Search

In this article, we present an efficient structure-preserving difference scheme for two-dimensional nonlinear space fractional wave models. We use the Crank-Nicolson scheme to discretize in the time direction, and adopt a shifted convolution quadrature (SCQ) formula to approximate the spatial direction. We show and prove an important lemma, and then based on this lemma, we rigorously derive the energy dissipation for the damped case and the approximate energy conservation in undamped case for the fully discrete scheme. In addition, we do the detailed analysis for error estimates with the optimal convergence result O (h x 2 + h y 2 + τ 2) , where h x , h y and τ denote the step length in space-time directions. Furthermore, we provide an efficient fast algorithm called the preconditioned fast BiCG (PF-BiCG) to reduce the cost of time and save memory. Finally, we carry out numerical tests by taking three numerical examples to validate the theories, to observe the performance behaviors of wave solutions, and to reveal the relationship between models by changing fractional parameters. [ABSTRACT FROM AUTHOR]

According to effective realism , scientific theories give us knowledge about the unobservable world, but not at the fundamental level. This view is supported by the well-received effective-field-theory (EFT) approach to high energy physics, according to which even our most successful physical theories are only applicable up to a certain energy scale and expected to break down beyond that. In this paper, I advance new challenges for effective realism and the EFT approach. I argue that effective quantum gravity (EQG) does not give us a realistic theory of spacetime even within its scope of validity. This also exposes a general interpretative dilemma faced by all EFTs concerning their indispensable references to classical spacetime beyond their scope of validity. [ABSTRACT FROM AUTHOR]

Quantum nonseparability is a central feature of quantum mechanics, and raises important philosophical questions. Interestingly, a particular theoretical development of quantum mechanics, called the process matrix formalism (PMF), features another kind of nonseparability, called causal nonseparability. The PMF appeals to the notion of quantum process, which is a generalisation of the concept of quantum state allowing to represent quantum-like correlations between quantum events over multiple parties without specifying a priori their spatiotemporal locations. Crucially, since the PMF makes no assumption about the global causal structure between quantum events, it allows for the existence of causally nonseparable quantum processes. Such processes are said to have an indefinite causal structure. This work aims at investigating the philosophical implications of causal nonseparability, especially for the notion of spatiotemporal relations. A preliminary discussion will first study the formal connection between quantum and causal nonseparability. It will be emphasised that, although quantum processes can be seen as a generalisation of density matrices, the conceptual distinction between the two notions yields significant differences between quantum and causal nonseparability. From there, it will be shown that, depending on the interpretative framework, causal nonseparability suggests some kind of indeterminacy of spatiotemporal relations. Namely, within a realist context, spatiotemporal relations can be epistemically or metaphysically indeterminate. Finally, it will be argued that, in spite of the disanalogies between standard and causal nonseparability, similar implications for spatial relations can already be defended in the context of standard quantum mechanics. This work highlights the potentially very fruitful explorations of the implications of quantum features on the conception of spacetime, keeping in mind that quantum and spacetime theories are expected to be unified in a future theory of quantum gravity. [ABSTRACT FROM AUTHOR]

In Gepner's pioneering work, the requirement that leads to a model having the desired N = 1 Spacetime supersymmetry and E (8) × E (6) Gauge symmetry was the requirement that the spacetime symmetry is compatible with modular invariance. In this work we show that the requirement for the simultaneous fulfillment of mutual locality of the left-moving vertices of physical states with the space-time symmetry generators and of right-moving vertices with generators of E (8) × E (6) -gauge symmetry, which arises after some special reduction together with the requirement of mutual locality of complete (left-right) vertices of physical states among themselves leads to the same Gepner models. [ABSTRACT FROM AUTHOR]

In this manuscript, we investigate the properties of Casimir wormholes within the framework of extended teleparallel gravity, incorporating the Generalized Uncertainty Principle. Both the Casimir effect and the Generalized Uncertainty Principle (GUP) originate from the concept of a fundamental minimum length. Our analysis explores the geometric and physical traits of these wormholes, examining two distinct GUP constructions namely the Kempf, Mangano, and Mann (KMM) model and the Detournay, Gabriel, and Spindel (DGS) model and their corresponding equations of state. We find that the resulting wormhole solutions exhibit anisotropic effects and violate the null energy condition, implying the presence of exotic fluid. By employing volume integral techniques, we compute the quantity of exotic fluid, providing new insights into the nature of these wormholes. Our study sheds light on the implications of GUP-corrected Casimir wormholes for our understanding of gravity and the structure of spacetime. [ABSTRACT FROM AUTHOR]

In this paper, we consider the Schwarzschild-Tangherlini black hole to investigate the process of scalar wave scattering by the black hole in a spacetime of (d + 1) dimensions and also with the generalized uncertainty principle (GUP). In this scenario, we analytically determine the phase shift and explore the effect of extra dimensions by calculating the differential scattering and absorption cross-section by applying the partial wave method at low and high-frequency limits. We show at high dimensions that the absorption is not zero as the mass parameter approaches zero. [ABSTRACT FROM AUTHOR]

We derive a closed-form expression for the mutual coherence function (MCF) of a twisted spatiotemporal optical vortex (STOV) beam after propagating a distance z in a linear dispersive medium. A twisted STOV beam is a partially coherent optical field that possesses a coherent STOV and a stochastic twist coupling its space and time dimensions. These beams belong to a special class of space–time-coupled light fields that carry transverse (to the direction of propagation) orbital angular momentum, making them potentially useful in numerous applications including quantum optics, optical manipulation, and optical communications. After presenting the derivation, we validate our new general MCF by showing that it simplifies to the MCFs for two example beams from the literature. Lastly, we present and analyze space–time beam profiles and complex arguments (phases) of the MCF at multiple z and differing amounts of material dispersion, field correlation or coherence, and beam twist to gain insight into how twisted STOV beams evolve in dispersive media. We conclude with a brief summary. • We derive the MCF for a twisted STOV beam propagating in dispersive media. • A twisted STOV beam is a space–time-coupled (STC) field that carries transverse OAM. • We observe interesting propagation behaviors not predicted in prior works. • Our analysis will be useful in applying these STC beams in optical tweezing, optical communications, etc. [Display omitted] [ABSTRACT FROM AUTHOR]

