Quasi-rigidity: some uniqueness issues

Quasi-rigidity means that one builds a theory for assemblies of grains under a slowly changing external load by using the deformation of those grains as a small parameter. Is quasi-rigidity a complete theory for these granular assemblies? Does it provide unique predictions of the assembly's behavior, or must some other process be invoked to decide between several possibilities? We provide evidence that quasi-rigidity is a complete theory by showing that two possible sources of indeterminacy do not exist for the case of disk shaped grains. One possible source of indeterminacy arises from zero-frequency modes present in the packing. This problem can be solved by considering the conditions required to obtain force equilibrium. A second possible source of indeterminacy is the necessity to choose the status (sliding or non-sliding) at each contact. We show that only one choice is permitted, if contacts slide only when required by Coulomb friction.Comment: 14 pages, 3 figures, submitted to Phys Rev E (introduction and conclusion revised

Degradation mechanisms and consequences for SOC stocks for the world's largest alpine pastoral ecosystem on the Tibetan Plateau

Approximately 1.5 million km² of the Tibetan Plateau are covered with grasslands. Thereof one third is occupied by the world’s largest pastoral alpine ecosystem (Kobresia pastures). Paleo-records indicate the grazing-induced origin of this ecosystem since more than 8000 years or at least since yak domestication since 4000 years. Long-term moderate grazing by yak and sheep increased belowground C allocation of Kobresia pygmaea, caused the development of dense root-mats and finally lead to an accumulation of soil organic carbon (SOC) and nutrients such as nitrogen (N) and phosphorus (P) in the topsoil. These pastures, however, are increasingly affected by large-scale degradation caused by overgrazing of these highly sensitive ecosystems. Loss of the topsoil threatens several ecosystem functions: i.e. SOC and nutrient storage, biodiversity, provision of grazing-ground and supply of clean water for large parts of SE-Asia. Here, we present a conceptual model and results of degradation processes combining anthropogenic and natural amplifications. To evaluate losses of SOC and nutrients we synthesize field observations and surveys in the highlands and validates this with own analyses in the Kobresia core area. We show that drought- and frost-induced polygonal cracking opens the root-mats, already weakened by overgrazing. This initiates a dying of the Kobresia turf, extends the surface cracks, triggers soil erosion and promotes SOC mineralization and leaching losses. Soil erosion caused further high losses of SOC and nutrients from the topsoil (i.e. 0-10 cm: ~5.1 kg C m-2), whereas SOC loss beneath the surface cracks was primary caused by both, decreasing C-input and SOC mineralization (mineralization-derived SOC loss: ~2.5 kg C m-2). The root biomass decreased with intensity of pasture degradation and lower C input constrains the ecosystem recovery. A negative δ13C shift of SOC reflected intensive decomposition and corresponded to a relative enrichment of 13C depleted lignin components. In sum, degradation triggered high SOC loss (up to 70% of intact soil in 0-30 cm: ~7.6 kg C m-2) from this ecosystem with profound consequences for carbon sequestration, atmospheric CO2, water quality and ecosystem stability

МНОГОФАЗНО-ОДНОФАЗНыЕ РЕВЕРСИВНыЕ ЭЛЕКТРОМАШИННО-ВЕНТИЛЬНыЕ ПРЕОБРАЗОВАТЕЛИ БЕСКОНТАКТНыХ МАШИН ДВОЙНОГО ПИТАНИЯ

Розглянуто процеси в багатофазно-однофазних реверсивних електромашинно-вентильних перетворю- вачах безконтактних машин подвійного живлення. Рассмотрены процессы в многофазно-однофазных реверсивных электромашинно-вентильных преобра- зователях бесконтактных машин двойного питания

Phase-field models for brittle and cohesive fracture

In this paper we first recapitulate some basic notions of brittle and cohesive fracture models, as well as the phase-field approximation to fracture. Next, a critical assessment is made of the sensitivity of the phase-field approach to brittle fracture, in particular the degradation function, and the use of monolithic versus partitioned solution schemes. The last part of the paper makes extensions to a recently developed phase-field model for cohesive fracture, in particular for propagating cracks. Using some simple examples the current state of the cohesive phase-field model is shown

