Analogue Models Research Articles

Analogue modelling of basin inversion: a review and future perspectives

Abstract. Basin inversion involves the reversal of subsidence in a basin due to compressional tectonic forces, leading to uplift of the basin's sedimentary infill. Detailed knowledge of basin inversion is of great importance for scientific, societal, and economic reasons, spurring continued research efforts to better understand the processes involved. Analogue tectonic modelling forms a key part of these efforts, and analogue modellers have conducted numerous studies of basin inversion. In this review paper we recap the advances in our knowledge of basin inversion processes acquired through analogue modelling studies, providing an up-to-date summary of the state of analogue modelling of basin inversion. We describe the different definitions of basin inversion that are being applied by researchers, why basin inversion has been historically an important research topic and what the general mechanics involved in basin inversion are. We subsequently treat the wide range of different experimental approaches used for basin inversion modelling, with attention to the various materials, set-ups, and techniques used for model monitoring and analysing the model results. Our new systematic overviews of generalized model results reveal the diversity of these results, which depend greatly on the chosen set-up, model layering and (oblique) kinematics of inversion, and 3D along-strike structural and kinematic variations in the system. We show how analogue modelling results are in good agreement with numerical models, and how these results help researchers to better understand natural examples of basin inversion. In addition to reviewing the past efforts in the field of analogue modelling, we also shed light on future modelling challenges and identify a number of opportunities for follow-up research. These include the testing of force boundary conditions, adding geological processes such as sedimentation, transport, and erosion; applying state-of-the-art modelling and quantification techniques; and establishing best modelling practices. We also suggest expanding the scope of basin inversion modelling beyond the traditional upper crustal “North Sea style” of inversion, which may contribute to the ongoing search for clean energy resources. It follows that basin inversion modelling can bring valuable new insights, providing a great incentive to continue our efforts in this field. We therefore hope that this review paper will form an inspiration for future analogue modelling studies of basin inversion.

A Lagrange Programming Neural Network Approach with an ℓ0-Norm Sparsity Measurement for Sparse Recovery and Its Circuit Realization

Many analog neural network approaches for sparse recovery were based on using ℓ1-norm as the surrogate of ℓ0-norm. This paper proposes an analog neural network model, namely the Lagrange programming neural network with ℓp objective and quadratic constraint (LPNN-LPQC), with an ℓ0-norm sparsity measurement for solving the constrained basis pursuit denoise (CBPDN) problem. As the ℓ0-norm is non-differentiable, we first use a differentiable ℓp-norm-like function to approximate the ℓ0-norm. However, this ℓp-norm-like function does not have an explicit expression and, thus, we use the locally competitive algorithm (LCA) concept to handle the nonexistence of the explicit expression. With the LCA approach, the dynamics are defined by the internal state vector. In the proposed model, the thresholding elements are not conventional analog elements in analog optimization. This paper also proposes a circuit realization for the thresholding elements. In the theoretical side, we prove that the equilibrium points of our proposed method satisfy Karush Kuhn Tucker (KKT) conditions of the approximated CBPDN problem, and that the equilibrium points of our proposed method are asymptotically stable. We perform a large scale simulation on various algorithms and analog models. Simulation results show that the proposed algorithm is better than or comparable to several state-of-art numerical algorithms, and that it is better than state-of-art analog neural models.

Analogue modelling of sedimentary breccias in a talus slope with or without extension—comparison with a natural case

Analogue modelling of sedimentary breccias in a talus slope with or without extension—comparison with a natural case

Computational Geodynamics of South American Plate: Contributions and Perspectives

