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In this article, we address resistance forces and torques acting onto a body with arbitrary shape moving in an unsteady Stokes flow. We start analyzing the functional form of the expressions for forces and torques, which depend on the frequency parameter and on the position of the body in the domain of the fluid, and determining the asymptotic limits for high and low frequencies. In this regard, we show that, for high frequencies (hence short times), forces and torques are obtained by the associated hydrodynamic problems considering ideal potential flows, independently of the geometry of the problem. Afterwards, with the aim of obtaining expressions for forces and torques valid in the entire range of frequencies, we extend to the unsteady case the reflection method, largely employed in the theory of the steady Stokes flows. In this way, general expressions are provided in terms of the Faxén operators of the body and the Green function associated with the geometry of the confinement, that are valid, to the leading order, at any frequency, independently of the geometry of the problem. Finally, as the application of the general expressions, explicit relations for the resistance forces acting onto a spherical body with no-slip boundary conditions near a plane wall with full-slip boundary conditions are obtained, valid over the entire frequency range, provided that the distance between the plane and the sphere is larger than one sphere radius. [ABSTRACT FROM AUTHOR]

This work investigates the mixing phenomenon within rectangular cavities of various aspect ratios, all four sides driven at the same speed in a clockwise direction. For the creeping flow regime, an analytical solution using real eigenfunction expansion is derived. Inertia's influence under higher flow rates is then numerically simulated using a built-in finite element technique in the Mathematica software. For a square cavity, the inherent structural symmetry is combined with the dynamical symmetry of the velocity field. However, changing the aspect ratio disrupts this symmetry in the horizontal and vertical velocities. Interestingly, unlike other wall-driven cavity flows found in the literature, the recirculating zone in this system forms a single vortex without any corner eddies at any Reynolds number. This unique feature offers tremendous potential for controlling the mixing process. In the highly viscous regime, the pressure field is dominated by odd functions in both x and y. As inertia increases, even functions in x and y become more significant, causing the velocities near the moving lids to overshoot their steady-state values. The extent of this overshoot depends on the cavity's aspect ratio, and such a fast mixing regime could be valuable for industrial fluid mixing applications. • The flow dynamics within a rectangular cavity of varying aspect ratios are studied. • The clockwise movement of all four lids at a constant speed are considered. • The slow-motion Stokes layer is analytically resolved by an eigenfunction technique. • Finite element simulations within Mathematica are performed. • A single recirculating vortex for mixing within the cavity occurs. [ABSTRACT FROM AUTHOR]

In this article, we address resistance forces and torques acting onto a body with arbitrary shape moving in an unsteady Stokes flow. We start analyzing the functional form of the expressions for forces and torques, which depend on the frequency parameter and on the position of the body in the domain of the fluid, and determining the asymptotic limits for high and low frequencies. In this regard, we show that, for high frequencies (hence short times), forces and torques are obtained by the associated hydrodynamic problems considering ideal potential flows, independently of the geometry of the problem. Afterwards, with the aim of obtaining expressions for forces and torques valid in the entire range of frequencies, we extend to the unsteady case the reflection method, largely employed in the theory of the steady Stokes flows. In this way, general expressions are provided in terms of the Faxén operators of the body and the Green function associated with the geometry of the confinement, that are valid, to the leading order, at any frequency, independently of the geometry of the problem. Finally, as the application of the general expressions, explicit relations for the resistance forces acting onto a spherical body with no-slip boundary conditions near a plane wall with full-slip boundary conditions are obtained, valid over the entire frequency range, provided that the distance between the plane and the sphere is larger than one sphere radius.

Inertial methods play a vital role in accelerating the convergence speed of optimization algorithms. We present an inertial forward-backward-half forward splitting algorithm, which mainly finds a zero of the sum of three operators, where two of them are cocoercive operator and monotone-Lipschitz continuous respectively. Meanwhile, the convergence analysis of the proposed algorithm is established under mild conditions. To overcome the difficulty in the calculation for the resolvent of the composite operator, relying on a primal-dual idea, we expand the proposed algorithm to solve the composite inclusion problem involving a linearly composed monotone operator. As an application, we make use of the obtained inertial algorithm to deal with a composite convex optimization problem. We also show extensive numerical experiments on the total variation-based image deblurring problem to demonstrate the efficiency of the proposed algorithm. Specifically, the proposed algorithm not only has a better quality of the deblurring image but also converges more rapidly than the original one. [ABSTRACT FROM AUTHOR]

This study aims to explore the influence of various geometrical and hydraulic parameters on flow behavior and hydraulic conductivity in a single artificial fracture through a series of laboratory experiments. Laboratory experiments were conducted to examine unconfined groundwater flow through an artificially constructed single fracture. The fracture model consisted of varying aperture sizes (3, 9, and 12 mm) and different surface roughness conditions (fine, medium, and coarse sand coatings). Non-Darcian turbulent flow characteristics were observed at different flow rates, and the gradient of Reynolds number versus average flow velocity increased with aperture size. Flow parameters of the Darcian, Izbash, and Forchheimer models were calculated to characterize the flow behavior. Both the Forchheimer and Izbash models were found suitable for describing the non-Darcian flow characteristics under the prevailing conditions. The study revealed that hydraulic conductivity depended on flow length for fractures with different apertures and surface roughnesses, likely due to the presence of 2-D torturous flow within the rough fracture surface. These findings contribute to a better understanding of groundwater flow in fractured rock aquifers and provide valuable insights for modeling and managing such systems. HIGHLIGHTS Flow in a single fracture for different surface roughness and aperture.; Analysis of Darcy, Forchheimer, and Izbash model parameters.; Analysis of variation in the gradient of Reynold's number with average flow velocity.; Evaluation of local cubic law and evaluation of spatial dependence of hydraulic conductivity.;

