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A solenoidal basis is constructed to compute velocities using a certain finite element method for the Stokes problem. The method is conforming, with piecewise linear velocity and piecewise constant pressure on the Powell-Sabin split of a triangulation. Inhomogeneous Dirichlet conditions are supported by constructing an interpolating operator into the solenoidal velocity space. The solenoidal basis reduces the problem size and eliminates the pressure variable from the linear system for the velocity. A basis of the pressure space is also constructed that can be used to compute the pressure after the velocity, if it is desired to compute the pressure. All basis functions have local support and lead to sparse linear systems. The basis construction is confirmed through rigorous analysis. Velocity and pressure system matrices are both symmetric, positive definite, which can be exploited to solve their corresponding linear systems. Significant efficiency gains over the usual saddle-point formulation are demonstrated computationally. [ABSTRACT FROM AUTHOR]

A spectropolarimeter based on spatial heterodyne spectroscopy and the channeled polarimetric technique (SSHSCP) is introduced. The SSHSCP uses a polarization grating for channel modulation, meaning that the Stokes parameter is no longer dependent on the wavenumber; this suppresses channel aliasing considerably and improves the polarization parameter reconstruction accuracy. The SSHSCP’s optical path structure is based on the Mach–Zehnder interferometer, ensuring efficient energy use. The spectral detection and polarization detection principles of the SSHSCP are derived, and a specific design example is presented. Simulations indicate that the SSHSCP can restore the target’s spectral and complete Stokes parameters with high accuracy for a broadband source and narrowband lines. The reconstructed Stokes parameter errors are of the order of 10−3 or less. The SSHSCP acquires spectral and polarization parameters in a single step and has no moving parts in a compact structure.

This paper considers the 2-species chemotaxis-Stokes system with competitive kinetics { (n 1) t + u ⋅ ∇ n 1 = Δ n 1 − χ ∇ ⋅ (n 1 ∇ w) + n 1 (λ 1 − μ 1 n 1 + a n 2) , x ∈ Ω , t > 0 , (n 2) t + u ⋅ ∇ n 2 = Δ n 2 + ξ ∇ ⋅ (n 2 ∇ z) + n 2 (λ 2 − μ 2 n 2 − b n 1) , x ∈ Ω , t > 0 , w t + u ⋅ ∇ w = Δ w − w + n 2 , x ∈ Ω , t > 0 , u ⋅ ∇ z = Δ z − z + n 1 , x ∈ Ω , t > 0 , u t + ∇ P = Δ u + (n 1 + n 2) ∇ ϕ , x ∈ Ω , t > 0 , ∇ ⋅ u = 0 , x ∈ Ω , t > 0 under no-flux boundary conditions for n 1 , n 2 , w and z in three-dimensional bounded domains and no-slip boundary conditions for u , this is ∂ n 1 ∂ ν = ∂ n 2 ∂ ν = ∂ w ∂ ν = ∂ z ∂ ν = 0 , u = 0 , x ∈ ∂ Ω , t > 0 , where χ > 0 , ξ > 0 , μ 1 ≥ 0 , μ 2 ≥ 0 , λ 1 ≥ 0 , λ 2 ≥ 0 , a ≥ 0 , b ≥ 0 and ϕ ∈ W 2 , ∞ (Ω). This system is a coupled system of the chemotaxis equations and viscous incompressible fluid equations. Under appropriate assumptions, this problem exhibits a global classical bounded solution. [ABSTRACT FROM AUTHOR]

We derive an ultraweak variational formulation of the quad-curl problem in two and three dimensions. We present a discontinuous Petrov–Galerkin (DPG) method for its approximation and prove its quasi-optimal convergence. We illustrate how this method can be applied to the Stokes problem in two dimensions, after an application of the curl operator to eliminate the pressure variable. In this way, DPG techniques known from Kirchhoff–Love plates can be used. We present an a priori error estimate that improves a previous approximation result for effective shear forces by using a less restrictive regularity assumption. Numerical experiments illustrate our findings. [ABSTRACT FROM AUTHOR]

