Von K\'arm\'an vortex street in a Bose-Einstein condensate

Vortex shedding from an obstacle potential moving in a Bose-Einstein condensate is investigated. Long-lived alternately aligned vortex pairs are found to form in the wake, as for the von K\'arm\'an vortex street in classical viscous fluids. Various patterns of vortex shedding are systematically studied and the drag force on the obstacle is calculated. It is shown that the phenomenon can be observed in a trapped system.Comment: 4 pages, 5 figure

Choquet integrals, Hausdorff content and fractional operators

It is shown that the fractional integral operator $I_{\alpha}$, $0<\alpha<n$, and the fractional maximal operator $M_{\alpha}$, $0\le\alpha<n$, are bounded on weak Choquet spaces with respect to Hausdorff content. We also investigate these operators on Choquet-Morrey spaces. These results are extensions of the previous works due to Adams, Orobitg and Verdera, and Tang. The results for the fractional integral operator $I_{\alpha}$ are essentially new.Comment: 12 page

Rayleigh-Taylor instability and mushroom-pattern formation in a two-component Bose-Einstein condensate

The Rayleigh-Taylor instability at the interface in an immiscible two-component Bose-Einstein condensate is investigated using the mean-field and Bogoliubov theories. Rayleigh-Taylor fingers are found to grow from the interface and mushroom patterns are formed. Quantized vortex rings and vortex lines are then generated around the mushrooms. The Rayleigh-Taylor instability and mushroom-pattern formation can be observed in a trapped system.Comment: 5 pages, 4 figure

Quantum Kelvin-Helmholtz instability in phase-separated two-component Bose-Einstein condensates

We theoretically study the Kelvin-Helmholtz instability in phase-separated two-component Bose-Einstein condensates using the Gross-Pitaevskii and Bogoliubov-de Gennes models. A flat interface between the two condensates is shown to deform into sawtooth or Stokes-like waves, leading to the formation of singly quantized vortices on the peaks and troughs of the waves. This scenario of interface instability in quantum fluids is quite different from that in classical fluids.Comment: 5 pages, 4 figure

Pressure drop evaluation based on two-phase flow observation in packed bed system

Two-phase pressure drop in the debris has been studied by many researchers concerning the debris cooling characteristics during a severe accident in a nuclear reactor. However, its flow regime transition of the two-phase flow in the debris has not been well understood, which strongly affects the interfacial drag and the pressure drop. Conventional models for gas-liquid two-phase flow pressure drop have not been established to evaluate interfacial drag accurately. In this study, high-speed imaging of a two-dimensional network model was performed to clarify the effect of flow patterns on interfacial drag and pressure drop. Usually, it would not be easy to visualize such two-phase flow behavior in a randomly packed bed due to the reflection/refraction of light and/or overlapping bubbles, even if the test section is made of transparent materials. Therefore, in this study, a test section, which simulates a two-dimensional network of porous structures, was fabricated to avoid overlapping bubbles. The two-phase flow pattern in the porous structure has been identified by high-speed imaging of the two-dimensional network model. The flow regime map based on the flow pattern visualization results is applied to the pressure drop evaluation and it could reduce the overestimation of experimental values. The experimental results suggested that the interfacial drag term should be modified in the gas-liquid two-phase flow pressure drop model

Capillary instability in a two-component Bose-Einstein condensate

Capillary instability and the resulting dynamics in an immiscible two-component Bose-Einstein condensate are investigated using the mean-field and Bogoliubov analyses. A long, cylindrical condensate surrounded by the other component is dynamically unstable against breakup into droplets due to the interfacial tension arising from the quantum pressure and interactions. A heteronuclear system confined in a cigar-shaped trap is proposed for realizing this phenomenon experimentally.Comment: 7 pages, 6 figure

