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In this paper, we construct and analyze divergence-free finite element methods for the Stokes problem on smooth domains. The discrete spaces are based on the Scott-Vogelius finite element pair of arbitrary polynomial degree greater than 2. By combining the Piola transform with the classical isoparametric framework, and with a judicious choice of degrees of freedom, we prove that the method converges with optimal order in the energy norm. We also show that the discrete velocity error converges with optimal order in the L 2 -norm. Numerical experiments are presented, which support the theoretical results. [ABSTRACT FROM AUTHOR]

This paper deals with an initial-boundary value problem in two-dimensional smoothly bounded domains for the system n t + u · ∇ n = Δ n - ∇ · (n S (n) ∇ v) , x ∈ Ω , t > 0 , v t + u · ∇ v = Δ v - v + w , x ∈ Ω , t > 0 , w t + u · ∇ w = Δ w - w + n , x ∈ Ω , t > 0 , u t + κ (u · ∇) u + ∇ P = Δ u + n ∇ ϕ , x ∈ Ω , t > 0 , ∇ · u = 0 , x ∈ Ω , t > 0 , (∗) which describes the mutual interaction of chemotactically moving microorganisms and their surrounding incompressible fluid, where κ ∈ R , the gravitational potential ϕ ∈ W 2 , ∞ (Ω) , and S (n) satisfies | S (n) | ≤ C S (1 + n) - α for all n ≥ 0 , C S > 0 and α > - 1. Under the boundary conditions (∇ n - n S (n) ∇ v) · ν = ∂ ν v = ∂ ν w = 0 , u = 0 , x ∈ ∂ Ω , t > 0 , it is shown in this paper that suitable regularity assumptions on the initial data entail the following: (i) If α > - 1 and κ = 0 , then the simplified chemotaxis-Stokes system possesses a unique global classical solution which is bounded. (ii) If α ≥ 0 and κ ∈ R , then the full chemotaxis-Navier–Stokes system admits a unique global classical solution. [ABSTRACT FROM AUTHOR]

This paper expands the isoparametric framework to construct a stable, H 1 -conforming, and divergence-free method for the Stokes problem in two dimensions based on the Scott-Vogelius pair on Clough-Tocher splits. The pressure space is defined through composition, whereas the velocity space is constructed via a new divergence-preserving mapping that imposes full continuity across shared edges in the isoparametric mesh. Our construction is motivated by operators and spaces found in isoparametric C 1 finite element methods. We prove the method is stable, pressure-robust, and has optimal order convergence. Numerical experiments are provided which confirm the theoretical results. [ABSTRACT FROM AUTHOR]

The latest geoid model "HELLAS GEOID 2023" (HG2023) derived by the Hellenic Military Geographical Service is the most comprehensive model for the entire Hellenic area. Long-term gravity data, orthometric and geometric heights, seabed topography and a high-resolution digital terrain model were implemented in the calculations. Data evaluation and their accuracy estimation were of major importance to ascertain compatibility among data sources. In this study, data from neighboring countries were used as they were essential for the completeness of the model developed. The technique remove–compute–restore was adopted for the separation of the gravity signal in the heterogeneous data utilizing EIGEN 6C4 (full degree and order 2190), since the global geodynamic model was found to fit best in the Greek region. Mean gravity residual contribution to the local geoid model was calculated using Stokes' theorem in the frequency domain and implementing the Fourier transform using the Wang and Core modification. The final surface of the resulting gravimetric geoid was adapted to the existing height system of the State utilizing the Least Squares Collocation method by fitting points of known orthometric and geometric heights, distributed throughout Greece. The external accuracy of the estimated geoid model was estimated at the level of 6 cm. [ABSTRACT FROM AUTHOR]

In this paper, we aim to determine the effective permeability of biporous solids containing fractures in a computational homogenization framework. Precisely, at the local scale, we use the Brinkman law for the porous solids and the Stokes equations within fractures. The resolution of the Brinkman/Stokes coupled equations is performed with the fast Fourier transform iterative scheme on periodic unit cells. The role of the dimensions and orientation of the cracks is investigated. The simulation results are also compared with an analytical formulation based on Mori–Tanaka estimates. The findings indicate that, depending on the considered flow direction, the dimensions and orientation of cracks strongly affect the effective permeability of fractured porous media. Besides, we also determine the macroscopic permeability for a population of fractures with regular and random orientations, dimensions and shapes. The results are then given and discussed. [ABSTRACT FROM AUTHOR]

