Laser induced surface deformations on silicon

Permanent deformations on silicon surfaces in the form of bubbles, resulting from pulsed laser irradiation with fluences well above the threshold for melting, are studied. The mechanism leading to deformations is discussed and a possibility to avoid them is demonstrated.     

Thermally induced deformations measured by shearography

In the present work, the thermo-mechanical behavior, temperature versus thermal deformation with respect to time, of different coating films were studied by a non-destructive technique (NDT) known as shearography. Organic coatings, i.e., Epoxy on metallic alloys, i.e., carbon steels, were investigated at a temperature range simulating the severe weather temperatures in Kuwait especially between the day-time and the night-time temperatures. The investigation focused on determining the in-plane displacement of the coatings, which amounts to the thermal deformation and stress with respect to temperature and time. Along with the experimental data, a mathematical relationship was derived describing the thermal deformation and stress of a coating film as a function of temperature. Furthermore, results of shearography indicate that the technique is a very useful NDT method not only for determining the thermo-mechanical behavior of different coatings but also can be used as a 2D microscope for monitoring the deformation of the coatings in real-time at a microscopic scale.     

Character twists

I present simple formulae for the determinants of laplacians acting on arbitrary flat vector bundles over hyperbolic Riemann surfaces. This has applications to non-chiral orbifolds, for non-abelian point groups and any twisted sector.     

String deformations induced by retardation effects in mesons

The rotating-string model is an effective model of mesons, in which the quark and the antiquark are linked by a straight string. We previously developed a method to estimate the retardation effects in this model, but the string was still kept straight. We now go a step further and show that this kind of retardation effects cause a small deviation of the string from the straight line. We first give general arguments constraining the string shape. Then, we find analytical and numerical solutions for the string deformation induced by retardation effects. We finally discuss the influence of the curved string on the energy spectrum of the model.     

Controlled decay of electrically induced deformations in nematic liquid crystals

The transient behavior of electrically induced deformations of parallel oriented nematic liquid crystal layers was investigated. The nematic material used was a mixture of disubstituted benzoyloxybenzoic acid esters the dielectric anisotropy of which is positive at dc and low frequencies, and changes sign in the kHz range. The decay time of a deformation induced by a low frequency field can be considerably reduced by switching the frequency to the range where the dielectric anisotropy is negative. This effect becomes even more pronounced for higher viscosities.     

Liberations and twists of real and complex spheres

We study the 10 noncommutative spheres obtained by liberating, twisting, and liberating +twisting the real and complex spheres $S_{\mathbb{R}}^{N-1},S_{\mathbb{C}}^{N-1}$. At the axiomatic level, we show that, under very strong axioms, these 10 spheres are the only ones. Our main results concern the computation of the quantum isometry groups of these 10 spheres, taken in an affine real/complex sense. We formulate as well a proposal for an extended formalism, comprising 18 spheres.     

Factorizing Drinfel'd twists and functional Bethe ansatz

A particular class of Drinfel'd twists is constructed for any finite-dimensional irreducible representation of the Yangian , by means of the functional Bethe ansatz technique for the XXX Heisenberg chain of arbitrary spins. These twists factorize the corresponding R-matrices in these representations, and induce a new basis of the space of states of the chain, particularly convenient for the computation of correlation functions.     

Giant deformations of a liquid-liquid interface induced by the optical radiation pressure

Because of the small momentum of photons, very intense fields are generally required to bend a liquid interface with the optical radiation pressure. We explore this issue in a near-critical phase-separated liquid mixture to vary continuously the meniscus softness by tuning the temperature. Low power continuous laser waves become sufficient to induce huge stationary bulges. Using the beam size to build an "optical" Bond number, Bo, we investigate the crossover from low to large Bo. The whole set of data collapses onto a single master curve which illustrates the universality of the phenomenon.     

Full chains of twists for orthogonal algebras

We show that for some Hopf subalgebras inU _F(so(M)) nontrivially deformed by a twistF it is possible to find the nonlinear primitive copies. This enlarges the possibilities to construct chains of twists. For orthogonal algebraU(so(M)) we present a method to compose the full chains with carrier space as large as the Borel subalgebraB(so(M)). These chains can be used to construct the new deformed Yangians. Presented at the 9-th Colloquium “Quantum Groups and Integrable Systems”, Prague, 22–24 June 2000. This work was partially supported by the Russian Foundation for Basic Research under the grant 00-01-00500 (VDL) and 98-01-00310 (PPK).     

Investigation of electric field induced elastic deformations of nematic liquid crystals by capacity measurements

An improved set-up is described which is universally applicable in electrooptic research work on liquid crystals. The main part of the test circuit consists of a highly stabilized and dc-free square wave generator with swept amplitude. An additional sine wave modulation with very good linearity up to high voltages allows capacity versus voltage measurements in a large frequency range. Measurements in the nematic phase of ap-disubstituted phenylcyclohexane (PCH) are reported as an example of the high performance of this set-up.     

Numerical study of deformations induced by ac electric field in insulating flexoelectric nematic layers

The influence of the frequency f of applied ac electric field on the time dependence of electric field induced deformations of homeotropic nematic layers is studied numerically. Three kinds of nematic liquid crystals were considered:

Electrically induced deformations of water–air and water–oil interfaces in relation with electrocoalescence

In connection with the phenomenon of electrocoalescence of water droplets in oil, the electrically induced deformations of some water–oil interfaces are studied. Such problems involve the strong coupling of hydrodynamics and electrostatics as well as the accurate tracking/capturing of the evolving interfaces. The paper presents a Finite–Element Arbitrary Lagrangian–Eulerian (FE–ALE) approach in deforming meshes to investigate the time-dependent deformation of the interface between highly conductive water and an insulating immiscible fluid. The developed numerical scheme is first tested and then used to solve two 2D axisymmetric EHD problems. Computed results are compared with predictions from asymptotic developments and with experimental measurements.     

Group deformations and relativity

A theory of deformation (homcomorphism but non-isomorphism) of topological groups is developed. In particular, a theory of deformation of subgroups structure is considered. The whole formalism is based on conceptions of holonomicity and relative geometry.A field is postulated to deform the symmetry group of a free physical system. It is shown that the classical fields deform the Poincare group. Thanks to this fact, gravitation appears as space-time curvature (non-holonomicity of the Lorentz subgroup mapping); and electromagnetism reveals itself by space-time torsion (non-holonomicity of the translation subgroup mapping). From physically evident premises it follows that space-time also has a torsion in the rotating and accelerated systems of reference.     

Four-dimensional heterotic string models with third-integral twists

The massless string states are constructed for a four-dimensional heterotic string model with the U(5) gauge group in the untwisted sector. The complete observable gauge group, quark and lepton generations, Higgs scalar structure, quark and lepton mass matrix, couplings to colour triplet scalars, and gauge symmetry breaking are studied for this model.     

4d fermionic superstrings with arbitrary twists

We present the rules for systematically constructing all consistent four-dimensional string theories, using free world-sheet fermions which pick up arbitrary phases when parallel transported around the string. These rules are necessary and sufficient for multi-loop modular invariance. They lead to theories with general Z_N (GSO-type) projections, whose merits for model-building we discuss. We classify all boundary conditions yielding massless space-time spinors. We show that, in contrast to the case of only real 2d fermions, all possible realizations of world-sheet supersymmetry are now allowed. This opens the way for the construction of a new class of supersymmetric string models.