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We find a stationary distribution of a stochastic process with delay at the origin. The trajectories of the process have linear growth and random jumps at random times. We use known results for regenerative processes and factorization technique for the study in boundary crossing problems for random walks.
Fe-3.8wt%Si transformer steels were processed using two different additive manufacturing (AM) techniques, laser powder bed fusion (LPBF) and directed energy deposition (DED). While the LPBF processed samples exhibited a strong <001> orientation of the BCC grains along the build axis, the DED processed samples exhibited a randomized texture along the build axis. DED processed samples showed substantially coarser columnar grains as compared to their LPBF counterparts. Here, the columnar grains exhibited a substantial number of low-angle sub-grain boundaries. All samples exhibited very good soft magnetic properties, with saturation magnetization (M s ) values ranging from 205 - 232 emu/gm, and coercivity (H c ) values ranging from 1.2 – 4.2 Oe. The Coercivity (H c ) values were significantly lower when the magnetic field was applied parallel to the build axis, as compared to being perpendicular, which can be rationalized based on the columnar nature of the grains, resulting in a higher number density of grain boundaries in case of the field applied perpendicular to the build axis.
Process-based models have been widely used for hydrologic modeling, and it is a common practice to use sensitivity analysis methods for excluding non-influential hydrologic processes from further investigation and/or model improvement. This study develops a new method called multi-model absolute difference-based sensitivity (MMADS) analysis method to screen non-influential system processes and parameters. MMADS is conceptually similar to the Morris method for addressing parametric uncertainty, but has a unique feature to address both process model uncertainty (i.e., a process may be represented by multiple process models) and process model parameter uncertainty (i.e., parameters associated with a process model are random). MMADS first evaluates absolute differences of a quantity of interest (i.e., a system model output) by varying process models and/or process model parameter values, and then calculates the mean and variance of the differences for investigating process influence. The mean measures overall influence of the process on the quantity of interest, and the variance estimates influence of nonlinear effects of the process and/or its interactions with other processes. MMADS is an extension of the Morris method from a parameter space to a joint parameter-model space for explicitly addressing both process model uncertainty and model parameter uncertainty. The performance of MMADS is evaluated by using two numerical experiments. One experiment is based on Sobol’s G*-function with ten product elements, and has analytical solutions of the MMADS mean and variance of absolute differences. The other experiment is for groundwater flow modeling which considers three processes (i.e., recharge, geology, and snowmelt) that interact with each other. Finally, results indicate that MMADS is computationally efficient and can identify non-influential processes of complex hydrological systems.
One of the most widely-used statistical procedures for dimensionality reduction of high dimensional random fields is Principal Component Analysis (PCA), which is based on the Karhunen-Lo eve expansion (KLE) of a stochastic process with finite variance. The KLE is analogous to a Fourier series expansion for a random process, where the goal is to find an orthogonal transformation for the data such that the projection of the data onto this orthogonal subspace is optimal in the L 2 sense, i.e, which minimizes the mean square error. In practice, this orthogonal transformation is determined by performing an SVD (Singular Value Decomposition) on the sample covariance matrix or on the data matrix itself. Sampling error is typically ignored when quantifying the principal components, or, equivalently, basis functions of the KLE. Furthermore, it is exacerbated when the sample size is much smaller than the dimension of the random field. In this paper, we introduce a Bayesian KLE procedure, allowing one to obtain a probabilistic model on the principal components, which can account for inaccuracies due to limited sample size. The probabilistic model is built via Bayesian inference, from which the posterior becomes the matrix Bingham density over the space of orthonormal matrices. We use a modified Gibbs sampling procedure to sample on this space and then build a probabilistic Karhunen-Lo eve expansions over random subspaces to obtain a set of low-dimensional surrogates of the stochastic process. We illustrate this probabilistic procedure with a finite dimensional stochastic process inspired by Brownian motion.
During non-classical growth of nanostructures via assembly of primary nuclei, nucleation and assembly are assumed to be distinct processes: nanoparticles nucleate randomly and aggregate to form extended structures through Brownian motion in the presence of long-range attractive interactions. Here we investigate the relationship between these two processes by using in situ AFM, in situ, ex situ and cryo TEM and UV-Vis spectroscopy to observe growth of colloidal gold and simulations to develop a mechanistic model of the process. Our results reveal an inexorable link between nucleation and assembly with nuclei forming almost exclusively within a ~ 1 nm interfacial region of existing particles. The new particles immediately close the gap either through a diffusive jump or via growth of a neck between the seed and new particle, generating aggregates exhibiting features commonly attributed to oriented attachment of independently nucleated particles. The results demonstrate that creation of initial particle interfaces leads to local environments that redirect growth towards non-classical processes.