In this paper, we consider a viscous droplet migrating in a viscous fluid of a different viscosity. Further, we assume that the surface of the droplet is partially contaminated with a stagnant layer of surfactant (surface active agent which reduces the interfacial tension). We analyze the effects of the following phenomena associated with the thermocapillary migration of a droplet in a transient Stokes flow. The first is the influence of surfactant cap for an arbitrary cap angle which is partially coated on the droplet surface for both high and low surface Péclet number cases. The second is the influence of the energy changes associated with stretching and shrinkage of the interfacial area elements, when the droplet is in motion. It can be noted that for the vanishing cap angle, both high and low surface Péclet number limits reduce to the case of a pure thermocapillary migration of a droplet in a transient Stokes flow. For a given ambient flow, the migration of the droplet is controlled by the magnitude of the ambient velocity and the surface tension variations due to temperature and surfactant concentration. In particular, these surface tension variations balance the tangential stress balance. Considering axisymmetric transient Stokes flow, we obtain analytical solutions in two limiting cases, namely low and high surface Péclet number. This work considers linear variation of interfacial tension on both thermal and surfactant gradients. The main contribution is pertaining to the capillary drift and the corresponding surfactant transport on the droplet for an axisymmetric hydrodynamic as well as thermal and surfactant fields. We have analyzed the level curves corresponding to stream function and temperature fields, i.e., streamlines and isotherms for various parameters in order to develop a realistic picture of the migration pattern and the influence of thermal fields. We observe that the streamlines in the vicinity of rear end of the droplet show asymmetry due to the surfactant accumulation at that region. Increasing cap angle breaks the symmetry of the induced stream. It is seen that increasing values of nondimensional parameter that accounts for the stretching and shrinkage of the droplet surface immobilizes the surface and offers retardation to the migrating droplet. The variation of migration velocity with time suggests a control mechanism for the migration of the drop under external/surface gradients and hence may serve as a useful tool in applications like targeted drug delivery systems. [ABSTRACT FROM AUTHOR]

In this paper, we consider the following system { n t + u ⋅ ∇ n = Δ n − ∇ ⋅ (n S (| ∇ c | 2) ∇ c) − n m , c t + u ⋅ ∇ c = Δ c − c + m , m t + u ⋅ ∇ m = Δ m − m n , u t = Δ u + ∇ P + (n + m) ∇ Φ , ∇ ⋅ u = 0 which models the process of coral fertilization, in a smoothly three-dimensional bounded domain, where S is a given function fulfilling | S (σ) | ≤ K S (1 + σ) − θ 2 , σ ≥ 0 with some K S > 0 . Based on conditional estimates of the quantity c and the gradients thereof, a relatively compressed argument as compared to that proceeding in related precedents shows that if θ > 0 , then for any initial data with proper regularity an associated initial-boundary problem under no-flux/no-flux/no-flux/Dirichlet boundary conditions admits a unique classical solution which is globally bounded, and which also enjoys the stabilization features in the sense that ∥ n (⋅ , t) − n ∞ ∥ L ∞ (Ω) + ∥ c (⋅ , t) − m ∞ ∥ W 1 , ∞ (Ω) + ∥ m (⋅ , t) − m ∞ ∥ W 1 , ∞ (Ω) + ∥ u (⋅ , t) ∥ L ∞ (Ω) → 0 as t → ∞ with n ∞ : = 1 | Ω | { ∫ Ω n 0 − ∫ Ω m 0 } + and m ∞ : = 1 | Ω | { ∫ Ω m 0 − ∫ Ω n 0 } + . [ABSTRACT FROM AUTHOR]

The treatment of exhaust gas from large diesel engines is an important factor to affect environment. Because of its advantages in reaction efficiency and heat transfer efficiency, circulating fluidized bed (CFB) has shown great potential with regard to save energy and purify emissions from large diesel engines. This paper mainly investigated a three-dimensional modeling of the CFB, and a rolling function is applied to simulate its unsteady working conditions, which is called the rolling circulation fluidized bed (RCFB). Two-fluid model based on Euler-Euler approach is utilized to numerically simulate the gas-solid two phases flow within the RCFB. In order to give the comparable results between the present simulation and the previous experiment, the effect of Stokes number on particle phase distribution behaviors in the RCFB is investigated. By simulating the overall swing condition of the RCFB based on a dynamic grid, the effect of the swing condition on particle radial distribution uniformity in the riser is obtained. The reliability of quantitative modeling is verified based on the experimental results of the extant literature. Based on this simulation, the influence of the Stokes number on the radial distribution of particles as well as the relationship between the uniformity of the distribution and particle size is obtained. [ABSTRACT FROM AUTHOR]