This paper uses the principles of polarisation to calculate the Stokes component of the polarisation image. It designs the spatial weighted fusion algorithm, focusing on the research and evaluation of the accuracy and time complexity of the spatial weighted fusion algorithm in the polarisation image fusion processing. The spatial weighted image fusion algorithm is used to fuse the polarisation degree image, the polarisation angle image, and the light intensity image. Finally, the algorithm function is realised through software programming to verify the effect and accuracy of the algorithm. Experimental results show that the spatial weighted fusion algorithm can keep the pixel value of the polarisation source image unchanged, avoid image distortion, artefacts and ringing effects algorithm is stable and efficient, with low time complexity. [ABSTRACT FROM AUTHOR]

This work investigates the creeping flow problem via a swarm of porous circular cylindrical particles using the cell model technique. Brinkman equation inside the porous cylindrical region is used, and Stokes equation for the clear fluid would be satisfied. The stress-jump condition, together with the continuity of the velocity components and the continuity of normal stress, are employed at the porous-liquid interfaces. In contrast, no-couple stress condition and no-spin condition are used on the outer boundary of the cell. In addition, we are applying no-slip boundary conditions on the surface of the solid core. Our problem is solved analytically, and stream function expressions are derived for the inside and outside flow fields. The influence of the drag force on each porous cylindrical particle in the cell is calculated. The graph depicts the variation of hydrodynamic permeability with various parameters and especially the impact of the jump coefficient. The results of this model may be used to examine the membrane filtration process.

The Hadamard–Rybczynski equation describes the steady‐state buoyant rise velocity of an unconfined spherical bubble in a viscous liquid. This solution has been experimentally validated for the case where the liquid viscosity is held constant. Here, we extend this result for non‐isothermal conditions, by developing a solution for bubble position in which we account for the time‐dependent liquid viscosity, liquid and gas densities, and bubble radius. We validate this solution using experiments in which spherical bubbles are created in a molten silicate liquid by cutting gas cavities into glass sheets, which are stacked, then heated through the glass transition interval. The bubble‐bearing liquid, which has a strongly temperature‐dependent viscosity, is subjected to various heating and cooling programs such that the bubble rise velocity varies through the experiment. We find that our predictions match the final observed position of the bubble measured in blocks of cooled glass to within the experimental uncertainty, even after the application of a complex temperature–time pathway. We explore applications of this solution for industrial, artistic, and natural volcanological applied problems. [ABSTRACT FROM AUTHOR]

We present a new enriched Galerkin (EG) scheme for the Stokes equations based on piecewise linear elements for the velocity unknowns and piecewise constant elements for the pressure. The proposed EG method augments the conforming piecewise linear space for velocity by adding an additional degree of freedom which corresponds to one discontinuous linear basis function per element. Thus, the total number of degrees of freedom is significantly reduced in comparison with standard conforming, non-conforming, and discontinuous Galerkin schemes for the Stokes equation. We show the well-posedness of the new EG approach and prove that the scheme converges optimally. For the solution of the resulting large-scale indefinite linear systems we propose robust block preconditioners, yielding scalable results independent of the discretization and physical parameters. Numerical results confirm the convergence rates of the discretization and also the robustness of the linear solvers for a variety of test problems. [ABSTRACT FROM AUTHOR]

The relaxation of a rigid particle suspended in a one-dimensional oscillating flow is calculated according to different drag models and the results are compared. Conditions are derived under which relaxation can be neglected or drag models can be substituted by simpler ones. This investigation is conducted analytically and graphically via the plane defined by the Reynolds number and amplitude parameter. This work matches various, mostly analytic drag models together to consider simple particle relaxation with a few, broad range input parameters and cover large parts of the plane spanned by Reynolds number and amplitude parameter. [ABSTRACT FROM AUTHOR]

We discuss how slip conditions for the Stokes equation can be handled using Nitsche method, for a stabilized finite element discretization. Emphasis is made on the interplay between stabilization and Nitsche terms. Well-posedness of the discrete problem and optimal convergence rates, in natural norm for the velocity and the pressure, are established, and illustrated with various numerical experiments. The proposed method fits naturally in the context of a finite element implementation while being accurate, and allows an increased flexibility in the choice of the finite element pairs. [ABSTRACT FROM AUTHOR]

