This paper is a continuation of our recent paper . We will consider the semi‐linear Cauchy problem for wave models with scale‐invariant time‐dependent mass and dissipation and power non‐linearity. ...The goal is to study the interplay between the coefficients of the mass and the dissipation term to prove global existence (in time) of small data energy solutions assuming suitable regularity on the L2 scale with additional L1 regularity for the data. In order to deal with this L2 regularity in the non‐linear part, we will develop and employ some tools from Harmonic Analysis.
In the Large High Altitude Air Shower Observatory (LHAASO), the main physics objective of the water Cherenkov detector array (WCDA) is to survey the sky for gamma-ray sources in the energy range of ...100 GeV to 30 TeV. In order to extend the dynamic range of the WCDA, a 1.5-inch photomultiplier tube (PMT) is placed aside the 8-inch PMT in each cell of the WCDA. All of these 1.5-inch PMTs (900 in total) consist of the WCDA dynamic extended system (WCDA++). These PMTs are required to maintain linearity within four orders of magnitude. The performance of the 1.5-inch PMTs with a specially designed bi-readout voltage divider is tested with a PMT test system. Accordingly, the effects of the working high voltage and signal width on the dynamic range of the PMTs are studied. The test results show that the dynamic range with a 5% non-linearity for a driven signal width of 5.5 ns is more than 200 kPEs (photoelectrons). The dark noise count rate is less than 200 Hz for a 1 mV threshold at a PMT gain of 2×105. These results confirm that the PMT performance meets the WCDA++ requirements.
•Photomultiplier tube performance of the WCDA++ experiment is presented.•A bi-readout divider circuit maintains linearity within four orders of magnitude.•The pulse signal width affects the linear maximum number of photoelectrons.•The light intensity does not affect the relation between gain and voltage.
Psychological science remains unclear about how individuals' trait perfectionism impacts their performance—is more perfectionism linearly better or does too perfect backfire? The present study ...investigates a potentially non-linear relationship and its underlying mediators. Based on the two-dimensional model of perfectionism that distinguishes perfectionistic concerns (PC) versus strivings (PS), we investigate the (non-)linear relationships of perfectionism and performance in the letter detection task. Additionally, we experimentally examined whether time pressure would moderate these findings. Our study results (N = 229) establish non-linearity: a quadratic function in the form of an inverted U-shape best explains the relationship between perfectionistic concerns and performance. Contrary to our hypothesis, perfectionistic strivings predicted task performance linearly but negatively. Upon further examination, we also found empirical support for a combinatory effect of both dimensions: Only individuals high in PC showed the negative effect of PS on task performance. Although performance differed in the timed versus untimed task, time pressure did not moderate the (non-)linear relationships of PS or PC on performance. Multiple mediation analyses revealed that perceived distress, rumination, and effort mediated the quadratic relationships of perfectionistic concerns. Overall, our results question the strict disentanglement of perfectionistic dimensions and emphasise the usefulness of a more holistic approach.
In this paper, we are concerned with the following elliptic equation involving a general gradient nonlinearity:−Δv=μ|v|p−1v+G(∇v)inΩ, where n≥1, either Ω=Rn is the whole space or ...Ω=R+n={x=(x1,…,xn)∈Rn:xn>0} is the half space, μ≥0, p∈R and G:Rn→R satisfies some suitable conditions. One particular case of G is G(γ)=∑i=1kai|γ|pi with ai>0 and pi>1 for any 1≤i≤k. When Ω=Rn, we establish a Bernstein estimate to prove some Liouville-type results of the equation under certain conditions on μ and p. When Ω=R+n, by combining the Bernstein estimates with a moving planes argument, we obtain the one-dimensional symmetry of the solution v with v=0 on ∂R+n. We note that the exponent p is allowed to be negative in our results. Finally, we obtain a gradient estimate in some special cases with μ>0 and p>1.