To advance our understanding of the movement of elastic microstructures in a viscous fluid, techniques that utilize available data to estimate model parameters are necessary. Here, we describe a Bayesian uncertainty quantification framework that is highly parallelizable, making parameter estimation tractable for complex fluid–structure interaction models. Using noisy in silico data for swimmers, we demonstrate the methodology’s robustness in estimating fluid and elastic swimmer parameters, along with their uncertainties. We identify correlations between model parameters and gain insight into emergent swimming trajectories of a single swimmer or a pair of swimmers. Our proposed framework can handle data with a spatiotemporal resolution representative of experiments, showing that this framework can be used to aid in the development of artificial micro-swimmers for biomedical applications, as well as gain a fundamental understanding of the range of parameters that allow for certain motility patterns. [ABSTRACT FROM AUTHOR]

This paper is concerned with the following attraction–repulsion Stokes system n t + u · ∇ n = Δ n - χ ∇ · (n ∇ c) + ξ ∇ · (n ∇ v) , x ∈ Ω , t > 0 , c t + u · ∇ c = Δ c - n c , x ∈ Ω , t > 0 , v t + u · ∇ v = Δ v - v + n , x ∈ Ω , t > 0 , u t + ∇ P = Δ u + n ∇ ϕ , x ∈ Ω , t > 0 , ∇ · u = 0 , x ∈ Ω , t > 0 , where Ω ⊂ R 2 is a general bounded domain with smooth boundary. It is shown that for any properly regular initial data, the above system with homogeneous Neumann boundary condition admits a unique classical solution which is globally bounded and particularly, if the uniform L ∞ -module of n fulfills ‖ n ‖ L ∞ (Ω × (0 , ∞)) < 2 K Ω m ξ 2 with m : = ∫ Ω n 0 and K Ω > 0 only depending on Ω , then ‖ n (· , t) - n ¯ 0 ‖ L ∞ (Ω) + ‖ c (· , t) ‖ W 1 , ∞ (Ω) + ‖ v (· , t) - n ¯ 0 ‖ W 1 , ∞ (Ω) + ‖ u (· , t) ‖ L ∞ (Ω) → 0 as t → ∞ , where n ¯ 0 : = 1 | Ω | ∫ Ω n 0. [ABSTRACT FROM AUTHOR]

We apply the AUSGeoid data processing and computation methodologies to data provided for the International Height Reference System (IHRS) Colorado experiment as part of the International Association of Geodesy Joint Working Groups 0.1.2 and 2.2.2. This experiment is undertaken to test a range of different geoid computation methods from international research groups with a view to standardising these methods to form a set of conventions that can be established as an IHRS. The IHRS can realise an International Height Reference Frame to be used to study physical changes on and within the Earth. The Colorado experiment study site is much more mountainous (maximum height 4401 m) than the mostly flat Australian continent (maximum height 2228 m), and the available data over Colorado are different from Australian data (e.g. much more extensive airborne gravity coverage). Hence, we have tested and applied several modifications to the AUSGeoid approach, which had been tailored to the Australian situation. This includes different methods for the computation of terrain corrections, the gridding of terrestrial gravity data, the treatment of long-wavelength errors in the gravity anomaly grid and the combination of terrestrial and airborne data. A new method that has not previously been tested is the application of a spherical harmonic high-pass filter to residual anomalies. The results indicate that the AUSGeoid methods can successfully be used to compute a high accuracy geoid in challenging mountainous conditions. Modifications to the AUSGeoid approach lead to root-mean-square differences between geoid models up to ~ 0.028 m and agreement with GNSS-levelling data to ~ 0.044 m, but the benefits of these modifications cannot be rigorously assessed due to the limitation of the GNSS-levelling accuracy over the computation area. [ABSTRACT FROM AUTHOR]

The coupled chemotaxis fluid system n t = ∇ · ((n + 1) m - 1 ∇ n) - ∇ · (n (n + 1) m - α - 1 ∇ c) - u · ∇ n , (x , t) ∈ Ω × (0 , T) , c t = Δ c - c + n - u · ∇ c , (x , t) ∈ Ω × (0 , T) , u t = Δ u + ∇ P + n ∇ ϕ , ∇ · u = 0 , (x , t) ∈ Ω × (0 , T) , ∇ c · ν = ∇ n · ν = 0 , u = 0 , (x , t) ∈ ∂ Ω × (0 , T) , n (x , 0) = n 0 (x) , c (x , 0) = c 0 (x) , u (x , 0) = u 0 (x) x ∈ Ω , is considered in a bounded domain Ω ⊂ R 3 , with smooth boundary, where m , α ∈ R . It is known that in the fluid-free case ( u ≡ 0 ), the system admits a global bounded solution if α > 1 3 . The purpose of this paper is to overcome difficulties arising from the presence of fluid interaction and to show that the same conclusion holds if m > - 1 3 . In the case m ≤ - 1 3 and α > 1 3 , global existence of classical solution will be shown. [ABSTRACT FROM AUTHOR]

