The nature of symmetric instability and its similarity to convective and inertial instability

It is shown that there exists a local similarity among SI (Symmetric Instability), BI (Buoyancy or Convective Instability), and II (Inertial Instability) even for fully nonlinear viscous motion. The most unstable slope angles for SI and Moist SI motions are analyzed based on parcel energetics. These considerations also suggest qualitatively that CSI (Conditional SI) circulations will be slantwise and lie between the moist most unstable slope and dry least stable slope of the basic state

Qualitative and quantitative analysis of stability and instability dynamics of positive lattice solitons

We present a unified approach for qualitative and quantitative analysis of stability and instability dynamics of positive bright solitons in multi-dimensional focusing nonlinear media with a potential (lattice), which can be periodic, periodic with defects, quasiperiodic, single waveguide, etc. We show that when the soliton is unstable, the type of instability dynamic that develops depends on which of two stability conditions is violated. Specifically, violation of the slope condition leads to an amplitude instability, whereas violation of the spectral condition leads to a drift instability. We also present a quantitative approach that allows to predict the stability and instability strength

A simple limit for slope instability

Ross and Thomas have shown that subschemes can K-destabilise polarised varieties, yielding a notion known as slope (in)stability for varieties. Here we describe a special situation in which slope instability for varieties (for example of general type) corresponds to a slope instability type condition for certain bundles, making the computations almost trivial.Comment: 11 page

Instability of dilute granular flow on rough slope

We study numerically the stability of granular flow on a rough slope in collisional flow regime in the two-dimension. We examine the density dependence of the flowing behavior in low density region, and demonstrate that the particle collisions stabilize the flow above a certain density in the parameter region where a single particle shows an accelerated behavior. Within this parameter regime, however, the uniform flow is only metastable and is shown to be unstable against clustering when the particle density is not high enough.Comment: 4 pages, 6 figures, submitted to J. Phys. Soc. Jpn.; Fig. 2 replaced; references added; comments added; misprints correcte

For Rich or for Poor: When does Uncovered Interest Parity Hold?

We present a model that simultaneously explains why uncovered interest parity holds for some pairs of countries and not for others. The flexible-price two-country monetary model is extended to include a consumption externality with habit persistence. Habit persistence is modeled using Campbell Cochrane preferences with ‘deep’ habits along the lines of the work of Ravn, Schmitt-Grohe and Uribe. By deep habits, we mean habits defined over goods rather than countries. The negative slope in the Fama regression arises when monetary instability is low and the precautionary savings motive dominates the intertemporal substitution motive. When monetary instability is high, the Fama slope is positive in line with uncovered interest parity. The model is simulated using the artificial economy methodology for 34 currencies against the US dollar. We conclude that, given the predominance of precautionary savings, the degree of monetary instability explains whether or not uncovered interest parity holds.Monetary instability; Uncovered interest parity; Forward biasedness puzzle; Carry trade; Habit persistence

Long surface wave instability in dense granular flows

In this paper we present an experimental study of the long surface wave instability that can develop when a granular material flows down a rough inclined plane. The threshold and the dispersion relation of the instability are precisely measured by imposing a controlled perturbation at the entrance of the flow and measuring its evolution along the slope. The results are compared with the prediction of a linear stability analysis conducted in the framework of the depth-averaged or Saint-Venant equations. We show that when the friction law proposed in Pouliquen (1999a) is introduced in the Saint-Venant equations, the theory is able to predict quantitatively the stability threshold and the phase velocity of the waves but fails in predicting the observed cutoff frequency. The instability is shown to be of the same nature as the long wave instability observed in classical fluids but with characteristics that can dramatically differ due to the specificity of the granular rheology.Comment: 29 pages, 20 figures, to be published in Journal of Fluid Mechanic

Nonequilibrium phase transition in surface growth

Conserved growth models that exhibit a nonlinear instability in which the height (depth) of isolated pillars (grooves) grows in time are studied by numerical integration and stochastic simulation. When this instability is controlled by the introduction of an infinite series of higher-order nonlinear terms, these models exhibit, as function of a control parameter, a non-equilibrium phase transition between a kinetically rough phase with self-affine scaling and a phase that exhibits mound formation, slope selection and power-law coarsening.Comment: 7 pages, 4 .eps figures (Minor changes in text and references.

