scholarly journals Numerical Study of Membrane Configurations

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Luka Mesarec ◽  
Miha Fošnarič ◽  
Samo Penič ◽  
Veronika Kralj Iglič ◽  
Samo Kralj ◽  
...  
Keyword(s):  
Numerical Study ◽  
Thin Sheet ◽  
Topological Defects ◽  
Spontaneous Curvature ◽  
Minimal Models ◽  
Nematic Ordering ◽  
Curvature Energy ◽  
Spherical Topology ◽  
Numerical Minimization ◽  
Orientational Ordering

We studied biological membranes of spherical topology within the framework of the spontaneous curvature model. Both Monte Carlo simulations and the numerical minimization of the curvature energy were used to obtain the shapes of the vesicles. The shapes of the vesicles and their energy were calculated for different values of the reduced volume. The vesicles which exhibit in-plane ordering were also studied. Minimal models have been developed in order to study the orientational ordering in colloids coated with a thin sheet of nematic liquid crystal (nematic shells). The topological defects are always present on the surfaces with the topology of a sphere. The location of the topological defects depends strongly on the curvature of the surface. We studied the nematic ordering and the formation of topological defects on vesicles obtained by the minimization of the spontaneous curvature energy.

scholarly journals Defects and perturbation

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Enrico M. Brehm
Keyword(s):  
Entanglement Entropy ◽  
Topological Defects ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Conformal Field

Abstract We investigate perturbatively tractable deformations of topological defects in two-dimensional conformal field theories. We perturbatively compute the change in the g-factor, the reflectivity, and the entanglement entropy of the conformal defect at the end of these short RG flows. We also give instances of such flows in the diagonal Virasoro and Super-Virasoro Minimal Models.

CRYO-Tem Measurements of Membrane Elasticity in Equilibrium Vesicle Systems: Two Distinct Mechanisms of Stability

2000 ◽  
Vol 6 (S2) ◽  
pp. 848-849
Author(s):  
B. Coldren ◽  
H.T. Jung ◽  
J. Zasadzinski
Keyword(s):  
Lipid Bilayers ◽  
Spontaneous Curvature ◽  
Aqueous Mixtures ◽  
Membrane Elasticity ◽  
Theoretical Concepts ◽  
Curvature Energy ◽  
Nanomaterials Synthesis ◽  
Equilibrium Phases ◽  
Image Position ◽  
New Applications

Aqueous mixtures of oppositely charged surfactants spontaneously form equilibrium phases of unilamellar vesicles.1 The wide variety of surfactants that display this behavior allows control over vesicle charge, size, and polydispersity. This may be useful for new applications in drug delivery, nanomaterials synthesis, and as tests of theoretical concepts of membrane organization and interactions.A subtle competition between the entropy of mixing and the elastic properties of surfactant and lipid bilayers determines their phase behavior and morphology. The curvature energy per unit area of bilayer, fc, iswhere R1 and R2 are the principle radii of curvature, K is the curvature modulus, and is the saddle-splay modulus. The spontaneous curvature, l/ro, is nonzero only if there is asymmetry between the two sides of the bilayer.

scholarly journals Nematic topological defects positionally controlled by geometry and external fields

2018 ◽  
Vol 9 ◽  
pp. 109-118 ◽  
Author(s):  
Pavlo Kurioz ◽  
Marko Kralj ◽  
Bryce S Murray ◽  
Charles Rosenblatt ◽  
Samo Kralj
Keyword(s):  
Electric Field ◽  
Topological Charge ◽  
Order Parameter ◽  
Topological Defects ◽  
Two Dimensional ◽  
External Fields ◽  
Nematic Ordering ◽  
Spatial Positioning ◽  
A Charge ◽  
The Impact

Using a Landau–de Gennes approach, we study the impact of confinement topology, geometry and external fields on the spatial positioning of nematic topological defects (TDs). In quasi two-dimensional systems we demonstrate that a confinement-enforced total topological charge of m > 1/2 decays into elementary TDs bearing a charge of m = 1/2. These assemble close to the bounding substrate to enable essentially bulk-like uniform nematic ordering in the central part of a system. This effect is reminiscent of the Faraday cavity phenomenon in electrostatics. We observe that in certain confinement geometries, varying the correlation length size of the order parameter could trigger a global rotation of an assembly of TDs. Finally, we show that an external electric field could be used to drag the boojum fingertip towards the interior of the confinement cell. Assemblies of TDs could be exploited as traps for appropriate nanoparticles, opening several opportunities for the development of functional nanodevices.

