An Eulerian Approach to the Analysis of Krause's Consensus Models

Abstract. In this paper we analyze a class of multi-agent consensus dynamical systems inspired by Krause’s original model. As in Krause’s, the basic assumption is the so-called bounded confidence: two agents can influence each other only when their state values are below a given distance threshold R. We study the system under an Eulerian point of view considering (possibly continuous) probability distributions of agents and we present original convergence results. The limit distribution is always necessarily a convex combination of delta functions at least R far apart from each other: in other terms these models are locally aggregating. The Eulerian perspective provides the natural framework for designing a numerical algorithm, by which we obtain several simulations in 1 and 2 dimensions

White dwarf envelopes: further results of a non-local model of convection

We present results of a fully non-local model of convection for white dwarf envelopes. We show that this model is able to reproduce the results of numerical simulations for convective efficiencies ranging from very inefficient to moderately efficient; this agreement is made more impressive given that no closure parameters have been adjusted in going from the previously reported case of A-stars to the present case of white dwarfs; for comparison, in order to match the peak convective flux found in numerical simulations for both the white dwarf envelopes discussed in this paper and the A-star envelopes discussed in our previous work requires changing the mixing length parameter of commonly used local models by a factor of 4. We also examine in detail the overshooting at the base of the convection zone, both in terms of the convective flux and in terms of the velocity field: we find that the flux overshoots by approximately 1.25 H_P and the velocity by approximately 2.5 H_P. Due to the large amount of overshooting found at the base of the convection zone the new model predicts the mixed region of white dwarf envelopes to contain at least 10 times more mass than local mixing length theory (MLT) models having similar photospheric temperature structures. This result is consistent with the upper limit given by numerical simulations which predict an even larger amount of mass to be mixed by convective overshooting. Finally, we attempt to parametrise some of our results in terms of local MLT-based models, insofar as is possible given the limitations of MLTComment: Accepted for publication in MNRAS; 11 pages, 5 figures, 3 table

A-star envelopes: a test of local and non-local models of convection

We present results of a fully non-local, compressible model of convection for A-star envelopes. This model quite naturally reproduces a variety of results from observations and numerical simulations which local models based on a mixing length do not. Our principal results, which are for models with Teff between 7200 K and 8500 K, are the following: First, the photospheric velocities and filling factors are in qualitative agreement with those derived from observations of line profiles of A-type stars. Second, the He II and H I convection zones are separated in terms of convective flux and thermal interaction, but joined in terms of the convective velocity field, in agreement with numerical simulations. In addition, we attempt to quantify the amount of overshooting in our models at the base of the He II convection zone.Comment: 5 pages with 4 figures (1a, 1b, 2 and 3), MNRAS (letter), in prin

Theoretical study of turbulent channel flow: Bulk properties, pressure fluctuations, and propagation of electromagnetic waves

In this paper, we apply two theoretical turbulence models, DIA and the recent GISS model, to study properties of a turbulent channel flow. Both models provide a turbulent kinetic energy spectral function E(k) as the solution of a non-linear equation; the two models employ the same source function but different closures. The source function is characterized by a rate n sub s (k) which is derived from the complex eigenvalues of the Orr--Sommerfeld (OS) equation in which the basic flow is taken to be of a Poiseuille type. The O--S equation is solved for a variety of Reynolds numbers corresponding to available experimental data. A physical argument is presented whereby the central line velocity characterizing the basic flow, U0 sup L, is not to be identified with the U0 appearing in the experimental Reynolds number. The theoretical results are compared with two types of experimental data: (1) turbulence bulk properties, and (2) properties that depend stongly on the structure of the turbulence spectrun at low wave numbers. The only existing analytical expression for Pi (k) cannot be used in the present case because it applies to the case of a flat plate, not a finite channel

G\"{o}del-type universes in energy-momentum-squared gravity

In this paper, a modification of general relativity is considered. It consists of generalizing the Lagrangian of matter in a non-linear way, that is, replacing the curvature scalar $R$ by a function $f(R,T_{\mu\nu} T^{\mu\nu} )$, where $T_{\mu\nu}$ is the energy-momentum tensor. The main objective is to investigate the issue of causality in this gravitational model. To study the causality and/or its violation the G\"{o}del-type solutions are used. For such development, different matter contents are chosen. A critical radius, beyond which causality is violated, is calculated. It is shown that both causal and non-causal solutions are allowed.Comment: 15 pages, accepted for publication in EPJ

