Space-time Dynamics Research Articles

Numerical relativity in spherical coordinates: A new dynamical spacetime and general relativistic MHD evolution framework for the Einstein Toolkit

We present SphericalNR, a new framework for the publicly available Einstein Toolkit that numerically solves the Einstein field equations coupled to the equations of general relativistic magnetohydrodynamics (GRMHD) in a 3+1 split of spacetime in spherical coordinates without symmetry assumptions. The spacetime evolution is performed using reference-metric versions of either the Baumgarte-Shapiro-Shibata-Nakamura equations or the fully covariant and conformal Z4 system with constraint damping. We have developed a reference-metric version of the Valencia formulation of GRMHD with a vector potential method, guaranteeing the absence of magnetic monopoles during the evolution. In our framework, every dynamical field (both spacetime and matter) is evolved using its components in an orthonormal basis with respect to the spherical reference-metric. Furthermore, all geometric information about the spherical coordinate system is encoded in source terms appearing in the evolution equations. This allows for the straightforward extension of Cartesian high-resolution shock-capturing finite volume codes to use spherical coordinates with our framework. To this end, we have adapted GRHydro, a Cartesian finite volume GRMHD code already available in the Einstein Toolkit, to use spherical coordinates. We present the full evolution equations of the framework, as well as details of its implementation in the Einstein Toolkit. We validate SphericalNR by demonstrating it passes a variety of challenging code tests in static and dynamical spacetimes.

A Process‐Based Framework to Characterize and Classify Runoff Events: The Event Typology of Germany

AbstractThis study proposes a new process‐based framework to characterize and classify runoff events of various magnitudes occurring in a wide range of catchments. The framework uses dimensionless indicators that characterize space–time dynamics of precipitation events and their spatial interaction with antecedent catchment states, described as snow cover, distribution of frozen soils, and soil moisture content. A rigorous uncertainty analysis showed that the developed indicators are robust and regionally consistent. Relying on covariance‐ and ratio‐based indicators leads to reduced classification uncertainty compared to commonly used (event‐based) indicators based on absolute values of metrics such as duration, volume, and intensity of precipitation events. The event typology derived from the proposed framework is able to stratify events that exhibit distinct hydrograph dynamics even if streamflow is not directly used for classification. The derived typology is therefore able to capture first‐order controls of event runoff response in a wide variety of catchments. Application of this typology to about 180,000 runoff events observed in 392 German catchments revealed six distinct regions with homogeneous event type frequency that match well regions with similar behavior in terms of runoff response identified in Germany. The detected seasonal pattern of event type occurrence is regionally consistent and agrees well with the seasonality of hydroclimatic conditions. The proposed framework can be a useful tool for comparative analyses of regional differences and similarities of runoff generation processes at catchment scale and their possible spatial and temporal evolution.

Explicit Lorentz violation in a static and spherically-symmetric spacetime

Lorentz violation is motivated by quantum gravity and it is generically described by nondynamical tensors. In this work a Lorentz violating extension of general relativity is studied where a nondynamical tensor couples to the Weyl tensor. A family of static and spherically symmetric solutions in vacuum is found, confirming that there are consistent solutions with explicit Lorentz violation in dynamical spacetimes. These solutions produce an unconventional dependence of the gravitational redshift, which, in turn, leads to the first bounds on such nondynamical tensor that do not rely on the physics of the early universe. Moreover, the bounds obtained in this work are competitive with respect to limits on similar nondynamical tensors.

Space-time dynamics of cab drivers' stay behaviors and their relationships with built environment characteristics

Understanding cab drivers' stay activities is essential for planning and managing certain urban facilities. This study analyzes cab drivers' stay behaviors using a taxi GPS trajectory dataset collected in Wuhan, China. By extracting cab drivers' stay activities from the dataset, we measure the activity frequency at the level of traffic analysis zones (TAZs) and examine their spatiotemporal dynamics. We then derive several built environment indicators and assess their associations with these activities using ordinary least squares regression (OLS) and geographically weighted regression (GWR) models. According to the results, the stay frequency decays dramatically over the TAZs, indicating that these activities tend to be concentrated in particular areas of the city. The rates of decay, as reflected by the rank-size and power-law distributions, are similar on weekdays and weekends. Cab drivers' stay activities exhibit similar spatial patterns during the same period on weekdays and weekends. The adjusted R-squared of OLS is 0.742 for weekdays and 0.676 for weekends, which suggests a close relationship between stay activities and built environment characteristics. The GWR models further reveal the spatial variations of the activity-environment linkage across the study area. The study provides useful insights that support future urban design and transport planning.

