Large-scale Geometries Research Articles

Three-Dimensional Modelling of a Large-Diameter Sealing Concept in a Deep Geological Radioactive Waste Disposal

The French National Radioactive Waste Management Agency is leading the design of a deep geological radioactive waste disposal to be located in the Callovo-Oxfordian formation. At the disposal main level, large-diameter galleries will ensure access to the storage cells and connection between zones. After a long operational period, the disposal will be closed by sealing structures located at some key positions to ensure post-closure safety over the long term. The seals are intended to prevent the flow of water and the migration of radionuclides from the disposal to the biosphere throughout the entire storage life. Thus, the long-term safety of the disposal relies to a large extent on the performance of these structures. The paper presents the work carried out to assess and simulate the phenomena underlying the response and performance of a large-diameter sealing concept under real disposal conditions. The complexity of the problem is addressed by considering in the simulations large-scale 3D geometries, advanced constitutive models, complex coupled phenomena, key geometric details at decimetre scale, and all the phases from the excavation to the post-closure period (~ a few thousand years).

The Maracangalha injectite complex: An overlooked hydrocarbon play in the Lower Cretaceous Recôncavo Basin, NE Brazil

The Recôncavo Basin is the third major natural gas producer in Brazil. Lower Cretaceous sandstones of the Maracangalha Formation (Caruaçu and Pitanga Members) hold the largest volumes of non-associated gas in this basin. However, these reservoirs are extremely complex due to a range of soft-sediment deformational process that modify the depositional architecture and impact on the original structure of the porous system. The cause of soft-sediment deformation is still contradictory because both mass movements and post-depositional fluidization has been proposed by previous studies. This uncertainty has drastic implications for reservoir predictability in the subsurface since mass-transport deposits and fluidization-remobilization complexes have very different architectures. To test these hypotheses, this study examines soft-sediment deformation structures (SSDS) in outcrop and core in order to interpret remobilization processes and to infer the main trigger mechanisms involved. Outcrop description was carried out in the coastal zone of the Todos os Santos Bay, NE Brazil, where the Maracangalha Formation is very well exposed. High-resolution core images from four producing fields located northward (Miranga, Jacuípe, Lamarão and Massapê) were also described. SSDS include a great variety of structures: 1) dish, 2) pillar, 3) consolidation lamination, 4) load structures, 5) tilted, convoluted, distorted and disrupted laminations, 6) flames, ball and pillow structures and pseudonodules, 7) large-scale mounded geometries, 8) penecontemporaneous faults and 9) sandstone intrusions/extrusions (dikes, sills, breccias and volcanoes). Intensely deformed sandstones are connected to sandstone intrusions that cut through finer-grained, low-permeability strata. Orientation of normal faults and sandstone intrusions suggests that they are genetically related. The Pitanga and Caruaçu Members are better described as facies, since they differ only by the degree of deformation. Pitanga facies is the product of remobilization of an undeformed (Caruaçu) facies. Unlike previous interpretations that indicated the action of slumps, we concluded that the upward movement of interstitial fluids (liquefaction and fluidization) was the main mechanism of remobilization, deformation and mixing of sediments. The overpressure of pore fluids and syn-rift faults propagation broke up seal-strata, releasing the fluids pressure and driving the upward movement of sediments. Key architectural elements of a sand complex are recognized in outcrop and core, including parent units, host-strata and sandstone intrusions. For the origin of this injectite complex we suggest a seismic trigger related to extensional tectonics of the rift system. The Maracangalha injectite complex comprises a new hydrocarbon play to be considered in further exploration and production (E&P) activities in the Recôncavo Basin.

