A convenient formulation of Sadowsky's model for elastic ribbons

2021 ◽  
Vol 477 (2255) ◽  
Author(s):  
Sébastien Neukirch ◽  
Basile Audoly
Keyword(s):  
Differential Equations ◽  
Constitutive Relation ◽  
Classical Problem ◽  
Constitutive Law ◽  
System Of Differential Equations ◽  
Dimensional Model ◽  
Simple Method ◽  
One Dimensional ◽  
Aspect Ratios ◽  
Nonlinear Constitutive Relation

Elastic ribbons are elastic structures whose length-to-width and width-to-thickness aspect ratios are both large. Sadowsky proposed a one-dimensional model for ribbons featuring a nonlinear constitutive relation for bending and twisting: it brings in both rich behaviours and numerical difficulties. By discarding non-physical solutions to this constitutive relation, we show that it can be inverted; this simplifies the system of differential equations governing the equilibrium of ribbons. Based on the inverted form, we propose a natural regularization of the constitutive law that eases the treatment of singularities often encountered in ribbons. We illustrate the approach with the classical problem of the equilibrium of a Möbius ribbon, and compare our findings with the predictions of the Wunderlich model. Overall, our approach provides a simple method for simulating the statics and the dynamics of elastic ribbons.

A control-oriented modular one-dimensional model for wall-flow diesel particulate filters

2017 ◽  
Vol 19 (3) ◽  
pp. 329-346 ◽  
Author(s):  
Soroosh Hassanpour ◽  
John McPhee
Keyword(s):  
Differential Equations ◽  
Dimensional Model ◽  
Orthogonal Collocation ◽  
Diesel Particulate ◽  
One Dimensional ◽  
Diesel Particulate Filters ◽  
Particulate Filters ◽  
Wall Flow ◽  
Flow Pressure ◽  
Regeneration Processes

A comprehensive modular one-dimensional physics-based mathematical model is developed for non-isothermal compressible flow, pressure drop, and filtration and regeneration processes in wall-flow diesel particulate filters. Employing a modified orthogonal collocation method and symbolic computation in Maple™, the governing partial differential equations are reduced to a control-oriented model governed by ordinary differential equations which can be solved in real time. Numerical examples are provided to indicate the accuracy and computational efficiency of the developed model and to study the different behaviors of wall-flow diesel particulate filters.

scholarly journals MATHEMATICAL ANALYSIS OF A ONE-DIMENSIONAL MODEL FOR AN AGING FLUID

2013 ◽  
Vol 23 (09) ◽  
pp. 1561-1602
Author(s):  
DAVID BENOIT ◽  
LINGBING HE ◽  
CLAUDE LE BRIS ◽  
TONY LELIÈVRE
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Mathematical Analysis ◽  
Newtonian Fluids ◽  
Well Posedness ◽  
Dimensional Model ◽  
Partial Differential ◽  
One Dimensional ◽  
Longtime Behavior

We study mathematically a system of partial differential equations arising in the modeling of an aging fluid, a particular class of non-Newtonian fluids. We prove well-posedness of the equations in appropriate functional spaces and investigate the longtime behavior of the solutions.

Accurate Radial Vaneless Diffuser One-Dimensional Model

2015 ◽  
Vol 137 (8) ◽  
Author(s):  
Fabio De Bellis ◽  
Angelo Grimaldi ◽  
Dante Tommaso Rubino ◽  
Riccardo Amirante ◽  
Elia Distaso
Keyword(s):  
Angular Momentum ◽  
Differential Equations ◽  
Loss Coefficient ◽  
Operating Conditions ◽  
Performance Estimation ◽  
Dimensional Model ◽  
Vaneless Diffuser ◽  
One Dimensional ◽  
Starting Point ◽  
Vaneless Diffusers

