4D Space-time Research Articles

Split Membrane 11D Spacetime = 1D Eleventh Dimension Interval Space + 6D Rishon Space + 3D Higgs Space + 1D Einstein Time: Cosmology

The paper posits that the cyclic universe cosmology involves the split of the membrane 11D (11 dimensional) spacetime into the 1D eleventh dimension orbifold interval space to form gravity, the 6D discrete interior rishon space (TTT-VVV for positron-neutrino or TTV-TVV for quarks) to form the Standard Model, the 3D Higgs space (attachment space to attach matter or detachment space to detach matter) to form the Higgs or reverse Higgs field, and 1D Einstein time to be shared by all spaces. To establish particle masses, spacetime dimension number decreases with decreasing speed of light, decreasing vacuum energy, and increasing rest mass. The 4D and the 10D have zero and the highest vacuum energies, respectively. The cyclic universe cosmology starts with the zero-energy 4D inter-universal void and the positive-energy membrane and negative-energy antimembrane 11D dual universe which is split into four equal 10D string branes, including the 10D positive-energy weak-gravity brane with matter, negative-energy strong-gravity brane, negative-energy weak-gravity brane with antimatter, and positive-energy strong-gravity brane in the 11D bulk with the 1D eleventh dimension interval space in between the strong and the weak-gravity branes. To form the home universe where we inhabit, the 10D positive-energy weak-gravity brane with attachment space absorbed the zero-energy 4D inter-universal void with detachment space, resulting in the combination of rest mass from attachment space and kinetic energy from detachment space, the formation of the 4D spacetime universe by transforming 6D connected exterior space into 6D discrete interior rishon space, and cosmic inflation. The other three branes did not absorb the inter-universal void, resulting in the oscillating dimension branes between 10D and 4D stepwise without kinetic energy. The three branes are hidden when D > 4, and they are dark energy when D = 4. The split 11D spacetime and cosmology provide the matter-antimatter imbalance and the accurately calculated masses for leptons, quarks, hadrons, gauge bosons, the Higgs boson, gravity, dark matter, and dark energy.

3D space–time visualization of individual settlement pathways of Mainland China-born migrants in Queensland, Australia

The number of migrants from Mainland China (MC) to Australia have been sharply increasing since 2000 and MC became the largest non-Commonwealth source country in 2011. The integration process of migrants to the host society involves the exposure and movement of migrants to the majority, which is reflected by the settlement pathways of migrants moving from ethnic to non-ethnic communities over time. Most of the existing research regarding migrants’ pathways is constrained by the limitations of cross-sectional data, which are usually available at the community or above levels. Little is known about the individual-level settlement pathways of migrants due to lack of data availability. In order to address this deficit, a 3D visualization is used to express the individual pathways of MC-born migrants based on primary survey data. This enables a more detailed, spatio-temporal picture of how long migrants live at each address and how they move across neighbourhoods.

Open Universe Models as Analogs of Multidimensional Electric Capacitors

A new approach to obtaining open Universes models as exact solutions of gravitational equations is considered. The proposed method is based on an analogy between electrostatics of conductors and open cosmological models which have a conformally-flat 4-metric in the Fock form. These cosmological models are solutions of the Einstein equations with the energy-momentum tensor of a Pascal perfect fluid. As a result, it is shown that the capacity of the multidimensional "ball" electric capacitor in multidimensional Euclidean auxiliary space is connected with harmonic functions by which the potentials of multidimensional capacitors are described. In turn, the conformal factor of the metric describing an open universe model in the Fock representation is a power function of this potential for each dimensionality of the Euclidean space. In particular, for 3D auxiliary Euclidean space in 4D space-time, there is the Friedman solution for an open universe filled with incoherent dust (with flat metric at spatial infinity). Further for 4D Euclidean space, we have an analogue of the open cosmological model with the equation of state of an ultra-relativistic gas. Other cases are listed in a table. A table of the matter states which generalizes this approach to multidimensional space-times is also constructed. Thus, the possibility of replacing the modelling problem in cosmology with the equivalent electrostatic problem for finding the capacity of capacitors is shown under specified boundary conditions. Exceptions from the general approach are also presented in the article.

