scholarly journals Derivation of a one-dimensional von Kármán theory for viscoelastic ribbons

2022 ◽  
Vol 29 (2) ◽  
Author(s):  
Manuel Friedrich ◽  
Lennart Machill
Keyword(s):  
Metric Spaces ◽  
Three Dimensional ◽  
Gradient Flows ◽  
Dimensional Model ◽  
Discrete Approximations ◽  
Three Dimensional Model ◽  
One Dimensional ◽  
Von Karman ◽  
Von Kármán ◽  
Appl Math

AbstractWe consider a two-dimensional model of viscoelastic von Kármán plates in the Kelvin’s-Voigt’s rheology derived from a three-dimensional model at a finite-strain setting in Friedrich and Kružík (Arch Ration Mech Anal 238: 489–540, 2020). As the width of the plate goes to zero, we perform a dimension-reduction from 2D to 1D and identify an effective one-dimensional model for a viscoelastic ribbon comprising stretching, bending, and twisting both in the elastic and the viscous stress. Our arguments rely on the abstract theory of gradient flows in metric spaces by Sandier and Serfaty (Commun Pure Appl Math 57:1627–1672, 2004) and complement the $$\Gamma $$ Γ -convergence analysis of elastic von Kármán ribbons in Freddi et al. (Meccanica 53:659–670, 2018). Besides convergence of the gradient flows, we also show convergence of associated time-discrete approximations, and we provide a corresponding commutativity result.

On the numerical study of thermohydrodynamics and biochemistry of inland water bodies

2021 ◽  
Author(s):  
Daria Gladskikh ◽  
Evgeny Mortikov ◽  
Victor Stepanenko
Keyword(s):  
Mixed Layer ◽  
Numerical Study ◽  
Three Dimensional ◽  
Water Bodies ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
One Dimensional ◽  
Lake Model ◽  
Upper Mixed Layer ◽  
The One

<p>The study of thermodynamic and biochemical processes of inland water objects using one- and three-dimensional RANS numerical models was carried out both for idealized water bodies and using measurements data. The need to take into account seiche oscillations to correctly reproduce the deepening of the upper mixed layer in one-dimensional (vertical) models is demonstrated. We considered the one-dimensional LAKE model [1] and the three-dimensional model [2, 3, 4] developed at the Research Computing Center of Moscow State University on the basis of a hydrodynamic code combining DNS/LES/RANS approaches for calculating geophysical turbulent flows. The three-dimensional model was supplemented by the equations for calculating biochemical substances by analogy with the one-dimensional biochemistry equations used in the LAKE model. The effect of mixing processes on the distribution of concentration of greenhouse gases, in particular, methane and oxygen, was studied.</p><p>The work was supported by grants of the RF President’s Grant for Young Scientists (MK-1867.2020.5, MD-1850.2020.5) and by the RFBR (19-05-00249, 20-05-00776). </p><p>1. Stepanenko V., Mammarella I., Ojala A., Miettinen H., Lykosov V., Timo V. LAKE 2.0: a model for temperature, methane, carbon dioxide and oxygen dynamics in lakes // Geoscientific Model Development. 2016. V. 9(5). P. 1977–2006.<br>2. Mortikov E.V., Glazunov A.V., Lykosov V.N. Numerical study of plane Couette flow: turbulence statistics and the structure of pressure-strain correlations // Russian Journal of Numerical Analysis and Mathematical Modelling. 2019. 34(2). P. 119-132.<br>3. Mortikov, E.V. Numerical simulation of the motion of an ice keel in stratified flow // Izv. Atmos. Ocean. Phys. 2016. V. 52. P. 108-115.<br>4. Gladskikh D.S., Stepanenko V.M., Mortikov E.V. On the influence of the horizontal dimensions of inland waters on the thickness of the upper mixed layer // Water Resourses. 2021.V. 45, 9 pages. (in press) </p>

scholarly journals Hydraulic modeling of combined sewers overflow integrating the results of the SWMM and CFX models.

