Lifespan Estimates Research Articles

Asymptotic behavior and life-span estimates for the damped inhomogeneous nonlinear Schrödinger equation

Asymptotic behavior and life-span estimates for the damped inhomogeneous nonlinear Schrödinger equation

Blow-up of solutions for coupled wave equations with damping terms and derivative nonlinearities

<p>This work was concerned with the weakly coupled system of semi-linear wave equations with time dependent speeds of propagation, damping terms, and derivative nonlinear terms in generalized Einstein-de Sitter space-time on $ \mathbb{R}^n $. Under certain assumptions about the indexes $ k_1, \, k_2 $, coefficients $ \mu_1, \, \mu_2 $, and nonlinearity exponents $ p, \, q $, applying the iteration technique, finite time blow-up of local solutions to the small initial value problem of the coupled system was investigated. Blow-up region and upper bound lifespan estimate of solutions to the problem were established. Compared with blow-up results in the previous literature, the new ingredient relied on that the blow-up region of solutions obtained in this work varies due to the influence of coefficients $ k_1, \, k_2 $.</p>

On the Cauchy problem for semilinear σ‐evolution equations with time‐dependent damping

In this paper, we would like to consider the Cauchy problem for semilinear ‐evolution equations with time‐dependent damping for any . Motivated strongly by the classification of damping terms in some previous papers, the first main goal of the present work is to make some generalizations from to and simultaneously to investigate decay estimates for solutions to the corresponding linear equations in the so‐called effective damping cases. For the next main goals, we are going not only to prove the global well‐posedness property of small data solutions but also to indicate blow‐up results for solutions to the semilinear problem. In this concern, the novelty which should be recognized is that the application of a modified test function combined with a judicious choice of test functions gives blow‐up phenomena and upper bound estimates for lifespan in both the subcritical case and the critical case, where is assumed to be any fractional number. Finally, lower bound estimates for lifespan in some spatial dimensions are also established to find out their sharp results.

Actuarial aging rates in human cohorts

Aging rate is an important characteristic of human aging. Attempts to measure aging rates through the Gompertz slope parameter lead to a conclusion that actuarial aging rates were stable during the most of the 20th century, but recently demonstrate an increase over time in the majority of studied populations. These findings were made using cross-sectional mortality data rather than by the analysis of mortality of real birth cohorts. In this study we analyzed historical changes of actuarial aging rates in human cohorts. The Gompertz parameters were estimated in the age interval 50-80 years using data on one-year cohort age-specific death rates from the Human Mortality Database (HMD). Totally, data for 2,294 cohorts of men and women from 76 populations were analyzed. Changes of the Gompertz slope parameter in the studied cohorts revealed two distinct patterns for actuarial aging rate. In higher mortality Eastern European countries actuarial aging rates showed continuous decline from the 1910 to 1940 birth cohort. In lower mortality Western European countries, Australia, Canada, Japan, New Zealand, and USA actuarial aging rates declined from the 1910th to approximately 1930th cohort and then increased. Overall, in 50 out of 76 populations (68%) actuarial aging rate demonstrated decreasing pattern of change over time. Compensation effect of mortality (CEM) was tested for the first time in human cohorts and the cohort species-specific lifespan was estimated. CEM was confirmed using cohort data and human cohort species-specific lifespan estimates were similar to the estimates obtained for the cross-sectional data published earlier.

Analysis of the Slanted-Edge Measurement Method for the Modulation Transfer Function of Remote Sensing Cameras

