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This paper presents a fast analytical model for estimating the components of the PM flux density distribution in the air-gap for a number of interior permanent magnet synchronous machines (IPMSMs). Deriving the two-dimensional (2-D) analytical model for IPMSMs is more challenging compared to that of surface-mounted permanent magnet synchronous machines (SPMSMs) due to the inconsistent geometry of the rotor in polar coordinates. IPMSMs are usually modeled by using 0-D or 1-D methods such as the magnetic equivalent circuit (MEC); however, the MEC method is unable to take into account the tangential component of the magnetic flux density vector. In this paper, a 2-D analytical no-load electromagnetic model for five rotor topologies of IPMSMs is proposed. The effects of the stator slots on the radial component of the PM flux density distribution in the air-gap are then included by defining an air-gap function. The effects of the stator slots on the tangential components of the PM flux density distribution in the air-gap are also considered by injecting virtual surface currents (VSCs) or virtual permanent magnets (VPMs). For verification purposes, the analytical results are compared with those of the finite element method (FEM) and the experimental results of one of the cases.

The slab-confined water at the nanoscale exhibits anomalous dielectric properties compared to bulk water, for example, significantly low dielectric constant. In this work, we study the dielectric properties of nanoscale water droplets at room temperature using molecular dynamics simulations. We find that the nanoscale water droplets feature weakly anisotropic dielectric constant: the radial component of dielectric constants is distinctly smaller than the tangential component although they both decrease with reducing droplet size in a similar way. Such dielectric behavior is closely related to the orientational preference of water molecules near the convex surface. The molecular dipole prefers to slightly orientate toward the interior of droplets in contrast to the out-of-plane preference for free-standing water films and slab-confined water, which suppresses the fluctuation of dipole moments in the radial direction. Meanwhile, it facilitates the formation of the open hydrogen-bond network in the surface layer and ultimately leads to the relatively weak suppression of tangential fluctuations. The differential suppression is responsible for the anisotropic dielectric constant of water droplets. This anisotropic characteristic is also found in dielectric relaxation: both the radial and the tangential relaxation are consistently slowed down upon approaching surface but the latter is universally slower.

This note presents a regularity result with proof for an initial-boundary value problem of a linear parabolic system involving curl of the unknown vector field, subjected to the boundary condition of prescribing the tangential component of the solution.

The goal of this research is to correlate the piezomagnetic field with the stress and the stress concentration degree of ferromagnetic steels. Specimens of X80 steels were machined into smooth plat...

To predict the parameters of the quality of the processed parts and the period of durability of the cutting tool, mathematical models are needed that will allow us to calculate not only the mathematical expectation of the parameters of the machining process, but also the dispersion of these parameters. The working capacity of the tool and the quality parameters of the parts depend significantly on the temperature on the contact surfaces of the tool, as well as on the surface of the workpiece. Mathematical dependences for calculating the components of the total heat generation capacity during turning are given. It is assumed that the yield stress, which determines the cutting and friction forces on the contact surfaces of the cutter, workpiece and chip, depends on the temperature in the area of plastic deformation. The heat transfer at the boundaries of objects in contact with the process fluid or air is given in the form of the Newton-Richman law. The equations of thermal conductivity of contacting objects were solved together with the general boundary conditions in the contact zone, using the finite element method. The results of numerical simulation of the main component of the cutting force and temperatures in the contact zones of the face of the cutter with the chips and the fiank surface with the workpiece, depending on the yield strength of the workpiece material, are presented. The values of fluctuations in the cutting force and contact temperatures depending on the spread of the yield stress of the workpiece material during turning of workpieces made of 45 and 12X18H10T steels are determined. Based on the results of numerical modeling, regression equations are obtained for calculating the tangential component of the cutting force, the temperatures on the face and flank surfaces of the cutter, and the temperature on the surface of the workpiece.

A spring-damping contact force model considering the normal friction force is proposed and discussed in this paper. This model is an extension and development of Hertz theoretical model. The physical model of contact force in the contact process is established. The friction force during the elastic compression and restitution phases is represented using the product of tangential component of contact force and friction coefficient, which is a function of contact force and deformation. The friction dissipation coefficient is proposed to characterize the energy dissipation under different material properties and initial velocities. A velocity exponential model is proposed, and the expressions of damping coefficient and contact force are derived. Numerical analysis is carried out and the model in this paper is compared with classical models under two conditions, which proves the correctness and effectiveness of the model. The spring-damping model with normal friction force is applied to a simple spring contact system, and the energy dissipation process under the action of spring prestress is analyzed.

The pulsed eddy current (PEC) technique is commonly used in the petrochemical and power generation industries to measure two parameters: the degree of pipe wall corrosion and the thickness of the insulation shield. These two parameters can be evaluated by examining the thickness of conductive materials and the lift-off distance, respectively. To explore a possible technique for simultaneously measuring the thickness and the lift-off, the present study envisaged the development of a PEC testing method based on detecting the tangential component of the magnetic flux density. The tangential component of the magnetic flux density was excited by two racetrack-type coils injecting currents in opposite directions that were picked up by a magnetic sensor. The slope in logarithmic scale and the time-to-peak of the magnetic signal were verified to characterise the features of the thickness and the lift-off, respectively. By analysing the simulation and experimental results, the feasibility of simultaneously measuring the thickness and the lift-off was demonstrated.

