arXiv subjects

Slobodan Žumer

Publications and source records attributed to Slobodan Žumer.

9 recordsLinked to original sources

arXiv2026

Molecular chirality controls droplet division and helical fiber formation in liquid crystal emulsions

Molecular chirality is a source of broken mirror symmetry, but using it to control mesoscale structures with a tunable length scale remains challenging. Here, we demonstrate that adding a chiral dopant to nematic liquid crystal droplets bounded by a deformable two-surfactant interface controls their morphogenesis: the ratio of droplet diameter to cholesteric pitch determines whether droplets divide asymmetrically or symmetrically upon cooling, and whether they transform into single- or double-strand helical fibers. The fiber periodicity and thickness both scale linearly with the cholesteric pitch, which varies by less than 2% with temperature across the self-shaping window. Numerical simulations reveal that chirality-driven elastic stresses at the interface destabilize the droplets and trigger cusp-mediated shape transformations. These results establish cholesteric pitch as a design variable to precisely control droplet division and decouple the dimensions of spontaneously formed mesoscale structures from temperature dependence.

cond-mat.soft↗

arXiv2019

Topology of three-dimensional active nematic turbulence confined to droplets

Active nematics contain topological defects which under sufficient activity move, create and annihilate in a chaotic quasi-steady state, called active turbulence. However, understanding active defects under confinement is an open challenge, especially in three-dimensions. Here, we demonstrate the topology of three-dimensional active nematic turbulence under the spherical confinement, using numerical modelling. In such spherical droplets, we show the three-dimensional structure of the topological defects, which due to closed confinement emerge in the form of closed loops or surface-to-surface spanning line segments. In the turbulent regime, the defects are shown to be strongly spatially and time varying, with ongoing transformations between positive winding, negative winding and twisted profiles, and with defect loops of zero and non-zero topological charge. The timeline of the active turbulence is characterised by four types of bulk topology-linked events --- breakup, annihilation, coalescence and cross-over of the defects --- which we discuss could be used for the analysis of the active turbulence in different three-dimensional geometries. The turbulent regime is separated by a first order structural transition from a low activity regime of a steady-state vortex structure and an offset single point defect. We also demonstrate coupling of surface and bulk topological defect dynamics by changing from strong perpendicular to inplane surface alignment. More generally, this work is aimed to provide insight into three-dimensional active turbulence, distinctly from the perspective of the topology of the emergent three-dimensional topological defects.

cond-mat.soft↗

arXiv2015

A mesh adaptivity scheme on the Landau-de Gennes functional minimization case in 3D, and its driving efficiency

This paper presents a 3D mesh adaptivity strategy on unstructured tetrahedral meshes by a posteriori error estimates based on metrics, studied on the case of a nonlinear finite element minimization scheme for the Landau-de Gennes free energy functional of nematic liquid crystals. Newton's iteration for tensor fields is employed with steepest descent method possibly stepping in. Aspects relating the driving of mesh adaptivity within the nonlinear scheme are considered. The algorithmic performance is found to depend on at least two factors: when to trigger each single mesh adaptation, and the precision of the correlated remeshing. Each factor is represented by a parameter, with its values possibly varying for every new mesh adaptation. We empirically show that the time of the overall algorithm convergence can vary considerably when different sequences of parameters are used, thus posing a question about optimality. The extensive testings and debugging done within this work on the simulation of systems of nematic colloids substantially contributed to the upgrade of an open source finite element-oriented programming language to its 3D meshing possibilities, as also to an outer 3D remeshing module.

physics.comp-ph↗

arXiv2014

Generation of vector beams with liquid crystal disclination lines

We report that guiding light beams, ranging from continuous beams to femtosecond pulses, along liquid crystal defect lines can transform them into vector beams with various polarization profiles. Using Finite Difference Time Domain numerical solving of Maxwell equations, we confirm that the defect in the orientational order of the liquid crystal induces a defect in the light field with twice the winding number of the liquid crystal defect, coupling the topological invariants of both fields. For example, it is possible to transform uniformly-polarized light into light with a radial polarization profile. Our approach also correctly yields a zero-intensity region near the defect core, which is always present in areas of discontinuous light polarization or phase. Using circularly polarized incident light, we show that defects with non-integer winding numbers can be obtained, where topological constants are preserved by phase vortices, demonstrating coupling between the light's spin, orbital angular momentum and polarization profile. Further, we find an ultrafast femtosecond laser pulse travelling along a defect line splits into multiple intensity regions, again depending on the defect's winding number, allowing applications in beam steering and filtering. Finally, our approach describing generation of complex optical fields via coupling with topological defect lines in optically birefringent nematic fluids can be easily extended to high-intensity beams that affect nematic ordering.

