Narrow Results

In this note we consider the moduli space of stable bundles of rank two on a very general quintic surface. We study the potentially obstructed points of the moduli space via the spectral covering of a twisted endomorphism. This analysis leads to generically non-reduced components of the moduli space, and components which are generically smooth of more than the expected dimension. We obtain a sharp bound asked for by O'Grady on when the moduli space is good.

We study the deformations of a smooth curve $C$ on a smooth projective $3$-fold $V$, assuming the presence of a smooth surface $S$ satisfying $C\subset S\subset V$. Generalizing a result of Mukai and Nasu, we give a new sufficient condition for a first order infinitesimal deformation of $C$ in $V$ to be primarily obstructed. In particular, when $V$ is Fano and $S$ is $K3$, we give a sufficient condition for $C$ to be (un)obstructed in $V$, in terms of $(-2)$-curves and elliptic curves on $S$. Applying this result, we prove that the Hilbert scheme ${Hilb}^{\mathrm{\text{sc}}}{V}_4$ of smooth connected curves on a smooth quartic $3$-fold $V_4\subset {\mathbb{P}}^4$ contains infinitely many generically non-reduced irreducible components, which are variations of Mumford’s example for ${Hilb}^{\mathrm{\text{sc}}}{\mathbb{P}}^3$.

Let $X$ be an elliptic surface over $P^1$ with $\kappa (X)=1$, and $M=M(c_2)$ be the moduli scheme of rank-two stable sheaves $E$ on $X$ with $(c_1(E),c_2(E))=(0,c_2)$ in $Pic(X)\times \mathbb{Z}$. We look into defining equations of $M$ at its singularity $E$, partly because if $M$ admits only canonical singularities, then the Kodaira dimension $\kappa (M)$ can be calculated. We show the following:

• ^(A)$E$ is at worst canonical singularity of $M$ if the restriction of $E_{\eta }$ to the generic fiber of $X$ has no rank-one subsheaf, and if the number of multiple fibers of $X$ is a few.
• ^(B)We obtain that $\kappa (M)=\{1+dim(M)\}/2$ and the Iitaka program of $M$ can be described in purely moduli-theoretic way for $c_2\gg 0$, when $\chi ({{𝒪}}_X)=1$, $X$ has just two multiple fibers, and one of its multiplicities equals $2$.
• ^(C)On the other hand, when $E_{\eta }$ has a rank-one subsheaf, it may be insufficient to look at only the degree-two part of defining equations to judge whether $E$ is at worst canonical singularity or not.

In this paper, we make a correction to Theorem 3.3 of the aforementioned paper (Internat. J. Math.28(13) (2017) 1750099). We also provide a counterexample to the theorem and point out an error in the proof.

As the Nagel–Schreckenberg model (NaSch model) became known as a realistic approach to describe traffic flow on single-lane streets, this model was extended to two-lane traffic by several groups. On the base of our two-lane model, we will now investigate the impact of a place of obstruction, e.g., because of road works, on partial fractions, densities and mean velocities.

We calculate the power spectral density and velocity correlations for a turbulent flow of a fluid inside a duct. Turbulence is induced by obstructions placed near the entrance of the flow. The power spectral density is obtained for several points at cross-sections along the duct axis, and an analysis is made on the way the spectra changes according to the distance to the obstruction. We show that the differences on the power spectral density are important in the lower frequency range, while in the higher frequency range, the spectra are very similar to each other. Our results suggest the use of the changes on the low frequency power spectral density to identify the occurrence of obstructions in pipelines. Our results show some frequency regions where the power spectral density behaves according to the Kolmogorov hypothesis. At the same time, the calculation of the power spectral densities at increasing distances from the obstructions indicates an energy cascade where the spectra evolves in frequency space by spreading the frequency amplitude.

This paper aims to detect memory loss of the symmetry of blockades in ducts and how far the information on the asymmetry of the obstacles travels in the turbulent flow from computational simulations with OpenFOAM. From a practical point of view, it seeks alternatives to detect the formation of obstructions in pipelines. The numerical solutions of the Navier–Stokes equations were obtained through the solver PisoFOAM of the OpenFOAM library, using the large Eddy simulation (LES) for the turbulent model. Obstructions were placed near the duct inlet and, keeping the blockade ratio fixed, five combinations for the obstacles sizes were adopted. The results show that the information about the symmetry is preserved for a larger distance near the ducts wall than in mid-channel. For an inlet velocity of 5m/s near the walls the memory is kept up to distance 40 times the duct width, while in mid-channel this distance is reduced almost by half. The maximum distance in which the symmetry breaking memory is preserved shows sensitivity to Reynolds number variations in regions near the duct walls, while in the mid channel that variations do not cause relevant effects to the velocity distribution.

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