Efficient computation of bifurcation diagrams with a deflated approach to reduced basis spectral element method

The majority of the most common physical phenomena can be described using partial differential equations (PDEs). However, they are very often characterized by strong nonlinearities. Such features lead to the coexistence of multiple solutions studied by the bifurcation theory. Unfortunately, in practical scenarios, one has to exploit numerical methods to compute the solutions of systems of PDEs, even if the classical techniques are usually able to compute only a single solution for any value of a parameter when more branches exist. In this work, we implemented an elaborated deflated continuation method that relies on the spectral element method (SEM) and on the reduced basis (RB) one to efficiently compute bifurcation diagrams with more parameters and more bifurcation points. The deflated continuation method can be obtained combining the classical continuation method and the deflation one: the former is used to entirely track each known branch of the diagram, while the latter is exploited to discover the new ones. Finally, when more than one parameter is considered, the efficiency of the computation is ensured by the fact that the diagrams can be computed during the online phase while, during the offline one, one only has to compute one-dimensional diagrams. In this work, after a more detailed description of the method, we will show the results that can be obtained using it to compute a bifurcation diagram associated with a problem governed by the Navier-Stokes equations

Numerical Evolution of axisymmetric vacuum spacetimes: a code based on the Galerkin method

We present the first numerical code based on the Galerkin and Collocation methods to integrate the field equations of the Bondi problem. The Galerkin method like all spectral methods provide high accuracy with moderate computational effort. Several numerical tests were performed to verify the issues of convergence, stability and accuracy with promising results. This code opens up several possibilities of applications in more general scenarios for studying the evolution of spacetimes with gravitational waves.Comment: 11 pages, 6 figures. To appear in Classical and Quantum Gravit

The Zeta Herculis binary system revisited. Calibration and seismology

We have revisited the calibration of the visual binary system Zeta Herculis with the goal to give the seismological properties of the G0 IV sub-giant Zeta Her A. We have used the most recent physical and observational data. For the age we have obtained 3387 Myr, for the masses respectively 1.45 and 0.98 solar mass, for the initial helium mass fraction 0.243, for the initial mass ratio of heavy elements to hydrogen 0.0269 and for the mixing-length parameters respectively 0.92 and 0.90 using the Canuto & Mazitelli (1991, 1992) convection theory. Our results do not exclude that Zeta Her A is itself a binary sub-system; the mass of the hypothetical unseen companion would be smaller than 0.05 solar mass. The adiabatic oscillation spectrum of Zeta Her A is found to be a complicated superposition of acoustic and gravity modes; some of them have a dual character. This greatly complicates the classification of the non-radial modes. The echelle diagram used by the observers to extract the frequencies will work for ell=0, 2, 3. The large difference is found to be of the order of 42 mu Hz, in agreement with the Martic et al. (2001) seismic observations.Comment: 12 pages, A&A in pres

Orbital Ferromagnetism and Quantum Collapse in Stellar Plasmas

The possibility of quantum collapse and characteristics of nonlinear localized excitations is examined in dense stars with Landau orbital ferromagnetism in the framework of conventional quantum magnetohydrodynamics (QMHD) model including Bohm force and spin-orbit polarization effects. Employing the concepts of effective potential and Sagdeev pseudopotential, it is confirmed that the quantum collapse and Landau orbital ferromagnetism concepts are consistent with the magnetic field and mass-density range present in some white dwarf stars. Furthermore, the value of ferromagnetic-field found in this work is about the same order of magnitude as the values calculated earlier. It is revealed that the magnetosonic nonlinear propagations can behave much differently in the two distinct non-relativistic and relativistic degeneracy regimes in a ferromagnetic dense astrophysical object. Current findings should help to understand the origin of the most important mechanisms such as gravitational collapse and the high magnetic field present in many compact stars.Comment: To appear in journal Physics of Plasma