2021 ◽  
Vol 37 (1) ◽  
Author(s):  
D. Pulgarín ◽  
J. Plaza ◽  
J. Ruge ◽  
J. Rojas
Keyword(s):  
Three Dimensional ◽  
Hydraulic Modeling ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
One Dimensional ◽  
Ansys Cfx ◽  
Combined Sewer ◽  
The One ◽  
Swmm Model

This study proposes a methodology for the calibration of combined sewer overflow (CSO), incorporating the results of the three-dimensional ANSYS CFX model in the SWMM one-dimensional model. The procedure consists of constructing calibration curves in ANSYS CFX that relate the input flow to the CSO with the overflow, to then incorporate them into the SWMM model. The results obtained show that the behavior of the flow over the crest of the overflow weir varies in space and time. Therefore, the flow of entry to the CSO and the flow of excesses maintain a non-linear relationship, contrary to the results obtained in the one-dimensional model. However, the uncertainty associated with the idealization of flow methodologies in one dimension is reduced under the SWMM model with kinematic wave conditions and simulating CSO from curves obtained in ANSYS CFX. The result obtained facilitates the calibration of combined sewer networks for permanent or non-permanent flow conditions, by means of the construction of curves in a three-dimensional model, especially when the information collected in situ is limited.

Three-Dimensional Model of the Human Eye-Head Saccadic System

1997 ◽  
Vol 77 (2) ◽  
pp. 654-666 ◽  
Author(s):  
Douglas Tweed
Keyword(s):  
Three Dimensional ◽  
Head Movements ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Gaze Shifts ◽  
One Dimensional ◽  
Human Eye ◽  
Saccadic System ◽  
Listing's Law ◽  
Listing’S Law

Tweed, Douglas. Three-dimensional model of the human eye-head saccadic system. J. Neurophysiol. 77: 654–666, 1997. Current theories of eye-head gaze shifts deal only with one-dimensional motion, and do not touch on three-dimensional (3-D) issues such as curvature and Donders' laws. I show that recent 3-D data can be explained by a model based on ideas that are well established from one-dimensional studies, with just one new assumption: that the eye is driven toward a 3-D orientation in space that has been chosen so that Listing's law of the eye in head will hold when the eye-head movement is complete. As in previous, one-dimensional models, the eye and head are feedback-guided and the commands specifying desired eye position eye pass through a neural “saturation” so as to stay within the effective oculomotor range. The model correctly predicts the complex, 3-D trajectories of the head, eye in space, and eye in head in a variety of saccade tasks. And when it moves repeatedly to the same target, varying the contributions of eye and head, the model lands in different eye-in-space positions, but these positions differ only in their cyclotorsion about the line of sight, so they all point that line at the target—a behavior also seen in real eye-head saccades. Between movements the model obeys Listing's law of the eye in head and Donders' law of the head on torso, but during certain gaze shifts involving large torsional head movements, it shows marked, 8° deviations from Listing's law. These deviations are the most important untested predictions of the theory. Their experimental refutation would sink the model, whereas confirmation would strongly support its central claim that the eye moves toward a 3-D position in space chosen to obey Listing's law and, therefore, that a Listing operator exists upstream from the eye pulse generator.

On the modeling of thermohydrodynamic and biogeochemical processes in the inland water objects

2020 ◽  
Author(s):  
Daria Gladskikh ◽  
Evgeny Mortikov ◽  
Victor Stepanenko
Keyword(s):  
Carbon Dioxide ◽  
Numerical Study ◽  
Three Dimensional ◽  
Measurement Data ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Inland Water ◽  
One Dimensional ◽  
Biochemical Processes ◽  
Dimensional Models