Computational geodynamics is a key tool in Earth Sciences, enabling the simulation of different geodynamic processes at any time scale in Nature or those which cannot be adequately reproduced by analogue modelling in laboratorial conditions. Specifically, the coupling of surface processes of erosion and sedimentation with the internal dynamics of the lithosphere is a complex problem that involves the solution of a set of differential equations that are only adequately solved by numerical models. During the last three decades, different numerical models were developed to explain the importance of the coupling between the surface and internal dynamics of the Earth, both in active margins and in stable tectonic domains, showing how the coupling leads to counter-intuitive results not observed when each process is analyzed separately. One example of this complex coupling is the feedback mechanism between erosion of the landscape and the regional isostatic response of the lithosphere. In this work, we present simple isostatic and flexural elements that highlight the importance of surface processes on the stress and strain pattern in lithospheric plates. Initially, we present a review on the development of computational geodynamics at University of São Paulo. This review is followed by an analysis of the density structure of the Earth and how the high-density contrast at the Earth’s surface creates a major impact on the isostatic equilibrium of the lithosphere when variations on topographic loads are taken into account. Additionally, we show that the wavelength of the denudation of the Earth’s surface due to fluvial dynamics corresponds to the characteristic length scale for flexural bending of the lithosphere, maximizing the flexural stresses in the lithosphere. Finally, we present recent works on the coupling between surface and lithospheric processes and future challenges for the development of computational geodynamics, with possible strategies to solve them.

Influence of rheologically weak layers on fault architecture: insights from analogue models in the context of the Northern Alpine Foreland Basin

We present a series of analogue models inspired by the geology of the Zürcher Weinland region in the Northern Alpine Foreland Basin of Switzerland to explore the influence of rheological weak, i.e. (partially) ductile layers on the 3D evolution of tectonic deformation. Our model series test the impact of varying weak layer thickness and rheology, as well as different kinematics of an underlying “basal fault”. Model analysis focuses on deformation in the weak layer overburden and, uniquely, within the weak layer itself. We find that for low to moderate basal fault displacements, the above-mentioned parameters strongly influence the degree of coupling between the basal fault and the weak layer overburden. Coupling between the basal fault and overburden decreases by reducing the strength of the weak layer, or by increasing the weak layer’s thickness. As a result, basal fault displacement is less readily transferred through the weak layer, leading to a different structural style in the overburden. By contrast, increasing the amount, or rate, of basal fault slip enhances coupling and leads to a more similar structural style between basal fault and overburden. Moreover, dip-slip displacement on the basal fault is more readily transferred to the overburden than strike-slip displacement of the same magnitude. Our model results compare fairly well to natural examples in the Northern Alpine Foreland Basin, explaining various structural features. These comparisons suggest that rheological weak layers such as the Jurassic Opalinus Clay have exerted a stronger control on fault zone architecture than is commonly inferred, potentially resulting in vertical fault segmentation and variations in structural style. Furthermore, the novel addition of internal marker intervals to the weak layer in our models reveals how complex viscous flow within these layers can accommodate basal fault slip. Our model results demonstrate the complex links between fault kinematics, mechanics and 3D geometries, and can be used for interpreting structures in the Alpine Foreland, as well as in other settings with similar weak layers and basal faults driving deformation in the system.

The Relationship Between Inverted Normal Faults and Pure Thrusting During the Tectonic Inversion of the Domeyko Cordillera, Northern Chile: Structural and Seismic Interpretation and Analog Modeling Experiments

AbstractThe orogenic growth of the Domeyko Cordillera was induced by a positive tectonic inversion. In this work, we have validated this interpretation from new field data, which were combined with 2‐D reflection seismic profile interpretations obtained along the Central Andes forearc of northern Chile. To compare with this information, we performed a new series of Analog Models dealing with positive tectonic inversion. On the basis of this, we propose an integrated kinematic model that describes the relationships between extensional structures, inversion structures, and pure thrust faulting. The proposed model is developed with an initial syn‐rift phase related to the filling of half‐graben basins, followed by a positive tectonic inversion phase. Our models show two main structural styles: partially inverted normal faults and newly formed pure thrust faulting. The partial inversion of previous normal faults represents the initial stage of exhumation of the syn‐rift deposits. The pure thrusting consists of east‐verging faults, which decapitate early or partially inverted normal faults. The first type of structures are compared with west‐verging inverted, or partially inverted, normal faults, inversion anticlines, and buttressing structures, exposed on the western flank of the Domeyko Cordillera. The second type of structures are compared with the east‐verging thrust faults exposed on the eastern flank of the Domeyko Cordillera. Finally, we consider that the architecture of the Domeyko Fault System is associated with inversion structures and pure thrust faulting; being these faults first‐order structures that led to the orogenic growth of the Domeyko Cordillera from the Upper Cretaceous.

