Initial Conditions

A mathematical model for the generation and transport of gas and heat in a sanitary landfill was developed based on earlier work on the Mountain View Controlled Landfill Project (MVCLP) in California, U.S.A. The present model incorporates biokinetic model equations describing the dynamics of the microbial landfill ecosystem into multi-layer, time-dependent transport and generation of gas and heat models. It is based on the fundamental principles governing the physical, chemical and microbiological processes in a porous media context such as a sanitary landfill. The model includes biochemical and temperature feedback loops to simulate the effects of their corresponding parameters on microbiological processes. The resulting integrated biokinetic, gas and heat generation and transport model was used to simulate field data from the MVCLP and to assess the sensitivity of model results to biological parameters. The model can be used to predict the rate and total production of methane in a landfill. The present work is presented in a series of three papers: (I) model formulation; (II) model application; and (III) sensitivity analysis * .

We study the turning point problem of a spherical pendulum. The special cases of the simple pendulum and the conical pendulum are noted. For simple initial conditions the solution to this problem involves the golden ratio, also called the golden section, or the golden number. This number often appears in mathematics where you least expect it. To put our result in perspective we briefly discuss its relevance in physics.

This work presents a mathematical model for the two-phase flows in the mortar systems and demonstrates the application of approximate Riemann solver on such model. The mathematical model for the two-phase gas-dynamical processes in the mortar tube consists of a system of first-order, nonlinear coupled partial differential equations with inhomogeneous terms. The model poses an initial value problem with discontinuous initial and boundary conditions that arise due to the design complexity and nonuniformity of granular propellant distribution in the mortar tube. The governing equations in this model possess characteristics of the Riemann problem. Therefore, a high-resolution Godunov-type shock-capturing approach was used to address the formation of flow structure such as shock waves, contact discontinuities, and rarefaction waves. A linearized approximate Riemann solver based on the Roe-Pike method was modified for the twophase flows to compute fully nonlinear wave interactions and to directly provide upwinding properties in the scheme. An entropy fix based on Harten-Heyman method was used with van Leer flux limiter for total variation diminishing. The three-dimensional effects were simulated by incorporating an unsplit multidimensional wave propagation method, which accounted for discontinuities traveling in both normal and oblique coordinate directions. A mesh generation algorithm was developed to account for the projectile motion and coupled with the approximate Riemann solver. The numerical method was verified by using exact solutions of three test problems. The specific system considered in this work is a 120 mm mortar system, which contains an ignition cartridge that discharges hot gas-phase products and unburned granular propellants into the mortar tube through multiple vent-holes on its surface. The model for the mortar system was coupled with the solution of the transient gas-dynamic behavior in the ignition cartridge. The numerical results were validated with experimental data. Based on the close comparison between the calculated results and test data, it was found that the approximate Riemann solver is a suitable method for studying the two-phase combustion processes in mortar systems. to 68.9.31.77. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm 3.5 Three-Dimensional Wave Propagation. Unsplit methods ͓20͔ were used for multidimensional wave propagation. Both the increment waves ͑i.e., flux vectors͒ and correction waves ͑i.e., second-order terms͒ were split into parts propagating in both the direction normal to the interface between two spatial locations and transverse direction by solving Riemann problems in coordinate directions tangential to the interfaces. This treatment calculates the cross derivative terms necessary for achieving both a stable and second-order accurate scheme. One-dimensional Riemann problems are solved at the interfaces. The scheme used in this

The objective of this paper is showing how global safety arguments can be fruitfully used to interpret experimental results of a pendulum parametrically excited by wave motion. In fact, the results of an experimental campaign developed with the aim of simulating sea-waves energy production by a parametric pendulum show that rotations exist in a region which is smaller than the theoretical one. This discrepancy can be partially attributed to the experimental approximations and constraints, but it has a deeper theoretical motivation. By comparing the experimental results with the dynamical integrity profiles we have found that experimental rotations exist only where a measure of dynamical integrity accounting for both attractor robustness and basin compactness is large enough, so that they can support experimental imperfections leading to changes in initial conditions.

