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I present a review of the recent advancements in scattering theory, which provides a unified approach to studying dispersive and hyperbolic equations with general interaction terms and data. These equations encompass time-dependent potentials, as well as NLS, NLKG, and NLW equations. Additionally, I discuss a series of open problems along with their significance and potential future applications in scattering and inverse scattering. [ABSTRACT FROM AUTHOR]

This paper presents the dynamics that one microorganism spatially expands with two nutrients in space-time periodic environment. The generalized principal eigenvalue defined by the linear periodic parabolic operator is applied as a threshold to discuss the associated initial value problem. When the generalized principal eigenvalue is nonnegative, the solutions approach to the microorganism-extinction equilibrium uniformly. When the generalized principal eigenvalue is negative, the spreading speeds of the model are established when the initial distribution of microorganism has nonempty compact support, which are determined by a family of periodic parabolic eigenvalue problems. In the homogeneous environment, we show that the solutions locally uniformly converge to the microorganism-existent steady state by constructing upper and lower solutions. Finally, numerical simulations are performed to illustrate that the leftward or rightward spreading speed is approximately a constant under various circumstances. [ABSTRACT FROM AUTHOR]

We construct a fundamental piece of the boundary of the maximal globally hyperbolic development (MGHD) of Cauchy data for the multi-dimensional compressible Euler equations, which is necessary for the local shock development problem. For an open set of compressive and generic H 7 initial data, we construct unique H 7 solutions to the Euler equations in the maximal spacetime region below a given time-slice, beyond the time of the first singularity; at any point in this spacetime, the solution can be smoothly and uniquely computed by tracing both the fast and slow acoustic characteristic surfaces backward-in-time, until reaching the Cauchy data prescribed along the initial time-slice. The future temporal boundary of this spacetime region is a singular hypersurface, containing the union of three sets: first, a co-dimension-2 surface of "first singularities" called the pre-shock; second, a downstream hypersurface called the singular set emanating from the pre-shock, on which the Euler solution experiences a continuum of gradient catastrophes; third, an upstream hypersurface consisting of a Cauchy horizon emanating from the pre-shock, which the Euler solution cannot reach. We develop a new geometric framework for the description of the acoustic characteristic surfaces which is based on the Arbitrary Lagrangian Eulerian (ALE) framework, and combine this with a new type of differentiated Riemann variables which are linear combinations of gradients of velocity, sound speed, and the curvature of the fast acoustic characteristic surfaces. With these new variables, we establish uniform H 7 Sobolev bounds for solutions to the Euler equations without derivative loss and with optimal regularity. [ABSTRACT FROM AUTHOR]

Among the various proposals for quantum ontology, both wavefunction realists and the primitive ontologists have argued that their approach is to be preferred because it relies on intuitive notions: locality, separability and spatiotemporality. As such, these proposals should be seen as normative frameworks asserting that one should choose the fundamental ontology which preserves these intuitions, even if they disagree about their relative importance: wavefunction realists favor preserving locality and separability, while primitive ontologists advocate for spatiotemporality. In this paper, first I clarify the main tenets of wavefunction realism and the primitive ontology approach, arguing that seeing the latter as favoring constructive explanation makes sense of their requirement of a spatiotemporal ontology. Then I show how the aforementioned intuitive notions cannot all be kept in the quantum domain. Consequently, wavefunction realists rank locality and separability higher than spatiotemporality, while primitive ontologists do the opposite. I conclude that however, the choice of which notions to favor is not as arbitrary as it might seem. In fact, they are not independent: requiring locality and separability can soundly be justified by requiring spatiotemporality, and not the other way around. If so, the primitive ontology approach has a better justification of its intuitions than its rival wavefunction realist framework. [ABSTRACT FROM AUTHOR]

The paper is devoted to the mathematical description of the whispering gallery waves modulated by amplitude and frequency. Space-time ray method for this problem is developed. [ABSTRACT FROM AUTHOR]

We consider quasiphotons, which are asymptotic solutions of the wave equation with a Gaussian-type localization around points moving along rays. We show in this note that well-known procedures of obtaining the formulas for quasiphotons lead to a complete class of quasiphotons described by the complex space-time ray method (STRM), in spite of the very restrictive normalizing condition. It is possible in the case of the constant velocity to derive formulas in explicit form for 3 × 3-matrices describing quasiphotons. (These matrices, in particular, can have all nonzero components). [ABSTRACT FROM AUTHOR]

