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This study introduces a novel approach to achieving nonreciprocal transmission by implementing time modulation to the bianisotropic metasurface. For the first time, we present the analytical solution of the excitation of anti-symmetric surface waves on penetrable metasurfaces depending on the excitation direction. Exploiting this finding, we numerically demonstrate asymmetric control of the transmission coefficient under a fast-time scale by employing solely time modulation. This approach lowers the complexity of the modulation scheme and implementation encountered in the space-time modulation technique. We develop and simulate a 3D unit cell model in the microwave domain, which forms a surface cavity that incorporates time-varying capacitors. The impedance transfer matrix method and harmonic balance numerical solutions are applied to the retrieved equivalent circuit for the numerical simulations. The results reveal optimized phase-coherent and incoherent nonreciprocal transmission at the significant isolation level (≥ 40 dB) for forward and backward transmissions. We discuss the consistency and discrepancies between numerical methods and consider the impact of the losses and nonlinearity on the metastructure performance. [ABSTRACT FROM AUTHOR]

Perception not only registers property instances, but also connects with and attributes properties to individual entities—so‐called sensory individuals, or SIs. But what are SIs? The most‐discussed answers are: (i) SIs are ordinary material objects—cohesive, temporally persistent objects extended and bounded in space, and (ii) SIs are locations or regions in spacetime. I will argue for the object view of SIs on the grounds that its rival, the locational view, faces obstacles concerning the relationship between SIs and spacetime: it makes a mystery of perception's representation of SIs as occupying locations in and moving in ordinary spacetime.

We point out that dark matter and dark energy arise naturally in a recently proposed model of combinatorial quantum gravity. Dark energy is due to the ground-state curvature at finite coupling, dark matter arises from allotropy in the discrete structure of space-time. The stable structure of the space-time 'crystal' represents the curved background, the coexisting metastable allotropes of higher curvature and energy are natural candidates for dark matter. We thus suggest that dark energy and dark matter are two manifestation of quantum gravity. [ABSTRACT FROM AUTHOR]

Geospatial expertise draws on and recognizes a vast array of seemingly unrelated interconnections allowing the geographer to find solutions to otherwise incomprehensible problems. Geospatial thinking involves both time and space, acknowledges cause-and-effect relationships of geographic phenomena at multiple scales, and recognizes the impact of spatial and temporal scale on processes. The complexity of geographic thinking necessitates an equally complex set of learning experiences that collectively are characterized by the professional geographer. Due to the inherent complexity of geospatial expertise, its nuanced relationship to spatial thinking, and a lack of research on how individuals attain geospatial expertise, we organized an interdisciplinary group of experts to present their perspectives on developing geospatial expertise in this special edition. In this introduction, we review geospatial expertise and distinguish it from spatial thinking, review research on developing geospatial expertise, and end with recommendations for future research. Through these reviews and recommendations, this introduction provides background context for the articles in this special edition and elucidates their connections. Given the complexity of geospatial expertise, it is only through connecting researchers and educators across multiple disciplines that the nature of one of the most integrative professional disciplines – that of the geographer – can be fully understood. [ABSTRACT FROM AUTHOR]

The article "Minkowski Diagrams Aid Understanding of Special Relativity" discusses the use of Minkowski space-time to visually represent special relativity, providing students with an alternative perspective to equations and thought experiments. It explains how Minkowski's work connects space and time, allowing for the visualization of events in both dimensions. The article also delves into the twin paradox and length contraction, showcasing how Minkowski spacetime can help resolve complex physics problems. Overall, the paper aims to encourage educators to incorporate visual approaches like Minkowski diagrams when teaching special relativity. [Extracted from the article]

In this paper we present some relatively unexpected mathematical questions emerging from the idea to approximate dissipative mechanical systems using Lagrangian formalism. We also explain potential consequences of these constructions for definition of representative space-time volume elements in modelling of metamaterials. [ABSTRACT FROM AUTHOR]

Given an extendible spacetime one may ask how much, if any, uniqueness can in general be expected of the extension. Locally, this question was considered and comprehensively answered in a recent paper of Sbierski [22], where he obtains local uniqueness results for anchored spacetime extensions of similar character to earlier work for conformal boundaries by Chruściel [2]. Globally, it is known that non-uniqueness can arise from timelike geodesics behaving pathologically in the sense that there exist points along two distinct timelike geodesics which become arbitrarily close to each other interspersed with points which do not approach each other. We show that this is in some sense the only obstruction to uniqueness of maximal future boundaries: Working with extensions that are manifolds with boundary we prove that, under suitable assumptions on the regularity of the considered extensions and excluding the existence of such "intertwined timelike geodesics", extendible spacetimes admit a unique maximal future boundary extension. This is analogous to results of Chruściel for the conformal boundary. [ABSTRACT FROM AUTHOR]

