Sharp Decay Research Articles

Characterization of strength, modulus, and fatigue damage properties of cement stabilized macadam based on the double modulus theory

• Flexural tensile strengths calculated with tensile and compressive differences are reduced by nearly 20 % when compared to those calculated without tensile and compressive differences. • A power function decay model of the tension–compression moduli of cement stabilized macadam was established in the four-point bending fatigue test. • The fatigue damage model of cement stabilized macadam was established and its accuracy was verified. Cement stabilized macadam (CSM) is a mixture created by combining cement as a binding material, water, and various particle sizes of minerals. The cement stabilized macadam material exhibits different moduli in tension and compression due to both its mechanical properties and the mechanical response in the asphalt pavement structure. To explore the strength, modulus and fatigue damage characteristics of CSM under different tensile and compressive modulus, this paper carried out the research. The calculation formulas for flexural tensile strength and tension–compression modulus were derived based on the difference in tension–compression modulus. A four-point bending strength test of CSM was carried out. Four-point bending fatigue tests with varying stress ratios were performed. It reveals deterioration laws of tension–compression modulus during fatigue process. The double logarithmic fatigue equation of CSM, as well as its nonlinear fatigue damage evolution equation, are established based on fatigue life results. The results of an analytical solution for fatigue life of rectangular section beams based on damage mechanics were obtained and compared to the results of four-point bending fatigue tests. The results reveal that the modulus of CSM differs in tension and compression. The calculated flexural tensile strength with the tension and compression difference is nearly 20 % lower than without the difference. The calculation approach that does not account for the difference in tension and compression overestimates the flexural tensile strength of CSM. The tension–compression moduli of CSM exhibit a power function decay law in the four-point bending fatigue processes. In the first stage, the dynamic modulus decays at a steady rate, accounting for 90 % of total fatigue life. The second stage in the life ratio of 0.9 occurs when the decay rate of the modulus rapidly increases and enters the stage of sharp decay. Based on the results of the four-point bending test, the modulus decay model was created. The decay parameter m has an exponential relationship with the stress ratio. The relative errors between the mean values of fatigue life tests and the predicted values of the analytical solutions range from 10.8 to 30.6 percent. The established fatigue damage equation for CSM can better reflect its fatigue damage evolution law. The research findings have great significance to solve the determination of pavement materials parameters based on the difference in tension and compression modulus. It also has a specific reference value for asphalt pavement design theory and calculation method when the varied modulus of tension and compression are considered.

Sharp Decay Estimates for Semigroups Associated with Some One-Dimensional Fluid-Structure Interactions Involving Degeneracy

Sharp Decay Estimates for Semigroups Associated with Some One-Dimensional Fluid-Structure Interactions Involving Degeneracy

The sharp time decay rates and stability of large solutions to the two-dimensional Phan-Thien–Tanner system with magnetic field

In this paper, we consider the magnetohydrodynamic (MHD) flow of an incompressible Phan-Thien–Tanner (PTT) fluid in two space dimensions. We focus upon the sharp time decay rates (upper and lower bounds) and global-in-time stability of large strong solutions for the PTT system with magnetic field. Firstly, the convergence of large solutions to the equilibrium have been investigated and these convergence rates are shown to be sharp. We then show that two large solutions converge globally in time as long as two initial data are close to each other. One of the main objectives of this paper is to develop a way to capture L 2 -convergence result via auxiliary logarithmic time decay estimates with the initial data in L p ( R 2 ) ∩ L 2 ( R 2 ). Improving time decay rates for the high-order derivatives of large solutions by using interpolation inequalities. In addition, time-weighted energy estimate, Fourier time-splitting method, semigroup method and iterative scheme have also been utilized.