A spectropolarimeter based on spatial heterodyne spectroscopy and the channeled polarimetric technique (SSHSCP) is introduced. The SSHSCP uses a polarization grating for channel modulation, meaning that the Stokes parameter is no longer dependent on the wavenumber; this suppresses channel aliasing considerably and improves the polarization parameter reconstruction accuracy. The SSHSCP's optical path structure is based on the Mach–Zehnder interferometer, ensuring efficient energy use. The spectral detection and polarization detection principles of the SSHSCP are derived, and a specific design example is presented. Simulations indicate that the SSHSCP can restore the target's spectral and complete Stokes parameters with high accuracy for a broadband source and narrowband lines. The reconstructed Stokes parameter errors are of the order of 10−3 or less. The SSHSCP acquires spectral and polarization parameters in a single step and has no moving parts in a compact structure. [ABSTRACT FROM AUTHOR]

The Keller-Segel-Stokes system

The Arnold-Winther element successfully discretizes the Hellinger-Reissner variational formulation of linear elasticity; its development was one of the key early breakthroughs of the finite element exterior calculus. Despite its great utility, it is not available in standard finite element software, because its degrees of freedom are not preserved under the standard Piola push-forward. In this work we apply the novel transformation theory recently developed by Kirby [SMAI J. Comput. Math., 4:197-224, 2018] to devise the correct map for transforming the basis on a reference cell to a generic physical triangle. This enables the use of the Arnold-Winther elements, both conforming and nonconforming, in the widely-used Firedrake finite element software, composing with its advanced symbolic code generation and geometric multigrid functionality. Similar results also enable the correct transformation of the Mardal-Tai-Winther element for incompressible fluid flow. We present numerical results for both elements, verifying the correctness of our theory. [ABSTRACT FROM AUTHOR]

In this paper we introduce and analyze, up to our knowledge for the first time, Banach spaces-based mixed variational formulations for nearly incompressible linear elasticity and Stokes models. Our interest in this subject is motivated by the respective need that arises from the solvability studies of nonlinear coupled problems in continuum mechanics that involve these equations. We consider pseudostress-based approaches in both cases and apply a suitable integration by parts formula for ad-hoc Sobolev spaces to derive the corresponding continuous schemes. We utilize known and new preliminary results, along with the Babuška-Brezzi theory in Banach spaces, to establish the well-posedness of the formulations for a particular range of the indexes of the Lebesgue spaces involved. Among the aforementioned new results from us, we highlight the construction of a particular operator mapping a tensor Lebesgue space into itself, and the generalization of a classical estimate in L 2 for deviatoric tensors, which plays a key role in the Hilbertian analysis of linear elasticity, to arbitrary Lebesgue spaces. No discrete analysis is performed in this work. [ABSTRACT FROM AUTHOR]

Most numerical approaches for coupling fluid flow with porous media flow rely either on Stokes equations in the fluid part of the domain and Darcy's law in the porous part, or on Brinkman's equation. In both cases, difficulties arise at the boundary between the two parts because the equations used in the porous part are not of Stokes type. In this paper, an alternative to Darcy's law is proposed for modeling flows in porous media. This alternative relies on equations of Stokes type where the permeability tensor is replaced by force and stress derivative tensors. Numerical procedures are presented to compute these tensors from simulations at pore scale. Simulations in domains containing both fluid and porous parts are finally conducted simply assuming continuity of velocity and pressure and hence without imposing any condition at the boundary between the two parts. Results show that the proposed method is accurate and hence a promising alternative to Darcy's law for problems involving both fluid and porous parts. • Alternative to Darcy's law relying on equations of Stokes type for modeling flows in porous media. • Permeability tensor replaced by force and stress derivatives tensors computed from simulations at pore scale. • Flows in domains containing both fluid and porous parts modeled without any boundary conditions between the two parts. [ABSTRACT FROM AUTHOR]

We present a general finite volume method to solve a coupled Stokes-Darcy problem, we propose two domains corresponding to fluid region and porous region with a physical intersection. At the contact interface between the fluid region and the porous media we impose two conditions; the first one is the normal continuity of the velocity and the second one is the continuity of the pressure. Furthermore, due to the lack of information about both the velocity and the pressure on the interface, we will use Schwarz domain decomposition. In Darcy equations, the tensor of permeability will be considered as variable, since it depends on both the properties of the porous medium and the viscosity of the fluid. Numerical examples are presented to demonstrate the efficiency of the proposed method.

