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We present an overview of both older and recent developments concerning scale separation in string theory. We focus on parametric scale separation obtained at the classical level in flux compactifications down to AdS vacua. We review the scenarios that have been proposed to achieve a hierarchy of scales between spacetime and the internal space, built from a low-dimensional perspective. We then discuss how they have been understood to arise from proper higher-dimensional descriptions. Eventually, limitations of these constructions as well as Swampland and holographic arguments addressing the question of scale separation in string theory are discussed. The purpose of the review is to draw an accurate picture of the state of the art of the subject at the moment. [ABSTRACT FROM AUTHOR]

The focus of this paper is to analyze the trends and locations of accidents in the Greater Melbourne Area (GMA) during a 15-year period (2006–2020). The places where accidents were most prevalent were discovered and the reasons which are contributing to the high accident rates in those areas are determined. Analyzing the patterns over time and variations in the frequency of accidents helped to identify areas that have improved or deteriorated in terms of road safety. A Tweedie model was developed to examine the intricate interaction between the accident frequency and its potential contributing factors such as socio-demographics, road transport infrastructure, and built environment. Ultimately, a clustering analysis was performed to elucidate the dispersion of road accident risk ratings among different local government areas (LGAs), offering useful insights into road safety initiatives and prioritization. • The study linked built environment to accidents with Twidee and Space-time Cube. • Accidents down overall (20 yrs), but hotspots move outward. • Melbourne suburbs form five risk clusters based on accident frequency. [ABSTRACT FROM AUTHOR]

In this work, a space-time Petrov-Galerkin (STPG) method is used to numerically analyze the two-dimensional regularized long-wave (RLW) equation. The STPG method is a nonstandard finite element method, that is, both of the spatial and temporal variables of this method are discretized by finite element method. Therefore, it can display the superiority of the finite element method in both spatial and temporal directions. In particular, it is easy to obtain space-time high accuracy and is unconditionally stable, thus this method is very appropriate for solving the nonlinear convection-diffusion equations. We prove the existence and uniqueness of the approximate solution and derive an optimal order error estimate in the maximum norm without requiring any compatibility between the space and time mesh size. In addition, some numerical experiments are presented to validate the accuracy and efficiency of the proposed method. Also, we provide several numerical experiments to confirm the conservation properties of discrete mass, energy and momentum for both the single and double-soliton waves. [ABSTRACT FROM AUTHOR]

We consider goal-oriented adaptive space-time finite-element discretizations of the regularized parabolic p-Laplace problem on completely unstructured simplicial space-time meshes. The adaptivity is driven by the dual-weighted residual (DWR) method since we are interested in an accurate computation of some possibly nonlinear functionals at the solution. Such functionals represent goals in which engineers are often more interested than the solution itself. The DWR method requires the numerical solution of a linear adjoint problem that provides the sensitivities for the mesh refinement. This can be done by means of the same full space-time finite element discretization as used for the primal non-linear problems. The numerical experiments presented demonstrate that this goal-oriented, full space-time finite element solver efficiently provides accurate numerical results for different functionals. [ABSTRACT FROM AUTHOR]

In this work, we consider Anderson acceleration for numerical solutions of nonlinear time dependent partial differential equations discretized by space–time spectral methods, where classical fixed-point methods converge slowly or even diverge. Specifically, we apply Anderson acceleration with finite window size w to speed up fixed-point methods in solving nonlinear reaction diffusion, nonlinear Schrödinger and Navier Stokes equations. We focus on studying the influence of the window size w on the number of iterations to numerical convergence. Numerical results show the high efficiency of Anderson acceleration in solving a variety of nonlinear time dependent problems discretized by space–time spectral methods, and a small value of w is enough to achieve good performance. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the problem of source recovery in a dynamical system utilizing space-time samples. This is a specific issue within the broader field of dynamical sampling, which involves collecting samples from solutions to a differential equation across both space and time with the aim of recovering critical data, such as initial values, the sources, the driving operator, or other relevant details. Our focus in this study is the recovery of unknown, stationary sources across both space and time, leveraging space-time samples. This research may have significant applications; for instance, it could provide a model for strategically placing devices to measure the number of pollutants emanating from factory smokestacks and dispersing across a specific area. Space-time samples could be collected using measuring devices placed at various spatial locations and activated at different times. We present necessary and sufficient conditions for the positioning of these measuring devices to successfully resolve this dynamical sampling problem. This paper provides both a theoretical foundation for the recovery of sources in dynamical systems and potential practical applications. [ABSTRACT FROM AUTHOR]

A one-dimensional space-time fractional reaction-diffusion problem is considered. We present a complete theory for the solution of the time-space fractional reaction-diffusion model, including existence and uniqueness in the case of using the spectral representation of the fractional Laplacian operator. An optimal error estimate is presented for the Galerkin spectral approximation of the problem under consideration. [ABSTRACT FROM AUTHOR]