The modulation transfer function (MTF) serves as a crucial technical index for assessing the imaging quality of remote sensing cameras, which is integral throughout their entire operational cycle. Currently, the MTF evaluation of remote sensing cameras primarily relies on the slanted-edge method. The factors influencing the slanted-edge method’s effectiveness are broadly classified into two categories: algorithmic factors and image factors. This paper innovatively comprehensively analyzes the influencing factors of the slanted-edge method and proposes an improved slanted-edge method to calculate the MTF testing method of remote sensing cameras, which is applied to the MTF testing of remote sensing cameras. Since the traditional algorithm can only be applied in the small angle situation, this paper proposes a new method of slanted-edge method test calculation based on the optimal oversampling rate (OSR) adaptive model of the slanted edge and uses simulation experiments to verify the reliability of the algorithm model through the deviation of the slanted-edge angle calculation and MTF measurement, and the results show that the algorithm improves the accuracy of the MTF measurement compared with the ISO-cos and OMINI-sine methods. Then, the effects of the slanted-edge angle, image region of interest (ROI), as well as image contrast and signal-to-noise ratio (SNR) on the accuracy of the MTF calculation by the slanted-edge method were quantitatively analyzed as the constraints of the slanted-edge method test. Based on the laboratory target experiment, the algorithm flow and various influencing factors obtained in the simulation stage are verified, and the experimental results are more consistent with the various test results obtained in the simulation stage. Consequently, the slanted-edge method introduced in this paper is applicable for future remote sensing camera MTF testing. This approach offers a valuable reference for on-orbit focusing, satellite operational condition monitoring, lifespan estimation, and image restoration.

Lifespan estimates and asymptotic stability for a class of fourth-order damped p-Laplacian wave equations with logarithmic nonlinearity

Lifespan estimates and asymptotic stability for a class of fourth-order damped p-Laplacian wave equations with logarithmic nonlinearity

Actuarial Aging Rates in Human Cohorts.

Aging rate is an important characteristic of human aging. Attempts to measure aging rates through the Gompertz slope parameter lead to a conclusion that actuarial aging rates were stable during the most of the 20th century, but recently demonstrate an increase over time in the majority of studied populations. These findings were made using cross-sectional mortality data rather than by the analysis of mortality of real birth cohorts. In this study we analyzed historical changes of actuarial aging rates in human cohorts. The Gompertz parameters were estimated in the age interval 50-80 years using data on one-year cohort age-specific death rates from the Human Mortality Database (HMD). Totally, data for 2,294 cohorts of men and women from 76 populations were analyzed. Changes of the Gompertz slope parameter in the studied cohorts revealed two distinct patterns for actuarial aging rate. In higher mortality Eastern European countries actuarial aging rates showed continuous decline from the 1910 to 1940 birth cohort. In lower mortality Western European countries, Australia, Canada, Japan, New Zealand, and USA actuarial aging rates declined from the 1910th to approximately 1930th cohort and then increased. Overall, in 50 out of 76 populations (68%) actuarial aging rate demonstrated decreasing pattern of change over time. Compensation effect of mortality (CEM) was tested for the first time in human cohorts and the cohort species-specific lifespan was estimated. CEM was confirmed using cohort data and human cohort species-specific lifespan estimates were similar to the estimates obtained for the cross-sectional data published earlier.

Wave breaking in the unidirectional non-local wave model

In this paper we study wave breaking in the unidirectional non-local wave model describing the motion of a collision-free plasma in a magnetic field. By analyzing the monotonicity and continuity properties of a system of the Riccati-type differential inequalities involving the extremal slopes of flows, we show a new sufficient condition on the initial data to exhibit wave breaking. Moreover, the estimates of life span and wave breaking rate are derived.

Blow-up of solutions to a scalar conservation law with nonlocal source arising in radiative gas

In this paper we consider a scalar conservation law with nonlocal source arising in radiative gas. We give a sufficient condition to assure that the solution blows up in a finite time. Moreover, the estimates of life span and blow-up rate are derived.