Some important problems in science do not have analytical solutions in four dimensions including QCD, but they are integrable in two dimensions. For many years, scientists have been trying to find a relation between two-dimensional and four-dimensional space-time to explain the real problem in four dimensions by accurately solving the appropriate model in two dimensions. In this paper, an interesting relation between g Y M 2 (generalized two-dimensional Yang–Mills) and Maxwell construction has been found, which can be a starting point for finding more relations between two-dimensional and four-dimensional space-time, so this paper can play an important role in the advancement of science. For this purpose, first, the large-N behavior of the quartic-cubic generalized two-dimensional Yang–Mills U(N) on a sphere is investigated for finite cubic couplings. It is shown that there are two phase transitions one of which is of third order, which is similar to previous papers, and the other one is of second order, which is a novel result. Second, g Y M 2 (for G (z) = z m + λ z n ; m = 4 , 6 ; n < m ) and Maxwell construction are compared with each other and a relationship between two-dimensional space-time, which is integrable, and four-dimensional space-time is obtained. [ABSTRACT FROM AUTHOR]

Everything in our environment moves through both space and time, and to effectively act we must be aware of both spatial and temporal elements in relation to our own bodies. Thus, perceptions of space and time have an intimate relationship. Walsh's a theory of magnitude (ATOM) suggests that space and time perception rely on a general magnitude system and their relationship should be roughly symmetrical. Alternatively, metaphor theory, which is based on the philosophical work of Lakoff and Johnson, argues that we represent time using a spatial metaphor and thus the relationship should be asymmetrical (with space influencing time more than time influences space). A compelling line of evidence for metaphor theory comes from the work of Casasanto & Boroditsky. Cognition, 106(2), 579–593. (2008) who experimentally demonstrated this asymmetric effect. However, in our previous unpublished online replication attempt of this work, we found a roughly symmetrical relationship between space and time, more in line with the theoretical predictions of ATOM. Given this, we performed a registered replication of Casasanto & Boroditsky. Cognition, 106(2), 579–593. (2008) in both an online and laboratory environment. [ABSTRACT FROM AUTHOR]

We consider a massless and minimally coupled self interacting quantum scalar field in the inflationary de Sitter spacetime. The scalar potential is taken to be a hybrid of cubic and quartic self interactions, V (ϕ) = λ ϕ 4 / 4 ! + β ϕ 3 / 3 ! ( λ > 0 ). Compared to the earlier well studied β = 0 case, the present potential has a rolling down effect due to the ϕ 3 term, along with the usual bounding effect due to the ϕ 4 term. We begin by constructing the Schwinger–Dyson equation for the scalar Feynman propagator up to two loop, at O (λ) , O (β 2) , O (λ 2) and O (λ β 2) . Using this equation, we consider first the local part of the scalar self energy and compute the rest mass squared of the scalar field, dynamically generated via the late time non-perturbative secular logarithms, by resumming the daisy-like graphs. The logarithms associated here are sub-leading, compared to those associated with the non-local, leading terms. We also argue that unlike the quartic case, considering merely the one loop results for the purpose of resummation does not give us any sensible result here. We next construct the non-perturbative two particle irreducible effective action up to three loop and derive from it the Schwinger–Dyson equation once again. This equation is satisfied by the non-perturbative Feynman propagator. By series expanding this propagator, the resummed local part of the self energy is shown to yield the same dynamical mass as that of the above. We next use this equation to resum the effect of the non-local part of the scalar self energy in the Feynman propagator, and show that even though the perturbatively corrected propagator shows secular growth at late times, there exists one resummed solution which is vanishing for large spacelike separations, in qualitative agreement with the well known result found via the stochastic formalism. [ABSTRACT FROM AUTHOR]

The null-surface formulation (NSF) of general relativity differs markedly from the conventional approach. The conventional approach to general relativity is concerned with local fields such as the metric, whereas the NSF focuses on surfaces. The NSF has two distinct but mathematically equivalent interpretations: (a) Future-directed light rays leave a spacetime point and intersect future null-infinity. The resulting surface, known as a light-cone cut, encodes the properties of the spacetime; (b) The angular coordinates (Bondi coordinates) of null-infinity are used to label past light cones, thereby producing a family of null surfaces. These will satisfy the NSF field equations and a solution of these equations provides a description of spacetime. This paper features a new exact solution that, for the first time, directly links the two interpretations, thereby illustrating both approaches and demonstrating their equivalence. The solution and its properties are first explored in 2+1 dimensions, after which, the generalization to 3+1 is outlined. [ABSTRACT FROM AUTHOR]

We study a model of the neutron star in κ -deformed space-time in the presence of the cosmological constant (Λ ). The Einstein tensor and the energy-momentum tensor are generalized to κ -deformed space-time and we construct the field equations with the cosmological constant. Considering the interior of the star to be a perfect fluid as in the commutative case, we find the Tolman–Oppenheimer–Volkoff equations with the inclusion of the cosmological constant in κ -deformed space-time. The behavior of the maximum allowed mass of the star and its radius are studied with the variation in the cosmological constant as well as the deformation parameter. We see that the non-commutativity enhances the mass of the star and its maximum mass increases with a decrease in the cosmological constant. The maximum mass varies from 3.44 to 3.68 M ⊙ as Λ varies from 10 - 10 to 10 - 15 m - 2 . We also obtain the compactness factor and surface redshift of the star. We observe that the compactness of the star increases as the cosmological constant decreases, whereas the surface redshift of the star decreases with a decrease in the cosmological constant. The compactness factor and surface redshift corresponding to the maximum mass of the neutron star remains almost constant as Λ decreases. [ABSTRACT FROM AUTHOR]

