Energy Decay Rate Research Articles

Dynamics of post-impact merged droplets under different droplet–droplet interaction modes upon successive impingement on the substrate of different wettabilities

Successive impingement of multiple droplets onto a substrate is common in applications. However, the effects of the substrate properties and droplet–droplet interaction modes on the dynamics of the post-impact merged droplet remain unclear. In this study, we simulate the successive impingement of two droplets and the dynamics of the merged droplet on a superhydrophobic surface and a hydrophilic–hydrophobic patterned surface under different droplet–droplet interaction modes, based on a two-dimensional single-component pseudopotential multiphase lattice Boltzmann model. On the superhydrophobic surface, if the leading droplet is at spreading stages upon successive impingement, the merged droplet's maximum spreading factor, rebounding height, and merged droplet–substrate contact time decrease with the spreading of the leading droplet. Conversely, if the leading droplet is at recoiling stages upon successive impingement, the merged droplet's maximum spreading factor and rebounding height remain a small constant, while the merged droplet–substrate contact time increases with recoiling of the leading droplet. The dynamics of the merged droplet on a superhydrophobic surface under different droplet–droplet interaction modes are attributed to amplifying or suppressing the leading droplet kinetic energy upon successive impingement. However, on the hydrophilic–hydrophobic patterned surface, it is found that the hydrophilic stripes enhance the merged droplet spreading. The relatively large viscous force of the hydrophilic stripes and the energy barrier at the boundary of the pattern stripes significantly dissipate the kinetic energy of the merged droplet. The merged droplet does not rebound on the hydrophilic–hydrophobic patterned surface and has a small oscillation amplitude and fast energy decay rate.

A stability result for viscoelastic piezoelectric system with nonlinear feedback

In this work, we consider a nonlinear viscoelastic piezoelectric beam in the presence of an infinite memory and a nonlinear frictional damping of general type. We investigate the interaction between the two dampings and establish, under general assumptions on the relaxation function and the nonlinear feedback, an explicit formula for the energy decay rates of this system.

Decay of secondary electron yield of MgO–Au composite film at different incident electron energies

The relationship between the incident electron energy and secondary electron yield (SEY) decay of MgO–Au composite film was investigated by the designed comparison experiments. Besides the incident current and the properties of the film, the SEY value and the incident electron energy were found to be the other two key factors affecting the SEY decay rate. The value of SEY and the incident electron energy have opposite influences on the SEY decay rate, which makes it necessary to analyze the curve of incident electron energy versus SEY decay rate by dividing it into three parts. In addition, the empirical formulas for SEY decay were derived from experimental data, enabling the estimation of the SEY and decay rate of the MgO–Au composite film at any moment during SEY decay. Furthermore, the cause of SEY decay was also analyzed based on the relationship between incident electron energy and the SEY decay rate. The thermal dissipation, surface roughness, and deposition of contaminants were proven not to be the determinants of SEY decay. The experiment results in this paper supported the inference that the charging effect was the primary cause of SEY decay.

Existence and stability of a weakly damped laminated beam with a nonlinear delay

AbstractA weakly damped laminated beam system with nonlinear time delay is studied. The existence and uniqueness are proved by Faedo–Galerkin approach. We prove that the system is stable under some specific conditions on the weight of the delay and the equal wave speeds of propagation. The general energy decay rate is established by using multiplier method and some properties of convex functions. This decay result is obtained without imposing any restrictive growth assumption on the damping term at the origin. In addition, our result improves and develops some existing results in the literature.

Extreme time extrapolation capabilities and thermodynamic consistency of physics-inspired neural networks for the 3D microstructure evolution of materials via Cahn–Hilliard flow

Abstract A Convolutional Recurrent Neural Network (CRNN) is trained to reproduce the evolution of the spinodal decomposition process in three dimensions as described by the Cahn–Hilliard equation. A specialized, physics-inspired architecture is proven to provide close accordance between the predicted evolutions and the ground truth ones obtained via conventional integration schemes. The method can accurately reproduce the evolution of microstructures not represented in the training set at a fraction of the computational costs. Extremely long-time extrapolation capabilities are achieved, up to reaching the theoretically expected equilibrium state of the system, consisting of a layered, phase-separated morphology, despite the training set containing only relatively-short, initial phases of the evolution. Quantitative accordance with the decay rate of the free energy is also demonstrated up to the late coarsening stages, proving that this class of machine learning approaches can become a new and powerful tool for the long timescale and high throughput simulation of materials, while retaining thermodynamic consistency and high-accuracy.

