The Works of Bronisław Knaster (1893–1980) in Continuum Theory

1997 ◽  
pp. 63-78
Author(s):  
Janusz J. Charatonik
Keyword(s):  
Continuum Theory

Freeze fracture imaging and computer simulation of liposome structure: Membrane geometry and defects

1983 ◽  
Vol 41 ◽  
pp. 646-647
Author(s):  
Joseph A. Zasadzinski
Keyword(s):  
Liquid Crystalline ◽  
Freeze Fracture ◽  
Continuum Theory ◽  
Closed Surfaces ◽  
Straight Line ◽  
Low Weight ◽  
Concentric Spheres ◽  
Membrane Geometry ◽  
Dupin Cyclides ◽  
Limiting Case

At low weight fractions, many surfactant and biological amphiphiles form dispersions of lamellar liquid crystalline liposomes in water. Amphiphile molecules tend to align themselves in parallel bilayers which are free to bend. Bilayers must form closed surfaces to separate hydrophobic and hydrophilic domains completely. Continuum theory of liquid crystals requires that the constant spacing of bilayer surfaces be maintained except at singularities of no more than line extent. Maxwell demonstrated that only two types of closed surfaces can satisfy this constraint: concentric spheres and Dupin cyclides. Dupin cyclides (Figure 1) are parallel closed surfaces which have a conjugate ellipse (r1) and hyperbola (r2) as singularities in the bilayer spacing. Any straight line drawn from a point on the ellipse to a point on the hyperbola is normal to every surface it intersects (broken lines in Figure 1). A simple example, and limiting case, is a family of concentric tori (Figure 1b).To distinguish between the allowable arrangements, freeze fracture TEM micrographs of representative biological (L-α phosphotidylcholine: L-α PC) and surfactant (sodium heptylnonyl benzenesulfonate: SHBS)liposomes are compared to mathematically derived sections of Dupin cyclides and concentric spheres.

The need of electron microscopy in the study of domains and domain walls in ferroelectrics

1994 ◽  
Vol 52 ◽  
pp. 550-551
Author(s):  
Wenwu Cao
Keyword(s):  
Domain Wall ◽  
Domain Walls ◽  
High Mobility ◽  
Continuum Theory ◽  
Polarization Vector ◽  
Ferroelectric Materials ◽  
Dielectric Constants ◽  
Nonlocal Coupling ◽  
Cubic Symmetry ◽  
Gradient Energy

Domain structures play a key role in determining the physical properties of ferroelectric materials. The formation of these ferroelectric domains and domain walls are determined by the intrinsic nonlinearity and the nonlocal coupling of the polarization. Analogous to soliton excitations, domain walls can have high mobility when the domain wall energy is high. The domain wall can be describes by a continuum theory owning to the long range nature of the dipole-dipole interactions in ferroelectrics. The simplest form for the Landau energy is the so called ϕ model which can be used to describe a second order phase transition from a cubic prototype,where Pi (i =1, 2, 3) are the components of polarization vector, α's are the linear and nonlinear dielectric constants. In order to take into account the nonlocal coupling, a gradient energy should be included, for cubic symmetry the gradient energy is given by,

scholarly journals Eigenvalue spectrum and scaling dimension of lattice $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Georg Bergner ◽  
David Schaich
Keyword(s):  
Anomalous Dimension ◽  
Finite Lattice ◽  
Continuum Theory ◽  
Lattice Volume ◽  
Yang Mills ◽  
Lattice Regularization ◽  
Perturbative Renormalization ◽  
Zero Values ◽  
Definition Of ◽  
Group Flow

Abstract We investigate the lattice regularization of $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory, by stochastically computing the eigenvalue mode number of the fermion operator. This provides important insight into the non-perturbative renormalization group flow of the lattice theory, through the definition of a scale-dependent effective mass anomalous dimension. While this anomalous dimension is expected to vanish in the conformal continuum theory, the finite lattice volume and lattice spacing generically lead to non-zero values, which we use to study the approach to the continuum limit. Our numerical results, comparing multiple lattice volumes, ’t Hooft couplings, and numbers of colors, confirm convergence towards the expected continuum result, while quantifying the increasing significance of lattice artifacts at larger couplings.

scholarly journals New insights on homogenization for hexagonal-shaped composites as Cosserat continua

Meccanica ◽  
2021 ◽  
Author(s):  
Marco Colatosti ◽  
Nicholas Fantuzzi ◽  
Patrizia Trovalusci ◽  
Renato Masiani
Keyword(s):  
Continuum Theory ◽  
Representative Elementary Volume ◽  
Elementary Volume ◽  
Displacement Fields ◽  
Micropolar Continuum ◽  
Rigid Particles ◽  
Hexagonal Shape ◽  
Classical Models ◽  
Elastic Interfaces ◽  
Cosserat Continua