Fold-and-thrust belts and associated basins: a perspective on their structure, sedimentation, and dynamics

Fold-and-thrust belts are structural features that accommodate upper-crustal shortening by the growth of a series of thrust faults and folds. Recent studies show that a better understanding of the structure and sedimentation styles of fold-and-thrust belts and their associated basins can provide crucial insights for improved interpretations of the evolution of ancient and modern convergent margins and the mechanisms of intracontinental deformation. To achieve a more comprehensive understanding of the development of contractional orogenic belts, this thematic collection gathers contributions that explore different types of fold-and-thrust belts at various scales around the world, via different approaches including theory development, structural and stratigraphic observations from the field, geophysical analyses, and numerical modelling. Case studies include the northern margin of the Tibetan plateau and Pamir region, the Timanian and Caledonian orogenies in northern Norway, orogenic belts in western Laurentia, and the Andes of western South America. These studies reemphasize the importance of integrating broad datasets when documenting the distribution, geometry, and kinematics of structures in fold-and-thrust belts and their associated basins, including field-based structural observations, provenance, low-temperature thermochronologic, geomorphologic, and subsurface data, and analog and numerical models. This thematic collection aims to encourage further efforts for comparative studies of the fold-and-thrust belts around the world and proposes interdisciplinary research to address outstanding questions in the study of contractional orogens. Thematic collection: This article is part of the Fold-and-thrust belts collection available at: https://www.lyellcollection.org/topic/collections/fold-and-thrust-belts-and-associated-basins

Strain Partitioning and Localization Due To Detachment Heterogeneities in Fold‐and‐Thrust Belts of Progressive Arcs: Results From Analog Modeling

AbstractAlthough most arcuate orogens are deformed as progressive arcs—curvature is acquired during shortening‐, they have been scarcely simulated by analog modeling. To investigate factors that control the growth of progressive curves in fold‐and‐thrust belts, we developed seven analog models where the backstop shape changed over time, and distinctive geometric heterogeneities were set in the detachment layer. These heterogeneities, often described in natural cases, include diapirs, thickness lateral variations (including pinch‐outs) of the viscous detachment layer as well as frontal pinch‐outs. Our results show that strain was partitioned between shortening structures showing radial transport directions, and both normal and oblique strike‐slip faults that accommodated arc‐lengthening. The location of any heterogeneity conditioned the nucleation of structures and thus, the wedge evolution and its resulting geometry. The presence of both diapirs and frontal silicone pinch‐outs favored the stagnation of the deformation front, and the subsequent wedge thickening up to reach the supercritical angle. Both diapirs and thickness lateral variations of the viscous layer localized arc‐parallel stretching. In addition, their configuration determined the amount and distribution of salients and recesses along the arcuate belt, diapirs and more frictional detachments favoring thicker wedges and less frontal propagation. The differential displacement between salients and recesses was accommodated by strongly partitioned transfer zones, localized by the boundaries between distinctive detachment domains. These results may be useful to investigate geometric and kinematic changes along natural progressive arcs such as the Gibraltar, Sulaiman and Zagros cases.

Understanding the Caviahue-Copahue volcanic complex through kinematic solutions, paleotensors and analogue modelling

