Dimensional Process Research Articles

Strong uniqueness for Dirichlet operators related to stochastic quantization under exponential/trigonometric interactions on the two-dimensional torus

We consider space-time quantum fields with exponential/trigonometric interactions. In the context of Euclidean quantum field theory, the former and the latter are called the Hoegh-Krohn model and the Sine-Gordon model, respectively. The main objective of the present paper is to construct infinite dimensional diffusion processes which solve modified stochastic quantization equations for these quantum fields on the two-dimensional torus by the Dirichlet form approach and to prove strong uniqueness of the corresponding Dirichlet operators.

Fractional Order Model of the Two Dimensional Heat Transfer Process

In this paper, a new, state space, fractional order model of a heat transfer in two dimensional plate is addressed. The proposed model derives directly from a two dimensional heat transfer equation. It employes the Caputo operator to express the fractional order differences along time. The spectrum decomposition and stability of the model are analysed. The formulae of impluse and step responses of the model are proved. Theoretical results are verified using experimental data from thermal camera. Comparison model vs experiment shows that the proposed fractional model is more accurate in the sense of MSE cost function than integer order model.

Robust Stabilization and Observer-Based Stabilization for a Class of Singularly Perturbed Bilinear Systems

An infinite-bound stabilization of a system modeled as singularly perturbed bilinear systems is examined. First, we present a Lyapunov equation approach for the stabilization of singularly perturbed bilinear systems for all ε∈(0, ∞). The method is based on the Lyapunov stability theorem. The state feedback constant gain can be determined from the admissible region of the convex polygon. Secondly, we extend this technique to study the observer and observer-based controller of singularly perturbed bilinear systems for all ε∈(0, ∞). Concerning this problem, there are two different methods to design the observer and observer-based controller: one is that the estimator gain can be calculated with known bounded input, the other is that the input gain can be calculated with known observer gain. The main advantage of this approach is that we can preserve the characteristic of the composite controller, i.e., the whole dimensional process can be separated into two subsystems. Moreover, the presented stabilization design ensures the stability for all ε∈(0, ∞). A numeral example is given to compare the new ε-bound with that of previous literature.

Study of two free-falling spheres interaction by coupled SPH–DEM method

In the present paper, the three dimensional (3D) settlement process of two side-by-side free-falling spheres in a water tank was numerically investigated using coupled Smoothed Particle Hydrodynamics (SPH)–Discrete Element Method (DEM) method. The maximum particle Reynolds number, calculated based on the terminal velocity and sphere diameter, is Rem=2.4×104. The accuracy of the model was firstly validated by simulating the single sphere water-entry, settlement of two circular cylinders arranged in series and two identical spheres settlement side by side problems, respectively. The simulation results exhibited a satisfactory agreement with the available numerical and experimental data in the literatures. Then, the settlement process of two spheres with different sizes and transverse distances were simulated. In particular, the motion patterns of two interacting spheres with different initial gaps and diameter ratios, including motion trajectory, vertical falling distance and flow field, were systematically investigated. The results demonstrate that when initial gap S0∗ < 0.75, sedimentation process in a water tank can be divided into four stages: slight gathering stage, accelerated separation stage, decelerated separation stage and re-approach stage. With the increase of diameter ratios, the trajectory of smaller sphere is more significantly affected by the larger sphere, while the effect for the larger one is just the opposite. The influence of different initial gaps is mainly reflected in the motion stage after the accelerated separation stage. When S0∗ > 0.75, the interaction between the two spheres are negligible. In addition, the interaction between particles would slow down the settling velocity and affect the terminal settling distance.

Moment generating function of non-Markov self-excited claims processes

This article establishes the moment generating function (mgf) of self-excited claim processes with memory functions that admit a Fourier's transform representation. In this case, the claim and intensity processes may be reformulated as an infinite dimensional Markov processes in the complex plane. Approaching these processes by discretization and next considering the limit allows us to find their moment generating function. We illustrate the article by fitting non-Markov self-excited processes to the time-series of cyber-attacks targeting medical and other services, in the US from 2014 to 2018.

3D heat flow effects in the imaging of subsurface graphical features in semi-transparent media by pulsed thermography

Pulsed thermography has proven to be a useful tool to detect subsurface features in ancient bookbindings and, in particular, to provide the IR image of texts buried beneath the end-leaves of the books. In this paper the theory is presented to analyze the influence of the geometrical and physical parameters involved in the processes leading to the distortion in the IR image of the detected buried graphical features. The distortion is mainly due to the lateral diffusion of the heat generated at the ink feature after the absorption of an excitation light. A comprehensive analysis taking into account the three dimensional heat diffusion process, in an optically semi-transparent medium, is considered. Numerical results are reported showing the behavior of the contrast and of a distortion parameter of the buried inked feature detected by the IR imaging in the various considered cases.

