Induced subarrays of Latin squares without repeated symbols

We show that for any Latin square L of order 2m, we can partition the rows and columns of L into pairs so that at most (m+3)/2 of the 2x2 subarrays induced contain a repeated symbol. We conjecture that any Latin square of order 2m (where m ≥ 2, with exactly five transposition class exceptions of order 6) has such a partition so that every 2x2 subarray induced contains no repeated symbol. We verify this conjecture by computer when m ≤ 4

On the Role of Mechanics in Chronic Lung Disease.

Progressive airflow obstruction is a classical hallmark of chronic lung disease, affecting more than one fourth of the adult population. As the disease progresses, the inner layer of the airway wall grows, folds inwards, and narrows the lumen. The critical failure conditions for airway folding have been studied intensely for idealized circular cross-sections. However, the role of airway branching during this process is unknown. Here, we show that the geometry of the bronchial tree plays a crucial role in chronic airway obstruction and that critical failure conditions vary significantly along a branching airway segment. We perform systematic parametric studies for varying airway cross-sections using a computational model for mucosal thickening based on the theory of finite growth. Our simulations indicate that smaller airways are at a higher risk of narrowing than larger airways and that regions away from a branch narrow more drastically than regions close to a branch. These results agree with clinical observations and could help explain the underlying mechanisms of progressive airway obstruction. Understanding growth-induced instabilities in constrained geometries has immediate biomedical applications beyond asthma and chronic bronchitis in the diagnostics and treatment of chronic gastritis, obstructive sleep apnea and breast cancer

Preliminary Results of Aerodynamic Heating Studies on the X-15 Airplane

Aerodynamic heating analysis of X-15 aircraft in fligh

Experimental Observation of a Fundamental Length Scale of Waves in Random Media

Waves propagating through a weakly scattering random medium show a pronounced branching of the flow accompanied by the formation of freak waves, i.e., extremely intense waves. Theory predicts that this strong fluctuation regime is accompanied by its own fundamental length scale of transport in random media, parametrically different from the mean free path or the localization length. We show numerically how the scintillation index can be used to assess the scaling behavior of the branching length. We report the experimental observation of this scaling using microwave transport experiments in quasi-two-dimensional resonators with randomly distributed weak scatterers. Remarkably, the scaling range extends much further than expected from random caustics statistics.Comment: 5 pages, 5 figure

Algebraic fidelity decay for local perturbations

From a reflection measurement in a rectangular microwave billiard with randomly distributed scatterers the scattering and the ordinary fidelity was studied. The position of one of the scatterers is the perturbation parameter. Such perturbations can be considered as {\em local} since wave functions are influenced only locally, in contrast to, e. g., the situation where the fidelity decay is caused by the shift of one billiard wall. Using the random-plane-wave conjecture, an analytic expression for the fidelity decay due to the shift of one scatterer has been obtained, yielding an algebraic $1/t$ decay for long times. A perfect agreement between experiment and theory has been found, including a predicted scaling behavior concerning the dependence of the fidelity decay on the shift distance. The only free parameter has been determined independently from the variance of the level velocities.Comment: 4 pages, 5 figure

Dynamical tunneling in mushroom billiards

We study the fundamental question of dynamical tunneling in generic two-dimensional Hamiltonian systems by considering regular-to-chaotic tunneling rates. Experimentally, we use microwave spectra to investigate a mushroom billiard with adjustable foot height. Numerically, we obtain tunneling rates from high precision eigenvalues using the improved method of particular solutions. Analytically, a prediction is given by extending an approach using a fictitious integrable system to billiards. In contrast to previous approaches for billiards, we find agreement with experimental and numerical data without any free parameter.Comment: 4 pages, 4 figure

Ridge regression processing

Current navigation requirements depend on a geometric dilution of precision (GDOP) criterion. As long as the GDOP stays below a specific value, navigation requirements are met. The GDOP will exceed the specified value when the measurement geometry becomes too collinear. A new signal processing technique, called Ridge Regression Processing, can reduce the effects of nearly collinear measurement geometry; thereby reducing the inflation of the measurement errors. It is shown that the Ridge signal processor gives a consistently better mean squared error (MSE) in position than the Ordinary Least Mean Squares (OLS) estimator. The applicability of this technique is currently being investigated to improve the following areas: receiver autonomous integrity monitoring (RAIM), coverage requirements, availability requirements, and precision approaches

Nodal domains in open microwave systems

Nodal domains are studied both for real $\psi_R$ and imaginary part $\psi_I$ of the wavefunctions of an open microwave cavity and found to show the same behavior as wavefunctions in closed billiards. In addition we investigate the variation of the number of nodal domains and the signed area correlation by changing the global phase $\phi_g$ according to $\psi_R+i\psi_I=e^{i\phi_g}(\psi_R'+i\psi_I')$. This variation can be qualitatively, and the correlation quantitatively explained in terms of the phase rigidity characterising the openness of the billiard.Comment: 7 pages, 10 figures, submitted to PR

Distribution of the S-matrix in chaotic microwave cavities with direct processes and absorption

We quantify the presence of direct processes in the S-matrix of chaotic microwave cavities with absorption in the one-channel case. To this end the full distribution P_S(S) of the S-matrix, i.e. S=\sqrt{R}e^{i\theta}, is studied in cavities with time-reversal symmetry for different antenna coupling strengths T_a or direct processes. The experimental results are compared with random-matrix calculations and with numerical simulations based on the Heidelberg approach including absorption. The theoretical result is a generalization of the Poisson kernel. The experimental and the numerical distributions are in excellent agreement with random-matrix predictions for all cases.Comment: 4 pages, 4 figure

Measurement of the Higgs Boson Mass with a Linear e+e- Collider

The potential of a linear e+e- collider operated at a centre-of-mass energy of 350 GeV is studied for the measurement of the Higgs boson mass. An integrated luminosity of 500 fb-1 is assumed. For Higgs boson masses of 120, 150 and 180 GeV the uncertainty on the Higgs boson mass measurement is estimated to be 40, 65 and 70 MeV, respectively. The effects of beam related systematics, namely a bias in the beam energy measurement, the beam energy spread and the luminosity spectrum due to beamstrahlung, on the precision of the Higgs boson mass measurement are investigated. In order to keep the systematic uncertainty on the Higgs boson mass well below the level of the statistical error, the beam energy measurement must be controlled with a relative precision better than 10-4.Comment: 19 pages, 10 Figure