Improvement of the signal-to-noise ratio in interferometry using multi-frame high-dynamic-range and normalization algorithms

Using both high dynamic range (HDR) and normalization methodologies, we show a method to improve the fringe pattern contrast in interferometric measurements normally used for phase recovering. In a simulated interferogram that mimics the main effects that can be found in an interferometric process (stray-light, photon noise, electronic noise, scattering phenomena, etc.) it was possible to improve the contrast of the fringes and to decrease the root mean square error by more than 35%. The method proposed is applied to experimental interferograms to measure wavefront error and retardance changes on liquid crystal (LC) devices. It is done by using a Mach–Zehnder set-up in which we used different polarization areas. The proposed method increases the quality of the phase recovered and decreases the root mean square error by 50%.     

Stable and Unstable Solitary-Wave Solutions of the Generalized Regularized Long-Wave Equation

Summary. Investigated here are interesting aspects of the solitary-wave solutions of the generalized Regularized Long-Wave equation For p>5 , the equation has both stable and unstable solitary-wave solutions, according to the theory of Souganidis and Strauss. Using a high-order accurate numerical scheme for the approximation of solutions of the equation, the dynamics of suitably perturbed solitary waves are examined. Among other conclusions, we find that unstable solitary waves may evolve into several, stable solitary waves and that positive initial data need not feature solitary waves at all in its long-time asymptotics. Received March 28, 2000; accepted August 24, 2000 %%Online publication November 15, 2000 Communicated by Thanasis Fokas     

Electron-hole excitations in NiO: LSDA+U-based calculations vs. inelastic X-ray scattering and ellipsometry measurements

The performance of the LSDA+U functional—in particular, the quality of the ground-state—is tested via calculations of the electron-hole excitations of NiO, which are compared with (non-resonant) inelastic X-ray scattering (IXS) and ellipsometry measurements. The dynamical density-response calculations are performed within the random-phase approximation (RPA), defining an LSDA+U/RPA density-response method. A significant success of this method is the insight it provides into the main loss present in the IXS data above the NiO optical gap, namely, a peak lying at ∼7.5 eV. This excitation, which is shown to be collective in nature, and to be induced by e_g-e_g transitions, provides a direct link between the correlated e_g-states and the IXS data. This finding illustrates the power of IXS, combined with correlated-band-structure theory (here, LSDA+U theory), for the investigation of the electronic structure of strongly correlated materials. At the same time, our results indicate that the LSDA+U/RPA response method does not represent a complete theory.     

Mathematical Aspects of the Periodic Law

We review different studies of the Periodic Law and the set of chemical elements from a mathematical point of view. This discussion covers the first attempts made in the 19th century up to the present day. Mathematics employed to study the periodic system includes number theory, information theory, order theory, set theory and topology. Each theory used shows that it is possible to provide the Periodic Law with a mathematical structure. We also show that it is possible to study the chemical elements taking advantage of their phenomenological properties, and that it is not always necessary to reduce the concept of chemical elements to the quantum atomic concept to be able to find interpretations for the Periodic Law. Finally, a connection is noted between the lengths of the periods of the Periodic Law and the philosophical Pythagorean doctrine.     

Challenges for the Periodic Systems of Elements: Chemical,Historical and Mathematical Perspectives

We celebrate 150 years of periodic systems that reached their maturity in the 1860s. They began as pedagogical efforts to project corpuses of substances on the similarity and order relationships of the chemical elements. However, these elements are not the canned substances wrongly displayed in many periodic tables, but rather the abstract preserved entities in compound transformations. We celebrate the systems, rather than their tables or ultimate table. The periodic law, we argue, is not an all-encompassing achievement, as it does not apply to every property of all elements and compounds. Periodic systems have been generalised as ordered hypergraphs, which solves the long-lasting question on the mathematical structure of the systems. In this essay, it is shown that these hypergraphs may solve current issues such as order reversals in super-heavy elements and lack of system predictive power. We discuss research in extending the limits of the systems in the super-heavy-atom region and draw attention to other limits: the antimatter region and the limit arising from compounds under extreme conditions. As systems depend on the known chemical substances (chemical space) and such a space grows exponentially, we wonder whether systems still aim at projecting knowledge of compounds on the relationships among the elements. We claim that systems are not based on compounds anymore, rather on 20th century projections of the 1860s systems of elements on systems of atoms. These projections bring about oversimplifications based on entities far from being related to compounds. A linked oversimplification is the myth of vertical group similarity, which raises questions on the approaches to locate new elements in the system. Finally, we propose bringing back chemistry to the systems by exploring similarity and order relationships of elements using the current information of the chemical space. We ponder whether 19th century periodic systems are still there or whether they have faded away, leaving us with an empty 150^th celebration.     

Microsolvation of small cations and anions

Recent advances in the theoretical treatment of microsolvation of small ions, a problem with practical implications in chemistry, physics, and biology, are exposed. In particular, we discuss sound stochastic approaches to sample complex energy landscapes and delve into the nature of bonding interactions that dictate both structural and energetical preferences. An in-depth analysis of the effect of formal charges in the surrounding network of solvent to solvent hydrogen bonds is also presented. The problem, as expected, is more complicated than simple definitions may forecast.     

How Many Water Molecules Does it Take to Dissociate HCl?

The potential energy surfaces of the HCl(H₂O)_n (n is the number of water molecules) clusters are systematically explored using density functional theory and high‐level ab initio computations. On the basis of electronic energies, the number of water molecules needed for HCl dissociation is four as reported by some experimental groups. However, this number is five owing to the inclusion of entropic factors. Wiberg bond indices are calculated and analyzed, and the results provide a quadratic correlation and classification of clusters according to the nondissociated, partially dissociated, and fully dissociated character of the H?Cl bond. Our computations show that if temperature is not controlled during the experiment, the values obtained for the dipole moment (or for any measurable property) are susceptible to change, providing a different picture of the number of water molecules needed for HCl dissociation in a nanoscopic droplet.     

Structure-fate relationships of organic chemicals derived from the software packages E4CHEM and WHASSE

A risk assessment of chemicals is to be performed on the basis of the model EUSES, developed by the Commission of the European Union. The model package E4CHEM (Exposure Estimation for Potentially Ecotoxic Environmental Chemicals), developed in 1984-1992, is presented and applied in this paper as a model which allows a model-supported evaluation of chemicals. E4CHEM consequently does not have the wide applicability and technical comfort of the more recently developed model EUSES. The simulation models of E4CHEM characterize the chemical behavior in the environment by many aspects. Hence, there is a need to condense all of these aspects to get a clear impression of what will be the fate of the chemicals. Starting with the already published concept of exposure maps, we will discuss how partial orders may be helpful in establishing generalized structure-fate relationships. The software WHASSE is applied.