Simple Summary: Equestrian sports include a diverse range of activities requiring a wide variety of technical skills, all of which are based on collaboration between a rider and a horse. During training, horses are taught to respond appropriately to the rider's cues or "aids". In addition to these trained responses, the rider's weight is associated with mechanical effects that are based on physical principles governing the behavior of, and interactions between, bodies in the environment. The effects of gravity, inertia, and turning have predictable effects on the horse, but these may be modified by the rider's symmetry, balance, and posture. The ultimate goal is for the rider to have a harmonious relationship with the horse, which is addressed in the final section of this article exploring the biomechanical underpinnings of the harmony between riders and horses. Movements of the horse and rider in equestrian sports are governed by the laws of physics. An understanding of these physical principles is a prerequisite to designing and interpreting biomechanical studies of equestrian sports. This article explains and explores the biomechanical effects between riders and horses, including gravitational and inertial forces, turning effects, and characteristics of rider technique that foster synchronous movement with the horse. Rider symmetry, posture, and balance are discussed in the context of their relationship to rider skill level and their effects on the horse. Evidence is presented to support the feasibility of improving equestrian performance by off-horse testing followed by unmounted therapy and exercises to target the identified deficiencies. The elusive quality of harmony, which is key to a true partnership between riders and horses, is explored and described in biomechanical terms. [ABSTRACT FROM AUTHOR]

Water lubricated hydrostatic journal bearings are widely used to support radial load of pumps in nuclear power plants. In some situations, these pumps may be required to operate with a mixture of water and air. This compressible air-water mixture will alter the dynamic characteristics of the hydrostatic journal bearings and can have a significant impact on the vibration behavior of the entire pump shaft line. This work is a parametrical investigation of the rotordynamic characteristics of these bearings relative to the volume fraction of the ingested air. The compressibility, the density, and the viscosity of the air-water mixture depend on this volume fraction. In order to evaluate this influence, a homogeneous air-liquid mixture model were developed. Moreover, for low viscosity lubricants, inertia effects can also have an important impact on bearing rotordynamic coefficients. Therefore, the flow is modeled first with the Reynolds equation and then with the bulk flow system of equations to evaluate this impact. The results show the variation of the direct and cross-coupling stiffness and of the direct damping with the evolution of inertial effects and of the level of air contamination. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of generalized split feasibility problem over the solution set of monotone variational inclusion problems, which includes the split common null point problem, the split variational problems, and other related split type problems. We propose a new self-adaptive stepsize method coupled with inertial extrapolation techniques for solving this problem in real Hilbert spaces. We prove that the sequence generated by the proposed method converges strongly to a solution of the problem under the assumption that the associated singlevalued operator in the monotone variational inclusion problem is not required to be inverse-strongly monotone. Our method uses the stepsizes that are generated at each iteration by some simple calculations, which allows it to be easily implemented without the prior knowledge of the operator norm or the Lipschitz constant of the singlevalued operator. Finally, we apply our results to solve optimal control problems, split linear inverse problems, and least absolute selection and shrinkage operator problems. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a stochastic approximation based algorithm for solving nonmonotone stochastic variational inequalities. Our algorithm combines the projection and contraction method with the inertial extrapolation technique. The self-adaptive step size sequence is generated by employing the Armijo's line search rule. We also investigate the almost sure convergence property without using the prior knowledge of the Lipschitz constant of the involved operator in our algorithm. Theoretical results related to the convergence rate and the oracle complexity are provided under mild assumptions. Primary numerical experiments are presented to demonstrate the efficiency of the algorithm. [ABSTRACT FROM AUTHOR]

We consider a stochastic Allen–Cahn–Navier–Stokes equations with inertial effects and multiplicative noise of jump type in a bounded domain D⊂Rd$D\subset \mathbb {R}^{d}$, d=2,3$d=2,3$, driven by a multiplicative noise. The existence of a global weak martingale solution is proved under non‐Lipschitz assumptions on the coefficients. The construction of the solution is based on the Faedo–Galerkin approximation, compactness method and the Skorokhod representation theorem. [ABSTRACT FROM AUTHOR]

The design of metamaterials based on triply periodic minimal surfaces (TPMS) is currently a very active field of research. An upscaling approach is used here to study the flow in TPMS-based porous media, with focus on the effects of advection. The effective medium permeability, function of the Reynolds number R e of the flow through the pores, is numerically evaluated for varying porosity θ , for six types of TPMS-based structures, namely Gyroid , I-WP , Schwarz P , Split P , Fischer–Koch S , and Neovius. Inertial effects are found to be significant; for instance, the permeability is reduced by 15 − 50 % (according to the surface type) as R e increases from 0 to 50000, when θ = 0. 98. [Display omitted] • Seepage in different triply-periodic-minimal-surface-based porous media is studied. • Analysis is conducted beyond the linear, Stokes flow regime. • Effective (rather than intrinsic) permeability in Darcy's law stems from upscaling. • Dependence of effective permeability on porosity and Reynolds number is explored. • Advection can significantly reduce permeability, particularly at large porosity. [ABSTRACT FROM AUTHOR]

