Steady-state Density Research Articles

Unveiling the principles of stochastic resonance and complex potential functions for bearing fault diagnosis

This paper introduces a novel and complex Unsaturated Piecewise Linear Quad-Stable Stochastic Resonance System (UPLQSR) to address the issue of output saturation in the Classical Quad-Stable Stochastic Resonance (CQSR) system. By linearizing the structure of the potential function, the constraints imposed by high-order terms are effectively eliminated, allowing Brownian particles to move more freely. Numerical simulations demonstrate that UPLQSR achieves significantly higher output signal amplitudes compared to CQSR, highlighting its remarkable signal amplification capability. By analyzing the structure of the potential function, the relationship between the height of the potential barrier and the aggressiveness of the particles jumping is determined. Utilizing adiabatic approximation theory, the paper derives the Steady-state Probability Density (SPD), Mean First Passage Time (MFPT), and Spectral Amplification (SA), revealing the specific process of the particle jumping, as well as the influence of the parameters on the performance of the UPLQSR. After optimizing parameters using the Adaptive Genetic Algorithm (GA), UPLQSR is applied to the early fault diagnosis of various bearing models under Gaussian white noise, demonstrating superior fault detection capabilities. In summary, this study pioneered the theory of non-saturation of quad-stable systems, optimized the weak signal detection technique, and provided a more accurate means of signal identification and analysis, highlighting its great value of application in engineering.

Stochastic resonance in Hindmarsh-Rose neural model driven by multiplicative and additive Gaussian noise

This paper investigates the occurrence of stochastic resonance in the three-dimensional Hindmarsh-Rose (HR) neural model driven by both multiplicative and additive Gaussian noise. Firstly, the three-dimensional HR neural model is transformed into the one-dimensional Langevin equation of the HR neural model using the adiabatic elimination method, and the effects of HR neural model parameters on the potential function are analyzed. Secondly the Steady-state Probability Density (SPD), the Mean First-Passage Time (MFPT), and the Signal-to-Noise Ratio (SNR) of the HR neural model are derived, based on two-state theory. Then, the effects of different parameters (a, b, c, s), noise intensity, and the signal amplitude on these metrics are analyzed through theoretical simulations, and the behavior of particles in a potential well is used to analyze how to choose the right parameters to achieve high-performance stochastic resonance. Finally, numerical simulations conducted with the fourth-order Runge–Kutta algorithm demonstrate the superiority of the HR neural model over the classical bistable stochastic resonance (CBSR) in terms of performance. The peak SNR of the HR neural model is 0.63 dB higher than that of the CBSR system. Simulation results indicate that the occurrence of stochastic resonance occur happens in HR neural model under different values of parameters. Furthermore, under certain conditions, there is a ‘suppress’ phenomenon that can be produced by changes in noise, which provides great feasibilities and practical value for engineering application.

Stochastic modelling of Karlotoxin influence on prey

Abstract Karlodinium veneficum is type of dinoflagellate plankton present in coastal regions. Harmful algae blooms resulting from uncontrolled growth of K. veneficum often leads to fish kills. They release a toxin named Karlotoxin that is known to affect their prey’s bio-locomotion by stunning and slowing them down. We investigate whether the toxin plays a role in aggregating the prey around the a predator, thereby leading to a local increase in prey density. To achieve this, we closely examine the toxin’s influence on the prey’s probability density distribution with different assumptions on their relative speed in 1D, with either the predator being stationary or swimming at a constant speed. When the predator is stationary, we fully solve the prey’s density distribution for all times, and verify the result by a Monte-Carlo simulation. For a swimming predator, we find the steady-state density distribution of prey analytically. When the predator’s speed $s$ is strictly greater (or less) than the prey ($s-1>0$ or $s-1<0$), the results are verified by Monte-Carlo simulations; when their relative speed $s-1$ has roots, we use the Frobenius method to perform a local analysis for the prey’s density at steady state near the roots, and use the result to derive a scheme for finding the analytical solution. This solution is then verified numerically using a finite difference method. When the roots $x_{1}$ and $x_{3}$ satisfy $s^{\prime}(x_{1})<0$ and $s^{\prime}(x_{3})>0$, we show that the probability density for the prey has a form $|x-x_{1}|^{-s^{\prime}(x_{1})^{-1} -1}$ near the root $x_{1}$, leading to either an integrable singularity or a local maximum. Near the root $x_{3}$, the prey’s density can be represented as a Taylor series and is smooth. In most of the cases mentioned above, toxin leads to the aggregation of prey, however the maximum density does not always occur where the toxin has the highest concentration.