In this paper, we prove the spacetime positive mass theorem for asymptotically flat spin initial data sets with arbitrary ends and a non-compact boundary. Moreover, we demonstrate a quantitative shielding theorem, subject to the tilted boundary dominant energy condition. Our results are established by solving a mixed boundary value problem for the Dirac-Witten operator with a Callias potential. [ABSTRACT FROM AUTHOR]

We attempt in this article to formulate a conceptual and testable framework weaving Cosmos, Mind and Matter into a whole. We build on three recent discoveries, each requiring more evidence: i. The particles of the Standard Model, SU(3) x SU(2) x U(1), are formally capable of collective autocatalysis. This leads us to ask what roles such autocatalysis may have played in Cosmogenesis, and in trying to answer, Why our Laws? Why our Constants? A capacity of the particles of SU(3) x SU(2) x U(1) for collective autocatalysis may be open to experimental test, stunning if confirmed. ii. Reasonable evidence now suggests that matter can expand spacetime. The first issue is to establish this claim at or beyond 5 sigma if that can be done. If true, this process may elucidate Dark Matter, Dark Energy and Inflation and require alteration of Einstein's Field Equations. Cosmology would be transformed. iii. Evidence at 6.49 Sigma suggests that mind can alter the outcome of the two-slit experiment. If widely and independently verified, the foundations of quantum mechanics must be altered. Mind plays a role in the universe. That role may include Cosmic Mind. 1. Ontologically Real Potentia and the Unmanifest; 2. Nonlocality as Fundamental; 3. Res potentia, Res extensa, and Actualization; 4. Mind and Qualia, Mind is not in Spacetime; 5. Quantum Vacuum = Potentia not in Spacetime = Mind not in Spacetime; 6. Mind can Actualize Potentia; 7. The emergence of the classical world; 8. Co-evolution of evermore complex matter; 9. Why "My Mind"?; 10. Each embodied mind is coupled bilaterally to the Quantum Vacuum that is Cosmic Mind; 11. Responsible Free Will. [ABSTRACT FROM AUTHOR]

One of the leading ideas for the beginning of the Universe is the Hartle-Hawking 'No-Boundary Proposal.' Since the Cobordism Conjecture claims that any spacetime allows for a dynamical boundary, we suggest that one may equally well consider a 'Boundary Proposal'. Specifically, the corresponding euclidean instanton is a sphere with two holes around north and south pole cut out. Analogously to the Hartle-Hawking proposal, the sphere is then cut in two at the equator and half of it is dropped. The equator is glued to an expanding Lorentzian de Sitter space, implementing a beginning of the Universe with a spacelike spherical boundary at its earliest moment. This process is in principle on equal footing with the one based on the no-boundary instanton. In fact, if the Linde-Vilenkin sign choice is used, this 'Boundary' creation process may even dominate. An intriguing implication arises if tensionless end-of-the-world branes, as familiar from type-IIA or M-theory, are available: Analogously to the Boundary Proposal, one may then be able to create a compact, flat torus universe from nothing, without any exponential suppression or enhancement factors. [ABSTRACT FROM AUTHOR]

It is well known that the theory of Cotton gravity proposed by Harada is trivially solved by all isotropic and homogeneous cosmologies. We show that this under-determination is more general. More precisely, the degree of arbitrariness in the solutions increases with the degree of symmetry. The inverse problem of finding the matter source generating a given spacetime geometry is similarly indeterminate in the case of highly symmetric configurations. We give two simple examples. The first is that of static spherically symmetric solutions, which depend on an arbitrary function of the radial coordinate. The second is that of anisotropic cosmologies, which depend on an arbitrary function of time. [ABSTRACT FROM AUTHOR]

We consider a model with two real Maxwell fields (or equivalently, a complex Maxwell field) minimally coupled to Einstein's gravity with a negative cosmological constant in four spacetime dimensions. Assuming a specific harmonic dependence of the vector fields, we show the existence of asymptotically anti-de Sitter (AdS) self-gravitating boson-star–like solitonic solutions, which are static and axially symmetric. Analytical solutions are found in the test-field limit, where the Maxwell equations are solved on a fixed AdS background. The fully nonlinear solutions are constructed numerically. [ABSTRACT FROM AUTHOR]

This Letter aims to advance unexplored properties of a new class of Closed Timelike Curves recently discovered in scalar–tensor gravity, reported in Nguyen and Lobo (2023) [31] and Nguyen and Azreg-Aïnou (2023) [30]. Therein, it was shown that when the Weak Energy Condition is violated, the topology of spacetime in scalar–tensor gravity is altered and directly enables the formation of two-way traversable wormholes. Furthermore, each of these wormholes acts a gateway between two time-mirrored worlds, where the two asymptotically flat sheets in the Kruskal–Szekeres diagram are glued antipodally along three directions—time t and the polar and azimuth angles (θ , φ) of the 2-sphere—to form a wormhole throat. This contrasts with the standard embedding diagram which typically glues the sheets only along the θ and φ directions. Crucially, due to the 'gluing' along the t direction, the wormhole becomes a portal connecting the two spacetime sheets with opposite physical time flows, enabling the emergence of closed timelike loops which straddle the throat. In this Letter, we shall point out that this portal mathematically permits the possibility of backward propagation of information against time. This feature is ubiquitous for wormholes in scalar–tensor theories. In addition, we formulate the Feynman sum for transition amplitudes of microscopic particles in the proximity of a wormhole throat in which we account for timelike paths that experience time reversal. [ABSTRACT FROM AUTHOR]

Damour-Solodukhin wormholes are intriguing theoretical constructs, closely mimicking many properties of black holes. This study delves into two distinct characteristics of the waveforms emitted from such wormholes, namely, the late-time tails and echoes, which can substantially be used to distinguish its identity. Notably, both features appear in the latter stages of quasinormal oscillations and stem from the singularities of the Green's function. The late-time tail, on the one hand, arises due to the branch cuts in the relevant Green's function. Within the Damour-Solodukhin wormhole paradigm, singularities are present in both ingoing and outgoing waveforms, which entails a generalization of the existing recipe for black hole metrics. On the other hand, the echoes are attributed to a new set of quasinormal poles, supplementing those of the respective black holes, reminiscent of the scenario where the spacetime metric possesses a discontinuity. It is inferred that both features are observationally relevant in distinguishing a wormhole from its black hole counterpart. Moreover, we suggest a potential interplay concerning the late-time evolution between the two mechanisms in question. [ABSTRACT FROM AUTHOR]

