Flow over mountains: Coriolis force, transient troughs and three dimensionality

Some issues, concerning uniform, stratified flow over a three-dimensional mountain, that have not been fully explored are studied using primitive-equation models.This research was in part supported by the National Science Foundation, Division of Atmospheric Science, under Grant ATM9106495

Observation of sub-Bragg diffraction of waves in crystals

We investigate the diffraction conditions and associated formation of stopgaps for waves in crystals with different Bravais lattices. We identify a prominent stopgap in high-symmetry directions that occurs at a frequency below the ubiquitous first-order Bragg condition. This sub-Bragg diffraction condition is demonstrated by reflectance spectroscopy on two-dimensional photonic crystals with a centred rectangular lattice, revealing prominent diffraction peaks for both the sub-Bragg and first-order Bragg condition. These results have implications for wave propagation in 2 of the 5 two-dimensional Bravais lattices and 7 out of 14 three-dimensional Bravais lattices, such as centred rectangular, triangular, hexagonal and body-centred cubic

Atrial fibrillation-related cardiomyopathy: a case report

Sustained chronic tachyarrhythmias often cause a deterioration of cardiac function known as tachycardia-induced cardiomyopathy or tachycardiomyopathy

Manipulating the ABCs of self-assembly via low-χ block polymer design

Block polymer self-assembly typically translates molecular chain connectivity into mesoscale structure by exploiting incompatible blocks with large interaction parameters (χ_ij). In this article, we demonstrate that the converse approach, encoding low-χ interactions in ABC bottlebrush triblock terpolymers (χ_(AC) ≲ 0), promotes organization into a unique mixed-domain lamellar morphology, which we designate LAM_P. Transmission electron microscopy indicates that LAM_P exhibits ACBC domain connectivity, in contrast to conventional three-domain lamellae (LAM_3) with ABCB periods. Complementary small-angle X-ray scattering experiments reveal a strongly decreasing domain spacing with increasing total molar mass. Self-consistent field theory reinforces these observations and predicts that LAM_P is thermodynamically stable below a critical χ_(AC), above which LAM_3 emerges. Both experiments and theory expose close analogies to ABA′ triblock copolymer phase behavior, collectively suggesting that low-χ interactions between chemically similar or distinct blocks intimately influence self-assembly. These conclusions provide fresh opportunities for block polymer design with potential consequences spanning all self-assembling soft materials

Regularity of higher codimension area minimizing integral currents

This lecture notes are an expanded version of the course given at the ERC-School on Geometric Measure Theory and Real Analysis, held in Pisa, September 30th - October 30th 2013. The lectures aim to explain the main steps of a new proof of the partial regularity of area minimizing integer rectifiable currents in higher codimension, due originally to F. Almgren, which is contained in a series of papers in collaboration with C. De Lellis (University of Zurich).Comment: This text will appear in "Geometric Measure Theory and Real Analysis", pp. 131--192, Proceedings of the ERC school in Pisa (2013), L. Ambrosio Ed., Edizioni SNS (CRM Series

Connected Green function approach to ground state symmetry breaking in Φ1+14\Phi^4_{1+1}-theory

Using the cluster expansions for n-point Green functions we derive a closed set of dynamical equations of motion for connected equal-time Green functions by neglecting all connected functions higher than $4^{th}$ order for the $\lambda \Phi^4$-theory in $1+1$ dimensions. We apply the equations to the investigation of spontaneous ground state symmetry breaking, i.e. to the evaluation of the effective potential at temperature $T=0$. Within our momentum space discretization we obtain a second order phase transition (in agreement with the Simon-Griffith theorem) and a critical coupling of $\lambda_{crit}/4m^2=2.446$ as compared to a first order phase transition and $\lambda_{crit}/4m^2=2.568$ from the Gaussian effective potential approach.Comment: 25 Revtex pages, 5 figures available via fpt from the directory ugi-94-11 of [email protected] as one postscript file (there was a bug in our calculations, all numerical results and figures have changed significantly), ugi-94-1

The (1+1)-dimensional Massive sine-Gordon Field Theory and the Gaussian Wave-functional Approach

The ground, one- and two-particle states of the (1+1)-dimensional massive sine-Gordon field theory are investigated within the framework of the Gaussian wave-functional approach. We demonstrate that for a certain region of the model-parameter space, the vacuum of the field system is asymmetrical. Furthermore, it is shown that two-particle bound state can exist upon the asymmetric vacuum for a part of the aforementioned region. Besides, for the bosonic equivalent to the massive Schwinger model, the masses of the one boson and two-boson bound states agree with the recent second-order results of a fermion-mass perturbation calculation when the fermion mass is small.Comment: Latex, 11 pages, 8 figures (EPS files

Tunneling and propagation of vacuum bubbles on dynamical backgrounds

In the context of bubble universes produced by a first-order phase transition with large nucleation rates compared to the inverse dynamical time scale of the parent bubble, we extend the usual analysis to non-vacuum backgrounds. In particular, we provide semi-analytic and numerical results for the modified nucleation rate in FLRW backgrounds, as well as a parameter study of bubble walls propagating into inhomogeneous (LTB) or FLRW spacetimes, both in the thin-wall approximation. We show that in our model, matter in the background often prevents bubbles from successful expansion and forces them to collapse. For cases where they do expand, we give arguments why the effects on the interior spacetime are small for a wide range of reasonable parameters and discuss the limitations of the employed approximations.Comment: 29 pages, 8 figures, typos corrected, matches published versio