Selection of dune shapes and velocities. Part 2: A two-dimensional modelling

We present in this paper a simplification of the dune model proposed by Sauermann et al. which keeps the basic mechanisms but allows analytical and parametric studies. Two kinds of purely propagative two dimensional solutions are exhibited: dunes and domes, which, by contrast to the former, do not show avalanche slip face. Their shape and velocity can be predicted as a function of their size. We recover in particular that dune profiles are not scale invariant (small dunes are flatter than the large ones), and that the inverse of the velocity grows almost linearly with the dune size. We furthermore get the existence of a critical mass below which no stable dune exists. However, the linear stability analysis of a flat sand sheet shows that it is unstable at large wavelengths and suggests a mechanism of dune initiation.Comment: submitted to Eur. Phys. J. B, 13 pages, 17 figure

On multicurve models for the term structure

In the context of multi-curve modeling we consider a two-curve setup, with one curve for discounting (OIS swap curve) and one for generating future cash flows (LIBOR for a give tenor). Within this context we present an approach for the clean-valuation pricing of FRAs and CAPs (linear and nonlinear derivatives) with one of the main goals being also that of exhibiting an "adjustment factor" when passing from the one-curve to the two-curve setting. The model itself corresponds to short rate modeling where the short rate and a short rate spread are driven by affine factors; this allows for correlation between short rate and short rate spread as well as to exploit the convenient affine structure methodology. We briefly comment also on the calibration of the model parameters, including the correlation factor.Comment: 16 page

Heap Formation in Granular Media

Using molecular dynamics (MD) simulations, we find the formation of heaps in a system of granular particles contained in a box with oscillating bottom and fixed sidewalls. The simulation includes the effect of static friction, which is found to be crucial in maintaining a stable heap. We also find another mechanism for heap formation in systems under constant vertical shear. In both systems, heaps are formed due to a net downward shear by the sidewalls. We discuss the origin of net downward shear for the vibration induced heap.Comment: 11 pages, 4 figures available upon request, Plain TeX, HLRZ-101/9

Pemodelan Dimensi Fraktal Multiskala untuk Mengenali Bentuk Daun

Penelitian ini membangun model untuk membedakan bentuk daun menggunakan dimensi fraktal multiskala. Identifikasi tumbuhan obat sangat penting mengingat keanekaragaman hayati di Indonesia dan peran pentingnya di Indonesia. Identifikasi tanaman dapat dilakukan menggunakan analisis bentuk dengan daun sebagai cirinya. Dimensi fraktal multiskala adalah salah satu metode analisis bentuk yang menganalisis bentuk melalui kompleksitasnya. Empat tipe bentuk daun dari spesies berbeda dimodelkan dalam penelitian ini. Analisis multiskala mampu memberikan informasi tambahan mengenai alur Perubahan luas bidang dilasi, namun tidak mencirikan bentuk daun yang diuji dalam penelitian ini

Delay of Disorder by Diluted Polymers

We study the effect of diluted flexible polymers on a disordered capillary wave state. The waves are generated at an interface of a dyed water sugar solution and a low viscous silicon oil. This allows for a quantitative measurement of the spatio-temporal Fourier spectrum. The primary pattern after the first bifurcation from the flat interface are squares. With increasing driving strength we observe a melting of the square pattern. It is replaced by a weak turbulent cascade. The addition of a small amount of polymers to the water layer does not affect the critical acceleration but shifts the disorder transition to higher driving strenghs and the short wave length - high frequency fluctuations are suppressed

Scarred Patterns in Surface Waves

Surface wave patterns are investigated experimentally in a system geometry that has become a paradigm of quantum chaos: the stadium billiard. Linear waves in bounded geometries for which classical ray trajectories are chaotic are known to give rise to scarred patterns. Here, we utilize parametrically forced surface waves (Faraday waves), which become progressively nonlinear beyond the wave instability threshold, to investigate the subtle interplay between boundaries and nonlinearity. Only a subset (three main types) of the computed linear modes of the stadium are observed in a systematic scan. These correspond to modes in which the wave amplitudes are strongly enhanced along paths corresponding to certain periodic ray orbits. Many other modes are found to be suppressed, in general agreement with a prediction by Agam and Altshuler based on boundary dissipation and the Lyapunov exponent of the associated orbit. Spatially asymmetric or disordered (but time-independent) patterns are also found even near onset. As the driving acceleration is increased, the time-independent scarred patterns persist, but in some cases transitions between modes are noted. The onset of spatiotemporal chaos at higher forcing amplitude often involves a nonperiodic oscillation between spatially ordered and disordered states. We characterize this phenomenon using the concept of pattern entropy. The rate of change of the patterns is found to be reduced as the state passes temporarily near the ordered configurations of lower entropy. We also report complex but highly symmetric (time-independent) patterns far above onset in the regime that is normally chaotic.Comment: 9 pages, 10 figures (low resolution gif files). Updated and added references and text. For high resolution images: http://physics.clarku.edu/~akudrolli/stadium.htm