Numerical tests of causal relativistic dissipative fluid dynamics

We present numerical methods to solve the Israel–Stewart (IS) equations of causal relativistic dissipative fluid dynamics with bulk and shear viscosities. We then test these methods studying the Riemann problem in (1+1)- and (2+1)-dimensional geometry. The numerical schemes investigated here are applicable to realistic (3+1)-dimensional modeling of a relativistic dissipative fluid.     

Geometric ergodicity of Harris recurrent Marcov chains with applications to renewal theory

Let (X_n) be a positive recurrent Harris chain on a general state space, with invariant probability measure π. We give necessary and sufficient conditions for the geometric convergence of λPⁿf towards its limit π(f), and show that when such convergence happens it is, in fact, uniform over f and in L¹(π)-norm. As a corollary we obtain that, when (Xn) is geometrically ergodic, ∝ π(dx)6Pⁿ(x,·)-π6 converges to zero geometrically fast. We also characterize the geometric ergodicity of (X_n) in terms of hitting time distributions. We show that here the so-called small sets act like individual points of a countable state space chain. We give a test function criterion for geometric ergodicity and apply it to random walks on the positive half line. We apply these results to non-singular renewal processes on [0,∞) providing a probabilistic approach to the exponencial convergence of renewal measures.     

Lattice Boltzmann Simulation of Flow-Induced Wall Shear Stress in Porous Media

The lattice Boltzmann method is increasingly utilized in the simulation of flow-induced wall shear stress needed in various applications. In image-based flow simulations, the simulation geometry is usually based on a three-dimensional reconstruction of the true structure of the pore space obtained, for example, by X-ray tomography. The geometry is then given in a voxel-based representation, which complicates an accurate determination of the surface-normal vectors that are necessary in the computation of the wall shear stress. To avoid this problem, we introduce here a method for the determination of surface-normal vectors directly from a greyscale image instead of its segmented binary image version. The proposed method is fast and automatic, and it can be used for an arbitrary pore space geometry provided in a greyscale form by any imaging modality. We show that this method can produce accurate surface-normal vectors even for binary images and that their accuracy is further increased when the original greyscale images are used instead. We compute wall shear stresses for generated benchmark geometries and then demonstrate the utility of the method for soil samples with ‘random’ pores imaged by X-ray tomography.     

Illumination with Ultraviolet or Visible Light Induces Chemical Changes in the Water-soluble Manganese Complex, [Mn4O6(bpea)4]Br4

We measured the photosensitivity of an artificial tetranuclear oxo–Mn(IV) complex, [Mn₄O₆(bpea)₄]Br₄, which has an adamantane-shaped {Mn₄O₆}⁴⁺ core. Illumination caused changes in the absorption spectrum of the compound consistent with a one-electron reduction in the compound. Bromide appears to be the most probable electron donor in the reaction system. Chemical modification of the cluster appears to destabilize it, predisposing it to reductive degradation. UV light was more efficient than visible light in causing the changes. The data support the suggestion that the natural oxygen-evolving Mn complex is photosensitive and can oxidize components of the oxygen-evolving complex in its excited state causing photoinhibition, and that photostability is an important issue in designing Mn complexes for artificial photosynthesis. Furthermore, light-induced oxidation of bromide by [Mn₄O₆(bpea)₄]⁴⁺ may suggest that oxidation of chloride is involved in natural water splitting or has been involved during the evolution of the water-splitting enzyme.     

Nano-scale copper oxidation on leadframe surface

Copper oxidation studies were carried out by means of field emission scanning electron microscopy (FESEM), atomic force microscopy (AFM), transmission electron microscopy (TEM), energy dispersive X-ray spectroscopy (EDS) and electron energy loss spectroscopy (EELS) techniques. The growth of copper oxide occurs as a copper surface comes in an oxygen containing environment. The reaction sequence leading to oxidation of the copper surface is generally accepted to be oxygen chemisorption, nucleation and growth of the surface oxide and bulk oxide growth. HRTEM examination of the cross section of the oxidized copper sample revealed the interface region in between the copper and copper oxide. At high oxidation temperature, formation of micro-voids and separations were observed along this interface region. Poor adhesion at this interface region due to micro-voids and separation were found to be the root cause of delamination issue. EELS analysis determined that for regions with intact interface the oxidation system is Cu/CuO/Cu₂O/CuO, however, in regions containing micro-voids or separation it is found to be Cu/Cu₂O/CuO.     

Hausdorff Dimension and Non-degenerate Families of Projections

We study parameterized families of orthogonal projections for which the dimension of the parameter space is strictly less than that of the Grassmann manifold. We answer the natural question of how much the Hausdorff dimension may decrease by verifying the best possible lower bound for the dimension of almost all projections of a finite measure. We also show that a similar result is valid for smooth families of maps from the n-dimensional Euclidean space to the m-dimensional one.     

The synthesis of α,α-difluoroaldehydes and ketones via claisen rearrangements

The Claisen rearrangements of reactants containing two fluorine atoms in either the allyl or vinyl fragment are described.     

Random source induced spontaneous symmetry breaking in scalar field theories

We study the effective potential for scalar field theories in the presence of gaussian random sources, coupled to the scalar field in a self-consistent way. We compute the effective potential both in the loop and in the 1/N expansions and find various instabilities. The only feasible instabilities are the ones induced by (formally) imaginary random sources. The pertinent phase transition is a first-order transition.     

On the vacuum structure in the Coulomb and Landau gauges

Vacuum structure in the SU(N) Coulomb and Landau gauges is studied by using the methods of harmonic maps. A systematic way for solving the Gribov vacuum copy equation is presented and many examples are discussed in both the Coulomb and Landau gauges as applications of the method. Finally, the physical interpretation of Gribov ambiguities is shortly reviewed from a topological point of view.