Immersed boundary-conformal isogeometric method for linear elliptic problems

We present a novel isogeometric method, namely the Immersed Boundary-Conformal Method (IBCM), that features a layer of discretization conformal to the boundary while employing a simple background mesh for the remaining domain. In this manner, we leverage the geometric flexibility of the immersed boundary method with the advantages of a conformal discretization, such as intuitive control of mesh resolution around the boundary, higher accuracy per degree of freedom, automatic satisfaction of interface kinematic conditions, and the ability to strongly impose Dirichlet boundary conditions. In the proposed method, starting with a boundary representation of a geometric model, we extrude it to obtain a corresponding conformal layer. Next, a given background B-spline mesh is cut with the conformal layer, leading to two disconnected regions: an exterior region and an interior region. Depending on the problem of interest, one of the two regions is selected to be coupled with the conformal layer through Nitsche’s method. Such a construction involves Boolean operations such as difference and union, which therefore require proper stabilization to deal with arbitrarily cut elements. In this regard, we follow our precedent work called the minimal stabilization method (Antolin et al in SIAM J Sci Comput 43(1):A330–A354, 2021). In the end, we solve several 2D benchmark problems to demonstrate improved accuracy and expected convergence with IBCM. Two applications that involve complex geometries are also studied to show the potential of IBCM, including a spanner model and a fiber-reinforced composite model. Moreover, we demonstrate the effectiveness of IBCM in an application that exhibits boundary-layer phenomena.

Study on Dynamic Stability of Single Floating Pier Under Waves

Considering the upper structure restraint effect of the floating bridge, the diffraction effect and radiation effect of linear monochromatic waves, the dynamic response equation of floating pier is derived and the factors affecting the dynamic stability of the floating pier are analyzed in this paper. Based on the theory of potential flow, the calculation domain is divided into the interior region and the exterior region. The wave diffraction and radiation problems are solved by the matched eigenfunction expansion method (MEEM). After obtaining the wave excitation force, additional mass and radiation damping coefficient, considering the restraint effect of the upper structure of the floating bridge, the motion differential equation of the floating pier is established, and the response amplitude operator (RAOs) of the floating pier is obtained. The effects of span, mass and stiffness of upper structure, as well as the draft depth, size and net height of floating pier on dynamic stability of floating pier under wave are analyzed. The results show that the increase in the span of upper structure will significantly increase the peak RAOs of sway and heave, and the increase in stiffness is helpful to reduce the peak RAOs of sway and heave. The increase of the floating pier radius can reduce the heave RAO, and the net height on the water surface of the floating pier increases the heave and roll.

Thick string-like braneworlds in f(T) gravity

We propose a codimension two warped braneworld model within the teleparallel [Formula: see text] gravity. Asymptotically, the bulk geometry converges to an [Formula: see text] spacetime whose cosmological constant is produced by the torsion parameters. Furthermore, the torsion induces an AdS-dS transition on the exterior region. As the torsion parameters vary, the brane undergoes a phase transition from a thick string-like brane into ring-like structures. The bulk-brane Planck mass ration is modified by the torsion. The analysis of the stress–energy condition reveals a splitting brane process satisfying the weak and strong–energy conditions for some values of the parameters. In addition, we investigate the behavior of the gravitational perturbations in this scenario. It turns out that the gravitational spectrum has a linear behavior for small masses and is independent of the torsion parameters for large masses. In the bulk, the torsion keeps a gapless nonlocalizable and stable tower of massive modes. Inside the brane core, the torsion produces new barriers and potential wells leading to small amplitude massive modes and a massless mode localized around the ring structures.

Conditioned medium from healthy women's endometrial stem cells improve inflammatory and stemness- expression genes in endometriosis women

Background. Endometriosis is a common, benign gynecological disease which is determined as an overspreading of endometrial tissue in exterior region of the uterine cavity. Evidence suggests that retrograde menstrual blood which contains mesenchymal stem cells with differential gene expression compared to healthy women may play a role in endometriosis creation. We aimed to identify whether the conditioned medium from Menstrual blood-derived stem cells (MenSCs) of healthy women can affect the expression level of inflammatory and stemness genes of MenSCs from endometriosis women. Methods and Results. Endometriosis derived MenSCs (E-MenSCs) were treated with conditioned medium (CM) derived from healthy women’s MenSCs (NE-MenSCs). Some CD markers were analyzed by flow cytometer before and after treatment compared with NE-MenSCs, and the expression level of inflammatory and stemness genes was evaluated by real-time PCR. Results. E-MenSCs show different morphology in vitro culture in comparison with NE-MenSCs, which were changed in the presence of CM, into a morphology more similar to normal cells and showed significant decrease expression of CD10 after CM treatment. In our results, the IL-1, COX-2, and HIF-1\(\alpha\) as an inflamaturay genes and OCT-4, NANOG, and SOX2 as a stemness genes showed significantly different expression level in E-MenSCs after treating with CM. Conclusions. Our study indicates that the expression level of some inflammatory- and stemness-related genes which have differential expression in E-MenSCs compared with NE-MenSCs, could be changed to normal status by using CM derived from NE-MenSCs.

