scholarly journals A Study on a Generalized Relaxed Curvature Energy Action

2018 ◽  
Vol 22 (Özel) ◽  
pp. 541
Author(s):  
Gözde ÖZKAN TÜKEL ◽  
Ahmet YÜCESAN
Keyword(s):  
Curvature Energy

On the Curvature Energy of Cartesian Surfaces

2021 ◽  
Author(s):  
Domenico Mucci
Keyword(s):  
Curvature Energy

Grain-oriented segmentation of images of porous structures using ray casting and curvature energy minimization

2014 ◽  
Vol 257 (2) ◽  
pp. 92-103
Author(s):  
H.-G. LEE ◽  
M.-K. CHOI ◽  
S.-C. LEE
Keyword(s):  
Energy Minimization ◽  
Ray Casting ◽  
Porous Structures ◽  
Curvature Energy ◽  
Segmentation Of Images

Leptodermous expansion of nuclear ground state energies and the anomaly in the nuclear curvature energy

Pramana ◽  
1994 ◽  
Vol 42 (2) ◽  
pp. 107-122
Author(s):  
S K Kataria ◽  
Aruna Nijasure ◽  
V S Ramamurthy ◽  
A K Dutta
Keyword(s):  
Ground State ◽  
Nuclear Ground State ◽  
Curvature Energy ◽  
Ground State Energies

scholarly journals Robust 1-bit compressed sensing via hinge loss minimization

2019 ◽  
Vol 9 (2) ◽  
pp. 361-422
Author(s):  
Martin Genzel ◽  
Alexander Stollenwerk
Keyword(s):  
Loss Function ◽  
Piecewise Linear ◽  
Single Point ◽  
Ground Truth ◽  
Risk Minimization ◽  
Strongly Convex ◽  
Hinge Loss ◽  
Curvature Energy ◽  
Locally Strongly Convex ◽  
Recovery Approach

Abstract This work theoretically studies the problem of estimating a structured high-dimensional signal $\boldsymbol{x}_0 \in{\mathbb{R}}^n$ from noisy $1$-bit Gaussian measurements. Our recovery approach is based on a simple convex program which uses the hinge loss function as data fidelity term. While such a risk minimization strategy is very natural to learn binary output models, such as in classification, its capacity to estimate a specific signal vector is largely unexplored. A major difficulty is that the hinge loss is just piecewise linear, so that its ‘curvature energy’ is concentrated in a single point. This is substantially different from other popular loss functions considered in signal estimation, e.g. the square or logistic loss, which are at least locally strongly convex. It is therefore somewhat unexpected that we can still prove very similar types of recovery guarantees for the hinge loss estimator, even in the presence of strong noise. More specifically, our non-asymptotic error bounds show that stable and robust reconstruction of $\boldsymbol{x}_0$ can be achieved with the optimal oversampling rate $O(m^{-1/2})$ in terms of the number of measurements $m$. Moreover, we permit a wide class of structural assumptions on the ground truth signal, in the sense that $\boldsymbol{x}_0$ can belong to an arbitrary bounded convex set $K \subset{\mathbb{R}}^n$. The proofs of our main results rely on some recent advances in statistical learning theory due to Mendelson. In particular, we invoke an adapted version of Mendelson’s small ball method that allows us to establish a quadratic lower bound on the error of the first-order Taylor approximation of the empirical hinge loss function.

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.

VESICLE TO MICELLE TRANSITION DRIVEN BY SURFACE SOLID-FLUID TRANSITION

2002 ◽  
Vol 16 (01n02) ◽  
pp. 375-382 ◽  
Author(s):  
JANAKY NARAYANAN ◽  
E. MENDES ◽  
C. MANOHAR
Keyword(s):  
Small Angle ◽  
Fluorescence Anisotropy ◽  
Small Angle Neutron Scattering ◽  
Unique Feature ◽  
Ion Pair ◽  
Single Chain ◽  
Double Chain ◽  
Micellar Phase ◽  
Curvature Energy ◽  
Oppositely Charged

This paper reviews the solution behavior of cetyltrimethylammonium hydroxynaphthalene carboxylate (CTAHNC), which has the unique feature of undergoing a transition from vesicle to worm-like micellar phase in three different ways, namely, increase in temperature, addition of a surfactant and on shearing. Fluorescence anisotropy, NMR, rheology, small angle neutron scattering studies etc gave evidence of the vesicle-micelle transition. CTAHNC can be looked upon as a complex formed by two oppositely charged surfactants (CTA+ and HNC-). This ion pair effectively acts as a double-chain lipid and has a tendency to form vesicles. On increasing the temperature, and/or adding single chain surfactants of shearing, the complex dissociates which changes the curvature energy of the surface. This leads to a 'surface melting' that brings forth the vesicle-micelle transition.

scholarly journals Minimal surfaces bounded by elastic lines

2012 ◽  
Vol 468 (2143) ◽  
pp. 1851-1864 ◽  
Author(s):  
L. Giomi ◽  
L. Mahadevan
Keyword(s):  
Materials Science ◽  
Soap Film ◽  
Boundary Curve ◽  
Plateau Problem ◽  
Rigid Boundary ◽  
Elastic Line ◽  
Physical Experiments ◽  
Curvature Energy ◽  
Total Squared Curvature ◽  
And Mathematics

In mathematics, the classical Plateau problem consists of finding the surface of least area that spans a given rigid boundary curve. A physical realization of the problem is obtained by dipping a stiff wire frame of some given shape in soapy water and then removing it; the shape of the spanning soap film is a solution to the Plateau problem. But what happens if a soap film spans a loop of inextensible but flexible wire? We consider this simple query that couples Plateau's problem to Euler's Elastica : a special class of twist-free curves of given length that minimize their total squared curvature energy. The natural marriage of two of the oldest geometrical problems linking physics and mathematics leads to a quest for the shape of a minimal surface bounded by an elastic line: the Euler–Plateau problem. We use a combination of simple physical experiments with soap films that span soft filaments and asymptotic analysis combined with numerical simulations to explore some of the richness of the shapes that result. Our study raises questions of intrinsic interest in geometry and its natural links to a range of disciplines, including materials science, polymer physics, architecture and even art.

scholarly journals Fast Simulation of Lipid Vesicle Deformation Using Spherical Harmonic Approximation

2016 ◽  
Vol 21 (1) ◽  
pp. 40-64
Author(s):  
Michael Mikucki ◽  
Yongcheng Zhou
Keyword(s):  
Harmonic Functions ◽  
Degrees Of Freedom ◽  
Finite Difference Methods ◽  
Harmonic Approximation ◽  
Lipid Vesicles ◽  
Membrane Curvature ◽  
Lipid Vesicle ◽  
Nonlinear Conjugate Gradient Method ◽  
Surface Harmonic ◽  
Curvature Energy

AbstractLipid vesicles appear ubiquitously in biological systems. Understanding how the mechanical and intermolecular interactions deform vesicle membranes is a fundamental question in biophysics. In this article we develop a fast algorithm to compute the surface configurations of lipid vesicles by introducing surface harmonic functions to approximate themembrane surface. This parameterization allows an analytical computation of the membrane curvature energy and its gradient for the efficient minimization of the curvature energy using a nonlinear conjugate gradient method. Our approach drastically reduces the degrees of freedom for approximating the membrane surfaces compared to the previously developed finite element and finite difference methods. Vesicle deformations with a reduced volume larger than 0.65 can be well approximated by using as small as 49 surface harmonic functions. The method thus has a great potential to reduce the computational expense of tracking multiple vesicles which deform for their interaction with external fields.

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