Lifespan Estimation of Galvanized Steel and Stainless Steel Pipe

Lifespan Estimation of Galvanized Steel and Stainless Steel Pipe

Unraveling capacity fading in lithium-ion batteries using advanced cyclic tests: A real-world approach

Battery lifespan estimation is essential for effective battery management systems, aiding users and manufacturers in strategic planning. However, accurately estimating battery capacity is complex, owing to diverse capacity fading phenomena tied to factors such as temperature, charge-discharge rate, and rest period duration. In this work, we present an innovative approach that integrates real-world driving behaviors into cyclic testing. Unlike conventional methods that lack rest periods and involve fixed charge-discharge rates, our approach involves 1000 unique test cycles tailored to specific objectives and applications, capturing the nuanced effects of temperature, charge-discharge rate, and rest duration on capacity fading. This yields comprehensive insights into cell-level battery degradation, unveiling growth patterns of the solid electrolyte interface (SEI) layer and lithium plating, influenced by cyclic test parameters. The results yield critical empirical relations for evaluating capacity fading under specific testing conditions.

New life-span results for the nonlinear heat equation

We obtain new estimates for the existence time of the maximal solutions to the nonlinear heat equation ∂tu−Δu=|u|αu,α>0 with initial values in Lebesgue, weighted Lebesgue spaces or measures. Non-regular, sign-changing, as well as non polynomial decaying initial data are considered. The proofs of the lower-bound estimates of life-span are based on the local construction of solutions. The proofs of the upper-bounds exploit a well-known necessary condition for the existence of nonnegative solutions. In addition, we establish new results for life-span using dilation methods and we give new life-span estimates for Hardy-Hénon parabolic equations.

The lifespan estimates of classical solutions of one dimensional semilinear wave equations with characteristic weights

In this paper, we study the lifespan estimates of classical solutions for semilinear wave equations with characteristic weights and compactly supported data in one space dimension. The results include those for weights by time-variable, but exclude those for weights by space-variable in some cases. We have interactions of two characteristic directions.

Molecular degradation mechanism of segmented polyurethane and life prediction through accelerated aging test

Polyurethane (PU) has numerous applications in daily life, such as coating, cushions, and insulation materials. It is also used as an encapsulation material for sensors. In the case of PU used as an encapsulant, PU elastomer containing an ether-based polyol is generally used and has a long lifespan in a general environment. However, it is challenging to predict its lifespan when used as an encapsulation material for sonar sensors because PU is exposed to the filling liquid. It is required to accurately predict the encapsulation material's lifespan to ensure the sensor's safety. For the exact estimation of PU lifespan, an accelerated aging experiment was conducted on PU elastomer in a filling solution at various temperatures. Fourier transform infrared spectroscopy was used to track the chemical changes in the PU elastomer, and it was observed that both urethane and urea bonds were degraded. Modulated differential scanning calorimetry and thermogravimetric analysis were also used to study changes in the structure of PU elastomer by heat aging. The tensile strength, elongation, and hardness of the heat-aged elastomer at various temperatures were obtained, and the Arrhenius plots were constructed. Finally, the lifespan was considered when the tensile strength was 70% of the initial state by using the ASTM D2000 standard. Thus, the lifespan of PU at 25 °C was calculated to be 12.2 years.

Blow-up of solutions for the Moore-Gibson-Thompson equations on exterior domain in two dimensions

This paper is devoted to investigating blow-up of solutions to initial boundary value problem of the Moore-Gibson-Thompson (MGT) equations on exterior domain in two dimensions. More precisely, upper bound lifespan estimates of solutions to the problem with power nonlinearity $|u|^{p}$, derivative nonlinearity $|u_{t}|^{p}$ and combined nonlinearities $|u_{t}|^{p} + |u|^{q}$ in the sub-critical and critical cases are established, respectively. The proofs are based on the new test function technique. Our main new contribution is that we improve the results in [36] in two dimensions. It is worth to mention that lifespan estimates of solutions are associated with the well-known Strauss and Glassey conjecture. Moreover, the variation trend of wave for the Cauchy problem of linear MGT equation with different initial values in two dimensions is showed by numerical simulation.

Blow-up of solutions to the semilinear wave equation with scale invariant damping on exterior domain

This paper is concerned with the blow-up of solutions to the initial boundary value problem for the wave equation with scale invariant damping term on the exterior domain, where the nonlinear terms are power nonlinearity |u|^{p} , derivative nonlinearity |u_{t}|^{p} and combined nonlinearities |u_{t}|^{p}+ |u|^{q} , respectively. Upper bound lifespan estimates of solutions to the problem are obtained by constructing suitable test functions and utilizing the test function technique. The main novelty is that lifespan estimates of solutions are associated with the well-known Strauss exponent and Glassey exponent. To the best of our knowledge, the results in Theorems 1.1–1.3 are new.

