Presence Of Memory Effects Research Articles

Hydrate Formation with the Memory Effect Using Classical Nucleation Theory

Methane hydrate formation is analytically studied in the presence of the water memory effect using the classical nucleation theory. The memory effect is introduced as a change in nucleation site from a three-dimensional heterogenous nucleation on a solid surface with cap-shaped hydrate clusters (3D-HEN) to a two-dimensional nucleation on the solid hydrate residue surface with monolayer disk-shaped hydrate clusters (2D-NOH). The analysis on the stationary nucleation of methane hydrate under isobaric conditions shows that the memory effect caused an average decrease of 4.4 K in metastable zone width, or subcooling. This decrease can be erased at higher dissociation temperatures (ΔT > 17.2 K) due to a decrease in the concentration of 2D-NOH nucleation sites. Moreover, the probability of hydrate formation is estimated for the purpose of quantifying risk associated with methane hydrate formation in the presence of the memory effect.

Mathematical modeling and analysis of monkeypox 2022 outbreak with the environment effects using a Cpauto fractional derivative

Monkeypox is a serious global challenge to human health after the COVID-19 pandemic. Although this infection is not new, still many variations have been noticed in its epidemiology. Numerous approaches have been applied to analyze the dynamics of this infection. In this study, we present a mathematical model to study various epidemiological aspects of monkeypox. Transmission from human to animal, human to human, and through the environment (surface) are considered while formulating the proposed model. The model is constructed based on a classical system of seven nonlinear differential equations. Further, the classical epidemic model is reconstructed using the standard Caputo derivative to examine the dynamical aspects of monkeypox disease in the presence of memory effects. Initially, the necessary mathematical properties of the fractional model are carried out. The model exhibits three equilibrium points: monkeypox-free equilibrium, infected animal-free endemic equilibrium, and coexistence equilibrium. Additionally, we give a thorough theoretical analysis that considers solution positivity and stability results of equilibriums of the Caputo monkeypox model. Furthermore, the parameters of the proposed model are estimated using the nonlinear least square method from the reported cases of monkeypox in the United States in a recent outbreak in 2022. Finally, the numerical solution of the model is carried out using the well-known Adams-Bashforth-Moulton scheme and simulation is performed to explore the role of memory index and various preventing measures on the disease incidence.

Machine-learning Kohn–Sham potential from dynamics in time-dependent Kohn–Sham systems

The construction of a better exchange-correlation potential in time-dependent density functional theory (TDDFT) can improve the accuracy of TDDFT calculations and provide more accurate predictions of the properties of many-electron systems. Here, we propose a machine learning method to develop the energy functional and the Kohn–Sham potential of a time-dependent Kohn–Sham (TDKS) system is proposed. The method is based on the dynamics of the Kohn–Sham system and does not require any data on the exact Kohn–Sham potential for training the model. We demonstrate the results of our method with a 1D harmonic oscillator example and a 1D two-electron example. We show that the machine-learned Kohn–Sham potential matches the exact Kohn–Sham potential in the absence of memory effect. Our method can still capture the dynamics of the Kohn–Sham system in the presence of memory effects. The machine learning method developed in this article provides insight into making better approximations of the energy functional and the Kohn–Sham potential in the TDKS system.

Detecting the gravitational wave memory effect with TianQin

The gravitational wave memory effect is a prediction of general relativity. The presence of memory effect in gravitational wave signals not only provides the chance to test an important aspect of general relativity, but also represents a potentially non-negligible contribution to the waveform for certain gravitational wave events. In this paper, we study the prospect of detecting the gravitational wave memory effect directly with the planned space-based gravitational wave detector -- TianQin. We find that during its 5 years operation, for the gravitational wave signals that could be detected by TianQin, about $0.5\sim2.0$ signals may contain displacement memory effect with signal-to-noise ratios (SNRs) greater than 3. This suggests that the chance for TianQin to detect the displacement memory effect directly is low but not fully negligible. In contrast, the chance to detect the spin memory is negligible. We also study that in which parameter space, the memory effect is expected to be significant in waveform modeling.

Probing non-Markovian quantum dynamics with data-driven analysis: Beyond “black-box” machine-learning models

A precise understanding of the influence of a quantum system's environment on its dynamics, which is at the heart of the theory of open quantum systems, is crucial for further progress in the development of controllable large-scale quantum systems. However, existing approaches to account for complex system-environment interaction in the presence of memory effects are either based on heuristic and oversimplified principles or give rise to computational difficulties. In practice, one can leverage on available experimental data and replace first-principles simulations with a data-driven analysis that is often much simpler. Inspired by recent advances in data analysis and machine learning, we propose a data-driven approach to the analysis of the non-Markovian dynamics of open quantum systems. Our method allows, on the one hand, capturing the most important characteristics of open quantum systems such as the effective dimension of the environment and the spectrum of the joint system-environment quantum dynamics, and, on the other hand, reconstructing a predictive model of non-Markovian quantum dynamics, and denoising the measured quantum trajectories. We demonstrate the performance of the proposed approach with various models of open quantum systems, including a qubit coupled with a finite environment, a spin-boson model, and the damped Jaynes-Cummings model.

