Small Noise Research Articles

Threshold estimation for jump-diffusions under small noise asymptotics

We consider parameter estimation of stochastic differential equations driven by a Wiener process and a compound Poisson process as small noises. The goal is to give a threshold-type quasi-likelihood estimator and show its consistency and asymptotic normality under new asymptotics. One of the novelties of the paper is that we give a new localization argument, which enables us to avoid truncation in the contrast function that has been used in earlier works and to deal with a wider class of jumps in threshold estimation than ever before.

Entanglement recovery in noisy binary quantum information protocols via three-qubit quantum error correction codes

The task of preserving entanglement against noises is of crucial importance for both quantum communication and quantum information transfer. To this aim, quantum error correction (QEC) codes may be employed to compensate, at least partially, the detriments induced by environmental noise that can be modeled as a bit-flip or a phase-flip error channel. In this paper, we investigate the effects of the simple three-qubit QEC codes to restore entanglement and nonlocality in a two-qubit system and consider two practical applications: superdense coding and quantum teleportation. Though the considered three-qubit QEC codes are known to perfectly work in the presence of very small noise, we show that they can avoid the sudden death of entanglement and improve the performance of the addressed protocols also for larger noise amplitudes.

Natural ageing systems of 6063 Al-alloys using diverse XRD ways

ABSTRACT The detailed estimation of XRD microstructural elements such as Scherrer (Sch.) size of crystallite, Williamson-Hall (WH) size of crystallite and microscopic strain was highlighted via a novel modelling approach which relies on the broadening parameters named as the experimental broadening, crystallite size broadening and strain broadening. This approach was applied on the strain aged 6063 Al-alloys which are considered one of the backbones in the applications related to energy industries and manufacturers like vehicles and planes due to their light densities, availabilities and facile in fabrication. Three divergent aged specimens deformed at different percentages 0%, 5% and 30% respectively. The XRD results through modelling approach was comparable to the Rietveld MAUD (RM) refinement approach, which was served as a comparing and confirming tool. The estimated microstructural factors as a variation of the ageing time by the broadening analysis using the novel method were in a good agreement with Rietveld analysis using MAUD software program. The behaviour of both size of crystallite and micro strain exhibits two opposite pathways via the ageing time variation including small noises until to reach 400 hours at which the mean values of both of them nearly being constant for all distorted and non-distorted specimens.

Melnikov’s method for controlled stochastic oscillations of a rocking block with fractional derivative

The problem of controlling a rocking block with fractional dissipation so as to prevent it from leaving a prescribed set of bounded oscillations has a number of interesting applications in many scientific and technological fields. This work develops an analytical framework to describe the influence of control on the behavior of a fractionally dissipative rocking block subject to random acceleration of the ground. Control equations are developed and control strategies leading to optimal suppression of instability are asymptotically described under the assumptions of weak dissipation along with a small energy noise. Under these assumptions, the behavior of the block is interpreted as weakly perturbed rocking oscillations close to a generic periodic solution, and the Melnikov approximations are considered as the necessary conditions of instability. The stochastic Melnikov criterion derived in this paper allows for an approximate calculation of an upper bound to the overturning probability as well as to the representation of an optimal control strategy. The Melnikov criterion for stochastic rocking oscillations in the presence of convenient control strategies are derived explicitly for the first time, using an extension of the Melnikov theory to a model with fractional derivative.

A large deviation principle for fluids of third grade

ABSTRACT This article establishes a large deviation principle for a non-Newtonian fluid of differential type, filling a two-dimensional non-axisymmetric bounded domain with slip boundary conditions. More precisely, we show that the solutions of small stochastic white noise perturbations of the third grade fluid equations converges to the deterministic solution, as the intensity of the noise goes to zero. Moreover, this convergence has an exponential rate given by a suitable rate function. To establish such asymptotic result, we follow the weak convergence approach introduced by Budhiraja, Dupuis and Ellis.

Mutation detection and fast identification of switching system based on data-driven method

In the engineering field, switching systems have been extensively studied, where sudden changes of parameter value and structural form have a significant impact on the operational performance of the system. Therefore, it is important to predict the behavior of the switching system, which includes the accurate detection of mutation points and rapid reidentification of the model. However, few efforts have been contributed to accurately locating the mutation points. In this paper, we propose a new measure of mutation detection — the threshold-based switching index by analogy with the Lyapunov exponent. We give the algorithm for selecting the optimal threshold, which greatly reduces the additional data collection and the relative error of mutation detection. In the system identification part, considering the small data amount available and noise in the data, the abrupt sparse Bayesian regression (abrupt-SBR) method is proposed. This method captures the model changes by updating the previously identified model, which requires less data and is more robust to noise than identifying the new model from scratch. With two representative dynamical systems, we illustrate the application and effectiveness of the proposed methods. Our research contributes to the accurate prediction and possible control of switching system behavior.