A simplified one-dimensional model for the performance estimation of vaneless radial diffusers is presented. The starting point of such a model is that angular momentum losses occurring in vaneless diffusers are usually neglected in the most common turbomachinery textbooks: It is assumed that the angular momentum is conserved inside a vaneless diffuser, although a nonisentropic pressure transformation is considered at the same time. This means that fluid-dynamic losses are taken into account only for what concerns pressure recovery, whereas the evaluation of the outlet tangential velocity incoherently follows an ideal behavior. Several attempts were presented in the past in order to consider the loss of angular momentum, mainly solving a full set of differential equations based on the various developments of the initial work by Stanitz (1952, “One-Dimensional Compressible Flow in Vaneless Diffusers of Radial or Mixed-Flow Centrifugal Compressors, Including Effects of Friction, Heat Transfer and Area Change,” Report No. NACA TN 2610). However, such formulations are significantly more complex and are based on two empirical or calibration coefficients (skin friction coefficient and dissipation or turbulent mixing loss coefficient) which need to be properly assessed. In the present paper, a 1D model for diffuser losses computation is derived considering a single loss coefficient, and without the need of solving a set of differential equations. The model has been validated against massive industrial experimental campaigns, in which several diffuser geometries and operating conditions have been considered. The obtained results confirm the reliability of the proposed approach, able to predict the diffuser performance with negligible drop of accuracy in comparison with more sophisticated techniques. Both preliminary industrial designs and experimental evaluations of the diffusers may benefit from the proposed model.

Extending the Concept of Isochrons from Oscillatory to Excitable Systems for Modeling an Excitable Neuron

1998 ◽  
Vol 08 (12) ◽  
pp. 2375-2385 ◽  
Author(s):  
Natsuhiro Ichinose ◽  
Kazuyuki Aihara ◽  
Kevin Judd
Keyword(s):  
Differential Equations ◽  
High Dimensional ◽  
Dimensional Model ◽  
One Dimensional ◽  
Excitable System ◽  
Response Characteristics ◽  
Model Response ◽  
Excitable Systems ◽  
The One ◽  
Excitable Neuron

In this paper, we study an excitable and nonoscillating neuron on the basis of a technique of extending the concept of isochrons from oscillatory to excitable systems. The extended isochrons allow reduction of an excitable system described by possibly high dimensional differential equations to a simpler system. We analytically derive a one-dimensional model of an excitable neuron stimulated by instantaneous pulses with the technique of the extended isochrons and show its similarity to an isochronal map numerically obtained from the FitzHugh–Nagumo model. Response characteristics of the one-dimensional model to periodic impulsive stimulations are also analyzed numerically.

Validation of a patient-specific one-dimensional model of the systemic arterial tree

2011 ◽  
Vol 301 (3) ◽  
pp. H1173-H1182 ◽  
Author(s):  
Philippe Reymond ◽  
Yvette Bohraus ◽  
Fabienne Perren ◽  
Francois Lazeyras ◽  
Nikos Stergiopulos
Keyword(s):  
Arterial Wall ◽  
Specific Model ◽  
Constitutive Law ◽  
Distributed Model ◽  
Patient Specific ◽  
Dimensional Model ◽  
Arterial Tree ◽  
One Dimensional ◽  
Flow Waveforms ◽  
Systemic Arterial Tree

The aim of this study is to develop and validate a patient-specific distributed model of the systemic arterial tree. This model is built using geometric and hemodynamic data measured on a specific person and validated with noninvasive measurements of flow and pressure on the same person, providing thus a patient-specific model and validation. The systemic arterial tree geometry was obtained from MR angiographic measurements. A nonlinear viscoelastic constitutive law for the arterial wall is considered. Arterial wall distensibility is based on literature data and adapted to match the wave propagation velocity of the main arteries of the specific subject, which were estimated by pressure waves traveling time. The intimal shear stress is modeled using the Witzig-Womersley theory. Blood pressure is measured using applanation tonometry and flow rate using transcranial ultrasound and phase-contrast-MRI. The model predicts pressure and flow waveforms in good qualitative and quantitative agreement with the in vivo measurements, in terms of wave shape and specific wave features. Comparison with a generic one-dimensional model shows that the patient-specific model better predicts pressure and flow at specific arterial sites. These results obtained let us conclude that a patient-specific one-dimensional model of the arterial tree is able to predict well pressure and flow waveforms in the main systemic circulation, whereas this is not always the case for a generic one-dimensional model.