Geodesics around oscillatons made of exponential scalar field potential

Oscillatons are spherically symmetric solutions to the Einstein Klein Gordon (EKG) equations for soliton stars made of real time dependent scalar fields. These equations are non singular and satisfy flatness conditions asymptotically with periodic time dependency. In this paper, we investigate the geodesic motion of particles moving around an oscillaton related to a time dependent scalar field. Bound orbital is found for these particles under the condition of particular values of angular momentum L and initial radial position. We discuss this topic for an exponential scalar field potential which could be of the exponential form with a scalar field and investigate whether the radial coordinates of such particles oscillate in time or not and thereby we could predict the corresponding oscillating period as well as amplitude. It is necessary to recall, in general relativity, a geodesic generalizes the notion of a straight line to curved space time. Importantly, the world line of a particle free from all external, non gravitational forces, is a particular type of geodesic. In other words, a freely moving or falling particle always moves along a geodesic. In general relativity, gravity can be regarded as not a force but a consequence of a curved space time geometry where the source of curvature is the stress energy tensor (representing matter, for instance). Thus, for example, the path of a planet orbiting around a star is the projection of a geodesic of the curved 4D space time geometry around the star onto 3D space.

Holographic reduction of Maxwell-Chern-Simons theory

The 3D Maxwell-Chern-Simons theory with planar, single-edged, boundary is considered. It is shown that its holographic reduction on a flat euclidean 2D spacetime is a scalar field theory describing a conserved chiral current, which corresponds to the electric continuity equation. Differently from the theory with planar, double-edged boundary, in this holographic bulk-boundary approach physical quantities like the chiral velocity of the edge excitations depend also on the non-topological Maxwell term.

Symmetries, holography, and quantum phase transition in two-dimensional dilaton AdS gravity

We present a revisitation of the Almheiri-Polchinski dilaton gravity model from a two-dimensional (2D) bulk perspective. We describe a peculiar feature of the model, namely the pattern of conformal symmetry breaking using bulk Killing vectors, a covariant definition of mass and the flow between different vacua of the theory. We show that the effect of the symmetry breaking is both the generation of an infrared scale (a mass gap) and to make local the Goldstone modes associated with the asymptotic symmetries of the 2D spacetime. In this way a non vanishing central charge is generated in the dual conformal theory, which accounts for the microscopic entropy of the 2D black hole. The use of covariant mass allows to compare energetically the two different vacua of the theory and to show that at zero temperature the vacuum with a constant dilaton is energetically preferred. We also translate in the bulk language several features of the dual CFT discussed by Maldacena et al. The uplifting of the 2D model to $(d+2)-$dimensional theories exhibiting hyperscaling violation is briefly discussed.

4D Remeshing Using a Space-Time Finite Element Method for Elastodynamics Problems

In this article, a Space-Time Finite Element Method (STFEM) is proposed for the resolution of mechanical problems involving three dimensions in space and one in time. Special attention will be paid to the non-separation of the space and time variables because this kind of interpolation is well suited to mesh adaptation. For that purpose, we have developed a technique of 4D mesh generation adapted to space-time remeshing. A difficulty arose in the representation of 4D finite elements and meshes. This original technique does not require coarse-to-fine and fine-to-coarse mesh-to-mesh transfer operators and does not increase the size of the linear systems to be solved, compared to traditional finite element methods. Space-time meshes are composed of simplex finite elements. Computations are carried out in the context of the continuous Galerkin method. We have tested the method on a linearized elastodynamics problem. Our technique of mesh adaptation was validated on elementary examples and applied to a problem of mobile loading. The convergence and stability of the method are studied and compared with existing methods. This work is a first implementation of 4D space-time remeshing. A stability criterion for the method is established, as well as a convergence rate of about two. Using simplex elements, it is possible to develop a technique of mesh adaptation able to follow a mobile loading zone.

4D Cubism: Modeling, Animation, and Fabrication of Artistic Shapes.

This article deals with creating artistic shapes in a cubist style. The authors propose adding cubist features to (or cubification of) time-variant sculptural shapes. A new concept of a 4D cubist camera is introduced for multiple projections from 4D space-time to 3D space, and 3D printing for stop-motion animation is applied.