This manuscript is concerned with the Keller-Segel-Stokes system (⋆) { n t + u ⋅ ∇ n = Δ n − ∇ ⋅ (n F (| ∇ c | 2) ∇ c) , c t + u ⋅ ∇ c = Δ c − c + n , u t = Δ u + ∇ P + n ∇ Φ , ∇ ⋅ u = 0 , under no-flux/no-flux/Dirichlet boundary conditions in smoothly bounded three-dimensional domains, with given suitably regular functions F and Φ. Here in accordance with recent developments in the literature on refined modeling of chemotactic migration, the introduction of suitably decaying F is supposed to adequately account for saturation mechanisms that limit cross-diffusive fluxes near regions of large signal gradients. In the context of such nonlinearities which suitably generalize the prototype given by F (ξ) = K F (1 + ξ) − α 2 , ξ ≥ 0 , with K F > 0 , known results addressing a fluid-free parabolic-elliptic simplification of (⋆) have identified the value α c = 1 2 as critical with regard to the occurrence of blow-up in the sense that some exploding solutions can be found when α < 1 2 , whereas all suitably regular initial data give rise to global bounded solutions when α > 1 2. The intention of the present study consists in making sure that the latter feature of blow-up prevention by suitably strong flux limitation persists also in the more complex framework of the fully coupled chemotaxis-fluid system (⋆). To achieve this, as a secondary objective of possibly independent interest the manuscript separately establishes some conditional bounds for corresponding fluid fields and taxis gradients in a fairly general setting that particularly includes the subsystem of (⋆) concerned with the evolution of (c , u , P). These estimates relate respective regularity features to certain integrability properties of associated forcing terms, as in the context of (⋆) essentially represented by the quantity n. The application of this tool to the specific problem under consideration thereafter facilitates the derivation of a result on global existence of bounded classical solutions to (⋆) for widely arbitrary initial data actually within the entire range α > 1 2 , and by means of an argument which appears to be significantly condensed when compared to reasonings pursued in previous works concerned with related problems. [ABSTRACT FROM AUTHOR]

The Keller-Segel-Stokes system { nt + u ⋅ ∇n = Δn − ∇ ⋅ (n∇c) + ρn − μnα, ct + u ⋅ ∇c = Δc − c + n, ut = Δu + ∇P − n∇Λ , ∇ ⋅ u = 0 (*), is considered in a bounded domain Ω ⊂ ℝ3 with smooth boundary, with parameters ρ ≥ 0, μ > 0 and α > 1, and with a given gravitational potential Λ ∈ W2,∞(Ω). It is shown that in this general setting, when posed under no-flux boundary conditions for n and c and homogeneous Dirichlet boundary conditions for u, and for any suitably regular initial data, an associated initial value problem possesses at least one globally defined solution in an appropriate generalized sense. Since it is well-known that in the absence of absorption, already the corresponding fluid-free subsystem with u ≡ 0 and μ = 0 admits some solutions blowing up in finite time, this particularly indicates that any power-type superlinear degradation of the form in (*) goes along with some significant regularizing effect. [ABSTRACT FROM AUTHOR]

This paper is concerned with the effects of nonlinear diffusion on global solvability and stabilization in a variety of models which generalizes the following prototype { n t + u ⋅ ∇ n = ∇ ⋅ (n m − 1 ∇ n) − ∇ ⋅ (n ∇ c) − ρ n , c t + u ⋅ ∇ c = Δ c − c + ρ , ρ t + u ⋅ ∇ ρ = Δ ρ − ρ n , u t + ∇ P = Δ u + (n + ρ) ∇ ϕ , ∇ ⋅ u = 0 with a given function ϕ ∈ W 2 , ∞ (Ω) , where Ω ⊂ R 3 is a general bounded domain with smooth boundary. Based on an energy-type argument combined with maximal Sobolev regularity theory, we conclude that if m > 37 33 , an associated initial-boundary value problem admits at least one globally bounded weak solution which stabilizes toward the spatial homogeneous equilibrium (n ∞ , ρ ∞ , ρ ∞ , 0) in the sense that ‖ n (⋅ , t) − n ∞ ‖ L p (Ω) + ‖ c (⋅ , t) − ρ ∞ ‖ W 1 , ∞ (Ω) + ‖ ρ (⋅ , t) − ρ ∞ ‖ W 1 , ∞ (Ω) + ‖ u (⋅ , t) ‖ L ∞ (Ω) → 0 as t → ∞ for any p > 1 , where n ∞ : = 1 | Ω | { ∫ Ω n 0 − ∫ Ω ρ 0 } + and ρ ∞ : = 1 | Ω | { ∫ Ω ρ 0 − ∫ Ω n 0 } +. [ABSTRACT FROM AUTHOR]

