Compact Boundary Research Articles

Tailoring the tribological performance of poly(ionic liquid)s brushes capped carbon dots by transforming the anion species

The tribological performance of poly(ionic liquid)s brushes capped carbon dots (CDs-PILs-X) as the additives of polyethylene glycol (PEG200) were well tailored by transforming the anion species (X-), where the X- were hexafluorophosphate (PF6-), bis(trifluorosulfonyl) imide (NTf2-), bis(salicylato) borate (BScB-) and oleate (OL-), respectively. Despite all of the CDs-PILs-X as additives of PEG200 exhibited excellent friction reduction and wear resistance properties, their tribological performance followed the order of CDs-PILs-OL > CDs-PILs-BScB > CDs-PILs-NTf2 > CDs-PILs-PF6. Typically, at a concentration of 2 wt%, the CDs-PILs-OL, CDs-PILs-BScB, CDs-PILs-NTf2 and CDs-PILs-PF6 made the average friction coefficient and wear volume of PEG200 reduce by 58.6 and 85.4%, 45.5 and 76.3%, 33.3 and 75.7%, and 28.6 and 72.6%, respectively, confirming the distinct influences of anion species on the tribological performance of CDs-PILs-X. The CDs-PILs-OL exhibited the best friction reduction and wear resistance performance because the anions of OL- with the lowest steric hindrance could form the densest absorbing layers and hence the most compact boundary lubrication films on the rubbing surfaces. The anions of PF6- and NTf2- might decompose to release corrosive substances (such as HF) during the friction process, largely weakening the lubrication functions of CDs-PILs-NTf2 and CDs-PILs-PF6. The CDs-PILs-OL can be a kind of promising lubricant additives for PEG200 because of their impressive performance, long service life, low cost and environmental friendliness.

Regularity of simple nuclear real C*-algebras under tracial conditions

AbstractThe Toms–Winter conjecture is verified for those separable, unital, nuclear, infinite-dimensional real C*-algebras for which the complexification has a tracial state space with compact extreme boundary of finite covering dimension.

Robust feedback stabilization by means of Lyapunov-like functions determined by Lie brackets

We use Lie brackets of unbounded vector fields to consider a dissipative relation that generalizes the differential inequality which defines classic control Lyapunov functions. Under minimal regularity assumptions, we employ locally semiconcave solutions of this extended relation, called in the following degree-k control Lyapunov functions, in order to design degree-k Lyapunov feedbacks, i.e. particular discontinuous feedback laws that stabilize the underlying system to a given closed target with compact boundary, in the sample and hold sense. We also prove that this feedback construction is robust when small measurement errors and external disturbances occur.

Electrochemical synthesis of chitosan/silver nanoparticles multilayer hydrogel coating with pH-dependent controlled release capability and antibacterial property

By coupling in situ electrochemical synthesis of silver nanoparticles (AgNPs) with the pre-deposited chitosan multilayer hydrogel, a novel type of nanocomposite coating was successfully fabricated on the stainless-steel needle electrode. Experimental results demonstrated the chitosan film can serve as a versatile medium for metal salt adsorption and stabilization, and finally electrochemical reduction of loaded silver ions to nanoparticles. The AgNPs were fabricated with a spherical shape and an average size of ∼15 nm endowing considerable antibacterial property to the hydrogel. Furthermore, the unique layered architecture consisted of porous segments and compact boundaries is almost retained, resulting in a pH-dependent and staged release pattern of silver nanoparticles based on acid triggered dissolution of the multi-membrane layer by layer. Thus, considering the mild synthesizing approach, multi-functionalities and relatively low cytotoxicity, this antibacterial hydrogel would show great potential either to be used as a newly coating material for interfacial improvement of implants or as a free-standing film after being peeled off for wound dressing.

Uniqueness Results for Free Boundary Minimal Hypersurfaces in Conformally Euclidean Balls and Annular Domains

In this paper, we prove that a flat free boundary minimal n-disk, $$n\ge 3$$ , in the unit Euclidean ball $${\mathbb {B}}^{n+1}$$ is the unique compact free boundary minimal hypersurface whose squared norm of the second fundamental form is less than either $$\frac{n^2}{4}$$ or $$\frac{(n-2)^2}{4|x|^2}$$ . Moreover, we prove analogous results for compact free boundary minimal hypersurfaces in annular domains or balls with a conformally Euclidean metric.