Almost Price's law in Schwarzschild and decay estimates in Kerr for Maxwell field

We consider the asymptotics of a Maxwell field in Schwarzschild and Kerr spacetimes. In a Kerr spacetime, we utilize the basic energy and Morawetz estimates proven in earlier work to derive pointwise estimates where the total power of decay rate for all components of the Maxwell field towards a stationary solution is −7/2. Moreover, on a Schwarzschild background, if the constructed Newman–Penrose constant vanishes (or does not vanish), we prove almost sharp Price's law decay v−2−sτ−3+s+ (or v−2−sτ−2+s+) for Maxwell field and v−2−sτ−2+s−ℓ0+ (or v−2−sτ−1+s−ℓ0+) for the ℓ≥ℓ0 modes of the field towards a static solution, with s being the spin weight of the Newman–Penrose components of Maxwell field. All estimates are uniform in the exterior of the black hole.

The developmentally timed decay of an essential microRNA family is seed-sequence dependent.

SUMMARYMicroRNA (miRNA) abundance is tightly controlled by regulation of biogenesis and decay. Here, we show that the mir-35 miRNA family undergoes selective decay at the transition from embryonic to larval development in C. elegans. The seed sequence of the miRNA is necessary and largely sufficient for this regulation. Sequences outside the seed (3′ end) regulate mir-35 abundance in the embryo but are not necessary for sharp decay at the transition to larval development. Enzymatic modifications of the miRNA 3′ end are neither prevalent nor correlated with changes in decay, suggesting that miRNA 3′ end display is not a core feature of this mechanism and further supporting a seed-driven decay model. Our findings demonstrate that seed-sequence-specific decay can selectively and coherently regulate all redundant members of a miRNA seed family, a class of mechanism that has great biological and therapeutic potential for dynamic regulation of a miRNA family’s target repertoire.

Correlation of histopathological patterns of OSCC patients with tumor site and habits

IntroductionOral cancer is considered a major global public health problem. The causes of OSCC are tobacco, alcohol, viral infections such as EBV, HPV, and herpes simplex virus, poor oral hygiene (including sharp teeth and decay), ill-fitting denture, ultraviolet (UV) exposure, nutrition, and genetic predisposition. The etiology of oral cancer varies in different populations due to area-specific etiological factors.ObjectiveFinding a correlation of histopathological pattern to the tumor site and habits as an outcome of OSCC.MethodsThis cross-sectional study was conducted in Karachi, Pakistan. A total of 100 known cases of an oral squamous cell carcinoma were diagnosed with the help of biopsy reports and were examined for histopathologic features, site of the lesion, and risk habits.Results48 years was the mean age at the time of diagnosis with a distribution of 61% men and 39% women. The frequently affected site was buccal mucosa and the prime risk habit was gutka followed by betel quid. Histologically, the degree of differentiation shows that moderately differentiated OSCC was most commonly present, while the most prevalent histopathological pattern was spindle cell carcinoma. The statistical relation between lesion site and tobacco habits was found to be significant with a p value (p = 0.01).ConclusionRates of oral squamous cell carcinoma are higher in males than females with a mean age at the time of diagnosis being less than 50 years. Frequently placing gutka in the buccal vestibule against buccal mucosa is responsible to make buccal mucosa the most common tumor site. This study provides baseline information regarding habits.

Oxygen vacancies enriched MOF-derived MnO/C hybrids for high-performance aqueous zinc ion battery

Manganese-based oxides are considered as a promising class of zinc storage materials. However, the dissolution problem of manganese-based oxides leads to a sharp decay of its capacity, hindering its further development. Herein, Mn-metal organic framework (Mn-MOF) derived manganese-based oxide hybrids are synthesized and developed to suppress the dissolution of manganese. The incorporation of oxygen vacancies can tune the electronic rearrangement and crystal microstructure via the different calcination atmospheres of air (Mn2O3) and Ar (MnO/C). Furthermore, the oxygen vacancy can effectively improve the conductivity, which promotes the reaction kinetics and electrochemical performance of manganese-based oxide hybrids. In addition, the storage mechanism of manganese-based oxide hybrids with oxygen vacancies on the insertion and de-intercalation of H+/Zn2+ is demonstrated. Oxygen vacancies enriched MnO/C hybrid cathode shows a high specific capacity of 336.8 mAh g−1 (0.1 A g−1) and the reversible capacity retention 73.8 % after 10,000 cycles at 1.0 A g−1, suggesting excellent long-cycle stability. Significantly, the solid-state zinc ions batteries (ZIBs) is assembled and exhibits a reversible capacity of 58.0 mAh g−1 at 1.0 A g−1. These results suggest that oxygen vacancies provide an effective strategy for exploring high-performance MOF-derived cathodes in aqueous batteries.

