair correlation function is shown to be inconsistent to the lowest order in the change of density on freezing, and to lead to erroneous predictions. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.

Is one-parameter scaling theory of localisation consistent? Comment on Schuh's comment

It is maintained that the one-parameter scaling theory is inconsistent with the physics of Anderson localisation.

Comment on path integration of a quadratic action with a generalized memory

Using the promeasure technique, we give an alternative evaluation of a path integral corresponding to a quadratic action with a generalized memory.

Comment on “path integration of a quadratic action with a generalized memory

Using the promeasure technique, we give an alternative evaluation of a path integral corresponding to a quadratic action with a generalized memory.

Comment: Eigenvalue sensitivity method for optimal stabilisation of linear systems

In a letter RauA proposed a new method for designing statefeedback controllers using eigenvalue sensitivity matrices. However, there appears to be a conceptual mistake in the procedure, or else it is unduly restricted in its applicability. In particular the equation — BR~lBTK = A/.I, in which K is a positive-definite symmetric matrix.

Note On The Stability Of Parallel Magnetic-Fields - Comment

It is shown that the conclusions arrived at regarding the instability of an incompressible fluid cylinder in the presence of the magnetic field and the streaming velocity in a recent communication easily follow from the study of propagation characteristics of Alfvén surface waves along cylindrical plasma columns made earlier.

Comment on "Pseudoelasticity of Cu-Zr nanowires via stress-induced martensitic phase transformations"

Recently, a novel stress-induced phase transformation in an initial < 100 >/{100} B2-CuZr nanowire has been reported for the first time [Sutrakar and Mahapatra, Mater. Lett. 63, 1289 (2009)]. Following this, a martenisitic phase transformation in Cu-Zr nanowire was shown [Cheng et al., Appl. Phys. Lett. 95, 021911 (2009)] using the same idea (Sutrakar and Mahapatra, Mater. Lett. 63, 1289 (2009)]. The pseudoelastic recovery of the bct phase of Cu-Zr by unloading has also been shown [Cheng et al., Appl. Phys. Lett. 95, 021911 (2009)]. They also tested the epitaxial bain path [Alippi et al., Phys. Rev. Lett. 78, 3892 (1997)] and reported that the bct phase in the nanowire is metastable, whereas the bulk counterpart is unstable. This aspect is re-examined in this comment with corrected results.