‘Life’ of dust originating from the irregular satellites of Jupiter

ABSTRACT The irregular satellites of Jupiter produce dust particles through the impact of interplanetary micrometeoroids. In this paper, the dynamics of these particles is studied by both high-accuracy numerical simulation and analytical theory, in order to learn their transport, final fate, and spatial distribution. The perturbation forces that are considered in our dynamical model include the solar radiation pressure, solar gravity, Poynting–Robertson drag, Jovian oblateness, and the Galilean satellites’ gravity. The trajectories of different size particles are simulated until they hit Jupiter, the Galilean satellites, or escape from the Jovian system. The average dynamical lifetimes of dust with different grain sizes are calculated, and the final fate of dust particles is reported and analysed. The steady-state spatial number density of particles is estimated by integrating the trajectories of dust particles over their initial size distribution, and compared to the previous work. The impact sites of dust on Callisto’s surface are recorded and provide an important clue for the study of the hemisphere asymmetry of Callisto. Besides, the mass accretion rate, cross-sectional area influx, and mass influx density of dust on Callisto are calculated. A ring outside the orbit of Callisto dominated by dust between 2 and 25 µm from Jupiter’s irregular satellites is suggested, with the average normal geometric optical depth of the order of 10−8 and the configuration of the ring ansae similar to Jupiter’s gossamer rings.

A Novel Two-Dimensional Quad-Stable Stochastic Resonance System for Bearing Fault Detection

A novel two-dimensional Quad-stable stochastic resonance (NTDQSR) system is proposed in this paper to address the poor signal detection capability of the original one-dimensional Quad-stable stochastic resonance (ODQSR) system. Firstly, expressions for the equivalent potential function and the steady-state probability density (SPD) function of the system are derived to study the impact of parameters on it. Secondly, the system is simulated numerically, and the performance of NTDQSR system is evaluated under trichotomous noise in this paper, because trichotomous noise exists widely in practical applications. Finally, the genetic algorithm (GA) is used to optimize the system parameters, and NTDQSR system is applied to bearing fault detection. In LDK UER204 ring fault detection, MSNRG in NTDQSR system is 0.9927 dB and 0.4805 dB higher than ODQSR and under-damped Quad-stable stochastic resonance (UQSR) system. In the outer ring experiment on the experimental bench at CWRU, MSNRG in NTDQSR system is 0.7255dB and 0.0734dB higher than the other two systems, while in the inner ring experiment, MSNRG is 0.6535dB and 0.1943dB higher than the other two systems, respectively. NTDQSR system is compared with ODQSR and UQSR systems to verify the good application value of NTDQSR system in practical engineering.

Dual-channel two-dimensional stochastic resonance and its application in bearing fault detection under alpha-stable noise

Coupled two-dimensional stochastic resonance (CTDSR) systems exhibit a higher quantity of steady-states and hold significant theoretical and practical value. However, the coupling between nonlinear systems generates multiplicative noise, which impairs signal transmission. In this paper, a novel dual-channel two-dimensional stochastic resonance (DCTDSR) model is proposed to harness multiplicative noise for enhancing system output. It is evident from the potential well analysis that multiplicative noise causes variations in the properties and amounts (from 2 to 4) of resonance peaks in the DCTDSR system. The steady-state probability density (SPD) of the novel system is derived by implementing the adiabatic approximation theory. In the background of alpha-stable noise, simulation results indicate that the DCTDSR system exhibits heightened detection capabilities for weak signals that are immersed in severe impulsive and heavy-tailed noise. Based on the stability of alpha-stable noise, an adaptive stochastic resonance fault diagnosis method that adjusts both parameters and multiplicative noise is designed to overcome the issue of insufficient single energy regulation. Experimental results have demonstrated that the DCTDSR system boosts noise energy transmission and offers improved bearing fault detection accuracy. Thus, effectively utilizing multiplicative alpha-stable noise can further enhance the practical applicability of stochastic resonance theory in engineering.

