Monotonic Drift Research Articles

(Digital Presentation) Monitoring Dendrite Growth in Aqueous Zinc Ion Batteries with Guided Ultrasonic Waves

Dendrites form on the surface of metal electrodes as a battery undergoes repeated charging and discharging. The formation of dendrites not only affects the electrochemical performances of a battery but may also cause internal short-circuiting and thermal runaway events. Hence, there is a clear need to understand the formation mechanisms and growth kinetics of dendrites. Currently available technologies such as (in-situ) X-ray computed tomography and scanning electron microscopy can be used in a laboratory environment to study dendrite formation. However, they are often prohibitively expensive or unsuitable for long-term, large-scale, and in-operando monitoring.In this study we present an ultrasound-based technique which is cheap, with potential to scale up, and suitable in both laboratory and industrial environments. Different from conventional ultrasonic approaches which excite ultrasonic waves that propagating through layers of cathode, anode and electrolyte, the method presented in this study utilises miniature transducers which excite fundamental shear-horizontal (SH0*) guided ultrasonic waves that propagate along the cathode and anode. Hence, the presented method can individually monitor the condition of multiple electrodes which may be undergoing different ion-insertion mechanisms.A proof-of-concept study was performed on a symmetric aqueous zinc ion cell to explore the sensitivity of SH0* mode guided ultrasonic waves to zinc metal plating/stripping and dendrite formation at the electrode-electrolyte interface. We observed that the attenuation and velocity of waves show cyclical variations when the cell was in a chronopotentiometric cycling test. Variations of wave attenuation and velocity on the opposing working and counter electrode are observed to be in the opposite senses and the increasing/decreasing trends depend on the states (i.e., charging/discharging) of the cell. The cyclical variations of the ultrasound properties are only partially reversible and a monotonic drift can be observed which increases with increasing number of cycles.Coupling the ultrasonic measurements with images acquired by an optical microscope, clear correlations can be observed between changes in ultrasonic wave properties and zinc dendrite thickness. The partially reversible cyclical variations can be attributed to zinc plating/stripping that occur at the electrode-electrolyte interface. The irreversible, monotonic drifting can be attributed to the growth of zinc dendrites on the electrode surface. Hence, these findings demonstrate that the SH0* mode guided ultrasonic waves can offer valuable insights on physical changes at the electrode-electrolyte interface. It is therefore possible to quantitatively model and predict dendrite growth based on ultrasonic measurements. In conclusion, we believe the presented method can inspire more quantitative research on dendrite formation and in-operando monitoring of battery health. Figure 1

Ultrasonic guided wave monitoring of dendrite formation at electrode–electrolyte interface in aqueous zinc ion batteries

The formation of dendrite affects the cycling life of a battery and lead to malfunctions such as internal short-circuiting and thermal runaway events. However, existing methods to observe dendrite formation, such as X-ray computed tomography and scanning electron microscopy are either prohibitively complicated or unsuitable for long-term, in-situ monitoring. In this study we present a method which uses the fundamental shear-horizontal mode (SH0*) guided ultrasonic waves to independently monitor the status of the electrodes in a symmetric aqueous zinc-ion battery. Experimental measurements show that the velocity and attenuation of the ultrasonic wave on the opposing electrodes vary in the opposite senses during the cycling. While the velocity and attenuation changes can be partially reversed, a monotonic drift can also be observed with increasing number of cycles. Coupled with optical microscopy, the partially reversible oscillations can be associated with zinc stripping/plating. The irreversible drifting can be associated with the formation of ‘dead’ zinc dendrite. The technique shows clear sensitivity to the formation of dendrite, especially in the early stages (∼10 cycles) of charging and discharging processes. This work should inspire future research to enable quantitative assessment of the technique sensitivity and to improve its resolution.

Backward Euler–Maruyama Method for the Random Periodic Solution of a Stochastic Differential Equation with a Monotone Drift

In this paper, we study the existence and uniqueness of the random periodic solution for a stochastic differential equation with a one-sided Lipschitz condition (also known as monotonicity condition) and the convergence of its numerical approximation via the backward Euler–Maruyama method. The existence of the random periodic solution is shown as the limit of the pull-back flows of the SDE and the discretized SDE, respectively. We establish a convergence rate of the strong error for the backward Euler–Maruyama method with order of convergence 1/2.