Comparison of dimensionality reduction and clustering methods for SARS-CoV-2 genome

This paper aims to conduct an analysis of the SARS-CoV-2 genome variation was carried out by comparing the results of genome clustering using several clustering algorithms and distribution of sequence in each cluster. The clustering algorithms used are K-means, Gaussian mixture models, agglomerative hierarchical clustering, mean-shift clustering, and DBSCAN. However, the clustering algorithm has a weakness in grouping data that has very high dimensions such as genome data, so that a dimensional reduction process is needed. In this research, dimensionality reduction was carried out using principal component analysis (PCA) and autoencoder method with three models that produce 2, 10, and 50 features. The main contributions achieved were the dimensional reduction and clustering scheme of SARS-CoV-2 sequence data and the performance analysis of each experiment on each scheme and hyper parameters for each method. Based on the results of experiments conducted, PCA and DBSCAN algorithm achieve the highest silhouette score of 0.8770 with three clusters when using two features. However, dimensionality reduction using autoencoder need more iterations to converge. On the testing process with Indonesian sequence data, more than half of them enter one cluster and the rest are distributed in the other two clusters.

A Piecewise Deterministic Limit for a Multiscale Stochastic Spatial Gene Network

We consider multiscale stochastic spatial gene networks involving chemical reactions and diffusions. The model is Markovian and the transitions are driven by Poisson random clocks. We consider a case where there are two different spatial scales: a microscopic one with fast dynamic and a macroscopic one with slow dynamic. At the microscopic level, the species are abundant and for the large population limit a partial differential equation (PDE) is obtained. On the contrary at the macroscopic level, the species are not abundant and their dynamic remains governed by jump processes. It results that the PDE governing the fast dynamic contains coefficients which randomly change. The global weak limit is an infinite dimensional continuous piecewise deterministic Markov process (PDMP). Also, we prove convergence in the supremum norm.

Asymptotics for infinite server queues with fast/slow Markov switching and fat tailed service times

We study a general k dimensional infinite server queues process with Markov switching, Poisson arrivals and where the service times are fat tailed with index When the arrival rate is sped up by a factor the transition probabilities of the underlying Markov chain are divided by and the service times are divided by n, we identify two regimes (”fast arrivals”, when and” equilibrium”, when ) in which we prove that a properly rescaled process converges pointwise in distribution to some limiting process. In a third” slow arrivals” regime, we show the convergence of the two first joint moments of the rescaled process.

Natural frequency analysis of shells of revolution based on hybrid dual-mixed [formula omitted]-finite element formulation

A newly-developed, dimensionally reduced, hp-type axisymmetric shell finite element model is extended to linear elastodynamic problems of thin shells of revolution. The hp-shell finite element relies on the hybridized version of a three-field dual-mixed variational formulation, the application of which dictates the obligate usage of the inverse three-dimensional constitutive relation for homogeneous and isotropic materials, thereby ensuring the volumetric locking-free characteristic of the shell model at theory level. The fundamental fields are the a priori non-symmetric stress tensor, the displacement vector, the infinitesimal rotation vector and the hybrid variable defined on the element interfaces. Since the dimensional reduction process guided by this hybrid-mixed formulation does not necessitate the use of any classical kinematic assumptions appearing in the scientific literature, the inverse 3D Hooke’s law does not have to be modified. The numerical performance of the shell finite element is analyzed comprehensively for natural frequency computations of clamped-free and simply supported, silicone, conoid, spherical and hyperboloid shells of revolution. From their relative error convergence behaviors it follows that the extended hybrid-mixed shell finite element is not sensitive to the decrease of the slenderness ratio, namely providing reliable, uniformly stable numerical results for both h- and p-approximation. From theoretical point of view, the beneficial properties of the hybrid-mixed hp shell finite element model are as follows: (i) this is effectively applicable to modeling not only extremely thin but also moderately thick shell structures with transverse shear deformations, as well as (ii) both the through-the-thickness variation and the membrane stress normal to the shell mid-surface are retained as independent variables, making it much easier to upbuild shell model for contact problems. From numerical point of view, the nice feature of the hybrid-mixed hp shell finite element is that the global flexibility matrix of the system can be inverted block-wise at element level at cheap computational cost during the assembling procedure because of the hybridization technique.

