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In this chapter we define notions of stochastic continuity and differentiability and describe Lindeberg’s condition for continuity of stochastic Markovian trajectories. We also show that the Fokker–Planck equation describes a continuous stochastic process. Finally, we derive the stationary solutions of the Fokker–Planck equation and define potential function of dynamics. © 2019, Springer Nature Switzerland AG  

In this chapter we define notions of stochastic continuity and differentiability and describe Lindeberg’s condition for continuity of stochastic Markovian trajectories. We also show that the Fokker–Planck equation describes a continuous stochastic process. Finally, we derive the stationary solutions of the Fokker–Planck equation and define potential function of dynamics. © 2019, Springer Nature Switzerland AG  

A Continuous model was developed to describe the kinetics of hydroconversion of Marlim crude oil in a slurry-phase reactor. The model was able to accurately predict the liquid product distributions as well as coke formation. The model contained one temperature-independent and six temperature-dependent parameters.The model parameters were obtained by an optimization procedure using experimental data available in the open literature for reaction temperatures of 440-460°C, hydrogen pressure of 14.7 MPa, liquid hourly space velocity (LHSV) of 0.5 h-1, and a hydrogen to oil ratio of 100 to 1 ft3/bbl. Comparison between experimental and predicted product distributions and coke yields indicated a... 

Multi-Facility Weber Problem (MFWP), also known as continuous location–allocation problem, entails determining the locations of a predefined number of facilities in a planar space and their related customer allocations. In this paper, we focus on a new variant of the problem known as Single-Source Capacitated MFWP (SSCMFWP). To tackle the problem efficiently and effectively, an iterative two-phase heuristic algorithm is put forward. At the phase I, we aim to determine proper locations for facilities, and during the phase II, assignment of customers to these facilities is pursued. As an alternative solution method, a simulated annealing (SA) algorithm is also proposed for carrying out the... 

A detailed pseudo-bulk model has been used for prediction of conversion and particle size distribution (PSD) of vinyl acetate in a continuous emulsion polymerization reactor. Finite volume (FV) and moment techniques are applied for solving population balance equation under continuous operation. It is found that both methods can predict sustained oscillations in the monomer conversion, however the FV method matches the experimental data better than the moment method. The monomer conversion and free surfactant concentration are controlled via two single control loops. In this work, a new control strategy for controlling monomer conversion has been proposed. It has been shown that monomer... 

In this paper we address the problem of image interpolation using Gaussian Mixture Models (GMM) as a prior. Previous methods of image restoration with GMM have not considered spatial (geometric) distance between patches in clustering, failing to fully exploit the coherency of nearby patches. The GMM framework in our method for image interpolation is based on the assumption that the accumulation of similar patches in a neighborhood are derived from a multivariate Gaussian probability distribution with a specific covariance and mean. An Expectation Maximization-like (EM-like) algorithm is used in order to determine patches in a cluster and restore them. The results show that our image... 

Endoscopic endonasal surgery is a minimal invasive surgery that has been used to dissect pituitary gland tumour via curettes with the help of endoscope. However, this type of surgery has a high risk of failure because curettes may cause damages to blood vessels and optical nerves that lead to more complication for the patient. The aim of this study is to develop a new technique to dissect the tumour by using liquid jet. A series of experimental tests have been performed on animal tissue to study the effect of liquid pressure and nozzle diameter on dissecting and cutting the tissue. Continuous/pulsed liquid jet used with variable nozzle diameters, distances, pressures and angles. The study... 

In the metal deposition process, the performance of the nozzle is crucial to the quality of clad. Continuous coaxial nozzles are broadly used in this process for repairing two- and three-dimensional parts, because it can create a homogeneous distribution of powder particles. In addition, an inert gas can be applied using this type of nozzles which shields powder particles and laser interaction zone, and prevents the surface from oxidizing at high process temperatures. However, when this type of nozzle is tilted from the vertical axis for cladding non-horizontal surfaces, the effect of gravity on powder particles affects the uniformity of powder distribution at the nozzle outlet. This matter... 

Continuity and reliability of electricity supply in a country are vital to the operational continuity of the critical infrastructure and government. High levels of cyber security are required to achieve such key measures in the electricity industry. We propose solutions and models on how to improve the cyber security using the maturity model in order to achieve continuity of electricity supplies. Maturity levels start from the relative level (level 1) and continue to the adaptive level (level 4). A total of 10 domains are defined in the model. The practices of cyber security are clustered into domains. The model is used for assessment of the strength and weakness factors for the... 

In this paper, an attractive and novel algorithm for improving irreducible model identification of continuous time(CT) MIMO systems has been presented. The algorithm is based on least - squares (LS) estimates of Markov parameters (MP) using input output data and residual whitening. By choosing a linear-in-parameters model structure, the estimation becomes linear and asymptotically robust to zero-mean additive disturbances. CT Markov parameters may result in diverging approximations even for stable systems. To remove the existing limitations in the case of systems with low or zero damping, Markov Poisson parameters have been used to lend much flexibility to the estimation model. The MIMO... 

