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The generalized three dimensional Navier–Stokes equations with damping are considered. Firstly, existence and uniqueness of strong solutions in the periodic domain T 3 are proved for 1 2 < α < 1 , β + 1 ≥ 6 α 2 α - 1 ∈ (6 , + ∞) . Then, in the whole space R 3 , if the critical situation β + 1 = 6 α 2 α - 1 and if u 0 ∈ H 1 (R 3) ⋂ H ˙ - s (R 3) with s ∈ [ 0 , 1 / 2 ] , the decay rate of solution has been established. We give proofs of these two results, based on energy estimates and a series of interpolation inequalities, the key of this paper is to give an explanation for that on the premise of increasing damping term, the well-posedness and decay can still preserve at low dissipation α < 1 , and the relationship between dissipation and damping is given. [ABSTRACT FROM AUTHOR]

The present study examines the effect of storage conditions on the characteristics of cryogenic hydrogen jets released into the atmosphere, relevant to an accidental leakage scenario during storage or transportation. The compressible Reynolds-Averaged Navier–Stokes equations, coupled with the Peng–Robinson equation of state for hydrogen-air mixtures, are solved for a range of operating conditions (storage pressures from 3 – 7 bar and storage temperatures of 50 – 70 K). Flow structures in the near-orifice and self-similar regions are analysed, showing that the presence of shock waves creates conditions favourable for possible condensation of hydrogen and air. In the self-similar region, decay laws based on the shock exit conditions are proposed, demonstrating a slower decay of centreline temperature in comparison to hydrogen concentration and velocity. Additionally, a universal relationship between the centreline mole fraction of hydrogen and temperature is observed, explained using an adiabatic mixing model. [Display omitted] • Numerical simulations of cryogenic hydrogen jet dispersion are performed. • Shock waves in the near-orifice region create conditions conducive to condensation of air. • Scaling of far-field flow quantities using shock exit conditions is more appropriate than using orifice exit conditions. • A universal relationship between the centreline mole fraction of hydrogen and temperature is found. • The found universal relationship can be explained by considering adiabatic mixing between hydrogen and air. [ABSTRACT FROM AUTHOR]

On 6 February 2023, Türkiye experienced a pair of consecutive earthquakes with magnitudes of Mw 7.8 and 7.5, and accompanied by an intense aftershock sequence. These seismic events were particularly impactful on the segments of the East Anatolian Fault Zone (EAFZ), causing extensive damage to both human life and urban centers in Türkiye and Syria. This study explores the analysis of a dataset spanning almost one year following the Turkiye mainshocks, including 471 events with a magnitude of completeness (Mc) ≥ 4.4. We employed the maximum likelihood approach to estimate the b-value and Omori-Utsu parameters (K, c, and p-values). The estimated b-value is 1.21 ± 0.1, indicating that the mainshocks occurred in a region characterized by elevated stress levels, leading to a sequence of aftershocks of larger magnitudes due to notable irregularities in the rupture zone. The aftershock decay rate (p-value = 1.1 ± 0.04) indicates a rapid decrease in stress levels following the main shocks. However, the c-value of 0.204 ± 0.058 would indicate a relatively moderate or low initial productivity of aftershocks. Furthermore, the k-value of 76.75 ± 8.84 suggests that the decay of aftershock activity commenced within a range of approximately 68 to 86 days following the mainshocks. The fractal dimension (Dc) was assessed using the correlation integral method, yielding a value of 0.99 ± 0.03. This implies a tendency toward clustering in the aftershock seismicity and a linear configuration of the epicenters. The slip ratio during the aftershock activity was determined to be 0.75, signifying that 75% of the total slip occurred in the primary rupture, with the remaining fraction distributed among secondary faults. The methodologies and insights acquired in this research can be extended to assist in forecasting aftershock occurrences for future earthquakes, thus offering crucial data for future risk assessment. [ABSTRACT FROM AUTHOR]

Persistence of spatial analyticity is studied for solutions of the generalized Korteweg‐de Vries (KdV) equation with higher order dispersion ∂tu+(−1)j+1∂x2j+1u=∂xu2k+1,$$\begin{equation*} \partial _{t} u+(-1)^{j+1}\partial _{x}^{2j+1} u= \partial _x{\left(u^{2k+1} \right)}, \end{equation*}$$where j≥2$j\ge 2$, k≥1$k\ge 1$ are integers. For a class of analytic initial data with a fixed radius of analyticity σ0$\sigma _0$, we show that the uniform radius of spatial analyticity σ(t)$\sigma (t)$ of solutions at time t$t$ cannot decay faster than 1t$\frac{1}{\sqrt t}$ as t→∞$t\rightarrow \infty$. In particular, this improves a recent result due to Petronilho and Silva [Math. Nachr. 292 (2019), no. 9, 2032–2047] for the modified Kawahara equation (j=2$j=2$, k=1$k=1$), where they obtained a decay rate of order t−4+$ t^{-4 +}$. Our proof relies on an approximate conservation law in a modified Gevrey spaces, local smoothing, and maximal function estimates. [ABSTRACT FROM AUTHOR]