Sap flow, a critical process in plant water use and ecosystem water cycles, is often measured using thermal dissipation probes (TDP) due to their ease of installation and continuous data collection. However, sap flow data frequently include noise, outliers, and gaps, creating challenges for analysis and requiring substantial manual processing. We developed S AP F LOWER , a tool that automates data preprocessing, model training, gap-filling, sapwood area scaling and modeling, and water use analysis. It integrates autocleaning, machine learning and deep learning models (e.g. random forest, Gaussian process regression, long short-term memory (LSTM), bidirectional LSTM (BiLSTM)), and efficient workflows to process sap flow data. S AP F LOWER can remove over 90% of noisy data while preserving legitimate variations and achieve high accuracy in gap-filling based on user-determined parameters. Random forest, LSTM, and BiLSTM models reduced root mean square error to 10% or less for long-term gaps. Model training and prediction can be performed efficiently within seconds. S AP F LOWER significantly enhances the efficiency and accessibility of TDP data analysis by automating complex tasks, enabling researchers without programming expertise to employ advanced techniques. Future improvements will focus on species-specific corrections for TDP and support for additional measurement methods. S AP F LOWER is openly available on GitHub (https://github.com/JiaxinWang123/SapFlower) and Zenodo (doi: 10.5281/zenodo.13665919).
The electric vehicle (EV) is an increasingly popu- lar mobility solution today. It is especially appealing for urban commercial usage including serving commuters and delivering goods. Commercial EVs, defined as electric taxi fleets in this paper, contribute a lot to the energy consumption and emission. One critical component to facilitate the adoption of EVs is to provide sufficient charging infrastructures for road users to alleviate the range anxiety. In this study, we develop an analytical model to profile the stationary spatial distribution of charging demand for any given fleet of commercial EVs, which serves as the necessary input for planning the location of charging infrastructures. Our model considers the movement of EVs as a random walk, with the underlying Markov process driven by the spatial demand that the commercial EV fleet needs to serve. We then define the electricity consumption and charging models and develop the probability distribution that an EV may need to recharge its battery at any given location in the city, based on the stationary distribution of the random walk process. We calibrate the performance parameters of EVs from the trip record and present numerical experiments based on New York City taxi trip data and compare the solution from simulation with our analytical solution. The result shows that analytical solution is quite close to the simulation result. This paper provides insights to the city agencies and private companies to make charging infrastructure location planning.
In this paper we study two-person nonzero-sum games for continuous-time jump processes with the randomized history-dependent strategies under the finite-horizon payoff criterion. The state space is countable, and the transition rates and payoff functions are allowed to be unbounded from above and from below. Under the suitable conditions, we introduce a new topology for the set of all randomized Markov multi-strategies and establish its compactness and metrizability. Then by constructing the approximating sequences of the transition rates and payoff functions, we show that the optimal value function for each player is a unique solution to the corresponding optimality equation and obtain the existence of a randomized Markov Nash equilibrium. Furthermore, we illustrate the applications of our main results with a controlled birth and death system.
A quantum random number generator is experimentally realized. The initial randomness source is a sequence of photocounts from quasi-single-photon radiation detected with a SiPM (Silicon Photo Multiplier) silicon avalanche detector array. The use of a SiPM provides a reliable control of the quantum nature of the Poisson photocount statistics. A special algorithm with nonexponential complexity allows one to extract from the Poisson process all the randomness contained in it, namely, a random uniform sequence of 0 and 1.
The randomness introduced by reactants is an issue when processing renewable bioresources. In this paper, we apply tools from dynamic stochastic programming theory to the biochemical process. Instead of introducing extra preprocessing units, we consider the inherent randomness of the process and optimize in expectation the performance of the system. In a general setting, this is a multistage stochastic optimization problem and we investigate its approximate solution via two approaches, namely stochastic dual dynamic programming (SDDP) and the finite state, finite action Markov decision process (MDP) framework. These two methods are implemented to a case study of lignin valorization that is crucial to a cost-effective biorefinery process using biomass as the feedstock.