After measuring density and viscosity of a mixture of glycerin and water contained in a vertical pipe, a variation of these properties according to depth is observed. These gradients are typical of non-equilibrium states related to the lower density of water and the fact that relatively long times are necessary to achieve homogeneity. In the same pipe, the falling velocity of five little spheres is measured as a function of depth, and then a numerical fit is performed which agrees very well with experimental data. Based on the generalization of these results, the applicability of Stokes method is discussed for measuring viscosity of mixtures with a concentration gradient.

We introduce new control-volume finite-element discretization schemes suitable for solving the Stokes problem. Within a common framework, we present different approaches for constructing such schemes. The first and most established strategy employs a non-overlapping partitioning into control volumes. The second represents a new idea by splitting into two sets of control volumes, the first set yielding a partition of the domain and the second containing the remaining overlapping control volumes required for stability. The third represents a hybrid approach where finite volumes are combined with finite elements based on a hierarchical splitting of the ansatz space. All approaches are based on typical finite element function spaces but yield locally mass and momentum conservative discretization schemes that can be interpreted as finite volume schemes. We apply all strategies to the inf-sub stable MINI finite-element pair. Various test cases, including convergence tests and the numerical observation of the boundedness of the number of preconditioned Krylov solver iterations, as well as more complex scenarios of flow around obstacles or through a three-dimensional vessel bifurcation, demonstrate the stability and robustness of the schemes. [Display omitted] • General control-volume finite-element framework. • Construction of overlapping control volumes giving more flexibility. • Hybrid approach using a hierarchical splitting for the MINI element. • Detailed numerical investigations for various test cases. [ABSTRACT FROM AUTHOR]

Laser diode-based optical chaos is attractive for the fundamental physics as well as practical tasks in such as secure communications, random number generation, and fiber sensing. The characteristics of Brillouin backscattering light generated by injecting a chaotic laser into a single mode fiber have been investigated experimentally. The Brillouin backscattering light still has the chaotic properties, and the position of the chaotic anti-Stokes frequency appears a dip, which has never been reported before. The power and linewidth variations of the Brillouin Stokes light and anti-Stokes light along with the input optical power also are analyzed. Particularly, we investigate the differences of Brillouin backscattering light between chaotic laser and narrow-linewidth laser, and analyze the interacted optical spectra when the chaotic laser and the narrow-linewidth laser inject into the 10 km single mode fiber simultaneously. With detailed analysis and experimental validation, we demonstrate that due to the chaotic self-similarity property, the chaotic laser at the location of anti-Stokes frequency transforms into the Stokes light in the stimulated Brillouin scattering process, which leads to the appearing of the dip.

In this article, a mechanistic process-based model is developed, for accurate predictions of pig farms wastewater behavior in free water constructed wetlands. Twenty-six variables were considered in order to simulate the simultaneous hydraulic, physical, biochemical and physico-chemical characteristics of different processes that are happening in this system. The proposed model was developed by optimization of the advection-diffusion-reaction equations. For that, Stokes equations and the Anaerobic Digestion Model No. 1 were implemented. The mathematical analysis of the model involves the use of a numerical model, the finite element method, and flowchart-based strategy planning. Numerical simulation in a two-dimensional model using open access software (FreeFem++) are presented to demonstrate the dynamic behavior of the proposed prototype. [ABSTRACT FROM AUTHOR]