New optical soliton solutions of space-time fractional nonlinear dynamics of microtubules via three integration schemes

New optical soliton solutions of space-time fractional nonlinear dynamics of microtubules via three integration schemes

Inertial motion of the quantum self-interacting electron

Attempt to represent the self-interacting quantum electron as the cyclic motion has been discussed. This motion obeys the quantum inertia principle expressed by the parallel transported energy–momentum generator along a closed geodesic in the space of the unlocated quantum states CP(3) . The affine gauge potential in the complex projective state space (similar to the Higgs potential) seriously deforms the Jacobi fields in the vicinity of the “north pole”. It was assumed that the divergency of the Jacobi field may be compensated by the fields of the Poincaré generators representing EM-like “field shell” of the electron in the dynamical spacetime. Thereby, the spacetime looks as ultimately deprecated in the role of the “container of matter” and it appears as the accompanied to the quantum electron functional space (dynamical spacetime). Meanwhile, the dynamics of the self-interacting electron is essentially non-linear and deterministic.

Breaking down calcium timing in heterogenous cells populations

Calcium controls a large number of cellular processes at different scales. Decades of studies have pointed out the importance of calcium signaling in regulating differentiation, apoptosis, mitosis and functions such as secretion, muscle contraction and memory. The space-time structure of calcium signaling is central to this complex regulation. In particular, cells within organisms behave as clocks beating their own biological time, although in several cases they can synchronize across long distances leading to an emergent space-time dynamics which is central for single cell and organ functioning. We use a mathematical model built on published experimental data of hepatic non-excitable cells, analyzing emerging calcium dynamics of cells clusters composed both of normally functioning cells and pathological aggregates. Calcium oscillations are investigated by varying the severity of dysfunction and size of pathological aggregate. We show how strong and localized heterogeneity in cellular properties can profoundly alter organized calcium dynamics leading to sub-populations of cells which create their own coordinated dynamical organization. Our simulations of Ca2+ signals reveal how cell behaviors differ and are related to intrinsic time signals. Such different cells clusters dynamically influence each other so that non-physiological although organized calcium patterns are generated. This new reorganization of calcium activity may possibly be a precursor of cancer initiation.

A four decades multiparametric investigation in a Mediterranean dynamic ecosystem: Mollusc assemblages answer to the environmental changes

The ecosystem changes of “Marinello coastal lakes” - a brackish dynamic area located on the Tyrrhenian coast of Sicily (Italy) - have been examined through the analysis of the adaptive response of mollusc assemblages to the geomorphological and environmental changes. In particular, we have contextually analysed the changes in salinity, mud and organic carbon together with mollusc abundance and distribution, comparing the data sets from several multidisciplinary investigations that we performed in about forty years.Our studies have evidenced that the space-time dynamics of the geomorphological, environmental and trophic parameters have led the progression of Marinello ecosystem, favoring the onset of transient windows of connectivity (TWCs) between different habitats. TWCs, by supporting continuous re-arrangements of mollusc populations, have contributed to increase the functional and ecological complexity of the system. Salinity in particular has proven to be the most affecting factor on the diversification of mollusc assemblages, explaining 63% and 44% of variation for brackish and marine species respectively. In addition, the distribution of both detritus and suspension feeders has been mostly affected by salinity.The interannual analysis of the mollusc assemblages has shown in the whole system a generalised increase in the number of species, likewise, also the species richness recorded in each basin generally increased with the time. Metapopulations in the Marinello ecosystem have shown to be related to significant modifications in the habitat patches, in turn connected to the anthropogenic interventions or to the geomorphological progression of the entire physiographic system.Significant relationships among biotic and abiotic parameters have highlighted important implications on the ecosystem functioning, suggesting their possible application in the improvement of investigation tools for the transitional environments.

