An agglomeration-based massively parallel non-overlapping additive Schwarz preconditioner for high-order discontinuous Galerkin methods on polytopic grids

In this article we design and analyze a class of two-level non-overlapping additive Schwarz preconditioners for the solution of the linear system of equations stemming from discontinuous Galerkin discretizations of second-order elliptic partial differential equations on polytopic meshes. The preconditioner is based on a coarse space and a non-overlapping partition of the computational domain where local solvers are applied in parallel. In particular, the coarse space can potentially be chosen to be non-embedded with respect to the finer space; indeed it can be obtained from the fine grid by employing agglomeration and edge coarsening techniques. We investigate the dependence of the condition number of the preconditioned system with respect to the diffusion coefficient and the discretization parameters, i.e., the mesh size and the polynomial degree of the fine and coarse spaces. Numerical examples are presented which confirm the theoretical bounds

The evolution of collision debris near the ν6\nu_6 secular resonance and its role in the origin of terrestrial water

This work presents novel findings that broadens our understanding of the amount of water that can be transported to Earth. The key innovation lies in the combined usage of Smoothed Particle Hydrodynamics (SPH) and $N$-body codes to assess the role of collision fragments in water delivery. We also present a method for generating initial conditions that enables the projectile to impact at the designated location on the target's surface with the specified velocity. The primary objective of this study is to simulate giant collisions between two Ceres-sized bodies by SPH near the $\nu_6$ secular resonance and follow the evolution of the ejected debris by numerical $N$-body code. With our method 6 different initial conditions for the collision were determined and the corresponding impacts were simulated by SPH. Examining the orbital evolution of the debris ejected after collisions, we measured the amount of water delivered to Earth, which is broadly 0.001 ocean equivalents of water, except in one case where one large body transported 7\% oceans of water to the planet. Based on this, and taking into account the frequency of collisions, the amount of delivered water varies between 1.2 and 8.3 ocean's worth of water, depending on the primordial disk mass. According to our results, the prevailing external pollution model effectively accounts for the assumed water content on Earth, whether it's estimated at 1 or 10 ocean's worth of water.Comment: 15 pages, 13 figure

Existence and equilibration of global weak solutions to Hookean-type bead-spring chain models for dilute polymers

We show the existence of global-in-time weak solutions to a general class of coupled Hookean-type bead-spring chain models that arise from the kinetic theory of dilute solutions of polymeric liquids with noninteracting polymer chains. The class of models involves the unsteady incompressible Navier-Stokes equations in a bounded domain in two or three space dimensions for the velocity and the pressure of the fluid, with an elastic extra-stress tensor appearing on the right-hand side in the momentum equation. The extra-stress tensor stems from the random movement of the polymer chains and is defined by the Kramers expression through the associated probability density function that satisfies a Fokker-Planck-type parabolic equation, a crucial feature of which is the presence of a center-of-mass diffusion term. We require no structural assumptions on the drag term in the Fokker-Planck equation; in particular, the drag term need not be corotational. With a square-integrable and divergence-free initial velocity datum for the Navier-Stokes equation and a nonnegative initial probability density function for the Fokker-Planck equation, which has finite relative entropy with respect to the Maxwellian of the model, we prove the existence of a global-in-time weak solution to the coupled Navier-Stokes-Fokker-Planck system. It is also shown that in the absence of a body force, the weak solution decays exponentially in time to the equilibrium solution, at a rate that is independent of the choice of the initial datum and of the centre-of-mass diffusion coefficient.Comment: 86 page

Which are Better Conditioned Meshes Adaptive, Uniform, Locally Refined or Localised

Adaptive, locally refined and locally adjusted meshes are preferred over uniform meshes for capturing singular or localised solutions. Roughly speaking, for a given degree of freedom a solution associated with adaptive, locally refined and locally adjusted meshes is more accurate than the solution given by uniform meshes. In this work, we answer the question which meshes are better conditioned. We found, for approximately same degree of freedom (same size of matrix), it is easier to solve a system of equations associated with an adaptive mesh.Comment: 4 Page