We prove local well-posedness of the initial-boundary value problem for the Korteweg-de Vries equation on right half-line, left half-line, and line segment, in the low regularity setting. This is accomplished by introducing an analytic family of boundary forcing operators. 1991 Mathematics Subject Classification. 35Q55. Key words and phrases. Korteweg-de Vries equation, initial-boundary value problem, Cauchy problem, local well-posedness. The content of this article appears as part of the author's Ph.D. thesis at the University of Chicago under the direction of Carlos Kenig. The author is partially supported by an NSF postdoctoral fellowship.

Blood velocity and pressure fields in large arteries are greatly influenced by the deformability of the vessel. Moreover, wave propagation phenomena in the cardiovascular system can only be described considering wall deformability since blood is usually described as an incompressible fluid. However, computational methods for simulating blood flow in three-dimensional models of arteries have either considered a rigid wall assumption for the vessel or significantly simplified or reduced geometries. Computing blood flow in deformable domains using standard techniques like the ALE method remains a formidable problem for large, realistic anatomic and physiologic models of the cardiovascular system.

The global linear stability of the flat-plate boundary-layer flow to three-dimensional disturbances is studied by means of an optimization technique. We consider both the optimal initial condition leading to the largest growth at finite times and the optimal time-periodic forcing leading to the largest asymptotic response. Both optimization problems are solved using a Lagrange multiplier technique, where the objective function is the kinetic energy of the flow perturbations and the constraints involve the linearized Navier-Stokes equations. The approach proposed here is particularly suited to examine convectively unstable flows, where single global eigenmodes of the system do not capture the downstream growth of the disturbances. In addition, the use of matrix-free methods enables us to extend the present framework to any geometrical configuration. The optimal initial condition for spanwise wavelengths of the order of the boundary-layer thickness are finite-length streamwise vortices exploiting the lift-up mechanism to create streaks. For long spanwise wavelengths, it is the Orr mechanism combined with the amplification of oblique wave packets that is responsible for the disturbance growth. This mechanism is dominant for the long computational domain and thus for the relatively high Reynolds number considered here. Three-dimensional localized optimal initial conditions are also computed and the corresponding wave packets examined. For short optimization times, the optimal disturbances consist of streaky structures propagating and elongating in the downstream direction without significant spreading in the lateral direction. For long optimization times, we find the optimal disturbances with the largest energy amplification. These are wave packets of Tollmien-Schlichting waves with low streamwise propagation speed and faster spreading in the spanwise direction. The pseudo-spectrum of the system for real frequencies is also computed with matrix-free methods. The spatial structure of the optimal forcing is similar to that of the optimal initial condition, and the largest response to forcing is also associated with the Orr/oblique wave mechanism, however less so than in the case of the optimal initial condition. The lift-up mechanism is most efficient at zero frequency and degrades slowly for increasing frequencies. The response to localized upstream forcing is also discussed. † Email address for correspondence: luca@mech.kth.se 2 A. Monokrousos, E.

Blood velocity and pressure fields in large arteries are greatly influenced by the deformability of the vessel. Moreover, wave propagation phenomena in the cardiovascular system can only be described considering wall deformability since blood is usually described as an incompressible fluid. However, computational methods for simulating blood flow in three-dimensional models of arteries have either considered a rigid wall assumption for the vessel or significantly simplified or reduced geometries. Computing blood flow in deformable domains using standard techniques like the ALE method remains a formidable problem for large, realistic anatomic and physiologic models of the cardiovascular system.

In this paper, we estimate a model of labor market dynamics among individuals in Romania using panel data for three years, 1994 to 1996. Our motivation is to gain insight into the functioning of the labor market and how workers are coping during this period of economic liberalization and transformation that began in 1990. Our models of labor market transitions for men and women examine changing movements in and out of employment, unemployment, and self-employment, and incorporate speci…c features of the Romanian labor market, such as the role of unemployment bene…ts. We take into account demographic characteristics, state dependence, and individual unobserved heterogeneity by modeling the employment transitions with a dynamic mixed multinomial logit.

