Nonlinear effects of dark energy clustering beyond the acoustic scales

We extend the resummation method of Anselmi & Pietroni (2012) to compute the total density power spectrum in models of quintessence characterized by a vanishing speed of sound. For standard $\Lambda$CDM cosmologies, this resummation scheme allows predictions with an accuracy at the few percent level beyond the range of scales where acoustic oscillations are present, therefore comparable to other, common numerical tools. In addition, our theoretical approach indicates an approximate but valuable and simple relation between the power spectra for standard quintessence models and models where scalar field perturbations appear at all scales. This, in turn, provides an educated guess for the prediction of nonlinear growth in models with generic speed of sound, particularly valuable since no numerical results are yet available.Comment: 28 pages, 12 figure

Expansion schemes for gravitational clustering: computing two-point and three-point functions

We describe various expansion schemes that can be used to study gravitational clustering. Obtained from the equations of motion or their path-integral formulation, they provide several perturbative expansions that are organized in different fashion or involve different partial resummations. We focus on the two-point and three-point correlation functions, but these methods also apply to all higher-order correlation and response functions. We present the general formalism, which holds for the gravitational dynamics as well as for similar models, such as the Zeldovich dynamics, that obey similar hydrodynamical equations of motion with a quadratic nonlinearity. We give our explicit analytical results up to one-loop order for the simpler Zeldovich dynamics. For the gravitational dynamics, we compare our one-loop numerical results with numerical simulations. We check that the standard perturbation theory is recovered from the path integral by expanding over Feynman's diagrams. However, the latter expansion is organized in a different fashion and it contains some UV divergences that cancel out as we sum all diagrams of a given order. Resummation schemes modify the scaling of tree and one-loop diagrams, which exhibit the same scaling over the linear power spectrum (contrary to the standard expansion). However, they do not significantly improve over standard perturbation theory for the bispectrum, unless one uses accurate two-point functions (e.g. a fit to the nonlinear power spectrum from simulations). Extending the range of validity to smaller scales, to reach the range described by phenomenological models, seems to require at least two-loop diagrams.Comment: 24 pages, published in A&

Multi-Particle Collision Dynamics -- a Particle-Based Mesoscale Simulation Approach to the Hydrodynamics of Complex Fluids

In this review, we describe and analyze a mesoscale simulation method for fluid flow, which was introduced by Malevanets and Kapral in 1999, and is now called multi-particle collision dynamics (MPC) or stochastic rotation dynamics (SRD). The method consists of alternating streaming and collision steps in an ensemble of point particles. The multi-particle collisions are performed by grouping particles in collision cells, and mass, momentum, and energy are locally conserved. This simulation technique captures both full hydrodynamic interactions and thermal fluctuations. The first part of the review begins with a description of several widely used MPC algorithms and then discusses important features of the original SRD algorithm and frequently used variations. Two complementary approaches for deriving the hydrodynamic equations and evaluating the transport coefficients are reviewed. It is then shown how MPC algorithms can be generalized to model non-ideal fluids, and binary mixtures with a consolute point. The importance of angular-momentum conservation for systems like phase-separated liquids with different viscosities is discussed. The second part of the review describes a number of recent applications of MPC algorithms to study colloid and polymer dynamics, the behavior of vesicles and cells in hydrodynamic flows, and the dynamics of viscoelastic fluids

Large-N expansions applied to gravitational clustering

We develop a path-integral formalism to study the formation of large-scale structures in the universe. Starting from the equations of motion of hydrodynamics (single-stream approximation) we derive the action which describes the statistical properties of the density and velocity fields for Gaussian initial conditions. Then, we present large-N expansions (associated with a generalization to N fields or with a semi-classical expansion) of the path-integral defined by this action. This provides a systematic expansion for two-point functions such as the response function and the usual two-point correlation. We present the results of two such expansions (and related variants) at one-loop order for a SCDM and a LCDM cosmology. We find that the response function exhibits fast oscillations in the non-linear regime with an amplitude which either follows the linear prediction (for the direct steepest-descent scheme) or decays (for the 2PI effective action scheme). On the other hand, the correlation function agrees with the standard one-loop result in the quasi-linear regime and remains well-behaved in the highly non-linear regime. This suggests that these large-N expansions could provide a good framework to study the dynamics of gravitational clustering in the non-linear regime. Moreover, the use of various expansion schemes allows one to estimate their range of validity without the need of N-body simulations and could provide a better accuracy in the weakly non-linear regime.Comment: 27 pages, published in A&

DYCAST: A finite element program for the crash analysis of structures

DYCAST is a nonlinear structural dynamic finite element computer code developed for crash simulation. The element library contains stringers, beams, membrane skin triangles, plate bending triangles and spring elements. Changing stiffnesses in the structure are accounted for by plasticity and very large deflections. Material nonlinearities are accommodated by one of three options: elastic-perfectly plastic, elastic-linear hardening plastic, or elastic-nonlinear hardening plastic of the Ramberg-Osgood type. Geometric nonlinearities are handled in an updated Lagrangian formulation by reforming the structure into its deformed shape after small time increments while accumulating deformations, strains, and forces. The nonlinearities due to combined loadings are maintained, and stiffness variation due to structural failures are computed. Numerical time integrators available are fixed-step central difference, modified Adams, Newmark-beta, and Wilson-theta. The last three have a variable time step capability, which is controlled internally by a solution convergence error measure. Other features include: multiple time-load history tables to subject the structure to time dependent loading; gravity loading; initial pitch, roll, yaw, and translation of the structural model with respect to the global system; a bandwidth optimizer as a pre-processor; and deformed plots and graphics as post-processors