Consideration Of Memory Effect Research Articles

Universal Symmetry of Optimal Control at the Microscale

Optimizing the energy efficiency of driving processes provides valuable insights into the underlying physics and is of crucial importance for numerous applications, from biological processes to the design of machines and robots. Knowledge of optimal driving protocols is particularly valuable at the microscale, where energy supply is often limited. Here, we experimentally and theoretically investigate the paradigmatic optimization problem of moving a potential carrying a load through a fluid, in a finite time and over a given distance, in such a way that the required work is minimized. An important step towards more realistic systems is the consideration of memory effects in the surrounding fluid, which are ubiquitous in real-world applications. Therefore, our experiments were performed in viscous and viscoelastic media, which are typical environments for synthetic and biological processes on the microscale. Despite marked differences between the protocols in both fluids, we find that the optimal control protocol and the corresponding average particle trajectory always obey a time-reversal symmetry. We show that this symmetry, which surprisingly applies here to a class of processes far from thermal equilibrium, holds universally for various systems, including active, granular, and long-range correlated media in their linear regimes. The uncovered symmetry provides a rigorous and versatile criterion for optimal control that greatly facilitates the search for energy-efficient transport strategies in a wide range of systems. Using a machine learning algorithm, we demonstrate that the algorithmic exploitation of time-reversal symmetry can significantly enhance the performance of numerical optimization algorithms. Published by the American Physical Society 2024

Fractional Dynamics with Depreciation and Obsolescence: Equations with Prabhakar Fractional Derivatives

In economics, depreciation functions (operator kernels) are certain decreasing functions, which are assumed to be equal to unity at zero. Usually, an exponential function is used as a depreciation function. However, exponential functions in operator kernels do not allow simultaneous consideration of memory effects and depreciation effects. In this paper, it is proposed to consider depreciation of a non-exponential type, and simultaneously take into account memory effects by using the Prabhakar fractional derivatives and integrals. Integro-differential operators with the Prabhakar (generalized Mittag-Leffler) function in the kernels are considered. The important distinguishing features of the Prabhakar function in operator kernels, which allow us to take into account non-exponential depreciation and fading memory in economics, are described. In this paper, equations with the following operators are considered: (a) the Prabhakar fractional integral, which contains the Prabhakar function as the kernels; (b) the Prabhakar fractional derivative of Riemann–Liouville type proposed by Kilbas, Saigo, and Saxena in 2004, which is left inverse for the Prabhakar fractional integral; and (c) the Prabhakar operator of Caputo type proposed by D’Ovidio and Polito, which is also called the regularized Prabhakar fractional derivative. The solutions of fractional differential equations with the Prabhakar operator and its special cases are suggested. The asymptotic behavior of these solutions is discussed.

Research on accurate modeling of hydrodynamic interaction forces on AUVs operating in tandem

The hydrodynamic interaction force between autonomous underwater vehicles (AUVs) operating in tandem can adversely affect the hydrodynamic prediction of individual AUVs and the formation control of the tandem fleet. Accurate modeling of hydrodynamic interaction forces is crucial to the model-based controller design of AUVs. In this paper, we innovatively propose a modeling method that can describe the hydrodynamic interaction relationship accurately and continuously (when the spacing between adjacent AUVs changes). First, an accurate hydrodynamic model for individual AUVs in tandem fleets is established by modifying the typical model through the consideration of memory effects. Second, a model of hydrodynamic interaction forces is derived by subtracting hydrodynamic forces acting on a single AUV operating independently from those acting on an AUV operating in tandem. To enable this model to continuously describe the hydrodynamic interaction relationship when the spacing changes, this model is further derived by taking the spacing as an independent variable based on the parameter conversion method. Finally, planar motion mechanism (PMM) tests are carried out using the computational fluid dynamics (CFD) method to verify the accuracy and continuity of the proposed modeling method. The results show that compared with the typical model, the average error of hydrodynamic forces predicted by the proposed model is reduced by 5.36%, which verifies the feasibility and effectiveness of the proposed modeling method.