Floods claim a high toll in fatalities and economic impacts. Despite their societal relevance, there is much more to learn about the projected changes in discharge and flooding. Here we force an ...operational hydrologic model over the state of Iowa with high‐resolution convection‐permitting climate‐model precipitation to evaluate the response of 140 watersheds to climate change. At the end of the century, under the most aggressive scenario in terms of fossil fuel use, we show that the transition from snow to rainfall and approximately 30% increase in extreme precipitation rates lead to a doubling of maximum discharge during the spring and extending the flood season into the fall. Total discharge volumes are also expected to increase. Our results suggest that flood projections based on extreme precipitation increases alone substantially underestimate future risk due to the non‐linearity of the hydrologic response explained by long‐term soil moisture memory and its feedbacks with precipitation. This study is one of the first to show floods are increasing due to the prevalence of rain‐on‐snow events, and indeed that discharge might increase more than precipitation.
The authors examined the projected changes in discharge under the most aggressive scenario in terms of fossil fuel use (RCP8.5) using high‐resolution convection‐permitting climate simulations. Our results show increasing potential flood risk under climate change for Iowa that far exceeds increases from precipitation alone.
•A comprehensive dynamic model has been proposed for electrostatic energy harvester.•Non-linear air damping force is studied in the model with various geometry.•“Pull-in” effect has been observed ...during vibration for the first time.•All the simulation from the model has shown good agreement with experimental results.
In this paper, a new comprehensive model is presented to optimize the design of vibration based electrostatic energy harvester working in standard atmosphere. This model considers the non-linear air damping force induced by the movement of proof mass as well as the “pull-in” effect from the electrostatic force. Important parameters such as the height of stoppers on the bottom plate, the initial gap between the bottom plate and proof mass and the surface potential of the electret layer have been investigated. With the microelectromechanical system (MEMS) technology, a series of energy harvesters have been fabricated with various parameters. The measurements of devices show excellent agreement with the simulations. For the first time, the “pull-in” phenomenon has been observed during the harvesting test as our expectation. The model provides a promising optimization route for the electrostatic energy harvester with broad bandwidth, decent power output while avoiding the “pull-in” effect.
The non-specific adsorption behaviors of various interferents on the surface of a molecularly imprinted polymer (MIP) are adverse for the selectivity of an MIP-based sensor, which can be overcome via ...a differential strategy by using the differential signal between MIP- and non-imprinted polymer (NIP)-based sensors. However, the normal differential mode is not suitable for the MIP-based sensors with non-linear calibration curves. Herein, an improved differential strategy is reported for an MIP-based sensor with a semi-logarithmic calibration curve, demonstrated by an electrochemiluminescence (ECL) sensor for dopamine (DA). Glassy carbon electrode (GCE) was modified by the mixture of g-C3N4, TiO2 nanoparticles (NPs) and carbon nanotubes (CNTs). MIP membrane for DA was fabricated on the surface of g-C3N4/TiO2NPs/CNTs/GCE using chitosan for film-forming, obtained MIP@GCE. To enhance the anti-interference ability of the MIP-based DA sensor, the difference between exponential functions ECL intensities of MIP@GCE and NIP@GCE is used as the analytical signal in the improved differential strategy. The differential signal was increased linearly with increasing DA concentration ranging from 10 pM to 0.10 μM, with the detection limit of 5.6 pM. The interference level of Cu2+ on DA determination in the improved differential mode is only 9.7% of that in the normal MIP mode. The improved differential strategy can be used in other MIP-based sensors with semi-logarithmic calibration curves.
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•Differential molecularly imprinting electrochemiluminescence sensor was reported.•An improved differential strategy for semi-logarithmic calibration curve was reported.•Interference level from non-specific adsorption is reduced by one order of magnitude.•The sensitivity of the sensor was enhanced in the differential measurement mode.