scholarly journals Local sensitivity analysis of the ‘Membrane shape equation’ derived from the Helfrich energy

2020 ◽  
Author(s):  
P. Rangamani ◽  
A. Behzadan ◽  
M. Holst
Keyword(s):  
Differential Equations ◽  
Lipid Bilayers ◽  
Numerical Study ◽  
Membrane Vesicles ◽  
Energy Functional ◽  
Specific Model ◽  
Model Systems ◽  
Spontaneous Curvature ◽  
Membrane Mechanics ◽  
Curvature Term

AbstractThe Helfrich energy is commonly used to model the elastic bending energy of lipid bilayers in membrane mechanics. The governing differential equations for certain geometric characteristics of the shape of the membrane can be obtained by applying variational methods (minimization principles) to the Helfrich energy functional and are well-studied in the axisymmetric framework. However, the Helfrich energy functional and the resulting differential equations involve a number of parameters, and there is little explanation of the choice of parameters in the literature, particularly with respect to the choice of the “spontaneous curvature” term that appears in the functional. In this paper, we present a careful analytical and numerical study of certain aspects of parametric sensitivity of Helfrich’s model. Using simulations of specific model systems, we demonstrate the application of our scheme to the formation of spherical buds and pearled shapes in membrane vesicles.

scholarly journals Local sensitivity analysis of the “membrane shape equation” derived from the Helfrich energy

2020 ◽  
pp. 108128652095388
Author(s):  
P Rangamani ◽  
A Behzadan ◽  
M Holst
Keyword(s):  
Differential Equations ◽  
Lipid Bilayers ◽  
Numerical Study ◽  
Membrane Vesicles ◽  
Energy Functional ◽  
Specific Model ◽  
Model Systems ◽  
Spontaneous Curvature ◽  
Membrane Mechanics ◽  
Curvature Term

The Helfrich energy is commonly used to model the elastic bending energy of lipid bilayers in membrane mechanics. The governing differential equations for certain geometric characteristics of the shape of the membrane can be obtained by applying variational methods (minimization principles) to the Helfrich energy functional and are well studied in the axisymmetric framework. However, the Helfrich energy functional and the resulting differential equations involve a number of parameters, and there is little explanation of the choice of parameters in the literature, particularly with respect to the choice of the “spontaneous curvature” term that appears in the functional. In this paper, we present a careful analytical and numerical study of certain aspects of parametric sensitivity of Helfrich’s model. Using simulations of specific model systems, we demonstrate the application of our scheme to the formation of spherical buds and pearled shapes in membrane vesicles.

scholarly journals Symmetry breaking and structure of a mixture of nematic liquid crystals and anisotropic nanoparticles

2010 ◽  
Vol 6 ◽  
Author(s):  
Marjan Krasna ◽  
Matej Cvetko ◽  
Milan Ambrožič
Keyword(s):  
Random Fields ◽  
Short Range ◽  
Liquid Crystalline ◽  
Short Range Order ◽  
Isotropic Phase ◽  
Nematic Ordering ◽  
Domain Type ◽  
Elastic Forces ◽  
Orientational Ordering ◽  
The Impact

Orientational ordering of a homogeneous mixture of uniaxial liquid crystalline (LC) molecules and magnetic nanoparticles (NPs) is studied using the Lebwohl–Lasher lattice model. We consider cases where NPs tend to be oriented perpendicularly to LC molecules due to elastic forces. We study domain-type configurations of ensembles, which are quenched from the isotropic phase. We show that for large enough concentrations of NPs the long range uniaxial nematic ordering is replaced by short range order exhibiting strong biaxiality. This suggests that the impact of NPs on orientational ordering of LCs for appropriate concentrations of NPs is reminiscent to the influence of quenched random fields which locally enforce a biaxial ordering.

An Experimental and Numerical Study of Dieless Water Jet Incremental Microforming

2019 ◽  
Vol 141 (4) ◽  
Author(s):  
Yi Shi ◽  
Weizhao Zhang ◽  
Jian Cao ◽  
Kornel F. Ehmann
Keyword(s):  
Numerical Model ◽  
Sheet Metal ◽  
Process Parameters ◽  
High Speed ◽  
Tool Path ◽  
Numerical Study ◽  
Single Point ◽  
Thin Sheet ◽  
Water Jet ◽  
Truncated Cone