Nitrogen-doped reduced graphene oxide/black phosphorus quantum dot composites for electrocatalytic treatment of choroidal melanoma

Choroidal melanoma (CM) is a melanocyte-derived intraocular malignancy that poses a great threat to patients’ vision and life. Electrochemical therapy, which relies on the generation of reactive oxygen species via an oxygen reduction reaction (ORR) to kill target cells, has emerged as a promising approach for the local treatment of malignant tumors. In this study, nitrogen-doped reduced graphene oxide (N-rGO) was electrostatically bound with black phosphorus (BP) quantum dots to form a composite system (N-rGO-BP) for tumor therapy. Owing to the synergistic effect of the two components, the optimal catalyst (N-rGO-BP-12) exhibits improved electrochemical properties and stability, achieving a more positive half-wave potential of 0.66 V and a larger steady-state current density of 2.76 mA cm−2 compared with the N-rGO precursor. In electrochemical therapy, N-rGO-BP-12 undergoes ORR via a two-electron pathway in the acidic microenvironment of the tumor, producing large amounts of hydrogen peroxide and hydroxyl radical to kill tumor cells; only 25 % of the human CM cells survive after 3 h of the treatment. This study provides a new approach for the synthesis and application of electrochemical catalysts for clinical tumor therapy.

The enhanced photoelectric performances and capacitance effects of In2O3/3D rGO

In this study, Indium oxide (In2O3) and 3D reduced graphene oxide (3D rGO) composites were obtained by hydrothermal treatment. The structure composition, morphology, surface area and band gap of In2O3/3D rGO were analyzed by a series of techniques. The relationship between the photoelectric properties and capacitance of In2O3/3D rGO composites with various mass proportions was investigated, and the results indicated that the steady-state photocurrent density of In2O3/3D rGO increased and then started to drop with the increase of the specific capacitance. The current density of In2O3/3D rGO reached a maximum of 0.11 mA/cm2 at the intermediate specific capacitance (77.8 mF/cm2). This photocurrent trend of the composites was attributed to the positive and negative effects of capacitance. The proper capacitance might result in the low recombination rate of photogenerated carriers and holes, while the overlarge capacitance might limit the release of electrons, thus reducing the photocurrent generation. This research result was expected to provide favorable conditions for further applications of 3D graphene and new strategies to improve the photoelectric performance of In2O3.

Adaptive detection of impact signals with two-dimensional piecewise tri-stable stochastic resonance and its application in bearing fault diagnosis

In this paper, we introduce an innovative method known as Adaptive Two-Dimensional Piecewise Tri-Stable Stochastic Resonance (TDPTSR) and discuss its applicability in extracting weak fault features. Initially, addressing the saturation issue of the Standard Tri-Stable Stochastic Resonance (STSR) system, we construct a novel piecewise tri-stable potential function. This function independently adjusts the depth and width of potential wells. We explore the particle output characteristics of the Piecewise Tri-Stable Stochastic Resonance (PTSR) system using the fourth-order Runge-Kutta algorithm. Subsequently, we delve into the performance analysis of the TDPTSR system. Leveraging adiabatic approximation theory, we derive the equivalent potential function, steady-state probability density (SPD), mean first-pass time (MFPT), and output signal-to-noise ratio (SNR) of the TDPTSR. We also investigate the impact of changes in system parameters on these metrics. Additionally, drawing from kurtosis and cosine similarity properties, we introduce a Modified Kurtosis Index (MKC) as a measurement index for impact signal detection. We propose a method for impact signal feature extraction by integrating MKC with the TDPTSR system. Simulation analysis demonstrates the suitability of MKC as an index for quantifying Stochastic Resonance and the superior detection capability of the TDPTSR system. Finally, we apply TDPTSR to the fault diagnosis of two types of bearings, optimizing system parameters using a genetic algorithm (GA). Comparative analysis with STSR and PTSR confirms that our proposed method in this paper yields further improvements in Signal-to-Noise Ratio Improvement (SNRI), higher spectral peak magnitude (Amout) at characteristic frequencies, and increased recognition quantity (Δ).