Dynamics of bubbles in a two-component Bose-Einstein condensate

The dynamics of a phase-separated two-component Bose-Einstein condensate are investigated, in which a bubble of one component moves through the other component. Numerical simulations of the Gross--Pitaevskii equation reveal a variety of dynamics associated with the creation of quantized vortices. In two dimensions, a circular bubble deforms into an ellipse and splits into fragments with vortices, which undergo the Magnus effect. The B\'enard--von K\'arm\'an vortex street is also generated. In three dimensions, a spherical bubble deforms into toruses with vortex rings. When two rings are formed, they exhibit leapfrogging dynamics.Comment: 6 pages, 7 figure

RNA-seq Transcriptional Profiling of an Arbuscular Mycorrhiza Provides Insights into Regulated and Coordinated Gene Expression in Lotus japonicus and Rhizophagus irregularis

Gene expression during arbuscular mycorrhizal development is highly orchestrated in both plants and arbuscular mycorrhizal fungi. To elucidate the gene expression profiles of the symbiotic association, we performed a digital gene expression analysis of Lotus japonicus and Rhizophagus irregularis using a HiSeq 2000 next-generation sequencer with a Cufflinks assembly and de novo transcriptome assembly. There were 3,641 genes differentially expressed during arbuscular mycorrhizal development in L. japonicus, approximately 80% of which were up-regulated. The up-regulated genes included secreted proteins, transporters, proteins involved in lipid and amino acid metabolism, ribosomes and histones. We also detected many genes that were differentially expressed in small-secreted peptides and transcription factors, which may be involved in signal transduction or transcription regulation during symbiosis. Coregulated genes between arbuscular mycorrhizal and root nodule symbiosis were not particularly abundant, but transcripts encoding for membrane traffic-related proteins, transporters and iron transport-related proteins were found to be highly co-up-regulated. In transcripts of arbuscular mycorrhizal fungi, expansion of cytochrome P450 was observed, which may contribute to various metabolic pathways required to accommodate roots and soil. The comprehensive gene expression data of both plants and arbuscular mycorrhizal fungi provide a powerful platform for investigating the functional and molecular mechanisms underlying arbuscular mycorrhizal symbiosis.ArticlePLANT AND CELL PHYSIOLOGY. 56(8):1490-1511 (2015)journal articl

Crossover between Kelvin-Helmholtz and counter-superflow instabilities in two-component Bose-Einstein condensates

Dynamical instabilities at the interface between two Bose--Einstein condensates that are moving relative to each other are investigated using mean-field and Bogoliubov analyses. Kelvin--Helmholtz instability is dominant when the interface thickness is much smaller than the wavelength of the unstable interface mode, whereas the counter-superflow instability becomes dominant in the opposite case. These instabilities emerge not only in an immiscible system but also in a miscible system where an interface is produced by external potential. Dynamics caused by these instabilities are numerically demonstrated in rotating trapped condensates.Comment: 10 pages, 9 figure

Neural Structure Fields with Application to Crystal Structure Autoencoders

Representing crystal structures of materials to facilitate determining them via neural networks is crucial for enabling machine-learning applications involving crystal structure estimation. Among these applications, the inverse design of materials can contribute to next-generation methods that explore materials with desired properties without relying on luck or serendipity. We propose neural structure fields (NeSF) as an accurate and practical approach for representing crystal structures using neural networks. Inspired by the concepts of vector fields in physics and implicit neural representations in computer vision, the proposed NeSF considers a crystal structure as a continuous field rather than as a discrete set of atoms. Unlike existing grid-based discretized spatial representations, the NeSF overcomes the tradeoff between spatial resolution and computational complexity and can represent any crystal structure. To evaluate the NeSF, we propose an autoencoder of crystal structures that can recover various crystal structures, such as those of perovskite structure materials and cuprate superconductors. Extensive quantitative results demonstrate the superior performance of the NeSF compared with the existing grid-based approach.Comment: 16 pages , 6 figures. 13 pages Supplementary Informatio