In this paper we use the Homotopy analysis method to obtain an analytic approximation for the entire photon trajectory in the Schwarzschild spacetime. This is usually expressed exactly in terms of an elliptic integral. We compare our approximation with other formulae found in the literature, which were specifically obtained for the Schwarzschild solution. Unlike some of these formulae, our approximation can be applied and maintains a good accuracy for emission point close to the event horizon and also for emission angles close to and greater than π / 2 . We show that our method can easily be applied to other spherically symmetric solutions such as the Reissner-Nordström solution. Such an approximation would be useful when accurate determination of the light trajectories around compact objects is required without the need to revert to time consuming numerical integration of elliptic integrals. [ABSTRACT FROM AUTHOR]

We present a systematic investigation of antilinear superoperators and their applications in studying open quantum systems, particularly focusing on quantum geometric invariance, entanglement distribution, and symmetry. We study several classes of antilinear superoperators, including antilinear quantum channels, antilinearly unital superoperators, antiunitary superoperators, and generalized Θ -conjugation. Using the Bloch representation, we present a systematic investigation of quantum geometric transformations in higher-dimensional quantum systems. By choosing different generalized Θ -conjugations, we obtain various metrics for the space of Bloch space-time vectors, including the Euclidean and Minkowskian metrics. Utilizing these geometric structures, we then investigate the entanglement distribution over a multipartite system constrained by quantum geometric invariance. The strong and weak antilinear superoperator symmetries of the open quantum system are also discussed. Additionally, Kramers' degeneracy and conserved quantities are examined in detail. [ABSTRACT FROM AUTHOR]

The diurnal cycle is an important mode of climatic variability associated with different aspects of micro, meso and large scale meteorological phenomena. Thus, we performed a study of the space-time variability of the diurnal cycle of precipitation with hourly sampling and covering all regions of Brazil. The dataset was collected during the period of 13-year, from 1st January 2008 to 31th December 2020. We used data from 411 rain gauges installed in automatic weather stations. To evaluate regional aspects, we conducted a cluster analysis with different configurations (4, 5 and 6 groups). We identified a considerable heterogeneity in the hour of maximum precipitation in Brazil and three main types of diurnal cycle were observed: (i) maximum precipitation at mid- to late afternoon associated with strong local convection activity; (ii) diurnal cycle with intense precipitation during nighttime at the Amazon basin, the coast of Northeast Brazil and the Southern region; (iii) semidiurnal cycles with low precipitation rate at the Northeast Brazil. [ABSTRACT FROM AUTHOR]

This paper considers two problems—one in philosophy of religion and another in philosophy of physics—and shows that the two problems have one solution. Some Christian philosophers have endorsed the views that (i) there was a first finitely long period of time, (ii) God is in time, and yet (iii) God did not have a beginning. If there was a first finitely long period of time and God is in time then there was a first finitely long period of time in God's life. But if God's life includes a first finitely long period of time, then, on one initially intuitive conception of beginning to exist, God began to exist. Thus, at first glance, (i)–(iii) are not mutually compatible. Meanwhile, on a variety of proposals for quantum gravity theories or interpretations of quantum theory, space-time is not fundamental to physical reality and instead can (somehow) be explained in terms of yet more fundamental physical substructures. As I show, there is a strong intuition that if space-time is not fundamental to physical reality, then, even if there were a first finitely long period in the life of physical reality, physical reality would be beginningless. Thus, both theistic philosophers and philosophers of physics have developed theories on which some beginningless entities have a first finitely long temporal period in their lives and so both groups should be interested in developing criteria that distinguish such entities from entities with a beginning. In this paper, I offer one necessary (but not sufficient) condition, namely, that entities that begin to exist are absent from the closest possible worlds without time. The view that I defend has one significant upshot: no sound argument can use the mere fact (if it is a fact) that past time is finite to reach the conclusion that the totality of physical reality had a beginning. [ABSTRACT FROM AUTHOR]

The motivation for constructing a thin-shell wormhole from a (2+1)-dimensional rotating black hole arises from the desire to study the effects of a nonminimally coupled scalar field in this particular spacetime. By investigating the behavior of such a field in the presence of rotation, we can gain insights into the interplay between gravity and scalar fields in lower-dimensional systems. Additionally, this construction allows us to explore potential connections between black hole physics and exotic phenomena like traversable wormholes. The radial perturbation around the equilibrium throat radius is considered to explore the stable configuration for specific values of physical parameters. Then, the equations of state, specifically the phantom-like and generalized Chaplygin gas model for exotic matter is used to conduct an extensive investigation into the stability of the counter-rotating thin-shell wormholes. Our results show that the presence of a scalar field enhances the stability of the counter-rotating thin-shell wormholes. [ABSTRACT FROM AUTHOR]