This paper discusses a semi-analytic solution for the volatile oil influx into the well on the base of Forchheimer flow law. The solution is developed employing the concept of binary model for the two-phase petroleum hydrocarbon system in view of phase transformations and interphase mass transfer. Algorithms are developed for calculating the volatile oil reservoir key performance indicators by applying the material balance equations, which take into account the compaction behavior of rocks. A computer simulator for the volatile oil reservoir is modeled, proceeding from these algorithms. The inertial effects on the development process of a volatile oil reservoir, the rocks of which are exposed to elastic deformation, are studied by this simulator. In regard thereto, the reservoir development process is simulated in two variants in conformity with the constant depression: in the first case, it is assumed that the filtration occurs according to Darcy's law, while in the second one, the process is considered on the base of Forchheimer equation. A comparison of the results of these options made it possible to demonstrate the nature of the inertial effects on the volatile oil reservoir key performance indicators. [ABSTRACT FROM AUTHOR]

This paper proposes a multiaxial macroelement for bridge abutments that can be included in the global structural model of a bridge to carry out nonlinear dynamic analyses with very much smaller computational effort than can be achieved using continuum representations of embankment and foundation soil behaviour. The proposed macroelement derives a constitutive force–displacement relationship within a rigorous thermodynamic framework and includes important features of non‐linearity and directional coupling in characterizing the interactions of the abutment with the soil. In a dynamic analysis, the frequency‐dependent response of the system is simulated through the combination of the macroelement with appropriate participating masses. The calibration procedure of the macroelement is based on the assessment of its ultimate capacity and of its response at small displacements, and it is shown that these ingredients can be derived through standardised procedures. In the paper, the macroelement response is validated against the results of fully coupled continuum numerical analyses for a reference soil–abutment system, under both static and seismic loading conditions. We show that the two models achieve similar predictions of maximum and permanent abutment deformations (less than 10–14% difference, respectively) for a suite of three‐axis seismic loading events. [ABSTRACT FROM AUTHOR]

The effects of droplet inertia on the reaction zone structure, overall burning rate, and flame surface area during interaction of water droplets with a statistically planar turbulent premixed stoichiometric n-heptane-air flame based on three-dimensional carrier phase Direct Numerical Simulations have been analysed. Different initially mono-sized droplets are considered for this study in order to analyse the inertial effects for different droplet sizes. Droplet inertia has been demonstrated to have an important influence on the extent of evaporation of water droplets and water vapour concentration arising from evaporation within the flame. It has been found that the residence time of droplets within the flame increases due to droplet inertia and therefore the evaporation and the cooling effect associated with the extraction of latent heat are stronger for inertial droplets than in the case of hypothetical inertialess droplets. The stronger cooling effects for inertial droplets lead to smaller burned gas temperature and thicker flame than the corresponding cases with inertialess droplets. The aforementioned cooling effect induced by latent heat of evaporation of water droplets reduces the burning rate and the likelihood of obtaining high gradient magnitudes of reaction progress variable and temperature within the flame for the cases with water droplets in comparison to the corresponding purely gaseous turbulent premixed flames, and this tendency is stronger for inertial droplets. The stronger cooling effect, along with the reduction of reactant concentrations within the flame due to greater extent of evaporation for inertial droplets, gives rise to a smaller extent of flame area generation and overall burning rate than in the corresponding cases with inertialess droplets. It has been found that water droplet inertia acts to reduce the burning rate and the consumption rate of reactants per unit flame surface area during the interaction of water droplets with turbulent premixed flames within the parameter range analysed in this paper. [ABSTRACT FROM AUTHOR]

We introduce a relaxed inertial forward-backward-forward (RIFBF) splitting algorithm for approaching the set of zeros of the sum of a maximally monotone operator and a single-valued monotone and Lipschitz continuous operator. This work aims to extend Tseng's forward-backward-forward method by both using inertial effects as well as relaxation parameters. We formulate first a second order dynamical system that approaches the solution set of the monotone inclusion problem to be solved and provide an asymptotic analysis for its trajectories. We provide for RIFBF, which follows by explicit time discretization, a convergence analysis in the general monotone case as well as when applied to the solving of pseudo-monotone variational inequalities. We illustrate the proposed method by applications to a bilinear saddle point problem, in the context of which we also emphasize the interplay between the inertial and the relaxation parameters, and to the training of Generative Adversarial Networks (GANs). [ABSTRACT FROM AUTHOR]

Movements of the horse and rider in equestrian sports are governed by the laws of physics. An understanding of these physical principles is a prerequisite to designing and interpreting biomechanical studies of equestrian sports. This article explains and explores the biomechanical effects between riders and horses, including gravitational and inertial forces, turning effects, and characteristics of rider technique that foster synchronous movement with the horse. Rider symmetry, posture, and balance are discussed in the context of their relationship to rider skill level and their effects on the horse. Evidence is presented to support the feasibility of improving equestrian performance by off-horse testing followed by unmounted therapy and exercises to target the identified deficiencies. The elusive quality of harmony, which is key to a true partnership between riders and horses, is explored and described in biomechanical terms.