A method to calculate the elastic shakedown limit of transportation systems (e.g. pavements and railways) supported by geogrid reinforced soils is presented. For the first time, lower-bound shakedown theory is combined with a strength-based geogrid simulation approach, resulting in a rapid method to quantify the benefit of geogrids on the elastic shakedown limit. It allows decoupling of elastic stress generation and shakedown calculations, meaning it is straightforward to implement, and requires minimal computational effort. Therefore it presents a useful tool to optimise geogrid design for transportation structures such as highway pavements and railways. To show the capability of the method, shakedown limits are calculated for a variety of geogrid configurations using elastic stresses induced by a moving Hertz load. The effect of geogrid depth, soil cohesion, soil friction angle and loading type (normal versus tangential) are investigated for reinforced and non-reinforced soils. It is found that the optimum depth is sensitive to the soil strength properties. Regarding loading, it is shown that for highly tangential loads, shallower geogrids are effective, while for loads with a minimal tangential component, deeper geogrids are effective.

Finite element method (FEM) is widely used in the modeling of electromagnetic systems and as a reliable method to verify analytical modeling of electromagnetic devices in design step. As the method is based on discretization of domains, the electromagnetic continuity conditions at the boundaries of elements should be confirmed. Electromagnetic continuity conditions in FEM modeling were investigated in this article. It was shown that the continuity of tangential component of magnetic field intensity is not guaranteed at the boundaries of elements. The inability of FEM to establish the continuity condition leads to some virtual surface current densities at the boundaries of adjacent elements which does not exist in reality. The existence of virtual surface currents is proved in an example. Then, with the help of a complicated example, it is shown that large number of elements and, consequently, the large number of boundaries between elements may cause great errors in FEM postprocess results, especially in calculating magnetic stored energy and electromagnetic forces acting on moving parts. It has been shown that it is very important to take into account the impact of these virtual current densities in energy conversion analysis by FEM.

We give some regularity criterion (of a weak $$-L^{p}$$ Serrin type) of a weak solution to the 3D Navier–Stokes equations in a bounded domain $$\Omega \subset \mathbb {R}^3$$ with a smooth boundary. In particular, in case of the half space, we give a regularity condition of a weak solution with respect to a tangential component of the velocity flow vector.

We use the tangential component $ \psi ^{T} $ of an immersion of a compact hypersurface of the Euclidean space $ \mathbf{E}^{m+1} $ in finding two characterizations of a sphere. In first characterization, we use $ \psi ^{T} $ as a geodesic vector field (vector field with all its trajectories geodesics) and in the second characterization, we use $ \psi ^{T} $ to annihilate the de-Rham Laplace operator on the hypersurface.

This report investigates the influence of microstructure topography on the restitution coefficient, maximum spreading diameter, and contact time of oblique drop impacts on superhydrophobic surfaces. The five surfaces tested allow for comparison of open- versus closed-cell structures, feature size and spacing, and hierarchical versus nanoscale-only surface structures. By decoupling the restitution coefficient into a normal (en) and tangential component (et), it is demonstrated that both en and et are largely independent of the microstructure topography. Instead, the restitution coefficient is governed almost exclusively by the normal Weber number. Next, a new model is presented that relates the maximum spreading diameter to an adhesion coefficient that characterizes the overall adhesive properties of the superhydrophobic microstructure during drop rebounding. Through this analysis, we discovered that surface geometries with greater microstructure roughness (i.e., overall surface area) promote a higher maximum spreading diameter than flatter geometries. Furthermore, the contact time of drop impacts on flat surfaces is positively correlated with the impact velocity due to penetration of the liquid into the porous nanostructure. However, this trend reverses for oblique impacts due to the presence of stretched rebounding behavior. Finally, substrates patterned with sparse pillar microstructures can exhibit pancake bouncing behavior, resulting in extremely low contact times. This unique bouncing mechanism also significantly influences the restitution coefficient and spreading diameter of oblique impacts.

To accurately and quickly predict the open-circuit air-gap magnetic field in interior permanent magnet synchronous machines (IPMSMs), an analytical model based on magnetic equivalent circuit (MEC) method is proposed. The analytical model can provide radial and tangential components of open-circuit magnetic field in the slotless air gap. The radial component is obtained from the MEC model, and the tangential component is obtained from boundary conditions of macroscopic equations. Then, a complex relative air-gap permeance is applied to take the effect of slots into account. As a result, an accurate solution of both radial and tangential components of the flux density in the slotted air gap is obtained. Additionally, the no-load back electromotive force (EMF) and cogging torque are calculated based on the open-circuit air-gap magnetic field. All the analytical results are verified by the finite element (FE) analysis and they are well matched. In the end, a direct measurement experiment of open-circuit air-gap magnetic field is proposed to verify the validity of both radial and tangential open-circuit air-gap magnetic fields.