cond-mat.soft↗

arXiv2013

Singular Values, Nematic Disclinations, and Emergent Biaxiality

Both uniaxial and biaxial nematic liquid crystals are defined by orientational ordering of their building blocks. While uniaxial nematics only orient the long molecular axis, biaxial order implies local order along three axes. As the natural degree of biaxiality and the associated frame, that can be extracted from the tensorial description of the nematic order, vanishes in the uniaxial phase, we extend the nematic director to a full biaxial frame by making use of a singular value decomposition of the gradient of the director field instead. New defects and degrees of freedom are unveiled and the similarities and differences between the uniaxial and biaxial phase are analyzed by applying the algebraic rules of the quaternion group to the uniaxial phase.

cond-mat.soft↗

arXiv2012

Quaternions and hybrid nematic disclinations

Disclination lines in nematic liquid crystals can exist in different geometric conformations, characterised by their director profile. In certain confined, colloidal and even more prominently in chiral nematics, the director profile may vary along the disclination line. We construct a robust geometric decomposition of director profile variations in closed disclination loops based on a quaternion description and use it to apply topological classification to linked loops with arbitrary variation of the profile. The description bridges the gap between the known abstract classification scheme derived from homotopy theory and the observable local features of disclinations. We compare the resulting decomposition of disclination loop features to a similar decomposition of nematic textures on closed surfaces.

cond-mat.soft↗

arXiv2012

Topological and geometric decomposition of nematic textures

Directional media, such as nematic liquid crystals and ferromagnets, are characterized by their topologically stabilized defects in directional order. In nematics, boundary conditions and surface-treated inclusions often create complex structures, which are difficult to classify. Topological charge of point defects in nematics has ambiguously defined sign and its additivity cannot be ensured when defects are observed separately. We demonstrate how the topological charge of complex defect structures can be determined by identifying and counting parts of the texture that satisfy simple geometric rules. We introduce a parameter called the defect rank and show that it corresponds to what is intuitively perceived as a point charge based on the properties of the director field. Finally, we discuss the role of free energy constraints in validity of the classification with the defect rank.

cond-mat.soft↗

arXiv2011

Reconfigurable knots and links in chiral nematic colloids

Tying knots and linking microscopic loops of polymers, macromolecules, or defect lines in complex materials is a challenging task for material scientists. We demonstrate the knotting of microscopic topological defect lines in chiral nematic liquid crystal colloids into knots and links of arbitrary complexity by using laser tweezers as a micromanipulation tool. All knots and links with up to six crossings, including the Hopf link, the Star of David and the Borromean rings are demonstrated, stabilizing colloidal particles into an unusual soft matter. The knots in chiral nematic colloids are classified by the quantized self-linking number, a direct measure of the geometric, or Berry's, phase. Forming arbitrary microscopic knots and links in chiral nematic colloids is a demonstration of how relevant the topology can be for the material engineering of soft matter.

cond-mat.soft↗

arXiv2011

Nematic braids: topological invariants and rewiring of disclinations

The conventional topological description given by the fundamental group of nematic order parameter does not adequately explain the entangled defect line structures that have been observed in nematic colloids. We introduce a new topological invariant, the self-linking number, that enables a complete classification of entangled defect line structures in general nematics, even without particles, and demonstrate our formalism using colloidal dimers, for which entangled structures have been previously observed. We also unveil a simple rewiring scheme for the orthogonal crossing of two -1/2 disclinations, based on a tetrahedral rotation of two relevant disclination segments, that allows us to predict possible nematic braids and calculate their self-linking numbers.

cond-mat.soft↗