Obtaining reliable and timely estimates of migration flows is critical for advancing the migration theory and guiding policy decisions, but it remains a challenge. Digital data provide granular information on time and space, but do not draw from representative samples of the population, leading to biased estimates. We propose a method for combining digital data and official statistics by using the official statistics to model the spatial and temporal dependence structure of the biases of digital data. We use simulations to demonstrate the validity of the model, then empirically illustrate our approach by combining geo-located Twitter data with data from the American Community Survey (ACS) to estimate state-level out-migration probabilities in the United States. We show that our model, which combines unbiased and biased data, produces predictions that are more accurate than predictions based solely on unbiased data. Our approach demonstrates how digital data can be used to complement, rather than replace, official statistics. [ABSTRACT FROM AUTHOR]

Using non-commutative spacetime quaternion algebra, we represent the generalization of one-dimensional and three-dimensional telegraph equations, which are widely applied to consider the propagation of an electromagnetic signal in communication lines, as well as to describe particle diffusion and heat transfer. It is shown that the system of telegraph equations can be represented in compact form as a single quaternion equation taking into account the spacetime properties of physical quantities. The distinctive features of the one-dimensional and three-dimensional telegraph equations are discussed. [ABSTRACT FROM AUTHOR]

The Barrow's Holographic Dark Energy (BHDE) Model is proposed in an axially symmetric anisotropic spacetime which is employing Hubble horizon as an infrared cutoff (IR cutoff). The transition of the universe from a matter dominated era to a dark energy dominated era is investigated in this model. Furthermore, the Equation of State (EoS) parameter explains how the universe evolves with non-extensive term or Barrow parameter Δ for both phase (i) phantom era ( ω B ≤ − 1) and (ii) quintessence era ( ω B ≥ − 1). In order to reconcile the dark energy, the reconstruction of scalar field potential is considered. Some of the physical properties of the model are also described. [ABSTRACT FROM AUTHOR]

We construct a rotationally invariant Ricci flow through surgery starting at any closed rotationally invariant Riemannian manifold. We demonstrate that a sequence of such Ricci flows with surgery converges to a Ricci flow spacetime in the sense of Kleiner and Lott [Acta Math. 219 (2017), pp. 65–134]. Results of Bamler-Kleiner [Acta Math. 228 (2022), pp. 1–215] and Haslhofer [Proc. Amer. Math. Soc. 150 (2022), pp. 5433–5437] then guarantee the uniqueness and stability of these spacetimes given initial data. We simplify aspects of this proof in our setting, and show that for rotationally invariant Ricci flows, the closeness of spacetimes can be measured by equivariant comparison maps. Finally we show that the blowup rate of the curvature near a singular time for these Ricci flows is bounded by the inverse of remaining time squared. [ABSTRACT FROM AUTHOR]

We prove that a globally hyperbolic smooth spacetime endowed with a C1-Lorentzian metric whose Ricci tensor is bounded from below in all timelike directions, in a distributional sense, obeys the timelike measure-contraction property. This result includes a class of spacetimes with borderline regularity for which local existence results for the vacuum Einstein equation are known in the setting of spaces with timelike Ricci bounds in a synthetic sense. In particular, these spacetimes satisfy timelike Brunn-Minkowski, Bonnet-Myers, and Bishop-Gromov inequalities in sharp form, without any timelike nonbranching assumption. If the metric is even C1,1, in fact the stronger timelike curvature-dimension condition holds. In this regularity, we also obtain uniqueness of chronological optimal couplings and chronological geodesics. [ABSTRACT FROM AUTHOR]

If entanglement builds spacetime, then conversely, disentanglement ought to destroy spacetime. From the quantum null energy condition and quantum focusing conjecture, we obtain disentanglement criteria which necessitate infinite energies and strong spacetime singularities. We apply our results to the strong cosmic censorship proposal, where singularities at the Cauchy horizons in black holes are desirable. Using our disentanglement criteria and without resorting to any detailed calculations, we provide an exceedingly general and physically transparent discussion of strong cosmic censorship in semiclassical black holes. We argue that strong cosmic censorship is enforced in asymptotically flat and de Sitter black holes by disentanglement and describe how similar disentanglement might be avoided in some anti-de Sitter cases. [ABSTRACT FROM AUTHOR]

The objective of this study is to examine the possible existence of traversable wormhole geometries within the context of f(R,Lm,T) gravity. To meet this objective, we employ the Karmarkar condition to construct the shape function that aids in identifying the wormhole configurations. This developed function is found to satisfy the essential conditions and provides a link between two asymptotically flat spacetime regions. We then assume the Morris–Thorne line element that expresses the wormhole configuration and formulate the anisotropic gravitational equations for a particular minimal matter-spacetime coupled model of the modified theory. Afterward, we develop three solutions and determine their viability by analyzing whether they violate the null energy conditions. Different stability methods are applied to the resulting geometries to explore the acceptance of the considered modified model. We conclude that the developed wormhole structures potentially fulfill the required criteria and thus exist in this modified gravity under all choices of the matter Lagrangian density. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the scenarios in which a holonomic versus a non-holonomic frame description of gravity theories are equivalent. It turns out that classically, the equivalence holds in a way that is independent of the particular dynamics and/or spacetime dimension. This includes general metric-affine dynamics. A global bundle-theoretical investigation is carried out, uncovering the equivalence principle as the culprit. The equivalence holds as long as the equivalence principle holds. This is not something to be expected when non-invertible configurations of the vielbein field are taken into account. In such cases, the gauge-theoretical description of gravity “unsolders” from spacetime, and one has to decide if gravity is spacetime geometry or an internal gauge theory. [ABSTRACT FROM AUTHOR]

