Dimensional Process Research Articles

Matrix normalised stochastic compactness for a Lévy process at zero

We give necessary and sufficient conditions for a $d$–dimensional Levy process $({\bf X}_t)_{t\ge 0}$ to be in the matrix normalised Feller (stochastic compactness) classes $FC$ and $FC_0$ as $t\downarrow 0$. This extends earlier results of the authors concerning convergence of a Levy process in $\Bbb{R} ^d$ to normality, as the time parameter tends to 0. It also generalises and transfers to the Levy case classical results of Feller and Griffin concerning real- and vector-valued random walks. The process $({\bf X}_t)$ and its quadratic variation matrix together constitute a matrix-valued Levy process, and, in a further extension, we show that the condition derived for the process itself also guarantees the stochastic compactness of the combined matrix-valued process. This opens the way to further investigations regarding self-normalised processes.

Global Well-Posedness and Dynamical Behavior of Delayed Reaction-Diffusion BAM Neural Networks Driven by Wiener Processes

This paper studies the global existence and uniqueness as well as asymptotic behavior of the reaction-diffusion bidirectional associative memory neural networks with S-type distributed delays and infinite dimensional Wiener processes. The conspicuous characteristics of this system are neurons in one layer interacting with neurons in another layer and the noise which disturbed this system has both time and spatial structure. First, several inequalities are proposed and proved for the preparation of future study. Then, the system is coped in the framework of semigroup theory and functional space. Furthermore, the local existence and uniqueness of mild solution for this system is proven by using the contraction mapping principle coupled with many functional inequalities such as Young inequality, Burkholder–Davis–Gundy inequality, Poincare inequality. The global well-posedness are proven through a prior estimate from constructing appropriate Lyapunov–Krasovskii functional. Moreover, the existence of equilibrium is solved by using the topological degree theory and homotopy invariance. At last, the globally exponential stability of the equilibrium in the mean square sense is studied by constructing appropriate vector Lyapunov–Krasovskii functional and using an improved inequality proposed by us. The criteria of stability are given in the form of matrix form. It is easy to verify them in the computer and they will have a wider application. We give an example to examine the availability of our result, and the code is performed in Matlab. The approach used in this paper can also be extended to other systems.

Estimating Ocean Chlorophyll Using the Penalized Three Dimensional (3D) Blending Technique

The Thin Plate Regression Spline (TPRS) was introduced as a means of smoothing off the differences between the satellite and in-situ observations during the two dimensional (2D) blending process in an attempt to calibrate ocean chlorophyll. The result was a remarkable improvement on the predictive capabilities of the penalized model making use of the satellite observation. In addition, the blending process has been extended to three dimensions (3D) since it is believed that most physical systems exist in the three dimensions (3D). In this article, an attempt to obtain more reliable and accurate predictions of ocean chlorophyll by extending the penalization process to three dimensional (3D) blending is presented. Penalty matrices were computed using the integrated least squares (ILS) and integrated squared derivative (ISD). Results obtained using the integrated least squares were not encouraging, but those obtained using the integrated squared derivative showed a reasonable improvement in predicting ocean chlorophyll especially where the validation datum was surrounded by available data from the satellite data set, however, the process appeared computationally expensive and the results matched the other methods on a general scale. In both case, the procedure for implementing the penalization process in three dimensional blending when penalty matrices were calculated using the two techniques has been well established and can be used in any similar three dimensional problem when it becomes necessary.

Micro Sequence Identification of DNA Data Using Pattern Mining Techniques

A rapid development of NGS(Next generation Sequencing) technologies can be able to produce large amounts of sequence data,which is leading in to a wide range of new applications. Sequence matches between a translated nucleotide sequence and a well known biological protein can able to provide a strong evidence for the presence of homologous coding region, and such similarities often be identified even between a distantly related genes. Common techniques often restrict indels in the alignment to improve time,speed, whereas more Flexible aligners are too slow for large-scale applications. Moreover, many current aligners are becoming inefficient as generated reads grow ever larger. To perform such high dimensional process, it requires a special hardware implementation & designing, such implementation can also increases a complexity of efficiency and hardware. The Field Programmable Gate Array is the well-known to design and we propose a high efficient algorithm for sequence detection in any of bioinformatics data. Unlike previous methods, the proposed pattern matching algorithm can identifies the sequence of each factor on the basis of their occurrences. This method can computes the multi-level similarity measure with an available sequences. Based on the multi-level sequence similarity measure computed a single sequence of bioinformatics data can be identified. The proposed method produces efficient result in sequence searching and detection and improves the hardware utilization which in terms reduces the time complexity as well.