<p>Currently, one-dimensional and three-dimensional models are widely used to model thermohydrodynamic and biochemical processes in lakes and water rеreservoirs. One-dimensional models are highly computationally efficient and are used to parameterize land water bodies in climate models, however, when calculating large lakes and reservoirs with complex geometry, such models may incorrectly reproduce processes associated with horizontal heterogeneity. This becomes especially important for the prediction of water quality and euthrophication.</p><p>A three-dimensional model of thermohydrodynamics and biochemistry of an inland water obect is presented, which is based on the hydrostatic RANS model [1-3], and the parameterization of biochemical processes is implemented by analogy with the scheme for calculating biochemistry in the one-dimensional LAKE model [4]. Thus, the three-dimensional model is supplemented by a description of the transport of substances such as oxygen (O<sub>2</sub>), carbon dioxide (CO<sub>2</sub>), methane (CH<sub>4</sub>), as well as phyto- and zooplankton. The effect of turbulent diffusion and large-scale water movements on the distribution of a methane concentration field is studied.</p><p>To verify the calculation results, idealized numerical experiments and comparison with the measurement data on Lake Kuivajärvi (Finland) were used.</p><p>The work was supported by grants of the RF President’s Grant for Young Scientists (MK-1867.2020.5, MD-1850.2020.5) and by the RFBR (18-05-00292, 18-35-00602, 20-05-00776). <br><br>References:<br>[1] Mortikov E.V. Numerical simulation of the motion of an ice keel in stratified flow // Izv. Atmos. Ocean. Phys. 2016. 52. P. 108-115.<br>[2] Mortikov E.V., Glazunov A.V., Lykosov V.N. Numerical study of plane Couette flow: turbulence statistics and the structure of pressure-strain correlations // Russian Journal of Numerical Analysis and Mathematical Modelling. 2019. V. 34, N 2. P. 119-132.<br>[3] D.S. Gladskikh, V.M. Stepanenko, E.V. Mortikov, On the influence of the horizontal dimensions of inland waters on the thickness of the upper mixed layer. // Water Resourses. 2019. 18 pages. (submitted)<br>[4] Victor Stepanenko, Ivan Mammarella, Anne Ojala, Heli Miettinen, Vasily Lykosov, and Vesala Timo. LAKE 2.0: a model for temperature, methane, carbon dioxide and oxygen dynamics in lakes. Geoscientific Model Development, 9(5): 1977–2006, 2016.</p>

Analysis of the Containment Thermal-Hydraulic Behavior of a Small Reactor During Loss of Coolant Accident

2017 ◽  
Author(s):  
Qian Lin ◽  
Weizhong Zhang
Keyword(s):  
Cooling System ◽  
Three Dimensional ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
One Dimensional ◽  
Loss Of Coolant Accident ◽  
Lumped Parameter ◽  
Loss Of Coolant ◽  
Calculation Results ◽  
The One

The containment thermal hydraulics of a small reactor during loss of coolant accident (LOCA) is studied by a lumped parameter one-dimensional model and a three-dimensional model. The capability of a kind of heat exchanger type passive containment cooling system (PCCS) is analyzed by the one-dimensional model. The calculation results show that, the decay heat can be removed and the containment pressure can be decreased by the proposed PCCS. The steam and non-condensable gas (the air) distribution in the containment is investigated, the mixing and stratification behaviors are analyzed for several different cases, in which the PCCS and condenser are located at higher, base or lower position. The sensitivity analysis of the PCCS elevation shows that, in despite of the different gas stratification, the containment pressures are nearly the same. Similar conclusions can be obtained by the one-dimensional model and three-dimensional model. The preliminary results may indicate that, the designed PCCS and condenser can be located at a lower part, which will be benefit for the economy of the small reactor or meet other requirements.

Evaluating 3-D and 1-D mathematical models for mass transport in heterogeneous biofilms

2000 ◽  
Vol 41 (4-5) ◽  
pp. 347-356 ◽  
Author(s):  
E. Morgenroth ◽  
H. Eberl ◽  
M.C. van Loosdrecht
Keyword(s):  
Three Dimensional ◽  
Average Concentration ◽  
Local Concentration ◽  
Concentration Profiles ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
One Dimensional ◽  
Bacterial Competition ◽  
Variable Diffusion ◽  
Three Dimensional Simulations

Results from a three dimensional model for heterogeneous biofilms including the numerical solution of hydrodynamics were compared to simplified one dimensional models. A one dimensional model with a variable diffusion coefficient over the thickness of the biofilm was well suited to approximate average concentration profiles of three dimensional simulations of rough biofilms. A new compartmentalized one dimensional model is presented that is then used to evaluate effects of pores and channels on microbial competition in heterogeneous biofilms. Surface and pore regions of the biofilm are modeled using separate compartments coupled by a convective link. Local concentration profiles from the three dimensional simulations could be adequately reproduced using the compartmentalized one dimensional model. The compartmentalized one dimensional model was then used to evaluate bacterial competition in a growing biofilm and in a mushroom type biofilm assuming different modes of detachment.

On astronomical refraction for a three-dimensional model atmosphere.

1979 ◽  
Vol 89 ◽  
pp. 35-37
Author(s):  
V.I. Sergienko
Keyword(s):  
Three Dimensional ◽  
Model Atmosphere ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
One Dimensional ◽  
Astronomical Refraction

The existing refraction theories for a one-dimensional model atmosphere do not account for anomalous refraction. The latter can be calculated using a three-dimensional model atmosphere.

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