Sharp gradient estimates on weighted manifolds with compact boundary

<p style='text-indent:20px;'>In this paper, we prove sharp gradient estimates for positive solutions to the weighted heat equation on smooth metric measure spaces with compact boundary. As an application, we prove Liouville theorems for ancient solutions satisfying the Dirichlet boundary condition and some sharp growth restriction near infinity. Our results can be regarded as a refinement of recent results due to Kunikawa and Sakurai.</p>

Edge States for the Magnetic Laplacian in Domains with Smooth Boundary

We are interested in the spectral properties of the magnetic Schrödinger operator $H_\varepsilon$ in a domain $\Omega \subset \mathbb{R}^2$ with compact boundary and with magnetic field of intensity $\varepsilon^{-2}$. We impose Dirichlet boundary conditions on $\partial\Omega$. Our main focus is the existence and description of the so-called edge states, namely eigenfunctions for $H_{\varepsilon}$ whose mass is localized at scale $\varepsilon$ along the boundary $\partial\Omega$. When the intensity of the magnetic field is large (i.e., $\varepsilon <<1$), we show that such edge states exist. Furthermore, we give a detailed description of their localization close to $\partial\Omega$, as well as how their mass is distributed along it.

Evaluation of Compact Boundary of Outage Probability in HetNet

In this paper, we investigate the outage probability of per‐tier in heterogeneous networks (HetNet) in the presence of aggregated interference from coexisting ad hoc networks. In ad hoc networks, a receiving node suffers the cross‐tier interference signal from cellular cell and aggregated interference signal from other transmitting nodes. In order to evaluate the effect of cross‐tier interference on the outage probability of ad hoc networks, we analyze the restricted region in cellular cell that the received signal interference noise ratio (SINR) of a receiving node does not exceed the SINR threshold considering the path loss model. Further, to evaluate the effect of aggregated interference of ad hoc networks, we divide the plane area into near‐field area and far‐field area according to whether the signal of a transmitting node could cause an outage independently or not. Based on this division, we derive the compact lower and upper boundaries of outage probability of per‐tier. The computer simulations validate the results of theoretical analysis and show the effect of different factors, such as transmit power, intensity of ad hoc nodes, on the outage probability.

Grid convergence of a combination of compact schemes and boundary compact schemes when practical grid spacing is used

Grid convergence of a combination of compact schemes and boundary compact schemes when practical grid spacing is used

The Hilbert manifold of asymptotically flat metric extensions

In [Commun Anal Geom 13(5):845–885, 2005], Bartnik described the phase space for the Einstein equations, modelled on weighted Sobolev spaces with local regularity (g,pi )in H^2times H^1. In particular, it was established that the space of solutions to the constraints form a Hilbert submanifold of this phase space. The motivation for this work was to study the quasi-local mass functional now bearing his name. However, the phase space considered there was over a manifold without boundary. Here we demonstrate that analogous results hold in the case where the manifold has an interior compact boundary, and the metric is prescribed on the boundary. Then, still following Bartnik’s work, we demonstrate the critical points of the mass functional over this space of extensions correspond to stationary solutions with vanishing Killing vector on the boundary. Furthermore, if this solution is smooth then it is in fact a static black hole solution. In particular, in the vacuum case, critical points only occur at exterior Schwarzschild solutions; that is, critical points of the mass over this space do not exist generically. Finally, we briefly discuss a version of the result when the boundary data is related to Bartnik’s geometric boundary data. In particular, by imposing different boundary conditions on the Killing vector, we show that stationary solutions in this case correspond to critical points of an energy resembling the difference between the ADM mass and the Brown–York mass of the boundary.