Asymmetries of frequency splittings of dipolar mixed modes: A window on the topology of deep magnetic fields

Context. Space asteroseismology is revolutionizing our knowledge of the internal structure and dynamics of stars. A breakthrough is ongoing with the recent discoveries of signatures of strong magnetic fields in the core of red giant stars. The key signature for such a detection is the asymmetry these fields induce in the frequency splittings of observed dipolar mixed gravito-acoustic modes. Aims. We investigate the ability of the observed asymmetries of the frequency splittings of dipolar mixed modes to constrain the geometrical properties of deep magnetic fields. Methods. We used the powerful analytical Racah-Wigner algebra used in quantum mechanics to characterize the geometrical couplings of dipolar mixed oscillation modes with various realistically plausible topologies of fossil magnetic fields. We also computed the induced perturbation of their frequencies. Results. First, in the case of an oblique magnetic dipole, we provide the exact analytical expression of the asymmetry as a function of the angle between the rotation and magnetic axes. Its value provides a direct measure of this angle. Second, considering a combination of axisymmetric dipolar and quadrupolar fields, we show how the asymmetry is blind to the unraveling of the relative strength and sign of each component. Finally, in the case of a given multipole, we show that a negative asymmetry is a signature of non-axisymmetric topologies. Conclusions. Asymmetries of dipolar mixed modes provide a key bit of information on the geometrical topology of deep fossil magnetic fields, but this is insufficient on its own. Asteroseismic constraints should therefore be combined with spectropolarimetric observations and numerical simulations, which aim to predict the more probable stable large-scale geometries.

On the numerical and mesh-dependent parameters in a computationally enhanced phase-field fracture model coupled with a novel mesh refinement strategy

The phase-field method has been proven as a robust and computationally efficient approach to model the propagation of fractures in brittle solids. However, the performance of this technique in the context of finite element method can be questioned due to restrictions in the mesh structure and the element size to capture the fracture as a diffusive damaged region. This study is dedicated to developing a methodology for finding an appropriate length-scale parameter to model the fracturing process in a way that matches the physical character of failure in materials. The fracture process zone is chosen as the key feature in this study to propose relationships for estimating the length-scale parameter based on the tensile strength and cracking properties, and the robustness of the method is verified using experimental data. To employ the phase-field method in modelling large-scale domains and complex geometries, a novel mesh refinement strategy is developed to increase the computational efficiency based on predicting a corrected tensile strength limit depending on the element size to capture the crack-tip effectively. The proposed mesh refinement strategy reduces the computational effort significantly. Reliability and robustness of the developed relationships are successfully examined by simulating benchmark cases and comparisons with physically measured data.

Recoater-Induced Distortions and Build Failures in Selective Laser Melting of Thin-Walled Ti6Al4V Parts

Additively manufactured thin-walled structures through selective laser melting (SLM) are of great interest in achieving carbon-neutral industrial manufacturing. However, residual stresses and warpages as well as recoater crashes often occur in SLM, leading to the build failure of parts, especially for large-scale and lightweight geometries. The challenge in this work consists of investigating how the recoater affects the warpage and (sometimes) causes the failure of different thin-walled Ti6Al4V parts (wall thickness of 1.0 mm). All these parts are printed on the same platform using a commercial SLM machine. After the loose powder removal and before the cutting operation, a 3D-scanner is used to obtain the actual warpage of each component. Next, an in-house coupled thermo-mechanical finite element model suitable for the numerical simulation of the SLM process is enhanced to consider the recoater effects. This numerical framework is calibrated to predict the thin-walled warpage as measured by the 3D-scanner. The combination of numerical predictions with experimental observations facilitates a comprehensive understanding of the mechanical behavior of different thin-walled components as well as the failure mechanism due to the recoater. The findings show that the use of a higher laser energy input causes larger residual stresses and warpage responsible for the recoater crashes. Finally, potential solutions to mitigate the warpage and the recoater crashes in the SLM of lightweight structures are assessed using the validated model.