In this paper, we deal with spacetimes allowing a semi-symmetric connection whose metric tensor is recurrent. We investigate the impact of this connection on spacetimes and establish a nontrivial example. We physically explain the properties of spacetime that we obtained. Under a certain condition, we demostrate that a spacetime admitting such a connection becomes the GRW spacetime as well as the anti-de Sitter and represents the dark matter era. Finally, we scrutinize in case such a spacetime admits a Ricci soliton and generalized Ricci soliton. [ABSTRACT FROM AUTHOR]

It is more than a century-old concept that the Minkowski spacetime is flat. From the pure geometric point of view, we explicitly address the issue of whether a noncommutative Minkowski spacetime is flat or not. In the framework of the twisted-diffeomorphism approach to noncommutative gravity with canonical type noncommutative (NC) coordinate structure, one important result that we get is that the NC Minkowski spacetime parametrized either with spherical polar coordinates or with parabolic coordinates has nontrivial NC corrections to Riemann curvature tensor, Ricci tensor and curvature scalars. Another crucial result is that the curvature scalars have singular behavior at certain points, and these singularities are not coordinate singularities. The nature of these singularities clearly points towards the idea of high-energetic probes turning into black holes. The absence of any such noncommutative corrections, and thus any such singularities, in the cases of Cartesian coordinates and cylindrical coordinates leads to the conclusion that high-energetic probes do not turn into black holes when the canonical NC structure is considered for these coordinates. [ABSTRACT FROM AUTHOR]

We study the formation of singularities of smooth solutions to the relativistic Euler equations of Chaplygin gases in Schwarzschild spacetime. The system is in the spherically symmetric form, and its coefficients and nonhomogeneous terms contain a parameter reflecting the mass of the black hole, which makes it highly nonlinear and complicated. To overcome the influence of the mass parameter of black hole, we introduce a pair of suitable auxiliary variables related to it and derive their characteristic decompositions to establish the estimates of the smooth solution. We show that, for a kind of initial data, the smooth solution develops singularity in finite time and the mass‐energy density itself approaches infinity at the blowup point. [ABSTRACT FROM AUTHOR]

In this work, we mainly focus on testing the spacetime properties around black holes surrounded by a dark fluid, which are potential candidates for dark energy described by the Chaplygin-like equation of state through its shadow. To do this, we first study the black hole's horizon structure and shadow for the non-rotating case. Then, we obtain a rotating black hole solution in the presence of a dark fluid using the generalized Newman–Janis algorithm and study the effects of the black hole spin and the fluid parameters on the black hole horizons. Also, we obtained the shadow cast of the rotating black hole using celestial coordinates and showed that the presence of the dark fluid causes an increase in shadow size. Moreover, we use the shadow size of supermassive black holes Sagittarius A* and M87* from Event Horizon Telescope observations to obtain constraints on the spin, black hole charge, and dark fluid parameters. Lastly, we investigate the energy emission rate of a charged black hole surrounded by a Chaplygin-like dark fluid, comparing it to both rotating and non-rotating cases. [ABSTRACT FROM AUTHOR]

Birth registration is an important channel that allows children to be documented, providing them with legal identity and nationality early in life and protecting them against violence, abuse and exploitation. However, this privilege has been denied to millions of children, particularly in developing countries. Registration is limited in Nigeria with about three in every five births unregistered. Using data from three waves of the Nigeria Demographic and Health Survey, we adopt a geostatistical model to assess the space-time variations in registration coverage across Nigeria and compute the exceedance maps at different probabilities. The findings indicate a North-South divide in coverage but with improved coverage over time across the country. The probability of attaining about 60% coverage is low in the northern part of the country. The generated maps provide guiding tools to the Nigerian government to set priorities in order to scale up birth registration coverage in the country. [ABSTRACT FROM AUTHOR]

In this paper, we perform a comprehensive analysis of conformal symmetries in the generalized Vaidya spacetime and establish several new results. First, a proper conformal Killing vector is shown to exist in the radial direction and interestingly the generalized Vaidya spacetimes with this symmetry are shown to be the subclass of those, which are embeddable in five-dimensional Euclidean space. The general form of the mass function that enables the proper and planar conformal symmetry in the v–r plane is also determined. This treatment also includes earlier results. We also consider the gravitational collapse of these spacetimes with proper planar conformal symmetry in the context of cosmic censorship conjecture. We obtain an interesting and novel result that censorship is always obeyed for these spacetimes, and no locally naked central singularity forms as the end state of the continual collapse. [ABSTRACT FROM AUTHOR]