Nitrogen Uptake in an Alpine Kobresia Pasture on the Tibetan Plateau: Localization by ¹⁵N Labeling and Implications for a Vulnerable Ecosystem

© 2015, Springer Science+Business Media New York. Grasslands are very important regionally and globally because they store large amounts of carbon (C) and nitrogen (N) and provide food for grazing animals. Intensive degradation of alpine grasslands in recent decades has mainly impacted the upper root-mat/soil horizon, with severe consequences for nutrient uptake in these nutrient-limited ecosystems. We used 15N labeling to identify the role of individual soil layers for N-uptake by Kobresia pygmaea—the dominating plant in the degraded Tibetan pasture ecosystems. We hypothesized a very efficient N-uptake corresponding mainly to the vertical distribution of living roots (topsoil > subsoil). We assume that K. pygmaea develops a very dense root-mat, which has to be maintained by small aboveground biomass, to enable this efficient N-uptake. Consequently, a higher N-investment into roots compared to shoots was hypothesized. The 15N recovery in whole plants (~70%) indicated very efficient N-uptake from the upper injection depths (0–5 cm). The highest 15N amounts were recovered in root biomass, whereby 15N recovery in roots strongly decreased with depth. In contrast, 15N recovery in shoots was generally low (~18%) and independent of the 15N injection depth. This clearly shows that the low N demand of Kobresia shoots can be easily covered by N-uptake from any depth. Less living root biomass in lower versus upper soil was compensated by a higher specific activity of roots for N-uptake. The 15N allocation into roots was on average 1.7 times higher than that into shoots, which agreed well with the very high R/S ratio. Increasing root biomass is an efficient strategy of K. pygmaea to compete for belowground resources at depths and periods with available resources. This implies high C-costs to maintain root biomass (~6.0 kg DM m−2), which must be covered by a very low amount of photosynthetically active shoots (0.3 kg DM m−2). It also suggests that Kobresia grasslands react extremely sensitively toward changes in climate and management that disrupt this above-/belowground trade-off mechanism

Rapid post-fire re-assembly of species-rich bryophyte communities in Afroalpine heathlands

Questions In some fire-prone ecosystems, bryophytes play a crucial role by providing the surface fuel that controls the fire return interval. Afroalpine heathlands are such an ecosystem, yet almost nothing is known about the bryophytes in this system. We do not know the level of species richness, or if there is a successive accumulation of species over time, or if some species are adapted to specific phases along the successional gradient, for example early-successional species sensitive to competition. Location Afroalpine heathlands in Ethiopia. Methods We made an inventory of all bryophytes in 48 plots of 5 m × 5 m, distributed along a chronosequence from 1 to 25 years post fire. The heathlands are located between 3500 m and 3800 m a.s.l. and are managed by traditional pasture burning with fire intervals of 8–20 years. Results We found in total 111 taxa of bryophytes. Post-fire mortality was almost 100%. The youngest plots had only a few cosmopolitan species often found after fire. Initially, species richness increased monotonically while starting to level off around 15 years after fire, when many plots had around 30 species and a high cover of Breutelia diffracta, which is a key ground-living species, important as surface fuel. Most species were found with sporophytes, a pattern even stronger for the most frequent species. Conclusions Interestingly, bryophyte diversity is already remarkably high by only 15 years after total eradication. The relatively slow accumulation of species in the first years after fire suggests that dispersal in space, and not time, is the major mechanism by which sites regain their diversity (i.e. spore banks play a smaller role than colonization of wind-borne spores). This indicates that the high species richness is built up through colonization from surrounding heathlands, and perhaps also from higher-altitude alpine grasslands and lower-altitude forests, and that the bryophyte diversity in this system is maintained by the traditional fire and grazing management

