Time-dependent Coefficients Research Articles

Stability and bifurcation analysis of simply supported rectangular nanoplate embedded on visco-Pasternak foundation based on first-order shear deformation theory

Vibrations of simply supported nanoplates embedded on visco-Pasternak foundation and stressed by in-plane periodic forces are investigated. The governing size-dependent equations employ the first-order shear deformation theory, nonlinear von Kármán strains, and the nonlocal elasticity theory. Reducing the governing system is carried out by the Bubnov-Galerkin method, which is based on two-mode model, thus the resulting system contains two ordinary differential equations with size- and time-dependent coefficients. Analysing the linearized system, the stability of the nanoplate structure is studied depending on the foundation parameters, force parameters and small-scale parameter. Nonlinear dynamics approaches are employed to determine the nature of vibration after the loss of stability. Time history, Poincare section, Lyapunov exponent are analysed for chosen values of excitation parameters, visco-Pasternak foundation parameters to indicate small-scale effects and nonlinear effects. The novelty of the work consists of the combined application of the nonlocal theory, first-order shear deformation theory, Floquet theory, methods of nonlinear dynamics and obtaining new results by a numerical experiment.

Determination of a time dependent source in semilinear pseudoparabolic equations with Caputo fractional derivative

This paper devoted to study unique solvability of inverse source problem for a semilinear time fractional pseudoparabolic equation perturbed by a damping term. Inverse problem consists of recovering a solely time dependent coefficient of right-hand side under a measurement in an integral form. The damped term acts in the equation as a nonlinear source or as an absorption, depending on its sign of coefficient, where it is positive or negative, respectively. In these both cases, we have established sufficient conditions on data, where the inverse problem has a global or local in time unique weak and strong solution.

Anticorrelation of net uptake of atmospheric CO2 by the world ocean and terrestrial biosphere in current carbon cycle models

Abstract. The rate at which atmospheric carbon dioxide (CO2) would decrease in response to a decrease in anthropogenic emissions or cessation (net zero emissions) is of great scientific and societal interest. Such a decrease in atmospheric CO2 on the centennial scale would be due essentially entirely to transfer of carbon into the world ocean (WO) and the terrestrial biosphere (TB), which are sink compartments on this timescale. The rate of decrease in excess atmospheric CO2 and the apportionment of this decrease into the two sink compartments have been examined in two prior model intercomparison studies, subsequent either to a pulse emission of CO2 or to abrupt cessation of anthropogenic CO2 emissions. The present study examines and quantifies inter-model anticorrelation in those studies in the net rate and extent of uptake of CO2 into the two sink compartments. Specifically, in each study the time-dependent coefficients characterizing the net transfer rate into the two sink compartments (evaluated as the net transfer rate normalized to excess atmospheric CO2 above the pre-pulse amount for the pulse experiment or as the net transfer rate divided by excess atmospheric CO2 above the preindustrial amount for the abrupt cessation experiment) were found to exhibit strong anticorrelation across the participating models. That is, models for which the normalized rate of uptake into the WO was high exhibited low uptake rate into the TB and vice versa. This anticorrelation in net transfer rate results in anticorrelation in net uptake extent into the two compartments that is substantially greater than would be expected simply from competition for excess CO2 between the two sink compartments. This anticorrelation, which is manifested in diminished inter-model diversity, can lead to artificially enhanced confidence in current understanding of the consequences of potential future reductions of CO2 emissions and in the global warming potentials of non-CO2 greenhouse gases relative to that of CO2.

Abstract 4144554: Revascularization of Patients with Low-Density Non-Calcified Plaque was Associated with Lower Occurrence of Acute Coronary Syndrome