The conformal scalar propagator as an explicit function of the Schwarzschild black-hole space-time has been established in the preceding three projects. The present project examines the precise relation which that propagator has to the amplitude the Schwarzschild black hole emit a scalar particle in a particular mode of positive energy. It is thereby established that the effect of infinite time-dilation on the event horizon results in both, the thermal radiation in the background of a static exterior space-time geometry and the detraction from thermality if energy-conservation is properly imposed as a constraint on scalar propagation. The derivation of the latter signifies an equivalent approach to the result of Parikh and Wilczek from the semi-classical perspective of the distant observer. From that perspective for that matter, Hawking radiation emerges in both contexts as the exclusive consequence of infinite time-dilation on the event horizon. These results are consistent with Hawking radiation as the exclusive consequence of the causal structure of the Schwarzschild black-hole space-time both, in a static exterior geometry and in such dynamical exterior geometry as energy-conservation signifies. The extension of the thermal case to other spin-fields and black-hole geometries is discussed. [ABSTRACT FROM AUTHOR]

In this paper, we show how the path integral for gravity and matter on a piecewise flat spacetime can be used to define the physical quantum gravity states and the related transition amplitudes. The physical states are given by the path integrals for open manifolds from a certain topological class, while the corresponding transition amplitudes are obtained by gluing two such open manifolds into a closed one and calculating the corresponding path integral. We also solve the problem of how to associate a quantum gravity state to an effective action. This is done by using the path integral for a closed manifold from the transition-amplitude topological class so that the state which corresponds to the effective action can be chosen to be the Hartle–Hawking or the Vilenkin wavefunction for the vacuum manifold component of the transition-amplitude manifold. [ABSTRACT FROM AUTHOR]

There is an apparent tension in Shepherd's accounts of space and time. Firstly, Shepherd explicitly claims that we know that the space and time of the unperceived world exist because they cause our phenomenal experience of them. Secondly, Shepherd emphasizes that empty space and time do not have the power to effect any change in the world. My proposal is that for Shepherd time has exactly one causal power: to provide for the continued existence of self-same or changing objects. Because Shepherd takes causation to be a relation whereby two objects combine to form a third, their effect, whenever we perceive a continually existing object, since time is a proper part of such objects, our perception of time is caused by time itself. Likewise, space's causal power is to provide for the possibility of the motion or rest of objects, and so when we perceive objects with space as a proper part, we come into causal contact with space. [ABSTRACT FROM AUTHOR]

In this paper, we develop a systematic deep learning approach to solve two-dimensional stationary quantum droplets (QDs) and investigate their wave propagation in the two-dimensional amended Gross-Pitaevskii equation with Lee-Huang-Yang correction and two kinds of potentials. Firstly, we use the initial-value iterative neural network algorithm for two-dimensional stationary QDs of stationary equations. Then, the learned stationary QDs are used as the initial value conditions for physics-informed neural networks to explore their evolutions in the space-time region. Especially, we consider two types of potentials, one is the twodimensional quadruple-well Gaussian potential and the other is the PT -symmetric harmonic-oscillator (HO)-Gaussian potential, which lead to spontaneous symmetry breaking and the generation of multicomponent QDs. The used deep learning method can also be applied to study wave propagations of other nonlinear physical models. [ABSTRACT FROM AUTHOR]

Emerging tensor network techniques for solutions of partial differential equations (PDEs), known for their ability to break the curse of dimensionality, deliver new mathematical methods for ultra-fast numerical solutions of high-dimensional problems. Here, we introduce a Tensor Train (TT) Chebyshev spectral collocation method, in both space and time, for the solution of the time-dependent convection-diffusion-reaction (CDR) equation with inhomogeneous boundary conditions, in Cartesian geometry. Previous methods for numerical solution of time-dependent PDEs often used finite difference for time, and a spectral scheme for the spatial dimensions, which led to a slow linear convergence. Spectral collocation space-time methods show exponential convergence; however, for realistic problems they need to solve large four-dimensional systems. We overcome this difficulty by using a TT approach, as its complexity only grows linearly with the number of dimensions. We show that our TT space-time Chebyshev spectral collocation method converges exponentially, when the solution of the CDR is smooth, and demonstrate that it leads to a very high compression of linear operators from terabytes to kilobytes in TT-format, and a speedup of tens of thousands of times when compared to a full-grid space-time spectral method. These advantages allow us to obtain the solutions at much higher resolutions. [ABSTRACT FROM AUTHOR]