This work aims to study the interaction between two of the most representative structural systems controlling the Caviahue-Copahue volcanic complex. To achieve this objective, a structural analysis based on outcrop-scale fault-slip data field surveys and analogue models were carried out. The deformation regime acting on the studied area was characterized, and the associated paleostresses were obtained from the kinematic data inversion.The performed analysis in Caviahue-Copahue volcanic complex allowed to define two main sets of faults controlling the deformation of the area: NE-SW to ENE-WSW, and WNW-ESE to NW-SE, respectively. The first group comprises high-angle normal faults, resulting in a horst-and-graben setting with along-strike lengths up to 2 km. The second group shows strike-slip kinematics with a minor normal component. These NW-SE faults are related to the Miocene-Pliocene fissure-related volcanism and define the major caldera axis direction. In the geothermal area, the obtained paleostress orientation shows a consistent vertical σ1, denoting a local extensional regime. Regarding the geothermal field, the NE-SW extensional fault system is proposed as the main circulation pathways for hydrothermal fluids rising to the surface. The major NW-SE faults would act as barriers for this circulation.The set of analogous experiments was used to contrast the obtained local structural kinematic results. Two non-coaxial extensional events were established to achieve a local scale approach to the structural configuration observed in the area. Simulations aimed to understand the structural behavior of the superposition of non-coaxial extensive events; they allowed us to assess the role of the different fault sets surveyed in the field within the system. Particularly, our findings support that the NW-SE-oriented structures compartmentalize the subsequent NE-SW-oriented faults, acting on occasions as transfer zones.

A validated geomechanical model for the strike-slip restraining bend in Lebanon

Most of the methodologies used to validate complex strike-slip structures mainly rely on comparison with other well-known geological features or analogue laboratory models. This study adopts an approach based on the boundary element method at the regional scale to test the structural interpretation of a complex transpressional mountain range. Lebanon restraining bend represents the most prominent topographic transpressional feature along the Dead Sea Transform (DST). It consists of two mountain ranges: the Mount Lebanon and the Anti-Lebanon ranges. We built a 3D geometrical model of the fault surfaces based on previously studied natural examples, structural maps, satellite images, DEM interpretation and experimental analogue models of restraining bend or transpressional structures. Using a boundary element method, we modelled fault deformation response to the regional stress field. The simulation accurately predicts the shape and magnitude of positive and negative topographic changes and fault slip directions throughout the study area. We propose an original approach, which uses implementation of well-known fault geometries, surface and subsurface data, for structural validation in the complex strike-slip domain. Our results, validated by structural evidences, highlight that various structural styles lead to formation of Mt. Lebanon, Anti-Lebanon and Palmyrides structures. Furthermore, this simulation supports the hypothesis that the restraining bend of the DST formed in the widespread crustal weakness zone developed in the Late Jurassic to Early Createceous. We also propose recent Neogene tectonic evolution of the region based on our modelling and integrated with published U/Pb dating of fault zones and tectonostratigraphic evidence.

Comment on “Analog Schwarzschild-like geometry in fluids with external pressure”

In Ref. [1], exact (not only conformally related) analogue models for the Schwarzschild and Reissner-Nordstr\"om spacetimes were found. The background non-relativistic fluid flow was sustained by an external body force which is not affected by the linearised fluctuations. Following a different route, by modelling the external force as the gradient of an external pressure, it was shown in~\cite{bilic} that the speed of sound is significantly modified. This effective speed of sound turns out to be inconsistent with the continuity equation. In this comment we analyse these two contradictory conclusions. We first show that the heuristic justification for the introduction of the external force via a variational principle given in Ref. [2] is conceptually incorrect. Then, by adding the external force appropriately, we show that the conclusions in [1] remain valid.

Mid-Miocene uplift and tectonic-sedimentary evolution of the Taiwan accretionary prism: Constraints from sedimentary records in the Hengchun Peninsula, southern Taiwan

