Semi-empirical model for prediction of unsteady forces on an airfoil with application to flutter

A semi-empirical model is described for predicting unsteady aerodynamic forces on arbitrary airfoils under mildly stalled and unstalled conditions. Aerodynamic forces are modeled using second order ordinary differential equations for lift and moment with airfoil motion as the input. This model is simultaneously integrated with structural dynamics equations to determine flutter characteristics for a two degrees-of-freedom system. Results for a number of cases are presented to demonstrate the suitability of this model to predict flutter. Comparison is made to the flutter characteristics determined by a Navier-Stokes solver and also the classical incompressible potential flow theory

Beltrami state in black-hole accretion disk: A magnetofluid approach

Using the magnetofluid unification framework, we show that the accretion disk plasma (embedded in the background geometry of a blackhole) can relax to a class of states known as the Beltrami-Bernoulli (BB) equilibria. Modeling the disk plasma as a Hall MHD system, we find that the space-time curvature can significantly alter the magnetic/velocity decay rate as we move away from the compact object; the velocity profiles in BB states, for example, deviate substantially from the predicted corresponding geodesic velocity profiles. These departures imply a rich interplay of plasma dynamics and general relativity revealed by examining the corresponding Bernoulli condition representing "homogeneity" of total energy. The relaxed states have their origin in the constraints provided by the two helicity invariants of Hall MHD. These helicities conspire to introduce a new oscillatory length scale into the system that is strongly influenced by relativistic and thermal effects.Comment: 8 figure

B→K∗ℓ+ℓ−B\to K^*\ell^+\ell^- Forward-backward Asymmetry and New Physics

The forward-backward asymmetry ${\cal A}_{\rm FB}$ in $B\to K^*\ell^+\ell^-$ decay is a sensitive probe of New Physics. Previous studies have focused on the sensitivity in the position of the zero. However, the short distance effective couplings are in principle complex, as illustrated by $B\to \rho\ell^+\ell^-$ decay within the Standard Model. Allowing the effective couplings to be complex, but keeping the $B\to K^*\gamma$ and $K^*\ell^+\ell^-$ rate constraints, we find the landscape for ${\cal A}_{\rm FB}(B\to K^*\ell^+\ell^-)$ to be far richer than from entertaining just sign flips, which can be explored by future high statistics experiments.Comment: RevTex 4 pages including 5 eps figures; Minor changes made, references adde

89Y NMR Probe of Zn Induced Local Magnetism in YBa2(Cu(1-y)Zn(y))3O(6+x)

We present detailed data and analysis of the effects of Zn substitution on the planar Cu site in YBa$_2$Cu$_3$O$_{6+x}$ (YBCO$_{6+x}$) as evidenced from our $^{89}$Y NMR measurements on oriented powders. For $x<<1$ we find additional NMR lines which are associated with the Zn substitution. From our data on the intensities and temperature dependence of the shift, width, and spin-lattice relaxation rate of these resonances, we conclude that the spinless Zn 3$d$$^{10}$ state induces local moments on the near-neighbour ($$) Cu atoms. Additionally, we conjecture that the local moments actually extend to the farther Cu atoms with the magnetization alternating in sign at subsequent $nn$ sites. We show that this analysis is compatible with ESR data taken on dilute Gd doped (on the Y site) and on neutron scattering data reported recently on Zn substituted YBCO$_{6 + x}$. For optimally doped compounds $^{89}$Y $nn$ resonances are not detected, but a large $T$% -dependent contribution to the $^{89}$Y NMR linewidth is evidenced and is also attributed to the occurence of a weak induced local moment near the Zn. These results are compatible with macroscopic magnetic measurements performed on YBCO$_{6 + x}$ samples prepared specifically in order to minimize the content of impurity phases. We find significant differences between the present results on the underdoped YBCO$_{6 + x}$ samples and $$Al NMR data taken on Al$^{3+}$ substituted on the Cu site in optimally doped La$_2$CuO$_4$. Further experimental work is needed to clarify the detailed evolution of the impurity induced magnetism with hole content in the cuprates.Comment: To be published in EPJB 15 pages of text and figures in eps forma

Systems of Linear Equations over F2\mathbb{F}_2 and Problems Parameterized Above Average

In the problem Max Lin, we are given a system $Az=b$ of $m$ linear equations with $n$ variables over $\mathbb{F}_2$ in which each equation is assigned a positive weight and we wish to find an assignment of values to the variables that maximizes the excess, which is the total weight of satisfied equations minus the total weight of falsified equations. Using an algebraic approach, we obtain a lower bound for the maximum excess. Max Lin Above Average (Max Lin AA) is a parameterized version of Max Lin introduced by Mahajan et al. (Proc. IWPEC'06 and J. Comput. Syst. Sci. 75, 2009). In Max Lin AA all weights are integral and we are to decide whether the maximum excess is at least $k$, where $k$ is the parameter. It is not hard to see that we may assume that no two equations in $Az=b$ have the same left-hand side and $n={\rm rank A}$. Using our maximum excess results, we prove that, under these assumptions, Max Lin AA is fixed-parameter tractable for a wide special case: $m\le 2^{p(n)}$ for an arbitrary fixed function $p(n)=o(n)$. Max $r$-Lin AA is a special case of Max Lin AA, where each equation has at most $r$ variables. In Max Exact $r$-SAT AA we are given a multiset of $m$ clauses on $n$ variables such that each clause has $r$ variables and asked whether there is a truth assignment to the $n$ variables that satisfies at least $(1-2^{-r})m + k2^{-r}$ clauses. Using our maximum excess results, we prove that for each fixed $r\ge 2$, Max $r$-Lin AA and Max Exact $r$-SAT AA can be solved in time $2^{O(k \log k)}+m^{O(1)}.$ This improves $2^{O(k^2)}+m^{O(1)}$-time algorithms for the two problems obtained by Gutin et al. (IWPEC 2009) and Alon et al. (SODA 2010), respectively