Extraction of compact boundary normalisation based geometric descriptors for affine invariant shape retrieval

Shape recognition and retrieval is a complex task on non-rigid objects and it can be effectively performed by using a set of compact shape descriptors. This paper presents a new technique for generating normalised contour points from shape silhouettes, which involves the identification of object contour from images and subsequently the object area normalisation (OAN) method is used to partition the object into equal part area segments with respect to shape centroid. Later, these contour points are used to derive six descriptors such as compact centroid distance (CCD), central angle (ANG), normalized points distance (NPD), centroid distance ratio (CDR), angular pattern descriptor (APD) and multi-triangle area representation (MTAR). These descriptors are a 1D shape feature vector which preserve contour and region information of the shapes. The performance of the proposed descriptors is evaluated on MPEG-7 Part-A, Part-B and multi-view curve dataset images. The present experiments are aimed to check proposed shape descriptor's robustness to affine invariance property and image retrieval performance. Comparative study has also been carried out for evaluating our approach with other state of the art approaches. The results show that image retrieval rate in OAN approach performs significantly better than that in other existing shape descriptors.

A two-piece property for free boundary minimal surfaces in the ball

We prove that every plane passing through the origin divides an embedded compact free boundary minimal surface of the euclidean 3 3 -ball in exactly two connected surfaces. We also show that if a region in the ball has mean convex boundary and contains a nullhomologous diameter, then this region is a closed halfball. Moreover, we prove the regularity at the corners of currents minimizing a partially free boundary problem by following ideas by Grüter and Simon. Our first result gives evidence to a conjecture by Fraser and Li.

P-Phenylenediaminium iodide capping agent enabled self-healing perovskite solar cell

In this study, p-Phenylenediaminium iodide (PDAI) is used to in-situ growth of 2D (PDA)2PbI4 perovskite layer between (FAPbI3)0.85(MAPbBr3)0.15 3D perovskite and CuSCN as a cheap hole transport layer. The results indicate that the incorporation of 5 mg mL−1 PDAI leads to enlarged grain sizes, compact grain boundaries, reduced trap density, efficient charge extraction, and enhanced stability of perovskite film. Passivation of perovskite film with the appropriate amount of PDAI helps in achieving efficient perovskite solar cell with a PCE as high as 16.10%, a JSC of 21.45 mA cm−2, a VOC of 1.09 V, and FF of 70.21%, with negligible hysteresis and excellent moisture stability which remains 99.01% of its initial PCE value after 5 h in high relative humidity of 90 ± 5% and shows unchanged PCE after 1440 h in low relative humidity of 15 ± 5%. Most strikingly, this ultra-thin 2D passivation layer by the use of PDA cations as a bulky spacer not only passivates the defects on the surface of perovskite film but also induces self-healing properties in PSCs which can be rapidly recovered after keeping away from water vapor exposure. This study introduces the cheap and extra stable perovskite solar cells with outstanding self-healing ability towards commercialization.

Rigidity results of free boundary maximal hypersurfaces in the region bounded by a de Sitter space

This paper provides the rigidity results of free boundary maximal hypersurfaces in a region bounded by a de Sitter space in the Lorentz–Minkowski space. First, it is proved that any smooth, compact free boundary maximal hypersurface in a de Sitter ball is the spacelike coordinate planar disk passing through the center of the de Sitter space. Second, a smooth, noncompact, complete free boundary maximal hypersurface in the exterior of a de Sitter ball is considered. For maximal hypersurfaces with one planar end in the exterior of a de Sitter ball, every complete noncompact free boundary maximal hypersurface is shown to be a part of the spacelike coordinate hyperplane.

Vertical Profiles of Wind-Blown Sand Flux over Fine Gravel Surfaces and Their Implications for Field Observation in Arid Regions

We used a compact boundary layer wind tunnel equipped with a turbulence generator and a piezoelectric blown-sand meter to investigate the effects of the surface coverage of fine gravel on wind-blown sand flux. The vertical profile of wind-blown sand over a flat sand surface showed an exponential distribution at all wind speeds, whereas the profile over gravel surfaces of 20% or greater coverage showed a non-monotonic vertical distribution. At 20% to 30% gravel coverages, a peak of wind-blown sand flux developed between 6 and 10 cm above the ground at all wind speeds because of less energy loss due to grain-bed collisions at that level. To analyze the erosional state of wind-blown sand, we used the Wu–Ling index (λ) of the mass-flux density of sand-bearing wind. Values of λ for all gravel coverages were greater than 1 at all wind speeds, indicating an unsaturated (erosional) state. Moreover, we found that the wind-blown sand flux at 4 cm height accounted for about 20% of the total flux regardless of wind speed and gravel coverage. This finding can simplify future estimations of total near-surface wind-blown sand flux based on field observations because such measurements can be taken at just one height.

