Narrow Results

In this study, we explore topologically spherical relativistic objects and analyze the factors that are involved in maintaining the smooth composition of anisotropic content. The corresponding field equations resulting from this extension show a different behavior due to the higher-order correction terms. We study the role of structure scalar in the possible modeling of complex objects in a well-known way, discussed by [L. Herrera, A. Di Prisco and J. Ospino, Phys. Rev. D98 (2018) 104059]. After orthogonally splitting the curvature tensor, the associated dynamical equations are evaluated. We examine the complexity of the pattern of evolution by considering the homologous constraint. Furthermore, in the presence and absence of dissipation, the behavior, characteristics, and stability of the self-gravitating structures are analyzed. It is inferred that correction terms are trying to disturb the usual scenario of the homologous evolution of the relativistic dynamical system.

In this paper, we explore a comprehensive analysis of the formalism governing the gravitational field equations in degenerate higher-order scalar–tensor theories. The propagation of these theories in the vacuum has a maximum of three degrees of freedom and is at most quadratic in the second derivative of the scalar field. We investigate the gravitational field equation for spherically symmetric anisotropic matter content along with its non-conserved equations. Our analysis focuses on the evaluation of structure scalars to assess their behavior under Einstein’s modification. We present a realistic mass contribution that sheds light on both geometric mass and total energy budget evaluations for celestial objects. Ultimately, we discuss two viable models restricted as minimal complexity and conformal flatness to enhance the scientific contribution of this paper.

The Piecewise Parabolic Method (PPM) hydrodynamics code and other codes based on the PPM technique have been used extensively for the simulation of astrophysical phenomena. A new version of the PPM hydrodynamics code under development at the Laboratory for Computational Science and Engineering (LCSE) at the University of Minnesota is described. This new code incorporates a version of dynamic local adaptive mesh refinement (AMR) targeted specifically at improving the treatment of shocks and contact discontinuities. This AMR technique is not intended to increase grid resolution in entire regions of the problem for which standard techniques of nonuniform grids and simple grid motion are adequate. Because the AMR is targeted at surfaces within a flow that can develop complex shapes, a cell-by-cell approach to the grid refinement is adopted in order to minimize the number of refined grid cells, with the hope of controlling the computational cost. As a result of this approach, the number of refined cells needed across a given shock or captured contact discontinuity is modest (< 10). Because the PPM method is very complex, ordinarily its wide difference stencil demands that a relatively large number of extra grid cells need to be added to each end of a grid strip, even when adapting to a thin feature of the flow. To avoid the work associated in handling these extra cells, only to conveniently produce valid data in the thin strip of actual interest, we have used intermediate results of the coarse grid calculation in order to eliminate the need for all but two of these extra cells at each end of the refined grid strip. The benefits of this approach will be described through sample results in 2D, and the method for handling the boundaries of the refined grid strips efficiently will be discussed. The data structures in this method are being carefully designed to permit efficient implementation of the algorithm on clusters of shared memory machines, with automatic dynamic balancing of computational loads over the cluster members.

A multiscale approach is used to simulate the translocation of DNA through a nanopore. Within this scheme, the interactions of the molecule with the surrounding fluid (solvent) are explicitly taken into account. By generating polymers of various initial configurations and lengths we map the probability distibutions of the passage times of the DNA through the nanopore. A scaling law behavior for the most probable of these times with respect to length is derived, and shown to exhibit an exponent that is in a good agreement with the experimental findings. The essential features of the DNA dynamics as it passes through the pore are explored.

Using Lattice Boltzmann numerical simulations, we analyse the hydrodynamic properties of both fractal aggregates and artificial fractal objects. First we show that the hydrodynamic radius actually depends on three quantities: the fractal dimension, the so-called prefactor and the inside connectivity. Second, from the simulated velocity field inside the aggregate, we observe that Darcy's law describes the flow better than Brinkman equation. Finally we measure the permeability - porosity relation and observed that it departs from the prediction of Happel's model.

Molecular-dynamics-coupled multiparticle collision dynamic (MPC-MD) simulations have emerged to be an efficient and versatile tool in the description of mesoscale colloidal dynamics. However, the compressibility of the coarse-grained fluid leads to this method being prone to spurious depletion interactions that may dominate the colloidal dynamics. In this paper, we review the existing methodology to deal with these interactions, establish and report depletion measurements, and present a method to avoid artificial depletion in mesoscale simulation methods.