Electrosynthesis of Superhydrophilic Nickel Nanosheets on a Three-Dimensional Microporous Template: Applicability toward MOR.

In this report, a nickel nanoscaled morphology was synthesized by two-step cathodic electrodeposition on a microporous copper template. The resulting morphology, nanosheets formed on 3D micropores, offers incredible cyclic stability of almost 100% and facilitates transport mechanisms while significantly preserving the active surface area. The origin of the nanosheets is assumed to be the presence of a small amount of iron cations in the electrolyte bath during the final deposition step. By altering the deposition current density of this step, three samples were prepared and compared in terms of the resulting morphology, chemical composition, surface area, wettability, and activation toward the methanol oxidation Reaction. Results show that an increase in the deposition current density in the range of this study produces finer and denser nanosheets, a higher content of reduced iron, a larger surface area, and greater activity toward MOR. The current density for methanol oxidation was exceptional among all other studies on nickel-containing electrocatalysts, yielding a steady-state current density of 135 mA cm-2 at 600 mV versus SCE. All samples offered superhydrophilicity.

Carbon Nanotube-Supported Bimetallic Core-Shell (M@Pd/CNT (M: Zn, Mn, Ag, Co, V, Ni)) Cathode Catalysts for H2O2 Fuel Cells.

M@Pd/CNT (M: Zn, Mn, Ag, Co, V, Ni) core-shell and Pd/CNT nanoparticles were prepared by sodium borohydride reduction and explored as cathode catalysts for the hydrogen peroxide reduction reaction. Electrochemical and physical characterization techniques are applied to explore the characteristics of the produced electrocatalysts. The cyclic voltammetry (CV) experiments show that Zn@Pd/CNT-modified electrodes have a current density of 273.2 mA cm-2, which is 3.95 times higher than that of Pd/CNT. According to the chronoamperometric curves, Zn@Pd/CNT has the highest steady-state current density for the H2O2 electro-reduction process among the synthesized electrocatalysts. Moreover, electrochemical impedance spectroscopy (EIS) spectra confirmed the previous electrochemical results due to the lowest charge transfer resistance (35 Ω) with respect to other electrocatalysts.

Active Brownian particles can mimic the pattern of the substrate

ABSTRACT Active Brownian particles (ABPs) have been identified as a successful way of modeling the moving microorganism on the substrate. In recent studies, it is shown that such organisms can sense the characteristics of the substrate. Motivated by such work, we studied the dynamics and the steady state of ABP moving on a substrate with space-dependent activity. On the substrate, some regions are marked as high in activity, and other regions are such that particles behave as passive Brownian particles. The system is studied in two dimensions with step, sigmoid, Gaussian, and cone shape distribution of activity profile on the substrate. The whole interface of the activity profile is symmetrically divided into two regions. This led to the flow of particles from the active region to the passive region. The final steady state of particle density profile, polarization and flux very much follows the structure of the inhomogeneous activity, and the density in high activity region is lower, maximum at the interface and nearly constant with mean density in the passive region. Further, the steady state density profile for various shapes and designs on two-dimensional substrates is studied. Hence, the collection of ABPs on an inhomogeneous substrate can mimic the inhomogeneity of the substrate.

Free vibration of a bi-layered composite plate of a piezoelectric semiconductor and a piezoelectric dielectric

We study the free vibration of a piezoelectric bi-layered plate composed of a piezoelectric semiconductor (PS) layer and a piezoelectric dielectric (PD) layer. The macroscopic theory of a PS consisting of the conventional theory of piezoelectricity and the drift-diffusion theory of semiconductors is used. The nonlinear equations for drift currents of electrons and holes are linearized for small perturbation of carrier density. The first-order zigzag approximation for in-plane displacements and electric potential through the thickness of each layer is used. Interfacial continuity of the displacement, the transverse shear stress, and the electric potential between the PS layer and the PD layer is ensured, which is very important and also experienced by layered structures. The number of independent unknown variables is reduced from 11 to 5 by using the interfacial continuity and the zero shear stress conditions at the top and bottom surfaces. The governing equation and corresponding boundary condition are derived using Hamilton’s principle. An analytical solution of a simply supported composite plate is obtained. The effects of steady-state electron density, axial force, and the geometric parameters on the vibration frequency and modes are discussed. The obtained results may be useful for further theoretical analysis of PS composites and practical application of piezotronic devices made from PS and PD materials.

