Coarse embeddings at infinity and generalized expanders at infinity

We introduce a notion of coarse embedding at infinity into Hilbert space for metric spaces, which is a weakening of the notion of fibred coarse embedding and a far generalization of Gromov's concept of coarse embedding. It turns out that a residually finite group admits a coarse embedding into Hilbert space if and only if one (or equivalently, every) box space of the group admits a coarse embedding at infinity into Hilbert space. Moreover, we introduce a concept of generalized expander at infinity and show that it is an obstruction to coarse embeddability at infinity.Comment: 20 page

A Bott periodicity theorem for ℓp\ell^p-spaces and the coarse Novikov conjecture at infinity

We formulate and prove a Bott periodicity theorem for an $\ell^p$-space ($1\leq p<\infty$). For a proper metric space $X$ with bounded geometry, we introduce a version of $K$-homology at infinity, denoted by $K_*^{\infty}(X)$, and the Roe algebra at infinity, denoted by $C^*_{\infty}(X)$. Then the coarse assembly map descents to a map from $\lim_{d\to\infty}K_*^{\infty}(P_d(X))$ to $K_*(C^*_{\infty}(X))$, called the coarse assembly map at infinity. We show that to prove the coarse Novikov conjecture, it suffices to prove the coarse assembly map at infinity is an injection. As a result, we show that the coarse Novikov conjecture holds for any metric space with bounded geometry which admits a fibred coarse embedding into an $\ell^p$-space. These include all box spaces of a residually finite hyperbolic group and a large class of warped cones of a compact space with an action by a hyperbolic group.Comment: 55 page

Controllable Preparation of Gold Nanocrystals with Different Porous Structures for SERS Sensing

Porous Au nanocrystals (Au NCs) have been widely used in catalysis, sensing, and biomedicine due to their excellent localized surface plasma resonance effect and a large number of active sites exposed by three-dimensional internal channels. Here, we developed a ligand-induced one-step method for the controllable preparation of mesoporous, microporous, and hierarchical porous Au NCs with internal 3D connecting channels. At 25 &deg;C, using glutathione (GTH) as both a ligand and reducing agent combined with the Au precursor to form GTH&ndash;Au(I), and under the action of the reducing agent ascorbic acid, the Au precursor is reduced in situ to form a dandelion-like microporous structure assembled by Au rods. When cetyltrimethylammonium bromide (C16TAB) and GTH are used as ligands, mesoporous Au NCs formed. When increasing the reaction temperature to 80 &deg;C, hierarchical porous Au NCs with both microporous and mesoporous structures will be synthesized. We systematically explored the effect of reaction parameters on porous Au NCs and proposed possible reaction mechanisms. Furthermore, we compared the SERS-enhancing effect of Au NCs with three different pore structures. With hierarchical porous Au NCs as the SERS base, the detection limit for rhodamine 6G (R6G) reached 10&minus;10 M

Heat Transfer Modeling on High-Temperature Charging and Discharging of Deep Borehole Heat Exchanger with Transient Strong Heat Flux

High-temperature charging and discharging by deep borehole heat exchanger is typical of a large heat exchange temperature difference and transient strong heat flux. Simulation of this problem is not only computationally expensive, but it is also challenging in terms of robustness and stability for numerical methods. This paper formulates a generic and efficient heat transfer model with two distinctive novelties: Firstly, it highlights unsteady- and quasi-steady-state modeling strategies for heat transfer outside and inside a borehole. Secondly, this model provides analytical solutions for the heat front propagation and heat flux density distribution for unsteady-state heat transfer in the rock zone. These analytical formulations prove to be generic and critical to relieve computational effort in the face of strong heat flux. This model is validated by a typical high-temperature heat storage case from the literature, as well as the pilot demonstration project in China. It was discovered that a large prediction error of the heat transfer model only exists in very short operation days during the initial unsteady stages of charging and discharging. Both relative errors under charging and discharging phases are within 5% during the steady-state period. A comparison of the simulation cost with OpenGeoSys software demonstrates its high efficiency. It proves that this heat transfer model achieves an acceleration ratio of 30 times relative to the fully numerical method. In general, the heat transfer model has four advantages: generic applicability, good accuracy, easy implementation, and high efficiency, but it is limited to the heat transfer of a single deep borehole heat exchanger under pure heat conduction

Heat Transfer Modeling on High-Temperature Charging and Discharging of Deep Borehole Heat Exchanger with Transient Strong Heat Flux