We present and analyze computationally Geometric MultiGrid (GMG) preconditioning techniques for Generalized Minimal RESidual (GMRES) iterations to space-time finite element methods (STFEMs) for a coupled hyperbolic–parabolic system modeling, for instance, flow in deformable porous media. By using a discontinuous temporal test basis, a time marching scheme is obtained. Higher order approximations that offer the potential to inherit most of the rich structure of solutions to the continuous problem on computationally feasible grids increase the block partitioning dimension of the algebraic systems, comprised of generalized saddle point blocks. Our V-cycle GMG preconditioner uses a local Vanka-type smoother. Its action is defined in an exact mathematical way. Due to nonlocal coupling mechanisms of 348 unknowns, the smoother is applied on patches of elements. This ensures damping of higher order error frequencies. By numerical experiments of increasing complexity, the efficiency of the solver for STFEMs of different polynomial order is illustrated and confirmed. Its parallel scalability is analyzed. Beyond this study of classical performance engineering, the solver's energy efficiency is investigated as an additional and emerging dimension in the design and tuning of algorithms on the hardware. [ABSTRACT FROM AUTHOR]

AbstractMining traffic congestion dynamics presents difficulties in data structure and spatiotemporal analysis. Existing studies mainly provide insights from a supply perspective, with a restricted examination of why congestion occurs and how travel demands affect congestion. This study introduces an innovative framework to mine congestion dynamics from the perspective of human mobility. In human mobility modeling, we refine the conventional origin-destination representation of activity flow by introducing "path flow" (PF) which considers space-time paths and movement patterns. In congestion scenarios, congestion-related path flow (CPF) and congested path sub-flow (CPSF) are extended to track individuals’ congestion exposure and explore the correlations between congestion and human mobility. To finely classify congestion-related travel demands, a Bayesian inference approach, incorporating destination and spatiotemporal heterogeneities, is developed to deduce trip purposes. The experiments conducted in Wuhan demonstrate the availability and importance of PF in spatiotemporal dynamics analysis of human mobility. Interestingly, we find that 1) the job-housing relationship is imbalanced, with massive residents opting for cross-district living and working; 2) individuals tend to visit tertiary hospitals on weekends and secondary medical facilities with less congestion on weekdays. Notably, path flow can promote the fine-grained modeling of human mobility and provide theoretical support for many urban issues. [ABSTRACT FROM AUTHOR]

An approach to renormalization of scalar fields on the Doplicher–Fredenhagen–Roberts (DFR) quantum spacetime is presented. The effective nonlocal theory obtained through the use of states of optimal localization for the quantum spacetime is reformulated in the language of (perturbative) Algebraic Quantum Field Theory. The structure of the singularities associated to the nonlocal kernel that codifies the effects of non-commutativity is analyzed using the tools of microlocal analysis. [ABSTRACT FROM AUTHOR]

There are two metaphysical pictures of spacetime: The evolutionary picture and the all-at-once picture. According to the evolutionary picture, spacetime is nothing but the evolution of space over time. In contrast, the all-at-once picture considers spacetime as ‘a global, four-dimensional boundary value problem’ that can be solved only in an all-at-once manner, i.e. as a whole which is fundamentally four-dimensional and non-decomposable into spatial and temporal parts. The two most-known formulations of general theory of relativity, i.e. the Hamiltonian (or the canonical) and the Lagrangian (or the standard) formulations, enjoy the evolutionary and all-at-once pictures of spacetime respectively. Here, we have argued that (1) the all-at-once picture is more aligned with the philosophy of relativity theory, i.e. uniting space and time into spacetime, (2) the evolutionary picture is not as general as the all-at-once, since only in special cases, such as globally hyperbolic spacetimes, is it possible to deal with spacetime as the evolution of a spatial slice over time, and (3) the all-at-once picture paves the way to better understanding four-dimensional physical entities, like event horizons, which cannot be explained within an evolutionary picture without raising a paradox. Therefore, the evolutionary picture is neither the fundamentally-true nor the naturally-chosen picture of spacetime. Rather, we choose the evolutionary picture for practical and computational reasons. While the all-at-once picture seems a more appropriate description of the quantum and cosmological reality, the evolutionary picture can be applied occasionally and locally, or quasi-locally, and is not the proper metaphysical picture of spacetime at the fundamental level of reality. [ABSTRACT FROM AUTHOR]

We study the sharp interface limit of the stochastic Cahn-Hilliard equation with cubic double-well potential and additive space-time white noise ε σ W, where ε>0 is an interfacial width parameter. We prove that, for a sufficiently large scaling constant σ>0, the stochastic Cahn-Hilliard equation converges to the deterministic Mullins-Sekerka/Hele-Shaw problem for ε→0. The convergence is shown in suitable fractional Sobolev norms as well as in the L p -norm for p∈(2,4] in spatial dimension d=2,3. This generalizes the existing result for the space-time white noise to dimension d=3 and improves the existing results for smooth noise, which were so far limited to p∈(2, d+2 2d+8) in spatial dimension d=2,3. As a byproduct of the analysis of the stochastic problem with space-time white noise, we identify minimal regularity requirements on the noise which allow convergence to the sharp interface limit in the H¹-norm and also provide improved convergence estimates for the sharp interface limit of the deterministic problem. [ABSTRACT FROM AUTHOR]

