Slow Decay Rate Research Articles

Dispersive estimates, blow-up and failure of Strichartz estimates for the Schrödinger equation with slowly decaying initial data

The initial value problem for the homogeneous Schr\"odinger equation is investigated for radially symmetric initial data with slow decay rates and not too wild oscillations. Our global wellposedness results apply to initial data for which Strichartz estimates fail.

Inelastic strain in the hypocentral region of the 2000 Western Tottori earthquake (M 7.3) inferred from aftershock seismic moment tensors

Inelastic deformation due to seismic activity is an important signal that reflects fault evolution. In particular, aftershock sequences indicate the evolution of damage in a medium that has experienced a large earthquake. Herein, we discuss the inelastic strain rate surrounding the fault that produced the M 7.3 Western Tottori earthquake in 2000 using long-term aftershock analysis. To obtain high-resolution focal mechanisms 18 years after the earthquake occurrence, we conducted dense seismic observations in the focal area. The inelastic strain rate estimated from the aftershock seismic moment tensor data showed spatial variations within a range of 10−7–10−11 per year, 18 years after the main shock. By comparing the inelastic strain rates from immediately after the earthquake and 18 years later, we detected the increase in the spatial variations in the inelastic strain rate; the variations are as small as 102 (= 10−5/10−7) for the early stage but as large as 104 (= 10−7/10−11) for the later period. In addition, the decay of the rate during these two periods varied spatially from spatial bin to bin. Certain bins in the northern segment of the earthquake fault, southern edge of the fault, and surrounding the location of the preceding swarm activity to the M 7.3 event showed slower decay rates than the inverse of the lapse time since the occurrence of the M 7.3 earthquake. We modeled this decay rate change as the relaxation response of a power-law fluid to an elastic strain input from the large earthquake. Most parts of the fault can be explained by this model. However, the areas with low decay rates suggest the presence of a dragging mechanism, such as aseismic slip, at or around these locations.

A Covalent Organic Framework for Fast-Charge and Durable Rechargeable Mg Storage

High-safety, low-cost, and high-volumetric-capacity rechargeable magnesium batteries (RMBs) are promising alternatives to lithium ion batteries. However, lack of high-power, high-energy, and stable cathodes for RMBs hinders their commercialization. Herein, an environmentally benign, low-cost, and sustainable covalent organic framework (COF) cathode for Mg storage is reported for the first time. It delivers a high power density of 2.8 kW kg-1, a high specific energy density of 146 Wh kg-1, and an ultralong cycle life of 3000 cycles with a very slow capacity decay rate of 0.0196% per cycle, representing one of the best cathodes to date. The comprehensive electrochemical analysis proves that triazine ring sites in the COF are redox centers for reversible reaction with magnesium ions, and the ultrafast reaction kinetics are mainly attributed to pseudocapacitive behavior. The high-rate Mg storage of the COF offers new opportunities for the development of ultrastable and fast-charge RMBs.

Long-range and tunable RKKY interaction in the topological channel of gated bilayer graphene

Two separate gate electrodes with opposite gate voltages can drive an AB-stacked bilayer graphene (BLG) under them into different quantum valley Hall states. And between the two topological domains there appears a one-dimensional boundary, dubbed the topological channel (TC). By means of the Lanczos method, we theoretically study the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two magnetic impurities in such a TC of BLG. We find that the RKKY interaction is long-range with an ${R}^{\ensuremath{-}1}$ decay rate as the distance $R$ between two magnetic impurities increases, whereas the slowest decay rate in any graphene structure is ${R}^{\ensuremath{-}2}$ according to previous literature. Moreover, we also find that the strength and sign of the RKKY interaction in the TC can be readily controlled by altering the gate voltage or carrier doping. Such a tunable and ${R}^{\ensuremath{-}1}$ decaying RKKY interaction implies the possibility of establishing and controlling a long-range magnetic ordering state in a dilute magnetic impurity-doped BLG.