Climate change in mechanical systems: the snapshot view of parallel dynamical evolutions

We argue that typical mechanical systems subjected to a monotonous parameter drift whose timescale is comparable to that of the internal dynamics can be considered to undergo their own climate change. Because of their chaotic dynamics, there are many permitted states at any instant, and their time dependence can be followed—in analogy with the real climate—by monitoring parallel dynamical evolutions originating from different initial conditions. To this end an ensemble view is needed, enabling one to compute ensemble averages characterizing the instantaneous state of the system. We illustrate this on the examples of (i) driven dissipative and (ii) Hamiltonian systems and of (iii) non-driven dissipative ones. We show that in order to find the most transparent view, attention should be paid to the choice of the initial ensemble. While the choice of this ensemble is arbitrary in the case of driven dissipative systems (i), in the Hamiltonian case (ii) either KAM tori or chaotic seas should be taken, and in the third class (iii) the best choice is the KAM tori of the dissipation-free limit. In all cases, the time evolution of the chosen ensemble on snapshots illustrates nicely the geometrical changes occurring in the phase space, including the strengthening, weakening or disappearance of chaos. Furthermore, we show that a Smale horseshoe (a chaotic saddle) that is changing in time is present in all cases. Its disappearance is a geometrical sign of the vanishing of chaos. The so-called ensemble-averaged pairwise distance is found to provide an easily accessible quantitative measure for the strength of chaos in the ensemble. Its slope can be considered as an instantaneous Lyapunov exponent whose zero value signals the vanishing of chaos. Paradigmatic low-dimensional bistable systems are used as illustrative examples whose driving in (i, ii) is chosen to decay in time in order to maintain an analogy with case (iii) where the total energy decreases all the time.

Strong approximation of monotone stochastic partial differential equations driven by multiplicative noise

We establish a general theory of optimal strong error estimation for numerical approximations of a second-order parabolic stochastic partial differential equation with monotone drift driven by a multiplicative infinite-dimensional Wiener process. The equation is spatially discretized by Galerkin methods and temporally discretized by drift-implicit Euler and Milstein schemes. By the monotone and Lyapunov assumptions, we use both the variational and semigroup approaches to derive a spatial Sobolev regularity under the $L_\omega^p L_t^\infty \dot H^{1+\gamma}$-norm and a temporal H\"older regularity under the $L_\omega^p L_x^2$-norm for the solution of the proposed equation with an $\dot H^{1+\gamma}$-valued initial datum for $\gamma\in [0,1]$. Then we make full use of the monotonicity of the equation and tools from stochastic calculus to derive the sharp strong convergence rates $O(h^{1+\gamma}+\tau^{1/2})$ and $O(h^{1+\gamma}+\tau^{(1+\gamma)/2})$ for the Galerkin-based Euler and Milstein schemes, respectively.

Temporal density extrapolation using a dynamic basis approach

Density estimation is a versatile technique underlying many data mining tasks and techniques, ranging from exploration and presentation of static data, to probabilistic classification, or identifying changes or irregularities in streaming data. With the pervasiveness of embedded systems and digitisation, this latter type of streaming and evolving data becomes more important. Nevertheless, research in density estimation has so far focused on stationary data, leaving the task of of extrapolating and predicting density at time points outside a training window an open problem. For this task, temporal density extrapolation (TDX) is proposed. This novel method models and predicts gradual monotonous changes in a distribution. It is based on the expansion of basis functions, whose weights are modelled as functions of compositional data over time by using an isometric log-ratio transformation. Extrapolated density estimates are then obtained by extrapolating the weights to the requested time point, and querying the density from the basis functions with back-transformed weights. Our approach aims for broad applicability by neither being restricted to a specific parametric distribution, nor relying on cluster structure in the data. It requires only two additional extrapolation-specific parameters, for which reasonable defaults exist. Experimental evaluation on various data streams, synthetic as well as from the real-world domains of credit scoring and environmental health, shows that the model manages to capture monotonous drift patterns accurately and better than existing methods. Thereby, it requires not more than 1.5 times the run time of a corresponding static density estimation approach.