The article shows the need for high-quality demagnetization of the axle of the wheelset, which is one of the most critical parts of the rolling stock. The main task of demagnetization is to bring the remanent magnetization to such a value at which the ferromagnetic particles formed during processing would not be retained on the surface of the axle, as a result of which its service life will significantly increase. The method of comparative analysis was used to assess the effectiveness of methods for demagnetizing the axle of a wheelset, which ensures the durability and operational reliability of the rolling stock. Based on the results of the analysis, three main methods of demagnetizing ferromagnetic parts and products are identified: a reverse pulse, a free oscillatory process and a pulse method. A method of demagnetization based on cyclic magnetization reversal by a sinusoidal changing magnetic field with an amplitude smoothly decreasing to zero has been selected and substantiated. The basic requirements for the device for demagnetizing the axles of wheelsets have been determined and analyzed. The proposed implementation of the device, which guarantees the required quality of demagnetization of the axle of a wheelset based on its magnetic state. The magnetization of the axis material is proposed to be estimated indirectly from the results of measuring the tangential component of the magnetic field strength on the axis surface with a fluxgate. To compensate for external magnetic fields, a second flux gate is used, located at some distance from the first. The output signals of the flux gates are connected according to the differential circuit. The difference signal of the flux gates is amplified and fed to a recording device, depending on the readings of which the demagnetizing field is corrected. The proposed implementation of the device, which guarantees the required quality of demagnetization of the axle of a wheelset on the basis of determining its magnetic state. The magnetization of the axis material is proposed to be estimated by an indirect method based on the results of measuring the fluxgate tangential component of the magnetic field strength on the axis surface. The direction of further research is the automation of the demagnetization process.

The present work deals with the machining performance of AISI304 stainless steel under a dry machining environment. Machining operations are performed with varying cutting speeds using uncoated tungsten carbide insert. The average tool-tip temperature, machining induced cutting forces and the flank wear progression depth were analyzed with regard to the cutting speeds. In addition, different wear mechanisms for the worn-out cutting inserts are studied. The work also extends study of chip macro-morphology. The maximum value of tangential component of cutting force (∼167 N) is attained at V = 190 m/min. Moreover, at V = 190 m/min, tool-tip temperature is recorded as 88.9 °C; which appears the maximum for all cutting speeds tested. At V = 247 m/min, depth of flank wear assumes the highest value (∼71.9 µm).

The final surface quality of the part and its geometric dimensions are formed by grinding operations.Research of the param-eters of grinding with an oriented tool in the blunting mode is an urgent task, since it will provide an increase in processing productivity. The operation of the tool in the bluntness mode provides the necessary geometric shapes of the part and surface roughness.On the other hand, this operating mode of the wheel is accompanied by clogging and a decrease in the cutting ability of the tool.Therefore, it is necessary to research the heat tension of the grinding process under these processing conditions. Methods of deep grinding with crossed axes of the tool and cylindrical part are considered.The results of an experimental research of finishing single-pass grinding of a cylindrical surface of a shaft with an oriented tool are presented.The features of the process of grinding work pieces made of plastic materials are considered.Lack of research on the heat tension of the process of grinding cylindrical surfaces by the periphery of an oriented circle in the bluntness mode. To research the heat tension of the process of grinding cylindrical surfaces by the periphery of an oriented circle in the bluntness mode. To analyze the influence of the constituent forces of grinding on the processing process. During the operation of the wheel in the bluntness mode, its cutting ability decreases and the heat tension of the grinding process and vibration increases.At the same time, the necessary geometric shape of the circle is created, which provides the specified roughness and dimensions of the part. The heat tension of the process of grinding cylindrical surfaces by the periphery of an oriented circle during its operation in the blunting mode is researched.According to the calculations, the tangential component of the grinding forces from the plastically deforming and cutting grains does not have a significant effect on the temperature rise at the calibration section.

Mechanochemical reactions can be induced in a solution by the collision of balls to produce high-temperature and high-pressure zones, with the reactions occurring through a dissolution–precipitation mechanism due to a change in solubility. However, only a fraction of the impact energy contributes to the mechanochemical reactions, while the rest is mainly consumed by the wear of balls and the heat generation. To clarify whether the normal or tangential component of collisions makes a larger contribution on the reaction, herein we studied the effect of collision direction on a wet mechanochemical reaction through combined analysis of the experimental reaction rates and simulated ball motion. Collisions of balls in the normal direction were found to contribute strongly to the wet mechanochemical reaction. These results could be used to improve the synthesis efficiency, predict the reaction, and lower the wear in the wet mechanochemical reactions.

We provide properties of almost η-Ricci and almost η-Yamabe solitons on submanifolds isometrically immersed into a Riemannian manifold whose potential vector field is the tangential component of a ...

In this work, a series of experimental studies was conducted, which confirmed the results of modeling temperature processes in the area of ​​centerless intermittent grinding of the rolling bearing surfaces of roller bearings. The dependences between the grinding temperature, the tangential component and the radial component during intermittent grinding with circles with different numbers of grooves have been experimentally established. Based on the use of the proposed prefabricated design of the intermittent grinding wheel, a highly efficient technology of centerless grinding of the surfaces of roller bearing rings with the ability to control the grain size of the prefabricated, working, calibration and care cutting zone. The combination of different grain sizes in the design of the prefabricated grinding wheel made it possible to improve the quality of ground surfaces to Ra 1.0-1.4 μm, reduce and stabilize the temperature in the grinding zone to 450 ° C and remove from the process of grinding the base surface of the ring one semi-roughing operation .