Diffusion limit for the partner model at the critical value

The partner model is an SIS epidemic in a population with random formation and dissolution of partnerships, and with disease transmission only occuring within partnerships. Foxall, Edwards, and van den Driessche [7] found the critical value and studied the subcritical and supercritical regimes. Recently Foxall [4] has shown that (if there are enough initial infecteds $I_0$) the extinction time in the critical model is of order $\sqrt{N} $. Here we improve that result by proving the convergence of $i_N(t)=I(\sqrt{N} t)/\sqrt{N} $ to a limiting diffusion. We do this by showing that within a short time, this four dimensional process collapses to two dimensions: the number of $SI$ and $II$ partnerships are constant multiples of the the number of infected singles. The other variable, the total number of singles, fluctuates around its equilibrium like an Ornstein-Uhlenbeck process of magnitude $\sqrt{N} $ on the original time scale and averages out of the limit theorem for $i_N(t)$. As a by-product of our proof we show that if $\tau _N$ is the extinction time of $i_N(t)$ (on the $\sqrt{N} $ time scale) then $\tau _N$ has a limit.

3D-Printed Biomimetic Super-Hydrophobic Structure for Microdroplet Manipulation and Oil/Water Separation.

Biomimetic functional surfaces are attracting increasing attention for various technological applications, especially the superhydrophobic surfaces inspired by plant leaves. However, the replication of the complex hierarchical microstructures is limited by the traditional fabrication techniques. In this paper, superhydrophobic micro-scale artificial hairs with eggbeater heads inspired by Salvinia molesta leaf was fabricated by the Immersed surface accumulation three dimensional (3D) printing process. Multi-walled carbon nanotubes were added to the photocurable resins to enhance the surface roughness and mechanical strength of the microstructures. The 3D printed eggbeater surface reveals interesting properties in terms of superhydrophobilicity and petal effect. The results show that a hydrophilic material can macroscopically behave as hydrophobic if a surface has proper microstructured features. The controllable adhesive force (from 23 μN to 55 μN) can be easily tuned with different number of eggbeater arms for potential applications such as micro hand for droplet manipulation. Furthermore, a new energy-efficient oil/water separation solution based on our biomimetic structures was demonstrated. The results show that the 3D-printed eggbeater structure could have numerous applications, including water droplet manipulation, 3D cell culture, micro reactor, oil spill clean-up, and oil/water separation.

Identification of robust probabilistic slow feature regression model for process data contaminated with outliers

Modeling of high dimensional dynamic process is considered as a challenging task. In this regard, probabilistic Slow Feature Analysis (PSFA), a dynamic latent variable model, is proven to be a useful tool which extracts temporally correlated dynamic features from the high-dimensional raw measurements. The extracted latent Slow Features (SFs) can capture process variations which are useful in developing dynamic models. Often times industrial data is affected by outliers, and modeling such data could result in inferior prediction performance. To deal with such scenarios, we propose a robust PSFA (RPSFA) based regression model that models outliers in the observation data using the Student's t-distribution. To estimate the parameters in RPSFA and to extract reduced dimension of SFs, we employ Expectation-Maximization (EM) algorithm under the Maximum Likelihood Estimation (MLE) framework considering SFs as hidden variables. To estimate the hidden SFs we propose a weighted gain Kalman filter based approach as the Normal distribution assumption of the observations is no longer valid. The validity and merits of the proposed approach are demonstrated though a simulated example, an industrial application and an experimental study.

