Space-time Behavior Research Articles

Quantum curvature fluctuations and the cosmological constant in a single plaquette quantum gravity model

Abstract Understanding the microscopic behavior of spacetime, in particular quantum uncertainty in the Ricci scalar, is critical for developing a theory of quantum gravity and perhaps solving the cosmological constant problem. To test this, we compute this quantity for a simple but exact discrete quantum gravity model based on a single plaquette of spacetime. Our results confirm initial speculations of Wheeler from 1955 in finding a UV divergence in the quantum uncertainty. We further show that this behavior is stable under renormalization, but potentially unstable with the introduction of a cosmological constant, suggesting that a bare cosmological constant is ruled out.

Green's function and pointwise space-time behaviors of the three-dimensional relativistic Boltzmann equation

The pointwise space-time behavior of the Green's function of the three-dimensional relativistic Boltzmann equation is studied in this paper. It is shown that the Green's function has a decomposition of the macroscopic diffusive waves and Huygens waves with the speed a2+b2 at low-frequency, the singular kinetic wave and the remainder term decaying exponentially in space and time. In addition, we establish the pointwise space-time estimate of the global solution to the nonlinear relativistic Boltzmann equation with non-smooth initial data based on the Green's function.

Exact solutions of the nonlinear space-time fractional Schamel equation

This study focuses on the nonlinear space-time behavior of a plasma system made up of electrons, positive ions, and negative ions using the fractional Schamel (FS) equation. The main goal is to find exact solutions to the nonlinear FS equation by applying the extended hyperbolic function (EHF) method. The study examines how the fractional order affects the phase velocity, amplitude, and wave width of solitary wave solutions. Different exact solutions were found based on various values of the fractional order. Graphical representations are included to show the physical properties of these solutions. Overall, the results demonstrate that the EHF method is effective and reliable for finding exact solutions to the nonlinear FS equation.

Quantum nature of spacetime near the black hole singularity

The concept of spacetime loses its usual interpretation at the essential singularity of a black hole. In consequence, all laws of physics must fail at this classical singularity. This unphysical behavior of spacetime at the singularity originates from general relativity. In order to have a consistent description of spacetime, this singularity must disappear in a quantum mechanical description of spacetime which is expected to be given by a quantum theory of gravity. In this paper, we therefore attempt to describe the quantum nature of spacetime in the vicinity of the (classical) singularity of a black hole. We take the Kantowsi–Sachs representation for the interior spacetime of a black hole and include inevitable vacuum fluctuations of matter field in the Klein–Gordon representation. Hence we obtain the Wheeler–DeWitt equation for the black hole interior and solve this equation exactly yielding a general expression for the interior wave function of the black hole. Admissible wave functions consistent with the DeWitt boundary condition implies that the Hilbert space has three nonoverlapping sectors distinguished by the relative character of the eigenvalues. Regular quantum black holes with admissible and well-behaved wave function having no singularity can exist only in two of those sectors. However, the remaining sector does not contain any regular quantum black hole.

Quasi periodic oscillations around Kerr-type black hole in the Starobinsky–Bel–Robinson theory of gravity

In this study of Kerr-type black hole within the Starobinsky–Bel–Robinson gravity, we unveil intriguing dynamics. We observe that the black hole spin weakens the effective potential, while the stringy parameter β of the Starobinsky–Bel–Robinson gravity, strengthens it, notably near the black hole. We further see that the deviations from the Kerr paradigm affect Innermost Stable Circular Orbit (ISCO) and Outermost Stable Circular Orbit (OSCO) regions. Moreover, the fundamental frequencies reveal the dominance of the β parameter near the black hole. Our analysis provides valuable insights into the possible black hole mass and β parameter for GRO J1655-40, XTE J1550-564, XTE J1859+226, GRS 1915+105 and H1743-322 under the Starobinsky–Bel–Robinson gravity, highlighting the role of quasi periodic oscillations behavior and black hole spin in defining these constraints. These findings have significant implications, highlighting the potential of the parameter β to rival or surpass the influence of the spin of the black hole, offering new insights into the behavior of black hole and spacetime beyond General Relativity.

Relations between Newtonian and Relativistic Cosmology

We start with the cosmic Friedmann equations, where we adopt a novel perspective rooted in a Lagrangian formulation, grounded in Newtonian mechanics and the first law of thermodynamics. Our investigation operates under the assumption that the universe is populated by either a perfect fluid or a scalar field. By elucidating the intricate interplay between the Lagrangian formulation and the cosmic Friedmann equations, we uncover the fundamental principles governing the universe’s dynamics within the framework of these elemental constituents. In our concluding endeavor, we embark on the task of harmonizing the classical equations—namely, the conservation, Euler, and Poisson equations—with the principles of General Relativity. This undertaking seeks to extend these foundational equations to encompass the gravitational effects delineated by General Relativity, thus providing a comprehensive framework for understanding the behavior of matter and spacetime in the cosmic context.