We derivate analytic expressions for the effective permeability of a doubly porous medium which contains cylindrical or spherical macropores. The homogenization procedure is based on the consideration of a unit cell with a prescribed macroscopic pressure gradient or macroscopic velocity on its boundary. Within the unit cell, we have to solve the coupled Darcy–Stokes equations with appropriate interface models. The effective permeability of the bi-porous solid is determined by considering the composite cylinder and sphere assemblages. The solutions with prescribed macroscopic pressure gradient and velocity are provided and the influence in the choice of the interface model on the effective permeability of the doubly porous solid is studied. Finally, the results are compared with existing expressions provided in the literature and the estimate for the case of a cylindrical macropore is compared with finite element solutions. [ABSTRACT FROM AUTHOR]

The NURBS-enhanced finite element method (NEFEM) combined with a hybridisable discontinuous Galerkin (HDG) approach is presented for the first time. The proposed technique completely eliminates the uncertainty induced by a polynomial approximation of curved boundaries that is common within an isoparametric approach and, compared to other DG methods, provides a significant reduction in number of degrees of freedom. In addition, by exploiting the ability of HDG to compute a postprocessed solution and by using a local a priori error estimate valid for elliptic problems, an inexpensive, reliable and computable error estimator is devised. The proposed methodology is used to solve Stokes flow problems using automatic degree adaptation. Particular attention is paid to the importance of an accurate boundary representation when changing the degree of approximation in curved elements. Several strategies are compared and the superiority and reliability of HDG-NEFEM with degree adaptation is illustrated. [ABSTRACT FROM AUTHOR]

A class of Keller-Segel-Stokes systems generalizing the prototype nt+u·∇n=Δn-∇·n(n+1)-α∇c,ct+u·∇c=Δc-c+n,ut+∇P=Δu+n∇ϕ+f(x,t),∇·u=0,(⋆)is considered in a bounded domain Ω⊂R3, where ϕ and f are given sufficiently smooth functions such that f is bounded in Ω×(0,∞). It is shown that under the condition that α>13,for all sufficiently regular initial data a corresponding Neumann-Neumann-Dirichlet initial-boundary value problem possesses a global bounded classical solution. This extends previous findings asserting a similar conclusion only under the stronger assumption α>12. In view of known results on the existence of exploding solutions when α<13, this indicates that with regard to the occurrence of blow-up the criticality of the decay rate 13, as previously found for the fluid-free counterpart of (⋆), remains essentially unaffected by fluid interaction of the type considered here. [ABSTRACT FROM AUTHOR]

This paper introduces a low-order discontinuous Petrov-Galerkin (dPG) finite element method (FEM) for the Stokes equations. The ultra-weak formulation utilizes piecewise constant and affine ansatz functions and piecewise affine and discontinuous lowest-order Raviart-Thomas test search functions. This low-order discretization for the Stokes equations allows for a direct proof of the discrete inf-sup condition with explicit constants. The general framework of Carstensen et al. (SIAM J Numer Anal 52(3):1335-1353, 2014) then implies a complete a priori and a posteriori error analysis of the dPG FEM in the natural norms. Numerical experiments investigate the performance of the method and underline its quasi-optimal convergence. [ABSTRACT FROM AUTHOR]

In a bounded domain Ω⊂R2, we consider the the chemotaxis-Stokes system nt+u·∇n=Δn-∇·(nS(x,n,c)·∇c),x∈Ω,t>0,ct+u·∇c=Δc-nf(c),x∈Ω,t>0,ut=Δu+∇P+n∇ϕ,∇·u=0,x∈Ω,t>0,(⋆)which arises as a model for populations of aerobic bacteria swimming in a sessile water drop. In accordance with refined modeling approaches, we do not necessarily assume the chemotactic sensitivity S herein to be a scalar function, but rather allow S to attain values in R2×2. As compared to the well-studied case of scalar-valued sensitivities in which an analysis can be based on favorable energy-type inequalities, this modification brings about significant new challenges which require to adequately cope with only little a priori information on regularity of solutions of (⋆). The present work creates a functional setup which despite this allows for the construction of certain global mass-preserving generalized solutions to an associated initial-boundary value problem in planar convex domains with smooth boundary, provided that the initial data and the parameter functions S, f and ϕ are sufficiently smooth, and that S is bounded and f is nonnegative with f(0)=0. [ABSTRACT FROM AUTHOR]

Fundamental solutions to the time-periodic Stokes and Oseen linearizations of the Navier-Stokes equations in dimension n≥2 are investigated. Integrability properties and pointwise estimates are established. [ABSTRACT FROM AUTHOR]