Facies distribution along salt walls: The Upper Cretaceous mixed siliciclastic-carbonate deposits of the Cotiella minibasins (Southern Pyrenees, Spain)

To assess the influence of growing salt structures on facies distribution, stratal pattern, and thickness trends, this paper provides the tectonostratigraphic framework of the outstandingly exposed Cotiella minibasins (South-Central Pyrenees, Spain). Based on detailed analysis of field cross-sections, our results showcase the syn-halokinetic upper Coniacian-lower Santonian Cotiella minibasins infill (1.5–3 km thick) records four shallow-marine depositional sequences, made of mixed siliciclastic-carbonate stratigraphic sequences. This infill is subdivided in three tectonostratigraphic units, identified by using large and small-scale halokinetic structures (i.e. wedges, megaflaps) and variations in facies associations, thicknesses, stratal patterns from the salt wall flanks to the central part of the minibasins. The first unit records the onset of salt movement with overlying laterally continuous sheet-like sedimentary layers and progressive facies transitions over distances of kms. The influence of halokinesis on sedimentation patterns was minor, and only impacted thickness trends and depocenters localization. The second unit records salt evacuation at the surface with the presence of salt-wall derived detritus, the rapid downbuilding and a increase of sand-rich facies proportions. The stratal pattern is characterized by sheet like layers, laterally discontinuous over distances of 300–600 m downdip to the salt wall. Topographically elevated salt walls likely amplified tidal currents, implying sand-rich facies accumulation along the salt wall margin. The halokinesis influence on sedimentation, thickness trends and depocenter localization was significant. The third unit records the end of the salt evacuation stage, marking a brutal decrease of sand-rich facies, likely controlled by regional controls such as eustacy and tectonics. The influence of halokinesis on sedimentation patterns, thickness trends, large-scale geometries and depocenter localization was significant. Our work indicates that distinguishing these large-scale tectonostratigraphic units and their characteristics is of prime importance to understand the archetypal facies distribution, thickness and stratal patterns along salt structures margins.

Controls on large-scale architecture and facies distribution of an oolitic-microbial carbonate shelf margin, Nanpanjiang Basin, south China

Carbonate factory types and facies architecture of carbonate depositional systems result from complex interactions among several space- and time-dependent variables, including paleobathymetry, tectonic setting, water chemistry and oceanographic setting, clastic sediment influx, and accommodation. Whereas tropical factories that dominate modern settings have been documented and modelled extensively, microbial-oolitic systems, which are very common throughout the Paleozoic and Mesozoic, have received less attention.Continuous exposures along a platform-to-basin transect of an Early Triassic (Induan) microbial-oolitic carbonate ramp to shelf system in the Nanpanjiang Basin, South China, serves as a viable analogue to similar systems, including the Jurassic Smackover Formation of the Gulf of Mexico, and provide a natural laboratory to test these variables. Carbonate deposition following end-Permian regional drowning and retreat of the Yangtze Platform resulted in low-angle margin-slope systems during the Early Triassic. Lower Triassic carbonate systems display shifts in carbonate factory types, including skeletal, microbial, and abiotic factories, and lateral and vertical architectural variability.We applied stratigraphic forward modelling using DIONISOSFLOW, calibrated with detailed stratigraphic sections and facies mapping, to assess the impact of carbonate factory type, antecedent topography, and variations in accommodation on facies distribution and large-scale geometries of the carbonate shelf margin. Results from model simulations suggest that in the absence of skeletal carbonates in the Lower Triassic, the architecture of the carbonate margin is mainly controlled by rate of microbial growth along the slope.

Clustering in laboratory and numerical turbulent swirling flows

We study the three-dimensional clustering of velocity stagnation points, of nulls of the vorticity and of the Lagrangian acceleration, and of inertial particles in turbulent flows at fixed Reynolds numbers, but under different large-scale flow geometries. To this end, we combine direct numerical simulations of homogeneous and isotropic turbulence and of the Taylor–Green flow, with particle tracking velocimetry in a von Kármán experiment. While flows have different topologies (as nulls cluster differently), particles behave similarly in all cases, indicating that Taylor-scale neutrally buoyant particles cluster as inertial particles.

