Non-standard Conditions Research Articles

Regularity Results for Bounded Solutions to Obstacle Problems with Non-standard Growth Conditions

In this paper, we consider a class of obstacle problems of the type min∫Ωf(x,Dv)dx:v∈Kψ(Ω)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} \\min \\left\\{ \\int _{\\Omega }f(x, Dv)\\, {\\mathrm d}x\\,:\\, v\\in {\\mathcal {K}}_\\psi (\\Omega )\\right\\} \\end{aligned}$$\\end{document}where psi is the obstacle, {mathcal {K}}_psi (Omega )={vin u_0+W^{1, p}_{0}(Omega , {mathbb {R}}): vge psi text { a.e. in }Omega }, with u_0 in W^{1,p}(Omega ) a fixed boundary datum, the class of the admissible functions and the integrand f(x, Dv) satisfies non standard (p, q)-growth conditions. We prove higher differentiability results for bounded solutions of the obstacle problem under dimension-free conditions on the gap between the growth and the ellipticity exponents. Moreover, also the Sobolev assumption on the partial map xmapsto A(x, xi ) is independent of the dimension n and this, in some cases, allows us to manage coefficients in a Sobolev class below the critical one W^{1,n}.

Characterization of Engineered Cerium Oxide Nanoparticles and Their Effects on Lung and Macrophage Cells

Cerium oxide nanoparticles are promising materials as novel nanoscale therapeutics and are commonly used materials in industrial processes. Most cytotoxicity studies on cerium oxide nanoparticles are made from in-lab prepared materials making comparison between studies challenging, especially when performed on unique cell lines under non-standard conditions. Using commercially available nanoparticles we show that particle stability/agglomeration may be critical in determining the cytotoxicity in some cell lines, while in other cell lines, larger sized primary particles are linked to higher cytotoxicity, contrasting what has been reported in the literature for smaller cerium nanoparticles. To accelerate the development of cerium oxide enabled commercial processes and biomedical innovations, a clearer understanding of the interactions between cerium oxide nanoparticles and cells is needed to better understand their fate in and impact on biological systems.

Nonlinear flexure mechanics of mixture unified gradient nanobeams

The mixture unified gradient theory of elasticity is invoked for the nanoscopic study of the nonlinear flexure mechanics of nanobeams. A mixed variational framework is conceived based on ad hoc functional space of kinetic test fields, wherein a complete set of governing equations, classical and non-standard boundary conditions, and the constitutive relations are integrated into a solitary functional. The size-effect phenomenon associated with the nonlinear flexure of nanobeams are efficiently realized as the stress gradient theory, the strain gradient theory, and the classical elasticity theory are consistently unified within the framework of the mixture unified gradient elasticity. A viable numerical approach is introduced based on the conceived mixed variational framework while the autonomous series solution of the kinematic and kinetic field variables is implemented. As the kinetic field variables are directly determined rather than utilizing post-computations, the established consistent variational theory provides an advantageous means for efficacious approximate approaches. The nonlinear flexural response of the mixture unified gradient beams with kinematics constraints of practical interest in nano-mechanics is detected and thoroughly compared with the linear counterparts in terms of the characteristic parameters. The detected nonlinear flexural characteristics of nano-sized beams can pave the way ahead in the nonlinear mechanics of nano-structures.

On the issue of taking into account new factors in the pathogenesis of occupational hearing loss (on the example of transport workers)