Geoid and quasigeoid modelling from gravity anomalies by the method of least squares modification of Stokes’s formula with additive corrections is adapted for the usage with gravity disturbances and Hotine’s formula. The biased, unbiased and optimum versions of least squares modification are considered. Equations are presented for the four additive corrections that account for the combined (direct plus indirect) effect of downward continuation (DWC), topographic, atmospheric and ellipsoidal corrections in geoid or quasigeoid modelling. The geoid or quasigeoid modelling scheme by the least squares modified Hotine formula is numerically verified, analysed and compared to the Stokes counterpart in a heterogeneous study area. The resulting geoid models and the additive corrections computed both for use with Stokes’s or Hotine’s formula differ most in high topography areas. Over the study area (reaching almost 2 km in altitude), the approximate geoid models (before the additive corrections) differ by 7 mm on average with a 3 mm standard deviation (SD) and a maximum of 1.3 cm. The additive corrections, out of which only the DWC correction has a numerically significant difference, improve the agreement between respective geoid or quasigeoid models to an average difference of 5 mm with a 1 mm SD and a maximum of 8 mm. [ABSTRACT FROM AUTHOR]

This paper deals with the following chemotaxis-Stokes system under no-flux boundary conditions in a bounded domain $$\Omega \subset \mathbb {R}^{3}$$ with smooth boundary, where $$m\ge 1$$ , $$\phi \in W^{1,\infty }(\Omega )$$ , f and S are given functions with values in $$[0,\,\infty )$$ and $$\mathbb {R}^{3\times 3}$$ , respectively. Here S satisfies $$|S(x,n,c)|\frac{7}{6}$$ , which insures the global existence of bounded weak solution. Our result covers completely and improves the recent result by Wang and Cao (Discrete Contin Dyn Syst Ser B 20:3235-3254, 2015) which asserts, just in the case $$m=1$$ , the global existence of solutions, but without boundedness, and that by Winkler (Calc Var Partial Differ Equ 54:3789-3828, 2015) which only involves the case of $$\alpha =0$$ and requires the convexity of the domain. [ABSTRACT FROM AUTHOR]

A variational approach is used to recover fluid motion governed by Stokes and Navier-Stokes equations. Unlike previous approaches where optical flow method is used to track rigid body motion, this new framework aims at investigating incompressible flows using optical flow techniques. We formulate a minimization problem and determine conditions under which unique solution exists. Numerical results using finite element method not only support theoretical results but also show that Stokes flow forced by a potential are recovered almost exactly. [ABSTRACT FROM AUTHOR]

This paper considers the following chemotaxis-Stokes system: in two-dimensional smoothly bounded domains, which can be seen as a model to describe the migration of aerobic bacteria swimming in an incompressible fluid. It is proved that the corresponding initial-boundary value problem possesses a global generalized solution for any sufficiently regular initial data $(n_{0}, c_{0}, u_{0})$ satisfying $n_{0}\geq0$ and $c_{0}>0$ . Moreover, the solution component c satisfies $c(\cdot,t)\overset{\star}{\rightharpoonup}0$ in $L^{\infty}(\Omega )$ as $t\rightarrow\infty$ and $c(\cdot,t)\rightarrow0$ in $L^{p}(\Omega)$ as $t\rightarrow\infty$ for any $p\in[1,\infty)$ . To the best of our knowledge, this is the first result on global solvability in a chemotaxis-Stokes system with singular sensitivity and signal absorption. [ABSTRACT FROM AUTHOR]

Conforming piecewise polynomial spaces with respect to cubic meshes are constructed for the Stokes problem in arbitrary dimensions yielding exactly divergence-free velocity approximations. The derivation of the finite element pair is motivated by a smooth de Rham complex that is well-suited for the Stokes problem. We derive the stability and convergence properties of the new elements as well as the construction of reduced elements with less global unknowns. [ABSTRACT FROM AUTHOR]

Topology optimization methods application for viscous flow problems is currently an active area of research. A general approach to deal with shape and topology optimization design is based on the topological derivative. This relatively new concept represents the first term of the asymptotic expansion of a given shape functional with respect to the small parameter which measures the size of singular domain perturbations, such as holes and inclusions. In previous topological derivative-based formulations for viscous fluid flow problems, the topology is obtained by nucleating and removing holes in the fluid domain which creates numerical difficulties to deal with the boundary conditions for these holes. Thus, we propose a topological derivative formulation for fluid flow channel design based on the concept of traditional topology optimization formulations in which solid or fluid material is distributed at each point of the domain to optimize the cost function subjected to some constraints. By using this idea, the problem of dealing with the hole boundary conditions during the optimization process is solved because the asymptotic expansion is performed with respect to the nucleation of inclusions - which mimic solid or fluid phases - instead of inserting or removing holes in the fluid domain, which allows for working in a fixed computational domain. To evaluate the formulation, an optimization problem which consists in minimizing the energy dissipation in fluid flow channels is implemented. Results from considering Stokes and Navier-Stokes are presented and compared, as well as two- (2D) and three-dimensional (3D) designs. The topologies can be obtained in a few iterations with well defined boundaries. [ABSTRACT FROM AUTHOR]

