Stochastic Phase Research Articles

Stochastic Phase Model with Reflective Boundary and Induced Beating: An Approach for Cardiac Muscle Cells

We examine stochastic phase models for the community effect of cardiac muscle cells. Our model extends the stochastic integrate-and-fire model by incorporating irreversibility after beating, induced beating, and refractoriness. We focus on investigating the expectation and variance in the synchronized beating interval. Specifically, for a single isolated cell, we obtain the closed-form expectation and variance in the beating interval, discovering that the coefficient of variation has an upper limit of 2/3. For two coupled cells, we derive the partial differential equations for the expected synchronized beating intervals and the distribution density of phases. Furthermore, we consider the conventional Kuramoto model for both two- and N-cell models. We establish a new analysis using stochastic calculus to obtain the coefficient of variation in the synchronized beating interval, thereby improving upon existing literature.

A theoretical study of a radiofrequency wave propagation through a realistic turbulent marine atmospheric boundary layer based on large eddy simulation

This study aims at modeling and investigating the impact of realistic turbulence inhomogeneity on radiowave propagation by utilizing large eddy simulations (LES). An up-to-date version of the X-LES method for generating realistic turbulent phase screens is first introduced. It combines atmospheric simulations with the classical Tatarski statistical modeling. This method naturally incorporates vertical turbulence inhomogeneity into phase screens at scales resolved by LES. It is then extended to sub-grid scales by weighting statistically generated phase variations with the vertical profile of the turbulent structure constant extracted from atmospheric data. This method is applied to replicate turbulence of a classical tropical marine atmospheric boundary layer. The impact of the generated medium on the propagation of a 10 GHz spherical wave emanating from a Gaussian aperture is analyzed through a statistical study of log-amplitude profiles performed for three different source altitudes. Results first show that contrary to a classical homogeneous turbulence modeling, log-amplitude profiles resulting from the propagation into inhomogeneous turbulence exhibit a statistical heterogeneity strongly dependent of source altitude. Furthermore, classical stochastic phase screen generation from a homogeneous Von-Kàrmàn Kolmogorov spectrum seems to give a statistically significant underestimation of the actual impact of turbulence compared to the X-LES method.

Exploring the impact of stochastic transient phases on the NOx emissions from NH3/H2 mixture rich combustion in gas turbines

To reduce climate impact, switching to carbon-free electrofuels is an interesting option to reduce greenhouse gas emissions from electricity generation. The emission of other pollutants than CO2, such as nitrogen oxides (NOx), however, remains a concern. This research focuses on investigating the impact of transient phases, such as start-up and load change, on the NOx emissions expected from the rich combustion of mixtures of hydrogen and ammonia in gas turbines. Stochastic processes account for the inherent variability and uncertainty on the transient trajectories. The trajectories are simulated using a one-dimensional premixed flame model built in Cantera to compute the levels of pollutant formations, among others. The results indicate significant variations in the equivalence ratio, leading to high NOx emission peaks. The study concludes that the impact of the uncertainties related to the transient trajectories on the NOx emissions is low compared to the overall variations of the equivalence ratio, although they can accentuate observed peaks.

Neural network enhanced time-varying parameter estimation via weak measurement

Weak measurement is employed to measure faint signals due to its capability to amplify detection results above technical noise. However, achieving high amplification effects requires accurate adjustment to the experimental system. Estimating unknown time-varying phases, accurately estimating phases, and sensitively perceiving phase changes pose challenges, demanding the system to continuously remain at the appropriate working range. To address this issue, we propose a neural network-based adaptive weak measurement scheme via single-channel light intensity detection. Through machine learning calibrating the experimental system, the reference phase can be dynamically and accurately adjusted, accommodating time-varying phase changes and ensuring the system operates optimally. Compared with traditional dual-channel weak measurement systems, the scheme reduces experimental complexity. Meanwhile, by accurately adjusting the reference phase, the scheme has higher sensitivity and estimation precision compared to the non-modulated scheme. We validate the effectiveness of the scheme in estimating the period and stochastic time-varying phase. The proposed method highlights the advancement of machine learning in weak measurement systems and can also be applied to other quantum-enhanced measurement schemes.