We study the numerical approximation by space-time finite element methods of a coupled hyperbolic-parabolic system modeling, for instance, poro- and thermoelasticity. The equations are rewritten as a first-order system in time. Discretizations by continuous Galerkin methods in time and inf-sup stable pairs of finite element spaces for the spatial variables are investigated. Optimal order error estimates are proved for the first-order energy of the system's variables. An important ingredient of the estimates is the control of the coupling terms by a tailored testing strategy. The techniques developed here can be generalized to other families of space-time finite element discretizations and related models. The error estimates are confirmed by numerical experiments, also for higher order piecewise polynomials in space and time. The latter lead to algebraic systems with complex block structure and put a facet of challenge on the design of iterative solvers. An efficient solution technique is referenced. [ABSTRACT FROM AUTHOR]

• A wider class of homogeneous spacetimes can be described using General Relativity. • The models are categorized into Bianchi I to IX, by employing Lie Algebras. • We explore several inflationary Mixmaster models by using potential inflaton fields. • Inflation affects the stability of the Bianchi IX model, which becomes more stable. The objective of this research is to investigate the dynamical behavior of the Bianchi IX Universe through various inflationary models induced by scalar fields. Specifically, we explore potentials for the inflaton field of the form V (ϕ) ∝ ϕ δ , where c varies from 1 to 4. To discern any chaotic behavior in the system, we calculate basin diagrams using the smaller alignment index (SALI) and the grid classification method. The fractal nature of the basins is evaluated through the utilization of two distinct indicators, namely the box-counting dimension and the boundary basin entropy. Our findings reveal that the inflaton affects the stability of the Bianchi IX model, which is intrinsically chaotic and becomes more stable as the power of the scalar-field potential increases. Moreover, except in the case δ = 1 , the impact of the scalar field on the dynamics is independent of the exponent δ. [ABSTRACT FROM AUTHOR]

The standard Hodge star operator is naturally associated with metric tensor (and orientation). It is routinely used to concisely write down physics equations on, say, Lorentzian spacetimes. On Galilean (Carrollian) spacetimes, there is no canonical (nonsingular) metric tensor available. So, the usual construction of the Hodge star does not work. Here we propose analogs of the Hodge star operator on Galilean (Carrollian) spacetimes. They may be used to write down important physics equations, e.g. equations of Galilean (Carrollian) electrodynamics. [ABSTRACT FROM AUTHOR]

The viscous Burgers' equation is a kind of quasi-linear important partial differential equation appeared in many fields. The nonlinear term contained in this equation results in difficulty in finding its high-precision numerical solution. In this paper, a space-time pseudospectral method for solving multi-dimensional Burgers' equations is proposed based on the Lagrange polynomials. The method is employed in time and space both at Chebyshev- Gauss- Lobbato(CGL) points. The spectral coefficients are found in such a way that the residual becomes minimum. The given problem is reduced to a system of nonlinear algebraic equations, which is solved by Newton-Raphson's method. Error bounds on discrete L 2 -norm and Sobolev norm (H p) are presented. The computational experiments are carried out to corroborate the theoretical results and to compare the present method with existing methods in the literature. Moreover, some model examples of multi-dimensional Burgers' equations are tested and a detailed comparison of the proposed method with various other methods is also given. When using the proposed method, some interesting phenomenon appears with the coefficient of kinematic viscous. [ABSTRACT FROM AUTHOR]

We consider a full-upwind DG approximation in space and time for the linear transport equation. Based on our results for linear symmetric Friedrichs systems we establish inf-sup stability and convergence in a mesh-dependent DG norm, and we construct an error indicator with respect to this norm. Numerical results of test problems with known solution demonstrate the efficiency of the a priori and a posteriori results as well for smooth and for non-smooth solutions. Then, we show that by introducing suitable degrees of freedom on the space-time element boundaries the corresponding hybrid formulation yields a reduction to a considerably smaller linear system. [ABSTRACT FROM AUTHOR]

A novel space-time discretization for the (linear) scalar-valued dissipative wave equation is presented. It is a structured approach, namely, the discretization space is obtained tensorizing the Virtual Element (VE) discretization in space with the Discontinuous Galerkin (DG) method in time. As such, it combines the advantages of both the VE and the DG methods. The proposed scheme is implicit and it is proved to be unconditionally stable and accurate in space and time. [ABSTRACT FROM AUTHOR]