In the metal deposition process, the performance of the nozzle is crucial to the quality of clad. Continuous coaxial nozzles are broadly used in this process for repairing two- and three-dimensional parts, because it can create a homogeneous distribution of powder particles. In addition, an inert gas can be applied using this type of nozzles which shields powder particles and laser interaction zone, and prevents the surface from oxidizing at high process temperatures. However, when this type of nozzle is tilted from the vertical axis for cladding non-horizontal surfaces, the effect of gravity on powder particles affects the uniformity of powder distribution at the nozzle outlet. This matter... 

We review our investigations on bismuth-oxide fiber as an amplifying medium for parametric amplifiers with continuous-wave pumping. The results lead to new applications in demultiplexing, which are discussed  

We introduce dynamic plastic continuous neural network (DPCNN), which is comprised of neurons distributed in a nonlinear plastic medium where wire-like connections of neural networks are replaced with the continuous medium. We use finite element method to model the dynamic phenomenon of information processing within the DPCNNs. During the training, instead of weights, the properties of the continuous material at its different locations and some properties of neurons are modified. Input and output can be vectors and/or continuous functions over lines and/or areas. Delay and feedback from neurons to themselves and from outputs occur in the DPCNNs. We model a simple form of the DPCNN where the... 

In this work, the effect of the number of stages on the productivity of a multi-effect active solar still was experimentally investigated for the first time. Moreover, system performances in continuous and non-continuous modes were compared. For this purpose, indoor experiments were conducted on 4 similar solar still devices with different stages (1-4 stages) in order to accurately control the environmental conditions. In addition, water production was hourly measured during the whole 24-h experiment. The results show that with increased number of stages, distillate production can be predicted with a quadratic function. Moreover, adding a maximum of 6 and 10 additional stages can... 

In this paper, a new approach to control continuous time chaotic systems with an unknown governing equation and limitation on the measurement of states, has been investigated. In many chaotic systems, disability to measure all of the states is a usual limitation, like in some economical, biological and many other engineering systems. Takens showed that a chaotic attractor has an astonishing feature in which it can embed to a mathematically similar attractor by using time series of one of the states. The new embedded attractor saves much information from the original attractor. This phenomenon has been deployed to present a new way to control continuous time chaotic systems, when only one of... 

Azo dye degradation in wastewater treatment is a subject which has garnered the attention of many research studies. In this study, an innovative approach, namely, an integrated system of five batches (ISFB), was developed to investigate the capability of Saccharomyces cerevisiae ATCC 9763 for continuous degradation of methyl red as a representative azo dye. Toward this end, an expanded immobilized microbial bed (EIMB) reactor was established with a bed of encapsulated yeast cells in sodium alginate. EIMB reactor was run in two modes, single batch and ISFB. Moreover, durability of the microbial cells was evaluated by repeating the continuous decolourization eight sequential times in EIMB at... 

In this paper, a mixed event-triggered and continuous-time control method is proposed, which can guarantee finite-time stabilisation of the fixed point in a class of time-varying nonlinear systems. Benefiting from an event-triggered framework, which is constructed based on the indefinite Lyapunov theory, the communication/computation costs in the transient time can be reduced by using the proposed method. In a special case, this method is converted to a fully event-triggered control strategy for asymptotic stabilisation of the fixed point in the considered class of time-varying nonlinear systems. The effectiveness of the proposed method is verified by numerical simulations. © 2021 Informa UK... 

Originally, the application of nano zero valent iron/nickel (nZVI/Ni) particles for nitrate removal in porous media was studied. nZVI/Ni was prepared and employed in batch and continuous modes. Based on batch experiments, the reaction kinetics was consistent with the adsorption model by the order of 1-1.5. The variation of the kinetics order depends on pH and nickel content. So that highest reactivity was observed for nZVI with 10% of Ni at pH ≤ 3. Nitrate remediation in a continuous system was mostly influenced by seepage velocity, quantity and freshness of nZVI/Ni and particle size of porous media. In a batch mode, the maximum nitrate removal was 99% while in a continuous mode it did not... 

In this paper, an attractive and novel algorithm for improving irreducible model identification of continuous time(CT) MIMO systems has been presented. The algorithm is based on least - squares (LS) estimates of Markov parameters (MP) using input output data and residual whitening. By choosing a linear-in-parameters model structure, the estimation becomes linear and asymptotically robust to zero-mean additive disturbances. CT Markov parameters may result in diverging approximations even for stable systems. To remove the existing limitations in the case of systems with low or zero damping, Markov Poisson parameters have been used to lend much flexibility to the estimation model. The MIMO... 

Energy harvesting has been developed as an effective technology for communication systems in order to extend their lifetime. In this paper, we consider a single-user energy harvesting wireless communication system, in which arrival data and harvested energy curves are modeled as continuous functions. Our first goal is to find an offline algorithm, which maximizes the amount of data, which is transmitted to the receiver node by a given deadline. If more than one scheme exists that transmits the maximum data, we choose the one with minimum utilized energy at the transmitter node. We find this optimal algorithm, by showing its properties. Next, we propose an online algorithm for this system and...