Convergence rate of dimension reduction in Bose-Einstein condensates

In this paper, we study dimension reduction of the three-dimensional (3D) Gross-Pitaevskii equation (GPE) modelling Bose-Einstein condensation under different limiting interaction and trapping frequencies parameter regimes. Convergence rates for the dimension reduction of 3D ground state and dynamics of the GPE in the case of disk-shaped condensation and cigar-shaped condensation are reported based on our asymptotic and numerical results. In addition, the parameter regimes in which the 3D GPE cannot be reduced to lower dimensions are identified.Comment: 27pages; 9 figure

Bogoliubov Hamiltonian as Derivative of Dirac Hamiltonian via Braid Relation

In this paper we discuss a new type of 4-dimensional representation of the braid group. The matrices of braid operations are constructed by q-deformation of Hamiltonians. One is the Dirac Hamiltonian for free electron with mass m, the other, which we find, is related to the Bogoliubov Hamiltonian for quasiparticles in $^3$He-B with the same free energy and mass being m/2. In the process, we choose the free q-deformation parameter as a special value in order to be consistent with the anyon description for fractional quantum Hall effect with $\nu = 1/2$.Comment: 3 pages, 5 figure

Spatial-Temporal Convolutional Attention for Mapping Functional Brain Networks

Using functional magnetic resonance imaging (fMRI) and deep learning to explore functional brain networks (FBNs) has attracted many researchers. However, most of these studies are still based on the temporal correlation between the sources and voxel signals, and lack of researches on the dynamics of brain function. Due to the widespread local correlations in the volumes, FBNs can be generated directly in the spatial domain in a self-supervised manner by using spatial-wise attention (SA), and the resulting FBNs has a higher spatial similarity with templates compared to the classical method. Therefore, we proposed a novel Spatial-Temporal Convolutional Attention (STCA) model to discover the dynamic FBNs by using the sliding windows. To validate the performance of the proposed method, we evaluate the approach on HCP-rest dataset. The results indicate that STCA can be used to discover FBNs in a dynamic way which provide a novel approach to better understand human brain.Comment: 5 pages, 5 figures, submitted to 20th IEEE International Symposium on Biomedical Imaging (ISBI 2023

Impact of high-frequency pumping on anomalous finite-size effects in three-dimensional topological insulators

Lowering of the thickness of a thin-film three-dimensional topological insulator down to a few nanometers results in the gap opening in the spectrum of topologically protected two-dimensional surface states. This phenomenon, which is referred to as the anomalous finite-size effect, originates from hybridization between the states propagating along the opposite boundaries. In this work, we consider a bismuth-based topological insulator and show how the coupling to an intense high-frequency linearly polarized pumping can further be used to manipulate the value of a gap. We address this effect within recently proposed Brillouin-Wigner perturbation theory that allows us to map a time-dependent problem into a stationary one. Our analysis reveals that both the gap and the components of the group velocity of the surface states can be tuned in a controllable fashion by adjusting the intensity of the driving field within an experimentally accessible range and demonstrate the effect of light-induced band inversion in the spectrum of the surface states for high enough values of the pump.Comment: 6 pages, 3 figure

Influence of Spartina alterniflora invasion stages on macrobenthic communities on a tidal flat in Wenzhou Bay, China

Muitos habitats costeiros vêm sendo alterados substancialmente pela invasão de Spartina alterniflora no leste da China. Em 2007, em uma planície de maré situada em Wenzhou Bay, foram analisadas riqueza de espécies, densidade e diversidade da macrofauna bêntica em relação a diferentes estágios da invasão da gramínea e à estação do ano. Para as medidas de diversidade foram usados os índices de Margalef (R) e de Shannon (H'). Foram detectados efeitos significativos do estágio de invasão e época do ano sobre a macrofauna. As comunidades macrofaunais foram mais complexas nas manchas onde a invasão de S. alterniflora estava no seu início, quando considerados os locais onde as manchas estavam em estágios mais avançados. Através das análises de agrupamento e ordenação as comunidades puderam ser classificadas pelo tipo de habitat formado em cada estágio de invasão da Spartina. Os resultados indicaram que a biodiversidade aumentou no estágio de invasão inicial (idade de invasão de 1 a 2 anos), mas diminuiu gradativamente com os estágios intermediário (idade de invasão de 3 a 4 anos) e completo (idade de invasão de 5 a 6 anos), mostrando assim o efeito deletério de S. alterniflora sobre a estrutura da macrofauna presente no local.Many coastal habitats in eastern China are being substantially altered by the invasion of Spartina alterniflora. The species richness, density, Margalef's diversity index (R) and Shannon's diversity index (H') of macrobenthic communities on a tidal flat in Wenzhou Bay, China, were analyzed with the factors of invasion stage and season, in 2007. A significant effect of invasion stage, season, and the interaction between them on communities was detected. The macrobenthic community was more complex in the patch of initial S. alterniflora invasion than in the patches of some other invasion stages. Macrobenthic communities were classified by cluster and ordination in accordance with the habitat character of the S. alterniflora invasion stage. Our research demonstrated that the S. alterniflora invasion stage affected the macrobenthic communities significantly. The results indicated that biodiversity increased in the initial stage of invasion (invasion age 1-2 years) and then decreased in the stage of invasion underway (invasion age 3-4 years) and in the stage of invasion completed (invasion age 5-6 years); this phenomenon was related to the change in the S. alterniflora canopy which accompanied the invasion stages