Coupled Polymer-Membrane Equilibration and Cavity Ring-down Spectrometry for the Highly Sensitive Determination of Dissolved Methane in Environmental Waters

High sensitivity field-based analysis of dissolved methane in surface water and groundwater is needed to monitor the environmental impacts of natural gas-field development and understand microbial carbon cycling in water bodies. A new analytical technique using a polymer membrane contactor coupled to a laser-based cavity ring-down spectrometer was developed and tested. By recirculating a water sample for approximately 10 mins, equilibrium was established between dissolved methane in the sample and methane in the measured gas phase according to Henry’s Law. The performance of the system was investigated by replicate analyses of several different water samples, spike recovery tests, comparison to analysis by head-space gas chromatography, and consideration of memory effects. The technique provided an adequate detection limit for the determination of natural background concentrations of methane in environmental waters and was approximately 28 times more sensitive than analysis by gas chromatography. The system is field-capable, simple to operate and calibrate, and takes advantage of the low-drift characteristics of the cavity ring-down spectrometer.

High-Performance Solution of Hierarchical Equations of Motion for Studying Energy Transfer in Light-Harvesting Complexes.

Excitonic models of light-harvesting complexes, where the vibrational degrees of freedom are treated as a bath, are commonly used to describe the motion of the electronic excitation through a molecule. Recent experiments point toward the possibility of memory effects in this process and require one to consider time nonlocal propagation techniques. The hierarchical equations of motion (HEOM) were proposed by Ishizaki and Fleming to describe the site-dependent reorganization dynamics of protein environments ( J. Chem. Phys. 2009 , 130 , 234111 ), which plays a significant role in photosynthetic electronic energy transfer. HEOM are often used as a reference for other approximate methods but have been implemented only for small systems due to their adverse computational scaling with the system size. Here, we show that HEOM are also solvable for larger systems, since the underlying algorithm is ideally suited for the usage of graphics processing units (GPU). The tremendous reduction in computational time due to the GPU allows us to perform a systematic study of the energy-transfer efficiency in the Fenna-Matthews-Olson (FMO) light-harvesting complex at physiological temperature under full consideration of memory effects. We find that approximative methods differ qualitatively and quantitatively from the HEOM results and discuss the importance of finite temperature to achieving high energy-transfer efficiencies.

Nonequilibrium description of dilepton production in heavy ion reactions

Time dependent medium modifications of low mass vector mesons are investigated within a nonequilibrium quantum field theoretical description on the basis of the Kadanoff-Baym equations. Time scales for the adaption of the spectral properties to changing self energies are given and, under use of a model for the fireball evolution, nonequilibrium dilepton yields from the decay of ρ- and ω-mesons are calculated. Comparison of the results with calculations that assume instantaneous adaption to the changing medium show that the consideration of memory effects is important.

On Fokker–Planck Equations for Turbulent Reacting Flows. Part 1. Probability Density Function for Reynolds-Averaged Navier–Stokes Equations

The accurate treatment of finite-rate chemistry is possible by the application of stochastic turbulence models which generalize Reynolds-averaged Navier–Stokes equations. Usually, one considers linear stochastic equations. In this way, fluctuations are generated by uncorrelated forces and relax with a frequency that is independent of the actual fluctuation. It has been proved that such linear equations are well appropriate to simulate near-equilibrium flows. However, the inapplicability or unfeasibility of other methods also results in a need for stochastic methods for more complex flow simulations. Their construction requires an extension of the simple mechanism of linear stochastic equations. Two ways to perform this are investigated here. The first way is the construction of a stochastic model for velocities where the relaxation frequency depends on the actual fluctuation. This is a requirement to involve relevant mixing variations due to large-scale flow structures. The stochastic model developed is applied to the simulation of convective boundary layer turbulence. Comparisons with the results of measurements provide evidence for its good performance and the advantages compared to existing methods. The second way presented here is the construction of scalar equations which involve memory effects regarding to both the stochastic forcing and relaxation of fluctuations. This allows to overcome shortcomings of existing stochastic methods. The model predictions are shown to be in excellent agreement with the results of the direct numerical simulation of scalar mixing in stationary, homogeneous and isotropic turbulence. The consideration of memory effects is found to be essential to simulate correctly the evolution of scalar fields within the first stage of mixing.