Universal selection of pulled fronts

We establish selection of critical pulled fronts in invasion processes as predicted by the marginal stability conjecture. Our result shows convergence to a pulled front with a logarithmic shift for open sets of steep initial data, including one-sided compactly supported initial conditions. We rely on robust, conceptual assumptions, namely existence and marginal spectral stability of a front traveling at the linear spreading speed and demonstrate that the assumptions hold for open classes of spatially extended systems. Previous results relied on comparison principles or probabilistic tools with implied nonopen conditions on initial data and structure of the equation. Technically, we describe the invasion process through the interaction of a Gaussian leading edge with the pulled front in the wake. Key ingredients are sharp linear decay estimates to control errors in the nonlinear matching and corrections from initial data.

Global Existence of Non-Cutoff Boltzmann Equation in Weighted Sobolev Space

This article presents a new approach of semigroup analysis and pseudo-differential calculus for deriving the regularizing estimate on non-cutoff linearized Boltzmann equation. We are able to obtain regularizing estimate of semigroup \(e^{tB}\) that is continuous from weighted Sobolev space \(H(a^{-1/2})H^m_x\) to \(H(a^{1/2})H^m_x\) with a sharp large time decay. With these properties, we prove the existence of global-in-time unique solution to the non-cutoff Boltzmann equation for hard potential on the whole space with weak regularity assumption on initial data. We consider the hard potential case since \(H(a^{1/2})\) can be embedded in \(L^2\). This work develops the application of pseudo-differential calculus, spectrum analysis and semigroup theory to non-cutoff Boltzmann equation.

Enhanced dissipation and transition threshold for the 2-D plane Poiseuille flow via resolvent estimate

In this paper, we study the transition threshold problem for the 2-D Navier-Stokes equations around the Poiseuille flow (1−y2,0) in a finite channel with Navier-slip boundary condition. Based on the resolvent estimates for the linearized operator around the Poiseuille flow, we first establish the enhanced dissipation estimates for the linearized Navier-Stokes equations with a sharp decay rate e−cνt. As an application, we prove that if the initial perturbation of vorticity satisfies‖ω0‖L2≤c0ν34 for some small constant c0>0 independent of the viscosity ν, then the solution does not transition away from the Poiseuille flow for any time.

Cosmic scenario of early universe in context of Euclidean wormhole in dilatonic Einstein–Gauss–Bonnet gravity

In this paper, we present some wormhole configurations using analytic and numerical solutions of the Euclidean field equations considering Einstein–Gauss–Bonnet dilaton coupled interaction in the Robertson–Walker metric. Analytic solutions invoking slow-roll type approximation for some potentials yield identical wormholes in the early era. Eventually, in later era, the universe enters to an expanding era much faster than usual inflation accompanied by oscillations with analytic continuation [Formula: see text]. The numerical solutions of wormholes in terms of the scale factor [Formula: see text] are almost identical for some standard potentials of the dilaton field, except for the evolution of potentials. The Hubble parameter and deceleration parameter obtained by curve fit of [Formula: see text] of the numerical solution of wormhole yield an inflationary era away from the throat of the wormhole using [Formula: see text]. A sharp decay of the potential is also observed.

Exponential Convergence Towards Consensus for Non-Symmetric Linear First-Order Systems in Finite and Infinite Dimensions

We consider finite and infinite-dimensional first-order consensus systems with timeconstant interaction coefficients. For symmetric coefficients, convergence to consensus is classically established by proving, for instance, that the usual variance is an exponentially decreasing Lyapunov function. We investigate here the convergence to consensus in the non-symmetric case: we identify a positive weight which allows to define a weighted mean corresponding to the consensus, and obtain exponential convergence towards consensus. Moreover, we compute the sharp exponential decay rate.