Variations in terms of CO2 capture and CH4 recovery during replacement processes in gas hydrate reservoirs, associated to the “memory effect”

The replacement of methane molecules, contained within natural hydrates reservoirs, with a theoretical equal number of carbon dioxide molecules, represents a promising opportunity for the near future. However, the maximum theoretical efficiency was proved to be approximately equal to 75% and, in the real applications, it is drastically lower. This article focused the attention on the possible reasons of such difference and found in the memory effect one of them. Firstly, the formation process of pure CH 4 and CO 2 hydrates was performed and thermodynamically characterized; then, the replacement process was realized on a system excluding memory and on a system including it. In the first situation, the theoretical efficiency was reached, while, in presence of memory effect, the results were drastically less effective, both in terms of methane recovery and in terms of carbon dioxide storage . When the system did not retain memory of previous formation processes, the quantity of CO 2 captured ranged from 73.97 to 75.05 vol% and the quantity of methane released was approximately equal to the one of CO 2 captured. Conversely, in presence of memory effect, the percentage of CO 2 captured dropped to 26 vol% and the quantity of methane release was still lower (24.97–26.03 vol%). • The influence of memory effect on the CO 2 /CH 4 replacement process was studied. • The memory effect was confirmed to be a kinetic promoter for hydrates formation. • The memory of previous CH 4 hydrates formation lowered the replacement efficiency. • Both the quantity of CH 4 released and CO 2 stored drastically decreased. • In absence of memory, the percentage of CO 2 storage reached the theoretical value.

Bifurcation from an Epidemic Model in the Presence of Memory Effects

In this paper, we consider a fractional SIS epidemic system with logistic growth demographic and saturated incidence rate for susceptibles. First, we validate our model by proving the global existence, positivity as well as boundedness of solutions. Then, we give necessary and sufficient conditions for the extinction and persistence of the disease from the population. We also study the local asymptotic stability of the unique positive equilibrium point by analyzing the corresponding characteristic equation. We find that combining logistic growth and saturated incidence for susceptibles can lead the system dynamic behavior to exhibit stability switches. By choosing the growth rate and the carrying capacity of the population as the bifurcation parameters, the stability of the positive equilibrium and the existence of Hopf bifurcation are investigated. Finally, numerical simulations are performed to verify the theoretical results, to fit real-time data from 10 June to 25 November of 2020 and also to predict the number of cumulative cases for COVID-19 in Morocco during 2021.

Fractional Study for Transient Free Convection Flow in a Channel with Mittag-Leffler Memory

Fractional-order convective transient flow of viscous and incompressible fluids transiting through two infinite hot parallel upright plates is investigated analytically in the presence of chemical reaction, radiative heat flux, and mass diffusion at the boundary. A physical model for transient incompressible unsteady flow is developed with a comparatively new fractional derivative, namely, Atangana–Baleanu with nonsingular, nonlocal kernel. The developed fractional model is studied with means of an integral transform, i.e., Laplace transform method. Results obtained for the concentration, velocity, and temperature are expressed in the form of generalized M q p y function. The impact of various physical parameters like fractional and flow parametric quantities is demonstrated diagrammatically. At last, we envisioned that for the fractional model, temperature and concentration could be enhanced for smaller fractional parameter α values while velocity for larger values of α , respectively. The proposed model gives the better results in the presence of memory effect besides the Caputo and Caputo–Fabrizio model when compared with the existing literature.

Quantification of surface charging memory effect in ionization wave dynamics

The dynamics of ionization waves (IWs) in atmospheric pressure discharges is fundamentally determined by the electric polarity (positive or negative) at which they are generated and by the presence of memory effects, i.e. leftover charges and reactive species that influence subsequent IWs. This work examines and compares positive and negative IWs in pulsed plasma jets (1 upmu s on-time), showing the difference in their nature and the different resulting interaction with a dielectric BSO target. For the first time, it is shown that a surface charging memory effect is produced, i.e. that a significant amount of surface charges and electric field remain in the target in between discharge pulses (200 upmu s off-time). This memory effect directly impacts IW dynamics and is especially important when using negative electric polarity. The results suggest that the remainder of surface charges is due to the lack of charged particles in the plasma near the target, which avoids a full neutralization of the target. This demonstration and the quantification of the memory effect are possible for the first time by using an unique approach, assessing the electric field inside a dielectric material through the combination of an advanced experimental technique called Mueller polarimetry and state-of-the-art numerical simulations.

