Note on the Kaplan-Yorke dimension and linear transport coefficients

A number of relations between the Kaplan-Yorke dimension, phase space contraction, transport coefficients and the maximal Lyapunov exponents are given for dissipative thermostatted systems, subject to a small external field in a nonequilibrium stationary state. A condition for the extensivity of phase space dimension reduction is given. A new expression for the transport coefficients in terms of the Kaplan-Yorke dimension is derived. Alternatively, the Kaplan-Yorke dimension for a dissipative macroscopic system can be expressed in terms of the transport coefficients of the system. The agreement with computer simulations for an atomic fluid at small shear rates is very good.Comment: 12 pages, 5 figures, submitted to J. Stat. Phy

Tree-root control of shallow landslides

Tree roots have long been recognized to increase slope stability by reinforcing the strength of soils. Slope stability models usually include the effects of roots by adding an apparent cohesion to the soil to simulate root strength. No model includes the combined effects of root distribution heterogeneity, stress-strain behavior of root reinforcement, or root strength in compression. Recent field observations, however, indicate that shallow landslide triggering mechanisms are characterized by differential deformation that indicates localized activation of zones in tension, compression, and shear in the soil. Here we describe a new model for slope stability that specifically considers these effects. The model is a strain-step discrete element model that reproduces the self-organized redistribution of forces on a slope during rainfall-triggered shallow landslides. We use a conceptual sigmoidal-shaped hillslope with a clearing in its center to explore the effects of tree size, spacing, weak zones, maximum root-size diameter, and different root strength configurations. Simulation results indicate that tree roots can stabilize slopes that would otherwise fail without them and, in general, higher root density with higher root reinforcement results in a more stable slope. The variation in root stiffness with diameter can, in some cases, invert this relationship. Root tension provides more resistance to failure than root compression but roots with both tension and compression offer the best resistance to failure. Lateral (slope-parallel) tension can be important in cases when the magnitude of this force is comparable to the slope-perpendicular tensile force. In this case, lateral forces can bring to failure tree-covered areas with high root reinforcement. Slope failure occurs when downslope soil compression reaches the soil maximum strength. When this occurs depends on the amount of root tension upslope in both the slope-perpendicular and slope-parallel directions. Roots in tension can prevent failure by reducing soil compressive forces downslope. When root reinforcement is limited, a crack parallel to the slope forms near the top of the hillslope. Simulations with roots that fail across this crack always resulted in a landslide. Slopes that did not form a crack could either fail or remain stable, depending on root reinforcement. Tree spacing is important for the location of weak zones but tree location on the slope (with respect to where a crack opens) is as important. Finally, for the specific cases tested here, intermediate-sized roots (5 to 20 mm in diameter) appear to contribute most to root reinforcement. Our results show more complex behaviors than can be obtained with the traditional slope-uniform, apparent-cohesion approach. A full understanding of the mechanisms of shallow landslide triggering requires a complete re-evaluation of this traditional approach that cannot predict where and how forces are mobilized and distributed in roots and soils, and how these control shallow landslides shape, size, location, and timing

An Application of CLP: Checking the Correctness of Theorems in Geometry

International audienceConstraint Logic Programming can be advantageously used to deal with quadratic constraints stemming from the verification of planar geometry theorems. A hybrid symbolic--numeric representation involving radicals and multiple precision rationals is used to denote the results of quadratic equations. A unification--like algorithm tests for the equality of two expressions using that representation. The proposed approach also utilizes geometric transformations to reduce the number of quadratic equations defining geometric constructions involving circles and straight lines. A large number (512) of geometry theorems has been verified using the proposed approach. Those theorems had been proven correct using a significantly more complex (exponential) approach in a treatise authored by Chou in 1988. Even though the proposed approach is based on verification -rather than strict correctness utilized by Chou- the efficiency attained is polynomial thus making the approach useful in classroom situations where a construction attempted by student has to be quickly validated or refuted

Spontaneous CP Violation in the Minimal Supersymmetric Standard Model at Finite Temperature

We show that in the Minimal Supersymmetric Standard Model one--loop effects at finite temperature may lead to a spontaneous breaking of CP invariance in the scalar sector. Requiring that the breaking takes place at the critical temperature for the electroweak phase transition, we find that the parameters space is compatible with a mass of the Higgs pseudoscalar in agreement with the present experimental lower bounds. Possible implications for baryogenesis are discussed.Comment: 13 pages, DFPD 93/TH/06 and UTS/DFT/93/

Constructing Sublinear Expectations on Path Space

We provide a general construction of time-consistent sublinear expectations on the space of continuous paths. It yields the existence of the conditional G-expectation of a Borel-measurable (rather than quasi-continuous) random variable, a generalization of the random G-expectation, and an optional sampling theorem that holds without exceptional set. Our results also shed light on the inherent limitations to constructing sublinear expectations through aggregation.Comment: 28 pages; forthcoming in 'Stochastic Processes and their Applications