AbstractPatterns created by buckling of thin films on substrates have important applications in many fields such as functional devices and surface engineering. Introducing hierarchy to such patterns may further enhance their functionalities. However, unpredictable geometrical and material defects may disturb the formation of patterns. It is thus attractive to construct robust hierarchical buckling patterns that are insensitive to defects. Here, inspired by the construction of topologically protected localized states insensitive to defects in wave mechanics, a thin film of finite length bonded on a simple Winkler substrate is quantitatively designed by just varying its width continuously. Under the action of specific compressive stresses within such a continuous thin film owing to thermal mismatch between the film and substrate, there really exists a hierarchical film-buckling mode generated by topologically protected localization. Conditions under which the topologically protected localization exists are given explicitly, and the underlying mechanism is intuitively demonstrated from the mechanical point of view. Moreover, an analytical solution for the decay rate of localization is obtained as a satisfactory second-order approximation, from which the associated influencing factors are clearly identified. This work is expected to provide a theoretical guidance for the design and optimization of hierarchical patterns in film/substrate systems via the concept of topology. [ABSTRACT FROM AUTHOR]

This paper is concerned with the stability of planar viscous shock wave for the 3-dimensional compressible Navier-Stokes-Poisson (NSP) system in the domain Ω : = R × T 2 with T 2 = (R / Z) 2. The stability problem of viscous shock under small 1-dimensional perturbations was solved in Duan-Liu-Zhang [7]. In this paper, we prove the viscous shock is still stable under small 3-d perturbations. Firstly, we decompose the perturbation into the zero mode and non-zero mode. Then we can show that both the perturbation and zero-mode time-asymptotically tend to zero by the anti-derivative technique and crucial estimates on the zero-mode. Moreover, we can further prove that the non-zero mode tends to zero with exponential decay rate. The key point is to estimate the non-zero mode of nonlinear terms involving electronic potential, see Lemma 6.1 below. [ABSTRACT FROM AUTHOR]

We study the asymptotic behavior of the nonlinear MGT plate equation in the unbounded domain. By using semigroup theory, we first establish the well-posedness result for the Cauchy problem related to the linear MGT plate equation. By using the energy method in the Fourier space, we then prove the optimal decay estimate results for the non-critical case, in which the optimality is analyzed by considering the asymptotic expansion of the eigenvalues. By using the contraction mapping, we also show the local existence for the Cauchy problem of the nonlinear plate in appropriate function spaces, based on which we prove a global existence result for small data by using a priori energy estimates. Finally, based on the decay estimation of linear problems, the decay results of nonlinear problems are obtained. [ABSTRACT FROM AUTHOR]

Gelatinous zooplankton (GZ) biomass is an important, yet often overlooked, vector of the particulate organic matter downward export and a nutritional prey source for the mesopelagic and benthic communities. To better quantify the potential impact of their blooms on biogeochemistry and food webs, we performed decomposition and sinking experiments under two different temperature regimes, 6 and 12 °C using 260 Salpa aspera, sampled in the Northeast Pacific (48.39°–50.40°N, 126.40°–145.00°W) during May 2021. Salps sank 1312 and 1424 m day−1 on average in 6 and 12 °C, respectively. The fast sinking is common among other salp species. Salp decay was exponential and occurred ~ 1.5 times faster under warmer conditions. Comparison of the published GZ decay rates supported their strong temperature dependence (Q10 = 3.46) and revealed that S. aspera decayed slower than most GZ taxa. Carcass sinking rates were higher than previously reported for this species and slowed after a prolonged decay. Biochemical (proteins, carbohydrates, lipids) and elemental (C: carbon, N: nitrogen) compositions were determined for salps at various decomposition stages. The high water content (~ 97%) and low organic content (27.8 ± 7.1% dry weight) were typical of other thaliaceans. The high C:N ratio (6.61 ± 1.14) of S. aspera, compared to many thaliaceans, suggested that their carcasses are valuable sources of carbon beyond the euphotic zone. [ABSTRACT FROM AUTHOR]

This paper studies the problems of stability analysis and stabilisation synthesis for a class of impulsive switched stochastic systems. By constructing a novel impulsive switching condition, the sufficient conditions of globally asymptotic stability in probability and stochastic input-to-state stability for the considered systems are presented. Furthermore, the stabilising controller design method can be presented for the corresponding closed-loop systems. Two examples are given to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

We consider the Cauchy problem of the compressible quantum Navier–Stokes–Maxwell equations with the linear damping in the isentropic case under the small perturbation of the constant equilibrium state in three dimensions. Based on the refined energy method, we establish the classical solution globally in time in Sobolev space. By the combination of the energy estimates with the interpolation between the positive Sobolev norms and the negative Sobolev norms ∥·∥Ḣ−s$\Vert \cdot \Vert _{\dot{H}^{-s}}$ with 0⩽s<3/2$0\leqslant s<3/2$ , we also obtain the algebraic decay rates of the classical solution. What is more, the Lp$L^p$–L2(1

In this paper, the authors establish the stability and the explicit decay estimates of the 2D incompressible magneto-micropolar fluid equations without magnetic diffusion and zero spin viscosity on a flat strip Ω : = T × [ 0 , 1 ] under the assumption that Navier type condition being imposed. The results are obtained heavily based on some time-weight energy estimates and a bootstrap argument. [ABSTRACT FROM AUTHOR]

The decomposition of deadwood plays a key role in forest carbon emissions. Most pieces of downed deadwood are partially suspended above the forest floor, but how this suspension affects decomposition rates is typically ignored and remains largely unexplored. Here, we combine field observations and experimental manipulations to explore how partial suspension of downed wood (that is, wood debris in contact with the ground) influences decomposer communities and patterns of decomposition in a lowland tropical forest. Experimental manipulations of wood sticks showed that small-scale suspension above the forest floor (ca. 5 cm) slowed decomposition and altered microbial community assembly, regardless of whether the suspended section was connected to a piece of downed wood. Across a 41-year chronosequence of dead trees, the average percent of wood volume suspended above the forest floor decreased during the initial 10 years post-death, but this trend reversed after 10 years, with the oldest logs being the most suspended. Among downed woody pieces sampled in situ, sections suspended above the forest floor had less moisture, fewer macrofungi, and more photosynthetic growth (for example, moss, algae, and so on) than downed sections of the same bole. Surprisingly, wood density, termite presence, and mass-specific respiration did not differ with ground contact. Combined, these data suggest that suspension within downed wood reduces moisture content, influences decomposer community assembly, and contributes to the strong variability in decomposition rates. The strong effect of partial suspension within downed wood pieces heightens concerns about the accuracy and applicability of experiments and surveys focused on down deadwood, which are the foundation of our understanding of wood decomposition and associated carbon losses. [ABSTRACT FROM AUTHOR]