Electronic Properties of Curved Few-Layers Graphene: A Geometrical Approach

We show the presence of non-relativistic Lévy-Leblond fermions in flat three- and four-layers graphene with AB stacking, extending the results obtained in Cariglia et al. 2017 for bilayer graphene. When the layer is curved we obtain a set of equations for Galilean fermions that are a variation of those of Lévy-Leblond with a well defined combination of pseudospin, and that admit Lévy-Leblond spinors as solutions in an approriate limit. The local energy of such Galilean fermions is sensitive to the intrinsic curvature of the surface. We discuss the relationship between two-dimensional pseudospin, labelling layer degrees of freedom, and the different energy bands. For Lévy-Leblond fermions, an interpretation is given in terms of massless fermions in an effective 4D spacetime, and in this case the pseudospin is related to four dimensional chirality. A non-zero energy band gap between conduction and valence electronic bands is obtained for surfaces with positive curvature.

Comparison of algebraic multigrid methods for an adaptive space–time finite‐element discretization of the heat equation in 3D and 4D

SummaryThe aim of this work is to compare algebraic multigrid (AMG) preconditioned GMRES methods for solving the nonsymmetric and positive definite linear systems of algebraic equations that arise from a space–time finite‐element discretization of the heat equation in 3D and 4D space–time domains. The finite‐element discretization is based on a Galerkin–Petrov variational formulation employing piecewise linear finite elements simultaneously in space and time. We focus on a performance comparison of conventional and modern AMG methods for such finite‐element equations, as well as robustness with respect to the mesh discretization and the heat capacity constant. We discuss different coarsening and interpolation strategies in the AMG methods for coarse‐grid selection and coarse‐grid matrix construction. Further, we compare AMG performance for the space–time finite‐element discretization on both uniform and adaptive meshes consisting of tetrahedra and pentachora in 3D and 4D, respectively. The mesh adaptivity occurring in space and time is guided by a residual‐based a posteriori error estimation.

Система операторов для пространственно-временного анализа динамических сцен

The rapid growth in the volume of information and the need for its comprehensive analysis lead to the development of new methods of working with multidimensional and space-time data. To work with such data, Qualitative Spatial Reasoning is often used to extract (produce) new knowledge based on facts established in one way or another. Despite the variety of formal analysis systems available, sets of operators do not allow for the identification of complex space-time relationships between objects. Existing software tools, such as SparQ, GQR, QAT, CLP (QS), are focused on analyzing one aspect and are applicable mainly for interval analysis of time series of events and production of conclusions about some spatial relationships. In practice, tools are usually used to analyze simple relationships in simple scenes. The lack of interfaces limits their combined use with quantitative analysis tools, necessary, for example, to establish primary facts, and use within the framework of the concepts of 4D (space-time), 5D (space-time and cost) and multi-D (multidimensional) modeling. This paper proposes a system of topological, metric, directional and temporal operators for complex spatial-temporal analysis of dynamic scenes. This system allows combined usage of qualitative and quantitative analysis methods, which is essential not only for determining initial facts, but also for producing new knowledge based on these facts. The system of operators proposed is deemed prospective for problems of spatial-temporal (4D) modeling and planning of industrial projects, and particularly for specifying and detecting of non-trivial conflicts in project schedules.

Modified Saez–Ballester scalar–tensor theory from 5D space-time

In this paper, we bring together the five-dimensional Saez–Ballester (SB) scalar–tensor theory (Saez and Ballester 1986 Phys. Lett. 113A 9) and the induced-matter-theory (IMT) setting (Wesson and Ponce de Leon 1992 J. Math. Phys. 33 3883), to obtain a modified SB theory (MSBT) in four dimensions. Specifically, by using an intrinsic dimensional reduction procedure into the SB field equations in five-dimensions, a MSBT is obtained onto a hypersurface orthogonal to the extra dimension. This four-dimensional MSBT is shown to bear distinctive new features in contrast to the usual corresponding SB theory as well as to IMT and the modified Brans–Dicke theory (MBDT) (Rasouli et al 2014 Class. Quantum Grav. 31 115002). In more detail, besides the usual induced matter terms retrieved through the IMT, the MSBT scalar field is provided with additional physically distinct (namely, SB induced) terms as well as an intrinsic self-interacting potential (interpreted as a consequence of the IMT process and the concrete geometry associated with the extra dimension). Moreover, our MSBT has four sets of field equations, with two sets having no analog in the standard SB scalar–tensor theory. It should be emphasized that the herein appealing solutions can emerge solely from the geometrical reductional process, from the presence also of extra dimension(s) and not from any ad-hoc matter either in the bulk or on the hypersurface. Subsequently, we apply the herein MSBT to cosmology and consider an extended spatially flat FLRW geometry in a five-dimensional vacuum space-time. After obtaining the exact solutions in the bulk, we proceed to construct, by means of the MSBT setting, the corresponding dynamic, on the four-dimensional hypersurface. More precisely, we obtain the (SB) components of the induced matter, including the induced scalar potential terms. We retrieve two different classes of solutions. Concerning the first class, we show that the MSBT yields a barotropic equation of state for the induced perfect fluid. We then investigate vacuum, dust, radiation, stiff fluid and false vacuum cosmologies for this scenario and contrast the results with those obtained in the standard SB theory, IMT and BD theory. Regarding the second class solutions, we show that the scale factor behaves in a similar way to a de Sitter (DeS) model. However, in our MSBT setting, this behavior is assisted by non-vanishing induced matter instead, without any a priori cosmological constant. Moreover, for all these solutions, we show that the extra dimension contracts with the cosmic time.

