A numerical investigation of the solution of a class of fourth-order eigenvalue problems

This paper is concerned with the accurate numerical approximation of the spectral properties of the biharmonic operator on various domains in two dimensions. A number of analytic results concerning the eigenfunctions of this operator are summarized and their implications for numerical approximation are discussed. In particular, the asymptotic behaviour of the first eigenfunction is studied since it is known that this has an unbounded number of oscillations when approaching certain types of corners on domain boundaries. Recent computational results of Bjorstad & Tjostheim, using a highly accurate spectral Legendre-Galerkin method, have demonstrated that a number of these sign changes may be accurately computed on a square domain provided sufficient care is taken with the numerical method. We demonstrate that similar accuracy is also achieved using an unstructured finite-element solver which may be applied to problems on domains with arbitrary geometries. A number of results obtained from this mixed finite-element approach are then presented for a variety of domains. These include a family of circular sector regions, for which the oscillatory behaviour is studied as a function of the internal angle, and another family of (symmetric and non-convex) domains, for which the parity of the least eigenfunction is investigated. The paper not only verifies existing asymptotic theory, but also allows us to make a new conjecture concerning the eigenfunctions of the biharmonic operator

Critical adsorption on non-spherical colloidal particles

We consider a non-spherical colloidal particle immersed in a fluid close to its critical point. The temperature dependence of the corresponding order parameter profile is calculated explicitly. We perform a systematic expansion of the order parameter profile in powers of the local curvatures of the surface of the colloidal particle. This curvature expansion reduces to the short distance expansion of the order parameter profile in the case that the solvent is at the critical composition.Comment: 9 pages, 7 figure

Critical Casimir interaction of ellipsoidal colloids with a planar wall

Based on renormalization group concepts and explicit mean field calculations we study the universal contribution to the effective force and torque acting on an ellipsoidal colloidal particle which is dissolved in a critical fluid and is close to a homogeneous planar substrate. At the same closest distance between the substrate and the surface of the particle, the ellipsoidal particle prefers an orientation parallel to the substrate and the magnitude of the fluctuation induced force is larger than if the orientation of the particle is perpendicular to the substrate. The sign of the critical torque acting on the ellipsoidal particle depends on the type of boundary conditions for the order parameter at the particle and substrate surfaces, and on the pivot with respect to which the particle rotates

High-Field Pauli-Limiting Behavior and Strongly Enhanced Upper Critical Magnetic Fields near the Transition Temperature of an Arsenic-Deficient LaO_0.9F_0.1FeAs_(1-\delta) Superconductor

We report upper critical field B_c2(T) data for disordered (arsenic-deficient) LaO_0.9F_0.1FeAs_(1-delta) in a wide temperature and magnetic field range up to 47 T. Because of the large linear slope of Bc2 about -5.4 T/K to -6.6 T/K near Tc = 28.5 K the T-dependence of the in-plane Bc2(T) shows a flattening near 23 K above 30 T which points to Pauli-limited behavior with Bc2(0) about 63-68 T. Our results are discussed in terms of disorder effects within conventional and unconventional superconducting pairings.Comment: Change of the title as suggested by the Editors, one author added, typos corrected, references updated, final published versio

Tunability of Critical Casimir Interactions by Boundary Conditions

We experimentally demonstrate that critical Casimir forces in colloidal systems can be continuously tuned by the choice of boundary conditions. The interaction potential of a colloidal particle in a mixture of water and 2,6-lutidine has been measured above a substrate with a gradient in its preferential adsorption properties for the mixture's components. We find that the interaction potentials at constant temperature but different positions relative to the gradient continuously change from attraction to repulsion. This demonstrates that critical Casimir forces respond not only to minute temperature changes but also to small changes in the surface properties.Comment: 4 figures; http://www.iop.org/EJ/article/0295-5075/88/2/26001/epl_88_2_26001.htm

