Antipolar ordering of topological defects in active liquid crystals

ATP-driven microtubule-kinesin bundles can self-assemble into two-dimensional active liquid crystals (ALCs) that exhibit a rich creation and annihilation dynamics of topological defects, reminiscent of particle-pair production processes in quantum systems. This recent discovery has sparked considerable interest but a quantitative theoretical description is still lacking. We present and validate a minimal continuum theory for this new class of active matter systems by generalizing the classical Landau-de Gennes free-energy to account for the experimentally observed spontaneous buckling of motor-driven extensile microtubule bundles. The resulting model agrees with recently published data and predicts a regime of antipolar order. Our analysis implies that ALCs are governed by the same generic ordering principles that determine the non-equilibrium dynamics of dense bacterial suspensions and elastic bilayer materials. Moreover, the theory manifests an energetic analogy with strongly interacting quantum gases. Generally, our results suggest that complex non-equilibrium pattern-formation phenomena might be predictable from a few fundamental symmetry-breaking and scale-selection principles.Comment: final accepted journal version; SI text and movies available at article on iop.or

Lattices of hydrodynamically interacting flapping swimmers

Fish schools and bird flocks exhibit complex collective dynamics whose self-organization principles are largely unknown. The influence of hydrodynamics on such collectives has been relatively unexplored theoretically, in part due to the difficulty in modeling the temporally long-lived hydrodynamic interactions between many dynamic bodies. We address this through a novel discrete-time dynamical system (iterated map) that describes the hydrodynamic interactions between flapping swimmers arranged in one- and two-dimensional lattice formations. Our 1D results exhibit good agreement with previously published experimental data, in particular predicting the bistability of schooling states and new instabilities that can be probed in experimental settings. For 2D lattices, we determine the formations for which swimmers optimally benefit from hydrodynamic interactions. We thus obtain the following hierarchy: while a side-by-side single-row "phalanx" formation offers a small improvement over a solitary swimmer, 1D in-line and 2D rectangular lattice formations exhibit substantial improvements, with the 2D diamond lattice offering the largest hydrodynamic benefit. Generally, our self-consistent modeling framework may be broadly applicable to active systems in which the collective dynamics is primarily driven by a fluid-mediated memory

The role of urea in neuronal degeneration and sensitization: an in vitro model of uremic neuropathy

Background: Uremic neuropathy commonly affects patients with chronic kidney disease (CKD), with painful sensations in the feet, followed by numbness and weakness in the legs and hands. The symptoms usually resolve following kidney transplantation, but the mechanisms of uremic neuropathy and associated pain symptoms remain unknown. As blood urea levels are elevated inpatients with CKD, we examined the morphological and functional effects of clinically observed levels of urea on sensory neurons. Methods: Rat DRG neurons were treated with 10or50 mMol/L urea for 48 hours, fixed and immunostained for PGP9.5 and βIII tubulin immunofluorescence, ,. Neurons were also immunostained for TRPV1, TRPM8 and Gap43 expression, and the capsaic insensitivity of urea or vehicle treated neurons was determined.Results: Urea treated neurons had degenerating neurites with diminished PGP9.5 immunofluorescence,and swollen, retracted growth cones. βIII tubulin appeared clumped after urea treatment. Neurite lengths were significantly reduced to 60 ± 2.6%(10 mMol/L, **P<0.01), and to 56.2± 3.3 %, (50 mMol/L, **P<0.01),urea treatmentfor 48 hours, compared with control neurons. Fewer neurons survived urea treatment,with 70.08 ± 13.3% remaining after 10 mMol/L (*P<0.05), and 61.49 ± 7.4 % after 50 mMol/L ureatreatment (**P<0.01), compared with controls. The proportion of neurons expressing TRPV1 wasreduced after urea treatment, but not TRPM8 expressing neurons. In functional studies, treatment with urea resulted in dose-dependent neuronal sensitization.Capsaicinresponses were significantly increased to 115.29 ± 3.4%(10 mMol/L, **P<0.01) and 125.3 ± 4.2%(50 mMol/L,**P<0.01), compared with controls. Sensitization due to urea was eliminated in the presence of the TRPV1 inhibitor SB705498, the MEKinhibitor PD98059,the PI3 kinase inhibitor LY294002, and the TRPM8 inhibitor AMTB. ConclusionNeurite degenerationandsensitization are consistent with uremic neuropathy,, and provide a disease-relevant model to test new treatments

Quantum Phase Transitions of Hard-Core Bosons in Background Potentials

We study the zero temperature phase diagram of hard core bosons in two dimensions subjected to three types of background potentials: staggered, uniform, and random. In all three cases there is a quantum phase transition from a superfluid (at small potential) to a normal phase (at large potential), but with different universality classes. As expected, the staggered case belongs to the XY universality, while the uniform potential induces a mean field transition. The disorder driven transition is clearly different from both; in particular, we find z~1.4, \nu~1, and \beta~0.6.Comment: 4 pages (6 figures); published version-- 2 references added, minor clarification

RG Flow from ϕ4\phi^4 Theory to the 2D Ising Model

We study 1+1 dimensional $\phi^4$ theory using the recently proposed method of conformal truncation. Starting in the UV CFT of free field theory, we construct a complete basis of states with definite conformal Casimir, $\mathcal{C}$. We use these states to express the Hamiltonian of the full interacting theory in lightcone quantization. After truncating to states with $\mathcal{C} \leq \mathcal{C}_{\max}$, we numerically diagonalize the Hamiltonian at strong coupling and study the resulting IR dynamics. We compute non-perturbative spectral densities of several local operators, which are equivalent to real-time, infinite-volume correlation functions. These spectral densities, which include the Zamolodchikov $C$-function along the full RG flow, are calculable at any value of the coupling. Near criticality, our numerical results reproduce correlation functions in the 2D Ising model.Comment: 31+12 page

The invariant measure of a walking droplet in hydrodynamic pilot-wave theory

We study the long time statistics of a walker in a hydrodynamic pilot-wave system, which is a stochastic Langevin dynamics with an external potential and memory kernel. While prior experiments and numerical simulations have indicated that the system may reach a statistically steady state, its long-time behavior has not been studied rigorously. For a broad class of external potentials and pilot-wave forces, we construct the solutions as a dynamics evolving on suitable path spaces. Then, under the assumption that the pilot-wave force is dominated by the potential, we demonstrate that the walker possesses a unique statistical steady state. We conclude by presenting an example of such an invariant measure, as obtained from a numerical simulation of a walker in a harmonic potential