Effective eddy viscosities in implicit modeling of decaying high Reynolds number turbulence with and without rotation

We assess the applicability of the numerical dissipation as an implicit turbulence model. The nonoscillatory finite volume numerical scheme MPDATA developed for simulations of geophysical flows is employed as an example of a scheme with an implicit turbulence model. A series of low resolution simulations of decaying homogeneous turbulence with and without Coriolis forces in the limit of zero molecular viscosity are performed. To assess the implicit model the long-time evolution of turbulence in the simulations is investigated and the numerical velocity fields are analyzed to determine the effective spectral eddy viscosity that is attributed to the numerical discretization. The detailed qualitative and quantitative comparisons are made between the numerical eddy viscosity and the theoretical results as well as the intrinsic eddy viscosity computed exactly from the velocity fields by introducing an artificial wave number cutoff. We find that the numerical dissipation depends on the time step and exhibits contradictory dependence on rotation: it is overestimated for rapid rotation cases and is underestimated for nonrotating cases. These results indicate that the numerical dissipation may fail to represent the effects of the physical subgrid scale processes unless the parameters of a numerical scheme are carefully chosen.     

A Criterion for Compatibility of Conformal and Projective Structures

In a space-time M, a conformal structure is defined by the distribution of light-cones. Geodesics are traced by freely falling particles, and the collection of all unparameterized geodesics determines the projective structure of M. The article contains a formulation of the necessary and sufficient conditions for these structures to be compatible, i.e. to come from a metric tensor which is then unique up to a constant factor. The theorem applies to all dimensions and signatures.     

Large N approach to Kaon decays and mixing 28 years later: \Delta I=1/2 rule, \hat{B}_K,and \Delta M_K

We review and update our results for $K\rightarrow \pi \pi $ decays and $K^0$ – $\bar{K}^0$ mixing obtained by us in the 1980s within an analytic approximate approach based on the dual representation of QCD as a theory of weakly interacting mesons for large $N$ , where $N$ is the number of colors. In our analytic approach the Standard Model dynamics behind the enhancement of $\hbox {Re}A_0$ and suppression of $\hbox {Re}A_2$ , the so-called $\Delta I=1/2$ rule for $K\rightarrow \pi \pi $ decays, has a simple structure: the usual octet enhancement through the long but slow quark–gluon renormalization group evolution down to the scales $\mathcal{O}(1\, {\hbox { GeV}})$ is continued as a short but fast meson evolution down to zero momentum scales at which the factorization of hadronic matrix elements is at work. The inclusion of lowest-lying vector meson contributions in addition to the pseudoscalar ones and of Wilson coefficients in a momentum scheme improves significantly the matching between quark–gluon and meson evolutions. In particular, the anomalous dimension matrix governing the meson evolution exhibits the structure of the known anomalous dimension matrix in the quark–gluon evolution. While this physical picture did not yet emerge from lattice simulations, the recent results on $\hbox {Re}A_2$ and $\hbox {Re}A_0$ from the RBC-UKQCD collaboration give support for its correctness. In particular, the signs of the two main contractions found numerically by these authors follow uniquely from our analytic approach. Though the current–current operators dominate the $\Delta I=1/2$ rule, working with matching scales $\mathcal{O}(1 \, {\hbox { GeV}})$ we find that the presence of QCD-penguin operator $Q_6$ is required to obtain satisfactory result for $\hbox {Re}A_0$ . At NLO in $1/N$ we obtain $R=\hbox {Re}A_0/\hbox {Re}A_2= 16.0\pm 1.5$ which amounts to an order of magnitude enhancement over the strict large $N$ limit value $\sqrt{2}$ . We also update our results for the parameter $\hat{B}_K$ , finding $\hat{B}_K=0.73\pm 0.02$ . The smallness of $1/N$ corrections to the large $N$ value $\hat{B}_K=3/4$ results within our approach from an approximate cancelation between pseudoscalar and vector meson one-loop contributions. We also summarize the status of $\Delta M_K$ in this approach.     