Surface textures decrease friction in lubricated sliding contact. Traditionally, the friction reduction for a given textured surface is determined by using the Reynolds equation, which neglects fluid inertia. However, as the separation and relative motion between the surfaces increase, inertia can affect the measured tangential and normal forces for flow over a textured surface, and thus cause the coefficient of friction to differ from the purely viscous, Stokes flow prediction. Here, the increase in torque and normal force between a moving plate and stationary textured surface, which simulates a textured thrust bearing, are calculated as a function of the Reynolds number in the thin film limit. The predictions for a non-textured thrust bearing are compared to fully 3-D numerical simulations of the incompressible Navier-Stokes equation, and the predictions for textured thrust bearings are compared to experimental data given in the literature. Good agreement is seen between the predictions and the data, validating the predicted scaling laws. This work also suggests that inertia can be used as a secondary effect to reduce friction in lubricated sliding, and textures that take advantage of the inertial effects will have lower friction than textures that only use purely viscous effects. [ABSTRACT FROM AUTHOR]

In this novel numerical investigation, the application of well-renowned numerical technique known as Galerkin finite element method on full form of Navier-Stokes equations presented peristaltic flow of non-Newtonian fluid confined by a uniformly saturated porous medium. The rheological aspects of non-Newtonian material are discussed by considering micropolar fluid. The flow model consists of system of nonlinear partial differential equations with mixed boundary condition. The flow also experienced an externally applied magnetic field. The effects of inertial forces and the results independent of wavelength are obtained by dropping the presumptions of lubrication theory in modelling the governing equations. The numerical solution for formulated problem in terms of partial differential expressions is worked out via Galerkin finite technique in view of six nodal triangular elements. The enhancement in the inertial forces gives impressive pressure enhancement against wavelength while opposed the fluid flow in the vicinity of peristaltic walls of the tube but supported the fluid flow in the central region of the tube. The present results are also compared with the available results after applying lubrication theory and found in reliable agreement. [ABSTRACT FROM AUTHOR]

We study the impact of inertial effects on neutrino oscillations and decoherence. Toward this end, we describe the propagation of neutrino wave packets by employing the density matrix formalism. We show that the acceleration and angular velocity of the observer's reference frame significantly influence neutrino coherence, the effects being in principle testable in strong regime.

We propose BIBPA, a block inertial Bregman proximal algorithm for minimizing the sum of a block relatively smooth function (that is, relatively smooth concerning each block) and block separable nonsmooth nonconvex functions. We show that the cluster points of the sequence generated by BIBPA are critical points of the objective under standard assumptions, and this sequence converges globally when a regularization of the objective function satisfies the Kurdyka-Łojasiewicz (KL) property. We also provide the convergence rate when a regularization of the objective function satisfies the Łojasiewicz inequality. We apply BIBPA to the symmetric nonnegative matrix tri-factorization (SymTriNMF) problem, where we propose kernel functions for SymTriNMF and provide closed-form solutions for subproblems of BIBPA. [ABSTRACT FROM AUTHOR]

This research is to assess the influences of the inertial mass from the girder on the dynamic characteristic, dynamic response, and structure-soil interaction of a pile-soil-pier subsystem in a scale-model of a cable-stayed bridge. Therefore, both connection configurations between the pile-soil-pier and girder, including the sliding and fixed connections, were designed to present various inertial mass from the superstructure delivered to the pile-soil-pier. The pile-soil-pier supported by a 3 × 3 pile-group in mixed soil placed in a shear box was tested using shaking tables. The dynamic characteristics, seismic responses, inertial interactions, and pile group effects of the pile-soil-pier between the sliding and fixed connections were analyzed under three input motions with different shaking amplitudes. These results showed that more inertial mass from the girder significantly increased the reinforcement strain and bending moment at the column bottom and pile top, displacement at the column top, inertial interaction effects, and pile group effects of the pile-soil-pier due to the sliding connection changing to the fixed connection. The inertial mass increment from the girder noticeably decreased the peak accelerations of the column of the pile-soil-pier when subjected to three input motions with different amplitudes. However, the inertial mass insignificantly affected the accelerations of the pile and free-soil. Therefore, the corresponding kinematic interaction effects were almost unaffected by the inertial mass. Additionally, the evident pile group effects were observed in the sliding and fixed connections between the pile-soil-pier and girder. The numerical model could approximately reproduce the macroscopic seismic responses of the pile-soil-piers with sliding and fixed connections and capture the typical response variations induced by the connection configuration change. [ABSTRACT FROM AUTHOR]