Diversity and space-time dynamics of the bacterial communities in cotton (Gossypium hirsutum) rhizosphere soil.

Rhizosphere bacteria are key determinants of plant health and productivity. In this study, we used PCR-based next-generation sequencing to reveal the diversity and community composition of bacteria in the cotton rhizosphere from samples collected in Xinjiang Province, China. We identified 125 bacterial classes within 49 phyla from these samples. Proteobacteria (33.07% of total sequences), Acidobacteria (19.88%), and Gemmatimonadetes (11.19%) dominated the bacterial community. Marked differences were evident in the α-diversity of rhizosphere bacteria during different cotton plant growth and development stages. The operational taxonomic unit (OTU) numbers were highest in seedling and bud stages and decreased at the flowering and fruit-boll-opening stages. Forty-three OTUs from the Proteobacteria were common to all four periods of cotton development. Proteobacteria were more abundant in the rhizospheres of cotton from southern Xinjiang than from northern Xinjiang, while the opposite trend was observed for Acidobacteria. Gemmatimonadetes frequency was broadly the same in both northern and southern Xinjiang. These results suggest that there is abundant diversity in the microbiota of cotton rhizosphere soil. Proteobacteria and Actinobacteria dominated this microbial niche and bacterial communities in the seedling, bud, flowering, and boll-opening stages appear to be more similar to one another than to communities at the other growth stages.

Holographic entropy cone in AdS-Vaidya spacetimes

We examine the five-region holographic entropy cone inequalities for the special case of the AdS$_3$-Vaidya metric for a variety of boundary configurations. This is done by numerically solving the geodesic equation in the bulk for various boundary configurations. In all the cases we examine, we find that all the inequalities are satisfied when the bulk satisfies the null energy condition, while the inequalities are all violated when the bulk spacetime violates the null energy condition. A proof of the five-region holographic entropy cone inequalities for the dynamical bulk case remains an open problem--our results provide evidence that these inequalities hold for dynamical bulk spacetimes.

Constrained gauge-gravity duality in three and four dimensions

The equivalence between Chern–Simons and Einstein–Hilbert actions in three dimensions established by Achúcarro and Townsend (Phys Lett B 180:89, 1986) and Witten (Nucl Phys B 311:46, 1988) is generalized to the off-shell case. The technique is also generalized to the Yang–Mills action in four dimensions displaying de Sitter gauge symmetry. It is shown that, in both cases, we can directly identify a gravity action while the gauge symmetry can generate spacetime local isometries as well as diffeomorphisms. The price we pay for working in an off-shell scenario is that specific geometric constraints are needed. These constraints can be identified with foliations of spacetime. The special case of spacelike leafs evolving in time is studied. Finally, the whole set up is analyzed under fiber bundle theory. In this analysis we show that a traditional gauge theory, where the gauge field does not influence in spacetime dynamics, can be (for specific cases) consistently mapped into a gravity theory in the first order formalism.

Space-time dynamics of the scientific potential of subjects of the Russian Federation

Space-time dynamics of the scientific potential of subjects of the Russian Federation

Time-Space Dynamics of Return and Circular Migration: Theories and Evidence

This chapter undertook the monumental task of providing a complete outlook about return, repeat, circular and onward migration by bringing together the perspectives of the host and the home country. In this endeavor, it reviewed and evaluated all theories about why people move, when they circulate, where they go, who are the people who migrate, who are the people who return, and how they change the economic and social structures in the home country. In the process, it revealed the new norm of joint decision-making by the family as a unit and underlined the importance of non-economic reasons for return. The chapter further provided a state-of-the-art literature review about empirical evidence regarding the disparate phenomena of return, circular and onward migration. It emphasized commonalities and compared differences in findings, while connecting them to the theories, policies and institutions. Return, repeat, and circular migrants are self-selected and extremely heterogeneous people and cannot conform under one theory or empirical study. Their de facto migration comportment can be understood by several different theories and, in the absence of good data, it can be explained by a variety of studies. The chapter ends with a critical conclusion and hope to inspire new avenues of research on the topic.