This article shows how to develop an efficient solver for a stabilized numerical space-time formulation of the advection-dominated diffusion transient equation. At the discrete space-time level, we approximate the solution using higher-order continuous B-spline basis functions in both spatial and temporal dimensions. This problem is very difficult to solve numerically using the standard Galerkin finite element method due to artificial oscillations present when the advection term dominates the diffusion term. However, a first-order constraint least-square formulation allows us to obtain numerical solutions avoiding oscillations. The advantages of space-time formulations are the use of high-order methods and the feasibility of developing space-time mesh adaptive techniques on well-defined discrete problems. We develop a solver for a least-square formulation to obtain a stabilized and symmetric problem on finite element meshes. The computational cost of our solver is bounded by the cost of the inversion of the space-time mass and stiffness (with one value fixed at a point) matrices and the cost of the GMRES solver applied for the symmetric and positive definite problem. We illustrate our findings on an advection-dominated diffusion space-time model problem and present two numerical examples: one with isogeometric analysis discretizations and the second one with an adaptive space-time finite element method. [ABSTRACT FROM AUTHOR]

This paper argues for the appropriateness of Maxwell spacetime as the minimal spacetime structure in which one may formulate a theory of Newtonian gravity. I begin by presenting an intrinsic characterization of Maxwell gravitation that, eschewing covariant derivative operators, makes use only of a standard of rotation and other more primitive structures. I then revisit the question of whether Maxwell gravitation and Newton-Cartan theory are equivalent, demonstrating that previous results may be extended to all but the vacuum case since candidate geometrizations are not free to vary through purely gravitational degrees of freedom. Lastly, I consider the space of possible geometrizations of Maxwell gravitation more broadly and argue for a sense in which curvature is not entirely a matter of convention in classical spacetimes. [ABSTRACT FROM AUTHOR]

To assess the distribution and clustering of coronavirus disease 2019 (COVID-19) testing and incidence over space and time, U.S. Department of Veteran's Affairs (VA) data were used to describe where and when veterans experienced highest proportions of test positivity. Data for 6,342,455 veterans who utilized VA services between January 1, 2018, and September 30, 2021, were assessed for COVID-19 testing and test positivity. Testing and positivity proportions by county were mapped and focused-cluster tests identified significant clustering around VA facilities. Spatial cluster analysis also identified where and when veterans experienced highest proportions of test positivity. Within the veterans study population and our time window, 21.3% received at least one COVID-19 test, and 20.4% of those tested had at least one positive test. There was statistically significant clustering of testing around VA facilities, revealing regional variation in testing practices. Veterans experienced highest test positivity proportions between November 2020 and January 2021 in a cluster of states in the Midwest, compared to those who received testing outside of the identified cluster (RR: 3.45). Findings reflect broad regional trends in COVID-19 positivity which can inform VA policy and resource allocation. Additional analysis is needed to understand patterns during Delta and Omicron variant periods. [ABSTRACT FROM AUTHOR]

In this article, we use space-time continuous Galerkin (STCG) method to find the numerical solution for two-dimensional (2D) Burgers' equation. The STCG method differs from conventional finite element methods, both the spatial and temporal variables are discretized by finite element method, thus it can easily obtain the high order accuracy in both time and space directions and the corresponding discrete scheme is unconditionally stable. We demonstrate the existence and uniqueness of numerical solution by using Brouwer's fixed point theorem and give the a priori error estimates without needing to satisfy the limitation of the space-time mesh ratio condition. At last, we provide two numerical examples to confirm the efficiency of the method. Moreover, the numerical experiments reveal that the proposed method can handle the bigger Reynolds number than the existing literatures in the case of the absence of stabilization techniques and has the better stability as well as does not need to impose a limitation on the time step size. [ABSTRACT FROM AUTHOR]

This paper presents an efficient parallel computing strategy to solve large-scale structural vibration problems. The proposed approach utilises a novel direct method that operates using simplex-shaped space-time finite elements and allows for the direct decoupling of variables during the assembly of global matrices. The method uses consistent stiffness, inertia and damping matrices and deals with non-symmetric matrices. One significant advantage of this approach is that the computational cost remains unaffected by the bandwidth of the matrix in the traditional sense because only non-zero coefficients are retained. The speed of computations demonstrates a noticeable increase as the number of nodes and the problem's dimensionality grow. To demonstrate the effectiveness of the parallel space-time approach, a comparison with a sequentially executed code was conducted. The results indicate that the proposed method enables calculations at least 20 times faster than those achieved using the classical finite element method. Furthermore, the parallelisation algorithm was successfully implemented to solve a dynamics problem involving a large-scale, three-dimensional railway structure subjected to a moving load. Remarkably, the problem was solved in a reasonable amount of time using a relatively low-cost personal computer. • Strategy allows efficient parallel computing for large scale structural problems. • Direct method uses simplex-shaped space-time finite elements. • Variables are decoupled while assembling global matrices. • Computational cost is independent of the bandwidth. • Simulations of travelling load problems exhibit twenty times faster computations. [ABSTRACT FROM AUTHOR]