Introduction. In the period from 2013 to 2021, industrial enterprises saw a reduction in jobs that did not meet sanitary and hygienic requirements for the level of exposure to noise, vibration, illumination, microclimate parameters and electromagnetic fields on the workers' bodies. However, the proportion of unfavorable workplaces that do not meet the standards for noise levels remains the largest, which determines the peculiarities of the structure of the occupational pathology of workers in the Russian Federation: professional pathology of the hearing organ - professional sensorineural hearing loss - remains in the first place. The transport industry is among the sectors of the economy with the most significant indicators of occupational diseases exceeding the average Russian indicator. The study aims to analyze additional causes of pathogenetic significance in the development of professional hearing loss using the example of employees of the driving professions of railway transport and flight professions of civil aviation aircraft. Materials and methods. We have analyzed the state of the auditory function in members of locomotive crews of JSC Russian Railways for 2017-2021 according to the Territorial Administration of Rospotrebnadzor for Railway Transport and persons of flight professions of civil aviation aircraft of the Russian Federation for 2010-2020 according to the data of the Federal Center for Hygiene and Epidemiology. Results. Professional sensorineural hearing loss prevails in the structure of occupational morbidity of railway and aviation transport workers. Despite the absence of excess in-cabin noise levels, the leading professional group for hearing loss in railway transport are locomotive drivers and assistants, in civil aviation - aircraft commanders and co-pilots. The complexity of the professional activities of persons of these professions, a high degree of responsibility for the safety of transportation of passengers and cargo, readiness to act in non-standard conditions, loads on visual and auditory analyzers, create a high degree of labor intensity that causes chronic stress. The factor of chronic stress causes a violation of adaptive mechanisms and causes a number of complex neuro-reflex and neurohumoral shifts in the body, as a result of which labor intensity need to consider as a pathogenetically significant factor in the development of professional sensorineural hearing loss. Conclusions. Chronic sensorineural hearing loss is a priority occupational disease in persons of driving and flying professions, it is registered even in persons working in conditions of regulatory levels of industrial noise and a high degree of labor intensity. It is necessary to discuss the possibility of including labor intensity indicators as an additional etiological, pathogenetically significant factor in the expert criteria for establishing the connection of hearing loss with professional activity.

Organizational innovations in the management of foreign trade companies in the context of sales markets transformation

The article reveals the problems of implementing organizational changes in the management of foreign trade companies in the context of changing sales markets. The article focuses on the fact that today’s realities orient foreign trade companies to implement new methods of distributing responsibility and authority among employees within the framework of certain activities that have undergone changes. The authors of the study propose a comprehensive approach to the introduction of innovations in business processes through an assessment of all levels of organization management. The article presents organizational pathologies that can occur at different levels of implementation of changes in companies engaged in foreign trade activities, and also suggests an algorithm for working with them when the sales market changes. The authors note that Russian companies will have the highest level of adaptation to non-standard environmental conditions, only with careful study of all levels of change management through certain criteria and setting management tasks when adjusting to the selected sales market. It is determined that when transforming business processes in modern conditions, the company must have a certain strategic maturity to enter a new market on the basis of the presented management principles of the company’s activities.

A Local Boundedness Result for a Class of Obstacle Problems with Non-Standard Growth Conditions

We prove the local boundedness for solutions to a class of obstacle problems with non-standard growth conditions. The novelty here is that we are able to establish the local boundedness under a sharp bound on the gap between the growth exponents.

THE MEMS-BASED BAROMETRIC ALTIMETER INACCURACY AND DRIFT PHENOMENON

MEMS technology has made sensors for measuring barometric pressure and altitude above sea level very cheap and widely used in many consumer electronic devices. This paper presents a theoretical analysis of the sources and types of errors in the barometric altimeter using the standard atmosphere model (ISA). Methods for correcting principal errors caused by non-standard sea level conditions are described and compared. A method of correcting errors in the case of altimeter horizontal movement to the air column and total pressure measurement was proposed. It was compared with another method known from the literature. In the numerical experiment, data recorded by a bicycle computer equipped with a MEMS-based barometric altimeter was analyzed. As the GPS data of the route covered was also known, it was possible to compare the recorded altimeter data with the heights determined from the digital terrain model (DTM), which in this case were considered accurate. The error of the measured altitude calculated in this way was tried to be divided into the principal error, the external error caused by the sensor movement, and the barometer drift. Hence, a numerical experiment was carried out in which, based on the recorded data, an attempt was made to reconstruct non-standard sea level conditions and the impact of speed on the sensor measurements. Furthermore, a method of solving such a reverse problem was proposed. The results of the presented studies can be used in the design of systems correcting the indications of barometric altimeters. The accuracy of the altitude measurement is especially important for small controlled flying objects (UAH) and when recording the route of vehicles moving on the ground.

