An exact quantification of backreaction in relativistic cosmology

An important open question in cosmology is the degree to which the Friedmann-Lemaitre-Robertson-Walker (FLRW) solutions of Einstein's equations are able to model the large-scale behaviour of the locally inhomogeneous observable universe. We investigate this problem by considering a range of exact n-body solutions of Einstein's constraint equations. These solutions contain discrete masses, and so allow arbitrarily large density contrasts to be modelled. We restrict our study to regularly arranged distributions of masses in topological 3-spheres. This has the benefit of allowing straightforward comparisons to be made with FLRW solutions, as both spacetimes admit a discrete group of symmetries. It also provides a time-symmetric hypersurface at the moment of maximum expansion that allows the constraint equations to be solved exactly. We find that when all the mass in the universe is condensed into a small number of objects (<10) then the amount of backreaction in dust models can be large, with O(1) deviations from the predictions of the corresponding FLRW solutions. When the number of masses is large (>100), however, then our measures of backreaction become small (<1%). This result does not rely on any averaging procedures, which are notoriously hard to define uniquely in general relativity, and so provides (to the best of our knowledge) the first exact and unambiguous demonstration of backreaction in general relativistic cosmological modelling. Discrete models such as these can therefore be used as laboratories to test ideas about backreaction that could be applied in more complicated and realistic settings.Comment: 13 pages, 9 figures. Corrections made to Tables IV and

Second Order Perturbations of Flat Dust FLRW Universes with a Cosmological Constant

We summarize recent results concerning the evolution of second order perturbations in flat dust irrotational FLRW models with $\Lambda\ne 0$. We show that asymptotically these perturbations tend to constants in time, in agreement with the cosmic no-hair conjecture. We solve numerically the second order scalar perturbation equation, and very briefly discuss its all time behaviour and some possible implications for the structure formation.Comment: 6 pages, 1 figure. to be published in "Proceedings of the 5th Alexander Friedmann Seminar on Gravitation and Cosmology", Int. Journ. Mod. Phys. A (2002). Macros: ws-ijmpa.cls, ws-p9-75x6-50.cl

In--out intermittency in PDE and ODE models

We find concrete evidence for a recently discovered form of intermittency, referred to as in--out intermittency, in both PDE and ODE models of mean field dynamos. This type of intermittency (introduced in Ashwin et al 1999) occurs in systems with invariant submanifolds and, as opposed to on--off intermittency which can also occur in skew product systems, it requires an absence of skew product structure. By this we mean that the dynamics on the attractor intermittent to the invariant manifold cannot be expressed simply as the dynamics on the invariant subspace forcing the transverse dynamics; the transverse dynamics will alter that tangential to the invariant subspace when one is far enough away from the invariant manifold. Since general systems with invariant submanifolds are not likely to have skew product structure, this type of behaviour may be of physical relevance in a variety of dynamical settings. The models employed here to demonstrate in--out intermittency are axisymmetric mean--field dynamo models which are often used to study the observed large scale magnetic variability in the Sun and solar-type stars. The occurrence of this type of intermittency in such models may be of interest in understanding some aspects of such variabilities.Comment: To be published in Chaos, June 2001, also available at http://www.eurico.web.co

Evolution of the density contrast in inhomogeneous dust models

With the help of families of density contrast indicators, we study the tendency of gravitational systems to become increasingly lumpy with time. Depending upon their domain of definition, these indicators could be local or global. We make a comparative study of these indicators in the context of inhomogeneous cosmological models of Lemaitre--Tolman and Szekeres. In particular, we look at the temporal asymptotic behaviour of these indicators and ask under what conditions, and for which class of models, they evolve monotonically in time. We find that for the case of ever-expanding models, there is a larger class of indicators that grow monotonically with time, whereas the corresponding class for the recollapsing models is more restricted. Nevertheless, in the absence of decaying modes, indicators exist which grow monotonically with time for both ever-expanding and recollapsing models simultaneously. On the other hand, no such indicators may found which grow monotonically if the decaying modes are allowed to exist. We also find the conditions for these indicators to be non-divergent at the initial singularity in both models. Our results can be of potential relevance for understanding structure formation in inhomogeneous settings and in debates regarding gravitational entropy and arrow of time. In particular, the spatial dependence of turning points in inhomogeneous cosmologies may result in multiple density contrast arrows in recollapsing models over certain epochs. We also find that different notions of asymptotic homogenisation may be deduced, depending upon the density contrast indicators used.Comment: 22 pages, 1 figure. To be published in Classical and Quantum Gravit

Optical response of supported gold nanodisks

It is shown that the ellipsometric spectra of short range ordered planar arrays of gold nanodisks supported on glass substrates can be described by modeling the nanostructured arrays as uniaxial homogeneous layers with dielectric functions of the Lorentz type. However, appreciable deviations from experimental data are observed in calculated spectra of irradiance measurements. A qualitative and quantitative description of all measured spectra is obtained with a uniaxial effective medium dielectric function in which the nanodisks are modeled as oblate spheroids. Dynamic depolarization factors in the long-wavelength approximation and interaction with the substrate are considered. Similar results are obtained calculating the optical spectra using the island-film theory. Nevertheless, a small in-plane anisotropy and quadrupolar coupling effects reveal a very complex optical response of the nanostructured arrays

