Related papers: Liquid crystals and their defects
These notes are connected to a "potpourri" topics class and deal with some special cases of norms of various objects which arise in classical analysis.
Some problems of testology are discussed.
In the calculation of the formation enthalpy of a defect, a stress term accompanying the formation volume of the defect appears. This formation volume is conventionally interpreted as the difference in volume between crystals with and…
Recently, it was shown that a theoretical description of nucleation based on fluctuating hydrodynamics and classical density functional theory can be used to determine non-classical nucleation pathways for crystallization (Lutsko, Sci. Adv.…
These are the notes from my courses on the arithmetic of quadratic forms.
Using numerical and analytical calculations we study the structure of vacancies and interstitials in two-dimensional colloidal crystals. In particular, we compare the displacement fields of the defect obtained numerically with the…
These informal notes deal with some basic properties of metric spaces, especially concerning lengths of curves.
These are the lecture notes for an introductory course on black holes and some aspects of their interaction with the classical and quantum world. The focus is on phenomena of "fundamental physics" in the immediate surroundings of the black…
We give a brief overview on the successes and theoretical problems of the Standard Model and discuss the basics of low-scale supersymmetry. We also address some of recent proposals for physics beyond the Standard Model and the connection to…
This is a short review about liquid-vapor and crystalline phase transitions in continuum and lattice Widom-Rowlinson models.
We investigate a one-dimensional model describing the motion of liquid drops sliding down an inclined plane (the so-called quasi-static approximation model). We prove existence and uniqueness of a solution and investigate its long time…
Oscillations of atomic nuclei in crystals are considered in this paper. It is shown that elastic nuclei oscillations relatively electron envelops (inherent, I-oscillations) and waves of such oscillations can exist in crystals at adiabatic…
Smectic liquid crystals are materials formed by stacking deformable, fluid layers. Though smectics prefer to have flat, uniformly-spaced layers, boundary conditions can impose curvature on the layers. Since the layer spacing and curvature…
We present nonlinear dynamic equations for nematic and smectic $A$ liquid crystals in the presence of an alternating electric field and explain their derivation in detail. The local electric field acting in any liquid-crystalline system is…
Intriguing analogies were found between a model of plastic deformation in crystals and turbulence in fluids. A study of this model provides remarkable explanations of known experiments and predicts fractal dislocation pattern formation.…
These are some informal notes concerning topological vector spaces, with a brief overview of background material and basic notions, and emphasis on examples related to classical analysis.
The exchange of mass, momentum and energy between a membrane of liquid crystal and its surroundings of stokesian fluids is added to the dynamic equations of membranes which were deduced from the Ericksen-Leslie's theory of liquid crystals…
Point defects are ubiquitous in two dimensional crystals and play a fundamental role in determining their mechanical and thermodynamical properties. When crystals are formed on a curved background, finite length grain boundaries (scars) are…
Recent calculations indicate that in the outer parts of neutron stars nuclei are rod-like or slab-like, rather than roughly spherical. We consider the elastic properties of these phases, and argue that they behave as liquid crystals, rather…
After a brief review of the historical development and CLASSICAL properties of the BLACK HOLES, we discuss how our present knowledge of some of their QUANTUM properties shed light on the very concept of ELEMENTARY PARTICLE. As an…