INTRODUCTION: Coronary CT angiography (CCTA) is a powerful noninvasive tool for identifying high-risk plaque, such as low-density non-calcified plaque (LD-NCP). Though, the optimal treatment of patients with LD-NCP remains unclear. This study explored the association of revascularization in the setting of LD-NCP with the occurrence of acute coronary syndrome (ACS). Methods: This was a post-hoc analysis of the ICONIC study. A subset of 234 patients that underwent CCTA with subsequent ACS were matched to 234 control patients who also underwent CCTA but did not have ACS during follow-up. Patients were also followed for occurrence of revascularization, either coronary artery bypass graft or percutaneous coronary intervention. Atherosclerosis imaging-enabled quantitative CT (AI-QCT) was used to measure diameter stenosis, and LD-NCP, non-calcified plaque, and calcified plaque volumes from each CCTA. LD-NCP was defined as plaque with -190 to 30 Hounsfield Units. Patients were stratified based on the presence of LD-NCP. Subgroup analysis was conducted to compare the occurrence of ACS with the rate of revascularization. Kaplan-Meier survival curves and extended Cox regression analysis were used to evaluate the effect size of revascularization and LD-NCP on occurrence of ACS. Results: AI-QCT was completed in 448/468 subjects (follow-up time [MEAN±SD] 2.44±2.48 years). The median of LD-NCP was 1.2 mm 3 for patients with >0 mm 3 LD-NCP. There were 85 patients with LD-NCP >1.2 mm 3 and 363 patients with LD-NCP ≤1.2 mm 3 . In patients with LD-NCP >1.2 mm 3 , the rate of revascularization in patients with and without ACS was 3/52 (5.8%) versus 14/33 (42.4%) (p<0.001). In patients with LD-NCP ≤1.2 mm 3 , the rate of revascularization in patients with and without ACS was 36/170 (21.2%) versus 39/193 (20.2%) (p=0.897). In comparison to patients without revascularization and LD-NCP ≤1.2 mm 3 , patients with LD-NCP >1.2 mm 3 and revascularization were less likely to have ACS during follow-up (adjusted HR: 0.20 [0.07, 0.61]; p=0.005). Additionally, patients with LD-NCP >1.2 mm 3 who did not undergo revascularization were more likely to have ACS (adjusted HR: 1.47 [1.03, 2.12]; p=0.036). Hazard ratios were adjusted for diameter stenosis, and non-calcified and calcified plaque volume. Time-dependent coefficients were included for diameter stenosis. Conclusion: Revascularization of patients with LD-NCP >1.2 mm 3 identified on CCTA with AI-QCT was associated with less risk for ACS.

Treatment and survival differences between patients with invasive lobular carcinoma versus invasive ductal carcinoma of the breast.

Invasive lobular carcinoma (ILC) exhibits differences in molecular and biological characteristics compared to invasive ductal carcinoma (IDC). We aim to compare breast cancer-specific survival (BCSS) between patients with ILC and IDC. We used data from the Surveillance, Epidemiology, and End Results database (1992-2020). Logistic regression analyses were conducted to identify factors associated with treatment modalities. We examined BCSS at different time points using a cox regression model with time-dependent coefficient. 343,397 patients with IDC and 39,859 patients with ILC were included. Patients with ILC had more advanced stage disease (stage II, 35% vs. 34%; stage III, 16% vs.11%), and higher rate of hormone receptor-positive disease (97% vs. 81%). Compared to patients with IDC, patients with ILC had better BCSS in the first five years (Hazard ratio [HR]=0.71, p <0.001), but worse BCSS in later years (HR=1.30, p<0.001 in year 6-10; HR=1.75, p<0.001 in year 11-15; HR=2.17, p<0.001 in year 16-20). Patients with ILC survive better in early years but worse in later years compared to patients with IDC. Future studies are required to identify patients with ILC who are at risk of late recurrence or mortality. The results of this study add to the currently conflicting literature of survival of ILC and demonstrate the importance of evaluating novel therapeutic approaches and extended therapy for patients with ILC.

Stability estimate for a time-dependent coefficient identification problem in parabolic equations

Stability estimate for a time-dependent coefficient identification problem in parabolic equations

New Solutions to the Fractional Perturbed Chen Lee Liu Model with Time-Dependent Coefficients: Applications to Complex Phenomena in Optical Fibersns

In this paper, we consider the fractional perturbed Chen Lee Liu model with time-dependent coefficients (FPCLLM-TDCs). We apply the mapping method in order to get hyperbolic, elliptic, trigonometric and rational fractional solutions. These solutions are vital for understanding some fundamentally complicated phenomena. The obtained solutions will be very helpful for applications such as fiber optics and plasma physics. Finally, we show how the conformable fractional derivative order affect the exact solutions of the FPCLLM-TDCs. Furthermore, we examine the effects of time-dependent coefficients when these coefficients take on special cases such as random variables, polynomials, and hyperbolic functions.

Quantile and expectile copula-based hidden Markov regression models for the analysis of the cryptocurrency market

The role of cryptocurrencies within the financial systems has been expanding rapidly in recent years among investors and institutions. It is therefore crucial to investigate this phenomenon and develop statistical methods able to capture their interrelationships, the links with other global systems and, at the same time, the serial heterogeneity. Here we introduce hidden Markov regression models for jointly estimating quantiles and expectiles of cryptocurrency returns using regime-switching copulas. The proposed approach allows us to focus on extreme returns and describe their temporal evolution by introducing time-dependent coefficients, evolving according to a latent Markov chain. Moreover to model their time-varying dependence structure, we consider elliptical copula functions defined by state-specific parameters. Maximum likelihood estimates are obtained via an expectation-maximization algorithm. The empirical analysis investigates the relationship between daily returns of five cryptocurrencies and major world market indices.