We study reflected diffusion on uniform domains where the underlying space admits a symmetric diffusion that satisfies sub-Gaussian heat kernel estimates. A celebrated theorem of Jones (Acta Math 147(1-2):71–88, 1981) states that uniform domains in Euclidean space are extension domains for Sobolev spaces. In this work, we obtain a similar extension property for metric spaces equipped with a Dirichlet form whose heat kernel satisfies a sub-Gaussian estimate. We introduce a scale-invariant version of this extension property and apply it to show that the reflected diffusion process on such a uniform domain inherits various properties from the ambient space, such as Harnack inequalities, cutoff energy inequality, and sub-Gaussian heat kernel bounds. In particular, our work extends Neumann heat kernel estimates of Gyrya and Saloff-Coste (Astérisque 336:145, 2011) beyond the Gaussian space-time scaling. Furthermore, our estimates on the extension operator imply that the energy measure of the boundary of a uniform domain is always zero. This property of the energy measure is a broad generalization of Hino's result (Probab Theory Relat Fields 156:739–793, 2013) that proves the vanishing of the energy measure on the outer square boundary of the standard Sierpiński carpet equipped with the self-similar Dirichlet form. [ABSTRACT FROM AUTHOR]

We consider the following stochastic heat equation ∂ t u (t , x) = 1 2 ∂ x 2 u (t , x) + b (u (t , x)) + σ (u (t , x)) W ˙ (t , x) , defined for (t , x) ∈ (0 , ∞) × R , where W ˙ denotes space-time white noise. The function σ is assumed to be positive, bounded, globally Lipschitz, and bounded uniformly away from the origin, and the function b is assumed to be positive, locally Lipschitz and nondecreasing. We prove that the Osgood condition ∫ 1 ∞ d y b (y) < ∞ implies that the solution almost surely blows up everywhere and instantaneously, In other words, the Osgood condition ensures that P { u (t , x) = ∞ for all t > 0 and x ∈ R } = 1. The main ingredients of the proof involve a hitting-time bound for a class of differential inequalities (Remark 3.3), and the study of the spatial growth of stochastic convolutions using techniques from the Malliavin calculus and the Poincaré inequalities that were developed in Chen et al. (Electron J Probab 26:1–37, 2021, J Funct Anal 282(2):109290, 2022). [ABSTRACT FROM AUTHOR]

In this paper, we present comparisons of the deflection angles of massless and massive particles in the Schwarzschild space-time. For the case of photons in a general static space-time, we construct a spatial 3D equation of motion for their path that leads to an implicit formula for the deflection angle. We then compare our results with well-known results of the literature in the Schwarzschild space-time. For the case of massive particles, we calculate the deflection angle only in the Schwarzschild space-time. The end result is that as the velocity of any massive particle diminishes, the deflection angle increases. To show the relevance of these comparisons, we constructed different black hole shadows for massive particles in order to be compared with a shadow made by photons. [ABSTRACT FROM AUTHOR]

The concept of wormholes is still hypothetical in physics but attractive among researchers. In this work, motivated by the important effect of f (R , T) gravity theory, we seek the existence of wormhole solutions. We consider the field equations that can be derived from two different choices of matter Lagrangian density and utilize them to find the possibility of having some wormhole geometry. This procedure is based on the specific choice of an equation-of-state that obeys a certain physical requirement on the matter stress-energy [S. Kar and D. Sahdev, Restricted class of traversable wormholes with traceless matter, Phys. Rev. D 52 (1995) 2030]. For this purpose, the functional form of the redshift function is taken into consideration, and the possible existence of wormhole solutions is proven. Finally, the work examines the energy conditions and shows that violations of null energy conditions hold throughout spacetime. [ABSTRACT FROM AUTHOR]

Exploring spatial-temporal interactions among group members is crucial for group activity recognition. However, most existing approaches cannot jointly consider it from multi-level cross-relations, which results in an incomplete representation. To address this issue, we propose a relational complementary module that comprehensively learns the interactions among members from both time-space and space-time perspectives. To suppress the information redundancy caused by this all-view interaction description, we introduce NH-Softmax to impose sparsity on the few relevant attention weights to generate robust and differentiated feature representations. In addition, to fully explore individual contextual interaction information, relaxed attention (RAT) is designed to enhance the feature information of each individual in a relaxed manner. It fleshes out individual representations by highlighting the most salient features and eases the computational burden. Our experiments on Volleyball dataset and Collective Activity dataset show significant improvements over previous state-of-the-art methods. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the discrete inf-sup condition and related error estimates for a modified Hilbert transformation as used in the space-time discretization of time-dependent partial differential equations. It turns out that the stability constant c S depends linearly on the finite element mesh size h. While the ratio c S / h decreases as 1 / T for T → ∞ , numerical results indicate a decay of c S / h ≃ ν − α for some α ∈ [ 1 4 , 1 3 ] in the polynomial degree ν of the finite element basis functions. However, in most cases, we can show optimal convergence. We present a series of numerical experiments which illustrate the theoretical findings. [ABSTRACT FROM AUTHOR]

