Existence of single peak solutions for a nonlinear Schrödinger system with coupled quadratic nonlinearity

We are concerned with the following Schrödinger system with coupled quadratic nonlinearity − ε 2 Δ v + P ( x ) v = μ v w , x ∈ R N , − ε 2 Δ w + Q ( x ) w = μ 2 v 2 + γ w 2 , x ∈ R N , v > 0 , w > 0 , v , w ∈ H 1 R N , $$\begin{equation}\left\{\begin{array}{ll}-\varepsilon^{2} \Delta v+P(x) v=\mu v w, & x \in \mathbb{R}^{N}, \\ -\varepsilon^{2} \Delta w+Q(x) w=\frac{\mu}{2} v^{2}+\gamma w^{2}, & x \in \mathbb{R}^{N}, \\ v>0, \quad w>0, & v, w \in H^{1}\left(\mathbb{R}^{N}\right),\end{array}\right. \end{equation}$$ which arises from second-harmonic generation in quadratic media. Here ε > 0 is a small parameter, 2 ≤ N < 6, μ > 0 and μ > γ, P(x), Q(x) are positive function potentials. By applying reduction method, we prove that if x 0 is a non-degenerate critical point of Δ(P + Q) on some closed N − 1 dimensional hypersurface, then the system above has a single peak solution (vε , wε ) concentrating at x 0 for ε small enough.

Differences in Formation Mechanism of Static Pressure Circumferential Distribution of Centrifugal Compressor Under Different Operating Conditions

The casing-wall static pressure of the centrifugal compressor behaves the double-peak distribution in the circumference at small flow rates but the single-peak distribution at large flow rates. A previous study shows that the double-peak distribution is induced by the redistribution of impeller outlet flow rates. In this paper, by using the similar simplified method of directly imposing pressure boundary to the diffuser outlet, the original reason for the formation process difference of pressure distribution in the circumference at different operating conditions is further investigated. The results show that at large flow rates, under the combined action of the specific downstream pressure distribution and the flow performance of the compressor itself, alternating low/high velocity airflow zones similar to those at small flow rates cannot be established in the diffuser when the impeller outlet flow rates are redistributed. Therefore, the static pressure can only express the single-peak distribution in the circumference. In fact, whether the static pressure exhibits the double-peak or single-peak distribution in the circumference depends on whether the impeller outlet flow mutation can destroy the original flow balance. When the flow mutation is dominant, the double-peak distribution is created, whereas when the original flow balance is prevailing, the single-peak distribution is formed.

A Single-Peak-Structured Solar Cycle Signal in Stratospheric Ozone based on Microwave Limb Sounder Observations and Model Simulations

Until now our understanding of the 11-year solar cycle signal (SCS) in stratospheric ozone has been largely based on high quality but sparse ozone profiles from the Stratospheric Aerosol and Gas Experiment (SAGE) II or coarsely resolved ozone profiles from the nadir-viewing Solar Backscatter Ultraviolet Radiometer (SBUV) satellite instruments. Here, we analyse 16 years (2005–2020) of ozone profile measurements from the Microwave Limb Sounder (MLS) instrument on the Aura satellite to estimate the 11-year SCS in stratospheric ozone. Our analysis of Aura-MLS data suggests a single-peak-structured SCS profile (about 3 % near 4 hPa or 40 km) in tropical stratospheric ozone, which is significantly different to the SAGE II and SBUV-based double-peak-structured SCS. We also find that MLS-observed ozone variations are more consistent with ozone from our control model simulation that uses Naval Research Laboratory (NRL) v2 solar fluxes. However, in the lowermost stratosphere where modelled ozone shows a negligible SCS compared to about 1 % in Aura-MLS data. An ensemble of Ordinary Least Square (OLS) and three regularised (Lasso, Ridge and ElasticNet) linear regression models confirms the robustness of the estimated SCS. Our analysis of MLS and model simulations also shows a large SCS in the Antarctic lower stratosphere that was not seen in earlier studies. We also analyse chemical transport model simulations with alternative solar flux data. We find that in the upper (and middle) stratosphere the model simulation with Solar Radiation and Climate Experiment (SORCE) satellite solar fluxes are also consistent with the MLS-derived SCS and agree well with the control simulation and one which uses Spectral and Total Irradiance Reconstructions (SATIRE) solar fluxes. Hence, our model simulation suggests that with recent adjustments and corrections, SORCE solar fluxes can be used to analyse effects of solar flux variations. Finally, we argue that the overall significantly different SCS compared to earlier estimates might be due to a combination of different factors such as much denser MLS measurements, almost linear stratospheric chlorine loading changes over the analysis period, as well as a stratospheric aerosol layer relatively unperturbed by major volcanic eruptions.

Effect of Multilayer Configuration on Spectral Response of Thin Film TiO2/NiO Heterojunction Photodetector

In this work, a multilayer design for the TiO2/NiO heterojunction device is proposed. In this design, layers of TiO2 nanostructures are consecutively deposited on layers of NiO nanostructures deposited on ITO substrates. This design was compared to the conventional design of thin film TiO2/NiO heterojunction device by measuring the spectral response of both designs in the spectral range of 200–1200 nm. The proposed design showed increased response intensity by 14%, narrowing spectral width by 23% and single peak of response at 440nm.