Steady-state two-relaxation-time lattice Boltzmann formulation for transport and flow, closed with the compact multi-reflection boundary and interface-conjugate schemes

We introduce the steady-state two-relaxation-time (TRT) Lattice Boltzmann method. Owing to the symmetry argument, the bulk system and the closure equations are all expressed in terms of the equilibrium and non-equilibrium unknowns with the half discrete velocity set. The local mass-conservation solvability condition is adjusted to match the stationary, but also the quasi-stationary, solutions of the standard TRT solver. Additionally, the developed compact, boundary and interface-conjugate, multi-reflection (MR) concept preserves the efficient directional bulk structure and shares its parametrization properties. The method is exemplified in grid-inclined stratified slabs for two-phase Stokes flow and the linear advection-diffusion equation featuring the discontinuous coefficients and sources. The piece-wise parabolic benchmark solutions are matched exactly with the novel Dirichlet, pressure-stress, Neumann flux and Robin MR schemes. The popular, anti-bounce-back and shape-fitted Dirichlet continuity schemes are improved in the presence of both interface-parallel and perpendicular advection velocity fields. The steady-state method brings numerous advantages: it skips transient numerical instability, overpasses severe von Neumann parameter range limitations, tolerates high physical contrasts and arbitrary MR coefficients. The method is promising for faster computation of Stokes/Brinkman/Darcy linear flows in heterogeneous soil, but also heat and mass transfer problems governed by an accurate boundary and interface treatment.

On some asymptotic representations of solutions to elliptic equations and their applications

The question on asymptotic representations of Green's function for classical boundary value problems for second-order elliptic equations depending on a complex parameter is considered. The equations are defined either in a domain with a compact boundary or in the whole space or the half-space. The main asymptotic term is written out. The results can be applied for the study of some inverse problems of recovering point sources in heat and mass transfer problems.

Compact block boundary value methods for semi‐linear delay‐reaction–diffusion equations with algebraic constraints

AbstractIn the present paper, we study a class of linear approximation methods for solving semi‐linear delay‐reaction–diffusion equations with algebraic constraint (SDEACs). By combining a fourth‐order compact difference scheme with block boundary value methods (BBVMs), a class of compact block boundary value methods (CBBVMs) for SDEACs are suggested. It is proved under some suitable conditions that the CBBVMs are convergent of order 4 in space and order p in time, where p is the local order of the used BBVMs, and are globally stable. With several numerical experiments for Fisher equation with delay and algebraic constraint, the computational effectiveness and theoretical results of CBBVMs are further illustrated.

Incremental small sphere and large margin for online recognition of communication jamming

In the anti-jamming field of radio communication, the problem of online and multiclass jamming recognition is fundamental to implement reasonable anti-jamming measures. The incremental small sphere and large margin (IncSSLM) is proposed, this model can learn the compact boundary for own communication signals and known jamming, which relieves the open-set problem of radio data. Meanwhile it can also update the model of classifier in real time, which avoids the large memory requirement for vast jamming data and saving much time for training. The core of proposed method is the small sphere and large margin (SSLM) approach, which makes the spherical area as compact as possible, like support vector data description (SVDD), and also makes the margin between them as far as possible, like support vector machine (SVM). In other words, it can minimize intra-class divergence and maximize inter-class space. Therefore, there is a significant enhancement of recognition performance when compared with open classifiers such as SVM, and considerable superiority of training efficiency when compared with the canonical SSLM algorithm. Numerical experiments based on synthetic data, practical complex feature data of high-resolution range profile (HRRP), and jamming data of radio communication demonstrate that IncSSLM is efficient and promising for multiple and online recognition of vase and open-set radio jamming.

Index estimates for free boundary constant mean curvature surfaces

In this paper, we consider compact free boundary constant mean curvature surfaces immersed in a mean convex body of the Euclidean space or in the unit sphere. We prove that the Morse index is bounded from below by a linear function of the genus and number of boundary components.