In this paper, we consider the initial boundary value problem of the generalized pseudo‐parabolic equation containing viscoelastic terms and associated with Robin conditions. We establish first the local existence of solutions by the standard Galerkin method. Then, we prove blow‐up results for solutions when the initial energy is negative or nonnegative but small enough or positive arbitrary high initial energy, respectively. We also establish the lifespan and the blow‐up rate for the weak solution by finding the upper bound and the lower bound for the blow‐up times and the upper bound and the lower bound for the blow‐up rate. For negative energy, we introduce a new method to prove blow‐up results with a sharper estimate for the upper bound for the blow‐up times. Finally, we prove both the global existence of the solution and the general decay of the energy functions under some restrictions on the initial data. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the well-posedness and large time behavior of Cauchy problem for Cahn–Hilliard equation in R n ( n ∈ Z + , n ≥ 3 ). First, based on the higher-order norm estimates of solutions and the mollifier technique, we obtain the local well-posedness of strong solutions. Then, by using pure energy method, standard continuity argument together with negative Sobolev norm estimates, one proves the global well-posedness and time decay estimates provided that the H n 2 + 1 -norm of initial data is sufficiently small. [ABSTRACT FROM AUTHOR]

We consider the linear field-road system, a model for fast diffusion channels in population dynamics and ecology. This system takes the form of a system of PDEs set on domains of different dimensions, with exchange boundary conditions. Despite the intricate geometry of the problem, we provide an explicit expression for its fundamental solution and for the solution to the associated Cauchy problem. The main tool is a Fourier (on the road variable)/Laplace (on time) transform. In addition, we derive estimates for the decay rate of the L ∞ norm of these solutions. [ABSTRACT FROM AUTHOR]

SARS-CoV-2 wastewater surveillance (WWS) at wastewater treatment plants (WWTPs) can reveal sewered community COVID-19 prevalence. For unsewered areas using septic tank systems (STSs) or holding tanks, how to conduct WWS remains unexplored. Here, two large STSs serving Zuma Beach (Malibu, CA) were studied. Supernatant and sludge SARS-CoV-2 concentrations from the directly-sampled STSs parameterized a dynamic solid–liquid separation, mass balance-based model for estimating the infection rate of users. Pumped septage before hauling and upon WWTP disposal was also sampled and assessed. Most (96%) STS sludge samples contained SARS-CoV-2 N1 and N2 genes, with concentrations exceeding the supernatant and increasing with depth while correlating with total suspended solids (TSS). The trucked septage contained N1 and N2 genes which decayed (coefficients: 0.09–0.29 h−1) but remained detectable. Over approximately 5 months starting in December 2020, modeled COVID-19 prevalence estimations among users ranged from 8 to 18%, mirroring a larger metropolitan area for the first 2 months. The approaches herein can inform public health intervention and augment conventional WWS in that: (1) user infection rates for communal holding tanks are estimable and (2) pumped and hauled septage can be assayed to infer where disease is spreading in unsewered areas. [ABSTRACT FROM AUTHOR]

The decay rate of solutions to a Bresse system in thermoelasticity of type III with respect to the distributed delay term is the subject of this study. We demonstrate our major finding utilising the energy approach in the Fourier space. [ABSTRACT FROM AUTHOR]

This paper aims to examine the effects of orientation and asymmetry on the mixing characteristics of circular and elliptical twin jets produced from sharp orifices. The twin jets that emerged from two similar orifices are termed as symmetrical twin jets, and the twin jets issued from two different orifices are referred to as asymmetrical twin jets. The twin jets are separated by the spacing ratio of 2, and numerical simulations are performed at a Mach number of 0.8 and a Reynolds number based on an equivalent exit diameter of 3.46×105. RANS-based two-equation turbulence model, namely SST k-ω model was used to carry out the simulations. It was observed that the core length is not affected by the orifice orientation. However, the spread rates and velocity decay are sensitive to orifice orientation, and among the tested twin jet configurations, the circular-elliptical major asymmetrical jet experienced the highest decay and spread rates. In addition, the turbulent intensity peak values of asymmetrical twin jets decreased by 8 % compared to symmetrical twin jets. [ABSTRACT FROM AUTHOR]

In this paper we study the von Karman plate model with long range memory. By using the assumptions on the relaxation function due to Tatar (J. Math. Phys. 52:013502, 2011), we show an arbitrary rate of decay, which is not necessarily of an exponential or polynomial decay. Our result is obtained without imposing the usual relation between the relaxation function h and its derivative. [ABSTRACT FROM AUTHOR]

