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We prove strong convergence of the sequence generated by implicit viscosity approximation method involving a multivalued nonexpansive mapping in framework of CAT(0) space. Under certain appropriate conditions on parameters, we show that such a sequence converges strongly to a fixed point of the mapping which solves a variational inequality. We also present some convergence results for the implicit viscosity approximation method in complete ℝ-trees without the endpoint condition.

In this research, we are interested about the monotone inclusion problems in the scope of the real Hilbert spaces by using an inertial forward–backward splitting algorithm. In addition, we have dis...

In the current study, prediction of the viscosity of branched alkanes was considered using the adaptive network-based fuzzy inference system optimized with an evolutionary algorithm named different...

The purpose of this paper is to introduce a modified viscosity implicit rules for finding a common element of the set of solutions of variational inequality problems for two inverse-strongly monotone operators and the set of fixed points of one nonexpansive mapping in Hilbert spaces. Under some suitable assumptions imposed on the parameters, we obtain some strong convergence theorems. We also apply our main results to solve fixed point problems for strict pseudocontractive mappings and equilibrium problems in Hilbert spaces. A numerical example is given for supporting our main results.

The study of the interaction between solid objects and magnetohydrodynamic (MHD) fluids is of great importance in physics as consequence of the significant phenomena generated, such as planets interacting with stellar wind produced by their host stars. There are several computational tools created to simulate hydrodynamic and MHD fluids, such as the FLASH code. In this code there is a feature which permits the placement of rigid bodies in the domain to be simulated. However, it is available and tested for pure hydrodynamic cases only. Our aim here is to adapt the existing resources of FLASH to enable the placement of a rigid body in MHD scenarios and, with such a scheme, to produce the simulation of a non-magnetized planet interacting with the stellar wind produced by a sun-like star. Besides, we consider that the planet has no significant atmosphere. We focus our analysis on the patterns of the density, magnetic field and velocity around the planet, as well as the influence of the viscosity on such patterns. At last, an improved methodological approach is available to other interested users., 16 pages, 35 figures

Various miniaturized viscometers have been developed utilizing several fabrication methods. Among them, microfluidic paper-based analytical devices ( $\mu $ PADs) are becoming popular due to their fabrication ease, cost-effectiveness, and the fact that the flow can be carried out using the embedded capillaries themselves. Mostly, $\mu $ PADs are reported to be fabricated by a solid-ink printer, which has significantly high capital and operational cost. To overcome such drawbacks, a novel rapid prototyping method has been proposed, wherein the formation of the hydrophobic regions was created by polycaprolactone (PCL) filament using a 3-D printer. To leverage this, $\mu $ PAD as a viscometer, velocity, or time between two points with known distances was required, which was carried out by an amperometric approach, established by fabricating the integrated screen-printed electrodes intersecting the microchannel of the $\mu $ PAD. The time measurement was fully automated by a microcontroller, and the relative viscosity was calculated by comparing the time taken by the reference fluid with that of a test fluid to cover a known length. Such integrated, automated, and low-cost paper-based microviscometer was leveraged to measure and analyze the viscosities of various milk variants, which has an accuracy of >92%.

peer-reviewed The ideal PAT tool is an inline instrument that can monitor and measure process parameters simultaneously in real time while operating in a highly automated environment. Instruments must be of sanitary design, operate robustly within the full process cycle (production and cleaning). Inline determination of the rheological properties of moving fluids (i.e. dairy concentrates) is one of the process parameters where PAT tools can be add real value in terms of optimising process control. Measurement of process viscosity is crucial in the monitoring and control of a variety of concentration processes in the dairy industry. Continuous monitoring of the rheological behaviour of the fluid can allow for optimisation of the process e.g. pumping (avoid pump blockage and failure), evaporation (limit fouling and maximise water removal) and spray drying (avoidance of nozzle fouling). This review concentrates on the state of the art developments being made in the area of process viscometry.

