Discretization error cancellation in the plane-wave approximation of periodic Hamiltonians with Coulomb singularities

In solid-state physics, energies of molecular systems are usually computed with a plane-wave discretization of Kohn-Sham equations. A priori estimates of plane-wave convergence for periodic Kohn-Sham calculations with pseudopotentials have been proved , however in most computations in practice, plane-wave cut-offs are not tight enough to target the desired accuracy. It is often advocated that the real quantity of interest is not the value of the energy but of energy differences for different configurations. The computed energy difference is believed to be much more accurate because of `discretization error cancellation', since the sources of numerical errors are essentially the same for different configurations. For periodic linear Hamiltonians with Coulomb potentials, error cancellation can be explained by the universality of the Kato cusp condition. Using weighted Sobolev spaces, Taylor-type expansions of the eigenfunctions are available yielding a precise characterization of this singularity. This then gives an explicit formula of the first order term of the decay of the Fourier coefficients of the eigenfunctions. It enables one to prove that errors on eigenvalue differences are reduced but converge at the same rate as the error on the eigenvalue.Comment: 14 pages, 3 figures, improved result on main theorem, corrected typo

Korean municipal orchestras : current problems and future prospects

This thesis is a study of Korean municipal orchestras which focuses on both the internal and external environment in order to examine and better understand arguments that they face 'challenges' that are not to be solved simply through 'efficiency' or 'better organisation', but are part of wider socio-cultural change that previous studies have failed to take adequately into consideration. This study, therefore, examines diverse aspects of the difficulties faced by contemporary Korean municipal orchestras while addressing five research questions concerning Korean cultural policy, the socio-economic context in which orchestras operate, job satisfaction, interpersonal conflict, and diminishing local government funding. In pursuit of this investigation, a triangulation methodology is adopted, which includes the scrutiny of documentation along with qualitative in-depth interviews (with orchestral players, administrative staff, and civil servants) and a quantitative questionnaire survey (with 128 players and 10 administrative staff). The research findings are given in detail in relevant chapters, but the key findings may be summarised here as follows: Political, economic, historic, and socio-cultural factors have greatly influenced the cultural policy of the Korean central government, but Korean municipal orchestras are influenced more by policies of local governments who provide them with a source of funding. Players in Korean municipal orchestras are highly satisfied with their work but dissatisfied with present pay, lack of authority, and the hierarchical structure. Orchestral administrative staff are dissatisfied with lack of autonomy and promotion. Male players have higher perception of intrapersonal conflict and intergroup conflict compared to female players, and male players have a greater preference for using integrating and compromising styles when managing interpersonal conflict with peers. Korean municipal orchestras, having a public service role, have been used to receiving relatively stable financial aid from local governments, but this has created a lack of commercial awareness about what is required to bolster their legitimacy in the face of potential financial cuts and small audiences. The 'civilizing mission' of the arts is no longer accepted as automatic justification. Although a complete governance change is considered a key factor for the success of municipal orchestras, such change is inadequate in itself: the real challenge for a brighter future lies with players, administrative staff, and the cities and their cooperation

Variational projector-augmented wave method: a full-potential approach for electronic structure calculations in solid-state physics

In solid-state physics, energies of crystals are usually computed with a plane-wave discretization of Kohn-Sham equations. However the presence of Coulomb singularities requires the use of large plane-wave cut-offs to produce accurate numerical results. In this paper, an analysis of the plane-wave convergence of the eigenvalues of periodic linear Hamiltonians with Coulomb potentials using the variational projector-augmented wave (VPAW) method is presented. In the VPAW method, an invertible transformation is applied to the original eigenvalue problem, acting locally in balls centered at the singularities. In this setting, a generalized eigenvalue problem needs to be solved using plane-waves. We show that cusps of the eigenfunctions of the VPAW eigenvalue problem at the positions of the nuclei are significantly reduced. These eigenfunctions have however a higher-order derivative discontinuity at the spheres centered at the nuclei. By balancing both sources of error, we show that the VPAW method can drastically improve the plane-wave convergence of the eigenvalues with a minor additional computational cost. Numerical tests are provided confirming the efficiency of the method to treat Coulomb singularities.Comment: 29 pages, 4 figure