Highlights: •The rigorous dynamics of a modulated Landau–Zener model is investigated. •Nonadiabatic evolution of the model could realize complete population transfer. •Imperfect effects caused by both the amplitude and phase damping are estimated. -- Abstract: We investigate a special time-dependent quantum model which assumes the Landau–Zener driving form but with an overall modulation of the intensity of the pulsing field. We demonstrate that the dynamics of the system, including the two-level case as well as its multi-level extension, is exactly solvable analytically. Differing from the original Landau–Zener model, the nonadiabatic effect of the evolution in the present driving process does not destroy the desired population transfer. As the sweep protocol employs only the finite driving fields which tend to zero asymptotically, the cutoff error due to the truncation of the driving pulse to the finite time interval turns out to be negligibly small. Furthermore, we investigate the noise effect on the driving protocol due to the dissipation of the surrounding environment. The losses of the fidelity in the protocol caused by both the phase damping process and the random spin flip noise are estimated by solving numerically the corresponding master equations within the Markovian regime.
Embedding catalysts inside of plastics affords accelerated chemical modification with programmable latency and pathways. Nanoscopically embedded enzymes can lead to near-complete degradation of polyesters via chain-end mediated processive depolymerization. The overall degradation rate and pathways have a strong dependence on the morphology of semicrystalline polyesters. Yet, most studies to date focus on pristine polymers instead of mixtures that contain additives and other components despite their nearly universal use in plastic production. Here, for this study, additives are introduced to purposely change the morphology of polycaprolactone (PCL) by increasing the bending and twisting of crystalline lamellae. These morphological changes immobilize chain ends preferentially at the crystalline/amorphous interfaces and limit chain-end accessibility by the embedded processive enzyme. This chain-end redistribution reduces the polymer-to-monomer conversion from >95% to less than 50%, causing formation of highly crystalline plastic pieces, including microplastics. By synergizing both random chain scission and processive depolymerization, it is feasible to navigate morphological changes in polymer/additive blends and to achieve near-complete depolymerization. The random scission enzymes in the amorphous domains create new chain ends that are subsequently bound and depolymerized by processive enzymes. Present studies further highlight the importance to consider how the host polymer's morphologies affect the reactions catalyzed by embedded catalytic species.
Here, microstructure and crystallographic texture and their correlation with impact toughness of high-frequency electric resistance welded (HF-ERW) X65 Grade pipeline steel have been investigated. X65 base metal after HF-ERW has formed a typical hourglass-shaped weld joint with four different regions, including the thermomechanical-affected zone (TMAZ), fine-grained heat affected zone (FGHAZ), coarse-grained heat affected zone (CGHAZ), and bondline (Weld Zone). X65 base metal shows prominent (113) [110] and (112) [110] texture components due to thermomechanical-controlled processing. TMAZ depicted random texture with a minor intensity of Cube component (001)[110] due to the partial recrystallization during welding. In the FGHAZ and CGHAZ, near the bondline, the base metal texture has been converted to rotated Goss (110) [110], Goss (110) [001], and rotated cube (001) [110] due to the recrystallization of the austenite and the shear deformation in the austenite temperature range. A high density of {100} and {110} cleavage planes is observed in the CGHAZ, which is often found to be the fracture location for the impact toughness testing.
Dispersion in polymer nanocomposites is determined by the kinetics of mixing and chemical affinity. Compounds like reinforcing filler/elastomer blends display some similarity to colloidal solutions in that the filler particles are close to randomly dispersed through processing. It is attractive to apply a pseudo-thermodynamic approach taking advantage of this analogy between the kinetics of mixing for polymer compounds and thermally driven dispersion for colloids. In order to demonstrate this pseudo-thermodynamic approach, two polybutadienes and one polyisoprene were milled with three carbon blacks and two silicas. These samples were examined using small-angle x-ray scattering as a function of filler concentration to determine a pseudo-second order virial coefficient, A 2 , which is used as an indicator for compatibility of the filler and polymer. It is found that A 2 follows the expected behavior with lower values for smaller primary particles indicating that smaller particles are less compatible and more difficult to mix. The measured values of A 2 can be used to specify repulsive interaction potentials for coarse grain DPD simulations of filler/elastomer systems. In addition, new methods to quantify the filler percolation threshold and filler mesh size as a function of filler concentration are obtained. Moreover, the results represent a new approach to understanding and predicting compatibility in polymer nanocomposites based on a pseudo-thermodynamic approach.