Polynomial decay of the energy of solutions of coupled wave equations with locally boundary fractional dissipation

In this paper, we investigate a system of coupled wave equations featuring boundary fractional damping applied to a portion of the domain. We first establish the well-posedness of the system, proving the existence and uniqueness of solutions through semi-group theory. While the system does not exhibit exponential stability, we demonstrate its strong stability. Furthermore, leveraging Arendt and Batty’s general criteria and certain geometric conditions, we prove a polynomial rate of energy decay for the solutions.

Convergence to the planar interface for a nonlocal free‐boundary evolution

AbstractWe capture optimal decay for the Mullins–Sekerka evolution, a nonlocal, parabolic free boundary problem from materials science. Our main result establishes convergence of BV solutions to the planar profile in the physically relevant case of ambient space dimension three. Far from assuming small or well‐prepared initial data, we allow for initial interfaces that do not have graph structure and are not connected, hence explicitly including the regime of Ostwald ripening. In terms only of initially finite (not small) excess mass and excess surface energy, we establish that the surface becomes a Lipschitz graph within a fixed timescale (quantitatively estimated) and remains trapped within this setting. To obtain the graph structure, we leverage regularity results from geometric measure theory. At the same time, we extend a duality method previously employed for one‐dimensional PDE problems to higher dimensional, nonlocal geometric evolutions. Optimal algebraic decay rates of excess energy, dissipation, and graph height are obtained.

A motivational-based learning model for mobile robots

Humans have needs motivating their behavior according to intensity and context. However, we also create preferences associated with each action’s perceived pleasure, which is susceptible to changes over time. This makes decision-making more complex, requiring learning to balance needs and preferences according to the context. To understand how this process works and enable the development of robots with a motivational-based learning model, we computationally model a motivation theory proposed by Hull. In this model, the agent (an abstraction of a mobile robot) is motivated to keep itself in a state of homeostasis. We introduced hedonic dimensions to explore the impact of preferences on decision-making and employed reinforcement learning to train our motivated-based agents. In our experiments, we deploy three agents with distinct energy decay rates, simulating different metabolic rates, within two diverse environments. We investigate the influence of these conditions on their strategies, movement patterns, and overall behavior. The findings reveal that agents excel at learning more effective strategies when the environment allows for choices that align with their metabolic requirements. Furthermore, we observe that incorporating pleasure as a component of the motivational mechanism affects behavior learning, particularly for agents with regular metabolisms depending on the environment. Our study also unveils that, when confronted with survival challenges, agents prioritize immediate needs over pleasure and equilibrium. These insights shed light on how robotic agents can adapt and make informed decisions in demanding scenarios, demonstrating the intricate interplay between motivation, pleasure, and environmental context in autonomous systems.

The energy decay rate of a transmission system governed by the degenerate wave equation with drift and under heat conduction with the memory effect

The energy decay rate of a transmission system governed by the degenerate wave equation with drift and under heat conduction with the memory effect

Indirect stabilization of locally weakly coupled second‐order evolution systems of hyperbolic type

The purpose of this work is to investigate the stabilization of locally weakly coupled second‐order evolution equations of hyperbolic type, where only one of the two equations is directly damped. As such system cannot be exponentially stable, we are interested in polynomial energy decay rates. Our main contributions concern strong abstract and polynomial stability properties based on stability properties of two auxiliary problems: the sole damped equation and the second equation with a damping related to the coupling operator. The main novelty is that the polynomial energy decay rates are obtained in different important situations not covered before; let us mention the case of a coupling operator not partially coercive and not necessarily bounded. The main tools are the use of the frequency domain approach combined with new multipliers technique based on the solutions of the resolvent equations of the two auxiliary problems mentioned before. Finally, our abstract framework is illustrated by several concrete examples not treated before.