We propose a new dimension-wise splitting with selective relaxation (DSSR) method for saddle point systems arising from the discretization of the incompressible Navier-Stokes equations. Using Fourier analysis, we determine the optimal choice of the relaxation parameter that leads to the best performance of the iterative method for the Stokes and the steady Oseen equations. We also explore numerically the influence of boundary conditions on the optimal choice of the parameter, the use of inner and outer iterations, and the performance for a lid driven cavity flow. [ABSTRACT FROM AUTHOR]

The coupled chemotaxis-fluid system is considered under no-flux boundary conditions for n and c and no-slip boundary conditions for u in three-dimensional bounded domains with smooth boundary, where $${r\geq 0}$$ and $${\mu > 0}$$ are given constants and $${\phi\in W^{1, \infty}(\Omega)}$$ and $${g\in C^1(\bar\Omega\times [0, \infty)) \cap L^\infty(\Omega\times (0,\infty))}$$ are prescribed parameter functions. It is shown that under the explicit condition $${\mu\geq 23}$$ and suitable regularity assumptions on the initial data, the corresponding initial-boundary problem possesses a global classical solution which is bounded. Apart from this, it is proved that if r = 0, then both n(·, t) and c(·, t) decay to zero with respect to the norm in $${L^\infty(\Omega)}$$ as $${t\to \infty}$$ , and that if, moreover, $${\int_0^\infty \int_\Omega |g|^2 < \infty}$$ , then also u(·, t)→ 0 in $${L^\infty(\Omega)}$$ as $${t\to \infty}$$ . [ABSTRACT FROM AUTHOR]

Removal of microcrystalline cellulose agglomerates in a dry-mixing system (lactose, 100 M) predominantly occurs via abrasion. The agglomerate abrasion rate potential is estimated by the Stokes abrasion (St) number of the system. The St number equals the ratio between the kinetic energy density of the moving powder bed and the work of fracture of the agglomerate. Basically, the St number concept describes the blending condition of the dry-mixing system. The concept has been applied to investigate the relevance of process parameters on agglomerate abrasion in tumbling blenders. Here, process parameters such as blender rotational speed and relative fill volumes were investigated. In this study, the St approach revealed a transition point between abrasion rate behaviors. Below this transition point, a blending condition exists where agglomerate abrasion is dominated by the kinetic energy density of the powder blend. Above this transition point, a blending condition exists where agglomerates show (undesirable) slow abrasion rates. In this situation, the blending condition is mainly determined by the high fill volume of the filler. [ABSTRACT FROM AUTHOR]

In this paper we establish corrector estimates for Stokes flow in slowly varying perforated media via two scale asymptotic analysis. Current methods and techniques are often not able to deal with changing geometries prevalent in applied problems. For example, in a deformable porous medium environment, the geometry does not remain periodic under mechanical deformation and if slow variation in the geometry occurs. For such problems, one cannot use classical homogenization results directly and new homogenization results and estimates are needed. Our work uses asymptotic techniques of Marusic-Paloka and Mikelic (Bollettino U.M.I 7:661-671, ) where the authors constructed a downscaled velocity which converges to the fine-scale velocity at a rate of ε where ε is the characteristic length scale. We assume a slowly varying porous medium and study homogenization and corrector estimates for the Stokes equations. Slowly varying media arise, e.g., in fluid-structure interaction (FSI) problems (Popov et al. in Iterative upscaling of flows in deformable porous media, ), carbonation of porous concrete (Peter in C. R. Mecanique 335:357-362, ; C. R. Mecanique 335:679-684, ), and various other multiphysics processes. To homogenize Stokes flows in such media we restate the cell problems of Marusic-Paloka and Mikelic (Bollettino U.M.I 7:661-671, ) in a moving RVE framework. Further, to recover the same convergence properties it is necessary to solve an additional cell problem and add one more corrector term to the downscaled velocity. We further extend the framework of Marusic-Paloka and Mikelic (Bollettino U.M.I 7:661-671, ) to three spatial dimensions in both periodic and variable pore-space cases. Next, we also propose an efficient algorithm for computing the correctors by solving a limited number of cell problems at selected spatial locations. We present two computational examples: one for a constructed medium of elliptical perforations, and another for a fractured medium with FSI driven deformation. We obtain numerical estimates that confirm the theory in these two examples. [ABSTRACT FROM AUTHOR]