The structural design of offshore wind turbines is based on the consideration of coupled dynamic phenomena. Wave loads cause the dynamic oscillation of the monopile, and the dynamic oscillation of the monopile affects the wave loads. The boundary conditions of the gravity-based foundation-monopile-turbine system are mostly affected by the flexural stiffness of the foundation plate, the elastic and creep behavior of the soil, and the inertia (translational and rotational) of the wind turbine mass. The design of the foundation should consider the dynamic response of the soil and the monopile, and the dynamic response of the soil and the monopile is affected by the design parameters of the foundation. The initial conditions of the system yield transient dynamic phenomena. A braking wave at t = 0 causes different dynamic response than the steady-state conditions due to a harmonic wave load. In the present work, an integrated analytical model simulating the above dynamic phenomena is proposed. With the aid of double integral transforms and generalized function properties, a solution of the corresponding differential equations for the monopile-soil-foundation system and the boundary and initial conditions is derived. A parametric study is carried out, and results of the effect of the design parameters and soil properties are presented and discussed. [ABSTRACT FROM AUTHOR]

A rigid in-plane matrix of suction cups is widely used in robotic end-effectors to grasp objects with flat surfaces. However, this grasping strategy fails with objects having different geometry e.g., spherical and cylindrical. Articulated rigid grippers equipped with suction cups are an underinvestigated solution to extend the ability of vacuum grippers to grasp heavy objects with various shapes. This paper extends previous work by the authors in the development of a novel underactuated vacuum gripper named Polypus by analyzing the impact of dynamic effects and grasping location on the vacuum force required during a manipulation cycle. An articulated gripper with suction cups, such as Polypus, can grasp objects by adhering to two adjacent faces, resulting in a decrease of the required suction action. Moreover, in the case of irregular objects, many possible grasping locations exist. The model explained in this work contributes to the choice of the most convenient grasping location that ensures the minimum vacuum force required to manipulate the object. Results obtained from an extensive set of simulations are included to support the validity of the proposed analytical approach.

In fractures where surface fluctuations are large compared to their aperture (narrow fractures), the flow is forced to move in tortuous paths that produce additional viscous friction and are subject to inertia effects. We consider the relation between the magnitude of surface roughness and the onset of inertial effects in the pressure driving the flow through a single open fracture. We performed experiments systematically varying the average aperture of the open fracture and covering a wide range of Reynolds numbers. For each aperture, we analyze the data in terms of the Forchheimer equation and show that the critical Reynolds number, defined as the Reynolds number at which inertial effects contribute 10% of the total pressure losses, is highly correlated with the roughness of the surface. In particular, we show that significant inertial effects appear earlier as the relative importance of surface roughness increases. Finally, we present results showing that the magnitude of the deviations in the pressure field compared to a linear profile, taken at different points in the fracture along the flow direction, is directly related to the relative surface roughness of the fracture. Key Points: Surface roughness leads to an early onset of inertial effectsSurface roughness leads to an increase in spatial pressure fluctuationsThe critical Reynolds number correlates with normalized surface roughness [ABSTRACT FROM AUTHOR]

Drifters designed to mimic floating marine debris and small patches of pelagic Sargassum were satellite tracked in four regions across the North Atlantic. Though subjected to the same initial conditions at each site, the tracks of different drifters quickly diverged after deployment. We explain the clustering of drifter types using a recent Maxey‐Riley theory for surface ocean inertial particle dynamics applied on multidata‐based mesoscale ocean currents and winds from reanalysis. Simulated trajectories of objects at the air‐sea interface are significantly improved when represented as inertial (accounting for buoyancy and size), rather than as perfectly Lagrangian (fluid following) particles. Separation distances between simulated and observed trajectories were substantially smaller for debris‐like drifters than for Sargassum‐like drifters, suggesting that additional consideration of its physical properties relative to fluid velocities may be useful. Our findings can be applied to model variability in movements and distribution of diverse objects floating at the ocean surface. Plain Language Summary: Predicting the fate of floating matter requires one to recognize that they respond differently than Lagrangian (i.e., infinitesimally small, neutrally buoyant) particles to the action of surface currents and winds. Indeed, the Maxey‐Riley equation of fluid mechanics—a Newton second‐law‐type ordinary differential equation—shows that even the motion of seemingly small neutrally buoyant particles immersed in a fluid in motion can substantively deviate from that of Lagrangian particles. The Maxey‐Riley equation has been recently extended to account for the combined effects of ocean current and wind drag on finite‐size particles floating at the ocean surface. We show here that the paths of drifters that mimic marine debris and small Sargassum patches cluster according to their inertial characteristics consistent with the Maxey‐Riley theory. Key Points: Custom‐made marine‐debris‐ and Sargassum‐like undrogued surface drifters are observed to cluster according to design typeThe clustering is explained as a result of inertial effects using a novel Maxey‐Riley theoryThe results have implications for maintaining ecosystem health, search‐and‐rescue operations, and marine safety [ABSTRACT FROM AUTHOR]