Stabilization of quasilinear systems with variable exponents: A modified approach for energy decay rate determination

This article investigates the stabilization of quasilinear systems governed by elliptic partial differential equations (PDEs) with variable exponents using the modified Tikhonov approach. Our main focus is to determine the energy decay rate of the solution. The findings have significant potential for practical applications in various fields of science and engineering, where the energy decay rate plays a vital role in system stability and control.

Asymptotic behavior of solutions of a viscoelastic Shear beam model with no rotary inertia: General and optimal decay results

Abstract In this study, we consider a viscoelastic Shear beam model with no rotary inertia. Specifically, we study ρ 1 φ t t − κ ( φ x + ψ ) x + ( g ∗ φ x x ) ( t ) = 0 , − b ψ x x + κ ( φ x + ψ ) = 0 , \begin{array}{rcl}{\rho }_{1}{\varphi }_{tt}-\kappa {\left({\varphi }_{x}+\psi )}_{x}+\left(g\ast {\varphi }_{xx})\left(t)& =& 0,\\ -b{\psi }_{xx}+\kappa \left({\varphi }_{x}+\psi )& =& 0,\end{array} where the convolution memory function g g belongs to a class of L 1 ( 0 , ∞ ) {L}^{1}\left(0,\infty ) functions that satisfies g ′ ( t ) ≤ − ξ ( t ) ϒ ( g ( t ) ) , ∀ t ≥ 0 , g^{\prime} \left(t)\le -\xi \left(t)\Upsilon \left(g\left(t)),\hspace{1.0em}\forall t\ge 0, where ξ \xi is a positive nonincreasing differentiable function and ϒ \Upsilon is an increasing and convex function near the origin. Using just this general assumptions on the behavior of g g at infinity, we provide optimal and explicit general energy decay rates from which we recover the exponential and polynomial rates when ϒ ( s ) = s p \Upsilon \left(s)={s}^{p} and p p covers the full admissible range [ 1 , 2 ) \left[1,2) . Given this degree of generality, our results improve some of earlier related results in the literature.

New decay results for Timoshenko system in the light of the second spectrum of frequency with infinite memory and nonlinear damping of variable exponent type

In this study, we consider a one-dimensional Timoshenko system with two damping terms in the context of the second frequency spectrum. One damping is viscoelastic with infinite memory, while the other is a non-linear frictional damping of variable exponent type. These damping terms are simultaneously and complementary acting on the shear force in the domain. We establish, for the first time to the best of our knowledge, explicit and general energy decay rates for this system with infinite memory. We use Sobolev embedding and the multiplier approach to get our decay results. These results generalize and improve some earlier related results in the literature.

Energy dissipation and evolutions of the nonlocal Cahn-Hilliard model and space fractional variants using efficient variable-step BDF2 method

In this work, an energy stable BDF2 scheme with general nonuniform time steps is developed for the nonlocal Cahn-Hilliard model to capture the multi-scale behavior of evolution efficiently and accurately. The fully discrete numerical scheme is demonstrated to inherit main physical properties of the continuous model, namely, mass conservation and energy dissipation. Recently, various variants of the Cahn-Hilliard model with nonlocal operators and fractional Laplacian have attracted great attention in terms of theoretical analysis and numerical approximation, while there is less emphasis on the comparisons among the different variant models. By comparing the impact of various parameters and coarsening behaviors, numerical results suggest that the nonlocal Cahn-Hilliard model bears a strong resemblance to the space fractional Cahn-Hilliard model derived from H−1 gradient flow of the nonlocal energy. Nevertheless, the order of the fractional Laplacian appears to affect only the rate of energy decay, without altering the profile of the solution for the fractional model relating to the H−β (0<β<1) gradient flow of the classical Ginzburg-Landau energy functional in one dimensional case.