Rayleigh and depinning instabilities of forced liquid ridges on heterogeneous substrates

Depinning of two-dimensional liquid ridges and three-dimensional drops on an inclined substrate is studied within the lubrication approximation. The structures are pinned to wetting heterogeneities arising from variations of the strength of the short-range polar contribution to the disjoining pressure. The case of a periodic array of hydrophobic stripes transverse to the slope is studied in detail using a combination of direct numerical simulation and branch-following techniques. Under appropriate conditions the ridges may either depin and slide downslope as the slope is increased, or first breakup into drops via a transverse instability, prior to depinning. The different transition scenarios are examined together with the stability properties of the different possible states of the system.Comment: Physics synopsis link: http://physics.aps.org/synopsis-for/10.1103/PhysRevE.83.01630

Curvature fluctuations and Lyapunov exponent at Melting

We calculate the maximal Lyapunov exponent in constant-energy molecular dynamics simulations at the melting transition for finite clusters of 6 to 13 particles (model rare-gas and metallic systems) as well as for bulk rare-gas solid. For clusters, the Lyapunov exponent generally varies linearly with the total energy, but the slope changes sharply at the melting transition. In the bulk system, melting corresponds to a jump in the Lyapunov exponent, and this corresponds to a singularity in the variance of the curvature of the potential energy surface. In these systems there are two mechanisms of chaos -- local instability and parametric instability. We calculate the contribution of the parametric instability towards the chaoticity of these systems using a recently proposed formalism. The contribution of parametric instability is a continuous function of energy in small clusters but not in the bulk where the melting corresponds to a decrease in this quantity. This implies that the melting in small clusters does not lead to enhanced local instability.Comment: Revtex with 7 PS figures. To appear in Phys Rev

Multitemporal dendrogeomorphological analysis of slope instability in Upper Orcia Valley (Southern Tuscany, Italy)

The Upper Orcia Valley (Southern Tuscany, Italy) is a key site for the comprehension of denudation processes typically acting in Mediterranean badlands (calanchi) areas, thanks to the availability of long-lasting erosion monitoring datasets and the rapidity of erosion processes development. These features make the area suitable as an open air laboratory for the study of badlands dynamic and changes in geoheritage due to erosion (i.e. active geomorphosites). Decadal multitemporal investigations on the erosion rates and the geomorphological dynamics of the study area allowed to highlight a decrease in the average water erosion rates during the last 60 years. More in detail, a reduction of bare land and, consequently, of erosion processes effectiveness and a contemporary increasing frequency of mass wasting events were recorded. These trends can be partly related to the land cover changes occurred in the study area from the 1950s onwards, which consist of the significant increase of reforestation practices and important other forms of human impacts on slopes, mainly land levelling for agricultural exploitation. In order to better identify the most significant phases of geomorphological instability occurred in this area during the last decades, an integrated approach based on multitemporal geomorphological mapping and dendrogeomorphology analysis on specimen of Pinus nigra Arn. was used. In detail, trees colonizing a denudation slope located in the surrounding of the Radicofani town (Tuscany, Italy) and characterized by calanchi and shallow mass movements deposits, were analyzed for the 1985-2012 time period. The analysis of the growth anomaly indexes and of compression wood allowed to determine a spatio-temporal differentiation along the slope and respect to an undisturbed reference site. The negative anomaly index results to be more pronounced in the trees located on the investigated slope with respect to the ones sampled in a non-disturbed area. Compression wood characterizes trees on slope sectors mainly affected by runoff and/or mass movements with a different persistence. Erosion rates were finally calculated through dendrogeomorphological analysis on tree roots exposure (0.31-3 cm/y runoff prevailing; 5.86-27.5 cm/y, mass movements prevailing). Dendrogeomorphological results are in accordance with those obtained in the investigated areas with multitemporal photogrammetric and geomorphologic analyses