In this manuscript, we introduce two iterative methods for finding the common zeros of two H-accretive mappings in uniformly smooth and uniformly convex Banach spaces. The proposed iterative methods are based on Mann and Halpern iterative methods and viscosity approximation method. Strong convergence results are established for iterative algorithms. Applications based on convex minimization problem, variational inequality problem and equilibrium problem are derived from the main result. Numerical implementation of the main results and application are demonstrated by some examples. Our results extend, generalize, and unify the previously known results given in literature.

We prove the existence and uniqueness of the viscosity solutions to the obstacle problems for second order differential partial equations under some conditions. As applications, we show some existence and uniqueness theorems of the viscosity solutions to the obstacle problems for k-Hessian equations, which include Monge-Ampere type equations when k = n .

In current design procedures, asphalt binder grades are represented by tables of potential parameter values. In the Mechanistic-Empirical Pavement Design Guide these are A-VTS pairs. The discretene...

Smoothed particle hydrodynamics (SPH) is a meshless method gaining popularity recently in geotechnical modeling. It is suitable to solve problems involving large deformation, free-surface, cracking and fragmentation. To promote the research and application of SPH in geotechnical engineering, we present LOQUAT, an open-source three-dimensional GPU accelerated SPH solver. LOQUAT employs the standard SPH formulations for solids with two geomechnical constitutive models which are the Drucker–Prager model and a hypoplastic model. Three stabilization techniques, namely, artificial viscosity, artificial pressure and stress regularization are included. A generalized boundary particle method is presented to model static and moving boundaries with arbitrary geometry. LOQUAT employs GPU acceleration technique to greatly increase the computational efficiency. Numerical examples show that the solver is convergent, stable and highly efficient. With a mainstream GPU, it can simulate large scale problems with tens of millions of particles, and easily performs more than one thousand times faster than serial CPU code.

This paper is concerned with an infinite horizon optimal control with unbounded value functions for a class of Hamilton–Jacobi equations (HJEs) in Banach spaces. Based on the uniqueness of $$\beta $$ -viscosity solutions of HJEs, which is first established in this paper, necessary and sufficient optimality conditions are derived.

BACKGROUND: How to accurately predict the occurrence of contamination in the fermentation process of Chlortetracycline? How to prompt field operators to take effective measures in time? This is a difficult problem that the fermentation process of Chlortetracycline has not been solved well. OBJECTIVE: The aim of this paper is to effectively predict whether the fermentation process of Chlortetracycline is contaminated or not. METHODS: A Gaussian process regression soft sensor modeling method with real time integration learning is studied in depth by combining two local learning strategies, namely just-in-time learning (JITL) method and integrated learning method, and a multi-model weighted Gaussian process regression (MWGPR) soft sensor modeling method based on real-time integration learning is proposed in the paper. This soft sensing method was used to study the relationship between the viscosity of fermentation broth and the contamination in fermentation process. A soft-sensing model based on the viscosity of fermentation broth for predicting the signs of contamination is established. RESULTS: The validity of this method is verified by field data. The experimental results demonstrate that the soft sensing model proposed in this paper can effectively determine whether the fermentation broth is infected by hybrid bacteria. CONCLUSIONS: The method proposed in this paper is innovative and practical so that field operators can issue early warning and take effective measures.

In this paper, we introduce two new iterative algorithms for solving monotone variational inequality problems in real Hilbert spaces, which are based on the inertial subgradient extragradient algorithm, the viscosity approximation method and the Mann type method, and prove some strong convergence theorems for the proposed algorithms under suitable conditions. The main results in this paper improve and extend some recent works given by some authors. Finally, the performances and comparisons with some existing methods are presented through several preliminary numerical experiments.

The global equi-continuity estimate on $$L^p$$ -viscosity solutions of bilateral obstacle problems with unbounded ingredients is established when obstacles are merely continuous. The existence of $$L^p$$ -viscosity solutions is established via an approximation of given data. The local Holder continuity estimate on the first derivative of $$L^p$$ -viscosity solutions is shown when the obstacles belong to $$C^{1,\beta }$$ , and $$p>n$$ .

