Penalty finite element method for Navier–Stokes equations with nonlinear slip boundary conditions

The penalty finite element method for Navier–Stokes equations with nonlinear slip boundary conditions is investigated in this paper. Since this class of nonlinear slip boundary conditions include the subdifferential property, the weak variational formulation is a variational inequality problem of the second kind. Using the penalty finite element approximation, we obtain optimal error estimates between the exact solution and the finite element approximation solution. Finally, we show the numerical results which are in full agreement with the theoretical results. Copyright © 2011 John Wiley & Sons, Ltd.     

Infrared sensitivity of unstable vacua

We discover that some unstable vacua have long memory. By that we mean that even in the theories containing only massive particles, there are correllators and expectation values which grow with time. We examine the cases of instabilities caused by the constant electric fields, expanding and contracting universes and, most importantly, the global de Sitter space. In the last case the interaction leads to a remarkable UV/IR mixing and to a large back reaction. This gives reasons to believe that the cosmological constant problem could be resolved by the infrared physics.     

Instability of the finite‐difference split‐step method applied to the generalized nonlinear Schrödinger equation. III. external potential and oscillating pulse solutions

This is the final part of a series of articles where we have studied numerical instability (NI) of localized solutions of the generalized nonlinear Schrödinger equation (gNLS). It extends our earlier studies of this topic in two ways. First, it examines differences in the development of the NI between the case of the purely cubic NLS and the case where the gNLS has an external bounded potential. Second, it investigates how the NI is affected by the oscillatory dynamics of the simulated pulse. The latter situation is common when the initial condition is not an exact stationary soliton. We have found that in this case, the NI may remain weak when the time step exceeds the threshold quite significantly. This means that the corresponding numerical solution, while formally numerically unstable, can remain sufficiently accurate over long times, because the numerical noise will stay small. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 633–650, 2017     

Über den Einfluß von Isotopieeffekten auf die Verbreitung der Isotope in der Natur

Die Isotopenzusammensetzung der chemischen Elemente in ihren natürlichen Vorkommen wird von kernphysikalischen Vorgängen, vom Einfall extraterrestrischer Materie und, namentlich bei den leichten Elementen (etwa bis zum Chlor), von kinetischen und thermodynamischen Isotopieeffekten beeinfluβt. Deshalb ist die Kenntnis der in der Natur wirkenden Isotopieeffekte eine entscheidende Voraussetzung für das Verständnis der Gesetzmäβigkeiten der Verbreitung der Isotope in der Natur und für die Anwendung dieser Gesetzmäβigkeiten als Mittel der geo- und kosmoswissenschaftlichen Forschung und der Umweltforschung [1].     

Füllstandsmessung mit Streustrahlungssonden

Es wird die Abhängigkeit der Impulsdichte vom Füllstand bei Meßanordnungen mit γ-Streustrahlungssonden verschiedener Länge untersucht. Verwendet werden die Nuklide ⁶⁰Co und ¹³⁷Cs. Ein nahezu linearer Anstieg der Impulsdichte mit dem Füllstand wird bei Füllgütern kleiner Ordnungszahl nur bei Sondenlängen L ≥ μ₀ ^?1.erzielt. Der Einfluß des Schüttwinkels und der Dichte des Füllgutes wird diskutiert.     

Normal halogen dependence of 13C NMR chemical shifts of halogenomethanes revisited at the four‐component relativistic level

The ‘Normal Halogen Dependence’ of ¹³C NMR chemical shifts in the series of halogenomethanes is revisited at the four‐component relativistic level. Calculations of ¹³C NMR chemical shifts of 70 halogenomethanes have been carried out at the density functional theory (DFT) and MP2 levels with taking into account relativistic effects using the four‐component relativistic theory of Dirac‐Coulomb within the different computational methods (4RPA, 4OPW91) and hybrid computational schemes (MP2 + 4RPA, MP2 + 4OPW91). The most efficient computational protocols are derived for practical purposes. Relativistic shielding effect reaches as much as several hundreds of ppm for heavy halogenomethanes, and to account for this effect in comparison with experiment at the qualitative level, relativistic Dyall's basis sets of triple‐zeta quality or higher are to be used within the framework of the four‐component relativistic theory taking into account solvent effects. Relativistic geometrical optimization (as compared with the non‐relativistic level) is essential for the molecules containing at least two iodines at one carbon atom. Copyright © 2016 John Wiley & Sons, Ltd.     

Fine Substituent Effects in Sandwich Complexes: A Threshold Ionization Study of Monosubstituted Chromium Bisarene Compounds

Mass‐analyzed threshold ionization spectra of jet‐cooled [(η⁶‐PhMe)(η⁶‐PhH)Cr] and [(η⁶‐Ph₂)(η⁶‐PhH)Cr] reveal with unprecedented accuracy the effects of methyl and phenyl groups on the electronic structure of bis(η⁶‐benzene)chromium. These “pure” substituent effects allow quantitative experimental determination of the ionization energy changes caused by the mutual substituent influence in bisarene systems. Two types of such influence have been revealed for the first time in bis(η⁶‐toluene)chromium.     

Doppler effects of an oscillating line source in shear flow with a free surface

The linearised water-wave radiation problem for the oscillating 2D submerged source in an inviscid shear flow with a free surface is investigated analytically. There is a nonzero surface velocity. The depth is infinite and the vorticity is uniform. The amplitudes radiated from the source are calculated analytically. Due to Doppler effects, there may be up to four different emitted waves, and there is resonance with zero group velocity and infinite amplitude.     

Predicting the tautomeric equilibrium of acetylacetone in solution. I. The right answer for the wrong reason?

This study investigates how the various components (method, basis set, and treatment of solvent effects) of a theoretical approach influence the relative energies between keto and enol forms of acetylacetone, which is an important model system to study the solvent effects on chemical equilibria from experiment and theory. The computations show that the most popular density functional theory (DFT) approaches, such as B3LYP overestimate the stability of the enol form with respect to the keto form by ～10 kJ mol^?1, whereas the very promising SCS‐MP2 approach is underestimating it. MP2 calculations indicate that in particular the basis set size is crucial. The Dunning Huzinaga double ζ basis (D95z(d,p)) used in previous studies overestimates the stability of the keto form considerably as does the popular split‐valence plus polarization (SVP) basis. Bulk properties of the solvent included by continuum approaches strongly stabilize the keto form, but they are not sufficient to reproduce the reversal in stabilities measured by low‐temperature nuclear magnetic resonance experiments in freonic solvents. Enthalpic and entropic effects further stabilize the keto form, however, the reversal is only obtained if also molecular effects are taken into account. Such molecular effects seem to influence only the energy difference between the keto and the enol forms. Trends arising due to variation in the dielectric constant of the solvent result from bulk properties of the solvent, i.e., are already nicely described by continuum approaches. As such this study delivers a deep insight into the abilities of various approaches to describe solvent effects on chemical equilibria. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Transition to Amplitude Death in Coupled System with Small Number of Nonlinear Oscillators

In this work, we investigate the amplitude death in coupled system with small number of nonlinear oscillators. We show how the transitions to the partial and the complete amplitude deathes happen. We also show that the partial amplitude death can be found in globally coupled oscillators either.