Subglacial clast/bed contact forces

A laboratory device was built to measure the forces that ice exerts on a 0.05 m diameter rigid plastic sphere in two different configurations: in contact with a flat bed or isolated from the bed. Measurements indicated that bed-normal contact forces were 1.8 times larger than drag forces due to creeping flow past a slippery sphere isolated from the bed. Measurements of forces as a function of the bed-normal ice velocity, estimations of the ice viscosity parameter and observations of markers in the ice indicate ice is Newtonian with a viscosity of ∼1.3 × 1011 Pa s. Newtonian behavior is expected due to small and transient stresses. A model of regelation indicates that it had a negligible (\u3c5%) influence on forces. Water pressure in the cavity beneath the sphere in contact with the bed had a likewise negligible influence on contact forces. When no cavity is present, drag forces can be correctly estimated using Stokes\u27s law (Newtonian viscosity) for a slippery sphere. The same law with a bed-enhancement factor of 1.8 is appropriate for estimating bed-normal contact forces. These results reinforce previous laboratory measurements and theories but provide no support for explanations of high debris/bed friction or rates of abrasion that depend on high contact forces

Preferences for rent control: Between political geography and political economy

Following geographically concentrated changes in housing markets, real estate prices have skyrocketed in many cities and metropolitan areas across Germany. These developments have not only shifted the macro-level distribution of asset wealth among homeowners but have also resulted in price spikes in rental markets, which in turn have intensified social and economic risks among renters. This preregistered study aims to provide a theoretical rationale for, and first-time insights into, the determinants of individual preferences for rent control. It argues that policy preferences are shaped by individuals' economic and geographic positions in the housing market. It not only explores differences between homeowners and renters but also considers how heterogeneity in exposure to the burden of rental costs - structured by local rents and disposable income - explains differences within the group of renters. The results reveal the precedence of egotropic considerations over geotropic effects of common market exposures. Homeowners oppose rent control far more strongly than renters do, whose support for rent control is primarily a function of income. Market rents, in contrast, only heighten support for rent control among low-income renters. These findings deepen our understanding of the politicization of housing policy in Germany and advance important debates on political reactions to housing markets

Between strategy and protest: how policy demand, political dissatisfaction and strategic incentives matter for far-right voting

What attracts voters to far-right parties? Emphasizing the repercussions of far-right parties' past achievements on the mobilization of voters' electoral demand, this paper develops an argument of context-dependent strategic far-right voting. Far-right parties seek to mobilize on a combination of demand for nativist policies and anti-establishment protest sentiment. Their capacity of doing so, however, critically depends on the strategic incentives they supply. My findings from a comparative analysis based on six waves of the European Election Study show that far-right parties' past attainment of legislative strength boosts the credibility of their policy appeal and broadens the scope of their protest appeal whereas their participation in government jeopardizes their capacity to mobilize on popular discontent

Ice flow across a warm-based/cold-based transition at a glacier margin

Where polythermal glaciers have frozen margins that buttress otherwise temperate-based sliding ice, longitudinal compression can strongly influence ice flow trajectory, and consequently sediment transport paths. Past efforts to model flow in the vicinity of a basal thermal transition (BTT) have generally relied on simplified boundary conditions or rheological idealizations, making these model results difficult to apply to real glacier termini. Herein, we present results of numerical simulations using a power-law rheology and with boundary conditions that better represent the frozen margin. Model results indicate that a transition to a non-sliding frozen margin causes a decline in surface velocity made possible by upward ice flow, implying either enhanced ablation for steady-state simulations or the formation of a surface bulge. Permitting ice loss by ablation combined with realistic treatment of basal slip conditions subdues basal stress concentrations and thereby inhibits development of structural discontinuities such as thrust faults. Upward ice flow is accommodated by vertical extension upglacier of the BTT. This strain regime can potentially account for key structural features in polythermal glacier termini without appealing to thrusting

Conditions for Thrust Faulting in a Glacier

Dipping, arcuate bands of debris-rich ice outcropping near the margins of glaciers are often interpreted as thrust faults, assumed to originate in zones of longitudinal compression. Identification of thrusts is typically based either on the geometry and sedimentology of the debris bands or on the crystal fabric of surrounding ice, but the physical processes necessary to generate thrusts are rarely evaluated. Herein, we combine a numerical model of compressive ice flow near a glacier margin with theoretical stress and strain rate criteria for ice fracture and stress criteria for frictional slip to determine the conditions necessary for thrust faulting in glaciers. This model is applied to two different glaciological settings where longitudinal compression has been documented: (1) the transition between warm-based and cold-based ice near the terminus of Storglaciären, Sweden, and (2) the downglacier extent of the 1983 surge front of Variegated Glacier where surging ice encountered stagnant ice. Simulations representing the margin of Storglaciären indicate that peak compressive strain rates are six orders of magnitude too small to induce fracture, whereas at Variegated Glacier, strain rates were an order of magnitude too small for compressive fracture. In both groups of simulations, preexisting fractures governed by Coulomb friction are susceptible to slip if they span the ice thickness, are oriented close to the optimal fracture angle, and, in the case of Storglaciären, are subject to water pressures that are a large fraction of ice overburden pressure. Variations about the optimal fracture orientation, low or zero water pressure, high sliding friction coefficient, and limited vertical or lateral fracture extent each tend to suppress thrusting