We present a spacetime DG method for 1D spatial domains and three linear hyperbolic, damped hyperbolic, and parabolic PDEs. The latter two correspond to Maxwell-Cattaneo-Vernotte (MCV) and Fourier heat conduction problems. The method is called the tent-pitcher spacetime DG method (tpSDG) due to its resemblance to the causal spacetime DG method (cSDG) wherein the solution advances in time by pitching spacetime patches. The tpSDG method extends the applicability of such methods from hyperbolic to parabolic and hyperbolic PDEs. For problems with a spatially uniform mesh, a transfer matrix approach is derived wherein the inflow, boundary, and source term values are mapped to the solution coefficient and output values. This resembles a finite difference scheme, but with grid points at the Gauss points of the spatial elements and arbitrarily tunable order of accuracy in spacetime. The spectral stability analysis of the method provides stability correction factors for the parabolic case. Numerical examples demonstrate the applicability of the method to problems with heterogeneous material properties. • Extended spacetime tent-pitcher methods from hyperbolic to hyperbolic-parabolic PDEs. • Transfer matrices relate inflow and outflow solutions of a patch at the Gauss points. • Polynomial order-independent stability limit of tent-pitcher method is shown for wave equation. • The stability limit for parabolic heat conduction is obtained using the transfer matrices. • The transfer matrix method advances the solution of 1D uniform grids with tunable order. [ABSTRACT FROM AUTHOR]

A space-time spectral method for the nonlinear Klein-Gordon equation is proposed. We use the Legendre-Galerkin method in space and Legendre-Petrov-Galerkin method in time. The nonlinear term in the equation is dealt with the Chebyshev spectral collocation method. The scheme results in a simple algebraic system by choosing appropriate basis functions. The stability and the optimal error estimates in L 2 -norm for the single and multiple interval methods are given. Numerical experiments are shown confirming the theoretical results. [ABSTRACT FROM AUTHOR]

Pregnancy is likely nature's most elaborate model of dynamic adaptations occurring over a distinct period of time at specific sites of the maternal body. Spatially-resolved transcriptomic analyses now enable the comprehensive decoding of these dynamic adaptations during the early onset stages of mammalian pregnancies and throughout fetal development. Pregnancy is likely nature's most elaborate model of dynamic adaptations occurring over a distinct period of time, at specific sites of the maternal body. Spatially-resolved transcriptomic analyses now enable the comprehensive decoding of these dynamic adaptations during the early onset stages of mammalian pregnancies and throughout fetal development. [ABSTRACT FROM AUTHOR]

This article concerns the study of perfect fluid spacetimes equipped with different types of gradient solitons. It is shown that if a perfect fluid spacetime with Killing velocity vector admits a τ-Einstein soliton of gradient type, then the spacetime represents phantom regime, or ψ remains invariant under the velocity vector field ρ. Besides, we establish that in a perfect fluid spacetime with constant scalar curvature, if the Lorentzian metric is the gradient τ-Einstein soliton, then either the τ-Einstein gradient potential function is pointwise collinear with ρ, or the spacetime represents stiff matter fluid. Furthermore, we prove that under certain conditions, a perfect fluid spacetime turns into a generalized Robertson–Walker spacetime, as well as a static spacetime and such a spacetime is of Petrov type I, D or O. We also characterize perfect fluid spacetimes whose Lorentzian metric is equipped with gradient m -quasi Einstein solitons and that the perfect fluid spacetime has vanishing expansion scalar, or it represents dark energy era under certain restriction on the potential function. [ABSTRACT FROM AUTHOR]

• A joint use of two sharing modes is adopted to exploit the remaining capacity. • A penalty cost based on load factors is introduced to represent the negative impacts of integrated transportation. • A Benders-based algorithm is proposed and enhanced with several acceleration techniques. • A computational study is conducted to demonstrate the applicability of integrated transportation. This study investigates the potential of a shared freight and passenger high-speed railway system in which different transportation resources are allowed to be shared under different sharing modes. A sharing-carriage mode is proposed and combined with a sharing-train mode to fully exploit the remaining capacity of the existing railway schedule. The manner in which these two sharing modes are jointly involved to utilize the available capacity is investigated and optimized. First, a space–time network is constructed to analyze the distribution of flow for a given train schedule. Subsequently, the influence of integrated transportation upon passenger satisfaction is included by introducing a load-factor-based penalty cost for each train. The model is first formulated as a mixed-integer program that minimizes service and routing costs and then reformulated into a path-based model. A Benders decomposition approach is proposed to decompose the problem into two subproblems. Instead of exploring every possible path for each commodity when solving the Benders subproblem, a column-pool-based approximation approach is proposed to generate feasible solutions. Finally, the proposed approach is tested on two small-scale examples and 12 scenarios from a real-world high-speed railway network. Different train load factors, penalty costs, sharing modes, and commodity volumes are investigated to demonstrate the applicability of integrated transportation. The performance of the algorithm and acceleration techniques is also analyzed. [ABSTRACT FROM AUTHOR]