We formulate a stochastic impulse control model for animal population management and a candidate of exact solutions to a Hamilton–Jacobi–Bellman quasi-variational inequality. This model has a qualitatively different functional form of the performance index from the existing monotone ones. So far, optimality and unique solvability of the Hamilton–Jacobi–Bellman quasi-variational inequality has not been investigated, which are thus addressed in this paper. We present a candidate of exact solutions to the Hamilton–Jacobi–Bellman quasi-variational inequality and prove its optimality and unique solvability within a certain class of solutions in a viscosity sense. We also present and examine a dynamical system-based numerical method for computing coefficients in the exact solutions.

In this work, we introduce a self-adaptive algorithm, based on viscosity approximation methods, to solve split common fixed point problems of demicontractive operators in real Hilbert spaces. Besid...

Purpose The purpose of this paper is to develop an integrated engineering process control (EPC)–statistical process control (SPC) methodology for simultaneously monitoring and controlling autocorrelated multiple responses, namely, brightness and viscosity of the pulp bleaching process. Design/methodology/approach The pulp bleaching is a process of separating cellulose from impurities present in cooked wood chips through chemical treatment. More chemical dosage or process adjustments may result in better brightness but adversely affect viscosity. Hence, the optimum chemical dosage that would simultaneously minimize the deviation of pulp brightness and viscosity from their respective targets needs to be determined. Since the responses are autocorrelated, dynamic regression is used to model the responses. Then, the optimum chemical dosage that would simultaneously optimize the pulp brightness and viscosity is determined by fuzzy optimization methodology. Findings The suggested methodology is validated in 12 cases. The validation results showed that the optimum dosage simultaneously minimized the variation in brightness and viscosity around their respective targets. Moreover, suggested solution has been found to be superior to the one obtained by optimizing the responses independently. Practical implications This study provides valuable information on how to identify the optimum process adjustments to simultaneously ensure autocorrelated multiple responses on or close to their respective targets. Originality/value To the best of the authors’ knowledge, this paper is the first to provide application of the integrated EPC–SPC methodology for simultaneously monitoring multiple responses. The study also demonstrates the application of dynamic regression to model autocorrelated responses.

We show that viscosity solutions of evolutionary weakly coupled systems of Hamilton--Jacobi equations can be approximated by iterated twisted Lax--Oleinik like operators. We establish convergence to the solution of the iterated scheme and discuss further properties of the approximate solutions.

We consider a pressure-stabilized Lagrange–Galerkin scheme for the transient Oseen problem with small viscosity. In the scheme we use the equal-order approximation of order k for both the velocity and pressure, and add a symmetric pressure stabilization term. We show an error estimate for the velocity with a constant independent of the viscosity if the exact solution is sufficiently smooth. We also show an error estimate of a discrete primitive of the pressure. Numerical examples show high accuracy of the scheme for problems with small viscosity.

The authors gratefully acknowledge the supports provided by the National Science Fund for Distinguished Young Scholars of China [No. 51525604], the Foundation for Innovative Research Groups of the National Natural Science Foundation of China [No.51721004], the National Basic Research Program of China [No. 2015CB251502] and 111 Project [No. B16038].

A Hamilton–Jacobi–Bellman Quasi-Variational Inequality (HJBQVI) for a river environmental restoration problem with wise-use of sediment is formulated and its mathematical properties are analyzed. A finite difference scheme with a penalization technique is then established for solving the HJBQVI. The scheme is free from any iterative solvers and is unconditionally stable and convergent in the viscosity sense under certain conditions. A demonstrative application example of the HJBQVI is finally presented.