This study aims to analyze the heat transfer phenomenon of power-law fluid with the occurrence of non-uniform heat source/sink within two stretchable disks which are parted with the constant distance and are co-axially rotating. The thermal conductivity is obeying the similar properties of power-law as that of viscosity. Von Karman’s generalized similarity transformation has been used firstly to reduce the physically modeled partial differential equations to nonlinear coupled ordinary differential equations and then tackled numerically with shooting method by finding missing initial conditions with the help of Newton–Raphson method and then system of equations are handled by means of RK-method. The influence of physical parameters for instance rotation as well as stretching, power-law index, Prandtl number, heat sink/source parameters upon non-dimensional velocity and temperature profiles are studied profoundly, later on, comprehensive analysis is expressed in discussion and results segment. The results which are computed numerically illustrate that the emerging parameters have substantial influences on velocity and temperature fields. In addition, rotation enhances the velocity components but temperature is predicting two diverse behaviors for shear-thinning and shear-thickening fluids, whenever upper and lower disk stretching it leads to an upsurge in radial and axial velocities but causes a decline in tangential velocity and temperature. Moreover, velocity and temperature distributions are in increasing trend except for the tangential component of the velocity which is decreasing by boosting the index of power-law. Furthermore, temperature decreases along with the similarity variable with the increasing Prandtl number but enhances with the enhancement in heat source/sink parameters. Finally, the skin friction in radial direction and local Nusselt number are escalating along the stretching parameters and Prandtl number but skin friction in tangential direction plummeting.

The aim of this article is to present a new analytical model developed for open-circuit magnetic field calculation in U-shape interior permanent magnet (IPM) machine. The model is developed based on the two-dimensional subdomain-model approach by solving Poisson's and Laplace's equations. The comprehensive theoretical derivations of the final analytical equations for the magnetic flux density distribution in the air gap and in the permanent magnets are explained in detail. We also provide the calculation algorithm in form of a flow diagram suitable for engineers to compute the radial and the tangential component of the magnetic flux density in all subdomains of slotless brushless machines with any possible number of rotor pole pairs of U-shaped IPMs. A slightly modified algorithm also applies to V-shaped IPMs.

The questions related to the peculiarities of determining such a physical characteristic of the process of grinding polycrystalline superhard materials by diamond circles on metal and organic bonds as a coefficient of grinding are considered. It is the ratio of the tangential and normal components of the cutting force when grinding. It is proposed to determine it using the effective component of the tangential component of the cutting force. Its establishment is based on the use of the phenomenon of adaptation of the grinding process in general and its individual component, the periodicity of change in time of physical and technological indicators of processing in particular. The physical nature of the occurrence of the periodicity with respect to the conditions of the controlled grinding process according to the elastic scheme and to the conditions of the process of grinding polycrystalline superhard materials diamond circles on organic bonds in the self-sharpening mode is disclosed. It was established that when using the first process as a factor of forced influence on the state of the cutting surface of a circle it is necessary to choose the magnitude of intensity of electrophysical solution of the metal ligament of the diamond circle, and in the second transverse supply to the depth of processing. Recommendations regarding the choice of factors of forced influence are given. It is shown, that the peculiarity of the elastic treatment scheme is that the normal component of the cutting force is constant in time. Therefore, the change (increase or decrease) of the effective component of the tangential component of the grinding force leads to similar changes in the grinding coefficient and can clearly judge the effectiveness of the method or conditions of grinding that explores. In contrast to the elastic circuit grinding when working on a rigid scheme, both components (tangential and normal) grinding force, which are used to define the grinding coefficient, depend on the processing conditions. This fact should be considered when analyzing the obtained experimental data. In the future, research results will help to improve the grinding processes of polycrystalline superhard materials.

It has been shown that locally measuring coercive force $${{H}_{{\text{c}}}}$$ based on the magnitude of demagnetizing current has a fundamental limitation on the measurement range. We have demonstrated the expediency of measuring coercive force in ferromagnetic objects locally, based on the magnitude of the tangential component of the magnetic field in the interpole space on the surface of the test object, that is, based on the internal field. This allows one to expand the range of measured values $${{H}_{{\text{c}}}}$$ by several times. Also, the influence of the gap between the transducer and the object, as well as the shape and size of test objects on the measurement results is significantly reduced. This makes it possible to measure the absolute values of $${{H}_{{\text{c}}}}$$ of homogeneous ferromagnetic objects, as well as the coercive force of objects with nonferromagnetic coatings of considerable thickness.

This article presents a new model of the flat surface grinding process vibration conditions. The study establishes a particular analysis and comparison between the influence of the normal and tangential components of grinding forces on the vibration conditions of the process. The bifurcation diagrams are used to examine the process vibration conditions for the depth of cut and the cutting speed as the bifurcation parameters. The workpiece is considered to be rigid and the grinding wheel is modeled as a nonlinear two-degrees-of-freedom mass-spring-damper oscillator. To verify the model, experiments are carried out to analyze in the frequency domain the normal and tangential dynamic grinding forces. The results of the process model simulation show that the vibration condition is more affected by the normal component than the tangential component of the grinding forces. The results of the tested experimental conditions indicate that the cutting speed of 30 m/s can permit grinding at the depth of cut up to 0.02 mm without sacrificing the process of vibration behavior.

