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The paper deals with the controversial charge and spin self-organization phenomena in the HTSC cuprates, of which neutron, X-ray, STM and ARPES experiments give complementary, sometimes apparently contradictory glimpses. The examination has…
We amplify previous arguments why mean curvature should be used as measure of integration in calculating the effective bending rigidity of fluid membranes subjected to a weak background curvature. The stiffening of the membrane by its…
In large deformations, internally pressurised elastic spherical shells and tubes may undergo a limit-point, or inflation, instability manifested by a rapid transition in which their radii suddenly increase. The possible existence of such an…
We investigate locality of the supercritical regime for Bernoulli percolation on transitive graphs with polynomial growth, by which we mean the following. Take a transitive graph of polynomial growth $\mathscr{G}$ satisfying…
In arXiv:1202.0691, Geloni et al. criticise our recent work describing the spontaneous emission by a relativistic, undulating electron beam. In particular they claim that our prediction of a quantum regime in which evolution of the electron…
Performing Monte Carlo simulations we study the temperature dependent self--organization of magnetic moments coupled to itinerant electrons in a finite--size one--dimensional nanostructure proximitized to a superconducting reservoir. At low…
In this dissertation we study the tractability of the information-based complexity $n(\varepsilon,d)$ for $d$-variate function approximation problems. In the deterministic setting for many unweighted problems the curse of dimensionality…
We investigate the emergence of chiral meso-structures in one-dimensional fluids consisting of stacked discotic particles and demonstrate that helical undulations are generated spontaneously from internal elastic stresses. The stability of…
The rheological properties of biological tissues are core to processes such as cancer metastasis, wound healing and embryo development. The emergence of tissue and organ structures during morphogenesis requires the precise formation of…
In 1993 Mahadevan and Keller used the Kirchhoff rod theory to predict the shape of a M\"obius band. Starting from the solution for a square cross-section (isotropic), they employ numerical continuation in the cross-sectional aspect ratio in…
Treatises on vibrations devote large space to study the dynamical behavior of an elastic system subject to known external tractions. In fact, usually a "system" is not an isolated body but it is part of a chain of mechanisms which disturb…
The swirling flow in a Francis type hydropower turbine is known to be susceptible to the formation of a large helical structure, commonly referred to as a vortex rope. This vortex rope can be interpreted as an unstable mode associated with…
Two-dimensional crystalline membranes have recently been realized experimentally in such systems as graphene and molybdenum disulfide, sparking a resurgence in interest in their statistical properties. Thermal fluctuations can significantly…
We study the dynamo threshold of a helical flow made of a mean (stationary) plus a fluctuating part. Two flow geometries are studied, either (i) solid body or (ii) smooth. Two well-known resonant dynamo conditions, elaborated for stationary…
The tridimensional configuration and the twist density of helical rods with varying cross section radius are studied within the framework of the Kirchhoff rod model. It is shown that the twist density increases when the cross section radius…
Ribbons are long narrow strips possessing three distinct material length scales (thickness, width, and length) which allow them to produce unique shapes unobtainable by wires or filaments. For example when a ribbon has half a twist and is…
Multicanonical ensemble simulations for the simulation of first-order phase transitions suffer from exponential slowing down. Monte Carlo autocorrelation times diverge exponentially with free energy barriers $\Delta F$, which in $L^d$ boxes…
Helically coiled filaments are a frequent motif in nature. In situations commonly encountered in experiments coiled helices are squeezed flat onto two dimensional surfaces. Under such 2-D confinement helices form "squeelices" - peculiar…
We investigate lower asymptotic bounds of number variances for invariant locally square-integrable random measures on Euclidean and real hyperbolic spaces. In the Euclidean case we show that there are subsequences of radii for which the…
Though the problem of sequence-reversed protein folding is largely unexplored, one might speculate that reversed native protein sequences should be significantly more foldable than purely random heteropolymer sequences. In this article, we…