O geopatrimônio e o potencial geoturístico no Distrito Federal, Brasil

O presente trabalho buscou abordar o geopatrimônio, a geoconservação e o geoturismo, apresentando um diagnóstico dos locais potenciais de interesse ao geopatrimônio. Partiu-se de mapear dois cenários: um com base em pontos de cunho geoturístico — sendo as principais cachoeiras e cavernas do Distrito Federal (DF), Brasil — e, num segundo contexto, foram utilizadas as jazidas minerais como recurso geocientífico, especialmente para o entendimento do potencial patrimonial da gênese geológica e geomorfológica do Distrito Federal. Assim, a pesquisa teve como objetivo indicar os locais em que os processos de origem da paisagem possam ser observados de maneira peculiar, abrigando a geodiversidade e o geopatrimônio da unidade federativa, oferecendo um novo olhar geográfico sobre o potencial geoturístico e educacional científico na região, propiciando a preservação e conservação do meio-ambiente. Essa abordagem, centrada nos aspectos descritos, resultou em um mapa com mais de duzentos pontos de interesse ao patrimônio geomorfológico no DF. A partir disso, foi possível propor uma nova metodologia, na qual a dinâmica do espaço-tempo é fundamental: a variação dos valores comumente atribuídos ao geopatrimônio num período de 12 meses.

Astrophysical and local constraints on string theory: Runaway dilaton models

One of the clear predictions of string theory is the presence of a dynamical scalar partner of the spin-2 graviton, known as the dilaton. This will violate the Einstein equivalence principle, leading to a plethora of possibly observable consequences which in a cosmological context include dynamical dark energy and spacetime variations of nature's fundamental constants. The runaway dilaton scenario of Damour, Piazza, and Veneziano is a particularly interesting class of string theory inspired models which can in principle reconcile a massless dilaton with experimental data. Here we use the latest background cosmology observations, astrophysical and laboratory tests of the stability of the fine-structure constant, and local tests of the weak equivalence principle to provide updated constraints on this scenario, under various simplifying assumptions. Overall we find consistency with the standard $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ paradigm. We improve the existing constraints on the coupling of the dilaton to baryonic matter by a factor of 6 and to the dark sector by a factor of 2. At the one-sigma level the current data already exclude dark sector couplings of order unity, which would be their natural value.

Turbulence of generalised flows in two dimensions

This paper discusses the generalised least-action principle and the associated concept of generalised flow introduced by Brenier (J. Am. Math. Soc., vol. 2, 1989, pp. 225–255), from the perspective of turbulence modelling. In essence, Brenier’s generalised least-action principle is a probabilistic generalisation of Arnold’s geometric interpretation of ideal fluid mechanics, whereby strong solutions to the Euler equations are deduced from minimising an action over Lagrangian maps. While Arnold’s framework relies on the deterministic concept of Lagrangian flow, Brenier’s least-action principle describes solutions to the Euler equations in terms of non-deterministic generalised flows, namely probability measures over sets of Lagrangian trajectories. In concept, generalised flows seem naturally fit to describe turbulent Lagrangian trajectories in terms of stochastic processes, an approach that originates from Richardson’s seminal work on turbulent dispersion. Still, Brenier’s generalised least-action principle has so far hardly found any practical application in the realm of fluid mechanics, let alone for turbulence modelling. The purpose of the present paper is to provide a hydrodynamical perspective on Brenier’s principle, and to assess its skills at coarse graining the Lagrangian motion of fluid particles, in order to reconstruct the space–time dynamics of the underlying Eulerian velocity fields. In practice, we rely on a statistical-mechanics interpretation of the concept of generalised flows, whereby the latter become akin to statistical ensembles of suitably defined ‘permutation flows’. We then employ Monte Carlo techniques to numerically solve the generalised least-action principle, and analyse the Eulerian and Lagrangian statistical features of the associated generalised flows. For simplicity, we restrict ourselves to two dimensions of space and consider situations of increasing complexity, ranging from solid rotation and cellular flows to freely decaying two-dimensional turbulence. Our analysis highlights a major caveat of the generalised variational principle. When used over long time lags, e.g. longer than a well-defined hydrodynamic turnover time, it generates artificial generalised flows, with non-physical statistical features. We argue that this limitation is not specifically inherent to Brenier’s formulation, but rather to the variational framework being formulated as a two-end boundary-value problem. When appropriately used over sufficiently short times, the generalised least-action principle is however relevant, and generalised flows can be explicitly constructed, that represent a space–time coarse graining of the underlying dynamics. We show numerical evidence that Brenier’s principle may then even accommodate irreversible Eulerian behaviours. This suggests that, if carefully used, generalised variational formulations could provide new tools to coarse grain genuine multi-scale hydrodynamics.