Space-time domain decomposition methods have been successfully applied to solve linear systems that arise from the discretization of time-dependent problems. In this paper, we present a space-time pure multiplicative Schwarz method for solving linear parabolic equations. With this method, the systems of equations are first coupled together and then solved by preconditioned GMRES, so the solutions at arbitrary time steps can be obtained simultaneously at a time. Under some mild assumptions, we develop an optimal convergence theory and show that the convergence rate is bounded independently of the mesh sizes, the subdomain partition and the window size. Some numerical results are reported to illustrate the optimality and scalability of the proposed method. Moreover, the numerical comparison also shows that our method has a faster convergence rate. [ABSTRACT FROM AUTHOR]

We study the semilinear wave equation with power type nonlinearity and small initial data in Schwarzschild spacetime. If the nonlinear exponent p satisfies 2 ≤ p < 1 + 2 , we establish the sharp upper bound of lifespan estimate, while for the most delicate critical power p = 1 + 2 , we show that the lifespan satisfies T (ε) ≤ exp ⁡ (C ε − (2 + 2)) , the optimality of which remains to be proved. The key novelty is that the compact support of the initial data can be close to the event horizon. By combining the global existence result for p > 1 + 2 obtained by Lindblad et al. (2014) [25] , we then give a positive answer to the interesting question posed by Dafermos and Rodnianski (2005) [22, the end of the first paragraph in page 1151] : p = 1 + 2 is exactly the critical power of p separating stability and blow-up. [ABSTRACT FROM AUTHOR]

The Stokes equations are a linearized version of the Navier-Stokes equations and model incompressible viscous fluid flow with low Reynolds numbers. Several spectral methods, exhibiting exponential decay in error when the solution is analytic, are known to solve the steady-state Stokes problem numerically. A common strategy to solve such a problem in the time-dependent case involves extending the spectral scheme in spatial derivatives by implementing a low-order finite difference scheme for the time derivatives. Instead, we implement and analyze a space-time spectral method for the Stokes problem, which converges exponentially in both space and time. This numerical scheme imposes spectral collocation in time and P N − P N − 2 spectral Galerkin scheme in space by using a recombined Legendre polynomial basis, resulting in a global spectral operator that is a saddle point matrix. The main objectives of the research are estimating the condition number of the global spectral operators and proving the spectral convergence of this scheme in space and time. The analysis is not quite complete because two of the estimates are based on numerical evidence. However, throughout the project, some intermediate results-such as the 2-norm of the pseudospectral derivative matrix for Chebyshev-Gauss-Lobatto nodes as well as the condition number of the mass matrix and discrete Laplacian for a recombined Legendre basis-were proved to obtain the aforementioned findings. Numerical experiments of this scheme verify the theoretical results. Also, the numerical result of applying this scheme to the Navier-Stokes equations is presented. [ABSTRACT FROM AUTHOR]

We consider four subsets of the complexified spacetime algebra, namely the real even part, the real odd part, the imaginary even part and the imaginary odd part. This naturally leads to the four connected components of the Lorentz group, supplemented each time by an additional symmetry. We then examine how these four parts impact the Dirac equation and show that four types of matter arise with positive and negative masses as well as positive and negative charges. [ABSTRACT FROM AUTHOR]

We propose a space-time scheme that combines an unfitted finite element method in space with a discontinuous Galerkin time discretisation for the accurate numerical approximation of parabolic problems with moving domains or interfaces. We make use of an aggregated finite element space to attain robustness with respect to the cut locations. The aggregation is performed slab-wise to have a tensor product structure of the space-time discrete space, which is required in the numerical analysis. As an alternative, we also propose a space-time ghost penalty stabilisation term to attain robustness. We analyse the proposed algorithm, providing stability, condition number bounds and anisotropic a priori error estimates. A set of numerical experiments confirm the theoretical results for a parabolic problem on a moving domain. The method is applied for a mass transfer problem with changing topology. [ABSTRACT FROM AUTHOR]

