The non-linear Glasma

We study the evolution of quantum fluctuations in the Glasma created immediately after the collision of heavy nuclei. It is shown how the presence of instabilities leads to an enhancement of non-linear interactions among initially small fluctuations. The non-linear dynamics leads to an enhanced growth of fluctuations in a large momentum region exceeding by far the originally unstable band. We investigate the dependence on the coupling constant at weak coupling using classical statistical lattice simulations for SU(2) gauge theory and show how these non-linearities can be analytically understood within the framework of two-particle irreducible (2PI) effective action techniques. The dependence on the coupling constant is only logarithmic in accordance with analytic expectations. Concerning the isotropization of bulk quantities, our results indicate that the system exhibits an order-one anisotropy on parametrically large time scales. Despite this fact, we find that gauge invariant pressure correlation functions seem to exhibit a power law behavior characteristic for wave turbulence.Comment: 16 pages, 7 figures, to appear in Phys. Rev.

Dynamic critical phenomena from spectral functions on the lattice

We investigate spectral functions in the vicinity of the critical temperature of a second-order phase transition. Since critical phenomena in quantum field theories are governed by classical dynamics, universal properties can be computed using real-time lattice simulations. For the example of a relativistic single-component scalar field theory in 2+1 dimensions, we compute the spectral function described by universal scaling functions and extract the dynamic critical exponent z. Together with exactly known static properties of this theory, we obtain a verification from first principles that the relativistic theory is well described by the dynamic universality class of relaxational models with conserved density (Model C).Comment: 18 pages, 6 figures, NPB version, minor change

Skin friction in zero-pressure-gradient boundary layers

A global approach leading to a self-consistent solution to the Navier-Stokes-Prandtl equations for zero-pressure-gradient boundary layers is presented. It is shown that as $Re_{\delta}\rightarrow \infty$, the dynamically defined boundary layer thickness $\delta(x)\propto x/\ln^{2}Re_{x}$ and the skin friction $\lambda=\frac{2\tau_{w}}{\rho U_{0}^{2}}\propto 1/\ln^{2}\delta(x)$. Here $\tau_{w}$ and $U_{0}$ are the wall shear stress and free stream velocity, respectively. The theory is formulated as an expansion in powers of a small dimensionless parameter $\frac{d\delta(x)}{dx}\rightarrow 0$ in the limit $x\rightarrow \infty$

Basin of attraction for turbulent thermalization and the range of validity of classical-statistical simulations

Different thermalization scenarios for systems with large fields have been proposed in the literature based on classical-statistical lattice simulations approximating the underlying quantum dynamics. We investigate the range of validity of these simulations for condensate driven as well as fluctuation dominated initial conditions for the example of a single component scalar field theory. We show that they lead to the same phenomenon of turbulent thermalization for the whole range of (weak) couplings where the classical-statistical approach is valid. In the turbulent regime we establish the existence of a dual cascade characterized by universal scaling exponents and scaling functions. This complements previous investigations where only the direct energy cascade has been studied for the single component theory. A proposed alternative thermalization scenario for stronger couplings is shown to be beyond the range of validity of classical-statistical simulations.Comment: 11 pages, 10 figures; version published in JHEP (minor revisions

The homotopy fixed point theorem and the Quillen-Lichtenbaum conjecture in hermitian K-theory

Let X be a noetherian scheme of finite Krull dimension, having 2 invertible in its ring of regular functions, an ample family of line bundles, and a global bound on the virtual mod-2 cohomological dimensions of its residue fields. We prove that the comparison map from the hermitian K-theory of X to the homotopy fixed points of K-theory under the natural Z/2-action is a 2-adic equivalence in general, and an integral equivalence when X has no formally real residue field. We also show that the comparison map between the higher Grothendieck-Witt (hermitian K-) theory of X and its \'etale version is an isomorphism on homotopy groups in the same range as for the Quillen-Lichtenbaum conjecture in K-theory. Applications compute higher Grothendieck-Witt groups of complex algebraic varieties and rings of 2-integers in number fields, and hence values of Dedekind zeta-functions.Comment: 17 pages, to appear in Adv. Mat

Common platforms and devices used to access news about Native Americans

The opening story about Ictinike and the buzzard is a traditional oral story from my Ioway Tribe culture. It represents the way in which Native American people historically shared information and stories. Today, Native stories are shared in multiple ways: oral, written, video, audio, websites, social media, etc. This research explored the ways in which Native Americans receive their stories today, specifically news stories about Native Americans. This research was done in order to see how news outlets could better serve Native populations in the U.S. In addition, I looked at which platforms and devices are most effective for Natives to access these stories. The Native population is unique, because they make up about two percent of the U.S. population, according to the Census in 2013. Of that population, about 22 percent of Natives live on reservations, according to the 2010 Census. Many reservations are in isolated locations, so a good portion Natives may not have easy access to news. Understanding how Natives access news is imperative to tribal and mainstream news outlets. Natives are also unique, because they are not commonly mentioned in mainstream news, according to Mary Hudetz in Mainstream Media’s Spotty Coverage of Native America. When mainstream media reports on Native Americans and Native issues, it only focuses on a few common themes: culture, crime and poverty. “Mary Hudetz, a member of the Crow Tribe of Montana, an AP editor in Phoenix and a board member of the Native American Journalists Association, says lack of time and resources at media outlets contribute to fewer stories about Natives,” (Sanders 2012). The article goes on to show how this issue contributes to misconceptions and stereotyping of Native American people. Because a lack of Native coverage in mainstream is a common issue, I also address it in this research in order to inform news outlets

Common platforms and devices used to access news about Native Americans

The opening story about Ictinike and the buzzard is a traditional oral story from my Ioway Tribe culture. It represents the way in which Native American people historically shared information and stories. Today, Native stories are shared in multiple ways: oral, written, video, audio, websites, social media, etc. This research explored the ways in which Native Americans receive their stories today, specifically news stories about Native Americans. This research was done in order to see how news outlets could better serve Native populations in the U.S. In addition, I looked at which platforms and devices are most effective for Natives to access these stories. The Native population is unique, because they make up about two percent of the U.S. population, according to the Census in 2013. Of that population, about 22 percent of Natives live on reservations, according to the 2010 Census. Many reservations are in isolated locations, so a good portion Natives may not have easy access to news. Understanding how Natives access news is imperative to tribal and mainstream news outlets. Natives are also unique, because they are not commonly mentioned in mainstream news, according to Mary Hudetz in Mainstream Media’s Spotty Coverage of Native America. When mainstream media reports on Native Americans and Native issues, it only focuses on a few common themes: culture, crime and poverty. “Mary Hudetz, a member of the Crow Tribe of Montana, an AP editor in Phoenix and a board member of the Native American Journalists Association, says lack of time and resources at media outlets contribute to fewer stories about Natives,” (Sanders 2012). The article goes on to show how this issue contributes to misconceptions and stereotyping of Native American people. Because a lack of Native coverage in mainstream is a common issue, I also address it in this research in order to inform news outlets