High-temperature charging and discharging by deep borehole heat exchanger is typical of a large heat exchange temperature difference and transient strong heat flux. Simulation of this problem is not only computationally expensive, but it is also challenging in terms of robustness and stability for numerical methods. This paper formulates a generic and efficient heat transfer model with two distinctive novelties: Firstly, it highlights unsteady- and quasi-steady-state modeling strategies for heat transfer outside and inside a borehole. Secondly, this model provides analytical solutions for the heat front propagation and heat flux density distribution for unsteady-state heat transfer in the rock zone. These analytical formulations prove to be generic and critical to relieve computational effort in the face of strong heat flux. This model is validated by a typical high-temperature heat storage case from the literature, as well as the pilot demonstration project in China. It was discovered that a large prediction error of the heat transfer model only exists in very short operation days during the initial unsteady stages of charging and discharging. Both relative errors under charging and discharging phases are within 5% during the steady-state period. A comparison of the simulation cost with OpenGeoSys software demonstrates its high efficiency. It proves that this heat transfer model achieves an acceleration ratio of 30 times relative to the fully numerical method. In general, the heat transfer model has four advantages: generic applicability, good accuracy, easy implementation, and high efficiency, but it is limited to the heat transfer of a single deep borehole heat exchanger under pure heat conduction

Spectral Element Numerical Investigation of Flow between Three Cylinders in an Equilateral-Triangular Arrangement with Different Spacing Distances

Two-dimensional incompressible Navier-Stokes equations are numerically solved using the high resolution spectral element method at Reynolds number 200. The flow between three cylinders in an equilateral-triangular arrangement is investigated. The center-to-center spacing distance ratio between two circular cylinders is varied from 1.5 to 12. Present numerical results show that the flow patterns and force characteristics are the result of the combined effects of Reynolds number, spacing distance, configuration arrangement, and incident angle. For the small spacing distance ratio of 1.5, the well-known biased flow phenomenon in the gap of downstream cylinders is found. And the biased flow is bistable in our study but not monostable. A small spacing distance means lower Strouhal number, drag, and root-mean-square lift coefficients. In the medium spacing distance ratio of 4.0, the suppressed effect of vortex shedding for the presence of the side-by-side downstream cylinders disappeared. Mean drag coefficients of downstream cylinders are basically identical to the value of flow past around a single circular cylinder. For the large spacing distance ratio of 8.0, the effects between three cylinders basically disappeared. The mean drag and lift coefficients, root-mean-square lift coefficients, and Strouhal number of three cylinders are essentially equivalent to those values of a single circular cylinder

SERS and machine learning based effective feature extraction for detection and identification of amphetamine analogs

Surface-enhanced Raman spectroscopy (SERS) is extensively researched in diverse disciplines due to its sensitivity and non-destructive nature. It is particularly considered a potential and promising technology for rapid on-site screening in drug detection. In this investigation, a technique was developed for fabricating nanocrystals of Ag@Au SNCs. Ag@Au SNCs, as the basic material of SERS, can detect amphetamine at concentrations as low as 1 μg/mL. The Ag@Au SNCs exhibits a strong surface plasmon resonance effect, which amplifies molecular signals. The SERS spectra of ten substances, including amphetamine and its analogs, showed a strong peak signal. To establish a qualitative distinction, we examined the Raman spectra and conducted density functional theory (DFT) calculations on the ten aforementioned species. The DFT calculation enabled us to determine the vibrational frequency and assign normal modes, thereby facilitating the qualitative differentiation of amphetamines and its analogs. Furthermore, the SERS spectrum of the ten mentioned substances was analysed using the support vector machine learning algorithm, which yielded a discrimination accuracy of 98.0 %

Thermal Performance Analysis on the Seasonal Heat Storage by Deep Borehole Heat Exchanger with the Extended Finite Line Source Model

Deep borehole heat exchanger is promising and competitive for seasonal heat storage in the limited space underground with great efficiency. However, seasonal heat storage performance of the essentially deep borehole heat exchanger reaching kilometers underground was seldom studied. In addition, previous research rarely achieved comprehensive assessment for its thermal performance due to seasonal heat storage. Insight into the complicated heat transfer characteristics during the whole process of prior charging and subsequent discharging of deep borehole heat exchanger is in urgent need to be clarified. To this end, an extended finite line source model is proposed to investigate thermal performance of the deep borehole heat exchanger during charging and discharging stages. It is developed with modifications of classical finite line source model to consider the spatio-temporally non-uniform distribution of heat flux density and anisotropic thermal conductivity of deep rock. In general, simulation results demonstrate that thermal performance of the deep borehole heat exchanger deteriorates rapidly both during charging and discharging stages, making it impossible to sustain long-term efficient operation. Specifically, it was discovered that low temperature heat storage utilized only upper section of the borehole as effective heat storage section, and enhancement for heat extraction potential during the heating season was not significant. While high temperature heat storage by deep borehole heat exchanger could only enhance the heat extraction potential for 30 to 40 days in the initial stage of heating. Throughout the discharging, maximum thermal performance enhancement up to 11.27 times was achieved and the heat storage efficiency was evaluated at 2.86 based on average heat exchange rate. The findings of this study are intended to provide a guidance for decisionmakers to determine the most suitable seasonal heat storage strategy for the deep borehole heat exchanger and facilitate the application in engineering practice