Active Brownian particles (ABPs), when subject to purely repulsive interactions, are known to undergo activity-induced phase separation broadly resembling an equilibrium (attraction-induced) gas-liquid coexistence. Here we present an accurate continuum theory for the dynamics of phase-separating ABPs, derived by direct coarse graining, capturing leading-order density gradient terms alongside an effective bulk free energy. Such gradient terms do not obey detailed balance; yet we find coarsening dynamics closely resembling that of equilibrium phase separation.

The computation of n-point Gaussian quadrature rules for symmetric weight functions is considered in this paper. It is shown that the nodes and the weights of the Gaussian quadrature rule can be retrieved from the singular value decomposition of a bidiagonal matrix of size n/2. The proposed numerical method allows to compute the nodes with high relative accuracy and a computational complexity of O(n). We also describe an algorithm for computing the weights of a generic Gaussian quadrature rule with high relative accuracy. Numerical examples show the effectiveness of the proposed approach.

Blue phases are liquid crystals made up by networks of defects, or disclination lines. While existing phase diagrams show a striking variety of competing metastable topologies for these networks, very little is known as to how to kinetically reach a target structure, or how to switch from one to the other, which is of paramount importance for devices. We theoretically identify two confined blue phase I systems in which by applying an appropriate series of electric field it is possible to select one of two bistable defect patterns.

This work introduces a novel extension of the 0/1 Knapsack Problem in which we consider the existence of so-called forfeit sets. A forfeit set is a subset of items of arbitrary cardinality, such that including a number of its elements that exceeds a predefined allowance threshold implies some penalty costs to be paid in the objective function value. A global upper bound on these allowance violations is also considered.

Recently, the network paradigm, an application of graph theory to biology, has proven to be a powerful approach to gaining insights into biological complexity, and has catalyzed the advancement of systems biology. In this perspective and focusing on the immune system, we propose here a more comprehensive view to go beyond the concept of network.

We present computer simulations of the response of a flexoelectric blue phase network, either in bulk or under confinement, to an applied field. We find a transition in the bulk between the blue phase I disclination network and a parallel array of disclinations along the direction of the applied field. Upon switching off the field, the system is unable to reconstruct the original blue phase but gets stuck in a metastable phase. Blue phase II is comparatively much less affected by the field.

FORUM (Far-infrared Outgoing Radiation Understanding and Monitoring) is a Fourier Transform Spectrometer (FTS) that will fly as the 9th ESA's Earth Explorer mission. FORUM will sound the atmosphere in the 100-1600 cm-1 region, covering the Far Infrared (FIR) and part of the Middle Infrared (MIR), accounting for more than 95% of the outgoing longwave flux lost by our planet. We review the constrains for the emissivity retrieval.