Imaging extended single crystal lattice distortion fields with multi-peak Bragg ptychography

Recent advances in phase-retrieval-based x-ray imaging methods have demonstrated the ability to reconstruct 3D distortion vector fields within a nanocrystal by using coherent diffraction information from multiple crystal Bragg reflections. However, these works do not provide a solution to the challenges encountered in imaging lattice distortions in crystals with significant defect content that result in phase wrapping. Moreover, these methods only apply to isolated crystals smaller than the x-ray illumination, and therefore cannot be used for imaging of distortions in extended crystals. We introduce multi-peak Bragg ptychography which addresses both challenges via an optimization framework that combines stochastic gradient descent and phase unwrapping methods for robust image reconstruction of lattice distortions and defects in extended crystals. Our work uses modern automatic differentiation toolsets so that the method is easy to extend to other settings and easy to implement in high-performance computers. This work is particularly timely given the broad interest in using the increased coherent flux in fourth-generation synchrotrons for innovative material research.

Static and dynamic damping mechanical performance of architected metal-epoxy interpenetrating phase composites

The present contribution investigates the static and dynamic damping mechanical response of architected aluminum-epoxy interpenetrating phase composites (IPCs), engineered with strut, triply periodic minimal surfaces (TPMS), and stochastic spinodal AlSi10Mg reinforcement phases. Both single-phase metamaterials and co-continuous, multi-phase composites are analyzed, assessing the role of the reinforcement phase design and the addition of silicon carbide (SiC) nano-whisker epoxy enhancements in the effective mechanical performance. Aluminum-epoxy IPCs yield a constitutive response with peak, plateau stress, and overall energy absorptions up to 25 times higher than the ones recorded for the underlying single-phase metamaterials. Inner plastic strains, probed through dedicated finite element analysis, provide insights into the inner damage evolution, leading to characteristic ductile failure patterns, as revealed by computer tomography analysis. The exceptional specific energy absorption attributes are complemented by outstanding dynamic performance characteristics, with significant loss moduli over a broad range of frequencies and damping ratios up to 0.29.

LoopSage: An energy-based Monte Carlo approach for the loop extrusion modeling of chromatin

The connection between the patterns observed in 3C-type experiments and the modeling of polymers remains unresolved. This paper presents a simulation pipeline that generates thermodynamic ensembles of 3D structures for topologically associated domain (TAD) regions by loop extrusion model (LEM). The simulations consist of two main components: a stochastic simulation phase, employing a Monte Carlo approach to simulate the binding positions of cohesins, and a dynamical simulation phase, utilizing these cohesins' positions to create 3D structures. In this approach, the system's total energy is the combined result of the Monte Carlo energy and the molecular simulation energy, which are iteratively updated. The structural maintenance of chromosomes (SMC) protein complexes are represented as loop extruders, while the CCCTC-binding factor (CTCF) locations on DNA sequence are modeled as energy minima on the Monte Carlo energy landscape. Finally, the spatial distances between DNA segments from ChIA-PET experiments are compared with the computer simulations, and we observe significant Pearson correlations between predictions and the real data. LoopSage model offers a fresh perspective on chromatin loop dynamics, allowing us to observe phase transition between sparse and condensed states in chromatin.

Stability of traveling waves for deterministic and stochastic delayed reaction–diffusion equation based on phase shift

In this paper, we establish the nonlinear orbital stability of the traveling wave solution of deterministic and stochastic delayed reaction–diffusion equation. Employing the deterministic phase shift and establishing a delayed-integral inequality, we obtain the exponential stability of the traveling wave solution for the deterministic delayed reaction–diffusion equation. Applying a stochastic phase shift and time transformation, we then verify that the traveling wave solution of the deterministic equation retain the nonlinear orbital stability when the noise intensity is small enough and the initial value sufficiently closes the traveling wave.

Noise Compensation Methods for Optical Fiber Frequency Sweeping Interferometry: A Review

Noise induced by the fluctuation of laser phase, frequency, intensity, etc., can deteriorate the point spread function (PSF) in distributed optical fiber sensing and testing systems, which is the core concern for measurement performance, such as measurement spatial resolution, length range, accuracy and dynamic range. In this paper, we review the development of noise compensation methods for improving the PSF in optical fiber frequency sweeping interferometry (OFFSI) systems and provide a reference to select appropriate compensation methods in different applications (e.g., fiber optics component characterization, optical fiber network diagnosis). A discussion of noise impacts on PSF is made, including laser source phase noise, laser source intensity noise and ambient noise. The most serious noise is the laser source phase noise involved in frequency tunable lasers, including deterministic frequency tuning nonlinearity and stochastic laser phase noise. Also, a comprehensive and detailed classification of the compensation strategies for different noise is provided according to the dominant noise in the laser source. Recent progress on each kind of compensation method is analyzed based on the principles, performance, advantages and limitations, and a comparison of compensation methods is presented. Finally, an overview of trends and future developments is given.

