A linear doubly stabilized Crank-Nicolson scheme for the Allen-Cahn equation with a general mobility

In this paper, a linear second order numerical scheme is developed and investigated for the Allen-Cahn equation with a general positive mobility. In particular, our fully discrete scheme is mainly constructed based on the Crank-Nicolson formula for temporal discretization and the central finite difference method for spatial approximation, and two extra stabilizing terms are also introduced for the purpose of improving numerical stability. The proposed scheme is shown to unconditionally preserve the maximum bound principle (MBP) under mild restrictions on the stabilization parameters, which is of practical importance for achieving good accuracy and stability simultaneously. With the help of uniform boundedness of the numerical solutions due to MBP, we then successfully derive $H^{1}$-norm and $L^{\infty}$-norm error estimates for the Allen-Cahn equation with a constant and a variable mobility, respectively. Moreover, the energy stability of the proposed scheme is also obtained in the sense that the discrete free energy is uniformly bounded by the one at the initial time plus a {\color{black}constant}. Finally, some numerical experiments are carried out to verify the theoretical results and illustrate the performance of the proposed scheme with a time adaptive strategy

A linear second-order maximum bound principle-preserving BDF scheme for the Allen-Cahn equation with general mobility

In this paper, we propose and analyze a linear second-order numerical method for solving the Allen-Cahn equation with general mobility. The proposed fully-discrete scheme is carefully constructed based on the combination of first and second-order backward differentiation formulas with nonuniform time steps for temporal approximation and the central finite difference for spatial discretization. The discrete maximum bound principle is proved of the proposed scheme by using the kernel recombination technique under certain mild constraints on the time steps and the ratios of adjacent time step sizes. Furthermore, we rigorously derive the discrete $H^{1}$ error estimate and energy stability for the classic constant mobility case and the $L^{\infty}$ error estimate for the general mobility case. Various numerical experiments are also presented to validate the theoretical results and demonstrate the performance of the proposed method with a time adaptive strategy.Comment: 25pages, 5 figure

Quantifying the Impact of Experimental Factors on the Measurement of Dynamic Capillary Effects in Unsaturated Porous Media

Multiphase flow is an important phenomenon in many natural and engineering systems; for example, oil recovery and water movement in the unsaturated zone are two common multiphase flow systems. The capillary pressure-saturation (Pc-Sw) relationship, a constitutive relationship between pressure between phases (the capillary pressure, Pc) and the water saturation (Sw), has been studied over nearly the past hundred years. Studies of Pc-Sw relationships are complicated by the often-reported observation of dynamic capillary effects. Dynamic capillary effects refer to a range of observed capillary phenomena which appear to occur under conditions of dynamic saturation change. One of the most widely investigated dynamic effects is the observed rate-dependence of capillary pressures. The focus of the work described here was on studying dynamic capillary effects in the Pc-Sw relationship. Specifically, the work aimed to understand how measurement factors impact the magnitude of observed dynamic capillary effects. A number of studies have experimentally investigated the magnitude of dynamic capillary effects. Many have calculated a dynamic capillary coefficient, τ, as a measure of the magnitude of dynamic capillary effects. The results of reported τ values have differed widely from each other, even for systems with seemingly very similar properties. Furthermore, studies have reported different dependencies between system properties and dynamic effects. However, few studies have examined how features of the measurement system have impacted the accuracy of data collected. In this study, three important factors in the measurement were examined: response rates of pressure sensors, gas pressure drops through porous media, and unavoidable spatial averaging in saturation measurement. Unsaturated drainage experiments in a small-size cell (1.27 cm ID × 2.54 cm H) and a larger column (2.54 cm ID × 15.24 cm H) were conducted to investigate the impact of sensor response and gas pressure gradients on measurement of dynamic effects, and simulations were used to evaluate the effects of gas pressure drops and unavoidable spatial averaging. Results show that the response rate of pressure sensors has a pronounced impact on the measurement of τ, particularly in systems where drainage is rapid. Even if sensors for both wetting and non-wetting phases respond rapidly, if their response rates do not match each other, the mismatched sensor responses can mimic dynamic capillary effects. Results also show that dynamic capillary pressures determined can be significantly greater than their actual values due to internal gas pressure drops or gradients, if inlet gas pressures are taken as gas phase pressures. The extent of gas pressure drops depends on both porous medium properties and boundary properties. Finally, results show that differences between local and spatially-averaged saturations as well as rates of saturation change can potentially amplify τ values calculated from measurements. The extent of the amplification is impacted by fluid properties and flow conditions of the multiphase flow system

A general approach for all-visible-light switching of diarylethenes through triplet sensitization using semiconducting nanocrystals

Coupling semiconducting nanocrystals (NCs) with organic molecules provides an efficient route to generate and transfer triplet excitons. These excitons can be used to power photochemical transformations such as photoisomerization reactions using low energy radiation. Thus, it is desirable to develop a general approach that can efficiently be used to control photoswitches using all-visible-light aiming at future applications in life- and materials sciences. Here, we demonstrate a simple ‘cocktail’ strategy that can achieve all-visible-light switchable diarylethenes (DAEs) through triplet energy transfer from the hybrid of CdS NCs and phenanthrene-3-carboxylic acid, with high photoisomerization efficiency and improved fatigue resistance. The size-tunable excitation energies of CdS NCs make it possible to precisely match the clear spectral window of the relevant DAE photoswitch. We demonstrate reversible all-visible-light photoisomerization of a series of DAE derivatives both in the liquid and solid state, even in the presence of oxygen. Our general strategy is promising for fabrication of all-visible-light activated optoelectronic devices as well as memories, and should in principle be adaptable to photopharmacology

Narrow-linewidth 852-nm DBR-LD with self-injection lock based on high-fineness optical cavity filtering

