We compute the absorption and emission energies and hence Stokes shifts of small diamondoids as a function of size using different theoretical approaches, including density-functional theory (DFT) and quantum Monte Carlo (QMC) calculations. The absorption spectra of these molecules are also investigated by time-dependent DFT and compared with experiment. We analyze the structural distortion and...

The short- and long-time breakdown of the classical Stokes-Einstein relation for colloidal suspensions at arbitrary volume fractions is explained here by examining the role that confinement and attractive interactions play in the intra- and inter-cage dynamics executed by the colloidal particles. We show that the measured short-time diffusion coefficient is larger than the one predicted by the ...

In this note we give a brief sketch of real interpolations, the Lorentz spaces and their applications to the NavierStokes equations. Introduction. This note is a brief sketch of real interpolation and the Lorentz spaces, and its application to the Navier-Stokes equations. There are two methods of interpolation: complex method and real method. Both of them survive because each has its advantages...

The Stokes drift argument put forth by Coy et al. (1986) to explain the monthly mean downward vertical velocities observed in the summer polar mesosphere by radars is critically re-exanfined. The size of the effect is quite sensitive to the choice of gravity wave wavenumber and phase speed. We reproduce the Coy et al. (1986) result for a monochromatic gravity wave and then generalize to a Garre...

We present the non-Abelian Stokes theorem for the Wilson loop in various forms and discuss its meaning. Its validity has been recently questioned by Faber, Ivanov, Troitskaya and Zach. We demonstrate that all points of their criticism are based on mistakes in mathematics. Finally, we derive a variant of our formula for the Wilson loop in lattice regularization.

In this paper, we study a free boundary problem for compressible spherically symmetric Navier-Stokes equations with a gravitational force and degenerate viscosity coefficients. Under certain assumptions that imposed on the initial data, we obtain the global existence and uniqueness of the weak solution and give some uniform bounds (with respect to time) of the solution. Moreover, we obtain some...

Calculations were carried out in order to probe the influence of turbulence on the solar oscillation frequencies as a possible explanation of the difference between observed and computed mode frequencies. As a first step the analysis is restricted to the radial oscillation modes. Corrections to the oscillation equations due to turbulence are determined with the help of perturbation theory, and ...

We investigate a family of axisymmetric solutions to a coupling of Navier-Stokes and Allen-Cahn equations in R3. Firstly, a 1D system of equations is derived from the method of separation of variables, which approximates the 3D system along its symmetry axis. Then based on them, by adding perturbation terms, we construct finite energy solutions to the 3D system. We prove the global regularity o...

The Adjoint Parabolized Stability Equations (APSE) are used to predict the receptivity of boundary layers to a variety of disturbances. The method is validated through comparisons to direct solutions of the linearized Navier–Stokes (LNS) and adjoint Navier–Stokes (ANS) equations and APSE is found to accurately predict receptivity with significant gains in efficiency compared to Navier–Stokes ba...

Abstract Recently, large-scale housing programmes have experienced a revival in many countries of the Global South. They are criticised for their top-down, standardised, and supply-driven nature, which hardly meets people’s demands. At heart problem lies concept “material decency”—a normative shelter-centric notion housing, inspired by colonial planning developmentalist thought. Many African co...