Large Scale Forming of Non-Crimp Fabrics for Aerostructures

The increased production rate targets of the aerospace industry have driven the development of dry fibre infusion processes. Biaxial Non-Crimp Fabrics (NCFs) are considered in this work due to their potential high deposition rates and higher mechanical performance to woven fabrics. Forming is an integral step prior to infusion and curing. Understanding the forming behaviour of NCFs at scale is therefore key to achieving high quality parts at high rates. To investigate the draping and shearing behaviour of NCFs, geometries with complexities associated with the composite structure are used. This study presents an experimental campaign on two large scale (2 metres in span) geometries with complexities seen in primary aerostructures. The combination of features such as ramps and curvature with corner radii leads to distinctive out-of-plane wrinkling. The relationship between geometry, material and resulting preform quality is observed through the use of 3D scans. Results show differing preform quality in terms of wrinkling phenomena, showing the importance of geometry of choice for material drapability tests at an industrial scale.

Linking chromospheric activity and magnetic field properties for late-type dwarf stars

ABSTRACT Spectropolarimetric data allow for simultaneous monitoring of stellar chromospheric $\log {R^{\prime }_{\rm {HK}}}$ activity and the surface-averaged longitudinal magnetic field, Bl, giving the opportunity to probe the relationship between large-scale stellar magnetic fields and chromospheric manifestations of magnetism. We present $\log {R^{\prime }_{\rm {HK}}}$ and/or Bl measurements for 954 mid-F to mid-M stars derived from spectropolarimetric observations contained within the PolarBase database. Our magnetically active sample complements previous stellar activity surveys that focus on inactive planet-search targets. We find a positive correlation between mean $\log {R^{\prime }_{\rm {HK}}}$ and mean log |Bl|, but for G stars the relationship may undergo a change between $\log {R^{\prime }_{\rm {HK}}}\sim -4.4$ and −4.8. The mean $\log {R^{\prime }_{\rm {HK}}}$ shows a similar change with respect to the $\log {R^{\prime }_{\rm {HK}}}$ variability amplitude for intermediately active G stars. We also combine our results with archival chromospheric activity data and published observations of large-scale magnetic field geometries derived using Zeeman–Doppler Imaging. The chromospheric activity data indicate a slight under-density of late-F to early-K stars with $-4.75\le \log {R^{\prime }_{\rm HK}}\le -4.5$. This is not as prominent as the original Vaughan–Preston gap, and we do not detect similar under-populated regions in the distributions of the mean |Bl|, or the Bl and $\log {R^{\prime }_{\rm HK}}$ variability amplitudes. Chromospheric activity, activity variability, and toroidal field strength decrease on the main sequence as rotation slows. For G stars, the disappearance of dominant toroidal fields occurs at a similar chromospheric activity level as the change in the relationships between chromospheric activity, activity variability, and mean field strength.

Fluid dynamic shape optimization using self-adapting nonlinear extension operators with multigrid preconditioners

In this article we propose a scalable shape optimization algorithm which is tailored for large scale problems and geometries represented by hierarchically refined meshes. Weak scalability and grid independent convergence is achieved via a combination of multigrid schemes for the simulation of the PDEs and quasi Newton methods on the optimization side. For this purpose a self-adapting, nonlinear extension operator is proposed within the framework of the method of mappings. This operator is demonstrated to identify critical regions in the reference configuration where geometric singularities have to arise or vanish. Thereby the set of admissible transformations is adapted to the underlying shape optimization situation. The performance of the proposed method is demonstrated for the example of drag minimization of an obstacle within a stationary, incompressible Navier–Stokes flow.

What are the limits of universality?

It is a central prediction of renormalization group theory that the critical behaviours of many statistical mechanics models on Euclidean lattices depend only on the dimension and not on the specific choice of lattice. We investigate the extent to which this universality continues to hold beyond the Euclidean setting, taking as case studies Bernoulli bond percolation and lattice trees. We present strong numerical evidence that the critical exponents governing these models on transitive graphs of polynomial volume growth depend only on the volume-growth dimension of the graph and not on any other large-scale features of the geometry. For example, our results strongly suggest that percolation, which has upper-critical dimension 6, has the same critical exponents onZ4and the Heisenberg group despite the distinct large-scale geometries of these two lattices preventing the relevant percolation models from sharing a common scaling limit. On the other hand, we also show that no such universality should be expected to hold on fractals, even if one allows the exponents to depend on a large number of standard fractal dimensions. Indeed, we give natural examples of two fractals which share Hausdorff, spectral, topological and topological Hausdorff dimensions but exhibit distinct numerical values of the percolation Fisher exponentτ. This gives strong evidence against a conjecture of Balankinet al.(2018Phys. Lett. A382, 12–19 (doi:10.1016/j.physleta.2017.10.035)).