Adaptive linear combination of heuristic orderings in constructing examination timetables

In this paper, we investigate adaptive linear combinations of graph coloring heuristics with a heuristic modifier to address the examination timetabling problem. We invoke a normalisation strategy for each parameter in order to generalise the specific problem data. Two graph coloring heuristics were used in this study (largest degree and saturation degree). A score for the difficulty of assigning each examination was obtained from an adaptive linear combination of these two heuristics and examinations in the list were ordered based on this value. The examinations with the score value representing the higher difficulty were chosen for scheduling based on two strategies. We tested for single and multiple heuristics with and without a heuristic modifier with different combinations of weight values for each parameter on the Toronto and ITC2007 benchmark data sets. We observed that the combination of multiple heuristics with a heuristic modifier offers an effective way to obtain good solution quality. Experimental results demonstrate that our approach delivers promising results. We conclude that this adaptive linear combination of heuristics is a highly effective method and simple to implement.     

The t-Tone Chromatic Number of Random Graphs

A proper 2-tone k-coloring of a graph is a labeling of the vertices with elements from \({\binom{[k]}{2}}\) such that adjacent vertices receive disjoint labels and vertices distance 2 apart receive distinct labels. The 2-tone chromatic number of a graph G, denoted τ ₂(G) is the smallest k such that G admits a proper 2-tone k coloring. In this paper, we prove that w.h.p. for \({p\geq Cn^{-1/4} {\rm ln}^{9/4}n, \tau_2(G_{n, p}) = (2 + o(1))\chi(G_{n, p})}\) where \({\chi}\) represents the ordinary chromatic number. For sparse random graphs with p = c/n, c constant, we prove that \({\tau_2(G_{n, p}) = \lceil{({\sqrt{8\Delta + 1} + 5})/{2}}}\) where Δ represents the maximum degree. For the more general concept of t-tone coloring, we achieve similar results.     

Robust Markov perfect equilibria

In this paper we study a Markov decision model with quasi-hyperbolic discounting and transition probability function depending on an unknown parameter. Assuming that the set of parameters is finite, the sets of states and actions are Borel and the transition probabilities satisfy some additivity conditions and are atomless, we prove the existence of a non-randomised robust Markov perfect equilibrium.     

Use of a Dynamic Light Scattering Technique for SDS/Water/Pentanol Studies

The interpretation of micelle/aggregate size obtained by use of the DLS technique for SDS/water/pentanol systems was discussed by comparison of the results of measurement with theoretical data. For most of the studied systems, the apparent radii (R _h,app ) did not satisfactorily characterize the size of the aggregates (R _h,app  < 1 nm). The use of a correction factor (f = 0.26) confirmed that the discrepancies were associated with the electrostatic intermicellar interactions. However, the fuzzy optical interface between dispersed and dispersing phases can also be the reason of such results. An increase of pentanol content caused a decrease of the droplet radius in w/o systems but in o/w systems the changes were negligible.     

PROPERTIES OF HIGHLY DISPERSED SILICAS PRECIPITATED IN AN ORGANIC MEDIUM

Silicas were obtained using a precipitation technique from metasilicate solution with an acidic agent. The precipitation process includes formation of silica particles and their aggregation.

Alcohol solutions were used in the production process of the highly dispersed silicas, resulting in a partial blocking of the silica surface silanol groups and, thus, in a decreased hydrophilicity of silica.

The precipitated silicas were subjected to physicochemical, structural, and microscopic evaluation, and their surface properties were examined. The effect of alcohols on the silica particle size distributions and on hydrophobicity of silica surface was tested.     

Facile and Versatile Room-Temperature Synthesis of N,N-Disubstituted Cyanoacetamides from Malonic Ester Chloride

A general method for the synthesis of various N,N-disubstituted cyanoacetamides from readily available methyl malonyl chloride and secondary amines, including sterically demanding aliphatic and aromatic amines, is described.