Dimensionality Reduction (DR) has found many applications in hyperspectral image processing. This book chapter investigates Projection Pursuit (PP)-based Dimensionality Reduction, (PP-DR) which includes both Principal Components Analysis (PCA) and Independent Component Analysis (ICA) as special cases. Three approaches are developed for PP-DR. One is to use a Projection Index (PI) to produce projection vectors to generate Projection Index Components (PICs). Since PP generally uses random initial conditions to produce PICs, when the same PP is performed in different times or by different users at the same time, the resulting PICs are generally different in terms of components and appearing orders. To resolve this issue, a second approach is called PI-based PRioritized PP (PI-PRPP) which uses a PI as a criterion to prioritize PICs. A third approach proposed as an alternative to PI-PRPP is called Initialization-Driven PP (ID-PIPP) which specifies an appropriate set of initial conditions that allows PP to produce the same PICs as well as in the same order regardless of how PP is run. As shown by experimental results, the three PP-DR techniques can perform not only DR but also separate various targets in different PICs so as to achieve unsupervised target detection.

Numerical stochastic integration is a powerful tool for the investigation of quantum dynamics in interacting many body systems. As with all numerical integration of differential equations, the initial conditions of the system being investigated must be specified. With application to quantum optics in mind, we show how various commonly considered quantum states can be numerically simulated by the use of widely available Gaussian and uniform random number generators. We note that the same methods can also be applied to computational studies of Bose-Einstein condensates, and give some examples of how this can be done.

The nature of cosmological solutions for a homogeneous, anisotropic Universe given by a Bianchi type-I (BI) model in the presence of a Cosmological constant Λ is investigated by taking into account dissipative process due to viscosity. The system in question is thoroughly studied both analytically and numerically. It is shown the viscosity, as well as the Λ term exhibit essential influence on the character of the solutions. In particular a negative Λ gives rise to an ever-expanding Universe, whereas, a suitable choice of initial conditions plus a positive Λ can result in a singularity-free oscillatory mode of expansion. For some special cases it is possible to obtain oscillations in the exponential mode of expansion of the BI model even with a negative Λ, where oscillations arise by virtue of viscosity.

To study the local Hubble flow, we have run constrained dark matter (DM) simulations of the Local Group (LG) in the concordance ΛCDM and OCDM cosmologies, with identical cosmological parameters apart from the Λ term. The simulations were performed within a computational box of 64 h −1 Mpc centred on the LG. The initial conditions were constrained by the observed peculiar velocities of galaxies and positions of X-ray nearby clusters of galaxies. The simulations faithfully reproduce the nearby large scale structure, and in particular the Local Supercluster and the Virgo cluster.

We undertake a comprehensive and rigorous analytic study of the evolution of radial profiles of covariant scalars in regular Lemaître-Tolman-Bondi dust models. We consider specifically the phenomenon of "profile inversions" in which an initial clump profile of density, spatial curvature or the expansion scalar, might evolve into a void profile (and vice versa). Previous work in the literature on models with density void profiles and/or allowing for density profile inversions is given full generalization, with some erroneous results corrected. We prove rigorously that if an evolution without shell crossings is assumed, then only the 'clump to void' inversion can occur in density profiles, and only in hyperbolic models or regions with negative spatial curvature. The profiles of spatial curvature follow similar patterns as those of the density, with 'clump to void' inversions only possible for hyperbolic models or regions. However, profiles of the expansion scalar are less restrictive, with profile inversions necessarily taking place in elliptic models. We also examine radial profiles in special LTB configurations: closed elliptic models, models with a simultaneous big bang singularity, as well as a locally collapsing elliptic region surrounded by an expanding hyperbolic background. The general analytic statements that we obtain allow for setting up the right initial conditions to construct fully regular LTB models with any specific qualitative requirements for the profiles of all scalars and their time evolution. The results presented can be very useful in guiding future numerical work on these models and in revising previous analytic work on all their applications.