Enhanced performance and electrocatalytic kinetics on porous carbon-coated SnS microflowers as efficient Li–S battery cathodes

Effectively adsorbing and suppressing the polysulfide shuttle by polar materials are of great importance in lithium-sulfur (Li–S) batteries. Herein, the multifunctional SnS@C MS heterostructure consisting of porous carbon shell and SnS microflower-like core is prepared and demonstrated as an efficient Li–S battery cathode with electrocatalytic activity. The integrated physical confinement, strong chemical interaction, and rapid polysulfides (LiPSs) conversion kinetics are mutually promoted to facilitate a successive LiPSs adsorption-conversion with a significantly suppressed shuttle effect. Notably, systematic investigations and experiments reveal that the porous carbon layer can strongly entrap the LiPSs and subsequently facilitate its conversion kinetics between the liquid and solid phases. As a result, SnS@C/S MS cathode can deliver a high initial capacity of 1074.7 mAh g−1 at 0.1 C and ultra-stable cycling performance with a slow capacity decay rate of 0.073% per cycle over 600 cycles at 0.5 C. Moreover, the excellent durability with higher S loading and current densities are also achieved. Thus, this work proffers a facile and promising approach to design and prepare efficient Li–S battery cathodes with high reversible capacities and excellent cycle performance.

Hidden dynamics in a fractional-order memristive Hindmarsh–Rose model

By showing that there is no any memristor in the integer-order Hindmarsh–Rose (H–R) model, the slow ion channel is remodeled by a fractional-order memristor, where the fractional-order derivative is related to the memory effect and the decay rate of the ion current. Then a fractional-order memristive (FOM) H–R model without equilibrium is proposed. Due to a small parameter, the FOM H–R model is a fast–slow system which can be taken as the small perturbation system of the fast subsystem. By Lyapunov direct method, the boundedness of the fast subsystem is proved. With the help of the boundedness and stability of the fast system, the hidden dynamics of the FOM H–R model is discussed. As the small parameter is fixed, it is shown that the membrane potential of the FOM H–R model limits to a quiescent state as the fractional order is less than 0.5 and limits to a periodic spiking as the fractional order is greater than 0.5 less than 1. Without the constraint of the small parameter, the periodic and chaotic bursting appears in the FOM H–R model, which implies the small parameter makes the membrane potential activity simpler. It can be drawn a conclusion that the ion current with the slow decay rate can inhibit the neurons.

Exciton-polariton dynamics modulated by exciton-photon detuning in a ZnO microwire

In a ZnO microcavity, the exciton-polariton effect with ultralarge Rabi splitting (can be as large as several hundreds of millielectron volts) may dominate the optical properties at the energies near the band edge. Due to the light-matter coupling, the renormalized energy states, i.e., the exciton-polariton states are expected to show very different dynamical behavior compared to the free exciton state. In this work, we used a femtosecond laser to pump a high-quality ZnO whispering gallery microcavity at room temperature. In the time-resolved photoluminescence measurements, we observed that both the fast and slow decay rates of the exciton-polaritons are faster than that of the free exciton due to the strong coupling between excitons and photons in a microcavity. The decay time constants are found to depend on the exciton-photon energy detuning (δ=Ephoton−Eexciton).

A highly emissive AIE-active luminophore exhibiting deep-red to near-infrared piezochromism and high-quality lasing.

Further development of high-efficiency and low-cost organic fluorescent materials is intrinsically hampered by the energy gap law and spin statistics, especially in the near-infrared (NIR) region. Here we design a novel building block with aggregation-induced emission (AIE) activity for realizing highly efficient luminophores covering the deep-red and NIR region, which originates from an increase in the orbital overlap and electron-withdrawing ability. An organic donor–acceptor molecule (BPMT) with the building block is prepared and can readily form J-type molecular columns with multiple C–H⋯N/O interactions. Notably, such synthesized materials can emit fluorescence centered at 701 nm with extremely high photoluminescence quantum yields (PLQYs) of 48.7%. Experimental and theoretical investigations reveal that the formation of the hybridized local and charge-transfer (HLCT) state and substantial C–H⋯N/O interactions contribute to a fast radiative decay rate and a slow nonradiative decay rate, respectively, resulting in high PLQYs in the solid state covering the NIR range. Remarkably, such BPMT crystals, as a first example, reveal strong-penetrability piezochromism along with a distinct PL change from the deep-red (λmax = 704 nm) to NIR (λmax = 821 nm) region. Moreover, such typical AIE-active luminophores are demonstrated to be a good candidate as a lasing medium. Together with epoxy resin by a self-assembly method, a microlaser is successfully illustrated with a lasing wavelength of 735.2 nm at a threshold of 22.3 kW cm−2. These results provide a promising approach to extend the contents of deep-red/NIR luminophores and open a new avenue to enable applications ranging from chemical sensing to lasing.

