scholarly journals Three-dimensional flows of pore pressure-activated Bingham fluids

2019 ◽  
Vol 29 (11) ◽  
pp. 2089-2125 ◽  
Author(s):  
Anna Abbatiello ◽  
Tomáš Los ◽  
Josef Málek ◽  
Ondřej Souček
Keyword(s):  
Pore Pressure ◽  
Three Dimensional ◽  
Large Data ◽  
Three Dimensions ◽  
Cauchy Stress ◽  
Internal Flows ◽  
Stick Slip ◽  
Slip Boundary ◽  
Advection Diffusion Equation ◽  
Long Time

We are concerned with a system of partial differential equations (PDEs) describing internal flows of homogeneous incompressible fluids of Bingham type in which the value of activation (the so-called yield) stress depends on the internal pore pressure governed by an advection–diffusion equation. After providing the physical background of the considered model, paying attention to the assumptions involved in its derivation, we focus on the PDE analysis of the initial and boundary value problems. We give several equivalent descriptions for the considered class of fluids of Bingham type. In particular, we exploit the possibility to write such a response as an implicit tensorial constitutive equation, involving the pore pressure, the deviatoric part of the Cauchy stress and the velocity gradient. Interestingly, this tensorial response can be characterized by two scalar constraints. We employ a similar approach to treat stick-slip boundary conditions. Within such a setting we prove long-time and large-data existence of weak solutions to the evolutionary problem in three dimensions.

scholarly journals On the Navier-Stokes equations with temperature-dependent transport coefficients

2006 ◽  
Vol 2006 ◽  
pp. 1-14 ◽  
Author(s):  
Eduard Feireisl ◽  
Josef Málek
Keyword(s):  
Stokes Equations ◽  
Transport Coefficients ◽  
Three Dimensional ◽  
Periodic Problem ◽  
Large Data ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Long Time ◽  
Spatially Periodic ◽  
Dependent Transport

We establish long-time and large-data existence of a weak solution to the problem describing three-dimensional unsteady flows of an incompressible fluid, where the viscosity and heat-conductivity coefficients vary with the temperature. The approach reposes on considering the equation for the total energy rather than the equation for the temperature. We consider the spatially periodic problem.

Three-Dimensional Laminar Flow for Localized Cellular Stimulation

2004 ◽  
Author(s):  
Jui-Ming Yang ◽  
Philip R. LeDuc
Keyword(s):  
Mammalian Cells ◽  
Single Cells ◽  
Three Dimensional ◽  
Fast Response ◽  
Laminar Flows ◽  
Three Dimensions ◽  
Chemical Agent ◽  
Potential Applications ◽  
Cellular Signal ◽  
Long Time

Stimulation of living mammalian cells is primarily accomplished by the delivery of chemical agents to single cells or cell populations. Due to the fast response time of diffusion for these agents over the small size scale of individual cells, localized stimulation is limited. Currently, there are alternate techniques that can produce localized gradients of chemical stimulants over single cells, but they lack the ability for long time scale events that are requisite for many cellular processes because of this diffusion limitation. We have developed a device that is able to create chemical agent separation in three dimensions along distinct boundaries that can be applied to cells. As many techniques are two-dimensionally constrained, this provides us with a more physiologically relevant system for investigating cellular signal transduction and can allow basal to apical activation separations. To accomplish this, multiple flow paths were introduced to manipulate spatiotemporally distinct regions inside a single capillary channel. Solutions that flow laminarly inside these fluidic channels deliver predefined chemicals to specific locations without turbulent mixing. Separation using this system under laminar flows created not only side by side domains in this capillary but also vertical as well. This device has multiple potential applications both in cell and molecular biology as well as in fluid dynamics and fabrication processes.

WEAK SOLUTIONS TO EQUATIONS OF STEADY COMPRESSIBLE HEAT CONDUCTING FLUIDS

2010 ◽  
Vol 20 (05) ◽  
pp. 785-813 ◽  
Author(s):  
PIOTR B. MUCHA ◽  
MILAN POKORNÝ
Keyword(s):  
Boundary Condition ◽  
Three Dimensional ◽  
Large Data ◽  
Slip Boundary Condition ◽  
Regularity Of Solutions ◽  
Energy Estimates ◽  
Navier Stokes ◽  
Heat Conducting ◽  
Existence Of A Solution ◽  
Slip Boundary

We consider the steady compressible Navier–Stokes–Fourier system in a bounded three-dimensional domain. We prove the existence of a solution for arbitrarily large data under the assumption that the pressure p(ϱ, θ) ~ ϱθ + ϱγ for [Formula: see text] assuming either the slip or no-slip boundary condition for the velocity and the Newton boundary condition for the temperature. The regularity of solutions is determined by the basic energy estimates, constructed for the system.

Three-Dimensional Massively Parallel Computing of Suspensions

1998 ◽  
Vol 09 (05) ◽  
pp. 759-775 ◽  
Author(s):  
B. Wachmann ◽  
S. Schwarzer
Keyword(s):  
Parallel Implementation ◽  
Brownian Particle ◽  
Particle Surface ◽  
Three Dimensional ◽  
Building Blocks ◽  
Liquid Mixtures ◽  
Three Dimensions ◽  
Navier Stokes ◽  
Particle Volume ◽  
Slip Boundary