Polynomial Energy Decay Rate for the Wave Equation with Kinetic Boundary Condition

Polynomial Energy Decay Rate for the Wave Equation with Kinetic Boundary Condition

Cooling of a granular gas mixture in microgravity

Granular gases are fascinating non-equilibrium systems with interesting features such as spontaneous clustering and non-Gaussian velocity distributions. Mixtures of different components represent a much more natural composition than monodisperse ensembles but attracted comparably little attention so far. We present the observation and characterization of a mixture of rod-like particles with different sizes and masses in a drop tower experiment. Kinetic energy decay rates during granular cooling and collision rates were determined and Haff’s law for homogeneous granular cooling was confirmed. Thereby, energy equipartition between the mixture components and between individual degrees of freedom is violated. Heavier particles keep a slightly higher average kinetic energy than lighter ones. Experimental results are supported by numerical simulations.

Energy decay rate of the wave–wave transmission system with Kelvin–Voigt damping

In this paper, we study the energy decay rate of the wave–wave transmission system with Kelvin–Voigt damping on a rectangular domain. The damping is imposed on one of wave equations. By the separation of variables method and the frequency domain method, we show that the optimal energy decay rate of the system is , which is independent of wave speeds.

On the interaction between the viscoelasticity and the boundary variable-exponent nonlinearity in plate systems

In this paper, we consider a viscoelastic plate system with a boundary frictional damping having a variable exponent m ( x ) . We investigate the competition between the two types of damping and their effects on the energy decay rates. Using the multiplier method, we establish explicit decay results depending on both m and the relaxation function g. Our results address both the optimality and generality and improve earlier related results in the literature.

Graphene nanomechanical vibrations measured with a phase-coherent software-defined radio

Software-defined radios (SDRs) are radio frequency transceivers designed to facilitate digital signal processing through the use of vast libraries of open-source software. Here, we assemble a simple data acquisition system whose architecture, based on SDR, allows us to develop a comprehensive suite of tools to study the vibrations of a few-layer graphene nanomechanical resonator. Namely, we measure the cross-spectrum of vibrations in the frequency domain, we measure their energy decay rate in the time domain, we perform vector measurements of their in-phase and quadrature components, and we control their phase using a time-dependent strain field –all with a single measurement platform. Our approach allows us to tailor our experiments at will and gives us control over every stage of data processing. Overall, our versatile system enables measuring a wide range of nanomechanical properties of graphene by customizing the signal acquisition and replacing some analog electrical circuits, such as filters, mixers, and demodulators, by blocks of code.

Modeling of multilayer water adsorption and condensation in slits of cement minerals by molecule simulation and adsorption isotherm

The interactions between water and multiscale pores affect significantly most of the physical and chemical properties of cementitious materials such as cement mortar, paste, and concrete. In this paper, molecular mechanism of multilayer water adsorption and condensation in micropores of typical cementitious minerals, the dicalcium silicate (C2S) and calcium silicate hydrate (C-S-H), were investigated by molecular simulations. Classical adsorption isotherm models were examined for their applicability to describe the adsorption law in molecular scales. Besides, the Kelvin equation was modified to satisfy the description of condensation at the microscale. Calculation results show that the most commonly used Brunauer-Emmett-Teller (BET) model can only describe the isotherms within a limited range of low water vapor pressures. In comparison, the modified Brunauer-Emmett-Teller-Pickett (BETP) model can describe the adsorption of water molecular on the surface of C2S and C-S-H more precisely, due to considering the adsorption layers as finite at saturation pressure and the reduced escape probability of the outermost layer of adsorbed water molecules. As for the condensation of water molecules in C2S and C-S-H slits, the traditional Kelvin equation is not applicable. Therefore, a refined Kelvin equation was proposed to describe the relationship between pore size and the pressure required for condensation accurately by considering the critical pore size, adsorption thickness, and decay rate of adsorption potential energy. Further analysis suggests that C2S releases more first-layer adsorption heat and thus shows stronger adsorption of water molecules compared to C-S-H.