Experimental realization of Fermi-Pasta-Ulam-Tsingou recurrence in a long-haul optical fiber transmission system

The integrable nonlinear Schrödinger equation (NLSE) is a fundamental model of nonlinear science which also has important consequences in engineering. The powerful framework of the periodic inverse scattering transform (IST) provides a description of the nonlinear phenomena modulational instability and Fermi-Pasta-Ulam-Tsingou (FPUT) recurrence in terms of exact solutions. It associates the complex nonlinear dynamics with invariant nonlinear spectral degrees of freedom that may be used to encode information. While optical fiber is an ideal testing ground of its predictions, maintaining integrability over sufficiently long distances to observe recurrence, as well as synthesizing and measuring the field in both amplitude and phase on the picosecond timescales of typical experiments is challenging. Here we report on the experimental realization of FPUT recurrence in terms of an exact space-time-periodic solution of the integrable NLSE in a testbed for optical communication experiments. The complex-valued initial condition is constructed by means of the finite-gap integration method, modulated onto the optical carrier driven by an arbitrary waveform generator and launched into a recirculating fiber loop with periodic amplification. The measurement with an intradyne coherent receiver after a predetermined number of revolutions provides a non-invasive full-field characterization of the space-time dynamics. The recurrent space-time evolution is in close agreement with theoretical predictions over a distance of 9000 km. Nonlinear spectral analysis reveals an invariant nonlinear spectrum. The space-time scale exceeds that of previous experiments on FPUT recurrence in fiber by three orders of magnitude.

Evaluative mapping of the area irrigated by center pivot in Mozambique

Knowledge of expansion, number; size and spatial distribution of center pivot irrigated areas may represent an important contribution to socio-economic and environmental studies of a given territory. In view of the above, this work aimed to understand the space-time dynamics of areas irrigated by central pivot in Mozambique using remote sensing. For this, images of Landsat satellites 5 and 8 were acquired respectively from the year 2000 to 2017. RGB images were generated for the discrimination of the targets. Based on the results, Mozambique has 200 central pivots. The province of Sofala has a larger number with 110 pivots followed by the province of Maputo with 49. The province of Niassa has a smaller number with 2 pivots. The central pivot irrigated area in Mozambique totals 14 685 ha and the average area irrigated by central pivot is approximately 80 ha.

Study of ionization waves in a pulse discharge in helium

The paper presents the results of experimental and numerical studies of the space-time dynamics of the formation of a discharge in helium under conditions of preliminary ionization of the gas. The effect of local field amplification regions on the discharge development is studied.

Optical and kinetic characteristics of a pulsed discharge in argon with aluminum vapor at atmospheric pressure

Experimental studies of the space-time dynamics of the formation and spectra of optical radiation of a pulsed discharge in argon in external electric and magnetic fields were performed. It was shown that during the formation of a pulsed discharge in argon in the process of diffuse luminescence propagation, cathode spots form on the cathode on it, as evidenced by the presence of lines of electrode material vapor in the plasma emission spectrum. Monte Carlo methods are used to study the kinetic characteristics of the drift of aluminum ions in argon.