Boundary control problems for a stationary model of magnetohydrodynamics of a viscous incompressible fluid are considered in a domain with non-ideal boundary. The role of the control is played by a tangential component of a magnetic field specified on an entire boundary. In the case when the control function is square integrable, the solvability of the control problem is proved. Under assumption that control possesses a higher smoothness described by the space Hs(Γ)3 for any s > 0, an optimality system is derived. Based on the analysis of an optimality system, the local stability estimates of optimal solutions are established with respect to small perturbations of a cost functional.

This article has been published in a revised form in Journal of Mechanics [https://doi.org/10.1017/jmech.2020.38]. This version is published under a Creative Commons CC-BY-NC-ND. No commercial re-distribution or re-use allowed. Derivative works cannot be distributed. © 2020 The Society of Theoretical and Applied Mechanics., To understand the lubrication-dominated permeation through a membrane, numerical simulations of permeation through a moving corrugated permeable membrane is carried out with a fully validated numerical method. Through comparisons between the numerical results and the results of an asymptotic analysis of permeate flux (under an infinitesimal permeability condition) using Reynolds lubrication equation, the effect of permeation on lubrication and its inverse effect (i.e., the dependence of permeation on lubrication) are discussed. The linear and nonlinear dependences of the relaxation of the lubrication pressure due to membrane permeation are identified. The effect of the tangential component of the permeate flux is evaluated by a linear analysis, and the limitation of Reynolds-type lubrication is discussed.

The radiation emission from high-speed digital circuit may result in radio-frequency interference (RFI) problems in modern electronic devices. In this paper, an improved equivalent dipole source based on a new transfer model and a new regularization method is proposed. The equivalent source is obtained by solving an inverse equation with near-field data. The tangential component of electric field used in conventional equivalent source extraction is replaced by the normal component, which can reduce the test difficulty and enhance the measurement efficiency. The new regularization method based on Tikhonov and truncated singular value decomposition (TSVD) can enhance the stability and accuracy of the dipole solution. In addition, the new transfer model and regularization method are verified by simulations and measurements.

The article deals with solving the problem of determination in the first approximation of the time of the interaction of tricone bit tooth with the rock and the maximum dynamic impact force. Considered the roller bit teeth are of types Sh and B. The shape of the bottom hole after the previous penetration the rock is adopted as having spherical mounds between paths. It is believed that deformations during the impact of the tooth occur only in the area of ​​the mounds, neglecting the masses of the rock material being deformed. The concept of the consolidated mass of the part of the rock, which is disintegrated and sections of the mass of the drill string with a roller bit is introduced. Separate consideration is given to determining the time and maximum impact force at the stages of sinking the rock and the raising of the tooth from it. In raising the plastic deformation of the material of the rock and its elastic return are taken into account. The determination of these parameters is carried out both without considering the moment of inertia of the roller bit, as well as taking into account this moment. It is shown that during the oblique impact of the tooth on the mound, taking into account the moment of inertia of the roller bit, it is necessary to know the coefficient of friction of the rocks over the tooth and the initial acceleration of the roller bit. In this case, the normal and the tangential component of the force of the specified impact of the tooth on the mound is considered separately. Were suggested analytical dependences for determination of the normal and tangent component of the shock interaction force module, as well as their maximum value.

Magnetic field distribution in the airgap of rotating machines, consisting of tangential and normal components, determines the instantaneous value of torque. Lorentz force (LF), Maxwell stress tensor (MST), and virtual work (VW) methods are commonly used to estimate its value. In their well-known forms, as used by design engineers of rotating machines, these three methods reflect distinct significance for field components. The LF method does not require the distribution of tangential field components to compute torque, whereas in MST and VW, it is required. In this article, torque expression-based equivalence of LF, MST, and VW methods is presented, starting from a simple two-coil conceptual system. Using this equivalence as a basis, certain indicative factors are derived, which provide insights on the typical significance of the tangential component in average and ripple torque. The analysis presented here helps designers obtain a better overview of the method-specific significance of field components and flux paths in instantaneous torque, from a numerical perspective.

In this paper, using the first-order Nedelec conforming edge element space of the second type, we develop and analyze a continuous interior penalty finite element method (CIP-FEM) for the time-harmonic Maxwell equation in the three-dimensional space. Compared with the standard finite element methods, the novelty of the proposed method is that we penalize the jumps of the tangential component of its vorticity field. It is proved that if the penalty parameter is a complex number with negative imaginary part, then the CIP-FEM is well-posed without any mesh constraint. The error estimates for the CIP-FEM are derived. Numerical experiments are presented to verify our theoretical results.

Rotary percussion drilling with pneumatic hammers is a promising, high-performance method widely used in the practice of geological exploration, the performance of which is determined mainly by pressure and the amount of cleaning agent supplied by the compressor. The parameters of commercially available high-pressure compressors do not allow drilling at a depth of more than 300 meters, which is one of the main limiting factors of its practical application in production conditions. One of the ways to improve the performance of the rotary-percussion drilling of wells, and at the same time the maximum depth of drilled wells is to improve the mechanism of rock destruction by applying eccentric impact pulses to the drilling tool, which will make it possible to implement more actively the tangential component of the impact pulse that affects the shape and the volumes of the fracture holes being formed, providing additional splitting of the rock in the direction of the rock face. The paper discusses the ways to perfect the known designs of bits for rotary-percussion drilling of wells implementing eccentric application of impact impulses, issues of geometric substantiation of the shape of an eccentric protrusion on a drill bit torus shim for rotary-percussion drilling and oscillations of torus shim when transmitting eccentric impact pulses from the point of view of enhancement durability of a construction and accuracy of transfer of eccentric impact pulses.

