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

STARK: Structured Dictionary Learning Through Rank-one Tensor Recovery

In recent years, a class of dictionaries have been proposed for multidimensional (tensor) data representation that exploit the structure of tensor data by imposing a Kronecker structure on the dictionary underlying the data. In this work, a novel algorithm called "STARK" is provided to learn Kronecker structured dictionaries that can represent tensors of any order. By establishing that the Kronecker product of any number of matrices can be rearranged to form a rank-1 tensor, we show that Kronecker structure can be enforced on the dictionary by solving a rank-1 tensor recovery problem. Because rank-1 tensor recovery is a challenging nonconvex problem, we resort to solving a convex relaxation of this problem. Empirical experiments on synthetic and real data show promising results for our proposed algorithm

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

μ\muSR and Neutron Diffraction Investigations on Reentrant Ferromagnetic Superconductor Eu(Fe{0.86}Ir{0.14})2As2

Results of muon spin relaxation ($\mu$SR) and neutron powder diffraction measurements on a reentrant superconductor Eu(Fe$_{0.86}$Ir$_{0.14}$)$_2$As$_2$ are presented. Eu(Fe$_{0.86}$Ir$_{0.14}$)$_2$As$_2$ exhibits superconductivity at $T_{\rm c\,on} \approx 22.5$~K competing with long range ordered Eu$^{+2}$ moments below $\approx 18$ K. A reentrant behavior (manifested by nonzero resistivity in the temperature range 10--17.5 K) results from an exquisite competition between the superconductivity and magnetic order. The zero field $\mu$SR data confirm the long range magnetic ordering below $T_{\rm Eu} = 18.7(2)$ K. The transition temperature is found to increase with increasing magnetic field in longitudinal field $\mu$SR which along with the neutron diffraction results, suggests the transition to be ferromagnetic. The neutron diffraction data reveal a clear presence of magnetic Bragg peaks below $T_{\rm Eu}$ which could be indexed with propagation vector k = (0, 0, 0), confirming a long range magnetic ordering in agreement with $\mu$SR data. Our analysis of the magnetic structure reveals an ordered magnetic moment of $6.29(5)\,\mu_{\rm B}$ (at 1.8 K) on the Eu atoms and they form a ferromagnetic structure with moments aligned along the $c$-axis. No change in the magnetic structure is observed in the reentrant or superconducting phases and the magnetic structure remains same for 1.8 K $\leq T \leq T_{\rm Eu}$. No clear evidence of structural transition or Fe moment ordering was found.Comment: 9 pages, 7 figures, to appear in Phys. Rev.

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

Ferromagnetic Ordering in CeIr2B2: Transport, magnetization, specific heat and NMR studies

We present a complete characterization of ferromagnetic system CeIr2B2 using powder x-ray diffraction XRD, magnetic susceptibility chi(T), isothermal magnetization M(H), specific heat C(T), electrical resistivity rho(T,H), and thermoelectric power S(T) measurements. Furthermore 11B NMR study was performed to probe the magnetism on a microscopic scale. The chi(T), C(T) and rho(T) data confirm bulk ferromagnetic ordering with Tc = 5.1 K. Ce ions in CeIr2B2 are in stable trivalent state. Our low-temperature C(T) data measured down to 0.4 K yield Sommerfeld coefficient gamma = 73(4) mJ/molK2 which is much smaller than the previously reported value of gamma = 180 mJ/molK2 deduced from the specific heat measurement down to 2.5 K. For LaIr2B2 gamma = 6(1) mJ/molK2 which implies the density of states at the Fermi level D(EF) = 2.54 states/(eV f.u.) for both spin directions. The renormalization factor for quasi-particle density of states and hence for quasi-particle mass due to 4f correlations in CeIr2B2 is 12. The Kondo temperature TK ~ 4 K is estimated from the jump in specific heat of CeIr2B2 at Tc. Both C(T) and rho(T) data exhibit gapped-magnon behavior in magnetically ordered state with an energy gap Eg ~ 3.5 K. The rho data as a function of magnetic field H indicate a large negative magnetoresistance (MR) which is highest for T = 5 K.While at 5 K the negative MR keeps on increasing up to 10 T, at 2 K an upturn is observed near H = 3.5 T. On the other hand, the thermoelectric power data have small absolute values (S ~ 7 {\mu}V/K) indicating a weak Kondo interaction. A shoulder in S(T) at about 30 K followed by a minimum at ~ 10 K is attributed to crystal electric field (CEF) effects and the onset of magnetic ordering. 11B NMR line broadening provides strong evidence of ferromagnetic correlations below 40 K.Comment: 10 pages, 11 figure