Exploring Optical Nanofibers for Atom-Photon Hybrid Quantum Systems: Chirality Effects and Optical Forces

Recent advancements have revealed the growing effectiveness of optical nanofibers in enabling the implementation of atom-photon hybrid quantum systems. These nanofibers serve as non-intrusive tools for probing cold atoms, offering a unique approach to circumvent the limitations imposed by the Rayleigh domain, thereby achieving increased intensities in a beam of light over long distances. This study investigates the interaction between the atom and light, focusing on the dipole transition in sodium atoms near a nanofiber. Notably, we uncover the influence of the direction of light propagation, known as the optical chirality effect, on the spatial distribution of the steady-state density matrix elements. Furthermore, we examine the optical forces acting on a two-level atom during the 32S1/2 →32P3/2 transition in sodium. Our findings demonstrate that optical chirality’s effect significantly impacts the magnitude of these optical forces. The concept of optical chirality holds great promise for advancing technology and enhancing our understanding of atomic behavior. The numerical results presented in this work are based on experimental parameters within a realistic range.

Run-and-tumble motion in a linear ratchet potential: Analytic solution, power extraction, and first-passage properties.

We explore the properties of run-and-tumble particles moving in a piecewise-linear "ratchet" potential by deriving analytic results for the system's steady-state probability density, current, entropy production rate, extractable power, and thermodynamic efficiency. The ratchet's broken spatial symmetry rectifies the particles' self-propelled motion, resulting in a positive current that peaks at finite values of the diffusion strength, ratchet height, and particle self-propulsion speed. Similar nonmonotonic behavior is also observed for the extractable power and efficiency. We find the optimal apex position for generating maximum current varies with diffusion and that entropy production can have nonmonotonic dependence on diffusion. In particular, for vanishing diffusion, entropy production remains finite when particle self-propulsion is weaker than the ratchet force. Furthermore, power extraction with near-perfect efficiency is achievable in certain parameter regimes due to the simplifications afforded by modeling "dry" active particles. In the final part, we derive mean first-passage times and splitting probabilities for different boundary and initial conditions. This work connects the study of work extraction from active matter with exactly solvable active particle models and will therefore facilitate the design of active engines through these analytic results.

Study on the Evolution of Risk Contagion in Urban River Ecological Management Projects Based on SEIRS

The risk transmission mechanisms of urban river ecological management engineering projects are examined in this study. Using the Susceptible Exposed Infectious Recovered Susceptible (SEIRS) model for risk transmission, a model of risk propagation delay for urban river ecological management engineering projects on scale-free networks is developed, which takes into account the effects of risk propagation and delay. We conducted a steady-state analysis of the model and obtained the basic reproduction number R. When R > 1, the equilibrium point of risk outbreak is stable, and when R < 1, the equilibrium point of risk disappearance is stable. Numerical simulations of the model were conducted using the MATLAB2022b to reveal the dynamic propagation patterns of risk in urban river ecological management engineering projects. The research results show that the steady-state density of the infected nodes in the network increases with the increase in the effective propagation rate and the propagation delay time; the propagation delay reduces the risk propagation threshold in the network and accelerates the occurrence of the equilibrium state of risk outbreak. There is a correlation between the transmission rate of latent nodes and the transmission rate of infected nodes, and the effective transmission rate of latent nodes has a greater influence on risk propagation. The spread of risk in the network can be effectively controlled and mitigated with targeted immunity for susceptible nodes. This article, based on the theory of complex networks and the mean-field theory, takes into account the propagation delay and spreading of latent nodes. Building a D-SEIRS model for risk propagation broadens the research perspective on urban river ecological management risk propagation.

