Cosmological perturbations in coherent oscillating scalar field models

The fact that fast oscillating homogeneous scalar fields behave as perfect fluids in average and their intrinsic isotropy have made these models very fruitful in cosmology. In this work we will analyse the perturbations dynamics in these theories assuming general power law potentials V(ϕ) = λ|ϕ|^n /n. At leading order in the wavenumber expansion, a simple expression for the effective sound speed of perturbations is obtained c_eff^ 2  = ω = (n − 2)/(n + 2) with ω the effective equation of state. We also obtain the first order correction in k^ 2/ω_eff^ 2 , when the wavenumber k of the perturbations is much smaller than the background oscillation frequency, ω_eff. For the standard massive case we have also analysed general anharmonic contributions to the effective sound speed. These results are reached through a perturbed version of the generalized virial theorem and also studying the exact system both in the super-Hubble limit, deriving the natural ansatz for δϕ; and for sub-Hubble modes, exploiting Floquet’s theorem.

Magnetic properties of ODP Site 191-1179 sediments

As reported by Shipboard Scientific Party (2001b, doi:10.2973/odp.proc.ir.191.104.2001) in the Site 1179 chapter of the Initial Reports volume, Leg 191 Site 1179 is located on abyssal seafloor northwest of Shatsky Rise, ~1650 km east of Japan. This part of the Pacific plate was formed during the Early Cretaceous, as shown by northeast-trending M-series magnetic lineations that become younger toward the northwest (Larson and Chase, 1972, doi:10.1130/0016-7606(1972)83[3627:LMEOTW]2.0.CO;2; Sager et al., 1988, doi:10.1029/JB093iB10p11753; Nakanishi et al., 1989, doi:10.1029/1999JB900002). The site is situated on magnetic Anomaly M8 (Nakanishi et al., 1999, doi:10.1029/1999JB900002), corresponding to an age of ~129 Ma and the Hauterivian stage of the Early Cretaceous (Gradstein et al., 1994, doi:10.1029/94JB01889; 1995). The sediments recovered at Site 1179 are split into four lithostratigraphic units based on composition and color (Shipboard Scientific Party, 2001b, doi:10.2973/odp.proc.ir.191.104.2001). Unit I (0-221.52 meters below seafloor [mbsf]) is a dominantly olive-gray clay- and radiolarian-bearing diatom ooze. Unit II (221.52-246.0 mbsf) is a yellowish brown to light brown clay-rich and diatom-bearing radiolarian ooze. Unit III (246.0-283.53 mbsf) is composed of brown pelagic clay. Unit IV (283.53-377.15 mbsf) is composed of chert and some porcellanite; any softer sediments present were washed out of the core barrel by the fluid circulating during the coring process.

Phase transitions in wave turbulence

We consider turbulence within the Gross-Pitaevsky model and look into the creation of a coherent condensate via an inverse cascade originating at small scales. The growth of the condensate leads to a spontaneous breakdown of statistical symmetries of overcondensate fluctuations: First, isotropy is broken, then a series of phase transitions marks the changing symmetry from twofold to threefold to fourfold. We describe respective anisotropic flux flows in the k space. At the highest level reached, we observe a short-range positional and long-range orientational order (as in a hexatic phase). In other words, the more one pumps the system, the more ordered the system becomes. The phase transitions happen when the system is pumped by an instability term and does not occur when pumped by a random force. We thus demonstrate nonuniversality of an inverse-cascade turbulence with respect to the nature of small-scale forcing.

The 100th anniversary of the four-point probe technique: the role of probe geometries in isotropic and anisotropic systems

The electrical conductivity of solid-state matter is a fundamental physical property and can be precisely derived from the resistance measured via the four-point probe technique excluding contributions from parasitic contact resistances. Over time, this method has become an interdisciplinary characterization tool in materials science, semiconductor industries, geology, physics, etc, and is employed for both fundamental and application-driven research. However, the correct derivation of the conductivity is a demanding task which faces several difficulties, e.g. the homogeneity of the sample or the isotropy of the phases. In addition, these sample-specific characteristics are intimately related to technical constraints such as the probe geometry and size of the sample. In particular, the latter is of importance for nanostructures which can now be probed technically on very small length scales. On the occasion of the 100th anniversary of the four-point probe technique, introduced by Frank Wenner, in this review we revisit and discuss various correction factors which are mandatory for an accurate derivation of the resistivity from the measured resistance. Among others, sample thickness, dimensionality, anisotropy, and the relative size and geometry of the sample with respect to the contact assembly are considered. We are also able to derive the correction factors for 2D anisotropic systems on circular finite areas with variable probe spacings. All these aspects are illustrated by state-of-the-art experiments carried out using a four-tip STM/SEM system. We are aware that this review article can only cover some of the most important topics. Regarding further aspects, e.g. technical realizations, the influence of inhomogeneities or different transport regimes, etc, we refer to other review articles in this field.