In this paper, we study the full parabolic attraction–repulsion Keller–Segel model with a fractional diffusion in ℝn$$ {\mathbb{R}}^n $$ for n=2$$ n=2 $$ or 3. We are more interested in the question that whether the solutions exist globally or blow up in finite time, which was studied in the classical attraction‐repulsion Keller‐Segel model by Jin and Wang (J. Differential Equations, 2016) through constructing a suitable energy functional. However, for the fractional attraction–repulsion Keller–Segel model, it is challenging to find a similar energy functional to study the existence of the solutions. In the present paper, under the condition of ξγ=χα$$ \xi \gamma =\chi \alpha $$, we introduce the Lp$$ {L}_p $$‐ Lq$$ {L}_q $$ estimates of the fractional derivative modulus of the solution to carry out the first step of the problem. Armed with a priori estimate, it is sufficient for us to obtain the global existence of the solutions by the Moser–Alikakos iterative method and finally arrive at the decay estimates of the solutions. [ABSTRACT FROM AUTHOR]

Hawkes processes with exponential kernels are a ubiquitous tool for modeling and predicting event times. However, estimating their decay parameter is challenging, and there is a remarkable variability among decay parameter estimates. Moreover, this variability increases substantially in cases of a small number of realizations of the process or due to sudden changes to a system under study, for example, in the presence of exogenous shocks. In this work, we demonstrate that these estimation difficulties relate to the noisy, non-convex shape of the Hawkes process' log-likelihood as a function of the decay. To address uncertainty in the estimates, we propose to use a Bayesian approach to learn more about likely decay values. We show that our approach alleviates the decay estimation problem across a range of experiments with synthetic and real-world data. With our work, we support researchers and practitioners in their applications of Hawkes processes in general and in their interpretation of Hawkes process parameters in particular. [ABSTRACT FROM AUTHOR]

Consider the non-stationary Navier-Stokes equation in the upper half space of R n. We prove the decay estimates of the strong solution and its derivatives in the setting of Besov and Triebel–Lizorkin spaces. This is the first time that the decay estimates of solutions to the non-stationary Navier-Stokes equations on Besov and Triebel-Lizorkin spaces are established. Our results not only extend the known results from Hardy spaces to Besov and Triebel-Lizorkin spaces but also imply new estimates on Sobolev spaces and give better decay estimates on Hardy spaces. [ABSTRACT FROM AUTHOR]

In this work, we investigate the global well-posedness and asymptotic behavior of a mathematical model of ultrasound-induced heating based on a coupled system of Westervelt's nonlinear acoustic wave equation and Pennes bioheat equation. To this end, under Dirichlet–Dirichlet boundary conditions, we prove global existence for sufficiently small and smooth solutions of the nonlinear model using an energy method. In addition, we show that the energy norm of the resulting pressure and temperature decays to the steady state exponentially fast. [ABSTRACT FROM AUTHOR]

Stability estimates are obtained for delayed linear periodic discrete-time systems. Bounds on the decay of the solution are derived via a suitable Lyapunov–Krasovskii-type functional and the solvability of some periodic discrete-time Lyapunov equations. [ABSTRACT FROM AUTHOR]

We consider the global well-posedness and large time behavior of solutions for epitaxy thin film growth model in R d with the dimensional d ≥ 3 . First, using the pure energy method and a standard continuity argument, we prove that there exists a unique global strong solution under the condition that the initial data is sufficiently small. Moreover, we also establish the suitable negative Sobolev norm estimates and obtain the optimal decay rates of the higher-order spatial derivatives of the strong solution. [ABSTRACT FROM AUTHOR]

In the US Virgin Islands (USVI), roof-harvested rainwater is a primary source of domestic water and is collected in large cisterns and pumped throughout the household premise plumbing system. However, previous literature suggests that roof-harvest rainwater is prone to microbial contamination. A common local water treatment practice is direct batch chlorination of this water (>20,000 L). Provided this local habit, Love City Strong (LCS) established a pilot program to evaluate if direct batch chlorination of water in cisterns was effective and economically feasible to produce consistently adequate levels of free chlorine residual (FCR) at the kitchen tap. A trained field team utilized nine actively used cisterns to conduct a series of chlorine dosing trials where the cistern water was dosed, and, subsequently, monitored every three days. Water quality data were collected throughout, and new trials were initiated once FCR values reached ≤0.05 ppm. Evaluation criteria included: (1) the variability in duration between a dosing event and an FCR measurement <0.2 ppm , (2) the variability of achieving a target FCR level of 1.5 ppm, (3) the variability in the first-order chlorine decay rate, and (4) the costs of the method. Results suggested that the variability in duration, achieving a target FCR, and the decay rate were prohibitively high for consistent use of the method. The duration ranged from 3 to 33 days (mean: 11.5; n=34). This large range may have been influenced by the low probability (18%) of achieving an initial target FCR between 1.25 and 1.75 ppm. In addition, the chlorine decay rate ranged from 0.095 to 0.482 d−1 (mean: 0.251 d−1), resulting in an estimated duration ranging between 5 and 22 days. Finally, the first-year cost was $622 ($244 excluding person-time costs), while annual costs thereafter were $567 ($204 excluding person-time costs). Given these data, we do not recommend the use of direct batch chlorination for treating cistern water for microbial contamination in USVI households. [ABSTRACT FROM AUTHOR]

A method for the determination of neotame in tobacco sweet tipping paper was established by high performance liquid chromatography with diode array detector (HPLC-DAD). Based on this method, the effects of different storage environments ( low temperature and normal humidity, normal temperature and normal humidity, normal temperature and dry) on the content of neotame were analyzed, and the decay behavior of different brands of tipping paper in various environments was fitted by reaction kinetics model. The results showed that the established analytical method exhibited good linearity in the concentration range of 1. 00 ~ 800. 00 µg/mL. The method had high recovery rate and precision, which could be applied for the detection and analysis of neotame in sweet tipping paper. Under different environments, the decay rate of neotame in all brands of tipping paper increased with the prolonged storage time. The low temperature and normal humidity environment was more conducive to the stable storage of sweet tipping paper, while the normal temperature and dry environment could promote the decay of neota-me. The decay behavior of neotame in different brand tipping papers conformed to different reaction kinetic models. The decay kinetic process of different tipping paper was affected by the environment, which may be related to the microstructure of the tipping paper or the interaction between neotame and the carrier. [ABSTRACT FROM AUTHOR]