Abstract Eulerian derivatives of shape functionals in shape optimization can be written in two formulations of boundary and volume integrals. The former is widely used in shape gradient descent algorithms. The latter holds more generally, although rarely being used numerically in literature. For shape functionals governed by the Stokes equation, we consider the mixed finite element approximations to the two types of shape gradients from corresponding Eulerian derivatives. The standard MINI and Taylor–Hood elements are employed to discretize the state equation, its adjoint and the resulting shape gradients. We present thorough convergence analysis with a priori error estimates for the two approximate shape gradients. The theoretical analysis shows that the volume integral formula has superconvergence property. Numerical results are presented to verify the theory and show that the volume formulation is more accurate. Highlights • We present convergence analysis of approximate shape gradients in Stokes equation. • Both volume and boundary formulations of shape gradients are considered. • MINI and Taylor–Hood elements are used to discretize shape gradients. • The volume formulation convergences faster and offers better accuracy. [ABSTRACT FROM AUTHOR]

Distributed temperature sensing (DTS) systems can be used to estimate the temperature along optic fibers of several kilometers at a sub-meter interval. DTS systems function by shooting laser pulses through a fiber and measuring its backscatter intensity at two distinct wavelengths in the Raman spectrum. The scattering-loss coefficients for these wavelengths are temperature-dependent, so that the temperature along the fiber can be estimated using calibration to fiber sections with a known temperature. A new calibration approach is developed that allows for an estimate of the uncertainty of the estimated temperature, which varies along the fiber and with time. The uncertainty is a result of the noise from the detectors and the uncertainty in the calibrated parameters that relate the backscatter intensity to temperature. Estimation of the confidence interval of the temperature requires an estimate of the distribution of the noise from the detectors and an estimate of the multi-variate distribution of the parameters. Both distributions are propagated with Monte Carlo sampling to approximate the probability density function of the estimated temperature, which is different at each point along the fiber and varies over time. Various summarizing statistics are computed from the approximate probability density function, such as the confidence intervals and the standard uncertainty (the estimated standard deviation) of the estimated temperature. An example is presented to demonstrate the approach and to assess the reasonableness of the estimated confidence intervals. The approach is implemented in the open-source Python package “dtscalibration”.

In this work, we develop and analyse a novel Hybrid High-Order discretisation of the Brinkman problem. The method hinges on hybrid discrete velocity unknowns at faces and elements and on discontinuous pressures. Based on the discrete unknowns, we reconstruct inside each element a Stokes velocity one degree higher than face unknowns, and a Darcy velocity in the Raviart–Thomas–Nédélec space. These reconstructed velocities are respectively used to formulate the discrete versions of the Stokes and Darcy terms in the momentum equation, along with suitably designed penalty contributions. The proposed construction is tailored to yield optimal error estimates that are robust throughout the entire spectrum of local (Stokes- or Darcy-dominated) regimes, as identified by a dimensionless number which can be interpreted as a friction coefficient. The singular limit corresponding to the Darcy equation is also fully supported by the method. Numerical examples corroborate the theoretical results. This paper also contains two contributions whose interest goes beyond the specific method and application treated in this work: an investigation of the dependence of the constant in the second Korn inequality on star-shaped domains and its application to the study of the approximation properties of the strain projector in general Sobolev seminorms. [ABSTRACT FROM AUTHOR]

This paper deals with the following chemotaxis-Stokes system n t + u ⋅ ∇ n = Δ n m − ∇ ⋅ ( n S ( x , n , c ) ⋅ ∇ c ) , x ∈ Ω , t > 0 , c t + u ⋅ ∇ c = Δ c − n f ( c ) , x ∈ Ω , t > 0 , u t = Δ u + ∇ P + n ∇ ϕ , x ∈ Ω , t > 0 , ∇ ⋅ u = 0 , x ∈ Ω , t > 0 in a bounded domain Ω ⊂ R 2 with smooth boundary, ϕ ∈ W 1 , ∞ ( Ω ) , f and S are given sufficiently smooth functions with values in [ 0 , ∞ ) and R 2 × 2 , respectively. Here S satisfies | S ( x , n , c ) | < S 0 ( c ) n α with α ≥ 0 and some nondecreasing nonnegative function S 0 . It is showed that when m > 1 + α and α ≥ 0 , the corresponding system possesses a global bounded weak solution for any sufficiently regular initial data ( n 0 , c 0 , u 0 ) satisfying n 0 ≥ 0 and c 0 ≥ 0 . [ABSTRACT FROM AUTHOR]