Effect of Aging Treatment on the Corrosion Resistance Properties of 7N01 Extrusion Aluminum Alloy

The influences of non-isothermal aging (the temperature range is 150–180 °C, and the heating rate is 5 and 20 °C/h alternately), single-peak aging (aging at 120 °C for 24 h, then water quenched was followed at room temperature), and two-stage aging (aging at 105 °C for 8 h first, then increasing aging temperature to 135 °C and keeping for 12 h, followed by water quenching at room temperature) on the corrosion resistance and microstructure of the 7N01 aluminum alloy under 3.5 wt.% NaCl were investigated using electric polarization curve test and exfoliation corrosion. After aging, the hardness of samples was measured by a Vickers micro-hardness tester, and the electrical conductivities were obtained using the eddy current method. The results show that the steady phase η and metastable phase η′ are precipitated in the grain boundary of 7N01 aluminum alloy after non-isothermal aging, and their distribution is discontinuous. The hardness of the alloy can reach 136.9 HV1 and the electrical conductivity can reach 35.8% IACS, which is close to the hardness of single-peak aging and the conductivity of two-stage aging, respectively. Compared with single-peak aging, the corrosion current density of non-isothermal aging is reduced by 15.5%, and that of two-stage aging is reduced by 28.9%.

Impact of Black Carbon on Surface Ozone in the Yangtze River Delta from 2015 to 2018

Despite the yearly decline in PM2.5 in China, surface ozone has been rapidly increasing recently, which makes it imperative to coordinate and control both PM2.5 and ozone in the atmosphere. This study utilized the data of pollutant concentrations and meteorological elements during 2015 to 2018 in Nanjing, China to analyze the daily correlation between black carbon and ozone (CBO), and the distribution of the pollutant concentrations under different levels of CBO. Besides, the diurnal variations of pollutant concentrations and meteorological elements under high positive and negative CBO were discussed and compared. The results show that the percentage of positive CBO had been increasing at the average rate of 7.1%/year, and it was 38.7% in summer on average, nearly twice of that in other seasons (19.2%). The average black carbon (BC), PM2.5 and NO2 under positive CBO was lower than those under negative CBO. It is noticeable that the surface ozone began to ascend when CBO was up to 0.2, with PM2.5 and NO2 decreasing and BC remaining steady. Under negative CBO, pollutant concentrations and meteorological elements showed obvious diurnal variations: BC showed a double-peak pattern and surface ozone, PM2.5, SO2 and CO showed single-peak patterns and NO2 showed a trough from 10:00 to 19:00. Wind speed and visibility showed a single-peak pattern with little seasonal difference. Relative humidity rose first, then it lowered and then it rose. Under positive CBO, the patterns of diurnal variations became less obvious, and some of them even showed no patterns, but just fluctuated at a certain level.

Study On Urban Rainstorm Pattern of Short-Duration Double-Peak

At present, researches on urban short-duration rainstorm patterns mainly focus on single-peak rainstorm patterns, and rarely involve double-peak rainstorm patterns, or convert double-peak patterns into single-peak patterns directly, even ignore the impact of double-peak patterns, which directly affects the urban flood planning and early warning and rescue. To scientifically and rationally deduce the urban short duration double-peak rain pattern, this paper proposes a new function fitting rain pattern method by constructing double-peak virtual rain peak rainfall and virtual rain peak coefficient (RPC), based on the idea of convert double-peak to singel-peak, then revert to the double-peak, directly deducing the double-peak rain pattern.The results show that (1) The rain pattern derived by the function fitting rain pattern method(FFRPM) can effectively improve the accuracy of the double-peak rain pattern, and is also more practical; (2) The fitting degree of function fitting rainfall pattern and actual rain pattern is more than 90%, accounting for 80%, the fitting degree of main and secondary peak rainfall is more than 90%, with an average of about 95%; the accuracy of the main and secondary peak positions is also relatively high; (3) Compared with the P&C rain pattern method(RPM), whether the overall accuracy or local peak rainfall, the FFRPM has the higher accuracy, especially more accurate on rain peak rainfall.

Development of a Fish-Like Robot with a Continuous and High Frequency Snap-Through Buckling Mechanism Using a Triangular Cam

This study focuses on the high maneuverability of fish in water to design a fish-like robot via snap-through buckling. The aim of this study is to improve swimming speed by increasing the frequency at which snap-through buckling occurs. Here, we propose a novel drive mechanism using a triangular cam that can continuously generate snap-through buckling at a high frequency. In addition, we developed a fish-like robot via the proposed mechanism and analyzed the influence of the frequency of snap-through buckling on swimming speed. The results obtained indicate that swimming speed is improved and that the relationship between frequency and swimming speed exhibits a single peak. In other words, the swimming speed is reduced when the frequency is significantly increased. We also determined that swimming speed was improved using a wide elastic thin plate as the driving mechanism.

Seasonal Gap Theory for ENSO Phase Locking

The life cycle of El Niño-Southern Oscillation (ENSO) typically follows a seasonal march, onset in spring, developing during summer, maturing in boreal winter, and decaying over the following spring. This feature is referred to as ENSO phase locking. Recent studies have noted that seasonal modulation of the ENSO growth rate is essential for this process. This study investigates the fundamental effect of a seasonally varying growth rate on ENSO phase locking using a modified seasonally-dependent recharge oscillator model. There are two phase locking regimes associated with the strength of the seasonal modulation of growth rate: (1) a weak regime in which only a single peak occurs; and (2) a strong regime in which two types of events occur either with a single peak or double peak. Notably, there is a seasonal gap in the strong regime, during which the ENSO peak cannot occur because of large-scale ocean-atmosphere coupled processes. We also retrieve a simple analytical solution of the seasonal variance of ENSO, revealing that the variance is governed by the time-integral of seasonally varying growth rate. Based on this formulation, we propose a seasonal energy index (SEI) that allows explaining the seasonal gap, and provides an intuitive explanation for ENSO phase locking, potentially applicable to global climate model ENSO diagnostics.