Analysis of Modal Resonance Between PLL and DC-Link Voltage Control in Weak-Grid Tied VSCs

Weak ac grid operation is known to challenge the stability of voltage source converters (VSCs). This paper provides an interpretation for the cause of such instability in view of a particular modal resonance within VSC's control, i.e., the resonance between dc-link voltage control (DVC) and synchronizing control-phase-locked loop (PLL). To characterize this modal interaction, a two degrees-of-freedom mass–spring–damper model is first proposed. Subsequently, based on a multi-modal decomposition approach, the amount of interaction is quantified by the incremental damping and frequency drift superimposed on each individual mode. Analytical results indicate that when the natural frequencies of PLL and DVC mode are close, strong interaction will push the lower-frequency mode to move toward the decreased frequency and damping direction, while causing the higher-frequency mode to go the opposite. Moreover, weaker ac grid operation will amplify such frequency/damping excursion and, thus, will render the lower-frequency mode unstable. Further, when the ac voltage control (AVC) is disregarded, a dynamic stability margin is analytically derived, and operation beyond the margin will result in monotonic drift. With the inclusion of AVC, owing to its introduced additional negative damping, by contrast, instability will occur in the presence of oscillations. Both eigenvalue analysis and simulations are conducted to verify the results.

Strong solutions to SPDEs with monotone drift in divergence form

We prove existence and uniqueness of strong solutions, as well as continuous dependence on the initial datum, for a class of fully nonlinear second-order stochastic PDEs with drift in divergence form. Due to rather general assumptions on the growth of the nonlinearity in the drift, which, in particular, is allowed to grow faster than polynomially, existing techniques are not applicable. A well-posedness result is obtained through a combination of a priori estimates on regularized equations, interpreted both as stochastic equations as well as deterministic equations with random coefficients, and weak compactness arguments. The result is essentially sharp, in the sense that no extra hypotheses are needed, bar continuity of the nonlinear function in the drift, with respect to the deterministic theory.

Strong completeness and semi-flows for stochastic differential equations with monotone drift

It is well-known that a stochastic differential equation (sde) on a Euclidean space driven by a (possibly infinite-dimensional) Brownian motion with Lipschitz coefficients generates a stochastic flow of homeomorphisms. If the Lipschitz condition is replaced by an appropriate one-sided Lipschitz condition (sometimes called monotonicity condition) and the number of driving Brownian motions is finite, then existence and uniqueness of global solutions for each fixed initial condition is also well-known. In this paper we show that under a slightly stronger one-sided Lipschitz condition the solutions still generate a stochastic semiflow which is jointly continuous in all variables (but which is generally neither one-to-one nor onto). We also address the question of strong Δ-completeness which means that there exists a modification of the solution which if restricted to any set A⊂Rd of dimension Δ is almost surely continuous with respect to the initial condition.

Isoline Drift Correction in Digital Processing of the Electrocardiosignal

The article discusses reduction of electrocardiosignal (ECS) drift based on statistical signal processing, comparing the results of applying statistical methods to a limited time frame for correction of isoline drift based on the additive mixture of drift and ECS components. A mathematical regression formula is provided to approximate a ranged sample of values of one ECS cycle. The study presents an effective method of eliminating monotonous isoline drift, allowing the use of programs for fast data sorting.

Frequency Ageing and Noise Evolution in a Distributed Feedback Quantum Cascade Laser Measured Over a Two-Month Period

We report on the evaluation of the frequency stability of a distributed feedback quantum cascade laser (QCL) at 8 μm that was continuously monitored over a 2-month period using a spectroscopic setup. The QCL was operated in continuous wave mode at room temperature (21.4 °C). It was driven by a home-made low-noise controller at a nominal current of ∼600 mA located in the middle of its operation range. Two distinctive behaviors were observed. A monotonous frequency drift of about 1.8 GHz was observed during slightly more than the first month, followed by a stable regime in the second month where the frequency remained within a 100 MHz range. In addition, the electrical flicker noise of the QCL was regularly measured during the same period, and similarly showed two different regimes. The noise regularly decreased at a small rate of about 0.3%/day during the first month, whereas it tends to stabilize during the second month. We believe that an improvement of the QCL contacts over time is responsible for this behavior. After the initial one-month period, the QCL showed a remarkably stable behavior that is beneficial for many applications that require stable long-term operation.