Background: Compliance to modern requirements to quality of motor oil to depends largely on level of automation of industrial process of their preparation. Existing and really functioning refinery processing units provide constancy of the target numerical index of the viscosity of oil only when the mix formulation of production is strictly observed. In mix formulation, the flow parameters of the base oil and additives are determined, the temperature in the reactor and the preparation time also exerts impact the technological process. Refinery processing units of production of motor oil of the type in question don't provide possible changes of flowrate of components in the reactor, which leads to a viscosity factor deviation from the desired one. Stringent control of technological process of production of motor oil provides: high stability of a product, good torque properties at low temperatures, necessary viscosity within working temperatures. Materials and methods: The system analysis of the technological process is carried out on the basis of the experimental data of operation of the unit for obtaining motor oil. The optimal control system is developed on the basis of the mathematical model of the research object in the software package of the SCADA-system Trace Mode. Results: Automated control system for the production of motor oil is developed based on Trace Mode which includes: a screen for setting technological parameters, a mnemonic diagram of the process, a control program. The realized program exercises control of process of giving in the reactor of base oil and additives, alarm on flow rate, control of the temperature of the mixture of base oil and additives in the reactor, carries out turning on of the engine of the mixing device, and also realizes the timer of preparation time of oil. Conclusions: Employment of the motor oil received by means of the embedded system will help to avoid: impurities of engines, corrosive wear when using high-sulphur fuel, breakdown.

The purpose of this paper is to introduce and study the general viscosity approximation methods for quasi-nonexpansive mappings in the setting of infinite-dimensional Hilbert spaces. Under suitable conditions, we prove that the sequences generated by the proposed new algorithm converge strongly to a fixed point of quasi-nonexpansive mappings in Hilbert spaces, which is also the unique solution of some variational inequality. Then this result is used to study the split equality fixed point problems, the split equality common fixed point problems, the split equality null point problems, etc. Our results improve and generalize many results in the literature and they should have many applications in nonlinear science.

A model system for decision-making support (a model of the blast-furnace process developed at Yeltsin Ural Federal University and PAO MMK) is considered. The basic model modules permit calculation of the material and thermal balances, simulation of the thermal, slag, and gas-dynamic conditions in the blast furnace, and selection of the batch composition. The model system, embodied as software, is integrated into the PAO MMK information system. The model for calculating the material and thermal balances permits determination of the Fe, S, Mn, and Ti balances. Introduction of the Slag Conditions software permits identification of the most important slag property to ensure normal slag conditions; determination of the ratio of the iron-ore materials so that the slag has the best viscosity and viscosity gradient; and the production of hot metal of the required quality. The introduction of Blast-Furnace Gas Dynamics software permits calculation and visual mapping of the gas-dynamic characteristics of the batch bed and assessment of the change in pressure difference and equilibration of the batch within individual zones of the furnace in the design period, with variation in the batch parameters and properties. The results obtained in practical use of this system are outlined. Recommendations are made regarding the solution of industrial problems.

The purpose of this paper is to investigate the problem of finding a common element of the set of zero points of the sum of two operators and the fixed point set of a quasi-nonexpansive mapping. We introduce modified forward-backward splitting methods based on the so-called inertial forward-backward splitting algorithm, Mann algorithm and viscosity method. We establish weak and strong convergence theorems for iterative sequences generated by these methods. Our results extend and improve some related results in the literature.

Strong convergence theorem of viscosity approximation methods for nonexpansive mapping have been studied. We also know that CQ algorithm for solving the split feasibility problem (SFP) has a weak c...

The purpose of this paper is to introduce and analyze a hybrid extragradient-like implicit rule for finding a common solution of a general system of variational inequalities (GSVI) and a common fixed point problem (CFPP) of a countable family of uniformly Lipschitzian pseudocontractive mappings and an asymptotically nonexpansive mapping in Hilbert spaces. Here the hybrid extragradient-like implicit rule is based on Korpelevich’s extragradient method, the viscosity approximation method and the Mann iteration method. We prove the strong convergence of this method to a common solution of the GSVI and the CFPP, which solves a certain variational inequality on their common solution set. As an application, we give an algorithm to solve common fixed point problems of nonexpansive and pseudocontractive mappings, variational inequality problems and generalized mixed equilibrium problems in Hilbert spaces.

In this paper, we study the existence and uniqueness of viscosity solutions to a kind of Hamilton--Jacobi--Bellman (HJB) equation combined with algebra equations. This HJB equation is related to a ...