The transport equations for the second-order velocity structure functions AE(du) 2 ae and AE(dq) 2 ae are used as a scale-by-scale budget to quantify the effect of initial conditions at low Reynolds numbers, typical of grid turbulence. The validity of these equations is first investigated via hot-wire measurements of velocity and transverse vorticity fluctuations. The transport equation for AE(dq) 2 ae is shown to be balanced at all scales, while anisotropy of the large scales leads to a significant imbalance in the equation for AE(du) 2 ae. The effect of using similarity to evaluate the transport equation is rigorously tested. This approach has the desirable benefit of requiring less extensive measurements to calculate the inhomogeneous term of the transport equation. The similarity form of the AE(dq) 2 ae equation produces nearly identical results as those obtained without the similarity assumption. In the case of the AE(du) 2 ae equation, the similarity method forces a balance at large separation, although the imbalance due to large scale anisotropy remains. The initial conditions of the turbulence at constant R M . 10,400 (28 £ R k £ 55) are changed by using three grids of different geometries. Initial conditions affect the shape and magnitude of the second-and third-order structure functions, as well as the anisotropy of the large scales. The effect of initial conditions on the scale-by-scale budget is restricted to the inhomogeneous term of the transport equations, while the dissipation term remains unaffected despite the low R k . Scales as small as k are affected by the changes in initial conditions.

This paper examines the development of the University of Rhodesia (UR) and identifies a pattern that developed in a path dependent way.  Path dependency captures the notion that choices, that are made when an institution is being formed, tend to have a continuing and lasting influence on the institution far into the future (Sydow, Schreyögg & Koch, 2009).  It is the tendency for a step in one direction to encourage the next step to be in a similar direction, thus keeping the development of an organisation in the same path (Greener, 2002). This study examines initial conditions as a factor that was crucial in the emergence of UR, and helped to perpetuate its dominance over time. The paper is based on a case study of UR from 1945 to 1980. It used semi-structured interviews and document analysis to give in-depth understanding of contextual issues and dynamics shaping the development of UR, and its ensuing path dependency.  Interview data was collected from 73 former students, current and former academics and administrators over a 10-month period. The purposive sampling technique was used to select the respondents, and the complete list of respondents evolved through the study using the snowballing technique. Qualitative data was collected and analysed (with the aid of data analysis software, Nvivo 8) according to the grounded theory approach. The study established that the evolution of UR was path dependent and influenced by initial conditions, increasing returns, self-reinforcement, positive feedback and lock-in. This paper looks at the influence of initial conditions as a source of competitive advantage in the evolution of UR.

In this paper, we investigate both theoretically and empirically the numerical bias due to the truncation of structurally infinite time forward-Iooking models, by the means of various terminal conditions. We shed light on the difficulties of numerical control using the latter instrurnents, and recornrnend a prior investigation of the individual dynamics generated by each variable of the models under consideration.

A systematic study of HBT radii of pions, produced in heavy ion collisions in the intermediate energy regime (SPS), from an integrated (3 + 1)d Boltzmann + hydrodynamics approach is presented. The calculations in this hybrid approach, incorporating an hydrodynamic stage into the Ultra-relativistic Quantum Molecular Dynamics transport model, allow for a comparison of different equations of state retaining the same initial conditions and final freeze-out. The results are also compared to the pure cascade transport model calculations in the context of the available data. Furthermore, the effect of different treatments of the hydrodynamic freeze-out procedure on the HBT radii are investigated. It is found that the HBT radii are essentially insensitive to the details of the freeze-out prescription as long as the final hadronic interactions in the cascade are taken into account. The HBT radii RL and RO and the RO /RS ratio are sensitive to the EoS that is employed during the hydrodynamic evolution. We conclude that the increased lifetime in case of a phase transition to a QGP (via a Bag Model equation of state) is not supported by the available data.

This paper presents a convenient shortcut method for implementing the Heckman estimator of the dynamic random effects probit model and other dynamic nonlinear panel data models using standard software. It then compares the estimators proposed by Heckman, Orme and Wooldridge, based on three alternative approximations, first in an empirical model for the probability of unemployment and then in a set of simulation experiments. The results indicate that none of the three estimators dominates the other two in all cases. In most cases all three estimators display satisfactory performance, except when the number of time periods is very small.