Procedure to minimize rotor vibrations from flow-induced excitations in Kaplan turbines

The flow pattern in the draft tube is commonly considered when investigating rotor vibration problems, especially for Francis turbines. However, phenomenon in the vaneless space for Kaplan turbines have been shown to induce rotor vibrations when operating in non-standard conditions such as speed no load (SNL). These flow disturbances develop in the vaneless space at small guide vane openings and high swirls. Depending on the number of flow disturbances and runner blades they can excite transversal, axial or torsional vibrations. In the case of transversal excitation they can in some cases cause resonance problems if the frequency is close to a natural frequency of the rotating structure. Recently it was observed that the excitation causes severe resonance in the rotating structure on a refurbished turbine when operated at SNL.The present paper presents frequency analysis of the flow-induced excitations coupled to the shaft vibrations on an old and a refurbished Kaplan turbine. To investigate the causes of the resonance problem, measurements have been performed on both the model and prototype turbine and on a twin unit with the old runner design. The measurements on the prototypes consist of pressure, shaft bending moment, and vibrations. Pressure and radial forces were measured on the model.The result shows the dependence of the runner blade opening on the transversal excitation and the frequency of the flow disturbances. The rotordynamic analysis showed the same phenomena with forward and backward precession. The results agree well between the model and prototype when measured data are normalized by the runner rotational frequency. It is proposed, when refurbishing a unit, to use measured pressures, shaft bending moment and vibrations on the prototype before the refurbishment and the new model turbine to identify critical excitation frequencies for the new prototype turbine, i.e., use the information from the tests to set rotordynamic requirements for the new prototype unit.

Gradient estimates of very weak solutions to general quasilinear elliptic equations

We establish a gradient estimate for a very weak solution to a quasilinear elliptic equation with a nonstandard growth condition, which is a natural generalization of the p-Laplace equation. We investigate the maximum extent for the gradient estimate to hold without imposing any regularity assumption on the nonlinearity other than basic structure assumptions. Our results also include a higher integrability result of the gradient and the existence for the very weak solutions to such nonlinear problems.

Hydraulic characterization and modeling of water diffusivity through direct neutron radiography measurement on unsaturated cracked sandstone

Water diffusivity in cracked rocks is of great importance in the recovery of conventional and unconventional resources and in the sequestration of carbon dioxide and nuclear wastes. However, the mechanism of water diffusivity is not clearly revealed in the unsaturated fractured sandstone due to the limitation of accurately identifying the dynamic wetting front and water content in the conventional methods. Based on a set of self-designed coupling loading device, the novel neutron radiography imaging is used to visualize the dynamic diffusivity process of forced water from a horizontal rough crack vertically imbibed into an unsaturated sandstone matrix with nonuniform boundary in real time. As a result, an anomalous diffusivity phenomenon, namely the time exponent less than 0.5 is discovered. The anomalous diffusivity may be mainly caused by the heterogeneity and anisotropy of matrix and complicated 3-D water imbibition due to nonuniform geometric boundary. The nonstandard imbibition experiment condition may be an additional important factor. The anomalous diffusivity was calculated by three methods, including the Generalized Fickian law, Lockington and Parlange (L-P) model and the developed Meyer-Warwick (M-W) model. The value of the diffusivity increases non-linearly with the increase of normalized water content θn. The diffusivity calculated by the developed M-W model increases rapidly with increasing θn from 0 to 0.2 mm3mm−3, which is almost the same as that calculated by L-P model. When θn> 0.2 mm3mm−3, the L-P model obviously overestimates the diffusivity, but the diffusivity calculated by the developed M-W model is closest to that obtained by the Generalized Fickian law. The developed M-W model provides an effective way to quantitatively describe the diffusivity of water in the sandstone matrix.

Generalized anisotropic elliptic Wentzell problems with nonstandard growth conditions

Let Ω⊆RN be a bounded Lipschitz domain with the W1,p→(⋅)-extension property, for N≥3. We investigate the solvability and global regularity of a class of quasi-linear elliptic equations involving the anisotropic p→(⋅)-Laplace operator Δp→(⋅), with nonhomogeneous anisotropic Wentzell boundary conditions ∑i=1N|∇u|pi(⋅)−2∂u∂xiνi−Δq→(⋅),Γu+β|u|qM(⋅)−2u∋0onΓ≔∂Ω,for β∈L∞(Γ)+ with a positive lower bound, where p→∈C0,1(Ω¯)N and q→∈C0,1(Γ)N−1 fulfill 1<pm−≤pM+<∞, and 1<qm−≤qM+<∞. Here Δq→(⋅),Γ denotes the anisotropic q→(⋅)-Laplace–Beltrami operator. We first show existence and uniqueness of weak solutions for the elliptic problem, and moreover, we prove that such solutions are globally bounded over Ω¯. Key L∞-type a priori estimates for the difference of weak solutions are provided, as well as Maximum principles and inverse positivity results. At the end, we establish a sort of “nonlinear anisotropic Fredholm alternative” for the corresponding anisotropic Wentzell problem of nonstandard structure.