Decay estimates for Schrödinger heat semigroup with inverse square potential in Lorentz spaces

Let \(H:=-\Delta +V\) be a nonnegative Schrödinger operator on \(L^2(\mathbf{R}^N)\), where \(N\ge 2\) and V is an inverse square potential. In this paper we obtain sharp decay estimates of the operator norms of \(e^{-tH}\) and \(\nabla e^{-tH}\) in Lorentz spaces.

Sharp Decay Rate for the Damped Wave Equation With Convex-Shaped Damping

Abstract We revisit the damped wave equation on two-dimensional torus where the damped region does not satisfy the geometric control condition. It was shown in [1] that, for sufficiently regular damping, the damped wave equation is stale at a rate sufficiently close to $t^{-1}$. We show that if the damping vanishes like a Hölder function $|x|^{\beta }$, and in addition, the boundary of the damped region is locally strictly convex with positive curvature, the wave is stable at rate $t^{-1+\frac {2}{2\beta +7}}$, which is better than the known optimal decay rate $t^{-1+\frac {1}{\beta +3}}$ for strip-shaped dampings of the same Hölder regularity. Moreover, we show by example that the decay rate is optimal. This illustrates the fact that the sharp energy decay rate depends not only on the order of vanishing of the damping but also on the shape of the damped region. The main ingredient of the proof is the averaging method (normal form reduction) developed by Hitrik and Sjöstrand ([20], [35]).

The sharp time decay rates for the incompressible Phan-Thien–Tanner system with magnetic field in [formula omitted

Our focus in this paper is to investigate the sharp time decay rates (upper and lower bounds) for the higher order spatial derivatives of large solutions to the magnetohydrodynamic (MHD) flow of an incompressible Phan-Thien–Tanner (PTT) fluid. In dimension two, the sharp time decay rates of large solution (u,H) and all its derivatives have been shown by Chen et al. (2022). The L2-decay rate of the stress tensor τ was improved to (1+t)−1, however, the sharp time decay rates of any spatial derivatives of τ cannot be achieved. Based on Fourier time-splitting and semigroup methods, we shall obtain the optimal upper and lower bounds of time decay rates for the higher spatial derivatives of order k (k=1,2) of τ. More precisely, the kth order spatial derivatives of τ decay at (1+t)−1−k2-rate, which will be shown to be sharp. In addition, our result is valid for the incompressible Oldroyd-B system.

Stationary solutions to the Keller–Segel equation on curved planes

We study stationary solutions to the Keller–Segel equation on curved planes. We prove the necessity of the mass being $8 \pi$ and a sharp decay bound. Notably, our results do not require the solutions to have a finite second moment, and thus are novel already in the flat case. Furthermore, we provide a correspondence between stationary solutions to the static Keller–Segel equation on curved planes and positively curved Riemannian metrics on the sphere. We use this duality to show the nonexistence of solutions in certain situations. In particular, we show the existence of metrics, arbitrarily close to the flat one on the plane, that do not support stationary solutions to the static Keller–Segel equation (with any mass). Finally, as a complementary result, we prove a curved version of the logarithmic Hardy–Littlewood–Sobolev inequality and use it to show that the Keller–Segel free energy is bounded from below exactly when the mass is $8 \pi$, even in the curved case.

Propagator norm and sharp decay estimates for Fokker–Planck equations with linear drift

We are concerned with the short- and large-time behavior of the $L^2$-propagator norm of Fokker-Planck equations with linear drift, i.e. $\partial_t f=\mathrm{div}_{x}{(D \nabla_x f+Cxf)}$. With a coordinate transformation these equations can be normalized such that the diffusion and drift matrices are linked as $D=C_S$, the symmetric part of $C$. The main result of this paper is the connection between normalized Fokker-Planck equations and their drift-ODE $\dot x=-Cx$: Their $L^2$-propagator norms actually coincide. This implies that optimal decay estimates on the drift-ODE (w.r.t. both the maximum exponential decay rate and the minimum multiplicative constant) carry over to sharp exponential decay estimates of the Fokker-Planck solution towards the steady state. A second application of the theorem regards the short time behaviour of the solution: The short time regularization (in some weighted Sobolev space) is determined by its hypocoercivity index, which has recently been introduced for Fokker-Planck equations and ODEs (see [5, 1, 2]). In the proof we realize that the evolution in each invariant spectral subspace can be represented as an explicitly given, tensored version of the corresponding drift-ODE. In fact, the Fokker-Planck equation can even be considered as the second quantization of $\dot x=-Cx$.