Water flow is an important piece of information in hydrological assessments, aiding in understanding variations in river flow and predicting its trends. Traditional contact-based methods for measuring water flow are greatly affected by environmental conditions during emergencies, with difficulties in installation and low measurement efficiency. To address this issue, this study explores a method for calculating video-based flow measurements using a non-contact spatio-temporal imaging approach. The study selects the Pukou section of the Chuhe River in Nanjing City as the experimental site for water flow detection. The detection method in this paper uses video flow measurement to measure the velocity of water flow. The collected data is processed visually and displayed on the interface of terminal equipment, and the collected data can be transmitted to a specified address in the format of the hydrological protocol. Experimental results indicate that using drones equipped with video flow measurement devices can rapidly and effectively complete water flow detection. The data can be displayed in a visual format on terminal equipment, facilitating viewing by relevant personnel. This form of detection is fast, safe, and environmentally adaptive, with the potential for practical applications. Further research into this detection method will promote the smart and integrated development of hydrological assessments. [ABSTRACT FROM AUTHOR]

The article presents a method of planning the flight trajectory of a swarm of drones using a modified RRT (Rapidly-exploring Random Tree) algorithm. The version of the RRT algorithm presented in the article is called Multiplatform Spacetime RRT*. The proposed modifications make it possible to determine the flight trajectory of UAVs taking into account time constraints related to the area occupied by each platform. Additionally, the proposed algorithm ensures the avoidance of potential collisions of platforms in the air by using a collision avoidance algorithm used in practice based on geometric methods. Two designed and tested modifications of RRT were presented, based on the basic RRT* and Informed RRT* algorithms. The algorithm used in both tested versions guarantees the determination of the optimal flight path for unmanned platforms in a finite, small number of steps, which solely depends on the number of UAVs involved. This algorithm takes into account the dynamic model of the fixed-wing UAV. The simulation results presented by planning the flight trajectory of a swarm, consisting of three and four UAVs using the Multiplatform Spacetime RRT* algorithm, are significantly better than the algorithms that were compared to achieve these results. [ABSTRACT FROM AUTHOR]

Globally, the issue of research impact has grown as governments articulate policies around research as a contributor to economic and societal development, often through an econometric justification. This has triggered much discussion amongst humanities scholars in public formally-reasoned peer-reviewed texts that are rarely empirically-based. This Denmark-based empirical study used an individual biographical and historical structural framework to explore how humanities academics in face-to-face semi-formal interactive interviews viewed this issue. The results highlighted a nuanced understanding of what we call the humanities-impact landscape, with three potential interactions falling along a continuum suggesting further inquiry is warranted. The study contributes a rich tapestry of the interwoven individual and structural elements at play when academics articulate how they locate themselves within the landscape, ones that might not be seen in more conceptual arguments. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the well-posedness of weak solutions to the time-fractional Fokker–Planck equation. Its dynamics is governed by anomalous diffusion, and we consider the most general case of space-time dependent forces. Consequently, the fractional derivatives appear on the right-hand side of the equation, and they cannot be brought to the left-hand side, which would have been preferable from an analytical perspective. For showing the model's well-posedness, we derive an energy inequality by considering nonstandard and novel testing methods that involve a series of convolutions and integrations. We close the estimate by a Henry–Gronwall-type inequality. Lastly, we propose a numerical algorithm based on a nonuniform L1 scheme and present some simulation results for various forces. [ABSTRACT FROM AUTHOR]

In this paper we study long time dynamics (i.e., scattering and blow-up) of solutions for the focusing NLS with a repulsive inverse-power potential and with initial data lying exactly at the mass-energy threshold, namely, when $ E_{V}(u_{0})M(u_{0}) = E_{0}(Q)M(Q) $. Moreover, we prove failure of the uniform space-time bounds at the mass-energy threshold. [ABSTRACT FROM AUTHOR]

In previous works, we have proven that there are local tetrads in four-dimensional curved Lorentzian spacetimes that can be written in terms of two kinds of local structures, the skeletons and the gauge vectors. These tetrads diagonalize locally and covariantly the stress–energy tensors for systems of differential equations of the Einstein–Maxwell kind in the Abelian electromagnetic case, or of the Einstein–Maxwell–Yang-Mills kind when non-Abelian Yang–Mills fields are included, along with suitable Yang–Mills stress–energy tensors. Under local Lorentz transformations, these new tetrads conserve their skeleton-gauge vector structure. In this short paper, we will prove that given any general unit orthogonal tetrad in spacetime, we will be able to construct a new tetrad in the skeleton-gauge vector form. We will prove a theorem stating that the original orthonormal tetrad can be constructed or reexpressed with this same local tetrad skeleton-gauge vector structures. The theorems proved in this paper will enable the demonstration of new results in group isomorphism theorems in the future. [ABSTRACT FROM AUTHOR]

