scholarly journals Elastic membranes in confinement

2016 ◽  
Vol 13 (120) ◽  
pp. 20160408 ◽  
Author(s):  
J. B. Bostwick ◽  
M. J. Miksis ◽  
S. H. Davis
Keyword(s):  
Internal Structure ◽  
Parameter Space ◽  
Continuation Methods ◽  
Elastic Membrane ◽  
Two Dimensional ◽  
Membrane Mechanics ◽  
Confinement Pressure ◽  
Elastic Membranes ◽  
Dimensional Shape ◽  
Secondary Bifurcations

An elastic membrane stretched between two walls takes a shape defined by its length and the volume of fluid it encloses. Many biological structures, such as cells, mitochondria and coiled DNA, have fine internal structure in which a membrane (or elastic member) is geometrically ‘confined’ by another object. Here, the two-dimensional shape of an elastic membrane in a ‘confining’ box is studied by introducing a repulsive confinement pressure that prevents the membrane from intersecting the wall. The stage is set by contrasting confined and unconfined solutions. Continuation methods are then used to compute response diagrams, from which we identify the particular membrane mechanics that generate mitochondria-like shapes. Large confinement pressures yield complex response diagrams with secondary bifurcations and multiple turning points where modal identities may change. Regions in parameter space where such behaviour occurs are then mapped.

Shock loading of fixed flexible thread and orthotropic elastic membrane

2003 ◽  
Vol 3 ◽  
pp. 52-59
Author(s):  
S.S. Komarov ◽  
N.Yu. Tsvileneva ◽  
N.I. Miskaktin
Keyword(s):  
Numerical Methods ◽  
Dynamic Loading ◽  
Elastic Deformation ◽  
Numerical Algorithm ◽  
Shock Loading ◽  
Elastic Membrane ◽  
Wave Dynamics ◽  
Elastic Membranes ◽  
Pneumatic Structures

The main problems of the wave dynamics of flexible filaments and elastic membranes are solved. The reliability of the numerical algorithm proposed by the authors for calculating the elastic deformation of pneumatic structures under dynamic loading is confirmed when compared with the results of known studies obtained by analytical and numerical methods.

COMPLEX BIFURCATION STRUCTURES IN THE HINDMARSH–ROSE NEURON MODEL

2007 ◽  
Vol 17 (09) ◽  
pp. 3071-3083 ◽  
Author(s):  
J. M. GONZÀLEZ-MIRANDA
Keyword(s):  
Phase Diagram ◽  
Bifurcation Diagram ◽  
Parameter Space ◽  
Neuron Model ◽  
Two Dimensional ◽  
Dimensional Parameter ◽  
Rapid Responses ◽  
Bifurcation Structures

The results of a study of the bifurcation diagram of the Hindmarsh–Rose neuron model in a two-dimensional parameter space are reported. This diagram shows the existence and extent of complex bifurcation structures that might be useful to understand the mechanisms used by the neurons to encode information and give rapid responses to stimulus. Moreover, the information contained in this phase diagram provides a background to develop our understanding of the dynamics of interacting neurons.

TERBIUM MOLYBDATE: GROUP THEORY AND FLUCTUATIONS

1987 ◽  
Vol 01 (05n06) ◽  
pp. 239-244
Author(s):  
SERGE GALAM
Keyword(s):  
Fixed Point ◽  
Group Theory ◽  
Parameter Space ◽  
Landau Theory ◽  
Two Dimensional ◽  
Stable Fixed Point ◽  
Theory Analysis ◽  
Continuous Transition ◽  
Dimensional Parameter ◽  
First Order

A new mechanism to explain the first order ferroelastic—ferroelectric transition in Terbium Molybdate (TMO) is presented. From group theory analysis it is shown that in the two-dimensional parameter space ordering along either an axis or a diagonal is forbidden. These symmetry-imposed singularities are found to make the unique stable fixed point not accessible for TMO. A continuous transition even if allowed within Landau theory is thus impossible once fluctuations are included. The TMO transition is therefore always first order. This explanation is supported by experimental results.

Bifurcation of rotating circular cylindrical elastic membranes

1980 ◽  
Vol 87 (2) ◽  
pp. 357-376 ◽  
Author(s):  
D. M. Haughton ◽  
R. W. Ogden
Keyword(s):  
Axial Force ◽  
Strain Energy ◽  
Elastic Strain Energy ◽  
Strain Energy Function ◽  
Angular Speed ◽  
Elastic Membrane ◽  
Axial Extension ◽  
End Conditions ◽  
Elastic Membranes ◽  
Realistic Choice