Wave Propagation on Microstate Geometries

Supersymmetric microstate geometries were recently conjectured (Eperon et al. in JHEP 10:031, 2016. https://doi.org/10.1007/JHEP10(2016)031) to be nonlinearly unstable due to numerical and heuristic evidence, based on the existence of very slowly decaying solutions to the linear wave equation on these backgrounds. In this paper, we give a thorough mathematical treatment of the linear wave equation on both two- and three-charge supersymmetric microstate geometries, finding a number of surprising results. In both cases, we prove that solutions to the wave equation have uniformly bounded local energy, despite the fact that three-charge microstates possess an ergoregion; these geometries therefore avoid Friedman’s “ergosphere instability” (Friedman in Commun Math Phys 63(3):243–255, 1978). In fact, in the three-charge case we are able to construct solutions to the wave equation with local energy that neither grows nor decays, although these data must have non-trivial dependence on the Kaluza–Klein coordinate. In the two-charge case, we construct quasimodes and use these to bound the uniform decay rate, showing that the only possible uniform decay statements on these backgrounds have very slow decay rates. We find that these decay rates are sublogarithmic, verifying the numerical results of Eperon et al. (2016). The same construction can be made in the three-charge case, and in both cases the data for the quasimodes can be chosen to have trivial dependence on the Kaluza–Klein coordinates.

A vector field method for massless relativistic transport equations and applications

In this article, we present a vector field method for the study of solutions to massless relativistic transport equations. Compared to [10], we remove the Lorentz boosts of the commutation vector fields and we prove a new functional inequality in order to derive pointwise decay estimates on the solutions. It makes our method more suitable for the study of systems coupling a massless Vlasov equation with an equation which has a different speed of propagation. We also believe that our approach can be adapted more easily to the context of curved backgrounds.In the second part of this paper, we apply our method in order to derive sharp decay estimates on the spherically symmetric small data solutions of the relativistic massless Vlasov-Poisson system. No compact support assumption is required on the data and, in particular, the initial decay in the velocity variable is optimal. In order to compensate the slow decay rate of the particle density near the light cone, we take advantage of the null structure of the equations.

Sulfiphilic Few‐Layered MoSe2 Nanoflakes Decorated rGO as a Highly Efficient Sulfur Host for Lithium‐Sulfur Batteries

AbstractLithium‐sulfur batteries (LSBs) have been regarded as a competitive candidate for next‐generation electrochemical energy‐storage technologies due to their merits in energy density. The sluggish redox kinetics of the electrochemistry and the high solubility of polysulfides during cycling result in insufficient sulfur utilization, severe polarization, and poor cyclic stability. Herein, sulfiphilic few‐layered MoSe2 nanoflakes decorated rGO (MoSe2@rGO) hybrid has been synthesized through a facile hydrothermal method and for the first time, is used as a conceptually new‐style sulfur host for LSBs. Specifically, MoSe2@rGO not only strongly interacts with polysulfides but also dynamically strengthens polysulfide redox reactions. The polarization problem is effectively alleviated by relying on the sulfiphilic MoSe2. Moreover, MoSe2@rGO is demonstrated to be beneficial for the fast nucleation and uniform deposition of Li2S, contributing to the high discharge capacity and good cyclic stability. A high initial capacity of 1608 mAh g−1 at 0.1 C, a slow decay rate of 0.042% per loop at 0.25 C, and a high reversible capacity of 870 mAh g−1 with areal sulfur loading of 4.2 mg cm−2 at 0.3 C are obtained. The concept of introducing sulfiphilic transition‐metal selenides into the LSBs system can stimulate engineering of novel architectures with enhanced properties for various energy‐storage devices.