When the frequencies of the elastic and pendular oscillations of an elastic pendulum or swinging spring are in the ratio 2:1, there is a regular exchange of energy between the two modes of oscillation. We refer to this phenomenon as pulsation. Between the horizontal excursions, or pulses, the spring undergoes a change of azimuth which we call the precession angle. The pulsation and stepwise precession are the characteristic features of the dynamics of the swinging spring. The modulation equations for the small-amplitude resonant motion of the system are the well-known three-wave equations. We use Hamiltonian reduction to determine a complete analytical solution. The amplitudes and phases are expressed in terms of both Weierstrass and Jacobi elliptic functions. The strength of the pulsation may be computed from the invariants of the equations. Several analytical formulas are found for the precession angle. We deduce simplified approximate expressions, in terms of elementary functions, for the pulsation amplitude and precession angle and demonstrate their high accuracy by numerical experiments. Thus, for given initial conditions, we can describe the envelope dynamics without solving the equations. Conversely, given the parameters which determine the envelope, we can specify initial conditions which, to a high level of accuracy, yield this envelope.

The evolution of grain mantles in various interstellar environments is studied. We concentrate mainly on water, methanol and carbon dioxide, which constitute nearly 90 per cent of the grain mantle. We investigate how the production rates of these molecules depend on the relative gas-phase abundances of oxygen and carbon monoxide and constrain the relevant parameter space that reproduces these molecules close to the observed abundances. Allowing the accretion of only H, O and CO on the grains and using the Monte Carlo method, we follow the chemical processes for a few million years. We allow the formation of multilayers on the grains and incorporate the freeze-out effects of accreting O and CO. We find that the formation of these molecules depends on the initial conditions as well as on the average cloud density. Specifically, when the number density of accreting O is less than three times that of CO, methanol is always overproduced. Using the available reaction pathways it appears to be difficult to match the exact observed abundances of all three molecules simultaneously. Only in a narrow region of parameter space are all three molecules produced within the observed limits. Furthermore, we found that the incorporation of the freeze-outs of O and CO leads to an almost steady state on the grain surface. The mantle thickness grows anywhere between 60 and 500 layers in a period of two million years. In addition, we consider a case in which the gas number density changes with time owing to the gradual collapse of the molecular cloud and present the evolution of the composition of different species as a function of the radius of the collapsing cloud.

An individual's a priori talent can affect movement performance during learning. Also, task requirements and motor-perceptual factors are critical to the learning process. This study describes changes in high bar swing performance after a 2-month practice period. Twenty-five novice participants were divided by a priori talent level (spontaneous-talented [ST] and nonspontaneous-talented [NST]) and compared to experienced gymnasts. Additionally, we assessed their perception of their performance level before and after practice. We defined three events independently for hip (H) and shoulder (S) angle joints and for the lag between consecutive events (phases [P]): the smallest angle during downswing (P1H, P1S), the largest angle after P1 (P2H, P2S), and the smaller angle during upswing (P3H, P3S). Movement performance variables were the maximum elevation on the downswing (Pi) and the upswing (Pf), and the total path between both (swing amplitude). Data were collected during pre-and postpractice sessions by two video cameras. At the end of both sessions, participants drew a sketch to represent their perception of their performance level relative to the Pi, Pf, and the hip events. Results showed a similar practice effect in the swing amplitude in both novice groups. However, the ST group's performance and perception variables on the downswing improved more than the NST group due to practice. This study suggests that (a) downswing improvements were easier than in the upswing, possibly due to familiarity of the visual reference in combination with proprioceptive feedback; and (b) being ST may involve a better or faster gain in perception of self-action compared to NST.

Taking a wide range of the initial conditions, including spatial density distribution and mass function etc, the dynamical evolution of globular clusters in the Milky Way is investigated in detail by means of Monte Carlo simulations. Four dynamic mechanisms are considered: stellar evaporation, stellar evolution, tidal shocks due to both the disk and bulge, and dynamical friction. It is found that stellar evaporation dominates the evolution of low-mass clusters and all four are important for massive ones. For both the power-law and lognormal initial clusters mass functions, we can find the best-fit models which can match the present-day observations with their main features of the mass function almost unchanged after evolution of several Gyr. This implies that it is not possible to determine the initial mass function only based on the observed ones today. Moreover, the dispersion of the modelled mass functions mainly depends on the potential wells of host galaxies with the almost constant peaks, which is consistent with current observations.

