Understanding Collective Dynamics of Soft Active Colloids by Binary Scattering

Collective motion in actively propelled particle systems is triggered on the very local scale by nucleation of coherently moving units consisting of just a handful of particles. These units grow and merge over time, ending up in a long-range ordered, coherently-moving state. So far, there exists no bottom-up understanding of how the microscopic dynamics and interactions between the constituents are related to the system's ordering instability. In this paper, we study a class of models for propelled colloids allowing an explicit treatment of the microscopic details of the collision process. Specifically, the model equations are Newtonian equations of motion with separate force terms for particles' driving, dissipation and interaction forces. Focusing on dilute particle systems, we analyze the binary scattering behavior for these models, and determine-based on the microscopic dynamics-the corresponding collision-rule, i.e., the mapping of pre-collisional velocities and impact parameter on post-collisional velocities. By studying binary scattering we also find that the considered models for active colloids share the same principle for parallel alignment: the first incoming particle (with respect to the center of collision) is aligned to the second particle as a result of the encounter. This behavior is distinctively different to alignment in non-driven dissipative gases. Moreover, the obtained collision rule lends itself as a starting point to apply kinetic theory for propelled particle systems in order to determine the phase boundary to a long-range ordered, coherently-moving state. The microscopic origin of the collision rule offers the opportunity to quantitatively scrutinize the predictions of kinetic theory for propelled particle systems through direct comparison with multi-particle simulations.Comment: 19 pages, 12 figure

The strong Novikov conjecture for low degree cohomology

We show that for each discrete group G, the rational assembly map K_*(BG) \otimes Q \to K_*(C*_{max} G) \otimes \Q is injective on classes dual to the subring generated by cohomology classes of degree at most 2 (identifying rational K-homology and homology via the Chern character). Our result implies homotopy invariance of higher signatures associated to these cohomology classes. This consequence was first established by Connes-Gromov-Moscovici and Mathai. Our approach is based on the construction of flat twisting bundles out of sequences of almost flat bundles as first described in our previous work. In contrast to the argument of Mathai, our approach is independent of (and indeed gives a new proof of) the result of Hilsum-Skandalis on the homotopy invariance of the index of the signature operator twisted with bundles of small curvature.Comment: 11 page

Critical Casimir Forces in Colloidal Suspensions

Some time ago, Fisher and de Gennes pointed out that long-ranged correlations in a fluid close to its critical point Tc cause distinct forces between immersed colloidal particles which can even lead to flocculation [C. R. Acad. Sc. Paris B 287, 207 (1978)]. Here we calculate such forces between pairs of spherical particles as function of both relevant thermodynamic variables, i.e., the reduced temperature t = (T-Tc)/Tc and the field h conjugate to the order parameter. This provides the basis for specific predictions concerning the phase behavior of a suspension of colloidal particles in a near-critical solvent.Comment: 29 pages, 14 figure

Polymer depletion effects near mesoscopic particles

The behavior of mesoscopic particles dissolved in a dilute solution of long, flexible, and nonadsorbing polymer chains is studied by field-theoretic methods. For spherical and cylindrical particles the solvation free energy for immersing a single particle in the solution is calculated explicitly. Important features are qualitatively different for self-avoiding polymer chains as compared with ideal chains. The results corroborate the validity of the Helfrich-type curvature expansion for general particle shapes and allow for quantitative experimental tests. For the effective interactions between a small sphere and a wall, between a thin rod and a wall, and between two small spheres quantitative results are presented. A systematic approach for studying effective many-body interactions is provided. The common Asakura-Oosawa approximation modelling the polymer coils as hard spheres turns out to fail completely for small particles and still fails by about 10% for large particles.Comment: 68 pages, 6 figure

Competing many-body instabilities and unconventional superconductivity in graphene

The band structure of graphene exhibits van Hove singularities (VHS) at doping x=+- 1/8 away from the Dirac point. Near the VHS, interactions effects, enhanced due to the large density of states, can give rise to various many-body phases at experimentally accessible temperatures. We study the competition between different many-body instabilities in graphene using functional renormalization group (FRG). We predict a rich phase diagram, which, depending on long range hopping as well as screening strength and absolute scale of the Coulomb interaction, contains a d+id-wave superconducting (SC) phase, or a spin density wave phase at the VHS. The d+id state is expected to exhibit quantized charge and spin Hall response, as well as Majorana modes bound to vortices. In the vicinity of the VHS, we find singlet d+id-wave as well as triplet f-wave SC phases.Comment: 4.5 pages, 4 figure

Expression of natural killer receptor alleles at different Ly49 loci occurs independently and is regulated by major histocompatibility complex class I molecules.

Ly49 receptor genes are expressed by subsets of natural killer (NK) cells in an overlapping fashion, accounting for the capacity of NK subsets to attack host cells that have selectively downregulated self-major histocompatibility complex (MHC) class I molecules. It was shown previously that most NK cells express only one or the other allele of a given Ly49 gene, while a smaller population expresses both alleles. However, the methods used to detect monoallelic and biallelic cells were nonquantitative. Here, new allele-specific antibodies were used to provide the first quantitative examination of biallelic and monoallelic expression of Ly49A and Ly49G2. The results demonstrate conclusively that most Ly49A(+) and Ly49G2(+) NK cells express the corresponding gene in a monoallelic fashion, with a smaller subset expressing both alleles. Unexpectedly, biallelic Ly49A(+) NK cells were more numerous than predicted by completely independent allelic expression, suggesting some heterogeneity among NK progenitors in the potential to express a given Ly49 gene. The data also show that cells expressing one allele of Ly49G2 may express Ly49A from the same or opposite chromosome with equal likelihood, indicating that the expressed allele is chosen independently for different Ly49 genes. Finally, the data demonstrate that biallelic expression of Ly49A or Ly49G2 occurs least frequently in mice that express ligands for these receptors (H-2(d) mice), and most frequently in class I-deficient mice. Thus, biallelic expression of Ly49 genes is regulated by interactions of NK cell progenitors with MHC class I molecules

The column density towards LMC X-1

We measure the neutral absorption towards the black hole X-ray binary system LMC X-1 from six archival soft X-ray spectra obtained with the gratings and/or CCD detectors on Chandra, XMM-Newton, and Swift. Four spectral models for the soft continuum have been investigated. While the powerlaw model may overestimate NH considerably, the others give consistent results. Taking the lower metalicity of the Large Magellanic Cloud into account, we find equivalent hydrogen column densities of N_H = (1.0-1.3)*10^22 cm^-2, with a systematic dependence on the orbital phase. This variation of the neutral absorption can nearly explain the orbital modulation of the soft X-ray flux recently detected with the All Sky Monitor (ASM) on the Rossi X-ray Timing Explorer (RXTE).Comment: 4 pages, accepted for publication as a Letter in Astronomy and Astrophysic