Fast and Accurate Numerical Integration of the Langevin Equation with Multiplicative Gaussian White Noise.

A univariate stochastic system driven by multiplicative Gaussian white noise is considered. The standard method for simulating its Langevin equation of motion involves incrementing the system's state variable by a biased Gaussian random number at each time step. It is shown that the efficiency of such simulations can be significantly enhanced by incorporating the skewness of the distribution of the updated state variable. A new algorithm based on this principle is introduced, and its superior performance is demonstrated using a model of free diffusion of a Brownian particle with a friction coefficient that decreases exponentially with the kinetic energy. The proposed simulation technique proves to be accurate over time steps that are an order of magnitude longer than those required by standard algorithms. The model used to test the new numerical technique is known to exhibit a transition from normal diffusion to superdiffusion as the environmental temperature rises above a certain critical value. A simple empirical formula for the time-dependent diffusion coefficient, which covers both diffusion regimes, is introduced, and its accuracy is confirmed through comparison with the simulation results.

Tribological behaviors of Zr-based bulk metallic glass against Si3N4 ceramic under linear reciprocating sliding

Tribological properties of bulk metallic glasses (BMGs) deeply affect their performances in potential applications, however, the main wear mechanisms remain partially understood, for the vastly varying contact conditions in friction. This work systematically reports tribological behaviors of Zr60.14Cu22.31Al9.7Fe4.85Ag3 BMG against Si3N4 ceramic during linear reciprocating sliding at different normal load (1–12 N) and reciprocating frequency (1–12 Hz). The time-dependent coefficient of friction (COF) indicates a prominent “running-in” stage during wear tests, which lengthens upon increased normal load while reduces at increased reciprocating frequency. Observation on worn surfaces indicates that the wear mechanism during “running-in” is mainly adhesive wear while in the stable stage is oxidative wear and adhesive wear. Intriguingly, high wear rate generally relates to adhesive wear and low wear rate relates to oxidative wear, while high COF relates to oxidative wear and low COF relates to adhesive wear. These results would help to understand the friction and wear of BMGs.

Fokker–Planck equation and Feynman–Kac formula for multidimensional stochastic dynamical systems with Lévy noises and time-dependent coefficients

The aim of this paper is to establish a version of the Feynman–Kac formula for the time-dependent multidimensional nonlocal Fokker–Planck equation corresponding to a class of time-dependent stochastic differential equations driven by multiplicative symmetric (or asymmetric) α-stable Lévy noise. First the forward nonlocal Fokker–Planck equation is derived by the adjoint operator method, overcoming the challenges posed by time-dependent multidimensional nonlinear symmetric α-stable Lévy noise. Subsequently, the Feynman–Kac formula for the forward multidimensional time-dependent nonlocal Fokker–Planck equation is established by applying techniques for the backward nonlocal Fokker–Planck equations, which is associated with the backward stochastic differential equation driven by the multiplicative symmetric α-stable Lévy noise. Notably, in the case of asymmetric α-stable Lévy noise case, the presence of the characteristic function in the nonlocal operator adds complexity to the analysis. Using the Feynman–Kac formula, it is demonstrated that the solution of the forward nonlocal Fokker–Planck equation can be readily simulated through Monte Carlo approximation, especially in scenarios involving long-time simulation settings with large steps. These concepts are illustrated with intriguing examples, and the dynamic evolution of the probability density function corresponding to the stochastic SIS model and the stochastic model for the MeKS network (reflecting the interactions among the MecA complex, ComK and ComS) are investigated over an extended period.

A Semi-Analytical numerical non-stationary creep analysis of a rotating disk made of Polyamid66 under mechanical and thermal loads

A semi-analytical numerical non-stationary creep analysis of constant and variable thickness rotating disks made of polyamide 66 under mechanical and thermal loads is presented using Mendelson’s method of successive approximation. The material properties are time, temperature, and stress-dependent, which vary along the disk’s radius due to effective stress variation and temperature distribution and are represented by Burger’s model. A non-homogeneous differential equation in terms of radial displacement with variable and time-dependent coefficients was established using equilibrium, strain-displacement, and stress-strain relations. First, the initial thermo-elastic stresses at zero time were calculated using the Galerkin method and Hermitian elements. The history of stresses and strains was then calculated using Burger’s viscoelastic model and Prandtl-Reuss relations. To validate the results, an analysis of a disk with constant thickness made of PVDF material was also carried out using the same method employed in this study. Very good agreement of the results was observed in both elastic and creep conditions. Creep analysis was performed for PA66 disks of constant and variable thickness conditions, and the results were compared together. It has been found that the radial displacements and effective stresses are increasing with time for both disks. However, effective stresses and radial displacements of variable-thickness disks are much lower than constant-thickness disks.

