اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدNematic equilibria on a two-dimensional annulus: defects and energies
104
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We study planar nematic equilibria on a two-dimensional annulus with strong and weak tangent anchoring, within the Oseen-Frank and Landau-de Gennes theories for nematic liquid crystals. We analyse the defect-free state in the Oseen-Frank framework and obtain analytic stability criteria in terms of the elastic anisotropy, annular aspect ratio and anchoring strength. We consider radial and azimuthal perturbations of the defect-free state separately, which yields a complete stability diagram for the defect-free state. We construct nematic equilibria with an arbitrary number of defects on a two-dimensional annulus with strong tangent anchoring and compute their energies; these equilibria are generalizations of the diagonal and rotated states observed in a square. This gives novel insights into the correlation between preferred numbers of defects, their locations and the geometry. In the Landau-de Gennes framework, we adapt Mironescus powerful stability result in the Ginzburg-Landau framework (P. Mironescu, On the stability of radial solutions of the Ginzburg-Landau equation, 1995) to compute quantitative criteria for the local stability of the defect-free state in terms of the temperature and geometry.
قيم البحث
اقرأ أيضاً
We use density--functional theory to study the structure of two-dimensional defects inside a circular nematic nanocavity. The density, nematic order parameter, and director fields, as well as the defect core energy and core radius, are obtained in a
thermodynamically consistent way for defects with topological charge $k=+1$ (with radial and tangential symmetries) and $k=+1/2$. An independent calculation of the fluid elastic constants, within the same theory, allows us to connect with the local free--energy density predicted by elastic theory, which in turn provides a criterion to define a defect core boundary and a defect core free energy for the two types of defects. The radial and tangential defects turn out to have very different properties, a feature that a previous Maier--Saupe theory could not account for due to the simplified nature of the interactions --which caused all elastic constants to be equal. In the case with two $k=+1/2$ defects in the cavity, the elastic regime cannot be reached due to the small radii of the cavities considered, but some trends can already be obtained.
In this paper we rigorously investigate the emergence of defects on Nematic Shells with genus different from one. This phenomenon is related to a non trivial interplay between the topology of the shell and the alignment of the director field. To this
end, we consider a discrete $XY$ system on the shell $M$, described by a tangent vector field with unit norm sitting at the vertices of a triangulation of the shell. Defects emerge when we let the mesh size of the triangulation go to zero, namely in the discrete-to-continuum limit. In this paper we investigate the discrete-to-continuum limit in terms of $Gamma$-convergence in two different asymptotic regimes. The first scaling promotes the appearance of a finite number of defects whose charges are in accordance with the topology of shell $M$, via the Poincare-Hopf Theorem. The second scaling produces the so called Renormalized Energy that governs the equilibrium of the configurations with defects.
Formation energies of charged point defects in semiconductors are calculated using periodic supercells, which entail a divergence arising from long-range Coulombic interactions. The divergence is typically removed by the so-called jellium approach. R
ecently, Wu, Zhang and Pantelides [WZP, Phys. Rev. Lett. 119, 105501 (2017)] traced the origin of the divergence to the assumption that charged defects are formed by physically removing electrons from or adding electrons to the crystal, violating charge neutrality, a key principle of statistical mechanics that determines the Fermi level. An alternative theory was constructed by recognizing that charged defects form by trading carriers with the energy bands, whereby supercells are always charge-neutral so that no divergence is present and no ad-hoc procedures need to be adopted for calculations. Here we give a more detailed exposition of the foundations of both methods and show that the jellium approach can be derived from the statistical-mechanics-backed WZP definition by steps whose validity cannot be assessed a priori. In particular, the divergence appears when the charge density of band carriers is dropped, leaving a supercharged crystal. In the case of charged defects in two-dimensional (2D) materials, unphysical fields appear in vacuum regions. None of these pathological features are present in the reformulated theory. Finally, we report new calculations in both bulk and 2D materials. The WZP approach yields formation energies that differ from jellium values by up to ~1 eV. By analyzing the spatial distribution of wave functions and defect potentials, we provide insights into the inner workings of both methods and demonstrate that the failure of the jellium approach to include the neutralizing electron density of band carriers, as is the case in the physical system, is responsible for the numerical differences between the two methods.
We initiate the study of intersecting surface operators/defects in four-dimensional quantum field theories (QFTs). We characterize these defects by coupled 4d/2d/0d theories constructed by coupling the degrees of freedom localized at a point and on i
ntersecting surfaces in spacetime to each other and to the four-dimensional QFT. We construct supersymmetric intersecting surface defects preserving just two supercharges in N = 2 gauge theories. These defects are amenable to exact analysis by localization of the partition function of the underlying 4d/2d/0d QFT. We identify the 4d/2d/0d QFTs that describe intersecting surface operators in N = 2 gauge theories realized by intersecting M2-branes ending on N M5-branes wrapping a Riemann surface. We conjecture and provide evidence for an explicit equivalence between the squashed four-sphere partition function of these intersecting defects and correlation functions in Liouville/Toda CFT with the insertion of arbitrary degenerate vertex operators, which are labeled by representations of SU(N).
We study the two-boundary extension of a loop model - corresponding to the dense phase of the O(n) model, or to the Q=n^2 state Potts model - in the critical regime -2 < n < 2. This model is defined on an annulus of aspect ratio tau. Loops touching t
he left, right, or both rims of the annulus are distinguished by arbitrary (real) weights which moreover depend on whether they wrap the periodic direction. Any value of these weights corresponds to a conformally invariant boundary condition. We obtain the exact seven-parameter partition function in the continuum limit, as a function of tau, by a combination of algebraic and field theoretical arguments. As a specific application we derive some new crossing formulae for percolation clusters.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