Suppression of stimulated Raman scattering in plasma by an ultra-wideband stochastic phase low-coherence laser

Suppression of the stimulated Raman scattering (SRS) by a stochastic phase low-coherence laser (SPLL) in homogeneous plasma is investigated by theoretical analysis and one-dimensional particle-in-cell (PIC) simulation. A simple model is established, in which the SPLL is modelled as a combination of a monochromatic laser and a broadband laser. When the phase randomness increases, the bandwidth of the SPLL is broadened and the energy proportion of the monochromatic laser component is reduced. PIC simulation shows that the SPLL can effectively suppress SRS and hot electron generation. Various phenomena in the nonlinear process, such as the nonlinear frequency shift and the competition between forward-scattering and back-scattering modes, are explained in detail.

Single Drug Therapy of PD-1/PD-L1 Checkpoint Inhibitors for Advanced Urothelial Bladder Cancer

Since the first approval of Atezolizumab in May 2016, immunotherapy, PD-1/PD-L has completely changed the way bladder cancer is treated, as chemotherapy was the sole available choice as a treatment for bladder cancer, and the results still was not optimistic, with five licensed drugs treating bladder cancer. Despite the generally poor prognosis of advanced bladder cancer, some patients show persistent responses to immune checkpoint inhibitors. This review summarizes the efficacies and safety of the five drugs: Durvalumab, Atezolizumab, Avelumab and other drugs - from different studies respectively for treating advanced bladder cancer and mentions the side effects and future perspectives. For the treatment, all inhibitors that was licensed have akin efficacy and safety traits, but they differ in terms of dosage, frequency, and financial burden. Only Pembrolizumab, to date, has revealed advantage over conventional chemotherapy in a stochastic Phase III scenario. Pembrolizumab and Atezolizumab are also well tolerated and approved for patients who are unable to receive cisplatin treatment. Patients with bladder cancer now have some hope, thanks to immunotherapy. The current environment is continuously evolving, and new immunotherapy-combination trials are being conducted to further enhance results.

Robust formation of metachronal waves in directional chains of phase oscillators

Biological systems can rely on collective formation of a metachronal wave in an ensemble of oscillators for locomotion and for fluid transport. We consider one-dimensional chains of phase oscillators with nearest-neighbor interactions, connected in a loop and with rotational symmetry, so each oscillator resembles every other oscillator in the chain. Numerical integrations of the discrete phase oscillator systems and a continuum approximation show that directional models (those that do not obey reversal symmetry), can exhibit instability to short wavelength perturbations but only in regions where the slope in phase has a particular sign. This causes short wavelength perturbations to develop that can vary the winding number that describes the sum of phase differences across the loop and the resulting metachronal wave speed. Numerical integrations of stochastic directional phase oscillator models show that even a weak level of noise can seed instabilities that resolve into metachronal wave states.

Integrating flexibility in open pit mine planning to survive commodity price decline

Historically the mining industry grew substantially across the globe, acquiring new licenses, investing in exploration activities, and opening new mines along with the boom in commodity prices. However, the steady decline in mineral commodities prices significantly affects mineral industry as well as commodity producing nations. Mining risk management is undertaken to mitigate the adverse effects of uncertainties such as price fluctuations using Net Present Value (NPV). In this article risk management of commodity price decline was undertaken by integrating a recourse action with mine planning. The framework was presented in four distinct phases namely commodity price simulation using autoregressive distributed lag forecasting method; formulation of the mathematical stochastic phase design structure of the stochastic graph framework, and parametric solution of the graph problem; estimation and analysis of risk by Value at Risk (Var) and Weibull exceedance of losses concepts respectively, and minimizing the risk by optimizing operating level using the Lagrange model on Cobb-Douglass model. The proposed methodology was applied on an anonymous gold mine and the analysis of potential losses using Gumbel exceedance shows that mine could incur an annual loss of $20 million with a recurrence period of 1 in 1.38 years with a probability of 0.72. The recourse action was identified using the Lagrange model on the Cobb-Douglass model which reduced the cost by about 50% and subsequently the production level. The NPVs for the stochastic minimum cut models after application of the recourse action was 54% of the NPV at full production showing that there is an increase in the value of the project.