Fish species lifespan prediction from promoter cytosine-phosphate-guanine density.

Lifespan is a key attribute of a species' life cycle and varies extensively among major lineages of animals. In fish, lifespan varies by several orders of magnitude, with reported values ranging from less than 1 year to approximately 400 years. Lifespan information is particularly useful for species management, as it can be used to estimate invasion potential, extinction risk and sustainable harvest rates. Despite its utility, lifespan is unknown for most fish species. This is due to the difficulties associated with accurately identifying the oldest individual(s) of a given species, and/or deriving lifespan estimates that are representative for an entire species. Recently it has been shown that CpG density in gene promoter regions can be used to predict lifespan in mammals and other vertebrates, with variable accuracy across taxa. To improve accuracy of lifespan prediction in a non-mammalian vertebrate group, here we develop a fish-specific genomic lifespan predictor. Our new model includes more than eight times the number of fish species included in the previous vertebrate model (n=442) and uses fish-specific gene promoters as reference sequences. The model predicts fish lifespan from genomic CpG density alone (measured as CpG observed/expected ratio), explaining 64% of the variance between known and predicted lifespans. The predictions are highly robust to variation in genome quality and are applicable to all classes of fish; a taxonomically diverse and speciose group. The results demonstrate the value of promoter CpG density as a universal predictor of fish lifespan that can applied where empirical data are unavailable, or impracticable to obtain.

Blow-up and lifespan estimates for solutions to the weakly coupled system of nonlinear damped wave equations outside a ball

In this paper, we consider the initial-boundary value problems with several fundamental boundary conditions (the Dirichlet/Neumann/Robin boundary condition) for the multi-component system of semi-linear classical damped wave equations outside a ball. By applying a test function approach with a judicious choice of test functions, which approximates the harmonic functions being subject to these boundary conditions on $$\partial \varOmega $$ , simultaneously we have succeeded in proving the blow-up result in a finite time as well as in catching the upper bound of lifespan estimates for small solutions in all spatial dimensions. Moreover, such kind of these results, which become sharp in the subcritical cases for one-dimensional case, will be discussed at the end of this paper.

Blow-up and lifespan estimate to a nonlinear wave equation in Schwarzschild spacetime

We study the semilinear wave equation with power type nonlinearity and small initial data in Schwarzschild spacetime. If the nonlinear exponent p satisfies 2≤p<1+2, we establish the sharp upper bound of lifespan estimate, while for the most delicate critical power p=1+2, we show that the lifespan satisfiesT(ε)≤exp⁡(Cε−(2+2)), the optimality of which remains to be proved. The key novelty is that the compact support of the initial data can be close to the event horizon. By combining the global existence result for p>1+2 obtained by Lindblad et al. (2014) [25], we then give a positive answer to the interesting question posed by Dafermos and Rodnianski (2005) [22, the end of the first paragraph in page 1151]: p=1+2 is exactly the critical power of p separating stability and blow-up.

Blow-up for the coupled system of wave equations with memory terms in Schwarzschild spacetime

This paper is concerned with blow-up results of solutions to the Cauchy problem for a coupled system of wave equations in Schwarzschild spacetime, where the nonlinear terms contain power-type memory terms, derivative-type memory terms, and combined-type memory terms, respectively. Upper-bound lifespan estimates of solutions to the Cauchy problem with small initial values and certain assumptions on the exponents in the memory terms are established by taking advantage of the Regge–Wheeler coordinate and iteration approach. Our main new contribution is that lifespan estimates of solutions to the problem are associated with the well-known Strauss conjecture and Glassey conjecture in Schwarzschild spacetime. To the best of the authors’ knowledge, the results in Theorems 1.1–1.3 are new.