Numerical simulations of suspensions often suffer from the fact that the simulated systems are rather small compared to experimental setups. We present a numerical scheme for non-Brownian particle-liquid mixtures in three dimensions at particle Reynolds numbers between 0.01 and 20 and describe its parallel implementation. The fluid equations are solved by a time-explicit pressure-implicit Navier–Stokes algorithm and the particle motion is tracked by molecular-dynamics methods. The two are coupled by imposing no-slip boundary conditions between the particles and the fluid. We integrate the stress distribution on the particle surface numerically to obtain forces and torques. The building blocks of the algorithm are local and scalable and we have reached particle numbers up to 106 (1.41*108 fluid nodes) on a 512 node CRAY-T3E. We compare our simulation results to theoretical predictions and experimental data and find good agreement for particle volume fractions up to 0.30.

convergent-beam diffraction from surfaces

1987 ◽  
Vol 45 ◽  
pp. 30-33
Author(s):  
J. A. Eades ◽  
A. E. Smith ◽  
D. F. Lynch
Keyword(s):  
Reciprocal Lattice ◽  
Three Dimensional ◽  
Grazing Incidence ◽  
Three Dimensions ◽  
Plane Figure ◽  
Transmission Electron ◽  
Convergent Beam ◽  
Beam Patterns ◽  
Beam Diffraction

It is quite simple (in the transmission electron microscope) to obtain convergent-beam patterns from the surface of a bulk crystal. The beam is focussed onto the surface at near grazing incidence (figure 1) and if the surface is flat the appropriate pattern is obtained in the diffraction plane (figure 2). Such patterns are potentially valuable for the characterization of surfaces just as normal convergent-beam patterns are valuable for the characterization of crystals.There are, however, several important ways in which reflection diffraction from surfaces differs from the more familiar electron diffraction in transmission.GeometryIn reflection diffraction, because of the surface, it is not possible to describe the specimen as periodic in three dimensions, nor is it possible to associate diffraction with a conventional three-dimensional reciprocal lattice.

Automated 3-D cell population analysis in thick tissue sections using laser-scanning confocal-microscopy data

1993 ◽  
Vol 51 ◽  
pp. 562-563
Author(s):  
Hakan Ancin
Keyword(s):  
Laser Scanning ◽  
Population Analysis ◽  
Three Dimensional ◽  
Large Data ◽  
Laser Scanning Confocal Microscopy ◽  
Tissue Slices ◽  
Scanning Confocal Microscopy ◽  
Tissue Sections ◽  
Spatially Adaptive ◽  
Microscopy Data

This paper presents methods for performing detailed quantitative automated three dimensional (3-D) analysis of cell populations in thick tissue sections while preserving the relative 3-D locations of cells. Specifically, the method disambiguates overlapping clusters of cells, and accurately measures the volume, 3-D location, and shape parameters for each cell. Finally, the entire population of cells is analyzed to detect patterns and groupings with respect to various combinations of cell properties. All of the above is accomplished with zero subjective bias.In this method, a laser-scanning confocal light microscope (LSCM) is used to collect optical sections through the entire thickness (100 - 500μm) of fluorescently-labelled tissue slices. The acquired stack of optical slices is first subjected to axial deblurring using the expectation maximization (EM) algorithm. The resulting isotropic 3-D image is segmented using a spatially-adaptive Poisson based image segmentation algorithm with region-dependent smoothing parameters. Extracting the voxels that were labelled as "foreground" into an active voxel data structure results in a large data reduction.

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

Diagnostic System of Gravitational Solid Flow Based on Weight and Accelerometer Signal Analysis Using Wireless Data Transmission Technology

2012 ◽  
Vol 17 (4) ◽  
pp. 319-326 ◽  
Author(s):  
Zbigniew Chaniecki ◽  
Krzysztof Grudzień ◽  
Tomasz Jaworski ◽  
Grzegorz Rybak ◽  
Andrzej Romanowski ◽  
...  
Keyword(s):  
Signal Analysis ◽  
Scale Up ◽  
Three Dimensional ◽  
Diagnostic System ◽  
Wireless Data ◽  
Stick Slip ◽  
Wireless Data Transmission ◽  
Accelerometer Signal ◽  
Flow Investigation ◽  
Material Information

Abstract The paper presents results of the scale-up silo flow investigation in based on accelerometer signal analysis and Wi-Fi transmission, performed in distributed laboratory environment. Prepared, by the authors, a set of 8 accelerometers allows to measure a three-dimensional acceleration vector. The accelerometers were located outside silo, on its perimeter. The accelerometers signal changes allowed to analyze dynamic behavior of solid (vibrations/pulsations) at silo wall during discharging process. These dynamic effects are caused by stick-slip friction between the wall and the granular material. Information about the material pulsations and vibrations is crucial for monitoring the interaction between silo construction and particle during flow. Additionally such spatial position of accelerometers sensor allowed to collect information about nonsymmetrical flow inside silo.

scholarly journals Free partition functions and an averaged holographic duality

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nima Afkhami-Jeddi ◽  
Henry Cohn ◽  
Thomas Hartman ◽  
Amirhossein Tajdini
Keyword(s):  
Partition Function ◽  
Spectral Gap ◽  
Central Charge ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Partition Functions ◽  
General Constraints ◽  
Dimensional Gravity ◽  
Holographic Duality

Abstract We study the torus partition functions of free bosonic CFTs in two dimensions. Integrating over Narain moduli defines an ensemble-averaged free CFT. We calculate the averaged partition function and show that it can be reinterpreted as a sum over topologies in three dimensions. This result leads us to conjecture that an averaged free CFT in two dimensions is holographically dual to an exotic theory of three-dimensional gravity with U(1)c×U(1)c symmetry and a composite boundary graviton. Additionally, for small central charge c, we obtain general constraints on the spectral gap of free CFTs using the spinning modular bootstrap, construct examples of Narain compactifications with a large gap, and find an analytic bootstrap functional corresponding to a single self-dual boson.

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