Algorithms exhibiting parallelization on many different levels are discussed for short-and long-range cellular automata implemented on scalar, vector, SIMD and MIMD machines. Short range cellular automata are commonly used for simulating hydrodynamic fluid flows, while long range cellular automata are applicable to neural networks at zero temperature. A common programming approach based upon multi-spin coding and including higher levels of parallelization when possible, has been used to implement these models on the SUN SPARC-1, the IBM-3090, the Alliant FX/2800, the NEC-SX3/11, the Cray-YMP/832 and the Connection Machine, CM-2. Section 4 of the paper compares the performance of these computers for the algorithms discussed in the text. Additionally, the major subroutines for each computer type are given in the Appendix.

We report on performance tests of pair interaction lattice gas automata in two and three dimensions coded in FORTRAN and C. The programs have been run on ALLIANT/FX-80, ALLIANT/FX-2800, CONVEX C2, CRAY-YMP, NEC/SX3, and SUN/IPC. The maximum update rates are 200 million site updates per second on the NEC/SX3 (FORTRAN), 117 (2D version) and 29 (3D version) on the CRAY-YMP (C). As a byproduct we give results for the performance of integer arithmetic and bit operations. Usually the C-programs were somewhat faster than the FORTRAN-programs except on the NEC/SX3 where the C-compiler was not able to vectorize the main loops.

We show that by including thermodynamic functions derived from a chosen free energy in a lattice-Boltzmann simulation of fluid flow it is possible to ensure that the fluid relaxes to a well-defined equlilibrium corresponding to the minimum of the input free energy. Two examples are given of phase separation in a binary fluid: bulk two-phase coexistence and a lamellar phase stabilised by a competition between negative surface tension and positive curvature energy. The lattice-Boltzmann framework simulates the Navier–Stokes equations of fluid flow and hence allows investigation of the effects of hydrodynamics on the kinetics of phase separation and on the rheology of the ordered structures.

We present a new lattice-Boltzmann method for hydrodynamic simulations, which is capable of handling very large density and temperature gradients. Unlike other LBGK models, the discrete velocities we used center at the local mean flow velocity, and their values vary according to the local temperature. The adiabatic index of the gas can be easily controlled by a parameter.

We propose a coarse-graining procedure for a fluid system that allows us to discuss from a conceptual point of view different "mesoscopic" approaches to hydrodynamic problems. Dissipative Particle Dynamics (DPD) and Smoothed Particle Dynamics (SPS) are discussed simultaneously within this framework. In particular, we give physical meaning to the weight function used in SPD. The close analogy between DPD and SPD suggests a synthesis of both approaches that overcomes the conceptual shortcomings of both.

In numerical large-scale hydrodynamics calculations, such as the description of a supernova explosion, instantaneous thermalization of the fluid matter is assumed independently of the size of the volume element used in the calculation. One expects, however, the appearance of transient processes such as convection currents, vortices, and other collective motion on smaller and smaller scales, which can delay equilibration. To account for these effects in a simple one-dimensional hydrodynamical calculation, we introduce retardation in the hydrodynamic equations and show that, when strong shocks are present, such effects may have considerable influence on the evolution of the system.

After a short discussion of recent discretization techniques for the lattice-Boltzmann equations we motivate and discuss some alternative approaches using implicit, nonuniform FD discretization and mesh refinement techniques. After presenting results of a stability analysis we use an implicit approach to simulate a boundary layer test problem. The numerical results compare well to the reference solution when using strongly refined meshes. Some basic ideas for a nonuniform mesh refinement (with non-cartesian mesh topology) are introduced using the standard discretization procedure of alternating collision and propagation.

Cellular automata (CA) and lattice-Boltzmann (LB) models are two possible approaches to simulate fluid-like systems. CA models keep track of the many-body correlations and provide a description of the fluctuations. However, they lead to a noisy dynamics and impose strong restrictions on the possible viscosity values. On the other hand, LB models are numerically more efficient and offer much more flexibility to adjust the fluid parameters, but they neglect fluctuations. Here we discuss a multiparticle lattice model which reconciles both approaches. Our method is tested on Poiseuille flows and on the problem of ballistic annihilation in two dimensions for which the fluctuations are known to play an important role.

Lattice-Boltzmann (LB) models provide a systematic formulation of effective-field computational approaches to the calculation of multiphase flow by replacing the mathematical surface of separation between the vapor and liquid with a thin transition region, across which all magnitudes change continuously. Many existing multiphase models of this sort do not satisfy the rigorous hydrodynamic constitutive laws. Here, we extend the two-dimensional, seven-speed Swift et al. LB model¹ to rectangular grids (nine speeds) by using symbolic manipulation (Mathematica^TM) and compare the LB model predictions with benchmark problems, in order to evaluate its merits. Particular emphasis is placed on the stress tensor formulation. Comparison with the two-phase analogue of the Couette flow and with a flow involving shear and advection of a droplet surrounded by its vapor reveals that additional terms have to be introduced in the definition of the stress tensor in order to satisfy the Navier–Stokes equation in regions of high density gradients. The use of Mathematica obviates many of the difficulties with the calculations "by-hand," allowing at the same time more flexibility to the computational analyst to experiment with geometrical and physical parameters of the formulation.