The young Taiwan orogenic belt is a classic example of a modern arc–continent convergence zone, which displays a longitudinal transition from active collision in the north to oceanic subduction in the south. However, the timing of its initial exposure above the sea level and the early-stage uplift mechanism has been a point of much debate. Here we applied major and trace element, Nd isotope and heavy minerals analysis on the Miocene sedimentary rocks from the Hengchun Peninsula to trace sediment provenance and to further constrain the tectonic-sedimentary evolution of the Taiwan accretionary prism. Results show that the Hengchun mudstones (∼11.6–6.5 Ma) are characterized by higher CaO (1.42 wt %) and MgO (2.57 wt %) contents, Cr/Zr (0.52) and Co/Th (1.58) ratios, and less negative ϵNd (t) values (−12 to −7) than those from the Chinese passive continental margin sediments. It indicates that the Chinese mainland was not exclusive sediment contributor for the Hengchun sediments. Combined with the high content of Cr-spinel heavy mineral (mean value ∼ 28.2%) in the Hengchun Miocene sandstones, and the presence of mafic lithic grains and N-MORB-type mafic rocks of 26-22 Ma in the Hengchun Peninsula, it is clear that the subducting South China Sea oceanic lithosphere should be also considered for the origin of the Hengchun sediments. The most likely source of these oceanic clasts being transported to the Hengchun Peninsula is the equivalent prism to the north, which had involved oceanic fragments during the subduction process. Consequently, Taiwan accretionary prism should have been already partly exposed prior to ∼11.6 Ma, considerably earlier than most previous estimates and the onset of arc-continent collision. Underplating of seamounts and/or the thinned Chinese continental margin beneath the overlying Taiwan accretionary prism, together with wedge extrusion tectonics, may have played an important role for this early-stage uplift, which now is also observed in the sandbox experiments, marine observation and analogue modeling. Our study not only better integrates the subduction and then erosion history of the South China Sea oceanic crust with sedimentary records in Taiwan, but also signifies a modern example from Taiwan that highlights the importance of soft exhumation mechanism in worldwide plate convergence zones relative to hard collision.

Electron modelling in conjunction witch vacuum modelling

Relevance. The relevance of the study and the corresponding results is based on the need for digital transfer of scientific physical and mathematical devices for modelling the studied objects and phenomena of the real world into a digital programme environment, which forms a powerful research tool with the possibility of multi-reading and multi-vector calculation and forecasting of the nature and qualities of simulated elements of the physical world with a different scientifically based configuration of the initial data. The quality and reliability of digital models depend on the quality and completeness of consideration of various physical aspects in the simulated research objects and phenomena. Therefore, it is appropriate and relevant to formulate the initial iteration of digital transfer – the creation of a dependence-correlation apparatus. The second aspect that confirms the relevance of the current study is the fact that there is no integral model of the electron: currently, the world scientific community knows models describing individual characteristics and elements of the studied elementary particle, but there are no models describing the electron as an integral object. Purpose. The purpose of the study is to develop a model of an electron associated with a simulated vacuum using appropriate analogue models from recognised fundamental studies. Methodology. The study uses the methods of analogue Dirac models, spinor field models, the six-dimensional space-time model of the Bartini world, and the Planck oscillator model. Results. Based on the results of experiments and physical and mathematical transformations in the current study, by integrating elements of the Ehrenfest paradox theory into the above models and basic elements of physical science, a complete model of the electron was formulated, which not only received a description of spatial and energy characteristics, but also allowed assessing the oetiological and morphological features of the development of the elementary particle, and individual physical and correlation dependencies were established. Conclusions. First, the Hubble constant is necessary as a vacuum parameter in modelling elementary particles; second, the Hubble constant is included in the equation of the classical electron radius; and third, based on model calculations, the hypothesis of differences between the electron, muon, and tauon is proposed

From Salt‐Bearing Rifted Margins to Fold‐And‐Thrust Belts. Insights From Analog Modeling and Northern Calcareous Alps Case Study

AbstractAnalog modeling is used to study the role played by the inherited salt‐sediment architecture of a salt‐bearing rifted margin, developed by minibasin downbuilding and margin‐scale gliding, and then incorporated into a fold‐and‐thrust belt system influenced by surface processes. Inherited salt bodies localize contractional deformation at different scales and the salt‐sediment architecture determines structural styles of fold‐and‐thrust belts. In our analog models, a large‐transport thrust detached along allochthonous model salt (silicone polymer) accumulated in a former distal raft system. And the squeezing of salt walls, together with the tilting of minibasins, accounted for most of the shortening in a salt wall‐minibasin province. Shortening and surface processes promote the extrusion and erosion of about 75% of the original model salt. The role played by salt tectonics during the contraction of salt‐bearing rifted margins could be underestimated because of the low salt‐sediment ratio found in fold‐and‐thrust belts. Our modeling results are compared with and assist in the interpretation of a section along the Northern Calcareous Alps.