Projector augmented-wave method: an analysis in a one-dimensional setting

In this article, a numerical analysis of the projector augmented-wave (PAW) method is presented, restricted to the case of dimension one with Dirac potentials modeling the nuclei in a periodic setting. The PAW method is widely used in electronic ab initio calculations, in conjunction with pseudopotentials. It consists in replacing the original electronic Hamiltonian $H$ by a pseudo-Hamiltonian $H^{PAW}$ via the PAW transformation acting in balls around each nuclei. Formally, the new eigenvalue problem has the same eigenvalues as $H$ and smoother eigenfunctions. In practice, the pseudo-Hamiltonian $H^{PAW}$ has to be truncated, introducing an error that is rarely analyzed. In this paper, error estimates on the lowest PAW eigenvalue are proved for the one-dimensional periodic Schr\"odinger operator with double Dirac potentials.Comment: 31 pages, 4 figure

Dissociation limit of the H2 molecule in the particle-hole random phase approximation

In this work, we consider the particle-hole random phase approximation (phRPA), an approximation to the correlation energy in electronic structure, and show that the phRPA energy of the H2 molecule correctly dissociates. That is, as the hydrogen atoms are pulled apart, the phRPA energy of the system converges to twice the phRPA energy of a single hydrogen atom. Despite the simplicity of the H2 system, the correct dissociation of H2 is known to be a difficult problem for density functional approximations. As part of our result, we prove that the phRPA correlation energy is well-defined

Sensitivity of Ru(bpy)_2dppz^(2+) Luminescence to DNA Defects

The luminescent characteristics of Ru(bpy)_2dppz^(2+) (dppz = dipyrido[3,2-a:2′,3′-c]phenazine), a DNA light switch, were investigated in the presence of oligonucleotides containing single base mismatches or an abasic site. In water, the ruthenium luminescence is quenched, but, bound to well matched duplex DNA, the Ru complex luminesces. Here we show that with DNAs containing a defect, rac-, Δ-, and Λ-Ru(bpy)_2dppz^(2+) exhibit significant luminescent enhancements above that with well matched DNA. In the presence of a single base mismatch, large luminescent enhancements are evident for the Δ-Ru isomer; the Λ-isomer shows particularly high luminescence bound to an oligonucleotide containing an abasic site. Similar increases are not evident with two common DNA-binding organic fluorophores, ethidium bromide and TO-PRO-3. Titrations with hairpin oligonucleotides containing a variable mismatch site show correlation between the level of luminescent enhancement and the thermodynamic destabilization associated with the mismatch. This correlation is reminiscent of that found earlier for a bulky rhodium complex that binds mismatched DNA sites through metalloinsertion, where the complex binds the DNA from the minor groove side, ejecting the mismatched bases into the major groove. Differential quenching studies with minor and major groove quenchers and time-resolved emission studies support this metalloinsertion mode for the dppz complex at the defect site. Certainly these data underscore the utility of Ru(bpy)_2dppz^(2+) as a sensitive luminescent reporter of DNA and its defects

Genome-wide analysis to predict protein sequence variations that change phosphorylation sites or their corresponding kinases

We define phosphovariants as genetic variations that change phosphorylation sites or their interacting kinases. Considering the essential role of phosphorylation in protein functions, it is highly likely that phosphovariants change protein functions and may constitute a proportion of the mechanisms by which genetic variations cause individual differences or diseases. We categorized phosphovariants into three subtypes and developed a system that predicts them. Our method can be used to screen important polymorphisms and help to identify the mechanisms of genetic diseases

Joseon mummies before mummy studies began in Korea

Mummy studies in Korea are instrumental in reconstructing the health and disease status of pre-modern Joseon peoples using firm scientific evidence. However, this scientific approach to such investigations in Korea is a relatively new discipline which began only within the last decade. Previous studies on Joseon tombs and their contents were performed exclusively by dress historians because most of the artefacts recoverable from Joseon tombs were textiles. In this report, we examine some of the excavation records left by dress historians in order to elucidate the approximate number and preservation status of Korean mummies discovered prior to the advent of their scientific investigation