Stability analysis of switched DC-DC converters is necessary because instability enhances current ripple and causes converter operation at unwanted voltage/current level. In the present study, stability analysis of switched converters using Lie Algebra has been performed considering the switched linear model of DC-DC converters. The switched linear system is asymptotically stable if the Lie bracket formed by the state matrices of the system is commutative. The Lie Algebra is generated and its derived series is also computed. The Lie Algebra is found to be solvable, consequently the switched system is exponentially stable under arbitrary switching. The effect of duty cycle variation and load resistance of DC-DC converters, working in continuous conduction mode (CCM) on the decay constant and decay coefficient, has also been studied. The decay coefficient and decay rate of this exponentially stable system are observed to increase with an increase in the duty cycle for a specific load resistance. [ABSTRACT FROM AUTHOR]

Samples of α-glycine (α-GLY; 230–350 nm) were irradiated in laboratory as a function of electron beam energies (0.25, 0.50, and 1.00 keV) at room temperature (293–295 K). The evolution of α-glycine irradiation process was monitored in real time by infrared spectroscopy (Fourier transform infrared - FTIR), through specific spectral bands: 2610, 2124, 1410, and 1333 cm−1. A phenomenological model is proposed to describe the column density decay when thick organic samples are processed by ionizing beams. The α-glycine radiolysis has exhibited transient and stationary modes in such thickness films. The first stage is mainly described by one exponential decay, whereas the latter foremost decays linearly; compaction processes have been neglected; glycine dissociation and sputtering processes are assumed to be responsible for the damage caused by the electron beam impact through the solid film. The second (stationary) stage is due to equilibrium between a partially shielded bulk radiolysis and sputtering of protective layers. The decay rates are measured for the transient and stationary modes and allow determining the processing velocity of the samples as a function of the electron beam energy. Finally, the model is applied to space weathering to find out the typical sputtering rate of organic compounds on the surface of astrophysical analogs with no protection layers attacked by solar wind (SW) electrons at ≈1 AU. Although the velocity of processing materials in SW has natural competing effects, such as regolith overturn by impacts of micro- and macrometeorites and downslope motion of material that is unstable due to changes in the geopotential of the airless bodies (e.g., asteroid 101955 Bennu), these competing processes are not included in the simulations presented here. [ABSTRACT FROM AUTHOR]

In a Hilbert space, we consider a class of nonlinear fractional equations having the Caputo fractional derivative of the time variable t and the space fractional function of the self-adjoint positive unbounded operator. We consider various cases of global Lipschitz and local Lipschitz source with time-singular coefficient. These sources are generalized of the well–known fractional equations such as the fractional Cahn–Allen equation, the fractional Burger equation, the fractional Cahn–Hilliard equation, the fractional Kuramoto–Sivashinsky equation, etc. Under suitable assumptions, we investigate the existence, uniqueness of maximal solution, and stability of solution of the problems with respect to perturbed fractional orders. We also establish some global existence and prove that the global solution can be approximated by known asymptotic functions as t → ∞ . [ABSTRACT FROM AUTHOR]

A wave equation in a bounded and smooth domain of ℝ n with a delay term in the nonlinear boundary feedback is considered. Under suitable assumptions, global existence and uniform decay rates for the solutions are established. The proof of existence of solutions relies on a construction of suitable approximating problems for which the existence of the unique solution will be established using nonlinear semigroup theory and then passage to the limit gives the existence of solutions to the original problem. The uniform decay rates for the solutions are obtained by proving certain integral inequalities for the energy function and by establishing a comparison theorem which relates the asymptotic behavior of the energy and of the solutions to an appropriate dissipative ordinary differential equation. [ABSTRACT FROM AUTHOR]

We designed two mutants of photoprotein Mnemiopsin 2 (Mn2) including M52I and V144I, where the mutations were applied in the EF-hand loops I and III. Far-UV CD measurements demonstrated that the stability of the helices in the wild-type (WT) protein is greater compared with the mutants. Heat-induced denaturation experiments in the apo-form of photoproteins showed that WT Mn2 has higher value of the enthalpy change for the unfolding process, indicating that it has more stabilizing interaction compared with mutants. According to the activity measurement data, both mutants, particularly V144I have lower initial intensity as well as slower decay rate as compared with the WT photoprotein. Importantly, it was found that V144I variant shows 25 nm of red shift in the characteristic wavelengths as compared with the WT photoprotein. This finding can be considered as an advantage for in vivo application of photoprotein for imaging purposes. It concluded that this position on loop III of Mn2 is a hotspot point for characteristic wavelength determination. However, further research on this mutant is needed for making stable variants of Mn2 with novel optical features. [ABSTRACT FROM AUTHOR]