Subduction and Slab Detachment Under Moving Trenches During Ongoing India‐Asia Convergence

AbstractThe dynamics of slab detachment and associated geological fingerprints have been inferred from various numerical and analog models. These invariably use a setup with slab‐pull‐driven convergence in which a slab detaches below a mantle‐stationary trench after the arrest of plate convergence due to arrival of continental lithosphere. In contrast, geological reconstructions show that post‐detachment plate convergence is common and that trenches and sutures are rarely mantle‐stationary during detachment. Here, we identify the more realistic kinematic context of slab detachment using the example of the India‐Asia convergent system. We first show that only the India and Himalayas slabs (from India's northern margin) and the Carlsberg slab (from the western margin) unequivocally detached from Indian lithosphere. Several other slabs below the Indian Ocean do not require a Neotethyan origin and may be of Mesotethys and Paleotethys origin. Additionally, the still‐connected slabs are being dragged together with the Indian plate forward (Hindu Kush) or sideways (Burma, Chaman) through the mantle. We show that Indian slab detachment occurred at moving trenches during ongoing plate convergence, providing more realistic geodynamic conditions for use in future numerical and analog experiments. We identify that the actively detaching Hindu Kush slab is a type‐example of this setting, whilst a 25–13 Ma phase of shallow detachment of the Himalayas slab, here reconstructed from plate kinematics and tomography, agrees well with independent, published geological estimates from the Himalayas orogen of slab detachment. The Sulaiman Ranges of Pakistan may hold the geological signatures of detachment of the laterally dragged Carlsberg slab.

From the Institute of Environmental Geology and Geoengineering of the National Research Council (CNR IGAG) to schools: introducing cultural heritage into classrooms to foster awareness about natural risk prevention

Through the establishment of an educational laboratory, the Institute of Environmental Geology and Geoengineering of the National Research Council (CNR IGAG) intends to provide the students of lower and upper secondary schools with an understanding of the concept of seismic and hydrogeological hazards and risks, and disseminate the knowledge on mitigation measures aimed at reducing the impact of disasters on cultural heritages (e.g., earthquakes and floods). A prestigious case study addressed in this context is offered by the city of Rome and the central archaeological area including the Colosseum and the Palatine Hill, since: i) three arches of the second ring of the Colosseum collapsed in 1703 due to an earthquake; ii) the underground structures of the Colosseum were flooded in 2011 when, after a very intense rainfall event, the hypogea were flooded to more than six metres from the ground. Starting with historical memory, the students will be encouraged to actively participate in the natural disasters preparedness throughout the use of analogue and digital models and solutions for the study of the Earth sciences focused on natural risks.

Forecasting the technical efficiency of mobile workover rigs

Purpose. To propose a method of comparative evaluation of technical efficiency of mobile workover rig by the criterion of life cycle cost. Methodology. The proposed method is based on the determination of the specific discounted costs related to the technical condition of the machine, spent on a conventional unit of work performed. It combines economic and technical indicators that characterize the performance of the machine. This makes it possible to indirectly assess its technical efficiency. Procedures for obtaining and processing input information, analytical dependences for establishing the components of the mathematical model and its solution are shown. Findings. Using the proposed method, a comparison is performed of three conventional similar models of workover rigs, which are positioned as more reliable, and two which are less reliable and cheaper. Their indicators are formed as a weighted average based on the analysis of an array of statistical information. The obtained values were used to indirectly determine the specific discounted costs for the maintenance of rigs in working order for a period of time; the rigs are characterized by the indicator of technical efficiency. The comparison of these indicators for similar workover rigs is performed for such characteristic points as the moment of balancing of expenses, expenses for the forecasted period of operation, the periods of operation at which expenses are balanced. It is confirmed that usually the gain from the greater durability far exceeds the reduction of the economic effect of the rise in price of the machine. Originality. The proposed method for engineering forecasting of technical efficiency of technological machines using values of economic and technical indicators available to engineers of the petroleum industry. Practical value. This assessment is intended to objectively compare several analogue models and make a reasonable choice of a more efficient technological machine.