Distribution of a Tagged Particle Position in the One-Dimensional Symmetric Simple Exclusion Process with Two-Sided Bernoulli Initial Condition

For the two-sided Bernoulli initial condition with density $$\rho _-$$ (resp. $$\rho _+$$ ) to the left (resp. to the right), we study the distribution of a tagged particle in the one dimensional symmetric simple exclusion process. We obtain a formula for the moment generating function of the associated current in terms of a Fredholm determinant. Our arguments are based on a combination of techniques from integrable probability which have been developed recently for studying the asymmetric exclusion process and a subsequent intricate symmetric limit. An expression for the large deviation function of the tagged particle position is obtained, including the case of the stationary measure with uniform density $$\rho $$ .

Observation of Hydraulic Fracture Morphology for Laboratory Experiments by Using Multiple Methods

How to monitor and identify fracture initiation and propagation is a significant work for the laboratory experiment studies of hydraulic fracturing. In this paper, four main monitoring methods are reviewed and compared through the tri-axial fracturing experiments with natural shale outcrops, including tracer labeling, acoustic emission (AE) monitoring, computerized tomography (CT) scanning and visual fracturing method. Results show that for tracer labeling, fluorescent tracer could visually monitor the hydraulic fracture distribution morphologies, but it has a poor compatibility with slippery water. For the method of AE monitoring, dynamic three dimensional (3D) hydraulic fracture propagation process can be monitored by fixing AE sensors on specimen surfaces. However, the AE signal might display inconsistency with fracture path, which is affected by shale heterogeneity, natural fractures and bedding planes. For the method of CT scanning, many internal rock features can be well recognized, including the location of primary and activated fractures, fracture scales and the interactions between hydraulic fracture and natural fractures. However, CT scanning method cannot identify some micron-and nanoscale fractures characteristics. For the method of visual fracturing, the injected low-temperature metal can extract the fractures skeleton and measure fracture morphologies precisely, but temperature have a significant impact on experiment results. Therefore, combinations of multiple monitoring methods are recommended in laboratory experiment studies. For example, the combination of AE monitoring and CT scanning can effectively identify the propagation behavior of complex fracture network.

Solid-state foaming of acrylonitrile butadiene styrene through microcellular 3D printing process

The lightweight products with superior specific strength are in great demand in numerous applications such as automotive, aerospace, biomedical, sports, etc. This work focussed on the manufacturing of lightweight products using the cellular three dimensional (3D) printing process. In this work, the continuous microcellular morphology has been developed in a single foamed filament using 3 D printing of carbon-di-oxide (CO2) saturated acrylonitrile butadiene styrene (ABS) filaments. The microcellular structures with average cell size in the range of 6–1040 µm were developed. The influence of printing parameters; nozzle temperature, feed rate, and flow rate on the foam characteristics and cell morphology at different levels were investigated. The different kinds of observed foamed extrudate irregularities were discussed.

Modified High-Order SVD for Spatiotemporal Modeling of Distributed Parameter Systems

Modeling high-spatial dimensional (high-D) distributed parameter systems (DPSs) is very difficult because of the spatially distributed characteristic and complex spatiotemporal coupling. In this article, a new framework based on high-order singular vector decomposition (HOSVD) is proposed to model a high-D DPS. A modified HOSVD is designed for separation of time and multiple spatial variables. It can well preserve the spatially distributed nature of the high-D DPS. It also considers the interaction across different spatial modes, which is an important part of spatiotemporal coupling in the high-D DPS. Experiments of a two-spatial dimensional thermal curing process are used to verify the effectiveness of the proposed method. An average prediction error near 1% of the curing temperature can be achieved.

Asymptotics of the hitting probability for a small sphere and a two dimensional Brownian motion with discontinuous anisotropic drift

We provide an approximation of the hitting probability for a small sphere for the following two dimensional process: In x-direction it is just a Brownian motion with positive constant drift, whereas in y-direction the process Yt is a Brownian motion with drift given by a negative constant times the sign of Yt. This process can be seen as the solution of a certain stochastic optimal control problem. It turns out that the approximating function can be expressed as the sum of a term involving a modified Bessel function and an ordinary Lebesgue integral.

