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We study radial solutions in a ball of $\mathbb{R}^N$ of a semilinear, parabolic-elliptic Patlak-Keller-Segel system with a nonlinear sensitivity involving a critical power. For $N = 2$, the latter reduces to the classical linear model,…
Neutrino experiments are often limited by low statistics, sizable systematic uncertainties, and coarse observable binning, which can hinder discrimination among competing beyond-the-Standard-Model (BSM) explanations of anomalous signals. In…
Numerical solutions to the nonlinear sigma model (NLSM), a wave map from 3+1 Minkowski space to S^3, are computed in three spatial dimensions (3D) using adaptive mesh refinement (AMR). For initial data with compact support the model is…
This paper develops an abstract framework for constructing ``seminormal forms'' for cellular algebras. That is, given a cellular R-algebra A which is equipped with a family of JM-elements we give a general technique for constructing…
We investigate the mean dimension of a cellular automaton (CA for short) with a compact non-discrete space of states. A formula for the mean dimension is established for (near) strongly permutative, permutative algebraic and unit…
We propose a fundamental setup for the realization of spontaneous symmetry breaking (SSB) and spontaneous antisymmetry breaking (SASB) in the framework of the nonlinear Schroedinger equation with the self-attractive and repulsive cubic…
We review the ab initio symmetry-adapted (SA) framework for determining the structure of stable and unstable nuclei, along with related electroweak, decay and reaction processes. This framework utilizes the dominant symmetry of nuclear…
Universality in cellular automata theory is a central problem studied and developed from their origins by John von Neumann. In this paper, we present an algorithm where any Turing machine can be converted to one-dimensional cellular…
We study a probabilistic cellular automaton obtained as a mixture of the additive elementary rules 60 and 102. We prove that, for any finite periodic lattice and for mixing parameter $\lambda=1/2$, the system almost surely reaches the…
We study sources of isomorphisms of additive cellular automata on finite groups (called index-group). It is shown that many isomorphisms (called regular) of automata are reducible to the isomorphisms of underlying algebraic structures (such…
A cellular automaton model is presented for random walkers with biologically motivated interactions favoring local alignment and leading to collective motion or swarming behavior. The degree of alignment is controlled by a sensitivity…
A cellular automaton is a deterministic and exactly computable dynamical system which mimics certain fundamental aspects of physical dynamics such as spatial locality and finite entropy. CA systems can be constructed which have additional…
Assuming universality of Yukawa coupling of the superpotential and maximal spontaneous CP violation, fermion masses and mixing angles including that of neutrinos are studied in an SUSY SO(10)$\times \Delta (48)\times$ U(1) model with small…
Cellular automata (CA) have been utilized for decades as discrete models of many physical, mathematical, chemical, biological, and computing systems. The most widely known form of CA, the elementary cellular automaton (ECA), has been…
We present an intuitive formalism for implementing cellular automata on arbitrary topologies. By that means, we identify a symmetry operation in the class of elementary cellular automata. Moreover, we determine the subset of topologically…
Number-conserving cellular automata are discrete dynamical systems that simulate interacting particles like e.g. grains of sand. In an earlier paper, I had already derived a uniform construction for all transition rules of one-dimensional…
Let M be a monoid (e.g. the lattice Z^D), and A an abelian group. A^M is then a compact abelian group; a linear cellular automaton (LCA) is a continuous endomorphism F:A^M --> A^M that commutes with all shift maps. Let mu be a (possibly…
Probabilistic cellular automata describe the dynamics of classical spin models, which, for sufficiently small temperature $T$, can serve as classical memory capable of storing information even in the presence of nonzero external magnetic…
The MadGraph5 aMC@NLO framework aims to automate all types of leading- and next-to-leading-order-accurate simulations for any user-defined model that stems from a renormalisable Lagrangian. In this paper, we present all of the key…
We present a neutrino mass model based on modular symmetry with the fewest input parameters to date, which successfully accounts for the 12 lepton masses and mixing parameters through 6 real free parameters including the modulus. The…