Yosida approximations for multivalued stochastic partial differential equations driven by Lévy noise on a Gelfand triple

We prove the existence and uniqueness of solutions for a class of multivalued stochastic partial differential equations with maximal monotone drift on Banach space driven by multiplicative Lévy noise. We also establish the strong convergence result for solutions of the approximating equations where the maximal monotone drift operator is replaced by its Yosida approximation. As an application, the existence and uniqueness of solutions for multivalued stochastic porous medium equations is obtained.

Ergodicity for nonlinear stochastic evolution equations with multiplicative Poisson noise

We study the asymptotic behavior of solutions to stochastic evolution equations with monotone drift and multiplicative Poisson noise in the variational setting, thus covering a large class of (fully) nonlinear partial differential equations perturbed by jump noise. In particular, we provide sufficient conditions for the existence, ergodicity, and uniqueness of invariant measures. Furthermore, under mild additional assumptions, we prove that the Kolmogorov equation associated to the stochastic equation with additive noise is solvable in $L_1$ spaces with respect to an invariant measure.

Large Deviations for Stochastic Evolution Equations with Small Multiplicative Noise

The Freidlin-Wentzell large deviation principle is established for the distributions of stochastic evolution equations with general monotone drift and small multiplicative noise. As examples, the main results are applied to derive the large deviation principle for different types of SPDE such as stochastic reaction-diffusion equations, stochastic porous media equations and fast diffusion equations, and the stochastic p-Laplace equation in Hilbert space. The weak convergence approach is employed in the proof to establish the Laplace principle, which is equivalent to the large deviation principle in our framework.

Hysteretic energy dissipation capacity and the cyclic to monotonic drift ratio for rectangular RC columns in flexure

AbstractPredictions of energy dissipation capacity and of the deterioration of deformation capacity due to cumulative damage have been made by means of a non‐parametric empirical approach, called the conditional average estimator method, using empirical data on rectangular reinforced concrete columns that failed in flexure. Five input parameters were used: axial load index, index related to confinement, shear span index, concrete compressive strength, and longitudinal reinforcement index. The energy capacity was expressed in three different normalized forms and the deterioration of deformation capacity was defined as the ratio of the cyclic to the monotonic ultimate drift. The longitudinal reinforcement index, the index related to confinement, and the axial load index are the most influential input parameters in the case of energy capacity, whereas the latter two indices exhibit the most significant influence in the case of the drift ratio. Energy capacity decreases with an increasing axial load index, whereas it increases with increasing longitudinal reinforcement and with better confinement. In the case of the shear span index, the trend is more complex. Normal concrete has a higher energy dissipation capacity than high‐strength concrete. Similar trends are observed for the drift ratio, with the exception of the influence of the axial load index, where the trend is opposite. The dispersion of the results is high. Copyright © 2008 John Wiley & Sons, Ltd.

Sur l'existence de solutions d'équations différentielles stochastiques progréssives rétrogrades couplées