This study retrieves some novel exact solutions to the family of 3D space–time fractional Wazwaz–Benjamin–Bona–Mahony (WBBM) equations in the context of diverse nonlinear physical phenomena resulting from water wave mechanics. The family of WBBM equations is transformed for this purpose using a space and time fractional transformation into an ordinary differential equation (ODE). The ODE then uses a strong method, namely the Unified Method. Consequently, lump solutions, dark-bright soliton, singular and multiple soliton solutions, and periodic solutions are investigated. The disparities between the current study's conclusions and previously acquired solutions via other approaches are examined. All wave solutions produced are determined to be novel in terms of fractionality, unrestricted parameters, and implemented technique sense. The impact of unrestricted parameters and fractionality on the obtained solutions are visually presented, along with physical explanations. It is observed that the wave portents are varied with the increase of unrestricted parameters as well as fractionality. We dynamically showed that the appropriate transformation and the applied Unified approach more proficient in the study of water wave dynamics and might be used in future researches to clarify the many physical phenomena. The novelty of this work validate that the proposed method seem simple and useful tools for obtaining the solutions in PDEs and it is expected to use in mathematical physics and optical engineering. [ABSTRACT FROM AUTHOR]

The center-of-mass energy of two colliding particles could be arbitrarily high in the vicinity of event horizons of the extremal Myers-Perry black holes if the angular momentum of colliding particles is fine-tuned to the critical values. We investigate the maximum efficiency of two colliding particles in four and six dimensions. The efficiency of collision for two particles near the four-dimensional Kerr black holes is 130%. We show that the efficiency increases to 145% for collision in six dimensions. We also show that the region for the polar angle in which the particle can reach the high energy is larger when the dimension of space-time increases. [ABSTRACT FROM AUTHOR]

The Carrier-Domain Method was introduced for high-resolution computation of time-periodic long-wake flows. The cost-effectiveness of the method makes such computations practical in 3D. A short segment of the wake domain, the carrier domain, moves in the free-stream direction, from the beginning of the long wake domain to the end. The data at the moving inflow plane comes from the time-periodic data computed at an earlier position of the carrier domain. With the high mesh resolution that can easily be afforded over the short domain segment, the wake flow patterns can be carried, with superior accuracy, far downstream. Computing the long-wake flow with a high-resolution moving mesh that covers a short segment of the wake domain at any instant during the computation would certainly be far more cost-effective than computing it with a high-resolution fixed mesh that covers the entire length. We present high-resolution 3D computation of time-periodic long-wake flow for a cylinder and a wind turbine, both computed with isogeometric discretization and the Space–Time Variational Multiscale method. In the isogeometric discretization, the basis functions are quadratic NURBS in space and linear in time. The cylinder flow is at Reynolds number 100. At this Reynolds number, the flow has an easily discernible vortex shedding period. The wake flow is computed up to 350 diameters downstream of the cylinder, far enough to see the secondary vortex street. In the wind turbine long-wake flow computation, the velocity data at the inflow boundary of the wake domain comes from an earlier wind turbine computation, with the turbine rotor having a diameter of 126 m , extracted by projection from a plane located 10 m downstream of the turbine. The wake flow is computed up to 482 m downstream of the wind turbine. In both the cylinder and wind turbine wake flow computations, the flow patterns obtained with the full domain and carrier domain show a near-perfect match, clearly demonstrating the effectiveness and practicality of the Carrier-Domain Method in high-resolution 3D computation of time-periodic long-wake flows. [ABSTRACT FROM AUTHOR]

Results achieved by the authors in the course of research activity on continuum mechanics and electrodynamics (CME) during the past twenty years are illustrated, revised and discussed. Adoption of a geometric approach leads to renewal of concepts and methods of classical CME and to formulation in Euclid (3+1)D ambient spacetime wherein innovation, clarity and depth of a geometric treatment naturally emerge. The dissemination of novel concepts and methods in CME is not delayable, with critical revisitation of problematic notions, analyses and results still currently on the scene. Material frame indifference, equilibrium in a reference configuration, extremality principles in Dynamics, finite elasticity, chain decomposition of finite strain in elasto-thermo-plasticity, variance of electro-magnetic induction laws under frame changes, action on electric charges moving in a magnetic field, are under the spotlight of innovation and advancement. Fostering basic knowledge of Differential Geometry and application of geometric notions and methods contribute effective tools in formulating meaningful rules, amending misstatements and dimming debates based on vague affirmations. [ABSTRACT FROM AUTHOR]

We consider a congruence of null geodesics in the presence of a quantized spacetime metric. The coupling to a quantum metric induces fluctuations in the congruence; we calculate the change in the area of a pencil of geodesics induced by such fluctuations. For the gravitational field in its vacuum state, we find that quantum gravity contributes a correction to the null Raychaudhuri equation which is of the same sign as the classical terms. We thus derive a quantum-gravitational focusing theorem valid for linearized quantum gravity. [ABSTRACT FROM AUTHOR]

