Triangular buckling patterns of twisted inextensible strips

When twisting a strip of paper or acetate under high longitudinal tension, one observes, at some critical load, a buckling of the strip into a regular triangular pattern. Very similar triangular facets have recently been observed in solutions to a new set of geometrically-exact equations describing the equilibrium shape of thin inextensible elastic strips. Here we formulate a modified boundary-value problem for these equations and construct post-buckling solutions in good agreement with the observed pattern in twisted strips. We also study the force-extension and moment-twist behaviour of these strips by varying the mode number n of triangular facets

The effect of weathering regime on uranium decay series and osmium in two soil profiles

Two soil profiles from the United States with radically different emplacement and climatic histories were analyzed for U, Th and members of the 238U decay series (234U, 230Th, 226Ra, 210Pb), 137Cs and osmium isotopes. The arid New Mexico profile is developed on an approximately 250,000 years old colluvium while the temperate New Hampshire profile is formed on till after the last glaciation at about 10,000 years ago. Both the profiles show significant 234U/238U, 230Th/234U and 226Ra/230Th disequilibria, however, in the New Hampshire profile, the disequilibria are far more pronounced in mid-depths (20-50 cm). High Os concentration with highly radiogenic 187Os/188Os is another characteristic of the mid-depths of the New Hampshire profile. This layer, particularly at about 30-40 cm depth has the characteristics of a soil developed on black shale, as evidenced from both the high U and Os concentrations and the large excess of 230Th over 238U. This profile clearly shows that the regolith on which the contemporary soil is developing was not homogeneous. The presence of measurable excess 226Ra activity over 230Th activity in both profiles suggests the need for a source of 226Ra external to the regolith in both cases. Atmospheric deposition of 226Ra is a possible source for this 226Ra excess and brings to light the important role of atmospheric deposiion of nuclides and their transport in the soil profile in pedogenic processes. It also shows that regolith developed by glacial processes need not be homogeneous, thereby confounding the understanding of vertically modified soil profiles

Evidence of hydrological control of Sr behavior in stream water (Strengbach catchment, Vosges mountains, France)

Strontium and particularly 87Sr/86Sr ratios in stream water have often been used to calculate weathering rates in catchments. Nevertheless, in the literature, discharge variation effects on the geochemical behavior of Sr are often omitted or considered as negligible. A regular survey of both Sr concentrations and Sr isotope ratios of the Strengbach stream water draining a granite (Vosges mountains, France) has been performed during one year. The results indicate that during low water flow periods, waters contain lower Sr concentrations and less radiogenic Sr isotope ratios (Sr=11.6 ppb and 87Sr/86Sr=0.7246 as an average, respectively) than during high water flow periods (Sr= 13 ppb and 87Sr/86Sr=0.7252 as an average, respectively). This is contrary to expected dilution processes by meteoric waters which have comparatively lower Sr isotopic ratios and lower Sr concentrations. Furthermore, 87Sr/86Sr ratios in stream water behave in 3 different ways depending on moisture and on hydrological conditions prevailing in the catchment. During low water flow periods (discharge < 9 l/s), a positive linear relationship exists between Sr isotope ratio and discharge, indicating the influence of radiogenic waters draining the saturated area during storm events. During high water flow conditions, rising discharges are characterized by significantly less radiogenic waters than the recession stages of discharge. This suggests a large contribution of radiogenic waters draining the deep layers of the hillslopes during the recession stages, particularly those from the more radiogenic north-facing slopes. These results allow one to confirm the negligible instantaneous incidence of rainwater on stream water chemistry during flood events, as well as the existence in the catchment of distinct contributive areas and reservoirs. The influence of these areas or reservoirs on the fluctuations of Sr concentrations and on Sr isotopic variations in stream water depends on both moisture and hydrological conditions. Hence, on a same bedrock type, 87Sr/86Sr ratios in surface waters can be related to flow rate. Consequently, discharge variations must be considered as a pre-requisite when using Sr isotopes for calculating weathering rates in catchments, particularly to define the range of variations of the end-members

Strontium as a tracer of weathering processes in a silicate catchment polluted by acid atmospheric inputs, Strengbach, France

This paper determines the weathering and atmospheric contributions of Ca in surface water from a small spruce forested silicate catchment (N–E France) receiving acid atmospheric inputs. The bedrock is a granite with K-feldspar and albite as dominant phases. The calcium content in plagioclase is low and the Ca/Na ratio in surface water is high, reflecting other sources of calcium from those expected from the weathering of major mineral phases. The biotite content is low. Only traces of apatite were detected while no calcite was found in spite of a major hydrothermal event having affected the granite. The strontium isotopic ratio 87Sr/86Sr and Sr content was used as a tracer of weathering and was determined in minerals and bulk bedrock, open field precipitation, throughfall, soil solution, spring and stream water. The Sr isotopic ratio of the reacting weathering end-member was predicted by simulating the alteration of the granite minerals by incorporating strontium into the water–rock interaction kinetic code KINDIS. In the early stages of water–rock interaction, K-feldspar and biotite strongly influence the isotopic composition of the weathering solution whereas, the Na-rich plagioclase appears to be the main long-term reactive weathering end-member. Approximately 50% of dissolved Sr in streamwater are atmospherically derived. The 87Sr/86Sr ratios of exchangeable Sr in the fine fraction at 1-m depth from a soil profile indicate that the amount of exchangeable Sr seems essentially controlled by atmospheric inputs. The exception is the deep saprolite where weathering processes could supply the Sr (and Ca). Na-Plagioclase weathering obviously control the chemistry and the isotopic composition of surface waters. The weathering of trace mineral plays a secondary role, the exception is for apatite when plagioclase is absent. Our hydrochemical, mineralogical and isotopic investigations show that a major part of the strong Ca losses detected in catchment hydrochemical budgets that result from the neutralization of acid precipitation has an atmospheric origin. Consequently, in the long term, in such areas, the availability of such an exchangeable base cation might be strongly limited and surface waters consequently acidified