Long-term fire resilience of the Ericaceous Belt, Bale Mountains, Ethiopia

Fire is the most frequent disturbance in the Ericaceous Belt (ca 3000- 4300 m.a.s.l.), one of the most important plant communities of tropical African mountains. Through resprouting after fire, Erica establishes a positive fire feedback under certain burning regimes. However, present-day human activity in the Bale Mountains of Ethiopia includes fire and grazing systems that may have a negative impact on the resilience of the ericaceous ecosystem. Current knowledge of Erica-fire relationships is based on studies of modern vegetation, lacking a longer time perspective that can shed light on baseline conditions for the fire feedback. We hypothesize that fire has influenced Erica communities in the Bale Mountains at millennial timescales. To test this, we (1) identify the fire history of the Bale Mountains through a pollen and charcoal record from Garba Guracha, a lake at 3950 m.a.s.l., and (2) describe the long-term bidirectional feedback between wildfire and Erica, which may control the ecosystem's resilience. Our results support fire occurrence in the area since ca 14 000 years ago, with particularly intense burning during the early Holocene, 10.8-6.0 cal ka BP. We show that a positive feedback between Erica abundance and fire occurrence was in operation throughout the Lateglacial and Holocene, and interpret the Ericaceous Belt of the Ethiopian mountains as a long-term fire resilient ecosystem. We propose that controlled burning should be an integral part of landscape management in the Bale Mountains National Park

Fate of Organic and Inorganic Nitrogen in Crusted and Non-Crusted Kobresia Grasslands

Copyright © 2016 John Wiley & Sons, Ltd.A widespread pattern of the Tibetan plateau is mosaics of grasslands of Cyperaceae and grasses with forbs, interspersed with patches covered by lichen crusts induced by overgrazing. However, the fate of inorganic and organic N in non-crusted and crusted patches in Kobresia grasslands remains unknown. We reported on a field 15N-labeling experiment in two contrasting patches to compare retention of organic and inorganic N over a period of 29 days. 15N as KNO3, (NH4)2SO4 or glycine was sprayed onto soil surface. Crusted patches decreased plant and soil N stocks. More 15N from three N forms was recovered in soil than plants in both patches 29 days after the labeling. In non-crusted patches, 15N recovery by the living roots was about two times higher than in crusted ones, mainly because of higher root biomass. Microorganisms in non-crusted patches were N-limited because of more living roots and competed strongly for N with roots. Inorganic N input to non-crusted patches could alleviate N limitation to plants and microorganisms, and leads to higher total 15N recovery (plant + soil) for inorganic N forms. Compared to non-crusted patches, microorganisms in crusted patches were more C-limited because of depletion of available C caused by less root exudation. Added glycine could activate microorganisms, together with the hydrophobicity of glycine and crusts, leading to higher 15N-glycine than inorganic N. We conclude that overgrazing-induced crusts in Kobresia grasslands changed the fate of inorganic and organic N, and lead to lower total recovery from inorganic N but higher from organic N. Copyright © 2016 John Wiley & Sons, Ltd

Fate of Organic and Inorganic Nitrogen in Crusted and Non-Crusted Kobresia Grasslands

© 2016 John Wiley & Sons, Ltd.A widespread pattern of the Tibetan plateau is mosaics of grasslands of Cyperaceae and grasses with forbs, interspersed with patches covered by lichen crusts induced by overgrazing. However, the fate of inorganic and organic N in non-crusted and crusted patches in Kobresia grasslands remains unknown. We reported on a field 15N-labeling experiment in two contrasting patches to compare retention of organic and inorganic N over a period of 29days. 15N as KNO3, (NH4)2SO4 or glycine was sprayed onto soil surface. Crusted patches decreased plant and soil N stocks. More 15N from three N forms was recovered in soil than plants in both patches 29days after the labeling. In non-crusted patches, 15N recovery by the living roots was about two times higher than in crusted ones, mainly because of higher root biomass. Microorganisms in non-crusted patches were N-limited because of more living roots and competed strongly for N with roots. Inorganic N input to non-crusted patches could alleviate N limitation to plants and microorganisms, and leads to higher total 15N recovery (plant+soil) for inorganic N forms. Compared to non-crusted patches, microorganisms in crusted patches were more C-limited because of depletion of available C caused by less root exudation. Added glycine could activate microorganisms, together with the hydrophobicity of glycine and crusts, leading to higher 15N-glycine than inorganic N. We conclude that overgrazing-induced crusts in Kobresia grasslands changed the fate of inorganic and organic N, and lead to lower total recovery from inorganic N but higher from organic N