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In this paper, we consider a reduction of a new system of partial difference equations, which was obtained in our previous paper [Classification of quad-equations on a cuboctahedron, arXiv:1906:06650, 2019] and shown to be consist...
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In this paper, we consider a reduction of a new system of partial difference equations, which was obtained in our previous paper [Classification of quad-equations on a cuboctahedron, arXiv:1906:06650, 2019] and shown to be consistent around a cuboctahedron. We show that this system reduces to A(1)? 2 -type discrete Painlev′e equations by considering a periodic reduction of a three-dimensional lattice constructed from overlapping cuboctahedra.
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Every second, millions of submilligram meteoroids enter the Earth's atmosphere producing dense plasmas. Radars easily detect these plasmas, and researchers use this data to characterize both the meteoroids and the atmosphere. This...
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Every second, millions of submilligram meteoroids enter the Earth's atmosphere producing dense plasmas. Radars easily detect these plasmas, and researchers use this data to characterize both the meteoroids and the atmosphere. This paper develops a first-principle kinetic theory describing the behavior of particles ablated from a small fast-moving meteoroid and then colliding with atmospheric molecules. These collisions result in partial ionization of the ablated particles and formation of a dense plasma around the meteoroid. This theory produces analytic expressions describing the spatial structure and velocity distributions of ions and neutrals near the ablating meteoroid. The analytical model will serve as a basis for a more accurate quantitative interpretation of radar measurements and should help calculate meteoroid and atmosphere parameters from radar head-echo observations. Plain Language Summary Every second, millions of submilligram meteoroids enter the Earth's atmosphere where they disintegrate, leaving behind atoms of iron, sulphur, carbon, oxygen, etc. Most of these small meteoroids cannot be seen by naked eye. However, when entering the atmosphere with the hypersonic speed of tens of kilometers per second, these meteoroids collide with atmosphere, heat up, and lose their material in a process called ablation. The ablated atoms and molecules further collide with atmospheric constituents, scatter, and ionize, producing dense plasmas around the meteoroid. Radars easily detect these plasmas and researchers use this data to characterize both the meteoroids and the atmosphere. This paper develops a first-principle theory describing the motion of ablated particles that happens after they collide once with atmospheric molecules. This theory produces analytic expressions describing the spatial structure and velocity distributions of ions and neutrals near the ablating meteoroid. The analytical model will serve as a basis for a more accurate quantitative interpretation of radar measurements and should help calculate meteoroid and atmosphere parameters from radar head-echo observations.
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Records in Around the Region are published for interest only; their inclusion does not imply acceptance by the records committee of the relevant country. All records refer to the period 1 January-31 May 2021 unless stated otherwis...
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Records in Around the Region are published for interest only; their inclusion does not imply acceptance by the records committee of the relevant country. All records refer to the period 1 January-31 May 2021 unless stated otherwise. All countries in the region have been affected to varying degrees by lockdown restrictions on travel due to the Covid-19 pandemic resulting in fewer records than normal during this time.
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Records in Around the Region are published for interest only; their inclusion does not imply acceptance by the records committee of the relevant country. All records refer to the period 1 January-31 May 2020 unless stated otherwis...
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Records in Around the Region are published for interest only; their inclusion does not imply acceptance by the records committee of the relevant country. All records refer to the period 1 January-31 May 2020 unless stated otherwise. All countries in the region have been affected to varying degrees by lockdown restrictions on travel due to the Covid-19 pandemic during March-May, resulting in fewer records than normal during this time.
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We discuss effects of pairwise aligning interactions in an ensemble of central place foragers or of searchers that are connected to a common home. In a wider sense, we also consider self-moving entities that are attracted to a cen...
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We discuss effects of pairwise aligning interactions in an ensemble of central place foragers or of searchers that are connected to a common home. In a wider sense, we also consider self-moving entities that are attracted to a central place such as, for instance, the zooplankton Daphnia being attracted to a beam of light. Single foragers move with constant speed due to some propulsive mechanism. They explore at random loops the space around and return rhytmically to their home. In the ensemble, the direction of the velocity of a searcher is aligned to the motion of its neighbors. At first, we perform simulations of this ensemble and find a cooperative behavior of the entities. Above an overcritical interaction strength the trajectories of the searcher qualitatively changes and searchers start to move along circles around the home position. Thereby, all searchers rotate either clockwise or anticlockwise around the central home position as it was reported for the zooplankton Daphnia. At second,the computational findings are analytically explained by the formulation of transport equations outgoing from the nonlinear mean field Fokker-Planck equation of the considered situation. In the asymptotic stationary limit,we find expressions for the critical interaction strength, the mean radial and orbital velocities of the searchers and their velocity variances.We also obtain the marginal spatial and angular densities in the undercritical regime where the foragers behave like individuals as well as in the overcritical regime where they rotate collectively around the considered home. We additionally elaborate the overdamped Smoluchowski-limit for the ensemble.
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An efficient route to the displacement field around a rigid spherical inclusion in an infinitely extended homogeneous elastic medium is presented in a slightly alternative way when compared to some common textbook methods.Moreover...