Fast and accurate mesh registration applied to in-line dimensional inspection processes

Dimensional inspection is a critical step in product manufacturing processes where final assemblers require very tight tolerance levels. New measurement tools such as 3D scanners are becoming a very good alternative to inspect parts where the whole surface needs to be analysed. This process involves registering input data from the scanner with a reference geometry in order to measure dimensional deviations. However it has high computing requirements due to the amount of points that are sampled from the surface of the part being inspected that makes it not suitable for in-line inspection processes. In this paper a fast and robust method is proposed to register 3D meshes with reference geometries for dimensional inspection purposes. It implements the standard metrology alignment pipeline based on geometrical reference features obtained from the reference mesh. Experiments on both real and synthetic data analyses the accuracy and robustness of the method, and compares its efficiency with commercially available software. The method has been validated in an industrial manufacturing environment demonstrating its effectiveness under real conditions.

Modeling and simulation of barite deposition in an annulus space of a well using CFD

In drilling industry, barite particles settling and barite sag as a major problem can potentially impose significant operational issues. Static conditions, in which well undergoes an extended shut-in period, could occur during different drilling and completion operations such fishing operation, tripping, and logging. Despite its importance, such phenomenon is not well understood yet. To avoid issues related to barite settlement and barite sag, a good understanding of the impact of different drilling parameters on barite settlement and sag phenomenon is required. Recently, the mathematical formulation and modeling of settlement and sag processes have gained more attention. In order to better design the drilling fluids and to optimize the operational conditions such as flow rate and drill pipe rotation speed, as well as drilling well trajectory design to avoid barite settlement, the mathematical formulation and modeling of such physical phenomena is required. This study is aimed at mathematically describing and analyzing the settling of barite particles in annular concentric space without axial flow by the means of computational fluid dynamic (CFD) simulation. The modeling approach consists of two main steps: a) simple vertical annular domain and b) complex three dimensional barite settlement process in a deviated well with rotational drill pipe. The current work is based on Eulerian two phase model. The settling of the single particle and the hindering effect of other particles on settling velocity have been investigated. Based on single particle model, the rate of barite settlement and fluid pressure reduction have been modeled. However, the single particle model cannot describe the particle to particle interactions and their impacts on settlement such as particle shearing viscosity, kinetic particle viscosity, and collisional effects. In this study, the accurate and comprehensive modeling of barite settlement has been done by applying the Eulerian-Eulerian approach. The models have been validated against available published experimental data in the literature. In addition, in order to further validate the model presented here, drill pipe rotation, fluid rheology, and inclination angle impacts have been experimental investigation and compared with results of the proposed model. The results indicate that the model based on using Eulerian-Eulerian approach accurately predicts the experimental data results. Afterward, the sensitivity analyses were carried out to show the impact of inclination angle, inner pipe rotation, fluid rheology, and barite content on the rate of settlement. This study showed that drag forces induced resuspension plays a vital role in barite settlement inside a deviated well. The results reveal that the settling rate is decreased with increasing the inner pipe rotation and the vortex effect created by inner pipe rotational, play a major role in the reduction of barite settlement. The results also show that the maximum settlement rate accrues at the deviation angles between of 45–60°.

Comparisons of Process Capability in Cold Chamber Die Casting of Aluminium Alloy

The purpose of the present investigations is to study and compare the effect of processing parameters on process capability of cold chamber die casting of Al alloy. The study presented in this paper is based on a previously published macro model (based on Taguchi design). Castings prepared at proposed parametric settings have been studied and compared using X chart, R chart and process capability histogram (for functional validation of the parts). The study suggested significant improvement in dimensional accuracy and process capability (expressed in terms of sigma ‘σ’ limit) at proposed parametric settings.

Spherically curved layer (SCL) model for metal 3-D printing of overhangs

Directed energy deposition (DED), equipped with 5-axis tool mechanism and no additional machining process, turned out to be able to deposit overhang/undercut features with no support directly on a part in multiple directions. When performing the deposition, two additional axes of rotating and tilting newly added to the working table where the part is typically fixed need to be precisely controlled using an advanced process management technique. The previous approach for slicing algorithm corresponding with multi-axis tool paths along the part and providing a simple stepwise two dimensional layering process of repetitive ±90 degree tilting of the base table can cause unavoidable process delay whenever the base table needs to be tilted for conforming the geometry of overhang/undercut features. Another clear and present barrier to the approach, in addition, is the physical interferences between the tool and the workpiece moving separately during the build. This study proposes a Spherically curved layer (SCL) model providing interference-free 5-axis tool-part movement, a continuous and synchronized interaction between the tool and the part each separately but precisely controlled while kept contacted together, for the build of overhangs. A methodological approach generating SCL information directly from an STL model, followed by the implementation onto various overhang problems as case studies using the proposed methodology, will be discussed in this paper.