Time-Dependent Power-Law Growth of Oxide with Anomalous Diffusion in the Thermal Oxidation of 4H-SiC\((11\bar{2}0)\) and 4H-SiC\((000\bar{1})\)

A model for the oxide growth in the thermal oxidation of SiC with a non-polar surface orientation is proposed. It is based on the reaction–diffusion equations (RDEs), in which the diffusion of both SiO and O2 molecules is considered. By taking the 4H-SiC\((11\bar{2}0)\) a-face as an example, the RDEs are integrated numerically at the oxidation temperature of T = 1150 °C and the partial pressure of oxygen molecules in the ambient environment of Pox = 0.25, 0.5, 1, 2, and 4 (atm). By analyzing the simulation results on the evolution of the oxide thickness xo, it is found that xo obtained by the simulations and those of the experiments reported in the literature collapse onto a single curve when they are plotted against the rescaled time t′ = (ωp/ω1)t, where t denotes the oxidation time and ωp is defined as ωp = Θs(Pox)νinc. Here, Θs(Pox) and νinc denote the steady-state density of the oxygen molecules chemisorbed on the oxide surface and the prefactor for the incorporation rate of the oxygen molecules from the oxide surface into the oxide layer, respectively; ω1 is a constant, which is given by \(\omega_{1} = \omega_{p}|_{P_{\text{ox}} = 1(\text{atm})}\). The curve yielded by the collapse is found to follow the time-dependent power law (TDPL) as xo(t) ∝ (t/τ)ν(t), where the exponent ν(t) is given by \(\nu (t) = 0.565 + 0.2/(1 + \sqrt{2t/\tau } )\) with τ [= 1 (h)] a constant. This property is found to be valid also for the oxidation of a polar surface, 4H-SiC\((000\bar{1})\), by comparing the results of the calculations according to xo(t) ∝ (t/τ)ν(t) with the experiments reported in the literature. Therefore, the oxide growth in these systems follows the TDPL with the anomalous diffusion of νD = 0.565, which is larger than the normal diffusion of νD = 0.5 observed in the thermal oxidation of Si. In addition, the transition between the etching mode at low Pox and the oxidation mode at high Pox on the 4H-SiC\((11\bar{2}0)\) a-face is found to occur at \(P_{\text{c}} \simeq 0.73\) (atm) at T = 1150 °C.

Inhibitory effect of La3+ on hydrogen damage of 27CrMo44S/1 steel in H2S-containing acidic solution

The effect of La3+ on the hydrogen permeation behavior of 27CrMo44S/1 steel in acidic environments containing H2S is investigated through the measurement of steady-state permeation current density (i∞), hydrogen diffusivity (D), and subsurface hydrogen concentration (C0). Results indicate that the addition of La3+ can remarkably reduce i∞. The corrosion products with La3+ involved in the film formation process in the H2S-free environment have a good hydrogen barrier effect, but the addition of La3+ hardly influence the D value of 27CrMo44S/1 steel in the H2S-containing environment. However, the presence of La3+ substantially reduces the C0 on metal surface regardless of the presence of H2S in the solution. Static immersion and tensile experiments illustrate that the addition of La3+ can improve the corrosion resistence and plasticity loss of the material in the H2S environment.

Stochastic dynamics and first passage analysis of iced transmission lines via path integration method

The mechanism of stochastic factors in wind load on iced transmission line galloping has attracted widespread attention. In this paper, the random part of wind load is simulated by Gaussian white noise, and a galloping model of the iced transmission line excited by stochastic wind is established. The path integration method based on the Gauss–Legendre formula and short-time approximation is used to solve the steady-state probability density function of the system and the evolution of the transient probability density. The resonance response of the system is considered when the fluctuating wind acts. Meanwhile, through path integration, the stability of galloping motion is evaluated based on the first passage theory. Comparing with the Monte Carlo simulation, the effectiveness of the proposed method is verified. It turns out that the large external excitation intensity and the small natural frequency are not conducive to the stability of iced transmission line galloping.

Integrated capture and solar-driven utilization of CO2 from flue gas and air

Integrated capture and solar-driven utilization of CO2 from flue gas and air