Charge transport in organic semiconductors from the mapping approach to surface hopping.

We describe how to simulate charge diffusion in organic semiconductors using a recently introduced mixed quantum-classical method, the mapping approach to surface hopping. In contrast to standard fewest-switches surface hopping, this method propagates the classical degrees of freedom deterministically on the most populated adiabatic electronic state. This correctly preserves the equilibrium distribution of a quantum charge coupled to classical phonons, allowing one to time-average along trajectories to improve the statistical convergence of the calculation. We illustrate the method with an application to a standard model for the charge transport in the direction of maximum mobility in crystalline rubrene. Because of its consistency with the equilibrium distribution, the present method gives a time-dependent diffusion coefficient that plateaus correctly to a long-time limiting value. The resulting mobility is somewhat higher than that of the relaxation time approximation, which uses a phenomenological relaxation parameter to obtain a non-zero diffusion coefficient from a calculation with static phonon disorder. However, it is very similar to the mobility obtained from Ehrenfest dynamics, at least in the parameter regimes we have investigated here. This is somewhat surprising because Ehrenfest dynamics overheats the electronic subsystem and is, therefore, inconsistent with the equilibrium distribution.

A (2+1) modified KdV equation with time-dependent coefficients: exploring soliton solution via Darboux transformation and artificial neural network approach

A (2+1) modified KdV equation with time-dependent coefficients: exploring soliton solution via Darboux transformation and artificial neural network approach

Heat equation for Sturm–Liouville operator with singular propagation and potential

Abstract This article considers the initial boundary value problem for the heat equation with the time-dependent Sturm–Liouville operator with singular potentials. To obtain a solution by the method of separation of variables, the problem is reduced to the problem of eigenvalues of the Sturm–Liouville operator. Further on, the solution to the initial boundary value problem is constructed in the form of a Fourier series expansion. A heterogeneous case is also considered. Finally, we establish the well-posedness of the equation in the case when the potential and initial data are distributions, also for singular time-dependent coefficients.

Investigation of exact solutions to the (2+1)-dimensional Sakovich equation with time dependent coefficients using analytical methods

In this paper, the exact solutions of the (2 + 1)-dimensional variable coefficient Sakovich equation are investigated. Four distinct analytical methods, containing the unified method, the modified Kudryashov method, the modified G′G2 -expansion method and the improved Riccati sub-equation method, are implemented to find new exact solutions of this equation. Soliton and periodic soliton solutions, elliptic solutions, kink solutions and traveling wave solutions, which are expressed in polynomial, rational, trigonometric and hyperbolic forms, have been obtained and are graphically represented with the aim of exhibiting the structures and dynamic behaviors of the equation. Furthermore, we have discussed the influence of variable coefficients on soliton behaviors in detail.

Bootstrapping Lagrangian perturbation theory for the large scale structure

We develop a model-independent approach to Lagrangian perturbation theory for the large scale structure of the universe. We focus on the displacement field for dark matter particles, and derive its most general structure without assuming a specific form for the equations of motion, but implementing a set of general requirements based on symmetry principles and consistency with the perturbative approach. We present explicit results up to sixth order, and provide an algorithmic procedure for arbitrarily higher orders. The resulting displacement field is expressed as an expansion in operators built up from the linear density field, with time-dependent coefficients that can be obtained, in a specific model, by solving ordinary differential equations. The derived structure is general enough to cover a wide spectrum of models beyond ΛCDM, including modified gravity scenarios of the Horndeski type and models with multiple dark matter species. This work is a first step towards a complete model-independent Lagrangian forward model, to be employed in cosmological analyses with power spectrum and bispectrum, other summary statistics, and field-level inference.