We investigate a new method for simulating polymer-solvent systems which combines a lattice-Boltzmann approach for the fluid with a continuum molecular dynamics (MD) model for the polymer chain. The two parts are coupled by a friction force which is proportional to the difference of the monomer velocity and the fluid velocity at the monomer's position. The strength of the coupling can be tuned by a friction coefficient. Using this approach we examine the dynamics of one monomer immersed in the fluid, and by adding fluctuations to the fluid and the monomer, also the velocity autocorrelation function of one monomer. This results in the definition of an effective friction coefficient for the dynamics of the monomer. Furthermore we analyze the mapping of the model to an MD simulation, allowing us to compare results obtained using the new method with MD.

AdS-hydrodynamics has proven to be a useful tool for obtaining transport coefficients observed in the collective flow of strongly coupled fluids like quark gluon plasma (QGP). Particularly, the ratio of shear viscosity to entropy density η/s obtained from elliptic flow measurements can be matched with the computation done in the dual gravity theory. The experimentally observed temperature dependence of η/s requires the study of scalar matter coupled AdS gravity including higher derivative curvature corrections. We obtain the backreaction to the metric for such a matter coupled AdS gravity in D-dimensional spacetime due to the higher derivative curvature corrections. Then, we present the backreaction corrections to shear viscosity η and entropy density s.

In the presence of a rotating Kerr black hole, we investigate hydrodynamics of the massive particles and massless photons to construct relations among number density, pressure and internal energy density of the massive particles and photons around the rotating Kerr black hole and to study an accretion onto the black hole. On equatorial plane of the Kerr black hole, we investigate the bound orbits of the massive particles and photons around the black hole to produce their radial, azimuthal and precession frequencies. With these frequencies, we study the black holes GRO J1655-40 and 4U 1543-47 to explicitly obtain the radial, azimuthal and precession frequencies of the massive particles in the flow of perfect fluid. We next consider the massive particles in the stable circular orbit of radius of 1.0 ly around the supernovas SN 1979C, SN 1987A and SN 2213-1745 in the Kerr curved spacetime, and around the potential supermassive Schwarzschild black holes M87, NGC 3115, NGC 4594, NGC 3377, NGC 4258, M31, M32 and Galatic center, to estimate their radial and azimuthal frequencies, which are shown to be the same results as those in no precession motion. The photon unstable orbit is also discussed in terms of the impact parameter of the photon trajectory. Finally, on the equatorial plane of the Kerr black hole, we construct the global flat embedding structures possessing (9 + 3) dimensionalities outside and inside the event horizon of the rotating Kerr black hole. Moreover, on the plane, we investigate the warp products of the Kerr spacetime.

We study the rest-frame instant form of a new formulation of relativistic perfect fluids in terms of new generalized Eulerian configuration coordinates. After the separation of the relativistic center of mass from the relative variables on the Wigner hyper-planes, we define orientational and shape variables for the fluid, viewed as a relativistic extended deformable body, by introducing dynamical body frames. Finally we define Dixon's multipoles for the fluid.

Hydrodynamics is the appropriate "effective theory" for describing any fluid medium at sufficiently long length scales. This paper treats the vacuum as such a medium and derives the corresponding hydrodynamic equations. Unlike a normal medium the vacuum has no linear sound-wave regime; disturbances always "propagate" nonlinearly. For an "empty vacuum" the hydrodynamic equations are familiar ones (shallow water-wave equations) and they describe an experimentally observed phenomenon — the spreading of a clump of zero-temperature atoms into empty space. The "Higgs vacuum" case is much stranger; pressure and energy density, and hence time and space, exchange roles. The speed of sound is formally infinite, rather than zero as in the empty vacuum. Higher-derivative corrections to the vacuum hydrodynamic equations are also considered. In the empty-vacuum case the corrections are of quantum origin and the post-hydrodynamic description corresponds to the Gross–Pitaevskii equation. We conjecture the form of the post-hydrodynamic corrections in the Higgs case. In the (1+1)-dimensional case the equations possess remarkable "soliton" solutions and appear to constitute a new exactly integrable system.