It is shown that the conforming Q- Q′ mixed element is stable, and provides optimal order of approximation for the Stokes equations on rectangular grids. Here, Q = Q × Q, and Q denotes the space of continuous piecewise-polynomials of degree 2 or less in the x direction but of degree 1 in the y direction. Q′ is the space of discontinuous bilinear polynomials, with spurious modes filtered. To be precise, Q′ is the divergence of the discrete velocity space Q. Therefore, the resulting finite element solution for the velocity is divergence-free pointwise, when solving the Stokes equations. This element is the lowest order one in a family of divergence-free element, similar to the families of the Bernardi-Raugel element and the Raviart-Thomas element. [ABSTRACT FROM AUTHOR]

The effect of an electric field on a liquid film flowing down an inclined wall is examined. The liquid film is treated as a perfect conductor and the air above the film is treated as a perfect dielectric. The electric field is created by a single or periodically repeated electrode of arbitrary shape charged to establish a prescribed potential difference between itself and the liquid-film surface. The steady deformation of the free surface in the presence of the electric field is computed first on the assumption of a thin film and next within the Stokes-flow regime. Calculations are performed for flow over a plane wall and over a step of asymptotically small height. In the latter case, the focused electric field obtained by positioning a circular electrode directly above the step is found to eliminate the capillary ridge identified by previous authors without significantly disrupting the flow away from the step. This result is confirmed numerically for Stokes flow over a step of arbitrary height using the boundary-element method. [ABSTRACT FROM AUTHOR]

We study the dynamics and interaction of two swimming bacteria, modeled by self-propelled dumbbell-type structures. We focus on alignment dynamics of a coplanar pair of elongated swimmers, which propel themselves either by "pushing" or "pulling" both in three- and quasi-two-dimensional geometries of space. We derive asymptotic expressions for the dynamics of the pair, which complemented by numerical experiments, indicate that the tendency of bacteria to swim in or swim off depends strongly on the position of the propulsion force. In particular, we observe that positioning of the effective propulsion force inside the dumbbell results in qualitative agreement with the dynamics observed in experiments, such as mutual alignment of converging bacteria. [ABSTRACT FROM AUTHOR]

The lipid bilayer is the diffusion barrier of biological membranes. Highly protective membranes such as the blood–brain barrier (BBB) are reinforced by ABC transporters such as P-glycoprotein (MDR1, ABCB1) and multidrug resistance associated proteins (MRPs, ABCCs). The transporters bind their substrates in the cytosolic lipid bilayer leaflet before they reach the cytosol and flip them to the outer leaflet. The large majority of drugs targeted to the central nervous system (CNS) are intrinsic substrates of these transporters. Whether an intrinsic substrate can cross the BBB depends on whether passive influx is higher than active efflux. In this paper, we show that passive influx can be estimated quantitatively on the basis of Stokesian diffusion, taking into account the ionization constant and the cross-sectional area of the molecule in its membrane bond conformation, as well as the lateral packing density of the membrane. Active efflux by ABC transporters was measured. The calculated net flux is in excellent agreement with experimental results. The approach is exemplified with several drugs and fatty acid analogs. It shows that compounds with small cross-sectional areas ( A D < 70 Å2) and/or intermediate or low charge exhibit higher passive influx than efflux and, therefore, cross the BBB despite being intrinsic substrates. Large ( A D > 70 Å2) or highly charged compounds show higher efflux than influx. They cannot cross the BBB and are, thus, apparent substrates for ABC transporters. The strict size and charge limitation for BBB permeation results from the synergistic interaction between passive influx and active efflux. [ABSTRACT FROM AUTHOR]

Raman lasers based on potassium gadolinium tungstate and lead tungstate crystals pumped by a≈120 ps Nd: YAG laser at 1.064 μm were developed. High reflection mirrors for the Stokes wavelength have been used to generate near-infrared and eye safe spectral region of 1.15–1.32 μm. Second harmonic generation of the generated Raman lasers was observed. Eifficient multiple Stokes and anti-Stokes picosecond generation in 64 crystals have been shown to exhibit stimulated Raman scattering on about 700 lines covering the whole visible and near-infrared spectrum. All stimulated Raman scattering (SRS) wavelengths in the visible and near-infrared spectrum are identified and attributed to the SRS-active vibration modes of these crystals. [ABSTRACT FROM AUTHOR]