Multipath Mitigation for BOC Signals Based on Prompt-Assisted-Offset Correlator

Tracking ambiguity and multipath are two serious threats in processing binary offset carrier (BOC) signals that are widely used in global navigation satellite systems (GNSS). Three-loop tracking methods, such as dual binary phase-shift keying tracking (DBT), use a delay lock loop (DLL), a phase lock loop (PLL), and a subcarrier PLL (SPLL) to track the code, carrier, and subcarrier, respectively, thus solving the tracking ambiguity problem. However, the multipath remains an important factor in the ranging performance deterioration of these tracking methods. Using the offset correlator (OC) technique in the SPLL can effectively mitigate subcarrier multipath errors, but it substantially raises thermal noise errors. To solve this contradiction, this paper proposes a prompt-assisted-offset correlator (PAOC) technique that combines the prompt and offset correlators in a complementary way to mitigate multipath for BOC signals. Compared with the original OC technique, the PAOC technique has less thermal noise performance loss. Moreover, this paper discovers and quantifies the interaction between carrier and subcarrier multipath errors by analyzing the coupling effect between SPLL and PLL. Most multipath mitigation methods for BOC signals ignore the carrier multipath in the PLL, so their subcarrier multipath performance is not optimal. Thus, this paper further proposes applying the PAOC technique in both PLL and SPLL to mitigate carrier and subcarrier multipath errors simultaneously. Theoretical analysis and experimental results demonstrate that the proposed method can significantly improve the multipath performance with small noise performance loss.

Development of flapping wing robot and vision-based obstacle avoidance strategy.

Due to the flight characteristics such as small size, low noise, and high efficiency, studies on flapping wing robots are being actively conducted. In particular, the flapping wing robot is in the spotlight in the field of search and reconnaissance. Most of the research focuses on the development of flapping wing robots rather than autonomous flight. However, because of the unique characteristics of flapping wings, it is essential to consider the development of flapping wing robots and autonomous flight simultaneously. In this article, we describe the development of the flapping wing robot and computationally efficient vision-based obstacle avoidance algorithm suitable for the lightweight robot. We developed a 27 cm and 45 g flapping wing robot named CNUX Mini that features an X-type wing and tailed configuration to attenuate oscillation caused by flapping motion. The flight experiment showed that the robot is capable of stable flight for 1.5 min and changing its direction with a small turn radius in a slow forward flight condition. For the obstacle detection algorithm, the appearance variation cue is used with the optical flow-based algorithm to cope robustly with the motion-blurred and feature-less images obtained during flight. If the obstacle is detected during straight flight, the avoidance maneuver is conducted for a certain period, depending on the state machine logic. The proposed obstacle avoidance algorithm was validated in ground tests using a testbed. The experiment shows that the CNUX Mini performs a suitable evasive maneuver with 90.2% success rate in 50 incoming obstacle situations.

Thermal oscillation in the hybrid Si3N4 - TiO2 microring.

The hybrid microcavity composed of different materials shows unique thermal-optical properties such as resonance frequency shift and small thermal noise fluctuations with the temperature variation. Here, we have fabricated the hybrid Si3N4 - TiO2 microring, which decreases the effective thermo-optical coefficients (TOC) from 23.2pm/K to 11.05pm/K due to the opposite TOC of these two materials. In this hybrid microring, we experimentally study the thermal dynamic with different input powers and scanning speeds. The distorted transmission and thermal oscillation are observed, which results from the non-uniform scanning speed and the different thermal relaxation times of the Si3N4 and the TiO2. We calibrate the distorted transmission spectrum for the resonance measurement at the reverse scanning direction and explain the thermal oscillation with a thermal-optical coupled model. Finally, we analyse the thermal oscillation condition and give the diagram about the oscillation region, which has significant guidance for the occurrence and avoidance of the thermal oscillation in practical applications.