Photodegradation is a key process impacting the lifetime of oxalate in the atmosphere, but few studies investigated this process in the field due to the complex mixing and sources of oxalate. Oxalate-containing particles were measured via single-particle aerosol mass spectrometry at coastal and suburban sites in Qingdao, a coastal city in North China in the summer of 2016. The mixing state and influence of different ambient conditions on the source and photodegradation of oxalate were investigated. Generally, 6.3% and 12.3% of the total particles (by number) contained oxalate at coastal and suburban sites, respectively. Twelve major types of oxalate-containing particles were identified, and they were classified into three groups. Biomass burning (BB)-related oxalate–K and oxalate–carbonaceous particles were the dominant groups, respectively, accounting for 68.9% and 13.6% at the coastal site and 72.0% and 16.8% at the suburban site. Oxalate–Heavy metals (HM)-related particles represented 14.6% and 9.3% of the oxalate particles at coastal and suburban sites, respectively, which were mainly from industrial emissions (Cu-rich, Fe-rich, Pb-rich), BB (Zn-rich), and residual fuel oil combustion (V-rich). The peak area of oxalate at the coastal site decreased immediately after sunrise, while it increased during the daytime at the suburban site. However, the oxalate peak area of Fe-rich particles at both sites decreased after sunrise, indicating that iron plays an important role in oxalate degradation in both environments. The decay rates (k) of Fe-rich and BB-Fe particles at the coastal site (−0.978 and −0.859 h−1, respectively), were greater than those at the suburban site (−0.512 and −0.178 h−1, respectively), owing to the high-water content of particles and fewer oxalate precursors. The estimated k values of oxalate peak area for different ambient conditions were in the same order of magnitude, which can help establish or validate the future atmospheric models. [ABSTRACT FROM AUTHOR]

In this paper, we consider a viscoelastic Bresse-type system subjects to nonlinear damping, nonlinear time delay term, a finite memory and with homogeneous Dirichlet-Neumann-Neumann boundary conditions. Under a condition between the weight of delay term in the feedback and the weight of the term without delay, we prove, in case of equal speeds of wave propagation, new decay results that generalise and improve the recent results in the literature. [ABSTRACT FROM AUTHOR]

Aims: Changes caused by single herbivore species grazing to soil and plant interfaces can significantly affect the leaf litter decomposition rates within ecosystems. However, we intended to study how grazing by multiple herbivore species regulate the litter decomposition process and associated soil or plant properties in Leymus chinensis dominant meadow steppe. Methods: Two consecutive randomized field experiments were conducted between May 2017 and May 2019: 1) a grazing experiment with four (control or no, sheep, cattle, and mixed (sheep + cattle)) grazing treatments to explore the effects of moderate grazing on soil properties and L. chinensis litter quality and 2) the litter decomposition experiment to evaluate the decay rate in grazed or non-grazed litter by using litter bag technique. Results: Litter decay rate was the highest in mixed grazed litter as compared to litter grazed by individual herbivore species. Both herbivore grazing and incubation time affected decay rate of L. chinensis litter by modifying soil moisture and nitrogen (N) content, as well as, litter N and lignin contents. Plant litter quality has been displayed to be a dominant regulator of litter decay rate than soil physical or chemical properties in mixed grazed litter. Conclusions: Livestock diversification benefited litter decomposition indirectly by modifying plant litter quality with time. Therefore, herbivore assemblages should be given more importance in future research on litter decomposition process to mediate nutrient cycling in grassland. [ABSTRACT FROM AUTHOR]

Plasmonic nanostructures offer an enticing prospect in many applications, ranging from lasing to biosensing, due to their unrivaled light concentration beyond the diffraction limit. However, this promise is substantially undercut by the intrinsically high losses in metals. Here, an experimental ultra‐high‐Q plasmon resonance with a linewidth down to 2 nm (Q‐factor ≈ 350) and a resonance intensity of 51% in an ultrasmooth gold nanogroove array is reported. Such an experimental ultranarrow resonance arises from two key factors. First, a geometrical‐induced coupling between the Fabry–Pérot and Wood's anomaly modes significantly suppresses the groove array's radiative damping. Second, an ultrasmooth gold surface fabricated by template stripping minimizes its surface scattering and grain boundary scattering. Benefiting from this ultranarrow resonance, a figure of merit (FOM) of 284 and an FOM* of 617 in refraction index (RI) sensing under normally incident detection are demonstrated, the former of which is the record FOM in all reported broad‐RI‐range plasmonic RI sensors. The array is further demonstrated as a surface thickness sensor for detecting mercaptocarboxylic acids with the surface sensitivity of 0.18 nm/CH2, which suggests that the array is a promising platform for thickness detection of surface analytes and label‐free biomedical sensing. [ABSTRACT FROM AUTHOR]

The asymptotic stability and long time decay rates of solutions to linear Caputo time-fractional ordinary differential equations are known to be completely determined by the eigenvalues of the coefficient matrices. Very different from the exponential decay of solutions to classical ordinary differential equations, solutions of time-fractional ordinary differential equations decay only polynomially, leading to the so-called Mittag-Leffler stability, which were already extended to linear fractional delay differential equations (FDDEs) with real constants by Čermák et al. (2017) [17]. This paper is devoted to the asymptotical stability and long time decay rates of the solutions for a class of fractional delay abstract evolution equations with complex-valued coefficients. By applying the spectral decomposition method, we reformulate the fractional delay abstract evolution equations to an infinite-dimensional FDDEs. Through the root locus technique, we develop a necessary and sufficient stability condition in a coefficient criterion for FDDEs. At the same time, we are able to deal with the awful singularities caused by delay and fractional exponent by introducing a novel integral path, and hence to give an accurate estimation for the fractional resolvent operators. We show that the long time decay rates of the solutions for both linear FDDEs and fractional delay abstract evolution equations with complex-valued coefficients are O (t − α). Finally, several application models including both time and time-space fractional Schrödinger equations are presented to illustrate the effectiveness of our proposed criteria. • A stability criterion is established for complex-valued fractional delay abstract evolution equations. • A novel integral path is introduced to give an accurate estimation for the fractional resolvent operators. • The long-time decay rate is proved to be polynomial. • Our results provide stability criteria for various models such as time and time-space fractional Schrodinger equations. [ABSTRACT FROM AUTHOR]