Spectral flow in 3D flat spacetimes

In this paper we investigate spectral flow symmetry in asymptotically flat spacetimes both from a gravity as well as a putative dual quantum field theory perspective. On the gravity side we consider models in Einstein gravity and supergravity as well as their "reloaded" versions, present suitable boundary conditions, determine the respective asymptotic symmetry algebras and the thermal entropy of cosmological solutions in each of these models. On the quantum field theory side we identify the spectral flow symmetry as automorphisms of the underlying symmetry algebra of the theory. Using spectral flow invariance we then determine the thermal entropy of these quantum field theories and find perfect agreement with the results from the gravity side. In addition we determine logarithmic corrections to the thermal entropy.

A Time–Space Symmetry Based Cylindrical Model for Quantum Mechanical Interpretations

Following a bi-cylindrical model of geometrical dynamics, our study shows that a 6D-gravitational equation leads to geodesic description in an extended symmetrical time–space, which fits Hubble-like expansion on a microscopic scale. As a duality, the geodesic solution is mathematically equivalent to the basic Klein–Gordon–Fock equations of free massive elementary particles, in particular, the squared Dirac equations of leptons. The quantum indeterminism is proved to have originated from space–time curvatures. Interpretation of some important issues of quantum mechanical reality is carried out in comparison with the 5D space–time–matter theory. A solution of lepton mass hierarchy is proposed by extending to higher dimensional curvatures of time-like hyper-spherical surfaces than one of the cylindrical dynamical geometry. In a result, the reasonable charged lepton mass ratios have been calculated, which would be tested experimentally.

Redshift in the model of embedded spaces

The non-configurational geometrization of the electromagnetic field can be realized using the Model of Embedded Spaces (MES). This model assumes the existence of proper 4D space-time manifolds of particles with a nonzero rest mass and declares that physical space-time is the metric result of the dynamic embedding of these manifolds: the value of the partial contribution of the element manifold is determined by element interactions. The space of the model is provided with a Riemann-like geometry, whose differential formalism is described by a generalization of the gradient operator ∂/∂x i → ∂/∂x i + 2u k ∂2/∂x[ i ∂u k ], where u i = dx i /ds is a matter velocity. In the paper, the redshift effect existing in the space of MES is considered, and its electromagnetic component is analyzed. It is shown that for cold matter of the modern Universe this component reduces to a shift in electric fields and is described by the expression $$\Delta {\omega _e}/\omega \simeq \mp \sqrt k \Delta {\varphi _e}/{c^2} = \mp 0.861 \cdot {10^{ - 21}}\Delta {\varphi _e}\left( V \right)$$ , where the potential is measured in volts and the sign must be determined experimentally. Testing of the effect is the “experimentum crusis” for MES.

Λ(t)CDM and the present accelerating expansion of the universe from 5D scalar vacuum

Abstract In this letter we investigate some consequences of considering our 4D observable universe as locally and isometrically embedded in a 5D spacetime, where gravity is described by a Brans–Dicke theory in vacuum. Once we impose the embedding conditions we obtain that gravity on the 4D spacetime is governed by the Einstein field equations modified by an extra term that can play the role of a dynamical cosmological constant. Two examples were studied. In the first we derive a cosmological model of a universe filled only with a cosmological constant. In the second we obtain a cosmological solution describing a universe filled with matter, radiation and a dynamical cosmological constant. We constrain the model by using the current observational data combination Planck + WP + BAO + SN. The present acceleration in the expansion of the universe is explained by the geometrically induced dynamical cosmological constant avoiding the introduction of a dark energy component and without addressing the underlying cosmological constant problem. Moreover, all 4D matter sources are geometrically induced in the same manner as it is usually done in the Wesson’s induced matter theory.