Heisenberg-limited metrology with a squeezed vacuum state, three-mode mixing, and information recycling

We have previously shown that quantum-enhanced atom interferometry can be achieved by mapping the quantum state of squeezed optical vacuum to one of the atomic inputs via a beamsplitter-like process [Phys. Rev. A 90, 063630 (2014)]. Here we ask the question: is a better phase sensitivity possible if the quantum state transfer (QST) is described by a three-mode-mixing model, rather than a beamsplitter? The answer is yes, but only if the portion of the optical state not transferred to the atoms is incorporated via information recycling. Surprisingly, our scheme gives a better sensitivity for lower QST efficiencies and with a sufficiently large degree of squeezing can attain near-Heisenberg-limited sensitivities for arbitrarily small QST efficiencies. Furthermore, we use the quantum Fisher information to demonstrate the near optimality of our scheme

On the influence of the Kozai mechanism in habitable zones of extrasolar planetary systems

Aims. We investigate the long-term evolution of inclined test particles representing a small Earth-like body with negligible gravitational effects (hereafter called massless test-planets) in the restricted three-body problem, and consisting of a star, a gas giant, and a massless test-planet. The test-planet is initially on a circular orbit and moves around the star at distances closer than the gas giant. The aim is to show the influences of the eccentricity and the mass of the gas giant on the dynamics, for various inclinations of the test-planet, and to investigate in more detail the Kozai mechanism in the elliptic problem. Methods. We performed a parametric study, integrating the orbital evolution of test particles whose initial conditions were distributed on the semi-major axis – inclination plane. The gas giant’s initial eccentricity was varied. For the calculations, we used the Lie integration method and in some cases the Bulirsch-Stoer algorithm. To analyze the results, the maximum eccentricity and the Lyapunov characteristic indicator were used. All integrations were performed for 105 periods of the gas giant. Results. Our calculations show that inclined massless test-planets can be in stable configurations with gas giants on either circular or elliptic orbits. The higher the eccentricity of the gas giant, the smaller the possible range in semi-major axis for the test-planet. For gas giants on circular orbits, our results illustrate the well-known results associated with the Kozai mechanism, which do not allow stable orbits above a critical inclination of approximately 40°. For gas giants on eccentric orbits, the dynamics is quite similar, and the massless companion exhibits limited variations in eccentricity. In addition, we identify a region around 35° consisting of long-time stable, low eccentric orbits. We show that these results are also valid for Earth-mass companions, therefore they can be applied to extrasolar systems: for instance, the extrasolar planetary system HD 154345 can possess a 35° degree inclined, nearly circular, Earth-mass companion in the habitable zone

Drivers of grassland loss in Hungary during the post-socialist transformation (1987–1999)

The increase in the speed of land-cover change experienced worldwide is becoming a growing concern. Major socio-economic transitions, such as the breakdown of socialism in Europe, may lead to particularly high rates of landscape transformations. In this paper we examined the loss of semi-natural grasslands in Hungary between 1987 and 1999. We studied the relationship between 9 potential driving forces and the fate of grasslands using logistic GLMs. Grassland loss was found to be very high (1.31 % per year), which is far higher than either before or after this period. The most influential predictors of grassland loss were environmental and landscape characteristics (soil type, area of remnant grassland patches), and the socio-economic context (distance to paved road, and nearest settlement, human population density). Several processes and relationships can only be understood from a historical perspective (e.g. large extent of afforestation, strong decrease of soil water table). Grassland loss during the study period emerged as a consequence of survival strategies of individual farmers seeking adaptation to the changing environmental and socio-economic conditions, and not urbanization and agricultural intensification which are the main underlying drivers for the ongoing landscape transformations in most parts of the developed world. Though globalization increasingly influences local land use decisions , reconstructing and modelling recent landscape changes cannot be done without a proper understanding of local history and culture. Our analysis shows the importance of large-area yet high resolution landscape change research, which may reveal unexpected patterns of land cover change, undetected at coarser scales