AbstractIn this work, particle composite materials with different kind of microstructures are analyzed. Such materials are described as made of rigid particles and elastic interfaces. Rigid particles of arbitrary hexagonal shape are considered and their geometry is described by a limited set of parameters. Three different textures are analyzed and static analyses are performed for a comparison among the solutions of discrete, micropolar (Cosserat) and classical models. In particular, the displacements of the discrete model are compared to the displacement fields of equivalent micropolar and classical continua realized through a homogenization technique, starting from the representative elementary volume detected with a numeric approach. The performed analyses show the effectiveness of adopting the micropolar continuum theory for describing such materials.

scholarly journals Complementary vasoactivity and matrix remodelling in arterial adaptations to altered flow and pressure

2008 ◽  
Vol 6 (32) ◽  
pp. 293-306 ◽  
Author(s):  
A Valentín ◽  
L Cardamone ◽  
S Baek ◽  
J.D Humphrey
Keyword(s):  
Smooth Muscle ◽  
Continuum Theory ◽  
Muscle Contractility ◽  
Smooth Muscle Contractility ◽  
Rates Of Change ◽  
Biomechanical Loading ◽  
Smooth Muscle Proliferation ◽  
And Function ◽  
Diverse Data ◽  
Induced Changes

Arteries exhibit a remarkable ability to adapt to sustained alterations in biomechanical loading, probably via mechanisms that are similarly involved in many arterial pathologies and responses to treatment. Of particular note, diverse data suggest that cell and matrix turnover within vasoaltered states enables arteries to adapt to sustained changes in blood flow and pressure. The goal herein is to show explicitly how altered smooth muscle contractility and matrix growth and remodelling work together to adapt the geometry, structure, stiffness and function of a representative basilar artery. Towards this end, we employ a continuum theory of constrained mixtures to model evolving changes in the wall, which depend on both wall shear stress-induced changes in vasoactive molecules (which alter smooth muscle proliferation and synthesis of matrix) and intramural stress-induced changes in growth factors (which alter cell and matrix turnover). Simulations show, for example, that such considerations help explain the different rates of experimentally observed adaptations to increased versus decreased flows as well as differences in rates of change in response to increased flows or pressures.

A Continuum Theory of Superfluid Turbulence based on Extended Thermodynamics

2009 ◽  
Vol 34 (3) ◽  
Author(s):  
Lucia Ardizzone ◽  
Giuseppa Gaeta ◽  
Maria Stella Mongiovì
Keyword(s):  
Continuum Theory ◽  
Extended Thermodynamics ◽  
Superfluid Turbulence

scholarly journals Instabilities, defects, and defect ordering in an overdamped active nematic

Soft Matter ◽  
2016 ◽  
Vol 12 (17) ◽  
pp. 3854-3859 ◽  
Author(s):  
Elias Putzig ◽  
Gabriel S. Redner ◽  
Arvind Baskaran ◽  
Aparna Baskaran
Keyword(s):  
Liquid Crystal ◽  
Nematic Liquid Crystal ◽  
Continuum Theory

We consider a phenomenological continuum theory for an extensile, overdamped active nematic liquid crystal, applicable in the dense regime.

Confirming the continuum theory of dynamic brittle fracture for fast cracks

Nature ◽  
10.1038/16891 ◽  
1999 ◽  
Vol 397 (6717) ◽  
pp. 333-335 ◽  
Author(s):  
Eran Sharon ◽  
Jay Fineberg
Keyword(s):  
Brittle Fracture ◽  
Continuum Theory ◽  
Dynamic Brittle Fracture ◽  
The Continuum

MAGNETOSTATIC MODES IN NANOMETER-SIZED FERROMAGNETIC AND ANTIFERROMAGNETIC TUBES

2007 ◽  
Vol 14 (03) ◽  
pp. 471-480 ◽  
Author(s):  
T. K. DAS ◽  
M. G. COTTAM
Keyword(s):  
Magnetic Field ◽  
Spin Dynamics ◽  
Continuum Theory ◽  
Inelastic Light Scattering ◽  
Dipole Interactions ◽  
Large Length ◽  
Magnetostatic Modes ◽  
Magnetostatic Spin Waves ◽  
Macroscopic Continuum ◽  
Cylindrical Axis

A theory is presented for the magnetostatic modes in ferromagnetic and antiferromagnetic nanotubes, which have a large length-to-radius aspect ratio and an external magnetic field parallel to the cylindrical axis. The surface and bulk magnetic excitations (or magnetostatic spin waves) are studied for cases where the dipole–dipole interactions are dominant in the spin dynamics. This situation can be realized at sufficiently small wavevectors by inelastic light scattering or magnetic resonance techniques. A macroscopic continuum theory is developed, using the magnetostatic form of Maxwell's equations and the electromagnetic boundary conditions, and the characteristic equations (or dispersion relations) are deduced for the magnetostatic modes. Numerical calculations are presented for ferromagnetic and antiferromagnetic nanostructures, taking Ni 80 Fe 20 and MnF 2, respectively. The spatial variations of the mode amplitudes are also investigated.

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