Born-Infeld particles and Dirichlet p-branes

Born-Infeld theory admits finite energy point particle solutions with $\delta$-function sources, BIons. I discuss their role in the theory of Dirichlet $p$-branes as the ends of strings intersecting the brane when the effects of gravity are ignored. There are also topologically non-trivial electrically neutral catenoidal solutions looking like two $p$-branes joined by a throat. The general solution is a non-singular deformation of the catenoid if the charge is not too large and a singular deformation of the BIon solution for charges above that limit. The intermediate solution is BPS and Coulomb-like. Performing a duality rotation we obtain monopole solutions, the BPS limit being a solution of the abelian Bogolmol'nyi equations. The situation closely resembles that of sub and super extreme black-brane solutions of the supergravity theories. I also show that certain special Lagrangian submanifolds of ${\Bbb C}^p$, $p=3,4,5$, may be regarded as supersymmetric configurations consisting of $p$-branes at angles joined by throats which are the sources of global monopoles. Vortex solutions are also exhibited.Comment: 40 pages Latex file, no figure

A Note on Classical Solution of Chaplygin-gas as D-brane

The classical solution of bosonic d-brane in (d+1,1) space-time is studied. We work with light-cone gauge and reduce the problem into Chaplygin gas problem. The static equation is equivalent to vanishing of extrinsic mean curvature, which is similar to Einstein equation in vacuum. We show that the d-brane problem in this gauge is closely related to Plateau problem, and we give some non-trivial solutions from minimal surfaces. The solutions of d-1,d,d+1 spatial dimensions are obtained from d-dimensional minimal surfaces as solutions of Plateau problem. In addition we discuss on the relation to Hamiltonian-BRST formalism for d-branes.Comment: 20 pages,No figures, Latex, Address change

Temporal variability of summer-time ozone and aerosols in the free troposphere over the eastern North Atlantic

In the free troposphere over Tenerife in the summer, O3 concentrations are anti-correlated with major pollutant aerosols (nss-SO = 4 and NO−3) and with 210Pb, a tracer for boundary layer sources. In contrast, O3 is highly correlated with 7Be, a product of cosmic ray interactions in the upper troposphere and stratosphere. This suggests that natural O3 sources (i.e. the stratosphere) might be playing an important role. Nonetheless our results do not preclude the possibility that substantial amounts of pollution-related O3 could be transported in the free troposphere. However, to be consistent with our results, the transport mechanisms would have to incorporate efficient processes for the removal of pollutant aerosol species and 210Pb

Transport and residence times of tropospheric aerosols inferred from a global three-dimensional simulation of 210_Pb

A global three‐dimensional model is used to investigate the transport and tropospheric residence time of Pb, an aerosol tracer produced in the atmosphere by radioactive decay of Rn emitted from soils. The model uses meteorological input with 4°×5° horizontal resolution and 4‐hour temporal resolution from the Goddard Institute for Space Studies general circulation model (GCM). It computes aerosol scavenging by convective precipitation as part of the wet convective mass transport operator in order to capture the coupling between vertical transport and rainout. Scavenging in convective precipitation accounts for 74% of the global Pb sink in the model; scavenging in large‐scale precipitation accounts for 12%, and scavenging in dry deposition accounts for 14%. The model captures 63% of the variance of yearly mean Pb concentrations measured at 85 sites around the world with negligible mean bias, lending support to the computation of aerosol scavenging. There are, however, a number of regional and seasonal discrepancies that reflect in part anomalies in GCM precipitation. Computed residence times with respect to deposition for Pb aerosol in the tropospheric column are about 5 days at southern midlatitudes and 10–15 days in the tropics; values at northern midlatitudes vary from about 5 days in winter to 10 days in summer. The residence time of Pb produced in the lowest 0.5 km of atmosphere is on average four times shorter than that of Pb produced in the upper atmosphere. Both model and observations indicate a weaker decrease of Pb concentrations between the continental mixed layer and the free troposphere than is observed for total aerosol concentrations; an explanation is that Rn is transported to high altitudes in wet convective updrafts, while aerosols and soluble precursors of aerosols are scavenged by precipitation in the updrafts. Thus Pb is not simply a tracer of aerosols produced in the continental boundary layer, but also of aerosols derived from insoluble precursors emitted from the surface of continents. One may draw an analogy between Pb and nitrate, whose precursor NO is sparingly soluble, and explain in this manner the strong correlation observed between nitrate and Pb concentrations over the oceans.Engineering and Applied Science