SummaryBifurcation from a finitely deformed circular cylindrical configuration of a rotating circular cylindrical elastic membrane is examined. It is found (for a physically realistic choice of elastic strain-energy function) that the angular speed attains a maximum followed by a minimum relative to the increasing radius of the cylinder for either a fixed axial extension or fixed axial force.At fixed axial extension (a) a prismatic mode of bifurcation (in which the cross-section of the cylinder becomes uniformly non-circular) may occur at a maximum of the angular speed provided the end conditions on the cylinder allow this; (b) axisyim-metric modes may occur before, at or after the angular speed maximum depending on the length of the cylinder and the magnitude of the axial extension; (c) an asymmetric or ‘wobble’ mode is always possible before either (a) or (b) as the angular speed increases from zero for any length of cylinder or axial extension. Moreover, ‘wobble’ occurs at lower angular speeds for longer cylinders.At fixed axial force the results are similar to (a), (b) and (c) except that an axisym-metric mode necessarily occurs between the turning points of the angular speed.

scholarly journals Variational modelling of nematic elastomer foundations

2018 ◽  
Vol 28 (14) ◽  
pp. 2863-2904
Author(s):  
Pierluigi Cesana ◽  
Andrés A. León Baldelli
Keyword(s):  
Liquid Crystal ◽  
Integral Functional ◽  
Elastic Membrane ◽  
Two Dimensional ◽  
Order Tensor ◽  
Asymptotic Regime ◽  
Liquid Crystal Elastomer ◽  
Energy Functionals ◽  
Shear Energy ◽  
Dimensional Integral

We compute the [Formula: see text]-limit of energy functionals describing mechanical systems composed of a thin nematic liquid crystal elastomer sustaining a homogeneous and isotropic elastic membrane. We work in the regime of infinitesimal displacements and model the orientation of the liquid crystal according to the order tensor theories of both Frank and De Gennes. We describe the asymptotic regime by analysing a family of functionals parametrised by the vanishing thickness of the membranes and the ratio of the elastic constants, establishing that, in the limit, the system is represented by a two-dimensional integral functional interpreted as a linear membrane on top of a nematic active foundation involving an effective De Gennes optic tensor which allows for low order states. The latter can suppress shear energy by formation of microstructure as well as act as a pre-strain transmitted by the foundation to the overlying film.

scholarly journals Surface energies emerging in a microscopic, two-dimensional two-well problem

2017 ◽  
Vol 147 (5) ◽  
pp. 1041-1089 ◽  
Author(s):  
Georgy Kitavtsev ◽  
Stephan Luckhaus ◽  
Angkana Rüland
Keyword(s):  
Surface Energy ◽  
Two Dimensional ◽  
Direct Control ◽  
First Order ◽  
Surface Energies ◽  
Energy Scaling ◽  
Continuous Analogue ◽  
Dimensional Shape ◽  
Set Up ◽  
Microscopic Modelling

In this paper we are interested in the microscopic modelling of a two-dimensional two-well problem that arises from the square-to-rectangular transformation in (two-dimensional) shape-memory materials. In this discrete set-up, we focus on the surface energy scaling regime and further analyse the Hamiltonian that was introduced by Kitavtsev et al. in 2015. It turns out that this class of Hamiltonians allows for a direct control of the discrete second-order gradients and for a one-sided comparison with a two-dimensional spin system. Using this and relying on the ideas of Conti and Schweizer, which were developed for a continuous analogue of the model under consideration, we derive a (first-order) continuum limit. This shows the emergence of surface energy in the form of a sharp-interface limiting model as well the explicit structure of the minimizers to the latter.

scholarly journals Development of Android-Based Appy Pie Learning Media on Mathematics in Elementary School

2020 ◽  
Vol 8 (2) ◽  
pp. 81
Author(s):  
Inas Sayyida Latifa ◽  
Aan Subhan Pamungkas ◽  
Trian Pamungkas Alamsyah ◽  
Indhira Asih Vivi Yandari
Keyword(s):  
Elementary School ◽  
3D Model ◽  
Fourth Grade ◽  
Average Score ◽  
Two Dimensional ◽  
Design And Development ◽  
Fourth Grade Students ◽  
Dimensional Shape ◽  
Expert Validation

This research aimed to develop Android-based Appy Pie learning media in mathematics subjects, especially two-dimensional shape material. Moreover, to determine the validity level of the android-based Appy Pie learning media developed and to determine the students' responses after using android-based Appy Pie learning media. This research uses the 3D model (define, design, and development) as the modification result of the 4D model by Thiagarajan. The subjects of this research were 45 fourth-grade students of SDN Rawu. The result of this research is the average score of media experts validation is 91.11% which included in the “very feasible” category, the average score of material expert validation is 98.33% which included in the “very feasible” category. The average score of the students response is 91.11% that included in the “very good” category, so it can be concluded that the Android-based Appy Pie learning media is feasible to use in the two-dimensional shape material of fourth-grade.

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