We propose a covariant method of constructing entire trajectories of physical states in superstring theory in the critical dimension. It is inspired by a recently developed covariant technology of excavating bosonic string trajectories, that is facilitated by the observation that the Virasoro constraints can be written as linear combinations of lowering operators of a bigger algebra, namely a symplectic algebra, which is Howe dual to the spacetime Lorentz algebra. For superstrings, it is the orthosymplectic algebra that appears instead, with its lowest weight states forming the simplest class of physical trajectories in the NS sector. To construct the simplest class in the R sector, the lowest weight states need to be supplemented with other states, which we determine. Deeper trajectories are then constructed by acting with suitable combinations of the raising operators of the orthosymplectic algebra, which we illustrate with several examples. [ABSTRACT FROM AUTHOR]

In this work, various types of soliton solutions for space–time conformable version of (n+1)-dimensional generalized Kadomtsev–Petviashvili (KP) equation were constructed via the approach of modified extended tanh. The derivatives involved were defined to reflect the sense of space–time conformable derivatives. Furthermore, with the help of a fractional wave transformation, the conformable KP equation was reduced into an ODE of a polynomial nature. Mathematica software was used to obtain a system of algebraic equations and then solved. Finally, a graphical illustration for some of the obtained results were provided to show the effect various values of order of the conformable derivative, α (alpha) as well as k, (the sum of linear terms in the equation). [ABSTRACT FROM AUTHOR]

Gravitational plane waves (when Ricci flat) belong to the VSI family. The achronym VSI stands for vanishing scalar invariants, meaning that all scalar invariants built out of Riemann tensor and its derivatives vanish, although the Riemann tensor itself does not. In the particular case of plane waves many interesting phenomena have been uncovered for strings propagating in this background. Here we comment on gravitons propagating in such a spacetime. [ABSTRACT FROM AUTHOR]

A general structure for space-time that preserves the classical notion of absolute time, and to which we refer as Proto-Galilean space-time, is presented. In this setting, space-time is modeled as a general fiber bundle over the time axis. The motion of a particle is a section of the fiber bundle. A recent framework for continuum mechanics, where configurations are represented by sections of a fiber bundle over the body manifold, is used to formulate the dynamics of a particle and the dynamics of a continuous body in a Proto-Galilean space-time. [ABSTRACT FROM AUTHOR]

Geometric underdetermination (i.e., the underdetermination of the geometric properties of space and time) is a live possibility in light of some of our best theories of physics. In response to this, geometric conventionalism offers a selective anti-realism, refusing to assign truth values to variant geometric propositions. Although often regarded as being dead in the water by modern philosophers, in this article we propose to revitalise the programme of geometric conventionalism both on its own terms, and as an attractive response to the above-mentioned live cases of geometric underdetermination. Specifically, we (1) articulate geometrical conventionalism as we conceive it, (2) anticipate various objections to the view, and defend it against those objections, and (3) demonstrate how geometric conventionalism plays out in the context of a wide variety of spacetime theories, both classical and relativistic. [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 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]

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]

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]

Beginning from the standard Arnowitt–Deser–Misner (ADM) formulation of general relativity we construct a tentative model of quantum gravity from the point of view of an observer with constant proper acceleration, just outside of a horizon of spacetime. In addition of producing the standard results of black-hole thermodynamics, our model makes an entirely new prediction that there is a certain upper bound for the energies of massive particles. For protons, for instance, this upper bound is around 1.1 × 10 21 eV. The result is interesting, because this energy is roughly of the same order of magnitude as are the highest energies ever measured for protons in cosmic rays. [ABSTRACT FROM AUTHOR]

According to studies by the Intergovernmental Panel on Climate Change (IPCC), tropical mountainous areas are experiencing increasingly unfavorable climatic conditions regarding geohazards due to a heightened occurrence of intense rainfall events. These climatic shifts contribute to heightened geological risks, notably an elevated frequency of landslides, exacerbating the challenges faced by these regions. There is an urgent need to understand and measure how rainfall variability affects geo-hydrological hazards, which remain difficult to determine and predict. The complex and non-linear space-time relationships and dynamics of rainfall, El Niño-Southern Oscillation (ENSO), and landslides in the Tropical Andean Mountain region in Colombia require an adequate analysis and understanding of their link in terms of its spatial and temporal component at different scales. By evaluation in annual, seasonal, and monthly scales, additional insights on the relationships using a wavelet spectral analysis and a space-time permutation scan statistics method using SaTScan™ are provided. In this study, a space-time and frequency analysis of landslides using a 42-year (1981–2022) rainfall and Multivariate ENSO Index v2.0 time series is presented. According to the results, landslides closely aligned with rainfall patterns, exhibiting a bimodal annual cycle. The ENSO added complexity, with La Niña years leading to more frequent landslides throughout the year and El Niño years showing concentrated occurrences in specific months. This study highlights the influence of rainfall patterns and antecedent rainfall on landslide occurrence, the impact of ENSO phases on rainfall and landslides, and the increasing trend of landslides in Colombia. [ABSTRACT FROM AUTHOR]

