Loop formulation of supersymmetric Yang-Mills quantum mechanics

We derive the fermion loop formulation of N=4 supersymmetric SU(N) Yang-Mills quantum mechanics on the lattice. The loop formulation naturally separates the contributions to the partition function into its bosonic and fermionic parts with fixed fermion number and provides a way to control potential fermion sign problems arising in numerical simulations of the theory. Furthermore, we present a reduced fermion matrix determinant which allows the projection into the canonical sectors of the theory and hence constitutes an alternative approach to simulate the theory on the lattice.

A review of air–ice chemical and physical interactions (AICI): liquids, quasi-liquids, and solids in snow

Snow in the environment acts as a host to rich chemistry and provides a matrix for physical exchange of contaminants within the ecosystem. The goal of this review is to summarise the current state of knowledge of physical processes and chemical reactivity in surface snow with relevance to polar regions. It focuses on a description of impurities in distinct compartments present in surface snow, such as snow crystals, grain boundaries, crystal surfaces, and liquid parts. It emphasises the microscopic description of the ice surface and its link with the environment. Distinct differences between the disordered air–ice interface, often termed quasi-liquid layer, and a liquid phase are highlighted. The reactivity in these different compartments of surface snow is discussed using many experimental studies, simulations, and selected snow models from the molecular to the macro-scale. Although new experimental techniques have extended our knowledge of the surface properties of ice and their impact on some single reactions and processes, others occurring on, at or within snow grains remain unquantified. The presence of liquid or liquid-like compartments either due to the formation of brine or disorder at surfaces of snow crystals below the freezing point may strongly modify reaction rates. Therefore, future experiments should include a detailed characterisation of the surface properties of the ice matrices. A further point that remains largely unresolved is the distribution of impurities between the different domains of the condensed phase inside the snowpack, i.e. in the bulk solid, in liquid at the surface or trapped in confined pockets within or between grains, or at the surface. While surface-sensitive laboratory techniques may in the future help to resolve this point for equilibrium conditions, additional uncertainty for the environmental snowpack may be caused by the highly dynamic nature of the snowpack due to the fast metamorphism occurring under certain environmental conditions. Due to these gaps in knowledge the first snow chemistry models have attempted to reproduce certain processes like the long-term incorporation of volatile compounds in snow and firn or the release of reactive species from the snowpack. Although so far none of the models offers a coupled approach of physical and chemical processes or a detailed representation of the different compartments, they have successfully been used to reproduce some field experiments. A fully coupled snow chemistry and physics model remains to be developed.

Supersymmetric quantum mechanics on the lattice: I. Loop formulation

Simulations of supersymmetric field theories on the lattice with (spontaneously) broken supersymmetry suffer from a fermion sign problem related to the vanishing of the Witten index. We propose a novel approach which solves this problem in low dimensions by formulating the path integral on the lattice in terms of fermion loops. For N=2 supersymmetric quantum mechanics the loop formulation becomes particularly simple and in this paper – the first in a series of three – we discuss in detail the reformulation of this model in terms of fermionic and bosonic bonds for various lattice discretisations including one which is Q-exact.

Snow shielding factors for cosmogenic nuclide dating inferred from long-term neutron detector monitoring

The depth-dependent attenuation of the secondary cosmic-ray particle flux due to snow cover and its effects on production rates of cosmogenic nuclides constitutes a potential source of uncertainty for studies conducted in regions characterized by frequent seasonal snow burial. Recent experimental and numerical modelling studies have yielded new constraints on the effect of hydrogen-rich media on the production rates of cosmogenic nuclides by low- and high-energy neutrons (<10(-3) MeV and >10(2) MeV, respectively). Here we present long-term neutron-detector monitoring data from a natural setting that we use to quantify the effect of snow cover on the attenuation of fast neutrons (0.1-10 MeV), which are responsible for the production of Ne-21 from Mg and Cl-36 from K. We use data measured between July 2001 and May 2008 at seven stations located throughout the Ecrins-Pelvoux massif (French Western Alps) and its surroundings, at elevations ranging from 200 to 2500 m a.s.l. From the cosmic-ray fluxes recorded during summer, when snow is absent, we infer an apparent attenuation length of 148 g cm(-2) in the atmosphere at a latitude of similar to 45 degrees N and for altitudes ranging from similar to 200 to 2500 m a.s.l. Using snow water-equivalent (SWE) values obtained through snow-coring campaigns that overlap in time the neutron monitoring for five stations, we show that fast neutrons are much more strongly attenuated in snow than predicted by a conventional mass-shielding formulation and the attenuation length estimated in the atmosphere. We suggest that such strong attenuation results from boundary effects at the atmosphere/snow interface induced by the high efficiency of water as a neutron moderator. Finally, we propose an empirical model that allows calculating snow-shielding correction factors as a function of SWE for studies using Ne-21 and Cl-36 analyses in Mg- and K-rich minerals, respectively. This empirical model is of interest for studies with a focus on cosmic-ray exposure dating, particularly if the target rocks are made up of mafic to ultramafic units where seasonal snow-cover is a common phenomenon.