Extrema of Wiener Processes

The extrema of Wiener processes are relevant to the pricing of so-called exotic options, which have many financial applications. The probability den-sities of such extrema are well known for one dimensional Wiener processes. We employ elementary methods to derive analytical expressions for the den-sities for multidimensional Wiener processes, with multiple extrema. These take the form of (possibly infinite) series expansions of Gaussian densities. This is undertaken using the characterization of the Wiener process by the heat equation, a well known connection in mathematical physics.

Robust Exponential Synchronization for Stochastic Delayed Neural Networks with Reaction–Diffusion Terms and Markovian Jumping Parameters

This paper investigates robust exponential synchronization for stochastic delayed neural networks with reaction–diffusion terms and Markovian jumping parameters driven by infinite dimensional Wiener processes. The novelty of this paper lives in the use of a new Lyapunov–Krasovskii functional and Poincare inequality to present some criteria for robust exponential synchronization in terms of linear matrix inequalities (LMIs) and matrix measure under Robin boundary conditions. Finally, two numerical examples are provided to illustrate the effectiveness of the easily verifiable synchronization LMIs in MATLAB toolbox.

Numerical modeling of melt-pool behavior in selective laser melting with random powder distribution and experimental validation

A three dimensional selective laser melting process simulation is developed to investigate the melt-pool behavior of a randomly-distributed powder bed with keyhole formation by Nd-YAG laser. In order to simulate a randomly-packed powder bed, the discrete element method is introduced to ensure a close match with real conditions. Also, to show the importance of evaporation during laser melting, the melt pool temperature, melt pool dimensions and the surface morphology are used as metrics for comparison. Numerical results show that the keyhole was formed as evaporation occurred, and the shape of the melt pool was narrow and deep, which implied the main direction of heat transfer had changed to being vertical. Through simulation, the transition from keyhole formation to the final convex surface at a local area was discovered. The simulation results are validated via good agreement with the experiment.

Effects of achievement differences for internal/external frame of reference model investigations: A test of robustness of findings over diverse student samples.

Achievement in math and achievement in verbal school subjects are more strongly correlated than the respective academic self-concepts. The internal/external frame of reference model (I/E model; Marsh, 1986, Am. Educ. Res. J., 23, 129) explains this finding by social and dimensional comparison processes. We investigated a key assumption of the model that dimensional comparisons mainly depend on the difference in achievement between subjects. We compared correlations between subject-specific self-concepts of groups of elementary and secondary school students with or without achievement differences in the respective subjects. The main goals were (1) to show that effects of dimensional comparisons depend to a large degree on the existence of achievement differences between subjects, (2) to demonstrate the generalizability of findings over different grade levels and self-concept scales, and (3) to test a rarely used correlation comparison approach (CCA) for the investigation of I/E model assumptions. We analysed eight German elementary and secondary school student samples (grades 3-8) from three independent studies (Ns 326-878). Correlations between math and German self-concepts of students with identical grades in the respective subjects were compared with the correlation of self-concepts of students having different grades using Fisher's Z test for independent samples. In all samples, correlations between math self-concept and German self-concept were higher for students having identical grades than for students having different grades. Differences in median correlations had small effect sizes for elementary school students and moderate effect sizes for secondary school students. Findings generalized over grades and indicated a developmental aspect in self-concept formation. The CCA complements investigations within I/E-research.

