WPI-SKCM² Spring Symposium: Nara, Japan

We report a model for hyperthermia therapies based on heat diffusion in a biological tissue containing a topological defect. Biological tissues behave like active liquid crystals with the presence of topological defects which are likely to anchor tumors during the metastatic phase of cancer evolution and the therapy challenge is to destroy the cancer cells without damaging surrounding healthy tissues. The defect creates an effective non-Euclidean geometry for low-energy excitations, modifying the bio-heat equation. Applications to protocols of thermal ablation for various biological tissues (liver, prostate, and skin) is analyzed and discussed.

Geometry and topology dramatically influence the dynamics and mechanics of polymer-based materials. For example, the properties of ring, branched, or star-shaped flexible polymers are strikingly different from their linear analogs. We study how the shape of rigid filaments influences the microscopic dynamics and macroscopic rheology. Shape-diblock copolymers comprising adjacent helical and straight segments become permanently jammed at very low concentrations. The rheological properties of such suspensions are similar to those of a cross-linked rubber. However, these properties do not arise due to permanent chemical cross-links, but rather by the incompatible dynamical modes of the adjoining shape segment, which ensure that filaments are trapped in frozen glass-like configurations. Subsequently, we study the behavior of helical filaments that can switch between two polymorphic states. We compare the mechanical transition of isolated filaments and those that are tightly entangled.

The bulk-edge correspondence is a key concept for topological phases that governs a wide range of phenomena from quantum materials to equatorial waves near the earth. It bridges topological numbers and experimental observables near the boundaries, such as surface states. In the talk, its relation to the linking in momentum space is demonstrated associated with a topological phase transition.

Proteins are linear polymers made up of amino-acid monomer building blocks. For most proteins, the polymer chain has to collapse and fold into a unique three-dimensional structure for the protein to be active and functional. Over 60 years of structural biology, the structures of many proteins have been solved and they show great diversity in both structure as well as function. One of the most surprising results came in the year 2000, when it was established that quite a number of protein structures exist in which the protein chain is knotted, slip-knotted or forms some other form of topologically complex structure. Such structures had been speculated on but dismissed as being incompatible with protein folding mechanisms known at that time. We now know that there are quite a large number of topologically knotted protein structures adopting a range of knot types from simple trefoil knots to more complex 7-1 knots. In my talk, I will provide an overview of the field from both an experimental and computational perspective and discuss how such knotted protein structures may have evolved, what we know about their folding pathways both in vitro and in vivo, whether they have special properties that set them apart from unknotted proteins, to recent studies designing de novo novel protein structures which contain knots.

The DNA origami technique has emerged as one of the most versatile bottom-up nanofabrication methods. In this talk I will discuss utility of DNA origami for fabrication of chiral metal nanostructures. More specifically, I will present fabrication of i) light-responsive dynamic chiral plasmonic assemblies with easily regulated steady out-of-equilibrium states; ii) chiral plasmonic systems with visually detectable reconfigurable optical activity; iii) metal shells with tailored complex morphologies and optical responses within near-infrared transparency window(s).

Multi-stranded helices serve as versatile building blocks for constructing chiral topological structures due to their highly ordered and simple preorganized nature. Herein, we present two examples of such topological structures based on multi-stranded helices. Firstly, a general approach to constructing torus knots from coaxially nested multi-stranded contra-helices is detailed, leading to the efficient synthesis of contra-helical trefoil knots with tunable emergent properties through topomechanical manipulation, showcasing potential for stimuli-responsive multifunctional materials design. Notably, one molecular knot demonstrates narcissistic self-sorting during crystallization, enabling manual enantiomer separation. Secondly, a concise method for constructing twisted polycatenanes using preorganized double helicates as templates and linking them crosswise with silver ions or triple bonds is described. Successful synthesis of twisted polycatenanes with covalent bonding employing Ag(I) ions and ethynylene units highlights the potential of multi-stranded metallohelicates for creating sophisticated mechanically interlocked molecules and polymers with applications in molecular nanotopology and materials design.