A new definition of entropy is introduced using a model that simulates an expanding space-time compatible with the fundamental principle of cosmology. The entropy is obtained by mean of a state function that measures the variation of the space-time normal curvature, from a highly compressed space to a lower compressed space. The defined entropy leads to work out a new understanding of the earliest conditions that last for a period estimated to 380,000 years after the Big Bang. It leads to understand via a short period of inflation the process that generates the uniform distribution of matter and energy at the surface of the last scattering. It involves gravitational singularities in a process of gradual decompression propitious to the incubation of matter recombination, and it allows to trace back gravity origin. [ABSTRACT FROM AUTHOR]

In this paper, we study a class of conformal metric deformations in the quasi-radial coordinate parametrizing the three-sphere in the conformally compactified Minkowski spacetime S 1 × S 3 . Prior to reduction of the associated Laplace–Beltrami operators to a Schrödinger form, a corresponding class of exactly solvable potentials (each one containing a scalar and a gradient term) is found. In particular, the scalar piece of these potentials can be exactly or quasi-exactly solvable, and among them we find the finite range confining trigonometric potentials of Pöschl–Teller, Scarf and Rosen–Morse. As an application of the results developed in the paper, the large compactification radius limit of the interaction described by some of these potentials is studied, and this regime is shown to be relevant to a quantum mechanical quark deconfinement mechanism. [ABSTRACT FROM AUTHOR]

In this paper, we study the topological effects of the global monopole spacetime on the energy eigenvalues of spherical symmetric potentials in the nonrelativistic regime. We deal with the radial equation by using the Wentzel, Kramers and Brillouim (WKB) approximation. In the cases where the energy levels of the ℓ -waves can be achieved, the WKB approximation is used based on the Langer transformation. [ABSTRACT FROM AUTHOR]

This paper examines the behavior of the universe around the bouncing point in the background of f (,) theory, where is the non-metricity and is the trace of the energy–momentum tensor. We derive the field equations that describe gravitational phenomena in the existence of non-metricity and matter source terms. By applying the reconstruction method for the Hubble parameter, a phenomenon of the bouncing universe for homogeneous spacetime filled with perfect fluid is studied. We consider specific models of this modified theory to evaluate the behavior of various cosmic parameters such as the Hubble, deceleration, equation of state and fluid parameters. When the null energy condition is violated, it follows a bouncing behavior. It is found that spacetime is composed of isotropic fluid, where a big bounce can occur and the universe turns into extremely unstable. We conclude that f (,) gravity successfully explains the early and late time cosmic expansion and evolution. [ABSTRACT FROM AUTHOR]

This paper explores cosmic evolution in f(R,T) gravity considering two distinct models with minimal coupling that are linear and quadratic in T; f(R,T) = R + αT and f(R,T) = R + αT2. The flat FRW space-time under the matter and radiation distribution has been considered to complete the analysis. In this background, the dynamical equations for dust in terms of dimensionless variables are developed. Via solutions of these dynamical equations, we develop significant cosmological parameters to compare the obtained results with the ΛCDM model and analyze them graphically. It is found that these parameters efficiently explain the expanding phenomenon of the universe for constrained values of the involved model parameters using some recent observational data. Moreover, the results are found to be stable via the square speed of sound. The matter and radiation fixed points are calculated by an autonomous set of dynamical equations, which are the stable and unstable saddle points. Also, the growth of matter perturbation in the f(R,T) theory has been discussed. Under this scenario, it is also checked that exact solutions of the dynamical equations are not possible for non-minimal coupling between geometry and matter. [ABSTRACT FROM AUTHOR]

The present communication explores n-dimensional cosmological models within the framework of the f(R,T) theory. The exploration is motivated by Kaluza–Klein theory, where the existence of extra dimensions becomes a focal point in understanding the fundamental forces of the universe. A cosmological model has been constructed by assuming Fractional quadratic deceleration parameter. H(t) and q(t) provide a crucial link between theoretical predictions and empirical observations. Through rigorous mathematical analysis and theoretical modeling, we investigate the implications of this extended gravitational theory on cosmic evolution and the structure of spacetime. Our findings shed light on the interplay between geometry, matter and gravitational dynamics in multidimensional space, offering new insights into the nature of gravity and cosmological phenomenon. [ABSTRACT FROM AUTHOR]

This study focuses on investigating the relativistic quantum dynamics of a fermionic oscillator field in the background of a minimal surface, specifically a catenoid bridge. Our primary objective is to analyze the bound-state solutions of this system by solving the non-perturbative radial wave equation. To achieve this, we consider two distinct scenarios. First, we explore the case where the particle is located inside the catenoid bridge and search for solutions to the wave equation. Subsequently, we extend our analysis to scenarios where the particle is positioned at a significant distance from the origin, comparable to the size of the catenoid bridge. In this regime, we obtain solutions to the wave equation to understand the behavior of the fermionic oscillator field. By examining these solutions, we investigate the influence of both the oscillator coupling and the spacetime background on the system. [ABSTRACT FROM AUTHOR]