Normal and lateral critical Casimir forces between colloids and patterned substrates

We study the normal and lateral effective critical Casimir forces acting on a spherical colloid immersed in a critical binary solvent and close to a chemically structured substrate with alternating adsorption preference. We calculate the universal scaling function for the corresponding potential and compare our results with recent experimental data [Soyka F., Zvyagolskaya O., Hertlein C., Helden L., and Bechinger C., Phys. Rev. Lett., 101, 208301 (2008)]. The experimental potentials are properly captured by our predictions only by accounting for geometrical details of the substrate pattern for which, according to our theory, critical Casimir forces turn out to be a sensitive probe.Comment: 6 pages, 3 figure

Міжнародна наукова конференція "Архівознавство як наука"

Проаналізовано внесок істориків і архівістів України в розвиток архівної науки. Вказуються основні розділи архівознавства як науки, що вимагають подальших досліджень.Проанализирован вклад историков и архивистов Украины в развитие архивной науки. Указываются основные разделы архивоведения как науки, которые требуют дальнейших исследований.A contribution of Ukrainian historians and archivists to the archival science development is covered. The basic sections of the archival science which need the further study are indicated

Electronic properties of LaOFFeAs in the normal state probed by NMR/NQR

We report 139La, 57Fe and 75As nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) measurements on powders of the new LaO1-xFxFeAs superconductor for x = 0 and x = 0.1 at temperatures up to 480 K, and compare our measured NQR spectra with local density approximation (LDA) calculations. For all three nuclei in the x = 0.1 material, it is found that the local Knight shift increases monotonically with an increase in temperature, and scales with the macroscopic susceptibility, suggesting a single magnetic degree of freedom. Surprisingly, the spin lattice relaxation rates for all nuclei also scale with one another, despite the fact that the form factors for each site sample different regions of q-space. This result suggests a lack of any q-space structure in the dynamical spin susceptibility that might be expected in the presence of antiferromagnetic correlations. Rather, our results are more compatible with simple quasi-particle scattering. Furthermore, we find that the increase in the electric field gradient at the As cannot be accounted for by LDA calculations, suggesting that structural changes, in particular the position of the As in the unit cell, dominate the NQR response.Comment: 17 pages, 6 figure

On Uniqueness of the Jump Process in Quantum Measurement Theory

We prove that, contrary to the standard quantum theory of continuous observation, in the formalism of Event Enhanced Quantum Theory the stochastic process generating individual sample histories of pairs (observed quantum system, observing classical apparatus) is unique. This result gives a rigorous basis to the previous heuristic argument of Blanchard and Jadczyk. Possible implications of this result are discussed.Comment: 31 pages, LaTeX, article; e-mail contact [email protected]

Opinion dynamics: models, extensions and external effects

Recently, social phenomena have received a lot of attention not only from social scientists, but also from physicists, mathematicians and computer scientists, in the emerging interdisciplinary field of complex system science. Opinion dynamics is one of the processes studied, since opinions are the drivers of human behaviour, and play a crucial role in many global challenges that our complex world and societies are facing: global financial crises, global pandemics, growth of cities, urbanisation and migration patterns, and last but not least important, climate change and environmental sustainability and protection. Opinion formation is a complex process affected by the interplay of different elements, including the individual predisposition, the influence of positive and negative peer interaction (social networks playing a crucial role in this respect), the information each individual is exposed to, and many others. Several models inspired from those in use in physics have been developed to encompass many of these elements, and to allow for the identification of the mechanisms involved in the opinion formation process and the understanding of their role, with the practical aim of simulating opinion formation and spreading under various conditions. These modelling schemes range from binary simple models such as the voter model, to multi-dimensional continuous approaches. Here, we provide a review of recent methods, focusing on models employing both peer interaction and external information, and emphasising the role that less studied mechanisms, such as disagreement, has in driving the opinion dynamics. [...]Comment: 42 pages, 6 figure