Wetlands play a critical role in global water and carbon cycles, yet monitoring their water extent remains difficult, particularly beneath dense vegetation. SAR-based techniques such as backscatter thresholding are limited by complex scattering mechanisms, while fully polarimetric SAR (PolSAR) data capable of detecting doublebounce scattering remain scarce. To address these challenges, this study evaluates the potential of Interferometric SAR (InSAR) for mapping water surfaces beneath vegetation, termed flooded vegetation, using the Atrato floodplain in Colombia as a case study. We develop an automated workflow combining InSAR fringe detection with local phase homogeneity analysis and random sampling of processing parameters to generate probabilistic flooded vegetation maps. Applied to ALOS PALSAR-1 L-band image pairs from 2007–2011, the workflow captures seasonal fluctuations in flooded extent ranging from 500 to 1,500 km2. Compared to other L-band SAR inundation products, the InSAR-based maps identify broader flooded areas, with ~70% agreement in pairwise comparisons. Around 84% of detections align with existing wetland inventories and seasonal changes correspond with regional hydrological indicators, including terrestrial water storage anomalies and water gauge measurements. PolSAR analysis shows that InSAR complements backscatter-based methods by detecting inundation in areas with weak double-bounce signals. These findings suggest that combining InSAR with backscatter-based methods can improve detection of flooded vegetation, which is especially relevant for the upcoming NISAR mission that will offer frequent global L-band observations.
Chiral halide perovskites (c-HPs) merge the chirality of organic cations with the semiconducting properties of metal halide frameworks, creating a family of chiral semiconductors with tunable chiroptoelectronic behavior. Here, we describe the impact of periodic banded morphologies of textured c-HP ( R/S -NEA) 2 PbBr 4 films (NEA = 1- (1-naphthyl)ethylammonium) on their chiroptical behavior. Due to the interplay between the crystalline and glassy phases, the c-HP film growth is driven by rhythmic precipitation, producing a distinctive controllable radial banded pattern with the ( R/S -NEA) 2 PbBr 4 inorganic planes oriented parallel to the substrate. The banded morphology can be controlled, as evidenced by the growth temperature dictating the ridge-to-ridge spacing as well as the density of banded regions. The resulting circular dichroism (CD) spectral shape, intensity, and polarity vary in a seemingly random manner across processing conditions. However, these spectral features can be explained by considering key features of the banded morphology, such as refraction of the incident light due to surface morphology, birefringence, and stacked, rotated crystallites. These effects cannot be canceled by averaging front and back CD spectra of c-HP films, and our model incorporating these effects reproduces all observed CD spectra remarkably well. The control over the c-HP morphology and prediction capabilities of our CD modeling leads to further understanding of this class of semiconductors and the possibility of exploiting structural features for light polarization control akin to enhanced metamaterials.
Here in this work, we applied internal quantum efficiency mapping to study the recombination activity of grain boundaries in High Performance Multicrystalline Silicon under different processing conditions. Wafers were divided into groups and underwent different thermal processing, consisting of phosphorus diffusion gettering and surface passivation with hydrogen rich layers. After these thermal treatments, wafers were processed into heterojunction with intrinsic thin layer solar cells. Light Beam Induced Current and Electron Backscatter Diffraction were applied to analyse the influence of thermal treatment during standard solar cell processing on different types of grain boundaries. The results show that after cell processing, most random-angle grain boundaries in the material are well passivated, but small-angle grain boundaries are not well passivated. Special cases of coincidence site lattice grain boundaries with high recombination activity are also found. Based on micro-X-ray fluorescence measurements, a change in the contamination level is suggested as the reason behind their increased activity. Published by AIP Publishing.
Landauer's principle states that erasing a bit of information at fixed temperature T costs at least $k$ B $T$ ln 2 units of work. Here we investigate erasure at varying temperature, to which Landauer's result does not apply. Here we formulate bit erasure as a stochastic nonequilibrium process involving a compression of configuration space, with physical and logical states associated in a symmetric way. Erasure starts and ends at temperature T, but temperature can otherwise vary with time in an arbitrary way. Defined in this way, erasure is governed by a set of nonequilibrium fluctuation relations that show that varying-temperature erasure can done with less work than $k$ B $T$ ln 2. As a result, erasure and the complementary process of bit randomization can be combined to form a work-producing engine cycle.