Topography plays an important role in solving many geodetic and geophysical problems. In the evaluation of a topographical effect, a planar model, a spherical model or an even more sophisticated model can be used. In most applications, the planar model is considered appropriate: recall the evaluation of gravity reductions of the free-air, Poincaré–Prey or Bouguer kind. For some applications, such as the evaluation of topographical effects in gravimetric geoid computations, it is preferable or even necessary to use at least the spherical model of topography. In modelling the topographical effect, the bulk of the effect comes from the Bouguer plate, in the case of the planar model, or from the Bouguer shell, in the case of the spherical model. The difference between the effects of the Bouguer plate and the Bouguer shell is studied, while the effect of the rest of topography, the terrain, is discussed elsewhere. It is argued that the classical Bouguer plate gravity reduction should be considered as a mathematical construction with unclear physical meaning. It is shown that if the reduction is understood to be reducing observed gravity onto the geoid through the Bouguer plate/shell then both models give practically identical answers, as associated with Poincaré's and Prey's work. It is shown why only the spherical model should be used in the evaluation of topographical effects in the Stokes–Helmert solution of Stokes' boundary-value problem. The reason for this is that the Bouguer plate model does not allow for a physically acceptable condensation scheme for the topography. [ABSTRACT FROM AUTHOR]

The time-dependent Navier—Stokes problem on an interior or exterior smooth domain, with nonhomogeneous Dirichlet boundary condition, is treated in anisotropic L p Sobolev spaces (1 < p < $ \infty $ ) of Bessel-potential type $ H^{s+2,s/2+1}_p $ or Besov type $ B^{s+2,s/2+1}_p $ by use of a reformulation of the linearized problem to a parabolic pseudodifferential boundary value problem. Earlier studies required $ s > {\frac 1p} - 1 $ ; the present work extends the solvability to spaces with $ s > {\frac 1p} - 2 $ for zero initial data ( $ s > - 2 $ if f = 0), $ s > {\frac 2p} - 2 $ for nonzero initial data, with s,p subject to other conditions stemming from the nonlinearity. [ABSTRACT FROM AUTHOR]

The cylindrically shaped cochlear outer hair cell (OHC) plays an important role in the transduction of acoustic energy into electrical energy in the cochlea. The extracisternal space (ECiS) of the lateral wall of the OHC is the fluid-filled space between the plasma membrane (PM) and the intracellular subsurface cisterna (SSC). In the ECiS, an array of cylindrical micropillars extends from the SSC to the PM. We obtain equations for the pressure, osmotic concentration and fluid velocity in the ECiS from the Brinkman-Stokes equations for steady incompressible flow in a plane channel that encloses an array of cylinders and whose upper wall, i.e. the plasma membrane, has a hydraulic conductivity of P PM. From these equations we obtain an estimate for the hydraulic conductivity of the ECiS, P ECiS. We show that the ECiS geometry accounts for P ECiS being several orders of magnitude larger than P PM and that P ECiS increases with the width of the ECiS and decreases with the length of the ECiS. [ABSTRACT FROM AUTHOR]

This paper describes an implementation of an adaptive finite element program for coupled fluid-structure problems using a network of workstations. A pool of task programming paradigm suitable for a heterogeneous distributed workstation environment is presented. The issues of load balancing and fault recovery are explored. Numerical results for this distributed programming paradigm are presented and compared with sequential and parallel programming models. [ABSTRACT FROM AUTHOR]

We prove that in general it is not possible to associate a pressure field to the velocity field of a weak solution of the Navier—Stokes equations, if the body force has values in the space V'. [ABSTRACT FROM AUTHOR]

This work introduces some uncoupling techniques for solving the three-dimensional incompressible Navier-Stokes equations in the vorticity-velocity representation. Without any loss of essential aspects, the analysis is conducted for the case of the underlying Stokes system. For some of these uncoupled formulations, only scalar problems defined on the boundary of the flow domain need to be solved, in order to determine the key field in the methodology, that is, a suitable harmonic component of the vorticity. [ABSTRACT FROM AUTHOR]

Using a commercial Fourier transform infrared spectrometer and the 1.064 μm line of a CW Nd∶YAG laser, we have measured the Raman spectra of a wide variety of materials. The Raman scattered light, Stokes shifted toward the mid-infrared, is collected, using a 90° lens geometry, and focused through the emission port of the spectrometer. After passing through the Michelson interferometer, the light is detected by a thermoelectrically-cooled high-sensitivity germanium detector. The Fourier transform of the resulting interferogram gives the Raman spectrum. This new technique allows spectra to be obtained of samples which were previously completely masked by competing fluorescence. In addition, FT-Raman also allows moieties, such as hydrocarbon chains, which are not present in resonance enhanced spectra, to be investigated. We will discuss our approach toward FT-Raman, which is compatible with traditional Raman spectroscopy, present representative spectra of liquids and solids, and draw some comparisons and contrasts between dispersive and FT measurements. [ABSTRACT FROM AUTHOR]