The integrated use of dockless bike-sharing (DBS) and metro has greatly promoted the development of multimodal transportations. It is challenging to understand the travel mobilities of DBS and metro due to their complicated flow structures. In this paper, we propose an interconnected double-layer network to analyze the mobilities, in which each travel mode constructs a layer network. The studied area is divided into grids with same size. The grids are considered as nodes and trips between nodes are considered as edges. The edges between different layers are transfer trips that are found by space-time constraints. The results show that the metro trip network is connected more tightly with high efficiency than DBS trip network. Moreover, the Gini coefficient of aggregate network is more than 0.9, which is larger than metro trip network and DBS trip network. It is observed that the transfer ratios between layers are high in morning peak, but low in evening peak. The multiplex participation coefficient is adopted to measure the disparity of degree distributions of a node in different layers. It is found that passengers are distributed more evenly in the central area than suburbs between two layers. Our findings could be helpful in planning and managing multimodal transportations. • Building a multilayer network to analyze the integrated use of dockless bike-sharing and metro. • The metro trip network is connected mote tightly with high efficiency than DBS trip network. • The metro trip network, DBS trip network and aggregate network show 'small world' characteristics. • The Gini coefficient of aggregate network is more than 0.9, which is larger than metro trip network and DBS trip network. [ABSTRACT FROM AUTHOR]

In this work, we propose and computationally investigate a monolithic space–time multirate scheme for coupled problems. The novelty lies in the monolithic formulation of the multirate approach as this requires a careful design of the functional framework, corresponding discretization, and implementation. Our method of choice is a tensor-product Galerkin space–time discretization. The developments are carried out for both prototype interface- and volume coupled problems such as coupled wave-heat-problems and a displacement equation coupled to Darcy flow in a poro-elastic medium. The latter is applied to the well-known Mandel's benchmark and a three-dimensional footing problem. Detailed computational investigations and convergence analyses give evidence that our monolithic multirate framework performs well. • Newly proposed monolithic space–time multirate scheme. • Developments apply to both interface-coupled and volume-coupled problems. • Numerical examples in heat, wave, and porous media. [ABSTRACT FROM AUTHOR]

In their seminal work, Morris and Thorne (1988) introduced the concept of traversable wormholes (WHs), which are geometric structures serving as bridges to connect two distinct spacetimes or different points within the same spacetime. The properties of these WHs are determined by the choice of the shape function. Extensive research has been conducted in the literature on WHs within modified theories of gravity, considering various types of shape functions. In this paper, we focus on deriving the simplest solutions for traversable WHs within the framework of f (R , T) gravity. Our specific focus lies on the functional form f (R , T) = R + α R 2 + λ T , where R represents the Ricci scalar and T denotes the trace of the energy–momentum tensor. By incorporating quadratic geometric and linear material corrections, we demonstrate that the matter content of WHs can obediently conform to the energy conditions (ECs). This study significantly advances our understanding of WHs within the context of modified gravity. Our findings shed new light on the behavior and properties of WHs, highlighting their compatibility with the f (R , T) gravity framework. By unveiling the ability of WHs to adhere to ECs through the inclusion of geometric and material corrections, we provide groundbreaking insights into these intriguing objects. Overall, our research contributes to the broader field of gravitational physics by presenting a unique perspective on WH modeling. By exploring WHs within the f (R , T) gravity framework and demonstrating their conformity to ECs, we expand our knowledge of these fascinating structures and pave the way for further investigations in this area. [ABSTRACT FROM AUTHOR]

This paper introduces a spatial queueing model for a single bottleneck during morning peak hours. Utilizing the logistic function and after appropriate calibration, it articulates the arrival and departure flows in continuous, differentiable terms. By validating the model across different peak periods and locations, the demand model's robustness is superior to other commonly used functions. This model also incorporates constant or varying capacity scenarios. It effectively captures key aspects of morning peak traffic, including the emergence of hysteresis loops in fundamental diagrams (FDs) of density and flow. The model's multi-stage approach recognizes three distinct phases in traffic flow: freeflow, transition, and queued segments, ensuring spatial consistency in flow and density across these stages. It accounts for the growth of the queued segment and vehicle spillback under various bottleneck intensities, with the resulting FDs for speed and density also displaying hysteresis loops. The calibration of model parameters utilizes time-series data of traffic flow and density space–time maps derived from real-world data. The validation results accurately reflect real traffic scenarios, emulating the counterclockwise hysteresis loops observed in density and its heterogeneity, and provide both planar and three-dimensional FDs at different points along the traffic link, each mirroring real-life traffic patterns. Additionally, a comparison with the cell transmission model (CTM) reveals that the proposed model exhibits superior generalization and robustness. • Accurate capture of peak traffic patterns with logistic model. • Spatially continuous multi-stage queueing approach. • Precise replication of hysteresis loops. • Concise model with superior performance to benchmarks. [ABSTRACT FROM AUTHOR]

Charged-flat black holes in the Rényi extended phase space demonstrate phase structures akin to those of a van der Waals fluid in four-dimensional spacetime and mirror the behaviors of Reissner-Nordstrom-Anti-de-Sitter black holes within the standard Gibbs-Boltzmann extended phase space. This study delves into the dynamics of states initially positioned within the unstable spinodal region of the phase space associated with the charged-flat black hole when subjected to time-periodic thermal perturbations. Our analysis based on the Mel'nikov method reveals that chaos emerges when the δ parameter surpasses a critical threshold, δ c. This critical quantity is dependent on the black hole charge; notably, a larger value of Q impedes the onset of chaos. Furthermore, we examine the effects of space-periodic thermal perturbations on its equilibrium state and find that chaos invariably occurs, irrespective of the perturbation amplitude. Hence, the chaotic dynamics observed in the analysis of charged-flat black holes under Rényi statistics exhibit resemblances to those of asymptotically AdS-charged black holes investigated via the Gibbs-Boltzmann formalism. This serves as yet another example of a potential and significant connection between the cosmological constant and the nonextensivity Rényi parameter. [ABSTRACT FROM AUTHOR]

