Search results for "rigidity"
showing 10 items of 83 documents
Spectral rigidity and invariant distributions on Anosov surfaces
2014
This article considers inverse problems on closed Riemannian surfaces whose geodesic flow is Anosov. We prove spectral rigidity for any Anosov surface and injectivity of the geodesic ray transform on solenoidal 2-tensors. We also establish surjectivity results for the adjoint of the geodesic ray transform on solenoidal tensors. The surjectivity results are of independent interest and imply the existence of many geometric invariant distributions on the unit sphere bundle. In particular, we show that on any Anosov surface $(M,g)$, given a smooth function $f$ on $M$ there is a distribution in the Sobolev space $H^{-1}(SM)$ that is invariant under the geodesic flow and whose projection to $M$ i…
Travelling Strings, Beams, Panels, Membranes and Plates
2013
In this chapter, we will introduce in a general manner some of the most common models for axially travelling materials, which will be used in the rest of the book. We will introduce the linear models of travelling strings, panels, and plates. It will be assumed that the material is thin, i.e. its planar dimensions are much larger than its thickness. We will work in the small displacement regime, that is, with linear models approximating the behaviour of the system near the trivial equilibrium. As is well known in the theory of elasticity, this approximation allows for a decoupling of the in-plane and out-of-plane components in the dynamics of the system. We will concentrate on small out-of-…
Geometric représentations of the braid groups
2010
We show that the morphisms from the braid group with n strands in the mapping class group of a surface with a possible non empty boundary, assuming that its genus is smaller or equal to n/2 are either cyclic morphisms (their images are cyclic groups), or transvections of monodromy morphisms (up to multiplication by an element in the centralizer of the image, the image of a standard generator of the braid group is a Dehn twist, and the images of two consecutive standard generators are two Dehn twists along two curves intersecting in one point). As a corollary, we determine the endomorphisms, the injective endomorphisms, the automorphisms and the outer automorphism group of the following grou…
Estimates for Divergence Velocities of Axially Moving Orthotropic Thin Plates
2014
Some models for axially moving orthotropic thin plates are investigated analytically via methods of complex analysis to derive estimates for critical plate velocities. Linearised Kirchhoff plate theory is used, and the energy forms of steady-state models are considered with homogeneous and inhomogeneous tension profiles in the cross direction of the plate. With the help of the energy forms, some limits for the divergence velocity of the plate are found analytically. In numerical examples, the derived lower limits for the divergence velocity are analysed for plates with small flexural rigidity. peerReviewed
Some conventional and unconventional educational column stability Problems
2006
Two interesting problems are considered for enriching the curriculum of the Strength of Materials course, in the light of recently developed functionally graded materials (FGMs), characterized with the smooth variation of the elastic modulus. These are problems associated with buckling of columns with variable flexural rigidity along the axis of the column. A simple semi-inverse method is proposed for determining closed-form solutions of axially inhomogeneous columns. In order for the presentation to be given in one package, the conventional problems are also recapitulated along with the novel ones. The main approach adopted here is the use of the second-order differential equation, instea…
Momentum-dependent interfacial tension in polymer solutions
2002
A model for the interface between a concentrated and a very dilute polymer solution is studied by Monte Carlo simulations at temperatures below the Theta temperature (in bad solvent conditions). The wave-number–dependent interfacial tension γ(q) is extracted from an analysis of the capillary wave amplitudes. It is shown that γ(q) decreases monotonically with q2, while no evidence is found for the predicted increase γ(q) ∝ κq2 with a positive bending rigidity κ of the interface at large q. Consequences for the interpretations of simulations and experiments on interfacial widths are briefly discussed.
Role of residual water hydrogen bonding in sugar/water/biomolecule systems: a possible explanation fortrehalose peculiarity
2007
We report on the set of experimental and simulative evidences which enabled us to suggest how biological structures embedded in a non-liquid water–saccharide solvent are anchored to the surrounding matrix via a hydrogen bond network. Such a network, whose rigidity increases by decreasing the sample water content, couples the degrees of freedom of the biostructure to those of the matrix and gives place to protein–saccharide–water structures (protein–solvent conformational substates). In particular, the whole set of data evidences that, while the protein–sugar interaction is well described in terms of a water entrapment hypothesis, the water replacement hypothesis better describes the sugar–m…
Double and triple calix[4]arenis connected via the oxygen functions
1990
New macrocyclic molecules are described containing two or three p-tert-butylcalix[4]arene subunits connected via their oxygen atoms. These macrocycles are available by two general methods which are capable of producing assemblies with bridges of varying rigidity and length.
Topology-Sensitive Microfluidic Filter for Polymers of Varying Stiffness
2017
The separation of polymers based on their size, rigidity, and topology is an essential but also highly challenging task for nanoscience and engineering. Using hybrid molecular dynamics simulations that correctly take into account hydrodynamics, we have designed microfluidic channels for separating linear from ring polymers in dilute solutions. We establish that the transport velocity of the polymers is independent of their topology and rigidity when the channel walls are smooth and repulsive. However, when the walls are decorated with attractive spots arranged on lines parallel to the flow, ring polymers exhibit an order of magnitude higher transport velocity compared to linear chains. The …
Elastic properties of polymer interfaces: Aggregation of pure diblock, mixed diblock, and triblock copolymers
2002
Block copolymers adsorbing to an interface between two immiscible homopolymers modify the elastic constants of this interface. Within self-consistent field calculations for Gaussian chains, we determine how the bending constants vary in dependence on the block copolymer concentration and architecture. Four phenomena are discussed. (i) When a tricritical or isotropic Lifshitz critical point is approached in a ternary mixture by varying the concentration of diblock copolymers or changing temperature, the elastic constants vanish. We determine the corresponding power laws, and show that the de Gennes--Taupin criterium for the stability of lamellar phases against undulations and the Ginzburg-La…