Our theoretical proposal how to create an analogue Dirac monopole in a dilute Bose–Einstein condensate (BEC) [Pietilä and Möttönen, PRL 103, 030401 (2009)] has been the basis of series of beautiful experiments imaging for the first time in three-dimensional continuous fields the following topological structures: a Dirac monopole analogue, isolated monopole as a topological point defect, quantum knot as a realization of the Hopf fibration, and a skyrmion. More recently, we managed to experimentally observe the relaxation of the isolated monopole into a Dirac monopole accompanied by the spontaneous appearance of ending vortex lines, or nodal lines as coined by Dirac. Earlier decay dynamics of the isolated monopole showed the appearance of a half-quantum vortex ring, or an Alice ring. Such a ring has an intriguing, yet experimentally unobserved, property that any monopole passing through it has to change its sign. Thus, although the family of experimentally observed topological defects is complete on a general level, major new discoveries still await. To this end, we have theoretically considered knotted vortex cores characterized by different non-Abelian groups. Remarkably, we have very recently found that such a knotted structure may exist in a BEC and be topologically stable, save reasonable physically motivated assumptions. The experimental realization of these stable vortex knots remains one of the greatest challenges in the study of fundamental topological defects in physics.

Cones with order in the local tangent plane provide a soft matter analog of the Aharonov-Bohm effect. We study two-dimensional liquid crystals with p-fold rotational symmetry (p-atics) on the surfaces of cones, and find both the ground state and a ladder of quantized metastable states as a function of both the cone angle and the liquid crystal symmetry p. These states are characterized by a fractional defect charge at the apex and the ground states are in general frustrated due to effects of parallel transport along the azimuthal direction on the cone. We check our predictions numerically for a set of commensurate cone angles, whose surfaces can be polygonized as a perfect triangular or square mesh, and find good agreement. When tangential boundary conditions are applied at the base, the cone apex absorbs and emits quantized defect charges, as a function of cone angle. Defect emission and absorption events at the apex change dramatically when we consider active nematics on cones.

Tools of spintronics and new magnetic heterostructure platforms developed over the past years open a wealth of opportunities to explore nonequilibrium and transport phenomena in solid-state systems. Current ideas go well beyond the conventional spin transport concepts, with much focus, in particular, on the active role of dynamic topological spin textures. Topological conservation laws thereof now allow us to envision new modalities of spintronic functionalities, which are enhanced by stable nonvolatile characteristics of certain magnetic configurations. In this talk, I will review two complementary thrusts in this research, based on topological spin textures: one using their control and manipulations as a new route towards high-endurance magnetic energy storage and the other, employing versatile regimes of magnetic winding dynamics, to realize all basic ingredients needed for building spiking neural networks.

In this talk, Rachel will tell you all you need to know about publishing your work in Nature journals, including an introduction to existing and new Nature journals, recent trends in publishing, options you have during your submission, and the editorial and peer review processes.

Nature provided us diverse examples of unique surface textures, chirality and structural colors, which can also be responsive to environment. In my talk, I will present liquid crystal elastomers (LCEs) of diverse and unique geometries and topologies, including microparticles, ribbons, and looped fibers. When shape changing, spindle-shaped LCE microparticles are spatially encoded in a conventional elastomer film, we realize complex shape morphing from 2D to 3D. When these particles are placed in a periodic lattice, we can reconfigure the lattice from chiral to achiral, then to chiral again, without breaking the translational symmetry. When LCE ribbons are embodied with twist intelligence, they can spontaneously snap-through its soft body upon active and adaptive obstacle negotiation or avoidance. When LCE fibers are connected into lobed loops, they demonstrate gait-like, autonomous, self-regulated, and repeated synchronization through the geometrically constrained snap-through instability.