Dynamic optimization constrained by partial differential equations (PDE) involves the state distribution on space, and can generate improved operational policies compared to ODE-constrained dynamic optimization. With the help of space–time orthogonal collocation on finite elements (ST-OCFE) which can guarantee relatively high accuracy in both space and time, PDE models are transformed into a set of algebraic equations. For solving PDE-constrained optimization problems, three direct approaches, namely ST-OCFE based single shooting, ST-OCFE based multiple shooting, and ST-OCFE based simultaneous collocation are proposed. The similarities and differences among these approaches are analyzed, where the discretized nonlinear programming problems to be solved in each algorithm are described. Furthermore, the first-order and second-order sensitivity computation for ST-OCFE based shooting approaches is introduced with algorithmic differentiation to efficiently evaluate the exact Hessian of the Lagrangian. Three cases including different dynamics and constraints are investigated. The optimal solution given by these ST-OCFE based direct approaches is consistent, demonstrating the effectiveness of these algorithms. • OCFE is used to discretize both space and time domain. • Single shooting, multiple shooting, and simultaneous collocation based on ST-OCFE. • Second-order sensitivity computation with algorithmic differentiation. • Comparison of these algorithms for PDE-constrained dynamic optimization. [ABSTRACT FROM AUTHOR]

We consider a space-time adaptive C0 Interior Penalty Discontinuous Galerkin (C0IPDG) approximation of the dynamic quasi-static von Kármán equations with homogeneous Dirichlet boundary conditions and an equilibrated a posteriori error estimator. The discretization in time is taken care of by the backward Euler scheme with respect of a partitioning of the time interval, whereas the C0IPDG method can be derived from a six-field formulation of the finite element discretized von Kármán equations. For each time step, the equilibrated a posteriori error estimator provides an upper bound for the discretization error in the broken W 2 , 2 norm in terms of the associated primal and dual energy functionals. It requires the construction of equilibrated fluxes and equilibrated moment tensors which can be computed on local patches around interior nodal points of the triangulations. The relationship with a residual-type a posteriori error estimator is studied as well. The fully discretized quasi-static von Kármán equations are solved by a predictor-corrector continuation strategy featuring constant continuation as a predictor and Newton's method as a corrector which allows an adaptive choice of the time steps. Numerical results illustrate the performance of the suggested approach. [ABSTRACT FROM AUTHOR]

Generalized Ricci recurrent spacetimes (GR) n are investigated in Gray's seven subspaces. It is proved that a (GR) n spacetime in all subspaces but one is an Einstein spacetime. The subspace ℐ cannot contain a (GR) n spacetime. Further, the subspaces ℐ ⊕ A and ℐ ⊕ B reduce to A and B , respectively. Next, we prove that a (GR) n spacetime is Ricci semi-symmetric if and only if either the spacetime is Einstein or the vector field Al is closed. Further, it is shown that the Ricci tensor of (GR) n is Riemann compatible if Al is closed. Finally, sufficient conditions are given on a (GR) n warped product manifold to guarantee that the factor manifolds are Einstein. Moreover, it is shown that a generalized Ricci recurrent GRW spacetime is an Einstein spacetime. [ABSTRACT FROM AUTHOR]

In this study, we analyze almost pseudo-Ricci symmetric spacetimes endowed with Gray's decomposition, as well as generalized Robertson—Walker spacetimes. For almost pseudo-Ricci symmetric spacetimes, we determine the form of the Ricci tensor in all the O (n)-invariant subspaces provided by Gray's decomposition of the gradient of the Ricci tensor. In three cases we obtain that the Ricci tensor is in the form of perfect fluid and in one case the spacetime becomes a generalized Robertson—Walker spacetime. In other cases we obtain some algebraic results. Finally, it is shown that an almost pseudo-Ricci symmetric generalized Robertson—Walker spacetime is a perfect fluid spacetime. [ABSTRACT FROM AUTHOR]

In this paper we are concerned with Trefftz discretizations of the time-dependent linear wave equation in anisotropic media in arbitrary space dimensional domains Ω ⊂ R d (d ∈ N). We propose two variants of the Trefftz DG method, define novel plane wave basis functions based on rigorous choices of scaling transformations and coordinate transformations, and prove that the corresponding approximate solutions possess optimal-order error estimates with respect to the meshwidth h and the condition number of the coefficient matrices, respectively. Besides, we propose the global Trefftz DG method combined with local DG methods to solve the time-dependent linear nonhomogeneous wave equation in anisotropic media. In particular, the error analysis holds for the (nonhomogeneous) Dirichlet, Neumann, and mixed boundary conditions from the original PDEs. Furthermore, a strategy to discretize the model in heterogeneous media is proposed. The numerical results verify the validity of the theoretical results, and show that the resulting approximate solutions possess high accuracy. [ABSTRACT FROM AUTHOR]