The entanglement dynamics of an anisotropic two-qubit Heisenberg XYZ system in the presence of intrinsic decoherence is studied. The usefulness of such system for performance of the quantum teleportation protocol T0 and entanglement teleportation protocol T1 is also investigated. The results depend on the initial conditions and the parameters of the system. For the product and maximally entangled initial states, increasing the size of spin-orbit interaction parameter D amplifies the effects of dephasing and hence decreases the asymptotic entanglement and fidelity of teleportation. We show that the XY and XYZ Heisenberg systems provide a minimal resource entanglement, required for realizing efficient teleportation. Also, we find that for the some special cases there are some maximally entangled states which are immune to intrinsic decoherence. Therefore, it is possible to perform the quantum teleportation protocol T0 and the entanglement teleportation T1 with perfect quality by choosing a proper set of parameters and employing one of these maximally entangled robust states as initial state of the resource.

The area of stable motion for fictitious Trojan asteroids around Neptune's equilateral equilibrium points is investigated with respect to the size of the regions and their shape, subject to the inclination of the asteroid's orbit. For this task, we used the results of extensive numerical integrations of orbits for a fine grid in initial conditions around the points L 4 and L 5 and analysed the stability of the individual orbits. Our basic dynamical model was the outer Solar system (Jupiter, Saturn, Uranus and Neptune) but for comparison reasons also simpler ones were tested. We integrated in our models the equations of motion for some 5 × 10 5 orbits of fictitious Trojans in the vicinity of the stable equilibrium points up to 10 9 yr. According to the three-dimensional model, the initial inclination of the asteroids' orbit was also varied in the range 0 • < i < 60 •. Using on one side a fine grid of initial conditions, the semimajor axis versus perihelion of the fictitious object and, on the other side, the proper eccentricity e p versus the libration width D f , we compiled stability maps separately for L 4 and L 5. In addition, we computed the escape-times of the individual objects and plotted the number of escapers per time-interval of 5 × 10 6 yr for different initial inclinations. Finally, integrations of the equations of motion in different dynamical models shed light on the reason of the asymmetry of the stability behaviour of orbits close to the two equilateral equilibrium points of Neptune. For low-inclined Trojan orbits, the stability area around L 4 and L 5 disappeared after some 10 8 yr, and for larger inclinations of the Trojans the stability area survived for the time-interval of integration of 10 9 yr. The largest stable regions exist for Neptune Trojans with 20 • < i < 50 •. The somewhat interesting asymmetry in the size and the shape of the preceding and following Lagrange points, which exist for Neptune Trojans, was confirmed, and was found to be caused mostly by the couple Saturn-Uranus.

We estimate the electromagnetic effect of the spectator charge on the momentum spectra of π + and π − produced in peripheral Pb+Pb collisions at SPS energies. We find that the effect is large and results in strongly varying structures in the x F dependence of the π + /π − ratio, especially at low transverse momenta where a deep valley in the above ratio is predicted at x F ∼ 0.15-0.20. It appears that the effect depends on initial conditions. Thus, it provides new information on the space and time evolution of the non-perturbative pion creation process.

Some exact solutions of boundary or initial conditions formulated for
Bogomolny equations (derived by using the strong necessary conditions
and associated with some ordinary equation and some partial differential
equations), have been found. Besides, a degeneracy of the hamiltonian
for the restricted baby Skyrme model has been established.

A local level model has a deterministic level when the signal-to-noise ratio q is zero. In this paper we investigate the properties of the maximum likelihood estimator of q , paying particular attention to the case where its true value is zero. These properties are shown to be crucially dependent on the initial conditions employed.