We study the one-loop effective action of the higher-spin gauge theory induced by the IKKT matrix model on a M 1 , 3 × K background, where M 1 , 3 is an FLRW cosmological spacetime brane and K are compact fuzzy extra dimensions. In particular, we show that all non-abelian (hs -valued) gauge fields in this model acquire mass via quantum effects, thus avoiding no-go theorems. This leads to a massive non-abelian quantum hs -Yang-Mills theory, whose detailed structure depends on K. The stabilization of K at one loop is understood as a result of the coupling between K and the U (1) -flux bundle on space-time. This flux stabilization induces the KK scale into the N = 4 SYM sector of the model, which break superconformal symmetry. [ABSTRACT FROM AUTHOR]

We have discovered two unconstrained forms of free Lagrangian for continuous spin(CS) theory in arbitrary flat spacetime dimension for bosonic case. These Lagrangians, unlike that by Schuster and Toro, do not include delta functions and are conventional. The first form consists of five kinds of totally symmetric helicity fields and one kind of gauge parameter. By introducing auxiliary creation and annihilation operators, each is combined into a state vector in Fock space, including all ranks one by one. The Lagrangian imposes no constraints, such as trace conditions, on these fields or the gauge parameter field. Additionally, the Lagrangian does not contain higher-order derivative terms. In the limit as CS parameter μ approaches zero, it naturally reproduces a Lagrangian for helicity fields in higher spin(HS) theory, known as unconstrained quartet formulation. Permitting third-order derivatives, we also obtain the second unconstrained form of Lagrangian that can be written in terms of three kinds of fields, including μ , similar to the formulation by Francia and Sagnotti. Partial gauge fixing and partial use of equations of motion (EOM) on this Lagrangian yield a Fronsdal-like Lagrangian with a single double-traceless field, including μ. By imposing further gauge fixing on the field in the EOM with respect to divergence and trace, we confirm the reproduction of the modified Wigner equations already known in literature. [ABSTRACT FROM AUTHOR]

Spacetime singularity is not observed directly as it is covered by event horizon. Naked singularities may be formed due to gravitational collapse without an event horizon. Therefore, cosmic censorship conjecture entails advanced ascertainment. Recently, Joshi et al. have discovered a naked singularity solution (known as JMN naked singularity), which emerges from the dynamical gravitational collapse of a massive matter cloud. Since several studies are needed to know more extra characteristics that may help to test cosmic censorship conjecture in general relativity, therefore, we thought it is pertinent to study the deflection of massive particles by the naked singularity. We shall examine massive particles paths and deflection angles near naked singularities in this research. To get the deflection angle, we employ the Gauss-Bonet technique and the Rindler-Ishak method. The results of the two procedures are compared in detail. [ABSTRACT FROM AUTHOR]

This work proposes a novel variational approximation of partial differential equations on moving geometries determined by explicit boundary representations. The benefits of the proposed formulation are the ability to handle large displacements of explicitly represented domain boundaries without generating body-fitted meshes and remeshing techniques. For the space discretization, we use a background mesh and an unfitted method that relies on the integration on cut cells. We perform this intersection by using clipping algorithms. To deal with the mesh movement, we pullback the equations to a reference configuration (the spatial mesh at the initial time slab times the time interval) that is constant in time. This way, the geometrical intersection algorithm is only required in 3D, another key property of the proposed scheme. At the end of the time slab, we compute the deformed mesh, intersect the deformed boundary with the background mesh, and consider an exact transfer mechanism between meshes to compute jump terms in the time discontinuous Galerkin integration. The transfer is also computed using geometrical intersection algorithms. We demonstrate the applicability of the method to fluid problems around rotating (2D and 3D) geometries described by oriented boundary meshes. We also provide a set of numerical experiments that show the optimal convergence of the method. • Space–time unfitted finite element formulation on moving 3D explicit geometries. • Reference configuration pullback to avoid 4D geometrical algorithms. • Exact time-slab mechanism transfer that relies on 3D intersection algorithms. • Solution of transient problems on complex unfitted domains with large displacements. [ABSTRACT FROM AUTHOR]

The primary focus of the current study is to explore the geometrical properties of the Vaidya-Bonner-de Sitter (briefly, VBdS) spacetime, which is a generalization of Vaidya-Bonner spacetime, Vaidya spacetime and Schwarzschild spacetime. In this study we have shown that the VBdS spacetime describes various types of pseudosymmetric structures, including pseudosymmetry due to conformal curvature, conharmonic curvature and other curvatures. Additionally, it is shown that such a spacetime is 2-quasi-Einstein, Einstein manifold of level 3, generalized Roter type, and that conformal 2-forms are recurrent. The geometric features of the Vaidya-Bonner spacetime, Vaidya spacetime, and Schwarzschild spacetime are obtained as a particular instance of the main determination. It is further established that the VBdS spacetime admits almost Ricci soliton and almost η -Yamabe soliton with respect to non-Killing vector fields. Also, it is proved that such a spacetime possesses generalized conharmonic curvature inheritance. It is interesting to note that in the VBdS spacetime the tensors Q (T , R) , Q (S , R) and Q (g , R) are linearly dependent. Finally, this spacetime is compared with the Vaidya-Bonner spacetime with respect to their admitting geometric structures, viz., various kinds of symmetry and pseudosymmetry properties. [ABSTRACT FROM AUTHOR]

Based on deformed translations in the κ -anti-de Sitter algebra, we derive a delay in the time of detection between a soft and a hard photon, which are simultaneously emitted at a distant event, to first order in the quantum gravity parameter. In the basis analyzed, the trajectories are undeformed, and the effect depends exclusively on the symmetry properties of the quantum algebra. The time delay depends linearly on the energy of the hard particle and has a sinusoidal dependence on the redshift of the source. [ABSTRACT FROM AUTHOR]

The uncertainty principle is deemed as one of cornerstones in quantum mechanics, and exploring its lower limit of uncertainty will be helpful to understand the principle's nature. In this study, we propose a generalized entropic uncertainty relation for arbitrary multiple-observable in multipartite system, and further derive a tighter lower bound by considering Holevo quality and mutual information. Importantly, we detailedly discuss the proposed uncertainty relations and quantum coherence in the context of Schwarzschild space-time. It is interesting to find that Hawking radiation will damage the coherence of the physically accessible region and increase the uncertainty. Furthermore, we argue that the properties of the uncertainty in Schwarzschild space-time can be explained from the systems' purity and the information redistribution of the different regions. Therefore, it is believed that our findings provide the generalized entropic uncertainty relations in multipartite systems, which may facilitate us deeper understanding of quantumness and information paradox of the black holes. [ABSTRACT FROM AUTHOR]