Inertial dissipation method applied to derive turbulent fluxed over the ocean during the Surface of the Ocean, Fluxes and Interactions with the Atmosphere Atlantic Stratocumulus Transition Experiment (SOFIA/ASTEX) and Structure des Echanges Mer-Atmosphere, Proprietes des Heterogeneites Oceaniques: Recherche Experimentale (SEMAPHORE) experiments with low to moderate wind speed

The transfer coefficients for momentum and heat have been determined for 10 m neutral wind speeds (U-10n) between 0 and 12 m/s using data from the Surface of the Ocean, Fluxes and Interactions with the Atmosphere (SOFIA) and Structure des Echanges Mer-Atmosphere, Proprietes des Heterogeneites Oceaniques: Recherche Experimentale (SEMAPHORE) experiments. The inertial dissipation method was applied to wind and pseudo virtual temperature spectra from a sonic anemometer, mounted on a platform (ship) which was moving through the turbulence held. Under unstable conditions the assumptions concerning the turbulent kinetic energy (TKE) budget appeared incorrect. Using a bulk estimate for the stability parameter, Z/L (where Z is the height and L is the Obukhov length), this resulted in anomalously low drag coefficients compared to neutral conditions. Determining Z/L iteratively, a low rate of convergence was achieved. It was concluded that the divergence of the turbulent transport of TKE was not negligible under unstable conditions. By minimizing the dependence of the calculated neutral drag coefficient on stability, this term was estimated at about -0.65Z/L. The resulting turbulent fluxes were then in close agreement with other studies at moderate wind speed. The drag and exchange coefficients for low wind speeds were found to be C-en x 10(3) = 2.79U(10n)(-1) + 0.66 (U-10n < 5.2 m/s), C-en x 10(3) = C-hn x 10(3) = 1.2 (U-10n greater than or equal to 5.2 m/s), and C-dn x 10(3) = 11.7U(10n)(-2) + 0.668 (U-10n < 5.5 m/s), which imply a rapid increase of the coefficient values as the wind decreased within the smooth flow regime. The frozen turbulence hypothesis and the assumptions of isotropy and an inertial subrange were found to remain valid at these low wind speeds for these shipboard measurements. Incorporation of a free convection parameterization had little effect.

Beyond the Cosmological Principle

Simplifying the Einstein field equation by assuming the cosmological principle yields a set of differential equations which governs the dynamics of the universe as described in the cosmological standard model. The cosmological principle assumes the space appears the same everywhere and in every direction and moreover, the principle has earned its position as a fundamental assumption in cosmology by being compatible with the observations of the 20th century. It was not until the current century when observations in cosmological scales showed significant deviation from isotropy and homogeneity implying the violation of the principle. Among these observations are the inconsistency between local and non-local Hubble parameter evaluations, baryon acoustic features of the Lyman-α forest and the anomalies of the cosmic microwave background radiation. As a consequence, cosmological models beyond the cosmological principle have been studied vastly; after all, the principle is a hypothesis and as such should frequently be tested as any other assumption in physics. In this thesis, the effects of inhomogeneity and anisotropy, arising as a consequence of discarding the cosmological principle, is investigated. The geometry and matter content of the universe becomes more cumbersome and the resulting effects on the Einstein field equation is introduced. The cosmological standard model and its issues, both fundamental and observational are presented. Particular interest is given to the local Hubble parameter, supernova explosion, baryon acoustic oscillation, and cosmic microwave background observations and the cosmological constant problems. Explored and proposed resolutions emerging by violating the cosmological principle are reviewed. This thesis is concluded by a summary and outlook of the included research papers.

Discrete breathers in a two-dimensional hexagonal Fermi-Pasta-Ulam lattice

We consider a two-dimensional Fermi-Pasta-Ulam (FPU) lattice with hexagonal symmetry. Using asymptotic methods based on small amplitude ansatz, at third order we obtain a eduction to a cubic nonlinear Schr{\"o}dinger equation (NLS) for the breather envelope. However, this does not support stable soliton solutions, so we pursue a higher-order analysis yielding a generalised NLS, which includes known stabilising terms. We present numerical results which suggest that long-lived stationary and moving breathers are supported by the lattice. We find breather solutions which move in an arbitrary direction, an ellipticity criterion for the wavenumbers of the carrier wave, symptotic estimates for the breather energy, and a minimum threshold energy below which breathers cannot be found. This energy threshold is maximised for stationary breathers, and becomes vanishingly small near the boundary of the elliptic domain where breathers attain a maximum speed. Several of the results obtained are similar to those obtained for the square FPU lattice (Butt \& Wattis, {\em J Phys A}, {\bf 39}, 4955, (2006)), though we find that the square and hexagonal lattices exhibit different properties in regard to the generation of harmonics, and the isotropy of the generalised NLS equation.