Narrow-linewidth lasers have high spectral purity, long coherent length and low phase noise, so they have important applications in cold atom physics, quantum communication, quantum information processing and optical precision measurement. We inject transmitted laser from a narrow-linewidth (15 kHz) flat-concave Fabry-Perot (F-P) cavity made of ultra-low expansion (ULE) optical glass into 852-nm distributed-Bragg-reflector type laser diode (DBR-LD), of which the comprehensive linewidth of 1.67 MHz for the free running case. With the increase of self-injection power, the laser linewidth is gradually narrowed, and the inject-locking current range is gradually increased. The narrowest linewidth measured by the delayed frequency-shifted self-heterodyne (DFSSH) method is 263 Hz. Moreover, to characterize the laser phase noise, we use a detuned F-P cavity to measure the conversion signal from laser phase noise to intensity noise for both the free running case and self-injection lock case. Laser phase noise for the self-injection lock case is significantly suppressed in the analysis frequency range of 0.1-10 MHz compared to the free running case. Especially, the phase noise is suppressed by more than 30dB at the analysis frequency of 100 kHz.Comment: 12 pages, 5 figure

A general approach for all-visible-light switching of diarylethenes through triplet sensitization using semiconducting nanocrystals

Coupling semiconducting nanocrystals (NCs) with organic molecules provides an efficient route to generate and transfer triplet excitons. These excitons can be used to power photochemical transformations such as photoisomerization reactions using low energy radiation. Thus, it is desirable to develop a general approach that can efficiently be used to control photoswitches using all-visible-light aiming at future applications in life- and materials sciences. Here, we demonstrate a simple \u27cocktail\u27 strategy that can achieve all-visible-light switchable diarylethenes (DAEs) through triplet energy transfer from the hybrid of CdS NCs and phenanthrene-3-carboxylic acid, with high photoisomerization efficiency and improved fatigue resistance. The size-tunable excitation energies of CdS NCs make it possible to precisely match the clear spectral window of the relevant DAE photoswitch. We demonstrate reversible all-visible-light photoisomerization of a series of DAE derivatives both in the liquid and solid state, even in the presence of oxygen. Our general strategy is promising for fabrication of all-visible-light activated optoelectronic devices as well as memories, and should in principle be adaptable to photopharmacology

Efficient Visible‐to‐UV Photon Upconversion Systems Based on CdS Nanocrystals Modified with Triplet Energy Mediators

Developing high-performance visible-to-UV photon upconversion systems based on triplet–triplet annihilation photon upconversion (TTA-UC) is highly desired, as it provides a potential approach for UV light-induced photosynthesis and photocatalysis. However, the quantum yield and spectral range of visible-to-UV TTA-UC based on nanocrystals (NCs) are still far from satisfactory. Here, three different sized CdS NCs are systematically investigated with triplet energy transfer to four mediators and four annihilators, thus substantially expanding the available materials for visible-to-UV TTA-UC. By improving the quality of CdS NCs, introducing the mediator via a direct mixing fashion, and matching the energy levels, a high TTA-UC quantum yield of 10.4% (out of a 50% maximum) is achieved in one case, which represents a record performance in TTA-UC based on NCs without doping. In another case, TTA-UC photons approaching 4\ua0eV are observed, which is on par with the highest energies observed in optimized organic systems. Importantly, the in-depth investigation reveals that the direct mixing approach to introduce the mediator is a key factor that leads to close to unity efficiencies of triplet energy transfer, which ultimately governs the performance of NC-based TTA-UC systems. These findings provide guidelines for the design of high-performance TTA-UC systems toward solar energy harvesting

Inspiratory-Activated Airway Vagal Preganglionic Neurones Excited by Thyrotropin-Releasing Hormone via Multiple Mechanisms in Neonatal Rats

The airway vagal preganglionic neurons (AVPNs) providing projections to intrinsic tracheobronchial ganglia are considered to be crucial to modulation of airway resistance in physiological and pathological states. AVPNs classified into inspiratory-activated AVPNs (IA-AVPNs) and inspiratory-inhibited AVPNs (II-AVPNs) are regulated by thyrotropin-releasing hormone (TRH)-containing terminals. TRH causes a direct excitatory current and attenuates the phasic inspiratory glycinergic inputs in II-AVPNs, however, whether and how TRH influences IA-AVPNs remains unknown. In current study, TRH regulation of IA-AVPNs and its mechanisms involved were investigated. Using retrogradely fluorescent labeling method and electrophysiology techniques to identify IA-AVPNs in brainstem slices with rhythmic inspiratory hypoglossal bursts recorded by a suction electrode, the modulation of TRH was observed with patch-clamp technique. The findings demonstrate that under voltage clamp configuration, TRH (100 nM) caused a slow excitatory inward current, augmented the excitatory synaptic inputs, progressively suppressed the inhibitory synaptic inputs and elicited a distinctive electrical oscillatory pattern (OP). Such a current and an OP was independent of presynaptic inputs. Carbenoxolone (100 μM), a widely used gap junction inhibitor, fully suppressed the OP with persistence of TRH-induced excitatory slow inward current and augment of the excitatory synaptic inputs. Both tetrodotoxin (1 μM) and riluzole (20 μM) functioned to block the majority of the slow excitatory inward current and prevent the OP, respectively. Under current clamp recording, TRH caused a slowly developing depolarization and continuously progressive oscillatory firing pattern sensitive to TTX. TRH increased the firing frequency in response to injection of a square-wave current. The results suggest that TRH excited IA-AVPNs via the following multiple mechanisms: (1) TRH enhances the excitatory and depresses the inhibitory inputs; (2) TRH induces an excitatory postsynaptic slow inward current; (3) TRH evokes a distinctive OP mediated by gap junction