An Approach to Quantum Physics Teaching through Analog Experiments

With quantum physics being a particularly difficult subject to teach because of its contextual distance from everyday life, the need for multiperspective teaching material arises. Quantum physics education aims at exploring these methods but often lacks physical models and haptic components. In this paper, we provide two analog models and corresponding teaching concepts that present analogies to quantum phenomena for implementation in secondary school and university classrooms: While the first model focuses on the polarization of single photons and the deduction of reasoning tools for elementary comprehension of quantum theory, the second model investigates analog Hardy experiments as an alternative to Bell’s theorem. We show how working with physical models to compare classical and quantum perspectives has proven helpful for novice learners to grasp the abstract nature of quantum experiments and discuss our findings as an addition to existing quantum physics teaching concepts.

Фазовые переходы сгущенного молока с сахаром в расширенных температурных диапазонах хранения

Sweetened condensed milk is a popular food in various climatic zones, including those regions where average winter temperature falls below –30°C. Such low temperatures can trigger crystallization because they disrupt the native structure of biopolymers. These processes spoil the quality of sweetened condensed milk. However, no scientific publications feature the cryoscopic temperature of sweet condensed milk or systematize the data on its low-temperature storage.
 Sugar, sugar-milk, and milk solutions of various concentrations were frozen to determine their cryoscopic temperature by the thermographic method using a Testo 176T4 meter (Germany) with K-type probes (NiCr-Ni) at –78.5°C. The phase transitions were studied using a Mettler Toledo DCS 822e DSC analyzer.
 The nucleation temperature, the cryoscopic temperature, and the subcooling degree depended on the concentration and the type of the solute. For sugar solutions, the cryoscopic temperature varied from –0.4 ± 0.1 to –6.4 ± 0.1°C; for sugar-milk solutions, it ranged from –2.1 ± 0.1 to –10.9 ± 0.1°C; for whole milk solutions, it was from –0.4 ± 0.1 to –4.6 ± 0.1°C. The thermographic method failed to obtain the phase transition and the cryoscopic temperature in analogue models of sweetened condensed milk. The loss of fluidity was about –30°C when the storage time exceeded 2 h. This effect was comparable to 54 min of storage at –35°C. The differential scanning calorimetry meth od showed that the phase transition occurred at –80°C.
 This research opens new prospects for differential scanning calorimetry studies of phase transitions in condensed sweetened dairy products.

Analog and Numerical Modeling of Rift‐Rift‐Rift Triple Junctions

AbstractRift‐Rift‐Rift triple junctions are key features of emergent plate boundary networks during fragmentation of a continent. A key example of such a setting is the Afar triple junction where the African, Arabian and Somalian plates interact. We performed analog and numerical models simulating continental break‐up in a Rift‐Rift‐Rift setting to investigate the resulting structural pattern and evolution. We modified the ratio between plate velocities, and we performed single‐stage (with all plates moving at the same time) and two‐stage (where one plate first moves alone and then all the plates move simultaneously) models. Additionally, the direction of extension was changed to induce orthogonal extension in one of the three rift branches. Our models suggest that differential extension velocities in the rift branches determine the localization of the structural triple junction, which is located closer to the rift branch experiencing slower extension velocities. Furthermore, imposed velocities affect the deformation resulting in end‐member fault patterns. The effect of applying similar velocities in all rift arms is to induce a symmetric fault pattern (generating a Y‐shaped geometry). In contrast, a faster plate generates structures trending orthogonal to dominant velocity vectors, while faults associated with the movement of the slower plates remain subordinate (generating a T‐shaped pattern). Two‐stage models reveal high‐angle faults interacting at the triple junction, confirming that differential extension velocities strongly affect fault patterns. These latter models show large‐scale similarities with fault patterns observed in the Afar triple junction, providing insights into the factors controlling the structural evolution of this area.