A Skeleton-stabilized IsoGeometric Analysis (SIGA) technique is proposed for incompressible viscous flow problems with moderate Reynolds number. The proposed method allows utilizing identical finite dimensional spaces (with arbitrary B-splines/NURBS order and regularity) for the approximation of the pressure and velocity components. The key idea is to stabilize the jumps of high-order derivatives of variables over the skeleton of the mesh. For B-splines/NURBS basis functions of degree k with C α -regularity ( 0 ≤ α < k ), only the derivative of order α + 1 has to be controlled. This stabilization technique thus can be viewed as a high-regularity generalization of the (Continuous) Interior-Penalty Finite Element Method. Numerical experiments are performed for the Stokes and Navier–Stokes equations in two and three dimensions. Oscillation-free solutions and optimal convergence rates are obtained. In terms of the sparsity pattern of the algebraic system, we demonstrate that the block matrix associated with the stabilization term has a considerably smaller bandwidth when using B-splines than when using Lagrange basis functions, even in the case of C 0 -continuity. This important property makes the proposed isogeometric framework practical from a computational effort point of view. [ABSTRACT FROM AUTHOR]

The BDDC (balancing domain decomposition by constraints) methods have been applied successfully to solve the large sparse linear algebraic systems arising from conforming finite element discretizations of second order elliptic and Stokes problems. In this paper, the Stokes equations are discretized using the weak Galerkin method, a newly developed nonconforming finite element method. A BDDC algorithm is designed to solve the linear system such obtained. Edge/face velocity interface average and mean subdomain pressure are selected for the coarse problem. The condition number bounds of the BDDC preconditioned operator are analyzed, and the same rate of convergence is obtained as for conforming finite element methods. Numerical experiments are conducted to verify the theoretical results. [ABSTRACT FROM AUTHOR]

A class of chemotaxis-Stokes systems generalizing the prototype { n t + u ⋅ ∇ n = ∇ ⋅ ( n m − 1 ∇ n ) − ∇ ⋅ ( n ∇ c ) , c t + u ⋅ ∇ c = Δ c − n c , u t + ∇ P = Δ u + n ∇ ϕ , ∇ ⋅ u = 0 , is considered in bounded convex three-dimensional domains, where ϕ ∈ W 2 , ∞ ( Ω ) is given. The paper develops an analytical approach which consists in a combination of energy-based arguments and maximal Sobolev regularity theory, and which allows for the construction of global bounded weak solutions to an associated initial-boundary value problem under the assumption that (0.1) m > 9 8 . Moreover, the obtained solutions are shown to approach the spatially homogeneous steady state ( 1 | Ω | ∫ Ω n 0 , 0 , 0 ) in the large time limit. This extends previous results which either relied on different and apparently less significant energy-type structures, or on completely alternative approaches, and thereby exclusively achieved comparable results under hypotheses stronger than (0.1) . [ABSTRACT FROM AUTHOR]

Việc thay thế hàm dị thường trọng lực trong các công thức Stokes và Vening-Meinesz bằng tập hợp các giá trị dị thường trọng lực được đo trên bề mặt vật lý trái đất hoặc trong không gian dẫn đến các sai số tất yếu khi tính dị thường độ cao và các thành phần góc lệch dây dọi. Mục đích của bài báo này là chỉ ra mối liên hệ giữa đại lượng các sai số đó với mức độ rời rạc của số liệu ban đầu. Bằng cách sử dụng phương pháp phân tích mật độ phổ hàm hiệp phương sai của trường trọng lực đã đưa ra được công thức đánh giá sai số dị thường trọng lực phụ thuộc vào bước rời rạc của số liệu và mức độ phức tạp của trường trọng lực.