Influences of droplet inertia on the reaction zone structure, burning rate and flame surface area in spherically expanding flames propagating into mono-sized droplet mists with an overall (liquid+ droplet phases) equivalence ratio of unity have been analysed based on three-dimensional carrier phase Direct Numerical Simulations for different droplet diameters and turbulence intensities. Droplet inertia has been demonstrated to have an important influence on gaseous equivalence ratio within the flame. The gaseous phase combustion in the cases with inertialess droplets has been shown to take place predominantly under leaner conditions and this trend strengthens further for higher turbulence intensities. Consequently, the flames in the case of inertialess droplets have been found to be thicker than the corresponding cases with inertial droplets. The number density of droplets within the flame remains smaller in the inertialess droplet cases than in the corresponding cases with inertial droplets, which leads to smaller extents of droplet-induced flame wrinkling. As a result, the probability density functions of flame curvature for the inertial droplet cases have been found to be wider than those in the corresponding inertialess droplet cases. The reduced probability of obtaining stoichiometric gaseous mixture within the flame for inertialess droplets leads to a smaller percentage share of total heat release rate from non-premixed mode of combustion than those with inertial droplets. This, along with the predominance of fuel-lean gaseous mixture composition within the flame, gives rise to smaller extent of flame area generation and burned gas volume in the inertialess droplet cases than in the corresponding cases with inertial droplets. This tendency strengthens with increasing turbulence intensity and the cases with large inertialess droplets under high turbulence intensity show indications of eventual flame extinction. [ABSTRACT FROM AUTHOR]

Inertial effects during the process of supercritical CO2 displacing brine in porous media may not be negligible according to recent studies. Capturing the inertial effects of the physical CO2‐brine system imposes a requirement on the grid resolution and viscosity to surface tension ratio for pore‐scale simulations, which some commonly used simulators may not be able to meet. To fulfill the parameter requirement, we combine the continuum‐surface‐force based color‐gradient lattice Boltzmann (LB) multiphase model and the geometrical wetting model and extend the model to 3D under the multiple‐relaxation‐time framework. We validate the model via simple benchmarks which show significant improvement over the traditional models. We then perform 3D drainage simulations in a heterogeneous micromodel where the simulation result agrees well with experimental data, while our previous work fails to reproduce certain displacement patterns in the experiment due to the use of a traditional LB model that cannot fulfill the parameter requirement. Finally, we perform high‐fidelity 3D drainage simulations to study the inertial effects in a Bentheimer sandstone sample. Our results show that stronger inertial effects generally help develop more CO2 flow pathways for the same capillary number which results in higher CO2 saturation, consistent with the micromodel results. The phenomena can be found in both low and high capillary number cases, indicating that the inertial effects are not dependent on the mean velocity. In addition, the change of the invasion patterns is not proportional to the change of inertial effects, thus exhibiting threshold behavior. Key Points: An advanced lattice Boltzmann model is developed to simulate scCO2 displacing brine in real rock geometriesInertial effects help develop CO2 flow pathways resulting in higher CO2 saturationInertial effects are independent of mean velocity and the change of inertial effects exhibits threshold behavior [ABSTRACT FROM AUTHOR]

Patterned vegetation dynamics in flat arid environments are investigated in the framework of a hyperbolic modified Klausmeier model. In particular, this study aims at elucidating how the properties exhibited by supercritical and subcritical patterns during the transient regime are affected by the inertial times. The present work encloses linear stability analysis to deduce the threshold condition for Turing pattern formation and weakly nonlinear analysis to describe the time evolution of the pattern amplitude close to the instability threshold. In our analysis, we consider the case in which the emerging patterns do not have any spatial structure, as it is typically assumed in small domains, as well as the scenario in which patterns form sequentially and propagate over a large domain in the form of a traveling wavefront. The hyperbolic model is also integrated numerically to validate the analytical predictions and to characterize more deeply the spatio-temporal evolution of vegetation patterns in both supercritical and subcritical regime. • Supercritical and Subcritical vegetation patterns in flat arid areas are analyzed. • The role of inertial effects in a hyperbolic modified Klausmeier model is studied. • The hyperbolicity allows an accurate description of dynamics in transient regime. • Amplitude and Modulation equations are deduced by multiple-scale weakly-nonlinear analysis. • Existence, features and vegetation types in super/sub-critical regimes are inspected. [ABSTRACT FROM AUTHOR]

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Abstract Liquid-vapor flow in porous media is studied in this article. To fulfill this goal, a double-distribution-function lattice Boltzmann (LB) model is proposed based on the separate-phase governing equations at the representative elementary volume (REV) scale. Importantly, besides the Darcy force and capillary force, which were commonly included in previous studies, the LB model in this article also considers the inertial force characterized by the Forchheimer term. This feature enables the model to offer an effective description of liquid-vapor flow in porous media at low, intermediate and even high flow rates. We validated the LB model by simulating a single-phase flow in porous media driven by a pressure difference and found its results are in good agreement with the available analytical solutions. We then applied the model to study water-vapor flow in a semi-infinite porous region bounded by an impermeable and heated wall. The numerical simulation reveals the flow and mass transfer characteristics under the compounding effects of inertial, Darcy and capillary forces. Through a comparison with the results given by the generalized Darcy's law, our numerical results directly evidence that the inertial force is a dominating factor when a fluid passes through porous media at an intermediate or high flow rate. [ABSTRACT FROM AUTHOR]

Motility-induced phase separation (MIPS) is of great importance and has been extensively researched in overdamped systems, nevertheless, what impacts inertia will bring on kinetics of MIPS is lack of investigation. Here, we find a nucleation-like MIPS instead of spinodal decomposition in the overdamped case, i.e. not only the phase transition changes from continuous to discontinuous, but also the formation of clusters does not exhibit any coarsening regime. This remarkable kinetics of MIPS stems from a competition between activity-induced accumulation of particles and inertia-induced suppression of clustering process. More interestingly, the discontinuity of MIPS still exists even when the ratio of particle mass to the friction coefficient reduces to be very small such as 10 ^−4 . Our findings emphasize the importance of inertia induced kinetics of MIPS, and may open a new perspective on understanding the nature of MIPS in active systems.