Testing encoding specificity and the diagnostic feature-detection theory of eyewitness identification, with implications for showups, lineups, and partially disguised perpetrators

The diagnostic feature-detection theory (DFT) of eyewitness identification is based on facial information that is diagnostic versus non-diagnostic of suspect guilt. It primarily has been tested by discounting non-diagnostic information at retrieval, typically by surrounding a single suspect showup with good fillers to create a lineup. We tested additional DFT predictions by manipulating the presence of facial information (i.e., the exterior region of the face) at both encoding and retrieval with a large between-subjects factorial design (N = 19,414). In support of DFT and in replication of the literature, lineups yielded higher discriminability than showups. In support of encoding specificity, conditions that matched information between encoding and retrieval were generally superior to mismatch conditions. More importantly, we supported several DFT and encoding specificity predictions not previously tested, including that (a) adding non-diagnostic information will reduce discriminability for showups more so than lineups, and (b) removing diagnostic information will lower discriminability for both showups and lineups. These results have implications for police deciding whether to conduct a showup or a lineup, and when dealing with partially disguised perpetrators (e.g., wearing a hoodie).

Multipole expansion of gravitational waves: from harmonic to Bondi coordinates

We transform the metric of an isolated matter source in the multipolar post-Minkowskian approximation from harmonic (de Donder) coordinates to radiative Newman-Unti (NU) coordinates. To linearized order, we obtain the NU metric as a functional of the mass and current multipole moments of the source, valid all-over the exterior region of the source. Imposing appropriate boundary conditions we recover the generalized Bondi-van der Burg-Metzner-Sachs residual symmetry group. To quadratic order, in the case of the mass-quadrupole interaction, we determine the contributions of gravitational-wave tails in the NU metric, and prove that the expansion of the metric in terms of the radius is regular to all orders. The mass and angular momentum aspects, as well as the Bondi shear, are read off from the metric. They are given by the radiative quadrupole moment including the tail terms.

Kantowski-Sachs Cosmology, Weyl Geometry and Asymptotic Safety in Quantum Gravity

A brief review of the essentials of Asymptotic Safety and the Renormalization Group (RG) improvement of the Schwarzschild Black Hole that removes the r = 0 singularity is presented. It is followed with a RG-improvement of the Kantowski-Sachs metric associated with a Schwarzschild black hole interior and such that there is no singularity at t = 0 due to the running Newtonian coupling G(t) (vanishing at t = 0). Two temporal horizons at t _- \simeq t_P and t_+ \simeq t_H are found. For times below the Planck scale t < t_P, and above the Hubble time t > t_H, the components of the Kantowski-Sachs metric exhibit a key sign change, so the roles of the spatial z and temporal t coordinates are exchanged, and one recovers a repulsive inflationary de Sitter-like core around z = 0, and a Schwarzschild-like metric in the exterior region z > R_H = 2G_o M. The inclusion of a running cosmological constant \Lambda (t) follows. We proceed with the study of a dilaton-gravity (scalar-tensor theory) system within the context of Weyl's geometry that permits to single out the expression for the classical potential V (\phi ) = \kappa\phi^4, instead of being introduced by hand, and find a family of metric solutions which are conformally equivalent to the (Anti) de Sitter metric. To conclude, an ansatz for the truncated effective average action of ordinary dilaton-gravity in Riemannian geometry is introduced, and a RG-improved Cosmology based on the Friedmann-Lemaitre-Robertson-Walker (FLRW) metric is explored.

A Non-degenerate Scattering Theory for the Wave Equation on Extremal Reissner–Nordström

It is known that sub-extremal black hole backgrounds do not admit a (bijective) non-degenerate scattering theory in the exterior region due to the fact that the redshift effect at the event horizon acts as an unstable blueshift mechanism in the backwards direction in time. In the extremal case, however, the redshift effect degenerates and hence yields a much milder blueshift effect when viewed in the backwards direction. In this paper, we construct a definitive (bijective) non-degenerate scattering theory for the wave equation on extremal Reissner–Nordström backgrounds. We make use of physical-space energy norms which are non-degenerate both at the event horizon and at null infinity. As an application of our theory we present a construction of a large class of smooth, exponentially decaying modes. We also derive scattering results in the black hole interior region.

Oxygen Inhomogeneity and Reversibility in Single Crystal LaNiO3−δ

LaNiO3−δ single crystals have been obtained via high pressure floating zone growth under 149 bar of oxygen pressure. We find a radial gradient in the magnetic properties of specimens extracted from the as-grown boule, which we correlate with the appearance of ordered oxygen vacancy structures. This radial oxygen inhomogeneity has been characterized systematically using a combination of magnetization and X-ray scattering measurements. We establish the presence of rhombohedral ( R 3 ¯ c ), oxygen stoichiometric specimens at the periphery of the boule and the presence of a dilute concentration of ordered oxygen-deficient orthorhombic La2Ni2O5 in the center. Furthermore, we demonstrate that the as-grown, oxygen-deficient central regions of the crystal can be annealed under high oxygen pressure, without loss of crystallinity, into fully oxygenated LaNiO3, recovering magnetic properties that are characteristic of stoichiometric specimens from the exterior region of the crystal. Thus, single crystals of LaNiO3−δ possess oxygen content that can be reversibly modified under oxidizing and reducing conditions.

Image reconstruction method for exterior circular cone-beam CT based on weighted directional total variation in cylindrical coordinates

The exterior cone-beam computed tomography (CBCT) appears when the x-rays can only pass through the exterior region of an object due to the restriction of the size of the detector, the energy of x-rays and many other factors. The exterior CBCT is an ill-posed inverse problem due to the missing projection data. The distribution of artifacts in exterior CBCT is highly related to the direction of missing projection data. In order to reduce artifacts and reconstruct high quality image, an image reconstruction method based on weighted directional total variation in cylindrical coordinates (cWDTV)is presented in this paper. The directional total variation is calculated according to the direction of missing projection data. The weights are set to reduce artifacts and preserve edges. The convexity of cWDTV and the relationship between cWDTV and classical TV are also illustrated to explain the advantages of our method. Simulated experiments show that our method can improve the performance on artifact reduction and edge preserving.