Development of a balanced experimental–computational approach to understanding the mechanics of proximal femur fractures

The majority of people who sustain hip fractures after a fall to the side would not have been identified using current screening techniques such as areal bone mineral density. Identifying them, however, is essential so that appropriate pharmacological or lifestyle interventions can be implemented. A protocol, demonstrated on a single specimen, is introduced, comprising the following components; in vitro biofidelic drop tower testing of a proximal femur; high-speed image analysis through digital image correlation; detailed accounting of the energy present during the drop tower test; organ level finite element simulations of the drop tower test; micro level finite element simulations of critical volumes of interest in the trabecular bone. Fracture in the femoral specimen initiated in the superior part of the neck. Measured fracture load was 3760 N, compared to 4871 N predicted based on the finite element analysis. Digital image correlation showed compressive surface strains as high as 7.1% prior to fracture. Voxel level results were consistent with high-speed video data and helped identify hidden local structural weaknesses. We found using a drop tower test protocol that a femoral neck fracture can be created with a fall velocity and energy representative of a sideways fall from standing. Additionally, we found that the nested explicit finite element method used allowed us to identify local structural weaknesses associated with femur fracture initiation.

Arctic moisture source for Eurasian snow cover variations in autumn

Eurasian fall snow cover changes have been suggested as a driver for changes in the Arctic Oscillation and might provide a link between sea-ice decline in the Arctic during summer and atmospheric circulation in the following winter. However, the mechanism connecting snow cover in Eurasia to sea-ice decline in autumn is still under debate. Our analysis is based on snow observations from 820 Russian land stations, moisture transport using a Lagrangian approach derived from meteorological re-analyses. We show that declining sea-ice in the Barents and Kara Seas (BKS) acts as moisture source for the enhanced Western Siberian snow depth as a result of changed tropospheric moisture transport. Transient disturbances enter the continent from the BKS region related to anomalies in the planetary wave pattern and move southward along the Ural mountains where they merge into the extension of the Mediterranean storm track.

Modelling the system behaviour of wet snow avalanches using an expert system approach for risk management on high alpine traffic roads

The presented approach describes a model for a rule-based expert system calculating the temporal variability of the release of wet snow avalanches, using the assumption of avalanche triggering without the loading of new snow. The knowledge base of the model is created by using investigations on the system behaviour of wet snow avalanches in the Italian Ortles Alps, and is represented by a fuzzy logic rule-base. Input parameters of the expert system are numerical and linguistic variables, measurable meteorological and topographical factors and observable characteristics of the snow cover. Output of the inference method is the quantified release disposition for wet snow avalanches. Combining topographical parameters and the spatial interpolation of the calculated release disposition a hazard index map is dynamically generated. Furthermore, the spatial and temporal variability of damage potential on roads exposed to wet snow avalanches can be quantified, expressed by the number of persons at risk. The application of the rule base to the available data in the study area generated plausible results. The study demonstrates the potential for the application of expert systems and fuzzy logic in the field of natural hazard monitoring and risk management.

Supersymmetric quantum mechanics on the lattice: II. Exact results

Simulations of supersymmetric field theories with spontaneously broken supersymmetry require in addition to the ultraviolet regularisation also an infrared one, due to the emergence of the massless Goldstino. The intricate interplay between ultraviolet and infrared effects towards the continuum and infinite volume limit demands careful investigations to avoid potential problems. In this paper – the second in a series of three – we present such an investigation for N=2 supersymmetric quantum mechanics formulated on the lattice in terms of bosonic and fermionic bonds. In one dimension, the bond formulation allows to solve the system exactly, even at finite lattice spacing, through the construction and analysis of transfer matrices. In the present paper we elaborate on this approach and discuss a range of exact results for observables such as the Witten index, the mass spectra and Ward identities.

Supersymmetric quantum mechanics on the lattice: III. Simulations and algorithms

In the fermion loop formulation the contributions to the partition function naturally separate into topological equivalence classes with a definite sign. This separation forms the basis for an efficient fermion simulation algorithm using a fluctuating open fermion string. It guarantees sufficient tunnelling between the topological sectors, and hence provides a solution to the fermion sign problem affecting systems with broken supersymmetry. Moreover, the algorithm shows no critical slowing down even in the massless limit and can hence handle the massless Goldstino mode emerging in the supersymmetry broken phase. In this paper – the third in a series of three – we present the details of the simulation algorithm and demonstrate its efficiency by means of a few examples.