Preparing LaMnO3 nanocrystals on surface graphitized micro-diamond for efficient oxygen reduction

Electrocatalysts for oxygen reduction reactions are the key to metal–air batteries. In this work, surface graphitized microdiamond (GMD) with a diamond core and graphitic carbon shell are prepared by spark plasma sintering technique. Perovskite-type LaMnO3 (LMO) nanoparticle/surface GMD samples are prepared by a sol–gel method using GMD as support. The LMO/GMD hybrid catalyst exhibits higher electrocatalytic activity than pure LMO and LMO/graphene. The suitability of the hybrid catalyst is tested for primary zinc–air batteries. Results demonstrate that the hybrid catalyst shows a high voltage plateau and slow decay rate. The excellent electrochemical performance is ascribed to the corrosion resistance of diamond, the coral-like structure of composite, the formation of electron transfer connector, and the spill effect of oxygen-containing species. Comparing the performance of differently sized graphitized diamond components in the catalysts proves that approximately 1 μm diamonds are extremely important for improving electrocatalytic activity.

Highly Efficient Thermally Activated Delayed Fluorescence via J-Aggregates with Strong Intermolecular Charge Transfer.

The development of high-efficiency and low-cost organic emissive materials and devices is intrinsically limited by the energy-gap law and spin statistics, especially in the near-infrared (NIR) region. A novel design strategy is reported for realizing highly efficient thermally activated delayed fluorescence (TADF) materials via J-aggregates with strong intermolecular charge transfer (CT). Two organic donor-acceptor molecules with strong and planar acceptor are designed and synthesized, which can readily form J-aggregates with strong intermolecular CT in solid states and exhibit wide-tuning emissions from yellow to NIR. Experimental and theoretical investigations expose that the formation of such J-aggregates mixes Frenkel excitons and CT excitons, which not only contributes to a fast radiative decay rate and a slow nonradiative decay rate for achieving nearly unity photoluminescence efficiency in solid films, but significantly decreases the energy gap between the lowest singlet and triplet excited states (≈0.3 eV) to induce high-efficiency TADF even in the NIR region. These organic light-emitting diodes exhibit external quantum efficiencies of 15.8% for red emission and 14.1% for NIR emission, which represent the best result for NIR organic light-emitting diodes (OLEDs) based on TADF materials. These findings open a new avenue for the development of high-efficiency organic emissive materials and devices based on molecular aggregates.

Conductive CoOOH as Carbon‐Free Sulfur Immobilizer to Fabricate Sulfur‐Based Composite for Lithium–Sulfur Battery

AbstractLithium–sulfur battery is recognized as one of the most promising energy storage devices, while the application and commercialization are severely hindered by both the practical gravimetric and volumetric energy densities due to the low sulfur content and tap density with lightweight and nonpolar porous carbon materials as sulfur host. Herein, for the first time, conductive CoOOH sheets are introduced as carbon‐free sulfur immobilizer to fabricate sulfur‐based composite as cathode for lithium–sulfur battery. CoOOH sheet is not only a good sulfur‐loading matrix with high electron conductivity, but also exhibits outstanding electrocatalytic activity for the conversion of soluble lithium polysulfide. With an ultrahigh sulfur content of 91.8 wt% and a tap density of 1.26 g cm−3, the sulfur/CoOOH composite delivers high gravimetric capacity and volumetric capacity of 1199.4 mAh g−1‐composite and 1511.3 mAh cm−3 at 0.1C rate, respectively. Meanwhile, the sulfur‐based composite presents satisfactory cycle stability with a slow capacity decay rate of 0.09% per cycle within 500 cycles at 1C rate, thanks to the strong interaction between CoOOH and soluble polysulfides. This work provides a new strategy to realize the combination of gravimetric energy density, volumetric energy density, and good electrochemical performance of lithium–sulfur battery.