Purpose: The self-consistent two-fluid model for the stationary axisymmetric magnetosphere of a pulsar is considered. Design/methodology/approach: Taking into account infinitesimal inertial effects, the zero- and first-order equations are solved. The general results are applied to the case of a small difference in the distributions of the two particle species in the magnetosphere of a monopolar structure. Results: The physically grounded distribution functions for the electron and positron constituents of the pulsar plasma are found, which sustain the force-free configuration of the magnetosphere. The approach developed enables us to consistently incorporate emission into the force-free model of the pulsar magnetosphere. Within the framework of our consideration, the plasma conductivity along the poloidal magnetic field appears of the order of the inverse particle mass, in contrast to the finite conductivity of “massless” particles typically assumed in the literature. Conclusions: The model constructed has important implications not only for the high-energy emission but also for the radio emission of pulsars. In the force-free plasma flow, the two-stream and diocotron instabilities can develop, leading to the radio emission generation and subpulse drift, respectively. Then, the pulsar radio emission appears physically connected to the high-energy emission.

Highlights • Dynamic fracture energy values are estimated for PA11 pipes. • Inertia effects depends strongly on boundary conditions and sample geometry. • The amount of created surface area should be considered for semicrystallines. • "Ring-off" and "snake" mechanisms do not appear during dynamic propagation. Abstract Dynamic fracture mechanism in Polyamide 11 (PA11) material has been described at laboratory scale to access to an intrinsic material parameter. A liquid transportation application is considered with polymer pipes. A preliminary numerical analysis of the rapid crack propagation (RCP) in polymer pipe is firstly realised. Two boundary conditions, imposed displacement or pressure, are numerically investigated. The work of external forces is not negligible for pressurized polymer pipe. A reliable estimate of the dynamic energy release rate G Id is in this last case not guaranteed. To limit unwanted structural effects a specific experimental device has been used to ensure a permanent regime of RCP in Pre-Stressed Pipe Specimen (PS2). Experimental dynamic fracture tests are realised with Polyamide 11 PS2. Dynamic instabilities inducing "ring-off" and "snake" mechanisms which could appear during full-scale test are not observed with this new test. A finite element procedure is used to estimate the material toughness G ID of PA11. Knowing the crack tip location during RCP inertia effects (i.e. kinetic energy) are quantified. The mean crack tip velocity is observed not to change in PA11 whatever the crack configuration (branching or not). This velocity is known to be the crack branching velocity (≈ 0.6 c R ). The average dynamic energy release rate 〈 G ID 〉 is equal to 1.5 ± 0.1 kJ m−2 at the crack branching velocity. The non-trivial fracture surface roughness is observed with a scanning electron microscope. [ABSTRACT FROM AUTHOR]

Based on a previously observed analogy between electromagnetic and non-inertial effects, we investigate the competition between magnetic field and rotation in the quantum motion of an electron constrained to the surface of a sphere. We solve numerically the Schrödinger equation of the problem for the energy eigenvalues and the eigenfunctions and compare the effects of the magnetic field and rotation. We obtain that, for a weak magnetic field, an electron can not distinguish between magnetic field and rotation, since they lead to equivalent behavior. But this is no longer true for strong magnetic fields. However, surprisingly, even though the rotation and magnetic fields play different roles in the electronic properties of the system, when together, each influence of the magnetic field on the energy levels can be separately balanced by rotation. We also show that no matter the intensity of the magnetic field, it is always possible to destroy the Landau levels in the sphere by rotation. [ABSTRACT FROM AUTHOR]

The flow in three-dimensional fibrous porous media is studied in the inertial regime by first simulating for the motion in unit, periodic cells, and then solving successive closure problems leading – after applying an intrinsic averaging procedure – to the components of the apparent permeability tensor. The parameters varied include the orientation of the driving pressure gradient, its magnitude (which permits to define a microscopic Reynolds number), and the porosity of the medium. All cases tested refer to situations for which the microscopic flow is steady. When the driving force is oriented in a direction which lies on the plane perpendicular to the fibers’ axis, the results found agree with those available the literature. The fact that the medium is composed by bundles of parallel fibers favours a deviation of the mean flow towards the fibers’ axis when the driving pressure gradient has even a small component along it, and this is enhanced by a decreasing porosity; this phenomenon is well quantified by the knowledge of the components of the permeability. Contrary to our initial expectations, for the over one hundred cases which we have simulated, the apparent permeability tensor remains, to a very good approximation, diagonal, a fact mainly related to the transversely isotropic nature of the medium. To obtain a complete, albeit approximate, database of the diagonal components of the apparent permeability tensor we have developed a metamodel, based on kriging interpolation, and carefully calibrated it. The resulting response surfaces can be invaluable in determining the force caused by the presence of inclusions in macroscopic simulations of the flow through bundles of fibers whose orientations and dimensions can vary in space and/or time. [ABSTRACT FROM AUTHOR]