CLUSTERING AND SYNCHRONIZATION IN A ONE-DIMENSIONAL MODEL FOR THE CA3 REGION OF THE HIPPOCAMPUS

2002 ◽  
Vol 12 (11) ◽  
pp. 2641-2653 ◽  
Author(s):  
N. MONTEJO ◽  
M. N. LORENZO ◽  
V. PÉREZ-MUÑUZURI ◽  
V. PÉREZ-VILLAR
Keyword(s):  
Time Delay ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Spatiotemporal Patterns ◽  
Transmission Time ◽  
Dimensional Model ◽  
One Dimensional ◽  
Dimensional Array ◽  
Ca3 Region

The behavior of a system of coupled ordinary differential equations is studied in order to characterize the CA3 region of the hippocampus. Clustering and synchronization behavior in a one-dimensional array of cells modeled by a modified Morris–Lecar model is analyzed in terms of a time delay included in the model. The random formation of phase dislocations whose number increases with the time delay seems to be responsible for complex spatiotemporal patterns that have been observed. Alterations to the transmission time between cells have been simulated by adding some noise to the system.

scholarly journals On the importance of the nonuniform aortic stiffening in the hemodynamics of physiological aging

2019 ◽  
Vol 317 (5) ◽  
pp. H1125-H1133
Author(s):  
Stamatia Z. Pagoulatou ◽  
Vasiliki Bikia ◽  
Bram Trachet ◽  
Theodore G. Papaioannou ◽  
Athanase D. Protogerou ◽  
...  
Keyword(s):  
Aortic Flow ◽  
Patient Specific ◽  
Diagnostic Tools ◽  
Dimensional Model ◽  
Arterial Tree ◽  
Simple Method ◽  
Peripheral Vessel ◽  
One Dimensional ◽  
Noninvasive Measurements ◽  
Effects Of Aging

Mathematical models of the arterial tree constitute a valuable tool to investigate the hemodynamics of aging and pathology. Rendering such models as patient specific could allow for the assessment of central hemodynamic variables of clinical interest. However, this task is challenging, particularly with respect to the tuning of the local area compliance that varies significantly along the arterial tree. Accordingly, in this study, we demonstrate the importance of taking into account the differential effects of aging on the stiffness of central and peripheral arteries when simulating a person’s hemodynamic profile. More specifically, we propose a simple method for effectively adapting the properties of a generic one-dimensional model of the arterial tree based on the subject’s age and noninvasive measurements of aortic flow and brachial pressure. A key element for the success of the method is the implementation of different mechanisms of arterial stiffening for young and old individuals. The designed methodology was tested and validated against in vivo data from a population of n = 20 adults. Carotid-to-femoral pulse wave velocity was accurately predicted by the model (mean error = 0.14 m/s, SD = 0.77 m/s), with the greatest deviations being observed for older subjects. In regard to aortic pressure, model-derived systolic blood pressure and augmentation index were both in good agreement (mean difference of 2.3 mmHg and 4.25%, respectively) with the predictions of a widely used commercial device (Mobil-O-Graph). These preliminary results encourage us to further validate the method in larger samples and consider its potential as a noninvasive tool for hemodynamic monitoring. NEW & NOTEWORTHY We propose a technique for adapting the parameters of a validated one-dimensional model of the arterial tree using noninvasive measurements of aortic flow and brachial pressure. Emphasis is given on the adjustment of the arterial tree distensibility, which incorporates the nonuniform effects of aging on central and peripheral vessel elasticity. Our method could find application in the derivation of important hemodynamic indices, paving the way for novel diagnostic tools.

scholarly journals A NUMERICAL MODEL OF THE ST. LAWRENCE RIVER

1972 ◽  
Vol 1 (13) ◽  
pp. 127
Author(s):  
David Prandle
Keyword(s):  
Numerical Model ◽  
Flow Distribution ◽  
Flow Visualisation ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Simple Method ◽  
One Dimensional ◽  
Two Dimensional Model ◽  
The One ◽  
St Lawrence River

A one-dimensional numerical model of a 340 mile section of the St. Lawrence River has been formulated to study tidal propagation. For a more detailed study of the flow distribution in a localised section of the river a two-dimensional model was used. A half mile square grid was used to schematise an area of approximately 20 miles long by 15 miles wide. This two-dimensional model was embodied within the one-dimensional model to permit a free interaction of flow across the boundaries. For the one-dimensional case, a comparison of model and prototype results is included for both elevation and velocity. For the two-dimensional model a comparison of flow distribution was made by using field results obtained from photographing ice movement and from drogue movement. To interpret the results of the two-dimensional model into a simple method of flow visualisation, use was made of animation techniques. A movie film was made that demonstrates both tidal rise and fall and the associated horizontal velocities. Elevation was reproduced by use of varying shades of coloured paper to simulate contours, velocities were represented by simulating drogue movement to produce smoke streaks.

Sign in / Sign up

Export Citation Format

Share Document