We examine the thermodynamics of a near-extremal Kerr black hole, and demonstrate that the geometry behaves as an ordinary quantum system with a vanishingly small degeneracy at low temperatures. This is in contrast with the classical analysis, which instead predicts a macroscopic entropy for the extremal Kerr black hole. Our results follow from a careful analysis of the gravitational path integral. Specifically, the low temperature canonical partition function behaves as Z ∼ T 3 2 e S 0 + c log S 0 , with S0 the classical degeneracy and c a numerical coefficient we compute. This is in line with the general expectations for non-supersymmetric near-extremal black hole thermodynamics, as has been clarified in the recent past, although cases without spherical symmetry have not yet been fully analyzed until now. We also point out some curious features relating to the rotational zero modes of the near-extremal Kerr black hole background that affects the coefficient c. This raises a puzzle when considering similar black holes in string theory. Our results generalize to other rotating black holes, as we briefly exemplify. [ABSTRACT FROM AUTHOR]

Space and time, which should properly be taken conjointly, are both communicatively produced and created with certain contextual perspectives—they are not independent physical entities. The standpoint of production makes the relationship between space and time comprehensible. They can either be mental-subjective, physical-objective, or social-intersubjective. Social and intersubjective (or E-series) spacetime might shed new light on biological thinking. For general readers, this paper provides a clue regarding an alternative conceptualization of spacetime based on biology. [ABSTRACT FROM AUTHOR]

We describe laboratory experiments in a 2D wave tank that aim at building up and monitor 2D shallow water soliton gas. The water surface elevation is obtained over a large ( ∼ 100 m 2 ) domain, with centimeter-resolution, by stereoscopic vision using two cameras. Floating particles are seeded to get surface texture and determine the wave field by image correlation. With this setup, soliton propagation and multiple interactions can be measured with a previously unreachable level of detail. The propagation of an oblique soliton is analyzed, and the amplitude decay and local incidence are compared to analytical predictions. We further present two cases of 2D soliton gas, emerging from multiple line solitons with random incidence ( | θ | < 30 ∘ ) and from irregular random waves forced with a JONSWAP spectrum ( | θ | < 45 ∘ ). To our knowledge, those are the first observations of random 2D soliton gas for gravity waves. In both cases, Mach reflections and Mach expansions result in solitons that mainly propagate in directions perpendicular to the wavemakers. [ABSTRACT FROM AUTHOR]

In this article, new traveling wave solutions are retrieved for two space-time fractional models: the resonant nonlinear Schrödinger equation and the Biswas–Milovic equation which illustrates the dynamics of optical soliton promulgation in optical fibers, both featuring Kerr law nonlinearity. These equations are explored via an efficient method namely, the extended simple equation method. The fractional derivative is used in the conformable sense to accomplish this analysis. The extracted solutions show dark, periodic, singular, and singular-periodic solitons behaviors, which are depicted graphically by using line, surface, and contour plots. The reported solutions are unique and novel. The proposed method distinguishes itself by its simplicity, reliability, and ability to generate novel soliton solutions for nonlinear Schrödinger equations within the realm of mathematical physics. [ABSTRACT FROM AUTHOR]

We investigate the response of Casimir energies to fluctuations in a scalar field in the background of a weak gravitational field in κ -deformed space-time. We model the Casimir plates in a gravitational field by κ -deformed Rindler coordinates and calculate the Casimir energy using the κ -deformed scalar field. We show that the Casimir energy accelerates in a weak gravitational field like a mass. Thus, our calculations show that the mass–energy equivalence principle holds in κ -deformed space-time even though a length scale is introduced through space-time non-commutativity. [ABSTRACT FROM AUTHOR]

Space–time prism is a fundamental concept in time geography that can model an individual's accessibility to resources under space–time constraints. A prism anchor is often defined by work, school, or home activity with a fixed location and schedule. Trips and other activities are relatively flexible and scheduled between prism anchors. This fixity-flexibility dichotomy may not capture the increasing complexity of human mobility behaviors or variations among individuals. Recent developments in location-aware technologies allow us to collect person-level mobility data with detailed space–time paths and contextual information. This article develops methods to extract prism anchors from these GPS-based survey data and examines whether home, work, and school activities can always be used to define prism anchors for everyone. To illustrate our methods, we use data collected in Minnesota and Beijing as two study cases. Results in both study cases suggest that not everyone has home, work, or school anchors, and people with the same socio-demographic background tend to have similar anchor types. By deriving home, work, and school anchors, we can better understand how a person's everyday schedules are governed by home, work, and school and refine person-based accessibility measures. [ABSTRACT FROM AUTHOR]