Developing a radiation field-based monitoring system for the transport and storage cask inventory during extended interim storage

Abstract. High-level radioactive waste must be stored safely for a very long time but a suitable site for long-term storage is yet to be found. Additionally, in Germany the licence for transport and storage of casks is limited to 40 years, beginning at the time of emplacement and begins to expire for the first containers in the 2030s. To resolve the conflict between not having a final repository in time and the licence expiring, the licence must be extended while ensuring uninterrupted safe storage and safe transport. The DCS-Monitor II research project supports this process by investigating approaches to noninvasive, radiation field-based diagnostics that enable the observation of potential geometric changes of the cask inventory. Previous feasibility studies in the predecessor project DCS-Monitor I showed that cask monitoring using gamma radiation, neutron fields and cosmic muons is promising. In the ongoing research project presented here, the investigations on the qualification of radiation field-based diagnostics are extended via simulations. For muon imaging, a suitable procedure which solves the inverse problem to monitor the cask inventory is implemented. In addition, a partially automated gamma and neutron measurement system is being constructed and a muon detector is being developed and built. Both systems will be tested in field studies on large scale geometries and real containers.

Lacustrine carbonate lithofacies characterization, paleontological content and depositional processes in the Mayrán Basin System

Lithofacies analyses were undertaken on a suite of well-exposed carbonate deposits from the (Pliocene) Mayrán Formation, in the Mayrán Basin system, northeast Mexico to investigate the controls on carbonate lithofacies variability in a series of linked lacustrine subbasins, with a common hydrology yet very different inputs. The lacustrine carbonates contain variable proportions of production-derived components, with subordinate proportions of detrital and early diagenetic components. The lithofacies contain, inorganic and organic calcite (average 91% CaCO3), and organic matter (10.5%–13.8% average 12.6% TOC), together with minor detrital minerals. Nine sub-facies were identified: ostracod mudstone-wackestone, clotted boundstones, gastropod wackestone-packstones, oncoid wackestone-packstones, charophyte wackestone-packstones, crystalline carbonate mudstone, stromatolites, crystalline carbonate, marlstone, and associated evaporite minerals. Isotopic composition of specific components such as micritic laminations in stromatolites (δ13Ccalcite −6.3‰ and δ18Ocalcite −8.0‰), and micrititic matrix from samples in all the subbasins (δ13Ccalcite −5.7‰ and δ18Ocalcite −7.8‰), indicate that overall calcite deposition occurred in freshwater lakes. Non luminescent (e.g. charophytes) to orange dull luminescencent micrite strongly suggest in situ carbonate production. Together these processes contributed to the local production of lime mud. Additionally, microtextural evidence of scour surfaces however, indicates that occasionally the sediment was reworked and transported laterally and basinward. Fossil content and diversity composed by Limnaeidae, Physidae, and Planorbidae types, together with phosphatised bone fragments, micro-oncoids, stromatolites, microbial morphotypes, charophytes, macrophyte phytoherms, and microcodium structres, are good references for lithofacies characterization and indicators of specific paleoenvironmental conditions. Intense to moderate bioturbation (BI 1 to 4), indicates that deposition took place under predominantly oxic conditions. Significant organic matter was preserved in these lacustrine rocks, likely controlled by moderate rates of carbonate mud production. The lacustrine lithofacies were deposited in proximal and distal lacustrine settings, making possible to recognize basin scale variability. Strata staking patterns are organized into shallowing upwards cycles (0.3–2.5 m thick), which are capped either by evaporites or beds with a pedogenic overprint. Their stacking patterns reflect lake level variations which can be recognized in all the subbasins. The lithofacies architecture within each subbasin forms parasequences that overall exhibit aggradational geometries. The lithofacies and their large scale geometries also indicate deposition occurred in a series of relatively shallow (<10 m), lake systems with ramp-like margins. The aggradational stacking patterns of the carbonates and the presence of subordinate evaporites suggest that basin hydrology (water supply and precipitation/evaporation ratios) had an important influence on facies architecture and cyclicity. The Mayrán Formation lacustrine lithofacies deposited under overfilled to balance-filled lake conditions; although balance-filled conditions with an open hydrology were more likely. Overall, facies variability in the lacustrine carbonate lithofacies was controlled by basin inherited geomorphology, accommodation, and basin hydrology, which ultimately controlled clastic trapping, solute inputs, water chemistry, primary production, and lake level changes. We interpret that all these controls were largely driven by climate.