The real-world experiences of young athletes follow a non-linear and dynamic trajectory and there is growing recognition that facing and overcoming a degree of challenge is desirable for aspiring ...elites and as such, should be recognized and employed. However, there are some misunderstandings of this "talent needs trauma" perspective with some research focusing excessively or incorrectly on the incidence of life and sport challenge as a feature of effective talent development. The objective of the study was to examine what factors associated with such "trauma" experiences may or may not discriminate between high, medium, and low achievers in sport, classified as super-champions, champions or almosts. A series of retrospective interviews were used with matched triads (i.e., super-champions, champions, or almosts) of performers (N = 54) from different sports. Data collection was organized in three phases. In the first phase, a graphic time line of each performer's career was developed. The second phase explored the specific issues highlighted by each participant in a chronological sequence. The third phase was a retrospective reflection on "traumatic" motivators, coach/significant other inputs and psychological challenges experienced and skills employed. Data suggested qualitative differences between categories of performers, relating to several perceptual and experiential features of their development. No evidence was found for the necessity of major trauma as a feature of development. There was a lack of discrimination across categories of performers associated with the incidence of trauma and, more particularly, life or non-sport trauma. These findings suggest that differences between levels of adult achievement relate more to what performers bring to the challenges than what they experience. A periodized and progressive set of challenge, preceded and associated with specific skill development, would seem to offer the best pathway to success for the majority.
The presence of non-linearity and, at the same time, the small number of datasets are often the constraints that appear together in the case of NIR spectra (381–1065nm). This makes some ...chemometricians think again about presenting a reasonable and robust calibration model using the linear calibration method. On the other hand, even though obtaining a high and robust calibration model, the NIR spectra-based approach is still an alternative method that must still consider low cost and ease of getting it. This study introduces a novel strategy for developing robust calibration models from small and non-linearity NIR spectra datasets. The prediction performance of two groups of chemometric methods, linear (partial least squares regression, PLSR) and non-linear calibration techniques (k-nearest neighbor, k-NN; Ada boosting, AB; Bayesian ridge regression, BRR), were also compared and investigated in depth. A total of forty raw NIR spectral data was used to develop a calibration model to predict the content of B-pinene, D-limonene, and safrole from the nutmeg fruit. The first strategy, non-linearity due to the effect of light scattering on the NIR spectral data, will be handled directly by the non-linear calibration technique algorithm from machine learning to generate the non-linearity model without preprocessing techniques. The second strategy, the robustness of the model, is tested by performing random splitting of data several times without supervision and ending with a rigorous statistical procedure adopted to ensure reliable comparison. The results suggest that the non-linear calibration method is the most promising among the investigated methods. Furthermore, although none of the techniques is always the best to predict on all references, k-NN (for prediction of B-pinene and safrole) and BRR (for prediction of B-pinene and D-limonene), some of them are found to be the most promising in terms of low prediction error (the maximum Rp2 is 81.6%, and RMSE is less than 1.139%). There are non-linear calibration techniques explored with limited success being achieved.
The technical note investigates the tensile force-displacement response of the hysteretic steel yielding brace known as Crescent Shaped Brace and characterized by a boomerang-like geometrical shape. ...The force-displacement curve is governed by three key performance points which correspond to the transition points separating the initial elastic behaviour, the flexural plastic behaviour, the geometrical hardening behaviour and the final axial plastic behaviour.
In particular, the influence of the main geometrical parameter of the device, the so-called “lever arm”, on the strongly non-linear force-displacement behavior is analyzed by means of a simplified kinematic model. Based on this, analytical estimations of the key performance points are derived and compared with numerically simulated force-displacement curves.
•The Crescent Shaped Braces allow to satisfy multiple seismic performance objectives through ad-hoc geometrical properties.•A strong coupling between geometrical and material non-linearities governs the behavior of the CSB in tension.•The full force-displacement curve is completely described through analytical estimation of three key performance points.•The analytical estimation is verified through non-linear numerical simulations.
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