Determination of Continuous Earthmoving Machinery Course Stability under the Conditions of Cyclic Lateral Loading

This article presents the results of complex theoretical and experimental studies on creating universal continuous earthmoving machinery operating under non-standard loading conditions, namely, cyclic lateral loading on the actuator during digging. The lateral loading is due to the complex nature of the actuator motion when digging the soil, namely, the longitudinal motion of the machinery, the actuator digging the soil, and the lateral reciprocating motion of the actuator. This allows for variable width excavations in the soil, whose width exceeds the width of the actuator. The key issue of this machinery operation is to provide its course stability. The article considers the choice of soil-developing actuator and shows the developed calculation schemes of external loading on the operating equipment and a base tractor when digging long excavations in the soil. The dependencies to define external forces acting on the actuator when digging the soil and determining the machinery course stability, considering their spatial nature, have been developed and suggested for practical use. The conditions to ensure the stability of the course of universal earthmoving machinery have been formulated and substantiated. The developed method for determining course stability can be used when creating industrial samples of trenching earthmoving machinery.

Fast computation of the Lorentz force induced by longitudinal electromagnetic stirring

In this work, we revisit a recent transient three-dimensional (3D) model for longitudinal electromagnetic stirring in the continuous casting of rectangular steel blooms. Whereas the earlier work was able to demonstrate accurate approximations to the solutions in two asymptotic limits, both of which gave economical alternatives to time-consuming 3D computations, here we show that the original governing equations can be manipulated to a form that allows for rapid computation even outside of these asymptotic limits. The resulting formulation requires the numerical solution of two steady-state complex Helmholtz-like equations in two dimensions that are coupled via a non-standard internal interface condition that is reminiscent of that occurring in the study of Marangoni convection; these equations are then solved numerically using the finite-element software Comsol Multiphysics. With this formulation, it is possible to compute the time-averaged Lorentz force components in a way that requires around four orders of magnitude less computational time than the fully 3D approach.

Modified Problems for Euler–Darboux Equations with Parameters with Absolute Values Equal to $$ \frac{1}{2} $$

We consider the Euler–Darboux equation with parameters such that their absolute values are equal to \( \frac{1}{2} \). Since the Cauchy problem in the classical formulation is ill-posed for such values of parameters, we propose formulations and solutions of modified Cauchy-type problems with the following values of parameters:(a) \( \alpha =\beta =\frac{1}{2}; \)(b) \( \alpha =-\frac{1}{2}\ \mathrm{and}\ \beta =\frac{1}{2}; \)(c) \( \alpha =\beta =-\frac{1}{2}. \)In case (a), the modified Cauchy problem is solved by the Riemann method. We use the obtained result to formulate the analog of the problem Δ1 in the first quadrant with translated boundary conditions on axes and nonstandard conjunction conditions on the singularity line of the coefficients of the equation y = x. The first condition is gluing normal derivatives of the solution and the second one contains limit values of a combination of the solution and its normal derivatives. The problem is reduced to a uniquely solvable system of integral equations.

Crouzeix-Raviart finite element method for non-autonomous variational problems with Lavrentiev gap

We investigate the convergence of the Crouzeix-Raviart finite element method for variational problems with non-autonomous integrands that exhibit non-standard growth conditions. While conforming schemes fail due to the Lavrentiev gap phenomenon, we prove that the solution of the Crouzeix-Raviart scheme converges to a global minimiser. Numerical experiments illustrate the performance of the scheme and give additional analytical insights.