Universal scattering laws for quiescent bouncing cosmology

Cosmological bounces occur in many gravity theories. We define singularity scattering maps relating large scale geometries before and after the bounce (assuming no BKL oscillations) and encoding microscopic details of the theory. By classifying all suitably local maps we uncover three universal laws: scaling of Kasner exponents, canonical transformation of matter, directional metric scaling. These are indeed obeyed by Bianchi I bounces in string theory, loop quantum cosmology and modified matter models; our classification then determines how inhomogeneities and anisotropies traverse bounces, and precisely extracts model-dependent degrees of freedom.

Rifted margins classification and forcing parameters

Rifted margins are the result of the successful process of thinning and breakup of the continental lithosphere leading to the formation of new oceanic lithosphere. Observations on rifted margins are now integrating an increasing amount of multi-channel seismic data and drilling of several Continent-Ocean Transitions. Based on large scale geometries and domains observed on high-quality multi-channel seismic data, this article proposes a classification reflecting the mechanical behavior of the crust from localized to diffuse deformation (strong/coupled to weak/decoupled mechanical behaviors) and magmatic intensity leading to breakup from magma-rich to magma-poor margins. We illustrate a simple classification based on mechanical behavior and magmatic production with examples of rifted margins. We propose a non-exhaustive list of forcing parameters that can control the initial rifting conditions but also their evolution through time. Therefore, rifted margins are not divided into opposing types, but described as a combination and continuum that can evolve through time and space.

Unveiling the traits of massive young stellar objects through a multi-scale survey

Context. The rarity and deeply embedded nature of young massive stars has limited the understanding of the formation of stars with masses larger than 8 M⊙. Previous work has shown that complementing spectral energy distributions with interferometric and imaging data can probe the circumstellar environments of massive young stellar objects (MYSOs) well. However, complex studies of single objects often use different approaches in their analysis. Therefore the results of these studies cannot be directly compared. Aims. This work aims to obtain the physical characteristics of a sample of MYSOs at ~0.01″ scales, at ~0.1″ scales, and as a whole, which enables us to compare the characteristics of the sources. Methods. We apply the same multi-scale method and analysis to a sample of MYSOs. High-resolution interferometric data (MIDI/VLTI), near-diffraction-limited imaging data (VISIR/VLT, COMICS/Subaru), and a multi-wavelength spectral energy distribution are combined. By fitting simulated observables derived from 2.5D radiative transfer models of disk-outflow-envelope systems to our observations, the properties of the MYSOs are constrained. Results. We find that the observables of all the MYSOs can be reproduced by models with disk-outflow-envelope geometries, analogous to the Class I geometry associated with low-mass protostars. The characteristics of the envelopes and the cavities within them are very similar across our sample. On the other hand, the disks seem to differ between the objects, in particular with regards to what we interpret as evidence of complex structures and inner holes. Conclusions. The MYSOs of this sample have similar large-scale geometries, but variance is observed among their disk properties. This is comparable to the morphologies observed for low-mass young stellar objects. A strong correlation is found between the luminosity of the central MYSO and the size of the transition disk-like inner hole for the MYSOs, implying that photoevaporation or the presence of binary companions may be the cause.