A theoretical study of the laminar squeeze flow of copper water and alumina water nanofluids between a flat circular stationary disk and a curved circular moving disk is carried out using energy integral method. The squeeze film behaviour is examined analytically and the effects of inertia and curvature on the squeeze film pressure, load carrying capacity of the fluid and temperature are analysed. Further, the problem is solved numerically for a sinusoidal motion of the upper curved disk taking an exponential form of the gap width. It is found that the copper water nanofluid is better than alumina water nanofluid for better heat transfer rates. While high inertia forces strongly influence the squeeze film behaviour, low inertia forces are favourable for temperature distribution. Further, concave nature of the upper disk gives better squeeze film characteristics than convex disk. However, convex disk is better than concave disk as far as the temperature distribution is concerned. [ABSTRACT FROM AUTHOR]

In this paper the formation of rhombic and hexagonal Turing patterns in bidimensional hyperbolic reaction–transport systems is addressed in the context of dryland ecology. To this aim, exploiting the guidelines of the Extended Thermodynamics Theory, a hyperbolic extension of the classical modified Klausmeier vegetation model for flat arid environments is here proposed. This framework accounts explicitly for the inertial effects associated with the involved species and allows a more suitable description of transient dynamics between a spatially-homogeneous steady-state towards a patterned configuration. To characterize the emerging Turing patterns, linear stability analysis on the uniform steady-states is firstly addressed. Then, to determine the Stuart–Landau equations ruling the time evolution of the pattern amplitudes close to onset, multiple-scale weakly nonlinear analysis is performed for the two abovementioned geometries. Finally, to validate the analytical predictions as well as to provide more insights into the spatio-temporal evolution of the resulting pattern in both transient and stationary regimes, numerical simulations have been also performed. • Rhombic and hexagonal pattern formation is studied in 2D hyperbolic vegetation models. • The 2D reaction–transport system is deduced via Extended Thermodynamics theory. • Weakly nonlinear analysis is employed to characterize rhombic and hexagonal patterns. • Stuart–Landau equations accounting for hyperbolicity are analytically obtained. • The role played by inertia in the formation of 2D stationary patterns is emphasized. [ABSTRACT FROM AUTHOR]

The present paper considers a new model for the formation of the dynamic error inertial component. It is very effective in the analysis and synthesis of measuring instruments positioned on moving objects and measuring their movement parameters. The block diagram developed within this paper is used as a basis for defining the mathematical model. The block diagram is based on the set-theoretic description of the measuring system, its input and output quantities and the process of dynamic error formation. The model reflects the specific nature of the formation of the dynamic error inertial component. In addition, the model submits to the logical interrelation and sequence of the physical processes that form it. The effectiveness, usefulness and advantages of the model proposed are rooted in the wide range of possibilities it provides in relation to the analysis and synthesis of those measuring instruments, the formulation of algorithms and optimization criteria, as well as the development of new intelligent measuring systems with improved accuracy characteristics in dynamic mode.

We present a comparative study of the onset and propagation dynamics of the fingering phenomenon in uniform porous media with a radial configuration. With the help of the Finite Element Method (FEM)-based 2D simulations and image processing techniques, we investigate finger morphology, growth rate, interfacial length, finger length and the number of fingers which are affected due to inertial forces and convective acceleration in a two-phase porous media flow. We considered a modified Darcy’s law with inertial force coupled with convective acceleration and investigate their impact on interfacial instability with different velocity-viscosity combinations. Interestingly, the consequences of inertial corrections become significant with changes in viscosity at high Reynolds numbers. Due to the intrinsic bifurcation nature of inertial forces in the radial flow geometry, finger morphology is changed mostly at high viscosity ratios. We find that the effects of inertia and convective acceleration are markedly significant at relatively high Reynolds numbers while the interfacial length and the number of fingers—which are important parameters for Enhanced Oil Recovery (EOR)—are most affected by the neglecting of these forces. Moreover, at high Reynolds numbers, the rate of growth of fingering instabilities and the fractal number tend to deviate from that for Darcy’s law.

The Darcy law provides the basic linear equation for single-phase fluid flow in porous media in ideally simplified conditions. The Darcy equation has been shown to be valid in flow processes happening in sufficiently low Reynolds number regimes. At higher Reynolds numbers, inertial effects cause extra hydrodynamic head loss and Darcy's law becomes invalid. The Forchheimer equation is a semi-empirical relationship which accounts for the effect of the inertial effects on apparent permeability reduction. In this research, the apparent permeability reduction due to inertial effects is studied in simple and complex porous structures. For this purpose a Lattice Boltzmann based simulator was developed to model single-phase fluid flow in porous media. The simulator was verified by experimental and analytical solution tests and then was implemented to study high Reynolds number flow processes in three dimensional regular and irregular shaped porous structures. The effects of inertial on the onset and extent of non-Darcy flow in different geometries was studied. It was also shown that the Forchheimer equation does not accurately fit the high Reynolds number flow in simple and complex porous media. It was observed that a quadratic relationship exists between the introduced “scaled permeability” and the mass flow rate in the range of moderate Reynolds numbers. A new empirical correlation was proposed that fits the scaled permeability and mass flow rate relationship results very well. The proposed correlation predicts the scaled permeability change due to inertial effects more accurate than the Forchheimer equation. [ABSTRACT FROM AUTHOR]