We develop the framework that reveals the intrinsic conserved stress tensor and current associated with the null infinity of a three-dimensional (3 d) asymptotically flat spacetime. These are, respectively, canonical conjugates of degenerate metric and Ehresmann connection of the boundary Carrollian geometry. Their conservation reproduces the Bondi-mass and angular momentum conservation equations if the asymptotic boundary is endowed with a torsional affine connection that we specify. Our analysis and results shed further light on the 3 d flat holography; the stress tensor and current give rise to an asymptotically flat fluid/gravity correspondence. The requirement of a well-defined 3 d action principle yields Schwarzian action at null infinity governing the dynamics induced by reparametrizations over the celestial circle, in accord with the codimension 2 holography of 3 d flat spacetimes. [ABSTRACT FROM AUTHOR]

We derive the complete expression for the Brans Class I exterior spacetime explicitly in terms of the energy and pressures profiles of a stationary spherisymmetric gravity source. This novel and generic expression is achieved in a parsimonious manner, requiring only a subset of the Brans-Dicke field equation and the scalar equation. For distant orbiting test particles, this expression promptly provides a simple, closed and exact formula of the γ Eddington parameter, which reads γ exact = ω + 1 + (ω + 2) Θ ω + 2 + (ω + 1) Θ , where Θ is the ratio of the star's "total pressure" integral over its energy integral. This non-perturbative result reproduces the usual Post-Newtonian ω + 1 ω + 2 expression in the case of a "Newtonian star", in which the pressure is negligible with respect to the energy density. Furthermore, it converges to the General Relativity value (γ GR = 1) as the star's equation of state approaches that of ultra-relativistic matter (in which case Θ approaches 1), a behavior consistent with broader studies on scalar-tensor gravity. Our derivation underscores the essence of these results involving (1) the key relevant portion of the Brans-Dicke field equations, (2) the uniqueness of the Brans Class I vacuum solution for the non-phantom action, viz. ω > − 3 / 2 , and (3) the involvement of only two free parameters in this solution, hence requiring two quantities (energy and pressure integrals) of the mass source to fully characterize the solution. From a practical standpoint, it elucidates how a given stellar interior structure model determines the star's exterior gravitational field and impacts the motions of light objects (such as planets and accretion disks) orbiting it. [ABSTRACT FROM AUTHOR]

How the spacetime evolved non-perturbatively in a landscape with multiple anti-de Sitter (AdS) vacua, which is theoretically well-motivated, has always been a matter of concern. As a step towards this issue, we perform (3+1)D numerical relativity simulations for the inhomogeneous universe in an AdS landscape, and find that large inhomogeneity of scalar field can develop into not only sphere-like bubbles, but also novel tube-like structures. It is observed that the bubble or tube wall (across the potential barrier) likely inflates as a quasi-dS space, while the different regions separated by the walls are in different AdS vacua and will collapse towards singularity. [ABSTRACT FROM AUTHOR]

Size effects are particular types of scale effect, where the response of a material is dependent to some extent on its size. These types of behaviour manifest to a greater or lesser extent in all materials, and pose a problem for constitutive models, where material parameters determined through experimentation at one size are inapplicable at different sizes. The origin of size effects is microstructural, through defects and structures ranging from cracks, fibres, grains, porosity, dislocations, precipitates, etc., and which has led to the creation of a plethora of microscale and mesoscale models in an attempt to represent the phenomena. In this paper an entirely different approach is taken where metamaterial constitutive models are created that eliminate entirely particular types of size effect. Such an approach has only recently been made possible with the arrival of a new scaling theory called finite similitude , which from a material-model standpoint starts from the unlikely position that it is founded on transport equations defined on a trial-spacetime manifold (where the scaled experiment resides). The approach however features a countably infinite number of similitude rules that in principle can capture any scale effect. It is this feature that enables metamaterials and metasystems to be defined on a projection of the trial spacetime manifold to the scaling-space manifold, where all physical quantities are dependent on a single dimensional scaling parameter. Metasystem and metamaterial models are shown to exist on the scaling space that feature the extraordinary ability to represent behaviours over a range of length scales. Although the models created are idealised they nevertheless provide a practical approach through testing at different sizes and it is demonstrated in the paper how real-world size effects can be captured efficiently. • Metamaterials and metasystems defined. • Scalable materials and systems shown to exist. • Rudimentary material models and systems presented with scale effects exactly captured. • Demonstration that practical systems in fluids and solids exist that are exactly scalable. [Display omitted] [ABSTRACT FROM AUTHOR]

This work proposes novel techniques for the efficient numerical simulation of parameterized, unsteady partial differential equations. Projection-based reduced order models (ROMs) such as the reduced basis method employ a (Petrov-)Galerkin projection onto a linear low-dimensional subspace. In unsteady applications, space–time reduced basis (ST-RB) methods have been developed to achieve a dimension reduction both in space and time, eliminating the computational burden of time marching schemes. However, nonaffine parameterizations dilute any computational speedup achievable by traditional ROMs. Computational efficiency can be recovered by linearizing the nonaffine operators via hyper-reduction, such as the empirical interpolation method in matrix form. In this work, we implement new hyper-reduction techniques explicitly tailored to deal with unsteady problems and embed them in a ST-RB framework. For each of the proposed methods, we develop a posteriori error bounds. We run numerical tests to compare the performance of the proposed ROMs against high-fidelity simulations, in which we combine the finite element method for space discretization on 3D geometries and the Backward Euler time integrator. In particular, we consider a heat equation and an unsteady Stokes equation. The numerical experiments demonstrate the accuracy and computational efficiency our methods retain with respect to the high-fidelity simulations. [ABSTRACT FROM AUTHOR]