We consider the Cauchy problem of a third order in time nonlinear equation known as the Jordan–Moore–Gibson–Thompson (JMGT) equation arising in acoustics as an alternative model to the well-known Kuznetsov equation. We show a local existence result in appropriate function spaces, and, using the energy method together with a bootstrap argument, we prove a global existence result for small data, without using the linear decay. Finally, polynomial decay rates in time for a norm related to the solution will be obtained. [ABSTRACT FROM AUTHOR]

The present study aims to understand microbial succession and dynamics of dry matter, carbon and nitrogen during the decomposition of leaf litters of Tephrosia candida (Roxb.) DC. and Oryza sativa L. in two fallow lands (FL) of 3 years (FL-3) and 8 years (FL-8) following shifting cultivation in Mizoram. A total of 64 microorganisms were isolated from two leaf litters by seri al dilution method, out of which 13 microbes were identified as decomposers as they exhibited a positive response towards the enzyme activity. Among these 13 microorganisms, 4 (SKT 02, SKT 05, SKT 09 and SKT 020) were bacteria (Streptobacillus sp. and Bacillus sp.), 5 (SKT 033, SKT 034, SKT 035, SKT 040 and SKT045) were fungi (Microsporum sp., Rhizopus sp. and Aspergillus sp.) and 4 (SKT 030, SKT 052, SKT 053 and SKT 060) were actinomycetes (Streptomycetes sp.). T. candida leaf litter possessed low initial Carbon/Nitrogen (8.77) and Lignin/Nitrogen ratio (2.29) and considered a high-quality resource exhibiting higher decomposition rate. Mass loss of carbon and nitrogen (~ 40-80%) was maximum during the initial two months, which slowed down in the later period of decomposition. It was concluded that the number of bacteria, fungi and actinomycetes regulate organic matter and nutrient dynamics in the soil through various enzymatic actions on high- and low-quality litters. The combination of O. sativa and T. candida litter is recommended to manage soil fertility in shifting cultivation of Mizoram, Northeast India. [ABSTRACT FROM AUTHOR]

Soil microbes can influence plant competitive outcomes by stabilizing plant community dynamics or mediating plant competitive hierarchies. Which effect dominates depends on whether microbial effects can extend beyond the focal conditioning individual. While it is well known that microbial effects can extend to other individuals through space, we lack an explicit theoretical understanding of the factors that regulate their spread to other individuals in subsequent generations. Here, we examine how the commonly assumed stabilizing effects of host-specific pathogens in fact depend on two factors that allow microbial effects to be cross-generational—which plant demographic vital rate is influenced by microbes and the conditioning and decay rates of soil microbial communities. With a novel patch occupancy model that incorporates the transition of soil states following plant colonization and mortality, we show that host-specific pathogens enable plant coexistence when they suppress conspecific plant colonization of empty patches but contribute to competitive hierarchies when they modify only the mortality and fecundity of the conditioning plant individual. In a series of model extensions, we further demonstrate that these latter microbial effects can still promote coexistence, but only when microbial communities decay slowly following plant death, thereby allowing microbial effects to be cross-generational. Our study calls for further empirical work quantifying the demographic rates most affected by soil microbes as well as the timescales of conditioning and decay. [ABSTRACT FROM AUTHOR]

In the present paper we consider the Standard Linear Solid model in R N coupled with the Cattaneo law of heat conduction. We show the well-posedness and asymptotic stability of the problem, giving decay rates for a norm related to the solution. These results are compared with those given for the Fourier problem in (Pellicer and Said-Houari (2020)) and the ones of the problem without heat conduction (see previous work (Appl Math. Optim80 (2019) 447–478)). The main difference is that the Cattaneo system exhibits the well-known regularity-loss phenomenon. The methods used to prove these results are the energy method in the Fourier space and the eigenvalues expansion method. [ABSTRACT FROM AUTHOR]

The contraction semigroup S (t) = e t A generated by the abstract linear dissipative evolution equation u ¨ + A u + f (A) u ˙ = 0 is analyzed, where A is a strictly positive selfadjoint operator and f is an arbitrary nonnegative continuous function on the spectrum of A. A full description of the spectrum of the infinitesimal generator A of S(t) is provided. Necessary and sufficient conditions for the stability, the semiuniform stability and the exponential stability of the semigroup are found, depending on the behavior of f and the spectral properties of its zero-set. Applications to wave, beam and plate equations with fractional damping are also discussed. [ABSTRACT FROM AUTHOR]

Global climate change is driving the expansion of mangroves into saltmarsh habitat, which may alter the rate and magnitude of organic matter decomposition and nutrient cycling due to differences in the structural complexity, litter quality, and other ecophysiological traits of foundation species. This work quantified and compared aboveground litter decomposition of the range-expanding mangrove, Avicennia germinans, and resident saltmarsh cordgrass, Spartina alterniflora, and decomposition of a standard substrate belowground, in the saltmarsh and saltmarsh-mangrove ecotone habitat along the Atlantic coast of Florida, USA. Plant and soil fractions were tested for natural abundances of δ13C and δ15N stable isotopes to elucidate soil nutrient sources. Although aboveground decomposition rates differed between marsh and mangrove species due to differences in litter quality, decomposition rates did not vary between saltmarsh and ecotonal habitats. Decay rates were higher for A. germinans leaf litter (0.007 ± 0.0003 k day−1) than for S. alterniflora (0.004 ± 0.0003 k day−1) regardless of habitat, which suggests that increasing inputs of A. germinans litter with encroachment may increase nutrient availability through rapid turnover. Furthermore, belowground decomposition was similar between habitats (0.015 ± 0.0008 k day−1), whereas soil δ13C and δ15N stable isotopes differed significantly. Collectively, these results suggest that mangrove encroachment may not modify the environmental factors driving decomposition, but alterations in foundation plant species may ultimately alter nutrient cycling within habitats through shifts in litter quality. [ABSTRACT FROM AUTHOR]