Prolonged heating in nontargeted tissue during MR-guided focused ultrasound of bone tumors.

Thermal dosimetry during MR-guided focused ultrasound (MRgFUS) of bone tumors underpredicts ablation zone. Intraprocedural understanding of heat accumulation near bone is needed to prevent undesired treatment of nontargeted tissue. Temperature decay rates predict prolonged, spatially varying heating during MRgFUS bone treatments. Prospective case series. Nine patients with localized painful bone tumors (five bone metastasis, four osteoid osteomas), were compared with five patients with uterine fibroid tumors treated using MRgFUS. Proton resonance frequency shift thermometry using 2D-GRE with echo-planar imaging at 3 T. Tissue response was derived by fitting data from extended thermometry acquisitions to a decay model. Decay rates and time to peak temperature (TTP) were analyzed in segmented zones between the bone target and skin. Decay rates were used to calculate intersonication cooling times required to return to body temperature; these were compared against conventional system-mandated cooling times. Kolmogorov-Smirnov tests for normality, and Student's t-test was used to compare decay rates. Spatial TTP delay and predicted cooling times used Wilcoxon signed rank tests. P < 0.05 was significant. Tissue decay rates in bone tumor patients were 3.5 times slower than those in patients with fibroids (τbone = 0.037 ± 0.012 vs. τfibroid = 0.131 ± 0.010, P < 0.05). Spatial analysis showed slow decay rates effecting baseline temperature as far as 12 mm away from the bone surface, τ4 = 0.015 ± 0.026 (median ± interquartile range [IQR]). Tissue within 9 mm of bone experienced delayed TTP (P < 0.01). In the majority of bone tumor treatments, system-predicted intersonication cooling times were insufficient for nearby tissue to return to body temperature (P = 0.03 in zone 4). MRgFUS near bone is susceptible to long tissue decay rates, and unwanted cumulative heating up to 1.2 cm from the surface of the bone. Knowledge of decay rates may be used to alter treatment planning and intraprocedural thermal monitoring protocols to account for prolonged heating by bone. 4 Technical Efficacy: Stage 4 J. Magn. Reson. Imaging 2019;50:1526-1533.

Bilayer Designed Hydrocarbon Membranes for All-Climate Vanadium Flow Batteries To Shield Catholyte Degradation and Mitigate Electrolyte Crossover.

The use of low-cost hydrocarbon membranes in vanadium flow batteries (VFBs) still remains a great challenge because of the strong oxidation of VO2+ catholyte and rapid capacity fading. Here, we report a bilayer design strategy using an antioxidant and dense cross-linked sulfonated polyimide (cSPI) layer as a protective layer for a sulfonated poly(ether ether ketone) (SPEEK) membrane to shield catholyte degradation and mitigate electrolyte crossover. A scalable process is developed to fabricate an integrated bilayer SPEEK/cSPI membrane without delamination by spraying a SPEEK transition layer between the two polymers. The tightly bridged cSPI layer not only protects the SPEEK membrane from degradation but also enhances its mechanical strength, puncture resistance, and proton/vanadium-ion selectivity. When assembled in a VFB, the bilayer SPEEK/cSPI membrane demonstrates excellent rate performance under current densities of 40-200 mA cm-2, high adaptability at a wide temperature range of -15 to 60 °C, very slow capacity decay rate of 0.054% per cycle at 160 mA cm-2, and a maximum power density of 480 mW cm-2. These merits make the bilayer SPEEK/cSPI membrane a promising candidate for the next-generation VFB to achieve low-cost, high-rate, and all-climate energy storage.

Numerical modeling of indirect excitons in double quantum wells in an external electric field

The ground state of an exciton in the GaAs-based double quantum well structure in an external electric field is calculated by the direct numerical solution of the three-dimensional Schrödinger equation. A formation of the indirect exciton is demonstrated by the study of the localization of the exciton wave function in the double quantum well structure for different electric field strengths. A relatively slow radiative decay rate of the indirect exciton is observed.

Micelle-Mediated Chemiluminescence as an Indicator for Micellar Transitions.