Adjoint-based inversion for stress and frictional parameters in earthquake modeling

We present an adjoint-based optimization method to invert for stress and frictional parameters used in earthquake modeling. The forward problem is linear elastodynamics with nonlinear rate-and-state frictional faults. The misfit functional quantifies the difference between simulated and measured particle displacements or velocities at receiver locations. The misfit may include windowing or filtering operators. We derive the corresponding adjoint problem, which is linear elasticity with linearized rate-and-state friction and, for forward problems involving fault normal stress changes, nonzero fault opening, with time-dependent coefficients derived from the forward solution. The gradient of the misfit is efficiently computed by convolving forward and adjoint variables on the fault. The method thus extends the framework of full-waveform inversion to include frictional faults with rate-and-state friction. In addition, we present a space-time dual-consistent discretization of a dynamic rupture problem with a rough fault in antiplane shear, using high-order accurate summation-by-parts finite differences in combination with explicit Runge–Kutta time integration. The dual consistency of the discretization ensures that the discrete adjoint-based gradient is the exact gradient of the discrete misfit functional as well as a consistent approximation of the continuous gradient. Our theoretical results are corroborated by inversions with synthetic data. We anticipate that adjoint-based inversion of seismic and/or geodetic data will be a powerful tool for studying earthquake source processes; it can also be used to interpret laboratory friction experiments.

The Time-Dependent Effect of Assistance on Peritoneal Dialysis Duration: An Analysis of Data from the French Language Peritoneal Dialysis Registry.

Key Points It is unknown whether the benefit of assisted peritoneal dialysis (PD) programs appears immediately after PD initiation or rather after some time spent on PD.The protective effect of assisted PD on the risk of transfer to hemodialysis was not constant over time; it started after the first 6 months on PD.Assisted PD programs should be sustainable for at least 6 months to observe their benefits. Background Peritoneal dialysis (PD) patient compliance is crucial for the prevention of complications. Assistance is associated with a lower risk of transfer to hemodialysis. As the risk of noncompliance increases over time, the protective effect of assistance on the risk of transfer to hemodialysis may not be immediate after PD initiation, but rather may appear after some time on PD. We aimed to analyze the time-varying effect of assistance on the risk of PD cessation. Methods This retrospective study was conducted using data from the French Language PD Registry of incident PD patients between 2002 and 2018. Because of nonproportional hazards, with a change in the effect of the assistance modality on the different outcomes appearing at 6 months after PD initiation, the associations between the assistance modality and the different outcomes were explored using time-dependent coefficient Cox regression. Results The study included 15,675 patients; 6717 deaths, 4973 transfers to hemodialysis, and 3065 kidney transplantations occurred. Both patients receiving nurse- and family-assisted PD had a lower risk of transfer to hemodialysis (mean cause-specific hazard ratio [cs-HR], 0.67; 95% confidence interval [CI], 0.62 to 0.72; and mean cs-HR, 0.75; 95% CI, 0.67 to 0.84). In the first 6 months after PD initiation, nurse-assisted PD patients had a greater risk of transfer to hemodialysis (&lt;6 months cs-HR, 1.18; 95% CI, 1.03 to 1.36) but had a lower likelihood afterward (≥6 months cs-HR, 0.57; 95% CI, 0.53 to 0.62). Family-assisted PD was not associated with the risk of transfer to hemodialysis in the first 6 months after PD initiation, and those patients had a lower risk of transfer to hemodialysis afterward (≥6 months cs-HR, 0.72; 95% CI, 0.63 to 0.82). Conclusions When implementing a national nurse-assisted PD program, its positive impact on PD duration should not be expected immediately after PD initiation. Assisted PD programs should be sustainable for at least 6 months to observe their benefits. Podcast This article contains a podcast at https://www.asn-online.org/media/podcast/K360/2024_10_31_KID0000000577.mp3

Development and Analysis of novel Integrable Nonlinear Dynamical Systems on Quasi-One-Dimensional Lattices. Parametrically Driven Nonlinear System of Pseudo-Excitations on a Two-Leg Ladder Lattice

Following the main principles of developing the evolutionary nonlinear integrable systems on quasi-one-dimensional lattices, we suggest a novel nonlinear integrable system of parametrically driven pseudo-excitations on a regular two-leg ladder lattice. The initial (prototype) form of the system is derivable in the framework of semi-discrete zero-curvature equation with the spectral and evolution operators specified by the properly organized 3 × 3 square matrices. Although the lowest conserved local densities found via the direct recursive method do not prompt us the algebraic structure of system’s Hamiltonian function, but the heuristically substantiated search for the suitable two-stage transformation of prototype field functions to the physically motivated ones has allowed to disclose the physically meaningful nonlinear integrable system with time-dependent longitudinal and transverse inter-site coupling parameters. The time dependencies of inter-site coupling parameters in the transformed system are consistently defined in terms of the accompanying parametric driver formalized by the set of four homogeneous ordinary linear differential equations with the time-dependent coefficients. The physically meaningful parametrically driven nonlinear system permits its concise Hamiltonian formulation with the two pairs of field functions serving as the two pairs of canonically conjugated field amplitudes. The explicit example of oscillatory parametric drive is described in full mathematical details.