We investigate the stability of a specific stationary solution to Boussinesq equations without thermal conduction in the flat strip Ω = T × (0 , 1) . Explicit decay rates of the vorticity/velocity are given as well as the limit state of the temperature. Our method is based on time-weighted energy estimates. [ABSTRACT FROM AUTHOR]

In this paper, we consider the standard linear solid model in R N coupled with the Fourier law of heat conduction. First, we give the appropriate functional setting to prove the well-posedness of this model under certain assumptions on the parameters (that is, 0 < τ ≤ β ). Second, using the energy method in the Fourier space, we obtain the optimal decay rate of a norm related to the solution. In particular, we prove that when 0 < τ < β the decay rate is the same as in the Cauchy problem without heat conduction (see Pellicer and Said-Houari in Appl Math Optim 80: 447–478, 2019), and that it does not exhibit the well-known regularity loss phenomenon which is present in some of these models. When τ = β > 0 (that is, when the only dissipation comes through the heat conduction), we still have asymptotic stability, but with a slower decay rate. We also prove the optimality of the previous decay rate for the solution itself by using the eigenvalues expansion method. Finally, we complete the results in Pellicer and Said-Houari (Appl Math Optim 80: 447–478, 2019) by showing how the condition 0 < τ < β is not only sufficient but also necessary for the asymptotic stability of the problem without heat conduction. [ABSTRACT FROM AUTHOR]

In this paper, we establish the Lp-norm (1 < p ≤ ∞) algebraic decay rate of solutions and higher-order derivative of solutions for 3D generalized Hall-MHD systemprovided that the L¹-norm of initial data is sufficiently small and the parameters α ∈ [ 5 4, 2 ],β ∈ [ 7 4, 2 ] . [ABSTRACT FROM AUTHOR]

Wound healing treatment after harvest is a critical step to protect sweet potatoes from pathogens. The method of phloroglucinol staining is commonly used for detecting callus. However, this method is not easy to identify the degree of callus as the color change is not obvious compared with non-curing roots for some cultivars. A new method based on the principle of starch test by iodine was developed for the detection of wound healing. After healing, the reducing sugar content increased while the starch content decreased to a lower level compared to that of the non-curing roots. Moreover, the antioxidant capacity of the sweet potato after wound healing was higher than that in the control. Wound healing combined with ethylene, 1-methylcyclopropene (1-MCP), chlorpropham or abscisic acid were studied for inhibiting sprout of sweet potato root caused by high temperature during curing. The results showed ethylene and 1-MCP treatment had no negative effect on wound healing. Moreover, 1-MCP treatment was the most effective one on the suppression of sprouting and decay of sweet potato. The results indicate that iodine solution staining is a useful and rapid method to identify the wound healing extent, and 1-MCP treatment can effectively inhibit root sprouting during wound healing and the subsequent long-term storage. [ABSTRACT FROM AUTHOR]

We consider a coupled system of viscoelastic wave equation with weak, strong damping and power nonlinearity. For a single viscoelastic wave equation, we have already obtained a global solution, its decay rate and finite‐time blow‐up [1]. In this paper, we extend these results to a coupled system. First, we obtain a global solution and derive its decay rate by a decreasing energy. Finally, we apply the concavity method in order to show that the solution blows up in finite time under nonclassic constraint on kernel functions. [ABSTRACT FROM AUTHOR]

Comparison of Computational Fluid Dynamics (CFD) predictions with measurements is presented for cryo-compressed hydrogen vertical jets. The stagnation conditions of the experiments are characteristic of unintended leaks from pipe systems that connect cryogenic hydrogen storage tanks and could be encountered at a fuel cell refueling station. Jets with pressure up to 5 bar and temperatures just above the saturation liquid temperature were examined. Comparisons are made to the centerline mass fraction and temperature decay rates, the radial profiles of mass fraction and the contours of volume fraction. Two notional nozzle approaches are tested to model the under-expanded jet that was formed in the tests with pressures above 2 bar. In both approaches the mass and momentum balance from the throat to the notional nozzle are solved, while the temperature at the notional nozzle was assumed equal to the nozzle temperature in the first approach and was calculated by an energy balance in the second approach. The two approaches gave identical results. Satisfactory agreement with the measurements was found in terms of centerline mass fraction and temperature. However, for test with 3 and 4 bar release the concentration was overpredicted. Furthermore, a wider radial spread was observed in the predictions possibly revealing higher degree of diffusion using the k-ε turbulence model. An integral model for cryogenic jets was also developed and provided good results. Finally, a test simulation was performed with an ambient temperature jet and compared to the cold jet showing that warm jets decay faster than cold jets. [Display omitted] • Cryo-compressed hydrogen jets are simulated. • Good agreement with experiments is found, though more lateral spreading is predicted. • Integral model for cryogenic jets is developed providing satisfactory results. • Ambient temperature jets decay faster than cold jets. [ABSTRACT FROM AUTHOR]