Coexisting Attractors and Multistate Noise-Induced Intermittency in a Cycle Ring of Rulkov Neurons

We study dynamics of a unidirectional ring of three Rulkov neurons coupled by chemical synapses. We consider both deterministic and stochastic models. In the deterministic case, the neural dynamics transforms from a stable equilibrium into complex oscillatory regimes (periodic or chaotic) when the coupling strength is increased. The coexistence of complete synchronization, phase synchronization, and partial synchronization is observed. In the partial synchronization state either two neurons are synchronized and the third is in antiphase, or more complex combinations of synchronous and asynchronous interaction occur. In the stochastic model, we observe noise-induced destruction of complete synchronization leading to multistate intermittency between synchronous and asynchronous modes. We show that even small noise can transform the system from the regime of regular complete synchronization into the regime of asynchronous chaotic oscillations.

Stochastic resonance of a multi-stable system and its application in bearing fault diagnosis

This paper investigates the stochastic resonance and mean-first passage time of a quad-stable potential in the presence of Gaussian white noise and periodic forcing. The analytical expressions of mean-first passage time and spectral amplification are obtained, respectively. It is found that even small noise intensity can lead to noise-assisted hopping between two adjacent potential wells for the case of small damping coefficient. For large noise intensity, the escape process of Brownian particles is accelerated in an underdamped nonlinear system. Moreover, the curve of spectral amplification displays a typical resonant peak at an optimal noise intensity, suggesting the onset of stochastic resonance. Meanwhile, with the decrease of periodic signal frequency, the peak value of spectral amplification is enhanced. Especially, an optimal quad-stable potential structure exists to maximize the stochastic resonance effect. The proposed multi-stable stochastic resonance method is applied to the fault diagnosis of inner and outer race bearing, and the quantum particle swarm optimization algorithm is used to optimize the system parameters and damping coefficient. The good agreement between fault frequency and theoretical value validates efficiency of the proposed method. Compared with the overdamped tri-stable stochastic resonance method, the performance of fault diagnosis is enhanced substantially by the proposed method.

Quasipotentials for coupled escape problems and the gate-height bifurcation.

The escape statistics of a gradient dynamical system perturbed by noise can be estimated using properties of the associated potential landscape. More generally, the Freidlin and Wentzell quasipotential (QP) can be used for similar purposes, but computing this is nontrivial and it is only defined relative to some starting point. In this paper we focus on computing quasipotentials for coupled bistable units, numerically solving a Hamilton- Jacobi-Bellman type problem. We analyze noise induced transitions using the QP in cases where there is no potential for the coupled system. Gates (points on the boundary of basin of attraction that have minimal QP relative to that attractor) are used to understand the escape rates from the basin, but these gates can undergo a global change as coupling strength is changed. Such a global gate-height bifurcation is a generic qualitative transition in the escape properties of parametrized nongradient dynamical systems for small noise.

Tailored Supramolecular Cage for Efficient Bio-Labeling.

Fluorescent chemosensors are powerful imaging tools used in a broad range of biomedical fields. However, the application of fluorescent dyes in bioimaging still remains challenging, with small Stokes shifts, interfering signals, background noise, and self-quenching on current microscope configurations. In this work, we reported a supramolecular cage (CA) by coordination-driven self-assembly of benzothiadiazole derivatives and Eu(OTf)3. The CA exhibited high fluorescence with a quantum yield (QY) of 38.57%, good photoluminescence (PL) stability, and a large Stokes shift (153 nm). Furthermore, the CCK-8 assay against U87 glioblastoma cells verified the low cytotoxicity of CA. We revealed that the designed probes could be used as U87 cells targeting bioimaging.

Stability and constructions of the Poincaré maps for a class of stochastic partial differential equations

This work is concerned with a class of stochastic partial differential equations with a multiplicative noise. The Poincaré map, as a main tool to study the periodic orbits, plays a crucially important role in the invariant sets of the system, which captures the dominated dynamical behavior of the trajectories. It derives out the existence and the stability of the stochastic Poincaré maps of the system, which return to a small neighborhood of a fixed point of a deterministic Poincaré map one time or even infinite times with the small noise disturbing. It further expresses the constructions of the stochastic Poincaré maps through the random invariant manifold and the moving orthonormal system.