Psychological Safety and Norm Clarity in Software Engineering Teams

In the software engineering industry today, companies primarily conduct their work in teams. To increase organizational productivity, it is thus crucial to know the factors that affect team effectiveness. Two team-related concepts that have gained prominence lately are psychological safety and team norms. Still, few studies exist that explore these in a software engineering context. Therefore, with the aim of extending the knowledge of these concepts, we examined if psychological safety and team norm clarity associate positively with software developers' self-assessed team performance and job satisfaction, two important elements of effectiveness. We collected industry survey data from practitioners (N = 217) in 38 development teams working for five different organizations. The result of multiple linear regression analyses indicates that both psychological safety and team norm clarity predict team members' self-assessed performance and job satisfaction. The findings also suggest that clarity of norms is a stronger (30\% and 71\% stronger, respectively) predictor than psychological safety. This research highlights the need to examine, in more detail, the relationship between social norms and software development. The findings of this study could serve as an empirical baseline for such, future work.Comment: Submitted to CHASE'201

Humoral immune consequences of Staphylococcus aureus ST239-associated bacteremia

The humoral immune responses against 46 different staphylococcal antigens in 27 bacteremia patients infected by clonally related methicillin-resistant Staphylococcus aureus (MRSA) strains of a single sequence type (ST) 239 were investigated. A group of non-infected patients (n = 31) hospitalized for different reasons served as controls. All strains were confirmed as ST 239 by S. aureus and mecA-specific PCR, spa, and multi-locus sequence typing (MLST). In each bacteremia patient, a unique pattern of S. aureus antigen-specific immune responses after infection was observed. Antibody levels among bacteremia patients were significantly higher than controls for HlgB (P = 0.001), LukD (P = 0.009), LukF (P = 0.0001), SEA (P = 0.0001), SEB (P = 0.011), SEC (P = 0.010), SEQ (P = 0.049), IsaA (P = 0.043), IsdA (P = 0.038), IsdH (P = 0.01), SdrD (P = 0.001), SdrE (P = 0.046), EsxA (P = 0.0001), and SA0104 (P = 0.0001). On the other hand, the antibody levels were significantly higher among controls for SSL3 (P = 0.009), SSL9 (P = 0.002), and SSL10 (P = 0.007) when the IgG level on the day of infection was compared with that measured on the day of admission. Diversity was observed in the immune response against the antigens. However, a set of antigens (IsaA, IsdA, IsdH, SdrD, and HlgB) triggered a similar type of immune response in different individuals. We suggest that these antigens could be considered when developing a multi-component (passive) vaccine. SEA and/or its specific antibodies seem to play a critical role during ST239 MRSA bacteremia and SEA-targeted therapy may be a strategy to be considered

Dynamically generated embeddings of spacetime

We discuss how embeddings in connection with the Campbell-Magaard (CM) theorem can have a physical interpretation. We show that any embedding whose local existence is guaranteed by the CM theorem can be viewed as a result of the dynamical evolution of initial data given in a four-dimensional spacelike hypersurface. By using the CM theorem, we establish that for any analytic spacetime, there exist appropriate initial data whose Cauchy development is a five-dimensional vacuum space into which the spacetime is locally embedded. We shall see also that the spacetime embedded is Cauchy stable with respect these the initial data.Comment: (8 pages, 1 figure). A section on Cauchy Stability of the embedding was added. (To appear in Class. Quant. Grav.

A cell-free SDKP-conjugated self-assembling peptide hydrogel sufficient for improvement of myocardial infarction

Biomaterials in conjunction with stem cell therapy have recently attracted attention as a new therapeutic approach for myocardial infarction (MI), with the aim to solve the delivery challenges that exist with transplanted cells. Self-assembling peptide (SAP) hydrogels comprise a promising class of synthetic biomaterials with cardiac-compatible properties such as mild gelation, injectability, rehealing ability, and potential for sequence modification. Herein, we developed an SAP hydrogel composed of a self-assembling gel-forming core sequence (RADA) modified with SDKP motif with pro-angiogenic and anti-fibrotic activity to be used as a cardioprotective scaffold. The RADA-SDKP hydrogel was intramyocardially injected into the infarct border zone of a rat model of MI induced by left anterior descending artery (LAD) ligation as a cell-free or a cell-delivering scaffold for bone marrow mesenchymal stem cells (BM-MSCs). The left ventricular ejection fraction (LVEF) was markedly improved after transplantation of either free hydrogel or cell-laden hydrogel. This cardiac functional repair coincided very well with substantially lower fibrotic tissue formation, expanded microvasculature, and lower inflammatory response in the infarct area. Interestingly, BM-MSCs alone or in combination with hydrogel could not surpass the cardiac repair effects of the SDKP-modified SAP hydrogel. Taken together, we suggest that the RADA-SDKP hydrogel can be a promising cell-free construct that has the capability for functional restoration in the instances of acute myocardial infarction (AMI) that might minimize the safety concerns of cardiac cell therapy and facilitate clinical extrapolation. © 2020 by the authors. Licensee MDPI, Basel, Switzerland