Measurements of Phase Dynamics in Planar Josephson Junctions and SQUIDs.

We experimentally investigate the stochastic phase dynamics of planar Josephson junctions (JJs) and superconducting quantum interference devices (SQUIDs) defined in epitaxial InAs/Al heterostructures, and characterized by a large ratio of Josephson energy to charging energy. We observe a crossover from a regime of macroscopic quantum tunneling to one of phase diffusion as a function of temperature, where the transition temperature T^{*} is gate-tunable. The switching probability distributions are shown to be consistent with a small shunt capacitance and moderate damping, resulting in a switching current which is a small fraction of the critical current. Phase locking between two JJs leads to a difference in switching current between that of a JJ measured in isolation and that of the same JJ measured in an asymmetric SQUID loop. In the case of the loop, T^{*} is also tuned by a magnetic flux.

Experimental and Numerical (Fluent-VOF, k-ϵ, DPM) Study of Variation of Trap Efficiency of Irregular Hexagonal SIT (Sediment Invert Trap) for Particle Removal in Rectangular Open Drains and Sewers

At some locations along the length of open sewers and drains, sediment particles get deposited on the bottom bed, reducing hydraulic efficiency. A sediment invert trap (SIT) can be implemented on the bottom of open sewers and drains to trap sediment particles moving on the bed surface. Several investigators have conducted experimental and computational studies to understand the particle trapping behavior of invert traps of various shapes and depths under varying sediment and flow parameters. In experimental studies, previous investigators have used actual and artificial sediment particles; in computational analyses, spherical particles have been considered. The current study investigated the particle trapping behavior of an irregular hexagonal sediment invert trap (SIT) through experiments and two-dimensional (2D) numerical modeling. Seventy-two experiments were performed using actual sewage solid particles in an open rectangular channel with a bottom-fitted invert trap with multiple depths. Sixty numerical simulations were performed using ANSYS Fluent 2020 R1 computational fluid dynamics (CFD) software, considering spherical and nonspherical sewage solid particles. The velocity field was predicted using the volume of fluid (VOF) model combined with the realizable k-ϵ turbulence model. Particle trap efficiency was predicted using a stochastic discrete phase model (DPM). Trap efficiency varied significantly with depth of flow, invert trap depth, slot aperture size, and particle size and shape. Analysis of the simulated flow field showed that variation of turbulent kinetic energy above the trap’s slot aperture was also responsible for variations in trap efficiency values. Fluent simulations considering particles as nonspherical (using shape factors) agreed well with experimentally measured trap efficiency, with mean absolute percentage errors (MAPE) of 6.23%, 8.79%, and 13.77% for particle size ranges SS1, SS2, and SS3, respectively, with both slot apertures at all flow depths. The 2D-CFD study consistently overpredicted trap efficiencies compared to the experimental findings. With a fixed length and width of 0.32 and 0.15 m, respectively, the optimal depth of the irregular hexagonal SIT was found to be 0.65 m with slot aperture sizes of 0.15 and 0.03 m, whereas with slot aperture size of 0.15 m only, invert trap depths equal to 0.58, 0.43, and 0.38 m was found as optimum.

Fabrication-robust silicon photonic devices in standard sub-micron silicon-on-insulator processes.

Perturbations to the effective refractive index from nanometer-scale fabrication variations in waveguide geometry plague high index-contrast photonic platforms; this includes the ubiquitous sub-micron silicon-on-insulator (SOI) process. Such variations are particularly troublesome for phase-sensitive devices, such as interferometers and resonators, which exhibit drastic changes in performance as a result of these fabrication-induced phase errors. In this Letter, we propose and experimentally demonstrate a design methodology for dramatically reducing device sensitivity to silicon width variations. We apply this methodology to a highly phase-sensitive device, the ring-assisted Mach-Zehnder interferometer (RAMZI), and show comparable performance and footprint to state-of-the-art devices, while substantially reducing stochastic phase errors from etch variations. This decrease in sensitivity is directly realized as energy savings by significantly reducing the required corrective thermal tuning power, providing a promising path toward ultra-energy-efficient large-scale silicon photonic circuits.