Excitation Energy Transfer Efficiency in Fluctuating Environments: Role of Quantum Coherence in the Presence of Memory Effects.

Several recent studies have interrogated the role of quantum coherence in affecting the transfer efficiency of an optical excitation to the designated "trap" state where the energy can be used for subsequent reactions, as in photosynthesis. However, these studies invoke a Markovian approximation for the time correlation function describing the environment-induced stochastic fluctuations. Here, we employ Kubo's quantum stochastic Liouville equation (QSLE) to include memory effects. We extend the existing QSLE scheme to introduce decay of a newly created excitation due to radiative and nonradiative channels and also by desired trapping toward the targeted chromophore. We show that the theoretical formalism based on the QSLE correctly reproduces the rate equation description in the Markovian limit, with the rate constants determined by an appropriate quantum limiting procedure. We find that under certain conditions, the efficiency of excitation transfer to the trap gains from the combined presence of quantum coherence and temporally correlated stochastic fluctuations. We work out different limiting situations in order to discover and quantify the optimum conditions for the energy transfer to the trapped state. We find that maximum energy transfer efficiency is achieved in the intermediate limit between coherent and incoherent transport.

Upper semicontinuity of global attractors for a viscoelastic equations with nonlinear density and memory effects

This paper is devoted to showing the upper semicontinuity of global attractors associated with the family of nonlinear viscoelastic equations urn:x-wiley:mma:media:mma5389:mma5389-math-0001 in a three‐dimensional space, for f growing up to the critical exponent and dependent on ρ ∈ [0,4), as ρ→0+. This equation models extensional vibrations of thin rods with nonlinear material density ϱ(∂tu) = |∂tu|ρ and presence of memory effects. This type of problems has been extensively studied by several authors; the existence of a global attractor with optimal regularity for each ρ ∈ [0,4) were established only recently. The proof involves the optimal regularity of the attractors combined with Hausdorff's measure.

Analysis of stacking disorder in ice I using pair distribution functions

Stacking-disordered materials display crystalline order in two dimensions but are disordered along the direction in which layered structural motifs are stacked. Countless examples of stacking disorder exist, ranging from close-packed metals, ice I and diamond to open-framework materials and small-molecule pharmaceuticals. In general, the presence of stacking disorder can have profound consequences for the physical and chemical properties of a material. Traditional analyses of powder diffraction data are often complicated by the presence of memory effects in the stacking sequences. Here it is shown that experimental pair distribution functions of stacking-disordered ice I can be used to determine local information on the fractions of cubic and hexagonal stacking. Ice is a particularly challenging material in this respect, since both the stacking disorder and the orientational disorder of the water molecules need to be described. Memory effects are found to contribute very little to the pair distribution functions, and consequently, the analysis of pair distribution functions is the method of choice for characterizing stacking-disordered samples with complicated and high-order memory effects. In the context of this work, the limitations of current structure-reconstruction approaches are also discussed.

Reconstructing non-Markovian quantum dynamics with limited control

The dynamics of an open quantum system can be fully described and tomographically reconstructed if the experimenter has complete control over the system of interest. Most real-world experiments do not fulfill this assumption, and the amount of control is restricted by the experimental set-up. That is, the set of performable manipulations of the system is limited. For instance, imagine a set-up where unitary operations are easy to make, but only one measurement at the end of the experiment is allowed. In this paper, we provide a general reconstruction scheme that yields operationally well-defined dynamics for any conceivable kind of experimental situation. If one additional operation can be performed, these `restricted' dynamics allow for the construction of witnesses for initial correlations and the presence of memory effects. We demonstrate the applicability of our framework for the the two important cases where the set of performable operations comprises only unitary operations or projective measurements, respectively, and show that it provides a powerful tool for the description of quantum control experiments.

Asymptotics of viscoelastic materials with nonlinear density and memory effects

This paper is concerned with the nonlinear viscoelastic equation|∂tu|ρ∂ttu−Δ∂ttu−Δu+∫0∞μ(s)Δu(t−s)ds+f(u)=h, suitable to modeling extensional vibrations of thin rods with nonlinear material density ϱ(∂tu)=|∂tu|ρ, and presence of memory effects. This class of equations was studied by many authors, but well-posedness in the whole admissible range ρ∈[0,4] and for f growing up to the critical exponent were established only recently. The existence of global attractors was proved in presence of an additional viscous or frictional damping. In the present work we show that the sole weak dissipation given by the memory term is enough to ensure existence and optimal regularity of the global attractor Aρ for ρ<4 and critical nonlinearity f.