Motivic Decomposition of Projective Pseudo-Homogeneous Varieties

Let G be a semi-simple algebraic group over a field k. Projective G-homogeneous varieties are projective varieties over which G acts transitively. The stabilizer or the isotropy subgroup at a point on such a variety is a parabolic subgroup which is always smooth when the characteristic of k is zero. However, when k has positive characteristic, we encounter projective varieties with transitive G-action where the isotropy subgroup need not be smooth. We call these varieties projective pseudo-homogeneous varieties. To every such variety, we can associate a corresponding projective homogeneous variety. In this thesis, we extensively study the Chow motives (with coefficients from a finite connected ring) of projective pseudo-homogeneous varieties for G inner type over k and compare them to the Chow motives of the corresponding projective homogeneous varieties. This is done by proving a generic criterion for the motive of a variety to be isomorphic to the motive of a projective homogeneous variety which works for any characteristic of k. As a corollary, we give some applications and examples of Chow motives that exhibit an interesting phenomenon. We also show that the motives of projective pseudo-homogeneous varieties satisfy properties such as Rost Nilpotence and Krull-Schmidt.

Exploring the internal kinematics of Galactic Globular Cluster cores

Globular clusters (GCs) are traditionally described as simple quasi-relaxed non-rotating stellar systems, characterized by spherical symmetry and isotropy in velocity space. However, recent studies have shown deviations from isotropic velocity distributions and significant internal rotation in many GCs, suggesting that their internal structure and kinematics are more complex than previously thought. The aim of this thesis is to investigate the internal kinematics of Galactic Globular Clusters (GGCs) as part of the Multi-Instrument Kinematic Survey (MIKiS), which exploits the capabilities of different ESO-VLT spectrographs to obtain comprehensive velocity dispersion (VD) and rotation profiles of GGCs. Moreover, this thesis has the particular goal of unraveling the kinematics of GC cores, which are still largely unexplored, by taking advantage of the exceptional spatial resolution of the adaptive-optics assisted integral-field spectrograph MUSE/NFM. The thesis presents a thorough kinematic study of three GGCs NGC 1904, NGC 6440, and NGC 6569. By combining the data sets acquired with four different spectrographs, we obtained the radial velocity (RV) of more than 1000 individual stars in each cluster, sampling from the innermost to the outermost regions. This allowed us to obtain the entire VD profile of each cluster and exclude the presence of an intermediate-mass black hole in the core of NGC 1904, at odds with previous findings obtained from integrated-light spectra. The studies also revealed signatures of internal rotation in each of the GCs studied. These results, supported by those of N-body simulations, prove that GCs were born with a significant initial rotation that they gradually lost through internal two-body relaxation and angular momentum loss carried away by escaping stars. Furthermore, we derived the structural parameters of NGC 6440 and NGC 6569, obtaining a comprehensive overview of the internal kinematics and structure of these GCs, which is necessary to properly reconstruct the evolutionary history of these systems.

IDeS methodology applied to automotive component re-engineering focused on lightweight and high-strength by additive manufacturing

The project aims to gather an understanding of additive manufacturing and other manufacturing 4.0 techniques with an eyesight for industrialization. First the internal material anisotropy of elements created with the most economically feasible FEM technique was established. An understanding of the main drivers for variability for AM was portrayed, with the focus on achieving material internal isotropy. Subsequently, a technique for deposition parameter optimization was presented, further procedure testing was performed following other polymeric materials and composites. A replicability assessment by means of the use of technology 4.0 was proposed, and subsequent industry findings gathered the ultimate need of developing a process that demonstrate how to re-engineer designs in order to show the best results with AM processing. The latest study aims to apply the Industrial Design and Structure Method (IDES) and applying all the knowledge previously stacked into fully reengineer a product with focus of applying tools from 4.0 era, from product feasibility studies, until CAE – FEM analysis and CAM – DfAM. These results would help in making AM and FDM processes a viable option to be combined with composites technologies to achieve a reliable, cost-effective manufacturing method that could also be used for mass market, industry applications.