Within the framework of classical electrodynamics, the model problem of current distribution on the surface of a superconducting sphere and of magnetic induction are analyzed in the presence of an external current flowing onto a given superconducting sphere. The possibility of using the Langevin and Gorter—Kasimir two-component theory to surface currents produced in superconducting structures is considered. Within the framework of the formulated problem, the current distributions are calculated in detail in the case where electrons flow onto a superconducting sphere. Theoretical analysis of the main electrodynamic and London equations shows that a constant current component, which is related to the external flowing current, appears. The boundary conditions are analyzed in detail. Using them, we conclude that there is no tangential component near the sphere surface. A part of the boundary conditions is written in terms of the surface current density, which is also fundamentally new in the theoretical presentation of this physical problem.

Interaction of an active electronic implant such as a deep brain stimulation (DBS) system and magnetic resonance imaging (MRI) radiofrequency (RF) fields can induce excessive tissue heating, limiting MRI accessibility. Efforts to quantify RF heating mostly rely on electromagnetic (EM) simulations to assess individualized specific absorption rate (SAR), but such simulations require extensive computational resources. Here, we investigate if a predictive model using machine learning (ML) can predict the local SAR in the tissue around tips of implanted leads from the distribution of the tangential component of the MRI incident electric field, E tan. A dataset of 260 unique patient-derived and artificial DBS lead trajectories was constructed, and the 1 g-averaged SAR, 1 g SARmax, at the lead-tip during 1.5 T MRI was determined by EM simulations. E tan values along each lead's trajectory and the simulated SAR values were used to train and test the ML algorithm. The resulting predictions of the ML algorithm indicated that the distribution of E tan could effectively predict 1 g SARmax at the DBS lead-tip ( R = 0.82). Our results indicate that ML has the potential to provide a fast method for predicting MR-induced power absorption in the tissue around tips of implanted leads such as those in active electronic medical devices.

We investigate the boundary value problem for steady-state magnetohydrodynamic (MHD) equations with inhomogeneous mixed boundary conditions for a velocity vector, given the tangential component of a magnetic field. The problem represents the flow of electrically conducting viscous fluid in a 3D-bounded domain, which has the boundary comprising several parts with different physical properties. The global solvability of the boundary value problem is proved, a priori estimates of the solutions are obtained, and the sufficient conditions on data, which guarantee a solution’s local uniqueness, are determined.

In the present investigation, machining performance of Ti6Al4V is studied under dry environment, pressurized air supply and distilled water based Minimum Quantity Lubrication (MQL). Machining (turning) performance is assessed in purview of cutting force (tangential component) magnitude, tool-tip temperature, width of tool flank wear progression, morphology of evolved chips and severity of vibrations at varied cutting speeds as well as cooling media. Characteristic features of spatial temperature distribution profile (at the vicinity of tool-tip) as influenced by varied cooling media are studied with the help of thermographs of the cutting zone. Mechanisms of cutting tool wear are studied as well. It is experienced that amongst three cutting environments tested, application of water-MQL is beneficial for machining of Ti6Al4V at low cutting speed. Severity of vibrations gets 50.39% reduced during machining under water-MQL than dry condition. Consequently, as compared to dry machining, water-MQL causes 79% reduced tool flank wear and 82% reduced crater wear at low cutting speed. Under water-MQL, reduced tool-tip temperature (66% reduced than dry condition) suppresses severity of tool wear. In comparison with high cutting speed, performance of water-MQL is found much better at low cutting speed. ‘Unaffected zones’ are identified at the worn-out tool rake face under water-MQL. High amplitude of vibration (maximum absolute mean value) causes low chip-segmentation ratio. On the contrary, chip reduction coefficient gets truncated with decrement in vibration amplitude. Vibration amplitude has positive influence on degree of chip-curl.

Classical integral or integro-differential equations of the Pocklington and Hallen type, describing radiation and scattering of electromagnetic fields by thin, ideally conducting wires, are of significant practical interest and have been extensively studied. These equations follow from the boundary condition that requires a vanishing of the tangential component of the total electric field at the wire surface. The total electric field consists of both a known incident field and a scattered field that is due to a generally unknown current induced in the wire. The scattered electric field for a given point on the wire surface consists both of a “far” field at distant points significantly exceeding the wire's radius $a$ , and by a “near” field due to arbitrarily nearby points. Expressions for the “near” field include a logarithmic singularity in the kernel of the associated Pocklington equation. This singularity is an important feature that makes the Pocklington equation solvable and well-posed. Thus, the Pocklington equation in its standard form can be considered as a Fredholm integral equation of the first kind with a singular kernel.

We consider the two-dimensional MHD Boundary layer system without hydrodynamic viscosity, and establish the existence and uniqueness of solutions in Sobolev spaces under the assumption that the tangential component of magnetic fields dominates. This gives a complement to the previous works of Liu-Xie-Yang [Comm. Pure Appl. Math. 72 (2019)] and Liu-Wang-Xie-Yang [J. Funct. Anal. 279 (2020)], where the well-posedness theory was established for the MHD boundary layer systems with both viscosity and resistivity and with viscosity only, respectively. We use the pseudo-differential calculation, to overcome a new difficulty arising from the treatment of boundary integrals due to the absence of the diffusion property for the velocity.