Nonlinear BSDEs were first introduced by Pardoux and Peng, 1990, Adapted solutions of backward stochastic differential equations, Systems and Control Letters, 14, 51–61, who proved the existence and uniqueness of a solution under suitable assumptions on the coefficient. Fully coupled forward–backward stochastic differential equations and their connection with PDE have been studied intensively by Pardoux and Tang, 1999, Forward–backward stochastic differential equations and quasilinear parabolic PDE's, Probability Theory and Related Fields, 114, 123–150; Antonelli and Hamadène, 2006, Existence of the solutions of backward–forward SDE's with continuous monotone coefficients, Statistics and Probability Letters, 76, 1559–1569; Hamadème, 1998, Backward–forward SDE's and stochastic differential games, Stochastic Processes and their Applications, 77, 1–15; Delarue, 2002, On the existence and uniqueness of solutions to FBSDEs in a non-degenerate case, Stochastic Processes and Their Applications, 99, 209–286, amongst others. Unfortunately, most existence or uniqueness results on solutions of forward–backward stochastic differential equations need regularity assumptions. The coefficients are required to be at least continuous which is somehow too strong in some applications. To the best of our knowledge, our work is the first to prove existence of a solution of a forward–backward stochastic differential equation with discontinuous coefficients and degenerate diffusion coefficient where, moreover, the terminal condition is not necessary bounded. The aim of this work is to find a solution of a certain class of forward–backward stochastic differential equations on an arbitrary finite time interval. To do so, we assume some appropriate monotonicity condition on the generator and drift coefficients of the equation. The present paper is motivated by the attempt to remove the classical condition on continuity of coefficients, without any assumption as to the non-degeneracy of the diffusion coefficient in the forward equation. The main idea behind this work is the approximating lemma for increasing coefficients and the comparison theorem. Our approach is inspired by recent work of Boufoussi and Ouknine, 2003, On a SDE driven by a fractional brownian motion and with monotone drift, Electronic Communications in Probability, 8, 122–134; combined with that of Antonelli and Hamadène, 2006, Existence of the solutions of backward–forward SDE's with continuous monotone coefficients, Statistics and Probability Letters, 76, 1559–1569. Pursuing this idea, we adopt a one-dimensional framework for the forward and backward equations and we assume a monotonicity property both for the drift and for the generator coefficient. At the end of the paper we give some extensions of our result.

A note on the Euler–Maruyama scheme for stochastic differential equations with a discontinuous monotone drift coefficient

It is shown that the Euler–Maruyama scheme applied to a stochastic differential equation with a discontinuous monotone drift coefficient, such as a Heaviside function, and additive noise converges strongly to a solution of the stochastic differential equation with the same initial condition. The proof uses upper and lower solutions of the stochastic differential equations and the Euler–Maruyama scheme.

Factors Determining the Stability, Resolution, and Precision of a Conventional Raman Spectrometer

We verified the performance of a conventional Raman spectrometer, which is composed of a 30 cm single polychromator, a Si based charge-coupled device (CCD) camera, and a holographic supernotch filter. For that purpose, the time change of the peak positions of Raman spectra of naphthalene and fluorescence spectra of ruby (Cr-doped Al(2)O(3)) were monitored continually. A time-dependent deviation composed of two components was observed: a monotonous drift up to 0.4 cm(-1) and a periodic oscillation with a range of 0.15 cm(-1). The former component was stabilized at approximately 2000 s after the CCD detector was cooled, indicating that incomplete refrigeration of the CCD detector induced the drift. The latter component synchronized with the periodic oscillation of the room temperature, indicating that thermal expansion or contraction of the whole apparatus induced this oscillation. The implemental deviation is reduced when measurements are conducted using a sufficiently cooled CCD detector at a constant room temperature. Moreover, the effect of the room temperature oscillation is lowered in a spectrum acquired over a duration that is longer than one cycle of this oscillation. Applying the least squares fitting method to carefully measured spectra enhanced the precision of the determination of the peak position to 0.05 cm(-1) using the spectrometer with pixel resolution of 1.5 cm(-1).

Effects of Temperature Fluctuations on X-Ray Stress Determination

The results presented in this paper are part of a process to analyse systematically the sources of uncertainty in X-ray stress determination. They concern one part of the effects of temperature variations which could intervene either as random fluctuations or as a monotonic drift during the acquisition. The proposed formulation is in agreement with the recommendations of the ISO guide on the expression of uncertainty (GUM). It was found that the effect is usually negligible for laboratory experiments which are often temperature controlled and for most materials. However the uncertainty can reach 20 MPa for austenitic steels and a temperature drift of 2 K.

On a SDE driven by a fractional Brownian motion and with monotone drift

Let ${B_{t}^{H},t\in \lbrack 0,T]}$ be a fractional Brownian motion with Hurst parameter $H \gt \frac{1}{2}$. We prove the existence of a weak solution for a stochastic differential equation of the form $X_{t}=x+B_{t}^{H}+ \int_{0}^{t}\left( b_{1}(s,X_{s})+b_{2}(s,X_{s})\right) ds$, where $ b_{1}(s,x)$ is a Holder continuous function of order strictly larger than $1-\frac{1}{2H}$ in $x$ and than $H-\frac{1}{2}$ in time and $b_{2}$ is a real bounded nondecreasing and left (or right) continuous function.