Chile is one of the most seismic countries in the world especially due to the subduction of the Nazca plate under the South America plate along the Chilean cost. Normally, the spatial distribution of seismic events tends to form spatial and temporal clusters around the main event including both precursor and aftershock events. However, it is very difficult to identify whether an event is a precursor, a main event or an aftershock. In the literature, only some large earthquakes are well described but it does not exist an automatic method to classify them. In this work, we propose a new density based clustering method, called ST-DBSCAN-EV (Space-time DBSCAN with Epsilon Variable), which allows the Epsilon parameter (the radius) to vary depending on the density of the points. The results of the ST-DBSCAN-EV are validated on three important earthquakes with magnitude greater than 8.0 Mw occurred in Chile in the last 20 years, by carrying out a series of experiments considering different combinations of parameters. A comparison with some traditional clustering techniques such as the DBSCAN, ST-DBSCAN, and the K-means has been implemented for assessing the performance of the proposed method. Almost in all cases ST-DBSCAN-EV outperformed traditional ones by providing an F1-Score metric higher than 0.8. Finally, the results of classification are compared with a declustering method. [ABSTRACT FROM AUTHOR]

Spatial topology endows topological solitons, such as skyrmions and hopfions, with fascinating dynamics. However, the temporal dimension has so far provided a passive stage on which topological solitons evolve. Here we construct spacetime magnetic hopfions: magnetic textures in two spatial dimensions that when excited by a time-periodic drive develop spacetime topology. We uncover two complementary construction routes using skyrmions by braiding their center of mass position and by controlling their internal low-energy excitations. Spacetime magnetic hopfions can be realized in nanopatterned grids to braid skyrmions and in frustrated magnets under an applied AC electric field. Their topological invariant, the spacetime Hopf index, can be tuned by the applied electric field as demonstrated by our collective coordinate modeling and micromagnetic simulations. The principles we have introduced to actively control spacetime topology are not limited to magnetic solitons, opening avenues to explore spacetime topology of general order parameters and fields. Topological solitons are localized structures whose stability emerges from the topology of their spatial structure, hence they are usually independent of the temporal dimension. The authors construct topological magnetic solitons in space-time from periodically driven magnetic structures that can be externally controlled. [ABSTRACT FROM AUTHOR]

We define a new gauge independent quasi-local mass and energy, and show its relation to the Brown–York Hamilton–Jacobi analysis. A quasi-local proof of the positivity, based on spacetime harmonic functions, is given for admissible closed spacelike 2-surfaces which enclose an initial data set satisfying the dominant energy condition. Like the Wang-Yau mass, the new definition relies on isometric embeddings into Minkowski space, although our notion of admissibility is different from that of Wang and Yau. Rigidity is also established, in that vanishing energy implies that the 2-surface arises from an embedding into Minkowski space, and conversely the mass vanishes for any such surface. Furthermore, we show convergence to the ADM mass at spatial infinity, and provide the equation associated with optimal isometric embedding. [ABSTRACT FROM AUTHOR]

Zika, a viral disease transmitted to humans by Aedes mosquitoes, emerged in the Americas in 2015, causing large-scale epidemics. Colombia alone reported over 72,000 Zika cases between 2015 and 2016. Using national surveillance data from 1121 municipalities over 70 weeks, we identified sociodemographic and environmental factors associated with Zika's emergence, re-emergence, persistence, and transmission intensity in Colombia. We fitted a zero-state Markov-switching model under the Bayesian framework, assuming Zika switched between periods of presence and absence according to spatially and temporally varying probabilities of emergence/re-emergence (from absence to presence) and persistence (from presence to presence). These probabilities were assumed to follow a series of mixed multiple logistic regressions. When Zika was present, assuming that the cases follow a negative binomial distribution, we estimated the transmission intensity rate. Our results indicate that Zika emerged/re-emerged sooner and that transmission was intensified in municipalities that were more densely populated, at lower altitudes and/or with less vegetation cover. Warmer temperatures and less weekly-accumulated rain were also associated with Zika emergence. Zika cases persisted for longer in more densely populated areas with more cases reported in the previous week. Overall, population density, elevation, and temperature were identified as the main contributors to the first Zika epidemic in Colombia. We also estimated the probability of Zika presence by municipality and week, and the results suggest that the disease circulated undetected by the surveillance system on many occasions. Our results offer insights into priority areas for public health interventions against emerging and re-emerging Aedes-borne diseases. [ABSTRACT FROM AUTHOR]

We investigate the turnaround radius of the Reissner–Nordström deSitter Spacetime and how the turnaround radius changes if a test particle carries charge. We also consider the Martínez–Troncoso–Zanelli (MTZ) solution of conformally coupled gravity and investigate how the turnaround radius changes for a scalar test charge. In both scalar and electric interaction cases we find that the Turnaround Radius depends on the particle's energy. [ABSTRACT FROM AUTHOR]

