We develop a Landau theory for bend flexoelectricity in liquid crystals of bent-core molecules. In the nematic phase of the model, the bend flexoelectric coefficient increases as we reduce the temperature toward the nematic to polar phase transition. At this critical point, there is a second-order transition from high-temperature uniform nematic phase to low-temperature nonuniform polar phase c...

Abrikosov’s solution of the linearized Ginzburg-Landau theory describing a periodic lattice of vortex lines in type-II superconductors at large inductions, is generalized to non-periodic vortex arrangements, e.g., to lattices with a vacancy surrounded by relaxing vortices and to periodically distorted lattices that are needed in the nonlocal theory of elasticity of the vortex lattice. Generaliz...

Triviality and Landau poles are often greeted as harbingers of new physics at 1 TeV. After briefly reviewing the ideas behind this, a model of singular quantum mechanics is introduced. Its ultraviolet structure, as well as some features of its vacuum, related to triviality, very much parallel λφ. The model is solvable, exactly and perturbatively, in any dimension. From its analysis we learn tha...

The Ginzburg–Landau theory of phase transitions is one of the most successful and elegant theories that have a very general applicability to a large variety of phenomena. Moreover, its extension into time domain has produced a wealth of interesting new predictions and applications all the way from materials science to cosmology. Here, we describe applications of time-dependent Ginzburg–Landau t...

Adhesion of microorganisms to various interfaces has been explained by the classical Derjaguin–Landau–Verwey– Overbeek (DLVO) theory of colloid stability. The theory has been used as a qualitative model, but also in a quantitative way to calculate adhesion free energy changes involved in microbial adhesion. In this paper some important investigations will be review that show how the DLVO theory...

In (2 + 1) dimensions, the Maxwell term − 1 4 F αβ F αβ can be replaced by the Chern-Simons three-form (κ/4)ǫ αβγ A α F βγ , yielding a novel type of 'electromagnetism'. This has been proposed for studying the Quantum Hall Effect as well as High-Temperature Superconductivity. The gauge field can be coupled to a scalar field either relativistically or non-relativistically. In both cases, one adm...

We investigate how well the shape parameterizations are applicable for studying the giant dipole resonance (GDR) in nuclei, in the low temperature and/or high spin regime. The shape fluctuations due to thermal effects in the GDR observables are calculated using the actual free energies evaluated at fixed spin and temperature. The results obtained are compared with Landau theory calculations don...

We study the superheating field of a bulk superconductor within Ginzburg-Landau theory, which is valid near the critical temperature. We calculate, as functions of the Ginzburg-Landau parameter κ , the superheating field Hsh and the critical momentum kc characterizing the wavelength of the instability of the Meissner state to flux penetration. By mapping the two-dimensional linear stability the...

We prove that the Faddeev-Popov ghost dressing function in the YangMills theory is non-zero and finite in the limit of vanishing momenta and hence the ghost propagator behaves like free in the deep infrared regime, within the Gribov-Zwanziger framework of the D-dimensional SU(N) Yang-Mills theory in the Landau gauge for any D > 2. This result implies that the Kugo-Ojima color confinement criter...

We examine the procedure of thermodynamical derivation of the Ginsburg–Landau equation for current, which is given unclear and contradictory interpretations in existing textbooks. We clarify all steps of this procedure and find as a consequence a limitation on the validity range of the thermodynamic Ginsburg–Landau theory, which does not seem to be explicitely stated up to now: we conclude that...