In this paper, we consider the Cauchy problem for the relativistic Boltzmann equation with near vacuum initial data where the distribution function depends on time, position and momenta. The collision kernel considered here corresponds to short range interactions and the background space-time is fixed and is of Bianchi type I. The existence of a unique global (in time) mild solution is obtained in a suitable weighted space. [ABSTRACT FROM AUTHOR]

Purpose: The present study investigates the spatiotemporal variations in suicide mortality and tests associations between several covariates and suicides for the years 20002019 in the contiguous USA. The epidemiological disease surveillance software was used to identify spatiotemporal variations in suicide mortality rates and to test for significant spatial and space-time clusters with elevated relative suicide risk.Methods: The analysis was done with age-adjusted suicide mortality counts data from the Centers for Disease Control (CDC) with International Classification of Diseases (ICD)-10 codes. Specifically, data with codes ICD-10 codes X60-X84.9 and Y87.0, plus ICD-10 113 codes from the CDC, was used. Fourteen significant spatial clusters and five significant space-time clusters of suicide in the contiguous USA were found, including nine significant bivariate spatial clusters of suicide deaths and opioid deaths.Results: Based on these data, there exist significant and non-random suicide mortality clusters after adjusting for multiple covariates or risk factors. The covariates studied provide evidence to develop a better understanding of possible associations in geographical areas where the suicide mortality rates are higher than expected. In addition, there is a significant association between several of the studied risk factors and suicide mortality. While most suicide clusters are also opioid clusters, there exist some clusters with high opioid deaths that are not suicide clusters.Conclusions: These results have the potential to provide a scientific framework that is based on surveillance, allowing health agencies to intervene and reduce elevated rates of suicides in selected counties in the U.S. The study is limited due to the resolution of the data at the county level, and some covariate data was unavailable for the entire period of the study. [ABSTRACT FROM AUTHOR]

The present paper revisits conventionalism about the geometry of classical and relativistic spacetimes. By means of critically examining a recent evaluation of conventionalism, we clarify key themes of, and rectify common misunderstandings about, conventionalism. Reichenbach's variant is demarcated from conventionalism simpliciter, associated primarily with Poincaré. We carefully outline the latter's core tenets—as a selective anti-realist response to a particular form of theory underdetermination. A subsequent double defence of geometric conventionalism is proffered: one line of defence employs (and thereby, to some extent, rehabilitates) a plausible reading of Reichenbach's idea of universal forces; another consists in independent support for conventionalism, unrelated to Reichenbach. Conventionalism, we maintain, remains a live option in contemporary philosophy of spacetime physics, worthy of serious consideration. [ABSTRACT FROM AUTHOR]

Spacetime singularities are often held to be pathologies which need to be resolved, and researchers working on the foundations of physics often pin their hopes on the elusive quantum theory of gravity to offer a way to resolve singularities. What is less agreed upon is what such a resolution would amount to: what criteria would a theory of quantum gravity have to fulfill to resolve spacetime singularities? In this paper, I critically analyze one criterion proposed within canonical quantum cosmology for the avoidance of the big bang singularity, to draw philosophical lessons about how to interpret such criteria. The criterion, when applied to symmetry-reduced cosmological models, claims to avoid the big bang by making the wavefunction of the universe vanish 'at' the singularity. I ask whether it works as intended, and even if it does, whether avoiding the singularity is the same as resolving the singularity. [ABSTRACT FROM AUTHOR]

• A novel meshless approach for phase-field modelling of dendritic growth. • Reduction of discretisation-induced anisotropy by the scattered nodes. • Increase in computational efficiency by a space-time adaptive approach. A novel adaptive numerical approach is developed for an accurate and computationally efficient phase-field modelling of dendritic solidification. The adaptivity is based on the dynamic quadtree domain decomposition. A quadtree decomposes the computational domain into rectangular sub-domains of different sizes. Each sub-domain is extended to ensure overlap communication between neighbouring sub-domains. In each sub-domain, uniform distribution of computational nodes is generated. The product between the node density and the sub-domain area is fixed to ensure the h-adaptivity. The adaptive approach provides the highest density of computational nodes at the solid-liquid interface and the lowest density in the bulk of the phases. The meshless radial basis function generated finite difference (RBF-FD) method is applied for the spatial discretisation of the partial differential equations which arise from the phase-field model. The RBF-FD method is especially appealing since it allows straightforward spatial discretisation of partial differential equations on scattered node distributions. The use of scattered node distribution reduces the discretisation-induced anisotropy in the phase-field modelling of dendritic growth. The forward Euler scheme is used for temporal discretisation. The adaptive time-stepping is employed to speed up the calculations further. The performance of the novel numerical approach is tested for dendritic solidification of supercooled pure melts and supersaturated dilute binary alloys at arbitrary preferential growth directions. The impact of the numerical parameters on the accuracy and computational efficiency is thoroughly analysed. It is shown that the RBF-FD method, defined on scattered node distribution, together with the space-time adaptive approach, represents an accurate and efficient technique for solving the phase-field models of dendritic solidification. [ABSTRACT FROM AUTHOR]