Dynamic Characteristic Analysis of Centrifugal Pump Impeller Based on Fluid-Solid Coupling

Purpose: Centrifugal pumps are prone to vibration problems during operation due to poor dynamic characteristics of its impellers that serve as the only running parts of such devices; the dynamic characteristics of the impeller during operation are the main reasons for the vibration of the centrifugal pump. Therefore, it is important to study the internal fluid flow and its influence on the dynamic characteristics of the pump impeller and to explore the causes of vibration during the transient start-up process. The understanding of such phenomena may lead to better design of such impellers. Methods: The geometry of the flow channel inside the centrifugal pump is established using Creo 4.0 software (American PTC company). The internal fluid flow computer simulation is carried out using Flomaster V9 software (UK Flowmaster company) to obtain the variation law of speed and flow during the start-up of the centrifugal pump, which is loaded into the simulation calculation of the centrifugal pump. The variation of speed and flow during the start-up process was further processed using the fluid-structure coupling method, and the structural vibration characteristics of the impeller under transient radial force are obtained by harmonic response analysis. Results: During the starting process of the centrifugal pump, the speed and flow first increased sharply and then decreased until reaching a stable process. During this period, the impeller vibration changed sharply; the overall vibration amplitude increased and fluctuated stably at the amplitude of 0.01 mm. In the unsteady numerical simulation of the centrifugal pump, the radial force on the impeller changes periodically. The time domain signal is transformed into a frequency domain signal, and the fundamental frequency of the impeller and the passing frequency of the blade are 101.67 Hz and 610 Hz, respectively. Conclusions: The radial force is the main cause of impeller vibration, and the transient radial force has the least dynamic impact on the impeller structure under the design condition and has a relatively large impact under the off-design condition. In order to ensure the stable operation of the centrifugal pump, it is necessary to avoid the centrifugal pump working under the non-standard flow condition, especially the small flow condition.

Covid-19: Twin Method for Verifying Real-World Effectiveness Under Everyday Conditions

The positive side of the Covid-19 pandemic is that it has provided a stimulation for innovations. As an example, we discuss the Pragmatic Controlled Trial (PCT), a twin study that can be used to confirm the real-world effectiveness (RWE) of health services under the non-standardized conditions of everyday care. Proof of the RWE could generally be important for health services with conditional approval. The PCT uses the Bayesian principle instead of randomization. It enables care under non-standardized everyday conditions and, by describing the endpoint-specific risks of each individual patient and by classifying the interventions, creates an unbiased evaluation in a non-experimental, but risk-stratified and controlled study. Patients expect a timely solution to their health problems. Until now, science has required sufficiently well-founded results before approving an innovation. The Covid-19 pandemic has shown that the demand for immediate and best possible care can be met through the conditional approval of a new care principle. With the PCT, we describe a procedure with which, after conditional approval, the missing data can be collected in order to successfully complete the approval process.

Planning kinematics of the manipulator’s motion using an artificial neural network

The research work focuses on the use of artificial neural networks in solving the inverse kinematics problem for the 3L flat robot manipulator on the Cartesian plane. The manipulator, designed by this method, will soon be equipped with an effector and will become an integral part of the agricultural robot complex. In a neural network on a Cartesian plane, the coordinates and direction of the point in question are used as input data, the network, in turn, calculates the corresponding angles between the links in order to bring the effector to the desired point. The kinematics of the manipulator’s movement is planned by a neural network. This new method of controlling the manipulator using a neural network allows you to reduce the positioning error in non-standard conditions.

Hot-carrier multijunction solar cells: sensitivity and resilience to nonidealities

The resilience against non-idealities of hot-carrier multijunction solar cells (HCMJSCs) is assessed and compared with two references, namely a multijunction solar cell (MJSC) and a hot carrier solar cell (HCSC). We investigate the impact on the efficiency of three deviations from the ideal case: nonoptimal design, internal limitations, and nonstandard operation conditions. We show that the HCMJSC maintains a high efficiency even when materials with nonoptimal bandgaps are considered, broadening the range of candidate materials for its implementation. We also show that the requirement for hot carriers’ thermalization is much less stringent than with the standard HCSC architecture, allowing to surpass the best MJSC efficiency with currently achievable thermalization coefficients. Finally, we estimate the influence of nonstandard illumination by varying the AM spectrum and estimate numerically the yearly averaged efficiency of devices installed in two different locations. Preliminary results on temperature dependence are also presented.

Approximation of solutions of DDEs under nonstandard assumptions via Euler scheme

We deal with approximation of solutions of delay differential equations (DDEs) via the classical Euler algorithm. We investigate the pointwise error of the Euler scheme under nonstandard assumptions imposed on the right-hand side function f. Namely, we assume that f is globally of at most linear growth, satisfies globally one-side Lipschitz condition but it is only locally Hölder continuous. We provide a detailed error analysis of the Euler algorithm under such nonstandard regularity conditions. Moreover, we report results of numerical experiments.