A Bayesian approach to modelling multimessenger emission from blazars using lepto-hadronic kinetic equations

ABSTRACT Blazar TXS 0506+056 is the main candidate for a coincident neutrino and gamma-ray flare event. In this paper, we present a detailed kinetic lepto-hadronic emission model capable of producing a photon and neutrino spectrum given a set of parameters. Our model includes a range of large-scale geometries and both dynamical and steady-state injection models for electrons and protons. We link this model with a Markov chain Monte Carlo sampler to obtain a powerful statistical tool that allows us to both fit the Spectral Energy Distribution and study the probability density functions and correlations of the parameters. Assuming a fiducial neutrino flux, we demonstrate how multimessenger observations can be modelled jointly in a Bayesian framework. We find the best parameters for each of the variants of the model tested and report on their cross-correlations. Additionally, we confirm that reproducing the neutrino flux of TXS 0506+056 requires an extreme proton to electron ratio either in the local acceleration process or from external injection.

INFINITE STRINGS AND THEIR LARGE SCALE PROPERTIES

AbstractThe aim of this paper is to shed light on our understanding of large scale properties of infinite strings. We say that one string $\alpha $ has weaker large scale geometry than that of $\beta $ if there is color preserving bi-Lipschitz map from $\alpha $ into $\beta $ with small distortion. This definition allows us to define a partially ordered set of large scale geometries on the classes of all infinite strings. This partial order compares large scale geometries of infinite strings. As such, it presents an algebraic tool for classification of global patterns. We study properties of this partial order. We prove, for instance, that this partial order has a greatest element and also possess infinite chains and antichains. We also investigate the sets of large scale geometries of strings accepted by finite state machines such as Büchi automata. We provide an algorithm that describes large scale geometries of strings accepted by Büchi automata. This connects the work with the complexity theory. We also prove that the quasi-isometry problem is a $\Sigma _2^0$ -complete set, thus providing a bridge with computability theory. Finally, we build algebraic structures that are invariants of large scale geometries. We invoke asymptotic cones, a key concept in geometric group theory, defined via model-theoretic notion of ultra-product. Partly, we study asymptotic cones of algorithmically random strings, thus connecting the topic with algorithmic randomness.

Turbulent deflagrations of mildly flammable refrigerant-air mixtures

With current concerns around global climate change, new hydrofluorocarbons with low Global Warming Potential (GWP) are being evaluated as alternative refrigerants. These alternative refrigerants, however, may be mildly flammable (as defined by the A2L safety group classification) and pose safety concerns for the heating, ventilation, air conditioning, and refrigeration (HVAC/R) industry. Consequently, careful assessments of different flammability characteristics and risks for these refrigerants are essential for their safe use in actual applications. In this study, deflagration propagation measurements for different mildly flammable refrigerants, including difluoromethane (R-32) and 2,3,3,3-tetrafluoropropene (R-1234yf), were undertaken in different geometries including a 9.1-m long conduit test rig and a closed cubical 12.5 m3 volume. Different tests were conducted for full volume deflagrations as well as with and without obstructions. Turbulent deflagration speeds for well-mixed, refrigerant-air mixtures have been shown to be orders of magnitude larger than their corresponding laminar flame speed values that are used in classifying flammable refrigerants in safety standards. Testing has also quantified the resulting severity as measured by the event overpressure which was shown to worsen with increased congestion or confinement as a consequence of increased induced turbulence. This work illustrates the importance for severity evaluations for actual large-scale or congested geometries of concern in practical applications. Even for mildly flammable refrigerants characterized by laminar flame speeds <2 cm/s, which is lower than the 10 cm/s limit for A2L refrigerants, relatively fast deflagrations can be generated for very congested geometries where downstream turbulence is generated as the flame front passes over obstacles in these situations.