Quadratic Klein-Gordon equations with a potential in one dimension

Abstract This paper proposes a fairly general new point of view on the question of asymptotic stability of (topological) solitons. Our approach is based on the use of the distorted Fourier transform at the nonlinear level; it does not rely only on Strichartz or virial estimates and is therefore able to treat low-power nonlinearities (hence also nonlocalised solitons) and capture the global (in space and time) behaviour of solutions. More specifically, we consider quadratic nonlinear Klein-Gordon equations with a regular and decaying potential in one space dimension. Additional assumptions are made so that the distorted Fourier transform of the solution vanishes at zero frequency. Assuming also that the associated Schrödinger operator has no negative eigenvalues, we obtain global-in-time bounds, including sharp pointwise decay and modified asymptotics, for small solutions. These results have some direct applications to the asymptotic stability of (topological) solitons, as well as several other potential applications to a variety of related problems. For instance, we obtain full asymptotic stability of kinks with respect to odd perturbations for the double sine-Gordon problem (in an appropriate range of the deformation parameter). For the $\phi ^4$ problem, we obtain asymptotic stability for small odd solutions, provided the nonlinearity is projected on the continuous spectrum. Our results also go beyond these examples since our framework allows for the presence of a fully coherent phenomenon (a space-time resonance) at the level of quadratic interactions, which creates a degeneracy in distorted Fourier space. We devise a suitable framework that incorporates this and use multilinear harmonic analysis in the distorted setting to control all nonlinear interactions.

Fourier transform of surface–carried measures of two-dimensional generic surfaces and applications

<p style='text-indent:20px;'>We give a simple proof of the sharp decay of the Fourier-transform of surface-carried measures of two-dimensional generic surfaces. The estimates are applied to prove Strichartz and resolvent estimates for elliptic operators whose characteristic surfaces satisfy the generic assumptions. We also obtain new results on the spectral and scattering theory of discrete Schrödinger operators on the cubic lattice.</p>

Tajik Depression and Greater Pamir Neotectonics From InSAR Rate Maps

AbstractUsing E‐W and vertical deformation‐rate maps derived from radar interferometric time‐series, we analyze the deformation field of an entire orogenic segment, that is, the Tajik depression and its adjoining mountain belts, Tian Shan, Pamir, and Hindu Kush. The data‐base consists of 900+ radar scenes acquired over 2.0–4.5 years and global navigation satellite system measurements. The recent, supra‐regional kinematics is visualized in an unprecedented spatio‐temporal resolution. We confirm the westward collapse of the Pamir‐Plateau crust, inverting the Tajik basin into a fold‐thrust belt (FTB) with shortening rates decaying westward from ∼15 to 2 mm/yr. Vertical rates in the Hindu Kush likely record slab‐dynamic effects, that is, the progressive break‐off of the Hindu Kush slab. At least 10 mm/yr of each, uplift and westward motion occur along the western edge of the Pamir Plateau, outlining the crustal‐scale ramp along which the Pamir Plateau overrides the Tajik depression. The latter shows a combination of basin‐scale tectonics, halokinesis, and seasonal/weather‐driven near‐surface effects. Abrupt ∼6 mm/yr horizontal‐rate changes occur across the kinematically linked dextral Ilyak strike‐slip fault, bounding the Tajik FTB to the north, and the Babatag backthrust, the major thrust of the FTB, located far west in the belt. The sharp rate decay across the Ilyak fault indicates a locking depth of ≤1 km. The Hoja Mumin salt fountain is spreading laterally at ≤350 mm/yr. On the first‐order, the modern 20–5 and fossil (since ∼12 Ma) 12–8 mm/yr shortening rates across the FTB correspond.