An iterative kernel-based method is proposed for solving the nonlinear generalized Benjamin-Bona-Mahony-Burgers equation in regular and irregular domains. The method is based on the positive definite kernels pseudospectral method. We have used an iterative linearization scheme to overcome the nonlinearity of the problem. The convergence of the linearization scheme is proved. The space-time kernels are used for the full discretization of the problems in the temporal and spatial domains. Here, we construct the multidimensional kernels using the product of one-dimensional kernels. Numerical results and comparisons are presented for the several two and three-dimensional problems with the various domains. The obtained results confirm the efficiency and accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

This article analyzed the location and concentration of forest bioelectricity in Brazil, from 2000 to 2019, available from the National Electric Energy Agency (ANEEL) and used the following indicators: Location Quotient (QL), Concentration Index [CR (k)], Herfindahl-Hirschman Index (HHI), Hoover Index (H) and Coefficient of Gini (G). The main results showed that the supply of electricity from Brazilian forest biomass increased from 562.90 MW and 11 thermoelectric plants in 2000 to 3532.61 MW and 115 thermoelectric plants in 2019, providing an average growth of 10.15% yy of the granted installed power and 13.20% p.a. of thermoelectric power plants. The QL inferred a high concentration of energy supply from black liquor (Rio Grande do Sul, Paraná, Espírito Santo, Bahia, Maranhão and Mato Grosso do Sul) and forest residues in several states, mainly in the North region. At the state level, the CR (4), CR (8) and HHI indexes indicated a deconcentration trend. The identification of the location and concentration pattern that the greatest offer was associated with industrial pulp and paper complexes. These results can indicate to investors the impact of electric power generation in the sector and the most relevant location for the installation of new thermoelectric plants. [ABSTRACT FROM AUTHOR]

• Dust effects of space/time factors on trough solar system are studied in alpine areas. • Dust distribution characteristics are described by multiple variables. • Experimental platform was built to test optical and thermal performance concurrently. • The relative reflectivity fell by 20.58% for dust density 0–2.46 g/m2. • Collecting/exergy efficiency fell by 48.30%/55.08% for dust density 0–2.46 g/m2. Based on the dust accumulation and distribution characteristics of concentrator surfaces in alpine regions, a comparative experimental platform for measuring the energy flux density of the focal plane and thermal performance was developed in this study. By combining theory and experimentation, the influence of time (dust deposition density) and space (concentrator tilt angle) on the dust distribution characteristics and photothermal performance of a trough solar system was studied. The optical loss caused by concentrator dust was evaluated based on the intercept factor, while the thermodynamic loss caused by dust was evaluated based on the collecting efficiency and exergy efficiency. The results demonstrate that concentrator dust at a tilt angle of 60° will lead to a maximum center shift of 1.66 mm of the focal plane. Importantly, the inconsistency between thermal performance and dust deposition density indicates that the dust distribution characteristics caused by tilt angle have a significant influence on the thermal performance of the system. Comparatively, an increase in dust deposition density from 0 to 2.46 g/m2 leads to a 20.58% relative reflectivity loss, together with 48.30% and 55.08% reductions in the collecting efficiency and exergy efficiency, respectively. This study revealed the influence of space–time factors on dust distribution characteristics and photothermal performance, which can provide design ideas regarding dust removal for the application of trough solar systems in alpine areas. [ABSTRACT FROM AUTHOR]

In this paper, an efficient space-time backward substitution method (STBSM) is presented for solving nonlinear transient heat conduction problems in 2D and 3D functionally graded materials (FGMs). To improve the computation efficiency of the traditional backward substitution method (BSM) for transient problems, the space-time radial basis function (STRBF) and space-time trigonometric basis function (STTBF) are introduced for interpolation in the proposed method. The time dimension is regarded as a pseudo-space dimension to generate the space-time Euler metric r T in STRBF, which can be applied to transform the d -dimensional transient governing equation into (d + 1) -dimensional steady-state governing equation. Benefiting from merits of the traditional BSM, an accurate numerical solution is available with only a few of computational points. Several examples are solved to verify the accuracy and efficiency of the proposed method and its merits and flaws are discussed in the end. • A space-time method is attempted for 2D and 3D heat conduction problems in FGMs. • Space-time domain and space-time radial basis function are introduced into backward substitution method. • By introducing pseudo-space-time dimension to transform the origin transient problem into steady-state problem. • The proposed method has excellent computational efficiency. [ABSTRACT FROM AUTHOR]

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]

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]