Mechanically steered scanning radars receive measurements in different azimuths sequentially rather than simultaneously for target detection and tracking. However, in conventional track-before-detect (TBD) methods, the requirement of waiting for all measurements of a whole scan, referring to a certain azimuth, leads to significant processing delays and boundary effect, which appears as that targets around the boundary may be scanned 0 or 2 times in a scan. This may also cause degraded detection and estimation performances. To solve these problems, a continuous TBD method is proposed for target detection and tracking in rotating radars. A space–time joint retrodiction method is presented to produce precise revisit intervals and retrodicted positions, which contribute to immediate and accurate energy integration. Once measurements in an azimuth cell are received, each range cell in this azimuth is retrodicted according to the space–time joint retrodiction method with an assumed velocity. Then, a number S of pseudo-spectra are constructed around the cell and its retrodicted positions in the past S − 1 scans. Samples of each pseudo-spectrum are added onto corresponding cells for energy accumulation. After that, some cells in the past (S − 1) th scan and their guard and reference cells complete energy integration, and thus are detected immediately. Continuous integration and detection are realized without waiting for measurements at the boundary of a scan. This eliminates the boundary effect and minimizes the processing latency. Experimental results corroborate the validity of the continuous TBD method. • Problems of processing delay and boundary effect in rotating radars are considered. • A space–time joint retrodiction method is proposed. • A continuous track-before-detect method based on the pseudo-spectrum is proposed. • The processing delay is minimized, and the boundary effect is eliminated. • Continuous integration and detection are realized. [ABSTRACT FROM AUTHOR]

In this manuscript, we study the relativistic dynamics of fermions and vector bosons within a (2+1)-dimensional magnetized space-time. We consider the Bonnor-Melvin magnetic space-time, characterized by a homogeneous magnetic field aligned along the symmetry axis and a non-zero cosmological constant. This space-time background, featuring cylindrical symmetry, retains the invariance of quantum field dynamics under Lorentz boosts along the z -direction. This enables us to explore (2+1)-dimensional realms, where the associated 2+1-dimensional spacetime background is recognized as the Bonnor-Melvin magnetic 2+1+0-brane solution within the framework of gravity coupled with nonlinear electrodynamics. We seek exact solutions for relativistic fermions and vector bosons within this space-time background. We have managed to derive the radial wave equations in both instances, securing precise eigenvalue solutions devoid of any approximations. Our findings extend seamlessly to massless fermions and vector bosons, ensuring generality. Moreover, we observe that the ground state energy of massless vector bosons (photons) within the examined space-time background is unequivocally zero. [ABSTRACT FROM AUTHOR]

This article studies a boundary element method for dynamic frictional contact between linearly elastic bodies. We formulate these problems as a variational inequality on the boundary, involving the elastodynamic Poincaré–Steklov operator. The variational inequality is solved in a mixed formulation using boundary elements in space and time. In the model problem of unilateral Tresca friction contact with a rigid obstacle we obtain an a priori estimate for the resulting Galerkin approximations. Numerical experiments in two space dimensions demonstrate the stability, energy conservation and convergence of the proposed method for contact problems involving concrete and steel in the linearly elastic regime. They address both unilateral and two-sided dynamic contact with Tresca or Coulomb friction. [ABSTRACT FROM AUTHOR]

The main objective of this manuscript is to investigate the bouncing cosmology in the background of f (Q) gravity, where Q defines the non-metricity. For this purpose, we use the reconstruction approach and consider a flat Friedmann–Robertson–Walker spacetime with perfect matter configuration. We examine how the first contracting phase gives the expansion by using a temporal derivative of the scale factor, i.e., a ̇ < 0 , a ̇ = 0 and a ̇ > 0 give contraction, bounce point and expansion phases, respectively. Further, we use the order reduction method to solve the modified field equations as these are very difficult due to the presence of additional non-linear expressions. It is analyzed that the original singularity of the universe diminishes for the required bounce conditions. We conclude that the acceleration occurs near the bouncing point and the considered f (Q) models are consistent with the current cosmic accelerated expansion. • Investigate the bouncing cosmology in the background of f(Q) gravity. • We use the reconstruction approach for a flat FRW spacetime with perfect matter configuration. • Examine how the first contracting phase gives the expansion through the scale factor. • The original singularity of the universe diminishes for the required bounce conditions. • The considered models of this gravity are consistent with the current cosmic accelerated expansion. [ABSTRACT FROM AUTHOR]

This paper uses the gravitational decoupling through the minimal geometric deformation approach and extends a known isotropic solution for a self-gravitating interior to two types of anisotropic spherical solutions in Rastall gravity in the presence of electromagnetic field. By deforming only the radial metric component, the field equations are decoupled into two sets, the first of which corresponds to an isotropic distribution of matter while the second set contains the anisotropic source. We obtain a solution of the first set by employing the charged isotropic Finch-Skea ansatz, whereas a solution for the second set is obtained by adopting two mimic constraints on the pressure and density. The matching conditions at the stellar surface are explored with the exterior geometry given by the deformed Reissner–Nordström spacetime. For the two fixed values of the Rastall and charge parameters, we investigate physical features of both solutions through graphical analysis of the energy conditions, equation of state parameters, surface redshift and compactness function. The stability of both solutions is also studied through the Herrera cracking approach and causality condition. We deduce that while both solutions are physically viable, only the solution corresponding to the pressure-like constraint is stable. • Gravitational decoupling approach is used to find charged exact solutions in Rastall gravity. • We obtain a solution by employing charged isotropic Finch-Skea ansatz. • Investigate physical viability of both solutions through graphical analysis of the physical quantities. • Stability of both solutions is also studied through the Herrera cracking approach and causality condition. • We deduce that both solutions are physically viable but only the first solution is stable. [ABSTRACT FROM AUTHOR]

We propose the doubly κ -dependent Yang quantum phase space which describes the generalization of D = 4 Yang model. We postulate that such model is covariant under the generalized Born map, what permits to derive this new model from the earlier proposed κ -Snyder model. Our model of D = 4 relativistic Yang quantum phase space depends on five deformation parameters which form two Born map-related dimensionful pairs: (M , R) specifying the standard Yang model and (κ , κ ˜) characterizing the Born-dual κ -dependence of quantum space-time and quantum fourmomenta sectors; fifth parameter ρ is dimensionless and Born-selfdual. In the last section, we propose the Kaluza-Klein generalization of D = 4 Yang model and the new quantum Yang models described algebraically by quantum-deformed o ˆ (1 , 5) algebras. [ABSTRACT FROM AUTHOR]