Conventional single-point incremental forming (SPIF) is already in use for small batch prototyping and fabrication of customized parts from thin sheet metal blanks by inducing plastic deformation with a rigid round-tip tool. The major advantages of the SPIF process are its high flexibility and die-free nature. In lieu of employing a rigid tool to incrementally form the sheet metal, a high-speed water jet as an alternative was proposed as the forming tool. Since there is no tool-workpiece contact in this process, unlike in the traditional SPIF process, no lubricant and rotational motion of the tool are required to reduce friction. However, the geometry of the part formed by water jet incremental microforming (WJIMF) will no longer be controlled by the motion of the rigid tool. On the contrary, process parameters such as water jet pressure, stage motion speed, water jet diameter, blank thickness, and tool path design will determine the final shape of the workpiece. This paper experimentally studies the influence of the above-mentioned key process parameters on the geometry of a truncated cone shape and on the corresponding surface quality. A numerical model is proposed to predict the shape of the truncated cone part after WJIMF with given input process parameters. The results prove that the formed part's geometric properties predicted by the numerical model are in excellent agreement with the actually measured ones. Arrays of miniature dots, channels, two-level truncated cones, and letters were also successfully fabricated on stainless-steel foils to demonstrate WJIMF capabilities.

scholarly journals Fusion of interfaces in Landau-Ginzburg models: a functorial approach

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Nicolas Behr ◽  
Stefan Fredenhagen
Keyword(s):  
Topological Defects ◽  
Polynomial Rings ◽  
Two Dimensional ◽  
Minimal Models ◽  
Actual Computation ◽  
Category Of Modules ◽  
Chiral Superfields ◽  
Functorial Approach

Abstract We investigate the fusion of B-type interfaces in two-dimensional supersymmetric Landau-Ginzburg models. In particular, we propose to describe the fusion of an interface in terms of a fusion functor that acts on the category of modules of the underlying polynomial rings of chiral superfields. This uplift of a functor on the category of matrix factorisations simplifies the actual computation of interface fusion. Besides a brief discussion of minimal models, we illustrate the power of this approach in the SU(3)/U(2) Kazama-Suzuki model where we find fusion functors for a set of elementary topological defects from which all rational B-type topological defects can be generated.

scholarly journals Defect dynamics in active nematics

2014 ◽  
Vol 372 (2029) ◽  
pp. 20130365 ◽  
Author(s):  
Luca Giomi ◽  
Mark J Bowick ◽  
Prashant Mishra ◽  
Rastko Sknepnek ◽  
M Cristina Marchetti
Keyword(s):  
Liquid Crystals ◽  
Numerical Study ◽  
Nematic Liquid Crystals ◽  
Topological Defects ◽  
Global Structure ◽  
Viscoelastic Behaviour ◽  
Global Changes ◽  
Local Sources ◽  
Orientational Structure ◽  
Local Deformations

Topological defects are distinctive signatures of liquid crystals. They profoundly affect the viscoelastic behaviour of the fluid by constraining the orientational structure in a way that inevitably requires global changes not achievable with any set of local deformations. In active nematic liquid crystals, topological defects not only dictate the global structure of the director, but also act as local sources of motion, behaving as self-propelled particles. In this article, we present a detailed analytical and numerical study of the mechanics of topological defects in active nematic liquid crystals.

scholarly journals Lipid membrane-mediated attraction between curvature inducing objects

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
Casper van der Wel ◽  
Afshin Vahid ◽  
Anđela Šarić ◽  
Timon Idema ◽  
Doris Heinrich ◽  
...  
Keyword(s):  
Colloidal Particles ◽  
Lipid Membrane ◽  
Numerical Study ◽  
Particle Diameter ◽  
Interaction Force ◽  
Membrane Curvature ◽  
Coarse Grained ◽  
Cellular Transport ◽  
Curvature Energy ◽  
Membrane Deformations

Abstract The interplay of membrane proteins is vital for many biological processes, such as cellular transport, cell division, and signal transduction between nerve cells. Theoretical considerations have led to the idea that the membrane itself mediates protein self-organization in these processes through minimization of membrane curvature energy. Here, we present a combined experimental and numerical study in which we quantify these interactions directly for the first time. In our experimental model system we control the deformation of a lipid membrane by adhering colloidal particles. Using confocal microscopy, we establish that these membrane deformations cause an attractive interaction force leading to reversible binding. The attraction extends over 2.5 times the particle diameter and has a strength of three times the thermal energy (−3.3 kBT). Coarse-grained Monte-Carlo simulations of the system are in excellent agreement with the experimental results and prove that the measured interaction is independent of length scale. Our combined experimental and numerical results reveal membrane curvature as a common physical origin for interactions between any membrane-deforming objects, from nanometre-sized proteins to micrometre-sized particles.

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