Diffusion in a continuum model of self-propelled particles with alignment interaction

In this paper, we provide the $O(\epsilon)$ corrections to the hydrodynamic model derived by Degond and Motsch from a kinetic version of the model by Vicsek & coauthors describing flocking biological agents. The parameter $\epsilon$ stands for the ratio of the microscopic to the macroscopic scales. The $O(\epsilon)$ corrected model involves diffusion terms in both the mass and velocity equations as well as terms which are quadratic functions of the first order derivatives of the density and velocity. The derivation method is based on the standard Chapman-Enskog theory, but is significantly more complex than usual due to both the non-isotropy of the fluid and the lack of momentum conservation

Geometric Permutations of Non-Overlapping Unit Balls Revisited

Given four congruent balls $A, B, C, D$ in $R^{d}$ that have disjoint interior and admit a line that intersects them in the order $ABCD$, we show that the distance between the centers of consecutive balls is smaller than the distance between the centers of $A$ and $D$. This allows us to give a new short proof that $n$ interior-disjoint congruent balls admit at most three geometric permutations, two if $n\ge 7$. We also make a conjecture that would imply that $n\geq 4$ such balls admit at most two geometric permutations, and show that if the conjecture is false, then there is a counter-example of a highly degenerate nature

Macroscopically degenerate localized zero-energy states of quasicrystalline bilayer systems in strong coupling limit

When two identical two-dimensional (2D) periodic lattices are stacked in parallel after rotating one layer by a certain angle relative to the other layer, the resulting bilayer system can lose lattice periodicity completely and become a 2D quasicrystal. Twisted bilayer graphene with 30-degree rotation is a representative example. We show that such quasicrystalline bilayer systems generally develop macroscopically degenerate localized zero-energy states (ZESs) in strong coupling limit where the interlayer couplings are overwhelmingly larger than the intralayer couplings. The emergent chiral symmetry in strong coupling limit and aperiodicity of bilayer quasicrystals guarantee the existence of the ZESs. The macroscopically degenerate ZESs are analogous to the flat bands of periodic systems, in that both are composed of localized eigenstates, which give divergent density of states. For monolayers, we consider the triangular, square, and honeycomb lattices, comprised of homogenous tiling of three possible planar regular polygons: the equilateral triangle, square, and regular hexagon. We construct a compact theoretical framework, which we call the quasiband model, that describes the low energy properties of bilayer quasicrystals and counts the number of ZESs using a subset of Bloch states of monolayers. We also propose a simple geometric scheme in real space which can show the spatial localization of ZESs and count their number. Our work clearly demonstrates that bilayer quasicrystals in strong coupling limit are an ideal playground to study the intriguing interplay of flat band physics and the aperiodicity of quasicrystals.Comment: 5 pages, 4 figures + Supplementary Material (12 pages,5 figures

Fractionalisation and dynamics of anyons at ν=n+1/3\nu=n+1/3 in fractional quantum Hall effect and their experimental signatures

We show the low-lying excitations at filling factor $\nu=n+1/3$ with realistic interactions are contained completely within the well-defined Hilbert space of "Gaffnian quasiholes". Each Laughlin quasihole can thus be understood as a bound state of two Gaffnian quasiholes, which in the lowest Landau level (LLL) behaves like "partons" with "asymptotic freedom" mediated by neutral excitations acting as "gluons". Near the experimentally observed nematic FQH phase in higher LLs, quasiholes become weakly bounded and fractionalise with rich dynamical properties. By studying the effective interactions between quasiholes, we predict a finite temperature phase transition of the Laughlin quasiholes even when the Laughlin ground state remains incompressible, and derive relevant experimental conditions for its possible observations.Comment: 4+ pages, 4 figures. Comments welcom

Cell-type specific potent Wnt signaling blockade by bispecific antibody.

Cell signaling pathways are often shared between normal and diseased cells. How to achieve cell type-specific, potent inhibition of signaling pathways is a major challenge with implications for therapeutic development. Using the Wnt/β-catenin signaling pathway as a model system, we report here a novel and generally applicable method to achieve cell type-selective signaling blockade. We constructed a bispecific antibody targeting the Wnt co-receptor LRP6 (the effector antigen) and a cell type-associated antigen (the guide antigen) that provides the targeting specificity. We found that the bispecific antibody inhibits Wnt-induced reporter activities with over one hundred-fold enhancement in potency, and in a cell type-selective manner. Potency enhancement is dependent on the expression level of the guide antigen on the target cell surface and the apparent affinity of the anti-guide antibody. Both internalizing and non-internalizing guide antigens can be used, with internalizing bispecific antibody being able to block signaling by all ligands binding to the target receptor due to its removal from the cell surface. It is thus feasible to develop bispecific-based therapeutic strategies that potently and selectively inhibit signaling pathways in a cell type-selective manner, creating opportunity for therapeutic targeting

Metal-organic ion transport systems

The design of synthetic membrane transporters for ions is a rapidly growing field of research, motivated by the potential medicinal applications of novel systems. Metal-organic coordination complexes provide access to a wide range of geometries, structures and properties and their facile synthesis and tunability offer advantages in the design of ion transport systems. In this review, the application of metal-organic constructs as membrane-spanning channels and ion carriers are explored, and the roles of the metal coordination complexes within these functional assemblies are highlighted