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In this paper, we introduce our millimeter-wave (mmWave) radio channel measurement for integrated sensing and communication (ISAC) scenarios with distributed links at dual bands in an indoor cavity; we also characterize the channel in delay and azimuth-angular domains for the scenarios with the presence of 1 person with varying locations and facing orientations. In our setting of distributed links with two transmitters and two receivers where each transceiver operates at two bands, we can measure two links whose each transmitter faces to one receiver and thus capable of line-of-sight (LOS) communication; these two links have crossing Fresnel zones. We have another two links capable of capturing the reflectivity from the target presenting in the test area (as well as the background). The numerical results in this paper focus on analyzing the channel with the presence of one person. It is evident that not only the human location, but also the human facing orientation, shall be taken into account when modeling the ISAC channel.

Let $G$ be a Lie group and $H$ be a subgroup of it. We can construct a bisimplicial manifold $NG(*) \rtimes NH(*)$ and the de Rham complex $\Omega^*(NG(*) \rtimes NH(*))$ on it. This complex is a triple complex and the cohomology of its total complex is isomorphic to $H^*(B(G \rtimes H))$. In this paper, we show that the total complex of the double complex $\Omega^q(NG(*) \rtimes NH(*))$ is isomorphic to the continuous cohomology $H_c^*(G \rtimes H;S^q{\mathcal G}^* \otimes S^q{\mathcal H}^*)$ for any fixed $q$., Comment: 9 pages

In this paper, we introduce a notion of a central $U(1)$-extension of a double Lie groupoid and show that it defines a cocycle in the certain triple complex., Comment: 12 pages

We exhibit the Chern-Simons forms of some characteristic classes in the simplicial de Rham complex., Comment: 13pages

We show that when a simplicial Lie group acts on a simplicial manifold $\{X_*\}$, we can construct a bisimplicial manifold and the de Rham complex on it. This complex is quasi-isomorphic to the equivariant simplicial de Rham complex on $\{X_*\}$ and its cohomology group is isomorphic to the cohomology group of the fat realization of the bisimplicial manifold. We also exhibit a cocycle in the equivariant simplicial de Rham complex., Comment: 11 pages

We exhibit a cocycle in the simplicial de Rham complex which represents the Euler class. As an application, we construct a Lie algebra cocycle on $L\mathfrak{so}(4)$., Comment: 13 pages

When a Lie group $G$ has a central $U(1)$-extension, there is a cocycle in the simplicial de Rham complex $\Omega^3(NG)$ which represents the Dixmier-Douady class. Mickelsson and Brylinski, McLaughlin constructed a central $U(1)$-extension $\widehat{LSU(2)} \rightarrow LSU(2)$ whose Dixmier-Douady class in $\Omega^3(NLSU(2))$ is a kind of transgression of the second Chern class. In this paper, we consider the case of unitary group and construct a central $U(1)$-extension of $LU(2)$. After that we construct also a cocycle in a certain triple complex., Comment: 15 pages

On the basis of Dupont's work, we exhibit a cocycle in the simplicial de Rham complex which represents the Chern character. We also prove the related conjecture due to Brylinski. This gives a way to construct a cocycle in a local truncated complex., Comment: 15 pages

We show that the cohomology group of the equivariant simplicial de Rham complex is isomorphic to the cohomology group of the classifying space of a semi-direct product group., Comment: 7 pages

On the basis of A. L. Carey, D. Crowley, M. K. Murray's work, we exhibit a cocycle in the simplicial de Rham complex which represents the Dixmier-Douady class., Comment: 9 pages; Differential Geometry. The author apologizes that there are some inaccurate description in this paper. Corrected description is given in "On some cocycles which represent the Dixmier-Douady class in simplicial de Rham complexes"

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 figures

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 figures

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 figures

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 figures

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 figures

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 figures