Dimensional comparisons: How academic track students’ achievements are related to their expectancy and value beliefs across multiple domains

In the present study, we investigated how students’ expectancies and values can be predicted by their achievements in multiple domains. Our major aim was to extend previous findings on dimensional comparison processes for expectancies to task values while systematically comparing multiple value facets defined in expectancy-value theory. We assessed the expectancies, values, and achievements of N = 857 students in Grades 5–12 from two German academic track schools in five academic domains. The results for students’ expectancies largely supported the predictions that were derived from dimensional comparison theory: We found strong evidence for negative cross-domain paths between achievements and expectancies in “far” domains such as math and languages, indicating contrast effects. There were also some positive cross-domain paths between achievements and expectancies in “near” domains such as math and physics, indicating assimilation effects. We also found similar patterns of cross-domain paths for students’ values. However, the results varied substantially across the nine value facets under investigation. We found the strongest evidence for dimensional comparison processes for the value facets most closely related to expectancy (e.g., intrinsic value and cost facets), whereas we found only a little evidence for dimensional comparison processes for the facets of utility value.

Conforming finite element methods for the stochastic Cahn–Hilliard–Cook equation

This paper is concerned with the finite element approximation of the stochastic Cahn–Hilliard–Cook equation driven by an infinite dimensional Wiener type noise. The Argyris finite elements are used to discretize the spatial variables while the infinite dimensional (cylindrical) Wiener process is approximated by truncated stochastic series spanned by the spectral basis of the covariance operator. The optimal strong convergence order in L2 and H˙−2 norms is obtained. Unlike the mixed finite element method studied in the existing literature, our method allows the covariance operator of the Wiener process to have an infinite trace, including the space–time white noise is allowed in our model. Numerical experiments are presented to illustrate the theoretical analysis.

Relativistic analysis of stochastic kinematics.

The relativistic analysis of stochastic kinematics is developed in order to determine the transformation of the effective diffusivity tensor in inertial frames. Poisson-Kac stochastic processes are initially considered. For one-dimensional spatial models, the effective diffusion coefficient measured in a frame Σ moving with velocity w with respect to the rest frame of the stochastic process is inversely proportional to the third power of the Lorentz factor γ(w)=(1-w^{2}/c^{2})^{-1/2}. Subsequently, higher-dimensional processes are analyzed and it is shown that the diffusivity tensor in a moving frame becomes nonisotropic: The diffusivities parallel and orthogonal to the velocity of the moving frame scale differently with respect to γ(w). The analysis of discrete space-time diffusion processes permits one to obtain a general transformation theory of the tensor diffusivity, confirmed by several different simulation experiments. Several implications of the theory are also addressed and discussed.

Design and characterization of a mouse trap based on a bistable mechanism

A mouse trap based on a compliant bistable mechanism (BM) is developed in this investigation. The gripping arms of the trap are the addition to the BM. Catch and release operation of the trap are accomplished by snap-through behaviors of the BM. Two stable equilibrium positions of the BM are correspondent to the baiting and gripping configurations of the trap. The proposed mechanism has no movable joints and gains its mobility from the deflection of compliant members. Device complexity is reduced by integration of jaws and gripping arms with the BM. Utilizing the snap-through behavior of the BM, self-closing function for catching mouse is attained without additional locking parts or latches. Therefore, the catch action is autonomous and does not require additional energy input to hold the trapped mouse. Analytical models are developed for design of the device. Prototypes of the mechanism are fabricated by a simple three dimensional printing process. The characteristics of the mechanism are verified by experiments. A “mouse” is caught and released though the linear motion of the BM. The mouse strap can also be used for assembly and disassembly of industrial parts.

Online incipient fault diagnosis based on Kullback‐Leibler divergence and recursive principle component analysis

AbstractFault detection and isolation (FDI) methods based on the principal component analysis (PCA) model have achieved a large number of theoretical studies and applications, especially for complex and highly dimensional processes. However, the Hotelling's T2, that is the most common used statistical distance, can fail in detecting small shifts such as a sensor incipient fault with low fault‐to‐noise ratio (FNR). Although an incipient fault develops slowly, it cannot be ignored and is necessary to be detected early enough to avoid more serious consequences. In this study, a realistic online diagnosis method for incipient faults with low FNR is presented. Based on probability distribution measure, the Kullback‐Leibler divergence (KLD) is utilized to compare the probability density of each of the latent scores to a reference one. Under the hypothesis of Gaussian distribution, dynamic changes of KLDs are computed via the mean and variance of score vectors, which can be updated online utilizing the recursive principal component analysis (RPCA). From simulations, it is shown that the proposed approach can detect, isolate, and estimate the sensor incipient fault of the multivariate AR system successfully.