In this paper we investigate theoretically the numerical bias due to the truncation of structurally infinite time forward-looking models, by the means of various terminal conditions. On a general multivariate optimal growth model, we first analytically confirm some well-known heuristic properties for certain extreme spectral cases. However, we show that the heuristic findings stated in the literature, relying on intermediate

We study the asymptotics of solutions of the Boltzmann equation describing the kinetic limit of a lattice of classical interacting anharmonic oscillators. We prove that, if the initial condition is a small perturbation of an equilibrium state, and vanishes at infinity, the dynamics tends diffusively to equilibrium. The solution is the sum of a local equilibrium state, associated to conserved quantities that diffuse to zero, and fast variables that are slaved to the slow ones. This slaving implies the Fourier law, which relates the induced currents to the gradients of the conserved quantities.

We study an evolutionary version of the spatial prisoner's dilemma game, where the agents are placed in a random graph. For lattices with fixed connectivity, α, we show that for low values of α the final density of cooperating agents depends on the initial conditions, while it does not depend for high connectivity lattices. We fully characterized the phase diagram of the system, using both, extensive numerical simulations and analytical computations. It is shown that two different behaviors are well defined: a Nash equilibrium one, where the density of cooperating agents ρc is fixed, and a non-stationary one, where ρc fluctuates in time. Moreover we study lattices with fluctuating connectivities and find that the phase diagram previously developed looses its meaning. In fact, multiple transitions appear and only one regime may be defined. This regime is completely characterized by a non stationary state where the density of cooperating agents varies in time.

We predict the biasing and clustering properties of galaxy clusters that are expected to be observed in the catalogues produced by two forthcoming X-ray and Sunyaev-Zel'dovich effect surveys. We study a set of flat cosmological models where the primordial density probability distribution shows deviations from Gaussianity in agreement with current observational bounds form the background radiation. We consider both local and equilateral shapes for the primordial bispectrum in non-Gaussian models. The two catalogues investigated are those produced by the eROSITA wide survey and from a survey based on South Pole Telescope observations. It turns out that both the bias and observed power spectrum of galaxy clusters are severely affected in non-Gaussian models with local shape of the primordial bispectrum, especially at large scales. On the other hand, models with equilateral shape of the primordial bispectrum show only a mild effect at all scales, that is difficult to be detected with clustering observations. Between the two catalogues, the one performing better is the eROSITA one, since it contains only the largest masses, that are more sensitive to primordial non-Gaussianity.

The description of the abundance and clustering of haloes for non-Gaussian initial conditions has recently received renewed interest, motivated by the forthcoming large galaxy and cluster surveys, which can potentially yield constraints of the order of unity on the non-Gaussianity parameter fNL. We present tests on N-body simulations of analytical formulae describing the halo abundance and clustering for non-Gaussian initial conditions. We calibrate the analytic non-Gaussian mass function of Matarrese, Verde & Jimenez and LoVerde et al. and the analytic description of clustering of haloes for non-Gaussian initial conditions on N-body simulations. We find an excellent agreement between the simulations and the analytic predictions if we make the corrections and , where q≃ 0.75, in the density threshold for gravitational collapse and in the non-Gaussian fractional correction to the halo bias, respectively. We discuss the implications of this correction on present and forecasted primordial non-Gaussianity constraints. We confirm that the non-Gaussian halo bias offers a robust and highly competitive test of primordial non-Gaussianity.

A systematic study of HBT radii of pions, produced in heavy ion collisions in the intermediate energy regime (SPS), from an integrated (3+1)d Boltzmann+hydrodynamics approach is presented. The calculations in this hybrid approach, incorporating an hydrodynamic stage into the Ultra-relativistic Quantum Molecular Dynamics transport model, allow for a comparison of different equations of state retaining the same initial conditions and final freeze-out. The results are also compared to the pure cascade transport model calculations in the context of the available data. Furthermore, the effect of different treatments of the hydrodynamic freeze-out procedure on the HBT radii are investigated. It is found that the HBT radii are essentially insensitive to the details of the freeze-out prescription as long as the final hadronic interactions in the cascade are taken into account. The HBT radii RL and RO and the RO/RS ratio are sensitive to the EoS that is employed during the hydrodynamic evolution. We conclude that the increased lifetime in case of a phase transition to a QGP (via a Bag Model equation of state) is not supported by the available data.