Anomalous diffusion due to the non-Markovian process of the dust particle velocity in complex plasmas

In this work, the motion of a dust particle under the influence of the random force due to dust charge fluctuations is considered as a non-Markovian stochastic process. Memory effects in the velocity process of the dust particle are studied. A model is developed based on the fractional Langevin equation for the motion of the dust grain. The fluctuation–dissipation theorem for the dust grain is derived from this equation. The mean-square displacement and the velocity autocorrelation function of the dust particle are obtained in terms of the Mittag-Leffler functions. Their asymptotic behavior and the dust particle temperature due to charge fluctuations are studied in the long-time limit. As an interesting result, it is found that the presence of memory effects in the velocity process of the dust particle as a non-Markovian process can cause an anomalous diffusion in dusty plasmas. In this case, the velocity autocorrelation function of the dust particle has a power-law decay like t−α−2, where the exponent α take values 0<α<1.

Solutions for a mass transfer process governed by fractional diffusion equations with reaction terms

We investigate the behavior of a mass transfer process governed by a set of fractional diffusion equations coupled by appropriate reaction terms. The presence of memory effects in the diffusive term is also considered. For this set of equations, we obtain solutions and analyze the influence of the reaction terms on the spreading of these solutions. Particularly, we observe that for reversible reaction processes the reaction terms play an important role for intermediate times and for long times the processes are essentially governed by the bulk equations. These results show a rich class of behaviors which can be connected to sub- or superdiffusive regime.

Finite Speed of Propagation and Waiting Time for Local Solutions of Degenerate Equations in Viscoelastic Media or Heat Flows with Memory

The finite speed of propagation (FSP) was established for certain materials in the 70’s by the American school (Gurtin, Dafermos, Nohel, etc.) for the special case of the presence of memory effects. A different approach can be applied by the construction of suitable super and sub-solutions (Crandall, Nohel, Diaz and Gomez, etc.). In this paper we present an alternative method to prove (FSP) which only uses some energy estimates and without any information coming from the characteristics analysis. The waiting time property is proved for the first time in the literature for this class of nonlocal equations.

Heterogeneity and Dynamics in Azobenzene Methacrylate Random and Block Copolymers: A Nanometer–Nanosecond Study by Electron Spin Resonance Spectroscopy

The dynamic response at nanometers and nanoseconds was investigated by electron spin resonance spectroscopy in random and block copolymers of an azobenzene methacrylate (MA4) and methyl methacrylate (MMA) with cholestane molecular tracer. The study evidenced the presence of different molecular sites for the reorientation at nanoscale, that were modulated by the amount of MA4 counits in the random copolymers and by the self-assembly in supramolecular structures in the block copolymers. A number of dynamics features was revealed, such as the presence of memory effects, the existence and the degree of coupling of the rotational dynamics to the structural relaxation of the matrix or to its viscosity, and the population of dynamic sites. This provided a detailed characterization of the mechanisms dictating the dynamic response of the structurally different copolymers. The influence of microstructure on the relaxation properties of the random copolymers was also discussed by considering the evaluated cooperativ...

A Generalized 2-D Linearity Enhancement Architecture for Concurrent Dual-Band Wireless Transmitters

A novel generalized two dimensional (2-D) digital predistortion (DPD) architecture for concurrent dual-band transmitters is presented. The proposed architecture is based on simultaneous injection of in-band intermodulation (IM) and cross-modulation (CM) distortion products. A general fundamental-frequency model for concurrent dual-band transmitter is developed theoretically and proofed experimentally. An individual impact of each IM and CM distortion component is theoretically derived and analyzed. It is clearly proven by theoretical analysis and experiments that the proposed predistorter improves the in-band and out-of-band performances of both signals. The simulation and experimental studies are performed using various signal sets. The proposed predistorter does not depend on frequency separation between bands and has low computational complexity in comparison with concurrent dual-band DPD's state-of-the-art. In addition, it is clearly shown in experiments that when using iterative simultaneous injections, a phenomenon known as distortion compensation limit can be reduced. A presence of memory effects and their mitigation in frequency domain for each band of concurrent dual-band transmitter are also demonstrated in experiments.

Effect of Clathrate Hydrate Formation and Decomposition on NMR Parameters in THF–D2O Solution

The NMR spin-lattice relaxation time (T(1)), spin-spin relaxation time (T(2)) and the diffusion coefficient D were measured for (1)H in a 1:17 mol % solution of tetrahydrofuran (THF) in D(2)O. The aim of the work was to clarify some earlier points raised regarding the utility of these measurements to convey structural information on hydrate formation and reformation. A number of irregularities in T(1) and T(2) measurements during hydrate processes reported earlier are explained in terms of the presence of interfaces and possible temperature gradients. We observe that T(1) and T(2) in solution are exactly the same before and after hydrate formation, thus confirming that the solution is isotropic. This is inconsistent with the presence of memory effects, at least those that may affect the dynamics to which T(1) and T(2) are sensitive. The measurement of the diffusion coefficient for a number of hours in the subcooled solution before nucleation proved invariant with time, again suggesting that the solution remains isotropic without affecting the guest dynamics and diffusion.