AN EXTENDED GREEN-SASAO HIERARCHY OF CANONICAL TERNARY GALOIS FORMS AND UNIVERSAL LOGIC MODULES

A new extended Green-Sasao hierarchy of families and forms with a new sub-family for many-valued Reed-Muller logic is introduced. Recently, two families of binary canonical Reed-Muller forms, called Inclusive Forms (IFs) and Generalized Inclusive Forms (GIFs) have been proposed, where the second family was the first to include all minimum Exclusive Sum-Of-Products (ESOPs). In this paper, we propose, analogously to the binary case, two general families of canonical ternary Reed-Muller forms, called Ternary Inclusive Forms (TIFs) and their generalization of Ternary Generalized Inclusive Forms (TGIFs), where the second family includes minimum Galois Field Sum-Of-Products (GFSOPs) over ternary Galois field GF(3). One of the basic motivations in this work is the application of these TIFs and TGIFs to find the minimum GFSOP for many-valued input-output functions within logic synthesis, where a GFSOP minimizer based on IF polarity can be used to minimize the many-valued GFSOP expression for any given function. The realization of the presented S/D trees using Universal Logic Modules (ULMs) is also introduced, whereULMs are complete systems that can implement all possible logic functions utilizing the corresponding S/D expansions of many-valuedShannon and Davio spectral transforms.   

Chromo-dynamic multi-component lattice Boltzmann equation scheme for axial symmetry

We validate the chromo-dynamic multi-component lattice Boltzmann equation (MCLBE) simulation for immiscible fluids with a density contrast against analytical results for complex flow geometries, with particular emphasis on the fundamentals of the method, i.e. compliance with inter-facial boundary conditions of continuum hydrodynamics. To achieve the necessary regimes for the chosen validations, we develop, from a three-dimensional, axially-symmetric flow formulation, a novel, two-dimensional, pseudo Cartesian, MCLBE scheme. This requires the inclusion in lattice Boltzmann methodology of a continuously distributed source and a velocity-dependent force density (here, the metric force terms of the cylindrical Navier–Stokes equations). Specifically, we apply our model to the problem of flow past a spherical liquid drop in Re = 0, Ca regime and, also, flow past a lightly deformed drop. The resulting simulation data, once corrected for the simulation’s inter-facial micro-current (using a method we also advance herein, based on freezing the phase field) show good agreement with theory over a small range of density contrasts. In particular, our data extend verified compliance with the kinematic condition from flat (Burgin et al 2019 Phys. Rev. E 100 043310) to the case of curved fluid–fluid interfaces. More generally, our results indicate a route to eliminate the influence of the inter-facial micro-current

The stochastic behavior of a molecular switching circuit with feedback

Background: Using a statistical physics approach, we study the stochastic switching behavior of a model circuit of multisite phosphorylation and dephosphorylation with feedback. The circuit consists of a kinase and phosphatase acting on multiple sites of a substrate that, contingent on its modification state, catalyzes its own phosphorylation and, in a symmetric scenario, dephosphorylation. The symmetric case is viewed as a cartoon of conflicting feedback that could result from antagonistic pathways impinging on the state of a shared component. Results: Multisite phosphorylation is sufficient for bistable behavior under feedback even when catalysis is linear in substrate concentration, which is the case we consider. We compute the phase diagram, fluctuation spectrum and large-deviation properties related to switch memory within a statistical mechanics framework. Bistability occurs as either a first-order or second-order non-equilibrium phase transition, depending on the network symmetries and the ratio of phosphatase to kinase numbers. In the second-order case, the circuit never leaves the bistable regime upon increasing the number of substrate molecules at constant kinase to phosphatase ratio. Conclusions: The number of substrate molecules is a key parameter controlling both the onset of the bistable regime, fluctuation intensity, and the residence time in a switched state. The relevance of the concept of memory depends on the degree of switch symmetry, as memory presupposes information to be remembered, which is highest for equal residence times in the switched states. Reviewers: This article was reviewed by Artem Novozhilov (nominated by Eugene Koonin), Sergei Maslov, and Ned Wingreen.Comment: Version published in Biology Direct including reviewer comments and author responses, 28 pages, 7 figure

Sterile neutrino dark matter: A tale of weak interactions in the strong coupling epoch

We perform a detailed study of the weak interactions of standard model neutrinos with the primordial plasma and their effect on the resonant production of sterile neutrino dark matter. Motivated by issues in cosmological structure formation on small scales, and reported X-ray signals that could be due to sterile neutrino decay, we consider $7$ keV-scale sterile neutrinos. Oscillation-driven production of such sterile neutrinos occurs at temperatures $T \gtrsim 100$ MeV, where we study two significant effects of weakly charged species in the primordial plasma: (1) the redistribution of an input lepton asymmetry; (2) the opacity for active neutrinos. We calculate the redistribution analytically above and below the quark-hadron transition, and match with lattice QCD calculations through the transition. We estimate opacities due to tree level processes involving leptons and quarks above the quark-hadron transition, and the most important mesons below the transition. We report final sterile neutrino dark matter phase space densities that are significantly influenced by these effects, and yet relatively robust to remaining uncertainties in the nature of the quark-hadron transition. We also provide transfer functions for cosmological density fluctuations with cutoffs at $k \simeq 10 \ h \ {\rm Mpc}^{-1}$, that are relevant to galactic structure formation.Comment: 28 pages, 11 figures, code repository at https://github.com/ntveem/sterile-d

Janus Droplet Formation via Thermally Induced Phase Separation: A Numerical Model with Diffusion and Convection

[Image: see text] Microscale Janus particles have versatile potential applications in many physical and biomedical fields, such as microsensor, micromotor, and drug delivery. Here, we present a phase-field approach of multicomponent and multiphase to investigate the Janus droplet formation via thermally induced phase separation. The crucial kinetics for the formation of Janus droplets consisting of two polymer species and a solvent component via an interplay of both diffusion and convection is considered in the Cahn–Hilliard–Navier–Stokes equation. The simulation results of the phase-field model show that unequal interfacial tensions between the two polymer species and the solvent result in asymmetric phase separation in the formation process of Janus droplets. This asymmetric phase separation plays a vital role in the establishment of the so-called core–shell structure that has been observed in previous experiments. By varying the droplet size, the surface tension, and the molecular interaction between the polymer species, several novel droplet morphologies are predicted in the development process of Janus droplets. Moreover, we stress that the hydrodynamics should be reckoned as a non-negligible mechanism that not only accelerates the Janus droplet evolution but also has great impacts on the coarsening and coalescence of the Janus droplets