Efficient Prediction of Real-Time Forming Forces in Flexible Stretch Bending

Stretch bending is commonly used in the mass production of profile-like products in many industrial sectors due to its high dimensional accuracy and process capabilities. One of the challenges of conventional stretch bending is low flexibility, however, making it difficult to meet today’s requirements for mass customization. As a countermeasure, a novel flexible rotary stretch bending process was presented (Ma and Welo, 2021), which allows the forming of complex shapes with varying curvatures and angles. However, less knowledge is known about the most fundamental force requirements during forming, which in turn limits the design and development of product and process. In this research, an analytical model is developed for accurate and efficient prediction of real-time forming forces in flexible rotary stretch bending, aiming to enhance the understanding of applied force requirements throughout the process. In this model, the entire kinematically-controlled loading (strain) history is considered to realize real-time monitoring of force. In addition, the elastic-plastic properties of profile, the profile dimensions, the tooling geometries as well as the tool-workpiece friction are comprehensively taken into account to improve the analytical accuracy of forming force predictions. As an explicit solution can be achieved, the analytical model presents high efficiency for quick prediction, which can be used in attempts to adaptively control the process. Based on finite element simulation, the analytical model is validated in the forming of aluminium rectangular, hollow profiles, showing very high accuracy and efficiency for predicting real-time forming forces of both clamp unit and bending die for forming with different pre-stretching levels.

A mathematical theory of gapless edges of 2d topological orders. Part II

This is the second part of a two-part work on the unified mathematical theory of gapped and gapless edges of 2+1D topological orders. In Part I, we have developed the mathematical theory of chiral gapless edges. In Part II, we study boundary-bulk relation and non-chiral gapless edges. In particular, we explain how the notion of the center of an enriched monoidal category naturally emerges from the boundary-bulk relation. After the study of 0+1D gapless walls, we give the complete boundary-bulk relation for 2+1D topological orders with chiral gapless edges (including gapped edges) and 0d walls between edges. This relation is stated precisely and proved rigorously as a monoidal equivalence, which generalizes the functoriality of the usual Drinfeld center to an enriched setting. We also develop the mathematical theory of non-chiral gapless edges and 0+1D walls, and explain how to gap out certain non-chiral 1+1D gapless edges and 0+1D gapless walls categorically. In the end, we show that all anomaly-free 1+1D boundary-bulk rational CFT's can be recovered from 2d topological orders with chiral gapless edges via a dimensional reduction process. This provides physical meanings to some mysterious connections between mathematical results in fusion categories and those in rational CFT's.

Moderate Deviations for the SSEP with a Slow Bond

We consider the one dimensional symmetric simple exclusion process with a slow bond. In this model, particles cross each bond at rate $N^2$, except one particular bond, the slow bond, where the rate is $N$. Above, $N$ is the scaling parameter. This model has been considered in the context of hydrodynamic limits, fluctuations and large deviations. We investigate moderate deviations from hydrodynamics and obtain a moderate deviation principle.

One Dimensional Exclusion Process with Dynein Inspired Hops: Simulation and Mean Field Analysis

We introduce a one-dimensional non-equilibrium lattice gas model representing the processive motion of dynein molecular motors over the microtubule. We study both dynamical and stationary state properties for the model consisting of hardcore particles hopping on the lattice with variable step sizes. We find that the stationary state gap-distribution exhibits striking peaks around gap sizes that are multiples of the maximum step size, for both open and periodic boundary conditions. We verified this feature using a mean-field calculation. For open boundary conditions, we observe intriguing damped oscillator-like distribution of particles over the lattice with a periodicity equal to the maximum step size. To characterize transient dynamics, we measure the mean square displacement that shows weak superdiffusive growth with exponent $$\gamma \approx 1.34$$ for periodic boundary and ballistic growth ( $$\gamma \approx 2$$ ) for open boundary conditions at early times. We also study the effect of Langmuir dynamics on the density profile.

Visual high dimensional industrial process monitoring based on deep discriminant features and t-SNE

Visual process monitoring allows operators to identify and diagnose faults intuitively and quickly. The performance of visual process monitoring depends on the quality of extracted features and the performance of the visual model to visualize these features. In this study, we propose a deep model for feature extraction. First, a stacked auto-encoder is used to obtain the feature representation of the input data. Second, the feature representation is fed into a multi-layer perceptron (MLP) with the Fisher criterion as the objective function. The outputs of the MLP are the extracted discriminant features. We combine the proposed feature extraction method with the visual model consisting of t-distributed stochastic neighbor embedding (t-SNE) and a back-propagation (BP) neural network (t-SNE-BP) for visual process monitoring. In this method, an industrial data set is reorganized into a dynamic sample set containing fault trend. Subsequently, the proposed feature extraction method is used to extract discriminant features from the dynamic sample set. Finally, the t-SNE-BP model maps these discriminant features into a two-dimensional space in which the normal and fault states are represented by different regions. Visual process monitoring is performed on this two-dimensional space. The Tennessee Eastman process is used to demonstrate the performance of the proposed feature extraction and visual process monitoring methods.