A Comprehensive Tool for Scenario Generation of Solar Irradiance Profiles

Despite their positive effects on the decarbonization of energy systems, renewable energy sources can dramatically influence the short-term scheduling of distributed energy resources (DER) in smart grids due to their intermittent and non-programmable nature. Renewables’ uncertainties need to be properly considered in order to avoid DER operation strategies that may deviate from the optimal ones. This paper presents a comprehensive tool for the scenario generation of solar irradiance profiles by using historical data for a specific location. The tool is particularly useful for creating scenarios in the context of the stochastic operation optimization of DER systems. Making use of the Roulette Wheel mechanism for generating an initial set of scenarios, the tool applies a reduction process based on the Fast-Forward method, which allows the preservation of the most representative ones while reducing the computational efforts in the next potential stochastic optimization phase. From the application of the proposed tool to a numerical case study, it emerged that plausible scenarios are generated for solar irradiance profiles to be used as input for DER stochastic optimization purposes. Moreover, the high flexibility of the proposed tool allows the estimation of the behavior of the stochastic operation optimization of DER in the presence of more fluctuating but plausible solar irradiance patterns. A sensitivity analysis has also been carried out to evaluate the impact of key parameters, such as the number of regions, a metric, and a specific parameter used for the outlier removal process on the generated solar irradiance profiles, by showing their influence on their smoothness and variability. The results of this analysis are found to be particularly suitable to guide users in the definition of scenarios with specific characteristics.

Graphop mean-field limits and synchronization for the stochastic Kuramoto model

Models of coupled oscillator networks play an important role in describing collective synchronization dynamics in biological and technological systems. The Kuramoto model describes oscillator's phase evolution and explains the transition from incoherent to coherent oscillations under simplifying assumptions, including all-to-all coupling with uniform strength. Real world networks, however, often display heterogeneous connectivity and coupling weights that influence the critical threshold for this transition. We formulate a general mean-field theory (Vlasov-Focker Planck equation) for stochastic Kuramoto-type phase oscillator models, valid for coupling graphs/networks with heterogeneous connectivity and coupling strengths, using graphop theory in the mean-field limit. Considering symmetric odd-valued coupling functions, we mathematically prove an exact formula for the critical threshold for the incoherence-coherence transition. We numerically test the predicted threshold using large finite-size representations of the network model. For a large class of graph models, we find that the numerical tests agree very well with the predicted threshold obtained from mean-field theory. However, the prediction is more difficult in practice for graph structures that are sufficiently sparse. Our findings open future research avenues toward a deeper understanding of mean-field theories for heterogeneous systems.

Stochastic rotating waves

Stochastic dynamics has emerged as one of the key themes ranging from models in applications to theoretical foundations in mathematics. One class of stochastic dynamics problems that has recently received considerable attention are traveling wave patterns occurring in stochastic partial differential equations (SPDEs). Here, one is interested in how deterministic traveling waves behave under stochastic perturbations. In this paper, we start the mathematical study of a related class of problems: stochastic rotating waves generated by SPDEs. We combine deterministic partial differential equation (PDE) dynamics techniques with methods from stochastic analysis. We establish two different approaches, the variational phase and the approximated variational phase, for defining stochastic phase variables along the rotating wave, which track the effect of noise on neutral spectral modes associated to the special Euclidean symmetry group of rotating waves. Furthermore, we prove transverse stability results for rotating waves showing that over certain time scales and for small noise, the stochastic rotating wave stays close to its deterministic counterpart.

Performance decay analysis of cementitious composite cladding structure under stochastic aging

Façade cladding structure made of cementitious composite is prone to cracking due to its brittle characteristics, despite being a non-load-bearing member. Served as building exteriors, aging of cementitious composite may further raise the risk of fracture failure under accidental loads, causing both financial loss and safety hazards. To address this issue, a computational approach, fusing together a novel physics-based stochastic aging model and phase field fracture model, is developed to assess the mechanical performance decay of aging cladding structure. In this study, stochastic leaching under inherent material uncertainty is taken as the primary aging concern, and the analysis is assisted with extended support vector regression for substantial efficiency enhancements. The proposed method is carefully validated against two designed benchmark problems and a real-life application. It is demonstrated to be able to predict the time-dependent reliability of cementitious composite cladding structures precisely and efficiently under stochastic leaching-induced aging.