Construction blasting in a tunnel in deep-buried soft rock will undoubtedly influence the cross section of the tunnel. Taking the deep-buried soft rock tunnel as the research background, a field monitoring experiment of the tunnel blast-induced vibrations is carried out. The cross section was established using 5 monitoring points to collect the peak particle velocity (PPV) data and frequency spectrum data. The results show that the maximum horizontal radial component of the blast-induced vibration velocity is greater than the maximum vertical component in the deep soft rock tunnel, and the maximum vertical component is greater than the horizontal tangential component. Due to the presence of an inclined shaft, the high domain frequencies have an amplification effect on the tunnel, while low frequencies do not exhibit significant amplification effects.

The classical problem of the electrophoretic motion of a spherical particle has been treated theoretically by Overbeek in his 1941 PhD thesis and almost 40 years later by O'Brien & White. Although both approaches used identical assumptions, the details are quite different. Overbeek solved for the pressure, velocity fields as well as the electrostatic potential, whereas O'Brien & White obtained the electrophoretic mobility without the need to consider the pressure and velocity explicitly. In this paper, we establish the equivalence of these two approaches that allow us to show that the tangential component of the fluid velocity has a maximum near the surface of the particle and outside the double layer, the velocity decays as 1/r3, where r is the distance from the sphere, instead of 1/r in normal Stokes flow. Associated with this behavior is that of an irrotational outer flow field. This is consistent with the fact that a sphere moving with a constant electrophoretic velocity experiences zero net force. A study of the forces on the particle also provides a physical explanation of the independence of the electrophoretic mobility on the electrostatic boundary conditions or dielectric permittivity of the particle. These results are important in situations where inter-particle interaction is considered, for instance, in electrokinetic deposition.

In this paper, we find a conformal vector field as well as a Killing vector field on a compact real submanifold of the canonical complex space form (Cm, J, h , i). In particular, using immersion ψ : M → Cm of a compact real submanifold M and the complex structure J of the canonical complex space form (Cm, J, h , i), we find conditions under which the tangential component of Jψ is a conformal vector field as well as conditions under which it is a Killing vector field. Finally, we obtain a characterization of n-spheres in the canonical complex space form (Cm, J, h , i).

Regimes of continuous spin detonation and continuous multifront detonation in a hydrogen–oxygen mixture are obtained in a plane-radial combustor with an inner diameter of 100 mm and exhaustion toward the periphery. The fuel-lean limits of detonation in terms of the specific flow rate of the mixture are determined. For continuous spin detonation, transverse detonation waves and the flow in their vicinity in the combustor plane are reconstructed. The detonation wave is found to be significantly curved because of the increase in the tangential component of the velocity along the combustor radius. It is demonstrated that the scale effect is manifested only in the number of rotating waves. However, their velocity increases with increasing the combustor size. The velocity deficit of continuous detonation is 20–40% as compared to the velocity of the ideal Chapman–Jouguet detonation. (The smaller value corresponds to the fuel-lean mixture.)

A new diffusion scheme satisfying the maximum principle on two-dimensional (2D) polygonal meshes is proposed. Being different from the existing schemes which are based on the nonlinear combination of the two one-side fluxes, the scheme in this paper is constructed by a modification of the conventional linear Two-Point Flux Approximation (TPFA) scheme, in which the two-side flux is constructed. To improve its accuracy on 2D skewed meshes, the TPFA scheme is rewritten by adding a tangential part, i.e., the tangential component of the flux multiplied with a nonlinear factor. A new method for the discretization of the tangential part is presented so that both the conservation condition and the maximum principle are satisfied, while the TPFA part remains unchanged. Moreover, by virtue of the harmonic averaging points for the calculation of the tangential part, the scheme has a minimal stencil, similar to the TPFA scheme. Finally, some numerical examples are presented to verify that it is second order accurate on 2D polygonal meshes for anisotropic diffusion problems.

In the problem on rolling of a heavy round homogeneous disk on a surface of revolution with a negative Gaussian curvature, the classical nonholonomic model is used in which, at each moment, the instantaneous velocity of the current drive point of the disk touching the support is zero. Stationary motions of the disk are found. We note that, within the nonholonomic model the tangential component of the reacton for a stationary motion can be larger than the pressure force. This means that such motion in practice cannot be implemented or observed if we assume that the force that provides the no-slip condition is the dry friction force with a coefficient between zero and unity. For stationary motions of the disk the conditions of the stability in the first approximation are obtained. The results of the numerical simulation of the rolling motion of the disk without slip while the mechanical energy dissipation occurs, are presented. The purpose of these studies was to verify the adequacy of the assumed nonholonomic model of coin movements observed in practice in the entertaining coinboxes of the plastic funnel type.