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An efficient route to the displacement field around a rigid spherical inclusion in an infinitely extended homogeneous elastic medium is presented in a slightly alternative way when compared to some common textbook methods.Moreover,two Faxén relations of next-higher order beyond the stresslet are calculated explicitly for compressible media.They quantify higher-order moments involving the force distribution on a rigid spherical particle in a deformed elastic medium.As a consequence,additional contributions to the distortions of the deformed elastic medium are identified that are absent to lower order.Furthermore,the displaceability and rotateability matrices for an ensemble of rigid spheres are calculated up to (including) sixth order in inverse particle separation distance.These matrices describe the interactions mediated between the rigid embedded particles by the elastic environment.In this way,additional coupling effects are identified that are absent to lower order,particularly when rotations and torques are involved.All methods and results can formally be transferred to the corresponding case of incompressible hydrodynamic low-Reynolds-number Stokes flow by considering the limit of an incompressible environment.The roles of compressibility of the embedding medium and of the here additionally derived higher-order contributions are highlighted by some selected example configurations.
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Conservation laws that describe the behavior of partially molten mantle rock have been established for several decades, but the associated rheology remains poorly understood. Constraints on the rheology may be obtained from recent...
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Conservation laws that describe the behavior of partially molten mantle rock have been established for several decades, but the associated rheology remains poorly understood. Constraints on the rheology may be obtained from recently published experiments involving deformation of partially molten rock around a rigid, spherical inclusion. These experiments give rise to patterns of melt segregation that exhibit the competing effects of pressure shadows and melt-rich bands. Such patterns provide an opportunity to infer rheological parameters through comparison with models based on the conservation laws and constitutive relations that hypothetically govern the system. To this end, we have developed software tools to simulate finite strain, two-phase flow around a circular inclusion in a configuration that mirrors the experiments. Simulations indicate that the evolution of porosity is predominantly controlled by the porosity-weakening exponent of the shear viscosity and the poorly known bulk viscosity. In two-dimensional simulations presented here, we find that the balance of pressure shadows and melt-rich bands observed in experiments only occurs for bulk-to-shear viscosity ratio of less than about five. However, the evolution of porosity in simulations with such low bulk viscosity exceeds physical bounds at unrealistically small strain due to the unchecked, exponential growth of the porosity variations. Processes that limit or balance porosity localization should be incorporated in the formulation of the model to produce results that are consistent with the porosity evolution in experiments.
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The circulation of iron-rich shelf waters around the Kerguelen Islands plays a crucial role for a climatically important, annually recurrent phytoplankton spring bloom over the sluggish shelf region and its downstream plume area a...
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The circulation of iron-rich shelf waters around the Kerguelen Islands plays a crucial role for a climatically important, annually recurrent phytoplankton spring bloom over the sluggish shelf region and its downstream plume area along the Antarctic circumpolar flow. However, there is a long-standing confusion about the Polar Front (PF) in the Kerguelen region due to diverse suggestions in the literature for its geographical location with an extreme difference over 10° of latitude. Based on abundant historical hydrographic data, the in situ hydrographic and current measurements during the 2011 KEOPS2 cruise, satellite chlorophyll images, and altimetry-derived surface velocity fields, we determine and validate an up-to-date location of the PF around the Kerguelen Islands. Artificial Lagrangian particle trajectories computed from altimetric velocity time series are analyzed for the possible pathways and sources of different surface/subsurface waters advected into the chlorophyll bloom area east off the islands studied during the KEOPS2 cruise. The PF location determined as the northernmost boundary of the Winter Water colder than 2°C, which is also associated with a band of strong currents, appears to be primarily controlled by topography. The PF rounds the Kerguelen Islands from the south to deflect northward along the eastern escarpment up to the northeastern corner of the Kerguelen Plateau before making its southward retroflection. It is shown that the major surface/subsurface waters found within the deep basin east of the Kerguelen Islands originate from the shelf around the Heard Island, rather than from the shallow shelf north of the Kerguelen Islands.
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We study notions of independence appropriate for a stability theory of metric abstract elementary classes (for short, MAECs).We build on previous notions used in the discrete case, and adapt definitions to the metric case. In part...
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We study notions of independence appropriate for a stability theory of metric abstract elementary classes (for short, MAECs).We build on previous notions used in the discrete case, and adapt definitions to the metric case. In particular, we study notions that behave well under superstability-like assumptions. Also, under uniqueness of limit models, we study domination, orthogonality and parallelism of Galois types in MAECs.
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[1] The 2011 Tohoku tsunami devastated the northeastern Japan coasts and caused localized damage to coastal infrastructure across the Pacific. The tsunami resulted in strong currents around the Hawaiian Islands that led to closure...
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[1] The 2011 Tohoku tsunami devastated the northeastern Japan coasts and caused localized damage to coastal infrastructure across the Pacific. The tsunami resulted in strong currents around the Hawaiian Islands that led to closure of harbors and marinas for up to 38 h after its arrival. We utilize a nonhydrostatic model to reconstruct the tsunami event from the seismic source for elucidation of the physical processes and inference of the coastal hazards. A number of tide gauges, bottom pressure sensors, and ADCPs provided point measurements for validation and assessment of the model results in Hawaii. Spectral analysis of the computed surface elevation and current reveals complex flow patterns due to multiscale resonance. Standing waves with 33-75 min period develop along the island chains, while oscillations of 27 min or shorter are primarily confined to an island or an island group with interconnected shelves. Standing edge waves with periods 16 min or shorter, which are able to form nodes on the reefs and inside harbors, are the main driving force of the observed coastal currents. Resonance and constructive interference of the oscillation modes provide an explanation of the impacts observed in Hawaii with implications for emergency management in Pacific island communities.
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