The process of the gravitational collapse might lead not only to a black hole but also to naked singularity formation. In this paper, we consider the generalized Vaidya spacetime with polytropic and generalized polytropic equations of state. We solve the Einstein and Einstein–Maxwell equations to obtain the explicit form of a mass function. We consider the limiting cases of solutions and find out, that generalized Vaidya spacetime might behave like Vaidya–de Sitter and Bonnor–Vaidya–de sitter solutions. Moreover, we explicitly show, that the part of solution, which depends on the polytropic index, is similar to cosmological fields surrounding both Vaidya and Bonnor–Vaidya black holes. The process of the gravitational collapse has been then considered. We have found out that the conditions of the naked singularity formation don't depend on the polytropic index. [ABSTRACT FROM AUTHOR]

The C*-algebraic construction of QFT by Buchholz and one of us relies on the causal structure of space-time and a classical Lagrangian. In one of our previous papers, we have introduced additional structure into this construction, namely an action of symmetries, which is related to fixing renormalization conditions. This action characterizes anomalies and satisfies a cocycle condition which is summarized in the unitary anomalous Master Ward identity. Here (using perturbation theory) we show how this cocycle condition is related to the Wess–Zumino consistency relation and the consistency relation for the anomaly in the BV formalism, where the latter follows from the generalized Jacobi identity for the associated L ∞ -algebra. In addition, we give a proof that perturbative agreement (i.e., independence of a perturbative QFT on the splitting of the Lagrangian into free and interacting parts) can be achieved by finite renormalizations. [ABSTRACT FROM AUTHOR]

Neutrinos from the cosmos have proven to be ideal for probing the nature of space-time. Previous studies on high-energy events of IceCube suggested that some of these events might be gamma-ray burst neutrinos, with their speeds varying linearly with their energy, implying also the coexistence of subluminal and superluminal propagation. However, a recent reanalysis of the data, incorporating revised directional information, reveals stronger signals that neutrinos are actually being slowed down compared to previous suggestion of neutrino speed variation. Thus, it is worth discussing its implications for the brane/string inspired framework of space-time foam, which has been used to explain previous observations. We revisit effects on neutrino propagation from specific foam models within the framework, indicating that the implied violation of Lorentz invariance could necessarily cause the neutrino to decelerate. We therefore argue that this sort of model is in agreement with the updated phenomenological indication just mentioned. An extended analysis of the revised IceCube data will further test these observations and stringy quantum gravity. [ABSTRACT FROM AUTHOR]

We use the semiclassical approach to solve the Klein–Gordon and Dirac equations in the presence of a time-varying electric field. Our objective is to calculate the density of particle creation in a cosmological anisotropic Bianchi- I space–time. We demonstrate that when the electric interaction is proportional to the Ricci scalar of curved space–time, the distribution of particles subjected to the electric field transforms into a thermal state. [ABSTRACT FROM AUTHOR]

The nonlinear space–time fractional Sasa–Satsuma and Schrödinger–Hirota equations with beta derivative describe optical soliton, photonics, plasmas, neutral scalar masons, and long-surface gravitational waves in the real world. Through the fractional wave transform, the models are converted into a single wave variable equation. In this article, we examine a range of compatible, useful, and typical wave solutions expressed in the forms of hyperbolic, trigonometric, and rational functions uniformly through the ( Q ′ / Q , 1 / Q )-expansion approach. When specific parameter values are set, the generalized wave solutions exhibit a wide range of shapes, including asymptotic, anti-asymptotic, dark-optical, breather, lump-periodic, kink, kink-bell-shaped, homoclinic-breather, bright, dark, and periodic solitons that resemble periodic breathing patterns. We also investigate the effect of the fractional parameter δ into the wave profile, revealing a clear correlation between changes in the fractional order derivative δ and variation in the soliton's shape. The results underscore the use of this approach for the exploration of diverse nonlinear fractional systems within the context of beta derivatives. Varying the fractional-order δ and maintaining specific fixed parameter values, we depict 3D-surface, 2D-surface, density, and contour plots to visualize some of the derived solutions. [ABSTRACT FROM AUTHOR]

In this work, we investigate coupled space–time fractional nonlinear Schrödinger equation (FNSE) arising in physics. The FNSE can be utilized to explain non-relativistic quantum mechanical phenomena. With the aid of the conformable fractional derivative (CFD) and fractional complex transform (FCT), we implement the extensive direct algebraic approach (EDAA), the behaviors of some of the generated solutions are shown as 3D-graphics for various with different fractal orders. The optical soliton solutions that are bright periodic, kink bright and kink-bright periodic are among these precise solutions. The acquired results demonstrate the simplicity, effectiveness, and capacity to produce additional kinds of exact solutions of these proposed methods, which are useful in deciphering the intricate physical interpretation of space–time FNSE. [ABSTRACT FROM AUTHOR]