Many processes in nature (e.g., physical and biogeochemical processes in hyporheic zones, and arterial mass transport) occur near the interface of free-porous media. A firm understanding of these processes needs an accurate prescription of flow dynamics near the interface which (in turn) hinges on an appropriate description of interface conditions along the interface of free-porous media. Although the conditions for the flow dynamics at the interface of free-porous media have received considerable attention, many of these studies were empirical and lacked a firm theoretical underpinning. In this paper, we derive a complete and self-consistent set of conditions for flow dynamics at the interface of free-porous media. We first propose a principle of virtual power by incorporating the virtual power expended at the interface of free-porous media. Then by appealing to the calculus of variations, we obtain a complete set of interface conditions for flows in coupled free-porous media. A noteworthy feature of our approach is that the derived interface conditions apply to a wide variety of porous media models. We also show that the two most popular interface conditions—the Beavers–Joseph condition and the Beavers–Joseph–Saffman condition—are special cases of the approach presented in this paper. The proposed principle of virtual power also provides a minimum power theorem for a class of flows in coupled free-porous media, which has a similar mathematical structure as the ones enjoyed by flows in uncoupled free and porous media. The derived interface conditions are summarized along with a pictorial description of the problem, which pertains to the flow of an incompressible fluid in coupled free-porous media. $$\Psi $$ is the power expended density along the interface. $$\mathbf {v}_{\text {free}}$$ and $$\mathbf {v}_{\text {por}}$$ are the velocities in the free and porous regions, respectively. A superposed asterisk on a (vectorial) quantity denotes its tangential component along the interface. $$v_n$$ is the normal component of the velocity at the interface from the free region into the porous region. $$\mathbf {T}_{\text {free}}^{\text {extra}}$$ and $$\mathbf {T}_{\text {por}}^{\text {extra}}$$ , respectively, denote the extra Cauchy stresses in the free and porous regions. $$\mathbf {t}_{\text {free}}$$ and $$\mathbf {t}_{\text {por}}$$ , respectively, denote the tractions on the free and porous sides of the interface with outward normals $$\widehat{\mathbf {n}}_{\text {free}}$$ and $$\widehat{\mathbf {n}}_{\text {por}}$$ . A unit tangential vector along the interface is denoted by $$\widehat{\mathbf {s}}$$ .

Considering two annular rotating electron beams in a dielectric-lined waveguide, the frequency spectrum of the azimuthal waves and their field profile distribution are investigated. The charged particle acceleration due to the tangential component of the electric field is simulated. The simulation is carried out for important factors, such as the electron energy gain (acceleration gradient) and the deflection angle in two different vacuum regions (the core and clad of the dielectric waveguide). The graphs of the mentioned parameters versus the traveled distance by the electron are presented, and they are compared with each other. It is found that in some cases, the tangential acceleration of the charged particle in the clad of the cylindrical waveguide can be more effective.

The process of the pivoting friction of ShKh15 steel over the flat surface of a prism made of R6M5 steel was studied and an analytical description of interaction of the pivoting friction moment with the radius of the wear scar, load, and time of loading was proposed. In the steady wear mode, the pivoting friction moment is steady as well. Change in the pivoting friction moment does not stay within the boundaries of one linear dependence, and several linear regions are observed and they may be interpreted by the law taking into account the moment of resistance to pivoting dictated by the tangential component of the equivalent forces of the molecular attraction of the friction surfaces.

In an attempt to correct the unrealistic material stiffness predicted by elastoplastic models which adopt an associative flow rule, this paper introduces an innovative technique for the computation of the inelastic contributions generated in a non-proportional loading path. The formulation of these inelastic contributions takes into account the plastic response along the direction normal to the plastic potential, neglecting the irreversible stretch caused by the tangential component of the stress rate. Here, the introduction of tangential plasticity, in combination with the return mapping technique, eliminates this drawback, allowing fast and accurate computation. The present paper focuses on the evaluation of the load-carrying capacity of a steel bridge pier, indicating the necessity of considering the additional tangential plasticity term for a correct description of the structural response.

In this paper, we deal with complete generalized linear Weingarten spacelike hypersurfaces immersed in a Lorentzian space form, which means that there exists a linear relation involving some of the higher order mean curvatures. In this setting, we show that such a spacelike hypersurface must be totally umbilical, provided that its Gauss mapping has some appropriate behavior and that the tangential component of a fixed nonzero vector has integrable norm along it. Our approach is based on a suitable divergence formula jointly with an appropriate maximum principle at the infinity.

The estimation of one-dimensional (1-D) isotropic structures is routine work in most receiver function (RF) analyses that generally use a reference radial RF (RRF) for each station. However, the assumption of negligible back-azimuthal dependencies in a set of RRFs for a station may not be valid because of anisotropic layering, dipping structures, or incorrect sensor orientations. This work presents a comprehensive procedure to obtain a station-representative isotropic RRF, which can be applied automatically to prepare RRF data. The method incorporates a harmonic stripping method with a grid-search for sensor orientations. An optimum angle for the sensor orientation is determined by searching for the angle that minimizes the energy in the tangential component RF (TRF). For each searched angle, possible effects by anisotropy and dipping structures are iteratively suppressed by an inversion process to exclude two- and four-robe back-azimuthal patterns. The performance of the method was first confirmed with a test using a set of highly noisy composite RRFs and TRFs. The method was then applied to RF data from the southern Korean Peninsula and southwestern Japan. Obtained isotropic RRFs and measured station orientations were found to be reliable in comparisons with results from neighboring stations and previous studies. As an automatized routine pre-process, the obtained isotropic RRF data are particularly useful for estimating 1-D isotropic structures in migration or inversion studies, which are potentially affected by back-azimuthal dependencies in RF data calculated through conventional averaging methods.