KPZ equation with a small noise, deep upper tail and limit shape

In this paper, we consider the KPZ equation under the weak noise scaling. That is, we introduce a small parameter $$\sqrt{\varepsilon }$$ in front of the noise and let $$\varepsilon \rightarrow 0$$ . We prove that the one-point large deviation rate function has a $$\frac{3}{2}$$ power law in the deep upper tail. Furthermore, by forcing the value of the KPZ equation at a point to be very large, we prove a limit shape of the solution of the KPZ equation as $$\varepsilon \rightarrow 0$$ . This confirms the physics prediction in Hartmann et al. (Phys Rev Res 1(3):032043, 2019), Kolokolov and Korshunov (Phys Rev B 75(14):140201, 2007, Phys Rev E 80(3):031107, 2009), Kamenev et al. (Phys Rev E 94(3):032108, 2016), Le Doussal et al. (Phys Rev Lett 117(7):070403, 2016) and Meerson et al. (Phys Rev Lett 116(7):070601, 2016).

µ-CT Investigation of Hydrogen-Induced Cracks and Segregation Effects in Austenitic Stainless Steel

Hydrogen can drastically degrade the mechanical properties of a variety of metallic materials. The so-called hydrogen environment embrittlement of austenitic CrNi-type steels is usually accompanied by the formation of secondary surface cracks, which can be investigated in order to assess the embrittlement process. The occurrence of hydrogen-induced cracks is often related to element segregation effects that locally impact the austenite stability. Since there is as yet a lack of investigation methods that can visualize both structures three-dimensionally, the present study investigates the imageability of hydrogen-induced cracks and element segregation structures in austenitic CrNi-steel via micro-computed tomography (CT). In order to improve the X-ray visibility of segregation structures, modified versions of the reference steel, X2CrNi18-9, that contain W and Si are designed and investigated. The investigations demonstrated that small differences in the X-ray attenuation, caused by the W or Si modifications, can be detected via CT, although segregation structures could not be imaged due to their small size scale and image noise. Hydrogen-induced cracks were characterized successfully; however, the detection of the smaller cracks is limited by the resolution capability.

Symmetries and Zero Modes in Sample Path Large Deviations

Sharp large deviation estimates for stochastic differential equations with small noise, based on minimizing the Freidlin–Wentzell action functional under appropriate boundary conditions, can be obtained by integrating certain matrix Riccati differential equations along the large deviation minimizers or instantons, either forward or backward in time. Previous works in this direction often rely on the existence of isolated minimizers with positive definite second variation. By adopting techniques from field theory and explicitly evaluating the large deviation prefactors as functional determinant ratios using Forman’s theorem, we extend the approach to general systems where degenerate submanifolds of minimizers exist. The key technique for this is a boundary-type regularization of the second variation operator. This extension is particularly relevant if the system possesses continuous symmetries that are broken by the instantons. We find that removing the vanishing eigenvalues associated with the zero modes is possible within the Riccati formulation and amounts to modifying the initial or final conditions and evaluation of the Riccati matrices. We apply our results in multiple examples including a dynamical phase transition for the average surface height in short-time large deviations of the one-dimensional Kardar–Parisi–Zhang equation with flat initial profile.

THE EFFECT OF AN ADDITIVE NOISE ON SOME SLOW-FAST EQUATION NEAR A TRANSCRITICAL POINT

We consider the effect of small additive noise with intensity $\sigma$ on trajectories of a slow-fast system with small parameter $\varepsilon$ which admits bifurcation delay at a transcritical point. We estimate the probability that the perturbed stochastic paths stay in some tubular neighborhood of the deterministic path to show that small but not exponentially small noise destroys the bifurcation delay caused by transcritical point and obtain a noise intensity threshold value $N(\varepsilon)$ of order $\varepsilon^{\frac{3}{4}}$. When <i>e</i>^{-1/$\varepsilon$}《<i>σ</i>＜$N(\varepsilon)$, the paths are likely to leave the neighborhood of the corresponding determinate path before some time of order $\sqrt{\varepsilon|log\sigma|}$. When $\sigma>N(\varepsilon) $, the paths are likely to leave before some time of order $\sigma^{\frac{2}{3}}$.

Destabilising nonnormal stochastic differential equations

&lt;p style='text-indent:20px;'&gt;In this article we address the stability of linear stochastic differential equations. In particular, we focus our attention on non-normality in stochastic differential equations. Following Higham and Mao we study a test problem for non-normal stochastic differential equations, that is stable without noise, and prove a property conjectured by Higham and Mao, that is that an exponentially small (in the dimension) noise term is able to destabilise in a mean-square sense the solution of the SDE.&lt;/p&gt;

Scalable Small Signal and Noise Modeling of InP HEMT for THz Application

Scalable Small Signal and Noise Modeling of InP HEMT for THz Application