The structural phase of micelles plays an important role in controlling the micellar performance. Despite the great developments of some advanced characterization techniques, it remains challenging to achieve fast and sensitive determination of micellar transitions in solution. Herein, a novel indicator system for micellar transitions was developed based on the micelle-mediated peroxyoxalate chemiluminescence that showed a sensitive response toward the changes of micellar morphologies. A peroxyoxalate derivative and a fluorophore were first coassembled into the hydrophobic cavities of micelles of the typical cationic surfactant cetyltrimethylammonium bromide (CTAB). A strong and rapidly falling chemiluminescence response was exhibited in spherical micelles as a result of the loose arrangement of CTAB molecules. By contrast, rodlike or wormlike micelles transformed from spherical micelles could induce a compact arrangement of CTAB molecules, leading to a weak chemiluminescence emission with a slow decay rate. The practicability and universality of the chemiluminescent indicator were demonstrated by determining the micellar transitions in a variety of surfactant solutions (ionic, nonionic, and polymeric). These findings open attractive perspectives for the practice of chemiluminescence technique in micelle characterization.

Effect of High Temperature Circumstance on Lithium-Ion Battery and the Application of Phase Change Material

As known, it is common for lithium ion battery (LIB) to be used under extreme circumstances, among the high temperature circumstance is included. Herein, a series of experiments were conducted at elevated temperatures of 50, 60, and 70°C to examine the performance of LIB. Besides, the application of phase change material (PCM) under such condition was also investigated. Based on the experimental results, it is found that ambient temperature has a remarkable impact on the heat generation of battery, which decreases with the increasing ambient temperature. In addition, it is revealed that the inconsistency among batteries will deteriorate under high temperature circumstance by aggravating the differences of temperature and voltage. Moreover, the capacity decay rate of battery is demonstrated to be accelerated greatly by high temperature. After employing PCM into high temperature circumstance, it is presented that battery exhibits better performance including more stable temperature variation, better discharging performance and slower decay rate. And the performance of PCM is related to its thickness.

Effects of oxygen challenging to tissue redox and pO2 status

Nitroxide free radicals can serve as redox-sensitive MRI contrast agents useful to image the redox status of tissue of interest. In this study, the effect of oxygen content in the inspired gas on the kinetics of metabolism of three nitroxides has been evaluated in the muscle and tumor in mice.SCC tumors (approximate size of 1.0 cm3) on the right hind leg of female C3H/Hen MTV- mice were prepared. Three nitroxides, 3-carboxy-2,2,5,5-tetramethylpyrrolidine-N-oxyl (CxP), 3-carbamoyl-2,2,5,5-tetramethylpyrrolidine-N-oxyl (CmP), and 4-hydroxy-tetramethylpiperidine-N-oxyl (TEMPOL), having different lipophilicities were compared using MR redox imaging. T1-mapping of the tissues was obtained using a multi-slice multi-echo (MSME) sequence with several TRs.The three nitroxides showed differences in accumulation and metabolism/clearance in muscle and tumor. The cell impermeable nitroxide CxP displayed kinetic patterns of slow enhancement followed by a slow decline typical of clearance rather than metabolism. The cell permeable CmP on the other hand showed a relatively faster uptake and metabolism with a modestly higher rate of metabolism in the tumor than muscle. The TEMPOL on the other hand displayed a rapid uptake and reduction with a trend of significantly rapid decay rate in tumor tissue, while slightly higher maximum signal intensity and slower decay rate was observed in normal muscle. The reduction rate of TEMPOL in the tumor was significantly enhanced when the breathing gas had 100%-oxygen while it was not significantly different in the muscle. EPR oximetry studies monitoring the oxygen dependent linewidth of TEMPOL showed that the pO2 in the healthy tissue during carbogen breathing significantly increased normal tissue pO2 compared to air breathing whereas breathing 100%-oxygen made normal tissue slight hypoxic. Since TEMPOL is a radioprotector, our studies show that a combination of 100%-oxygen breathing and TEMPOL has a potential to enhance radioprotective effects to normal tissue.