An evolutionary Navier–Stokes-type equation is considered. Due to the presence of a bilinear operator term in it, it is possible to introduce a small parameter and expand the solution in it. The main objective of the paper is to find the conditions for the ordinary (not asymptotic) convergence of the series obtained in this case.

A viscosity approach is introduced for the Dirichlet problem associated to complex Hessian type equations on domains in $\C^n$. The arguments are modelled on the theory of viscosity solutions for real Hessian type equations developed by Trudinger. As consequence we solve the Dirichlet problem for the Hessian quotient and special Lagrangian equations. We also establish basic regularity results for the solutions., 29 pages

With the increase of conversion and viscosity, a batch free radical polymerization (FRP) may encounter complicated phenomena, including the gel, glass, and cage effects. These effects normally lead to a conditional modeling formulation described by a set of differential-algebraic equations (DAEs). Discontinuous gradient exists at model switches triggered by occurrence of the effects, which cause difficulty for dynamic optimization on the batch process. To deal with the discontinuity, interior-point smooth approximations are proposed to describe the model switches at the occurrence of the effects. An adaptive smoothing strategy, which can efficiently balance the efficiency of optimization and the accuracy of the approximated model, is proposed for the dynamic optimization. To show the effectiveness of this smoothing strategy, case studies for optimal operating profiles in a polymerization process of methyl methacrylate are conducted. Good computational performance is achieved with the proposed strategy.

It is well known that the quadratic-cost optimal transportation problem is formally equivalent to the second boundary value problem for the Monge--Ampere equation. Viscosity solutions are a powerfu...

In this paper, we identify a class of input constrained optimal control problems which can be approximately solved using Reinforcement Learning (RL) approaches. We start with a general class of problems which do not admit the theoretical assumptions used to derive RL frameworks. We then restrict this class by extra conditions on the dynamics and the objective function as deemed necessary. Our attention concerns two assumptions: (i) the smoothness of the value function which is typically not satisfied in input constrained problems, and (ii) the form of the objective function which can be more general than what has been proposed in previous formulations. For the first assumption, we use the method of vanishing viscosity to derive the conditions under which RL approaches can be used to find an approximate solution. These conditions relax a differentiability assumption to a continuity assumption of the value function thereby extending the applicability of RL frameworks. For the second assumption, we generalize the specific integrand form of the control cost used in previous formations to a more general class of cost functions that guarantee continuity of the control policy. Using these results, we present a new partially model-free RL framework for optimal control of input constrained continuous-time systems. Our RL framework requires an initial stabilizing policy and guarantees uniformly ultimate boundedness of the state variables. We demonstrate our results by simulation examples.

In this paper, we study a general viscosity explicit rule for approximating the solutions of the variational inclusion problem for the sum of two monotone operators. We then prove its strong convergence under some new conditions on the parameters in the framework of Hilbert spaces. As applications, we apply our main result to the split feasibility problem and the LASSO problem. We also give some numerical examples to support our main result. The results presented in this paper extend and improve the corresponding results in the literature.

International audience; Motivated by the result of invariance of regular-boundary open sets in \cite{CannarsaDaPratoFrankowska2009} and multi-stability issues in gene networks, our paper focuses on three closely related aims. First, we give a necessary local Lipschitz-like condition in order to expect invariance of open sets (for deterministic systems). Comments on optimality are provided via examples. Second, we provide a border avoidance (near-viability) counterpart of \cite{CannarsaDaPratoFrankowska2009} for controlled Brownian diffusions and piecewise deterministic switched Markov processes (PDsMP). We equally discuss to which extent Lipschitz-continuity of the driving coefficients is needed. Finally, by applying the theoretical result on PDsMP to Hasty's model of bacteriophage (\cite{hasty_pradines_dolnik_collins_00}, \cite{crudu_debussche_radulescu_09}), we show the necessity of explicit modeling for the environmental cue triggering lysis.