Topological arguments are currently being used as a novel scheme to discern the properties of black holes while ignoring their detailed structure and specific field equations. Among various avenues of black hole physics, where this novel approach is being utilized, the phase transition in black hole thermodynamics lies at the forefront. There are several types of phase transition in black holes; such as the van der Waals type phase transition, Davies-type phase transition, extremal phase transition, and Hawking-Page (HP) transition. So far, the topological interpretation, where the critical point has been identified with the non-zero topological charge, has been obtained only for the van der Waals type phase transition and HP transition in different spacetimes. To complete the picture, here we provide the same interpretation for two other phase transitions: Davies-type phase transition and extremal phase transition. The entire analysis is general and is valid for any spacetime where these types of phase transitions are observed. More importantly, our analysis suggests that amid the apparent differences in these phase transitions, they share the same topological characteristics, i.e. non-zero topological charge arising from different thermodynamic potentials in different types of phase transition. [ABSTRACT FROM AUTHOR]

A quest for phenomenological footprints of quantum gravity is among the central scientific tasks in the rising era of gravitational wave astronomy. We study gravitational wave dynamics within the noncommutative geometry framework, based on a Drinfeld twist and newly proposed noncommutative Einstein equation, and obtain the leading quantum correction to Regge-Wheeler potential up to first order in the noncommutativity parameter. By calculating the quasinormal mode frequencies we show that the noncommutative Schwarzschild black hole remains stable under axial gravitational perturbations. [ABSTRACT FROM AUTHOR]

In this letter, we prove the existence of resummed expressions for the diagonal of the heat kernel and the effective action of a quantum field which interacts with a scalar or an electromagnetic background. Working in an arbitrary number of spacetime dimensions, we propose an Ansatz beyond the Schwinger–DeWitt proposal, effectively resumming an infinite number of invariants which can be constructed from powers of the background, as well as its first and second derivatives in the Yukawa case. This provides a proof of the recent conjecture that all terms containing the invariants F μ ν F μ ν and F ˜ μ ν F μ ν in the proper-time series expansion of the SQED effective action can be resummed. Possible generalizations and several applications are also discussed—in particular, the existence of an analogue of the Schwinger effect for Yukawa couplings. [ABSTRACT FROM AUTHOR]

Lidar-assisted wind turbine control has been proven to be beneficial for turbine load reduction. It relies on the preview of incoming turbulence provided by a nacelle lidar, which allows the turbine controller to react to the flow disturbances before their impact on the turbine. When assessing its benefits, previous studies mainly use the standard turbulence parameters suggested by the IEC 61400-1 standard and assume Taylor's frozen hypothesis. Based on atmospheric turbulence observations, the parameters of the Mann spectral turbulence model differ significantly from the values recommended in the standard, and they vary, e.g., with atmospheric stability. Also, turbulence evolution from upstream to the rotor position conflicts with the frozen turbulence hypothesis, and its effect on the preview quality by a nacelle lidar still needs quantification. This work presents a simple method to extend the Mann model to account for the temporal evolution of turbulence using a space-time spectral velocity tensor. Under various atmospheric stability conditions, we derive the space-time tensor parameters and evaluate the space-time tensor using data from a five-beam lidar and a meteorological mast, we found good agreement between the space-time tensor and the measurement data. In addition, a numerical method for simulating a four-dimensional (4D) space-time velocity field based on the space-time tensor is presented. In the end, we analyze the importance of including the temporal evolution of turbulence for assessing lidar wind preview quality. Lidar-assisted wind turbine control has been proven to be beneficial for turbine load reduction. It relies on the preview of incoming turbulence provided by a nacelle lidar, which allows the turbine controller to react to the disturbances prior their impact on the turbine. This work presents a simple method to extend the Mann model to account for the temporal evolution of turbulence using a space-time spectral velocity tensor. Under various atmospheric stability conditions, we derive the space-time tensor parameters and evaluate the space-time tensor using data from a five-beam lidar and a meteorological mast, we found good agreement between the space-time tensor and the measurement data. We analyze the importance of including the temporal evolution of turbulence for assessing lidar wind preview quality. Figure 1: Typical nacelle lidar measurements over a wind field. The evolved turbulence (more transparent) illustrates the actual rotor disturbance while the upstream turbulence is observed by the lidar. A Gaussian range weighting shape/function is shown for LOS measurements (the LOS speeds along the beam are weight averaged by this function to get lidar LOS measurement). [Display omitted] [ABSTRACT FROM AUTHOR]

We study the K -item knapsack problem (i.e. , 1.5-dimensional knapsack problem), a generalization of the famous 0–1 knapsack problem (i.e. , 1-dimensional knapsack problem) in which an upper bound K is imposed on the number of items selected. This problem is of fundamental importance and is known to have a broad range of applications in various fields. It is well known that, there is no fully polynomial time approximation scheme (FPTAS) for the d -dimensional knapsack problem when d ≥ 2 , unless P = NP. While the K -item knapsack problem is known to admit an FPTAS, the complexity of all existing FPTASs has a high dependency on the cardinality bound K and approximation error ɛ , which could result in inefficiencies especially when K and ɛ − 1 increase. The current best results are due to Mastrolilli and Hutter (2006), in which two schemes are presented exhibiting a space–time tradeoff-one scheme with time complexity O (n + K z 2 / ɛ 2) and space complexity O (n + z 3 / ɛ) , and another scheme that requires a run-time of O (n + (K z 2 + z 4) / ɛ 2) but only needs O (n + z 2 / ɛ) space, where z = min { K , 1 / ɛ }. In this paper we close the space–time tradeoff exhibited in Mastrolilli and Hutter (2006) by designing a new FPTAS with a running time of O ˜ (n + z 2 / ɛ 2) , while simultaneously reaching a space complexity 1 1 O ˜ notation hides terms poly-logarithmic in n and 1 / ɛ. of O (n + z 2 / ɛ). Our scheme provides O ˜ (K) and O (z) improvements on the state-of-the-art algorithms in time and space complexity respectively, and is the first scheme that achieves a running time that is independent of the cardinality bound K (up to logarithmic factors) under fixed ɛ. Another salient feature of our algorithm is that it is the first FPTAS that achieves better time and space complexity bounds than the very first standard FPTAS over all parameter regimes. [ABSTRACT FROM AUTHOR]