This work presents a technique based on optical tracking of the free fall in a Newtonian fluid used in falling ball viscometers. Classical techniques have shown, on one hand a limit in the ball falling height measurement, on the other hand a limit in the accuracy estimation of velocity and therefore a weak precision on the viscosity calculation of the fluids. Our method consist to measure the fall height by taking video scenes of the ball during its fall and thus to estimate its terminal velocity which is a preponderant parameter in the kinematic velocity computing, using both the Stokes or Hoppler formalisms. The precision reached in this approach adjoins encouraging values for future works in the purpose to improve this method further.

Dielectrophoretic force is an electric force experienced by particles subjected to non-uniform electric fields. In recent years, plenty of dielectrophoretic force (DEP) applications have been developed. Most of these works have been centered on particle positioning and manipulation. DEP particle characterization has been left in the background. Likewise, these characterizations have studied the electric properties of particles from a qualitative point of view. This article focuses on the quantitative measurement of cells’ dielectric force, specifically yeast cells. The measures are obtained as the results of a theoretical model and an instrumental method, both of which are developed and described in the present article, based on a dielectrophoretic chamber made of two V-shaped placed electrodes. In this study, 845 cells were measured. For each one, six speeds were taken at different points in its trajectory. Furthermore, the chamber design is repeatable, and this was the first time that measurements of dielectrophoretic force and cell velocity for double yeast cells were accomplished. To validate the results obtained in the present research, the results have been compared with the dielectric properties of yeast cells collected in the pre-existing literature.

We study the application of the Isogeometric Finite Cell Method (IGA-FCM) to mixed formulations in the context of the Stokes problem. We investigate the performance of the IGA-FCM when utilizing some isogeometric mixed finite elements, namely: Taylor–Hood, Sub-grid, Raviart–Thomas, and Nédélec elements. These element families have been demonstrated to perform well in the case of conforming meshes, but their applicability in the cut-cell context is still unclear. Dirichlet boundary conditions are imposed by Nitsche’s method. Numerical test problems are performed, with a detailed study of the discrete inf–sup stability constants and of the convergence behavior under uniform mesh refinement. [ABSTRACT FROM AUTHOR]

In this paper, we consider the following Keller–Segel(–Navier)–Stokes system (⋆) { n t + u ⋅ ∇ n = Δ n − ∇ ⋅ ( n χ ( c ) ∇ c ) , x ∈ Ω , t > 0 , c t + u ⋅ ∇ c = Δ c − c + n , x ∈ Ω , t > 0 , u t + κ ( u ⋅ ∇ ) u = Δ u + ∇ P + n ∇ ϕ , x ∈ Ω , t > 0 , ∇ ⋅ u = 0 , x ∈ Ω , t > 0 , where Ω ⊂ R N ( N = 2 , 3 ) is a bounded domain with smooth boundary ∂ Ω , κ ∈ R and χ ( c ) is assumed to generalize the prototype χ ( c ) = χ 0 ( 1 + μ c ) 2 , c ≥ 0 . It is proved that i) for κ ≠ 0 and N = 2 or κ = 0 and N ∈ { 2 , 3 } , the corresponding initial–boundary problem admits a unique global classical solution which is bounded; ii) for κ ≠ 0 and N = 3 , the corresponding initial–boundary problem possesses at least one global weak solution. [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]

In this work we develop a discretisation method for the Brinkman problem that is uniformly well-behaved in all regimes (as identified by a local dimensionless number with the meaning of a friction coefficient) and supports general meshes as well as arbitrary approximation orders. The method is obtained combining ideas from the Hybrid High-Order and Discrete de Rham methods, and its robustness rests on a potential reconstruction and stabilisation terms that change in nature according to the value of the local friction coefficient. We derive error estimates that, thanks to the presence of cut-off factors, are valid across all the regimes and provide extensive numerical validation. [ABSTRACT FROM AUTHOR]

Using the heuristic method of formal asymptotic expansions, we analyze the order of magnitude of the diferent physical entities involved in the phenomenon of fluid exchange between geometric regions, where the velocity of the fluid flow has diferent scale. We give the modeling equations, coupling conditions and express the velocity and pressure with formal asymptotic expansions. Then we compute the averages and observe the order of magnitude of each physical effect. Finally, we deduce a Darcy-Brinkman two way coupled system of partial differential equations as the "averaged" or "homogenized" problem.