In this paper, we investigate a path-dependent American option problem and provide an efficient and implementable numerical scheme for the solution of its associated path-dependent variational inequality. We obtain the viscosity characterization of our value function and suggest a monotone, stable and consistent numerical scheme, the convergence of which is proven thanks to the uniqueness property. We further enrich our study by providing and implementing a numerical algorithm. Some numerical results are also included.

In this paper, we study a general system of variational inequalities with a hierarchical variational inequality constraint for an infinite family of nonexpansive mappings. We introduce general implicit and explicit iterative algorithms. We prove the strong convergence of the sequences generated by the proposed iterative algorithms to a solution of the studied problems.

Introduction: Oral feeding safety is necessary to provide nutrition, hydration, and eating pleasure for patients with dysphagia. Commercial thickeners are prescribed for these patients to change food viscosity and may alter the proper preparation of modified food. Objective: Analyze composition, employed terminology, preparation instructions, recommended amount and weight of provided measuring spoons, nutritional information, and viscosity of 7 commercial thickeners. Methods: The sample comprised all thickeners from different brands available in Brazil, named A to G. Products were submitted to viscosity analysis using viscometer and the International Dysphagia Diet Standardization Initiative (IDDSI) test. Samples were prepared with mineral water (25°C) and with the amount of thickener recommended to obtain intermediate viscosity (level 2) according to the manufacturer’s instructions. Results: Products B, C, and E presented similar composition. Manufacturer’s information about the amount and preparation procedure, time, temperature, and base liquid was incomplete. Viscosity tests revealed that thickener C was basically solid while D displayed results out of the desired viscosity level. Conclusions: The study showed differences in components and viscosity, beyond the lack of label details. There was no established correlation between viscosity classifications provided by National Dysphagia Diet and IDDSI.

We study the problem of maximising expected utility of terminal wealth under constant and proportional transaction costs in a multidimensional market with prices driven by a factor process. We show that the value function is the unique viscosity solution of the associated quasi-variational inequalities and construct optimal strategies. While the value function turns out to be truly discontinuous, we are able to establish a comparison principle for discontinuous viscosity solutions which is strong enough to argue that the value function is unique, globally upper semicontinuous, and continuous if restricted to either borrowing or non-borrowing portfolios.

In recent years, research and development of 3D food printers have been actively conducted. In the Food Layer Manufacturing (FLM) 3D food printer, the molding conditions must be set for physical properties of the each material. In the previous study, it is reported that the modeling accuracy improves as viscosity increases. However, since it is difficult to use a rheometer or a viscometer at each household, a simple physical property measuring device is necessary. Therefore, in this study, we will investigate whether the shaping conditions can be determined from the concentric circle spreading out of the container after vibrating the gel contained in the cylindrical container with the diaphragm.

In order to improve the performance of the piezoelectric micro jetting dispenser used in opto-electronic packaging industry, a new structure of the needle with a pin joint is suggested. Dynamic characteristics of the proposed micro jetting dispenser has been improved because the needle can swing around the joint and motion interference between the needle and the guiding part is decreased with the new structure. Compared with the original dispenser, the needle stroke of the proposed dispenser is increased 1.8 times, and the velocity of the needle increased 1.4 times. The jet performance is also improved. Adhesives with viscosity of 1.8 Pa s are jetted by the new micro dispenser smoothly. The mathematical models and dynamics simulation model are established. The tested results agree with the simulation ones, which proves that the models and the structure of the proposed dispenser are reliable.

Most of the existing numerical schemes developed to solve Burgers' equation cannot exhibit its correct physical behavior for very small values of viscosity. This difficulty can be overcome by using splitting methods derived for near-integrable system. This class of methods has positive real coefficients and can be used for non-reversible systems such as Burgers' equation. It also has the advantage of being able to account small viscosity in the accuracy. The algorithm is based on the combination of implicit-explicit finite difference schemes to solve each simplified problem and filtering technique to treat nonlinear instability. The resulting algorithm is accurate, efficient and easy to implement. The new numerical results are compared with numerical and exact solutions reported in the literature and found that they are very accurate for small values of the viscosity. (C) 2018 Elsevier B.V. All rights reserved.