Let Δ S n denote the Laplace-Beltrami operator on the n -dimensional unit sphere S n , n ≥ 2. In this paper we show that ‖ e i t Δ S n f ‖ L 4 ([ 0 , 2 π) × S n) ≤ C ‖ f ‖ W α , 4 (S n) holds if α > (n − 2) / 4. The range of α is sharp in the sense that the estimate fails for α < (n − 2) / 4. As a consequence, we obtain space-time L p -estimates for e i t Δ S n for 2 ≤ p ≤ ∞. We also prove that the maximal operator f → sup 0 ≤ t < 2 π ⁡ | e i t Δ S n f | is bounded from W α , 2 (S n) to L 6 n / (3 n − 2) (S n) for α > 1 / 3 whenever f are zonal functions on S n. [ABSTRACT FROM AUTHOR]

Peridynamics is a nonlocal theory for dynamic fracture analysis consisting in a second order in time partial integro-differential equation. In this paper, we consider a nonlinear model of peridynamics in a two-dimensional spatial domain. We implement a spectral method for the space discretization based on the Fourier expansion of the solution while we consider the Newmark- β method for the time marching. This computational approach takes advantages from the convolutional form of the peridynamic operator and from the use of the discrete Fourier transform. We show a convergence result for the fully discrete approximation and study the stability of the method applied to the linear peridynamic model. Finally, we perform several numerical tests and comparisons to validate our results and provide simulations implementing a volume penalization technique to avoid the limitation of periodic boundary conditions due to the spectral approach. [ABSTRACT FROM AUTHOR]

We investigate a relativistic positioning system where the coordinates of the users are determined by the proper times broadcasted by clocks in motion in spacetime: these are the so-called emission coordinates. In particular, we focus on emission coordinates in flat spacetime: in this case, we show that these coordinates can be defined using an approach based on simple geometrical properties of geodesic triangles. We analyze the 2-dimensional case and then we show how the whole procedure can be applied to 4 dimensions, also in terms of ordinary three-dimensional spheres. An analytic solution for the coordinates of the receiver is obtained. The solution remains valid at almost any place, in particular when redundancy in the number of emitters can be exploited. [ABSTRACT FROM AUTHOR]

This essay explores Kaila's interpretation of the special theory of relativity. Although the relevance of his work to logical empiricism is well-known, not much has been written on what Kaila calls the 'Einstein-Minkowski invariance theory'. Kaila's interpretation focuses on two salient features. First, he emphasizes the importance of the invariance of the spacetime interval. The general point about spacetime invariance has been known at least since Minkowski, yet Kaila applies his overall tripartite theory of invariances to space, time and spacetime in an original way. Second, Kaila provides a non-conventionalist argument for the isotropic speed of electromagnetic signals. The standard Einstein synchrony is not a mere convention but a part of a larger empirical theory. According to Kaila's holistic principle of testability, which stands in contrast to the theses of translatability and verification, different items in the theory cannot be sharply divided into conventional and empirical. Kaila's invariantism/non-conventionalism about relativity reflects an interesting case in the gradual transition from positivism to realism within the philosophy of science. [ABSTRACT FROM AUTHOR]

The present paper offers a reconstruction of what Feynman calls: "the overall spacetime view". To provide some background, I will rehearse Feynman's works on the absorber theory of radiation and on path integrals to emphasize the rejection of the so-called "customary view". Afterward, I will argue that Feynman's doctoral thesis was instrumental in developing the idea of enclosing a given quantum system into a spacetime boundary. This will be later applied to the path integral formulation and will play a substantial role in the use of asymptotic states in the theory of positron. It is in this latter work that Feynman uses the expression: "overall spacetime view", referring to the necessity of looking at all the possible quantum phenomena happening within the spacetime boundary. In the last part of the paper, I analyze how such a view applies to Feynman's work on quantum electrodynamics and Feynman diagrams. [ABSTRACT FROM AUTHOR]

We propose some efficient space-time Jacobi rational spectral methods for solving second order time-dependent problems on unbounded domains in this paper. Based on the Jacobi rational functions on the whole line, we first construct a set of Fourier-like basis functions for the spatial discretization which are simultaneously orthogonal in both L 2 - and H 1 -inner products. Meanwhile, composite (multi-domain) Legendre-Gauss collocation schemes with the knowns being time function values are developed for time integration. Owing to the simultaneously diagonal mass and stiffness matrices in space, the resulted linear system is eventually decoupled into a system of discrete ordinary differential equations stemmed from the multi-domain Legendre-Gauss collocation in time. Next, rigorous error estimates are carried out for the one-dimensional parabolic equations. Finally, some numerical results are presented to illustrate the spectral accuracy and the high efficiency of our space-time spectral methods, and to validate our main theory. [ABSTRACT FROM AUTHOR]

Non-Uniform Rational B-Spline (NURBS) surfaces are commonly used within Computer-Aided Design (CAD) tools to represent geometric objects. When using isogeometric analysis (IGA), it is possible to use such NURBS geometries for numerical analysis directly. Analyzing fluid flows, however, requires complex three-dimensional geometries to represent flow domains. Defining a parametrization of such volumetric domains using NURBS can be challenging and is still an ongoing topic in the IGA community. With the recently developed NURBS-enhanced finite element method (NEFEM), the favorable geometric characteristics of NURBS are used within a standard finite element method. This is achieved by enhancing the elements touching the boundary by using the NURBS geometry itself. In the current work, a new variation of NEFEM is introduced, which is suitable for three-dimensional space-time finite element formulations. The proposed method makes use of a new mapping which results in a non-Cartesian formulation suitable for fluid-structure interaction (FSI). This is demonstrated by combining the method with an IGA formulation in a strongly-coupled partitioned framework for solving FSI problems. The framework yields a fully spline-based representation of the fluid-structure interface through a single NURBS. The coupling conditions at the fluid-structure interface are enforced through a Robin-Neumann type coupling scheme. This scheme is particularly useful when considering incompressible fluids in fully Dirichlet-bounded and curved problems, as it satisfies the incompressibility constraint on the fluid for each step within the coupling procedure. The accuracy and performance of the introduced spline-based space-time finite element approach and its use within the proposed coupled FSI framework are demonstrated using a series of two- and three-dimensional benchmark problems. [ABSTRACT FROM AUTHOR]