Geometrical interpretation of electromagnetism in a 5-dimensional manifold

In this paper, Kaluza–Klein theory is revisited and its implications are elaborated. We show that electromagnetic 4-potential can be considered as a shearing-like deformation of a 5-dimensional (5D) manifold along the fifth (5th) axis. The charge-to-mass ratio has a physical meaning of the ratio between the movement along the direction of the 5th axis and the movement in the 4D space-time. In order to have a 5D matter which is consistent with the construction of the 5D manifold, a notion of particle-thread is suggested. Examinations on the compatibility of reference frames reveal a covariance breaking of the 5th dimension. The field equations which extend Einstein’s field equations give the total energy-momentum tensor as a sum of that of matter, electromagnetic field, and the interaction between electric current and electromagnetic potential. Finally, the experimental implications are calculated for the weak potential case.

3D space-time analysis of ATWS in compact high temperature reactor with integrated thermal-hydraulic model in code ARCH-TH

The Compact High Temperature Reactor (CHTR) is being designed as a technology demonstrator for comprehensive Indian high temperature reactor programme for hydrogen production and similar process heat applications. The 100kWth CHTR core consists of 233U-Th based TRISO coated fuel particles, BeO moderator and LBE coolant with natural circulation in vertical prismatic fuel assemblies. The CHTR being a new conceptual design, necessitates comprehensive integrated Neutronics/Thermal-Hydraulics (N-TH) analyses and study. For design and safety studies, 3D space-time analyses of anticipated transient without scram (ATWS) in CHTR have been carried out in detail with indigenous code system with various cases of temperature feedbacks. One of the striking features observed in the analysis is that in case of weak Doppler feedback due to high fissile content and high temperature core conditions in CHTR, the BeO moderator plays a crucial role to limit the rise in nuclear power as well as peak fuel and coolant temperatures during such transient. For these studies, 1D-radial heat conduction in multi-channel based TH module has been developed in 3D space-time code ARCH. The viability of neutronics and adiabatic Doppler feedback capability of the code has also been examined with AER benchmark problems (AER-DYN01 & 02) and results are discussed. The analysis shows that the transient peak fuel and coolant temperatures are limiting at values much below the fuel safety criteria of TRISO particle (∼1600°C) and boiling point of LBE coolant (1670°C) even with scram failure. The significance of temperature feedback effects of BeO moderator in CHTR is seems to be a first of its kind observation and is not reported in the literature.

4D Visual Delivery of Big Climate Data: A Fast Web Database Application System

This paper develops a web database application to make space-time 4D visual delivery (4DVD) of big climate data. The delivery system shows climate data in a 4D space-time box and allows users to visualize the data. Users can zoom in or out to help identify desired information for particular locations. Data can then be downloaded for the spatial maps and historical climate time series of a given location after the maps and time series are identified to be useful. These functions enable a user to quickly reach the core interested features without downloading the entire dataset in advance, which saves both time and storage space. The 4DVD system has many graphical display options such as displaying data on a round globe or on a 2D map with detailed background topographic images. It can animate maps and show time series. The combination of these features makes the system a convenient and attractive multimedia tool for classrooms, museums, and households, in addition to climate research scientists, industrial applicants, and policy makers. To demonstrate the 4DVD’s usage, several application examples are included in this paper, such as the La Nina’s influence on land temperature.

Time travel and coincidence-free local dynamical theories

I criticize Lockwood’s solution to the “paradoxes” of time travel, thus endorsing Lewis’s more conservative position. Lockwood argues that only in the context of a 5D space-time-actuality manifold is the possibility of time travel compatible with the Autonomy Principle (according to which global constraints cannot override what is physically possible locally). I argue that shifting from 4D space-time to 5D space-time-actuality does not change the situation with respect to the Autonomy Principle, since the shift does not allow us to have a coincidence-free local dynamical theory.