Phygital time geography, or: what about technology in tourists’ space-time behaviour?

The paper argues for the renewed relevance of time geography in tourism in light of the use of mobile technologies and ubiquitous connectivity. The paper proposes the concept of phygitality to understand how digital technologies are used in physical space, and how the interaction between the physical and the digital reconfigures tourists’ projects, paths, bundles, and constraints. The theoretical contribution builds on fifteen semi-structured interviews. The analysis shows that capability, coupling, and authority constraints are altered and mediated by digital devices. In the phygital time-space, tourists orient themselves in physical spaces, influenced by digital information; they create phygital paths and move between stations that result from the overlaying of digital information onto the physical space. Tourists’ goal-oriented mobility results in phygital projects, where logics of efficiency and optimization reduce the liminality of the tourist experience. Tourists’ bundles are created within and outside the physical vacation prism through digital communication.

A basic analysis of accelerating and anthropotropic chemical models in several modified theories of gravitation

Email: manishiitbhu87@gmail.com Abstract - Anisotropic and spatially homogenous cosmological models are important tools for explaining the universe's large-scale characteristics. Bianchi space-times have a uniform spatial structure and are globally hyperbolic. On the one hand, the asymptotic behaviour of the most rigid Bianchi space-time (Bianchi I and II space time) is straightforward and well-defined. Nonetheless, the asymptotic behaviour of generic Bianchi space time (Bianchi VIll and IX space-time) is considered to remain chaotic and oscillatory at their initial singularity over an extended period of time. Numerous hoovers Bianchi VIll and IX space-times display extraordinarily complicated aceillatory behaviour around their original singularity; even little changes to such a space-time's initial Cauchy data produce a significant shift in its asymptotic behaviour. Bianchi space-times are asymptotically silent, defying Misner's notion. Bianchi spaces l X are critical for modelling spatially homogeneous and anisotropic cosmologies. Dirac was the first to propose the idea of a variable gravitational constant G in the framework of relativity. Lau proposed changes to relate the G and A variants within the framework of general relativity. Because a variation in the A equations is technically followed by a variation in G, the significance of the change allows us to continue using Einstein's field without modification.

Space-time behavior of the compressible Navier-Stokes equations with hyperbolic heat conduction

We consider compressible Navier-Stokes equations with hyperbolic heat conduction in R3. A space-time description of the classical solution is given when the initial perturbation is suitable small. The result implies that all of the unknowns obey the generalized Huygens’ principle as the classical compressible Navier-Stokes equations in Liu and Wang [Commun. Math. Phys. 196, 145–173 (1998)]. Additionally, we show that the decay of the flux q is faster than the other unknowns.

Space-time behavior for radiative hydrodynamics model with or without heat conduction

We consider space-time behaviors of smooth solutions for the radiative hydrodynamics system with or without heat conduction in the whole space \(R^3\) by using Green's function method. This result exhibits the generalized Huygens' principle as the classical compressible Navier-Stokes equations [3,26], which is different from the Hamer model for radiating gases in [36].
 For more information see https://ejde.math.txstate.edu/Volumes/2023/60/abstr.html

Physics-informed neural networks (PINNs) for 4D hemodynamics prediction: An investigation of optimal framework based on vascular morphology

Hemodynamic parameters are of great significance in the clinical diagnosis and treatment of cardiovascular diseases. However, noninvasive, real-time and accurate acquisition of hemodynamics remains a challenge for current invasive detection and simulation algorithms. Here, we integrate computational fluid dynamics with our customized analysis framework based on a multi-attribute point cloud dataset and physics-informed neural networks (PINNs)-aided deep learning modules. This combination is implemented by our workflow that generates flow field datasets within two types of patient personalized models - aorta with fine coronary branches and abdominal aorta. Deep learning modules with or without an antecedent hierarchical structure model the flow field development and complete the mapping from spatial and temporal dimensions to 4D hemodynamics. 88,000 cases on 4 randomized partitions in 16 controlled trials reveal the hemodynamic landscape of spatio-temporal anisotropy within two types of personalized models, which demonstrates the effectiveness of PINN in predicting the space-time behavior of flow fields and gives the optimal deep learning framework for different blood vessels in terms of balancing the training cost and accuracy dimensions. The proposed framework shows intentional performance in computational cost, accuracy and visualization compared to currently prevalent methods, and has the potential for generalization to model flow fields and corresponding clinical metrics within vessels at different locations. We expect our framework to push the 4D hemodynamic predictions to the real-time level, and in statistically significant fashion, applicable to morphologically variable vessels.

Pore-scale model of freezing inception in a porous medium

The article describes a new model of water–ice phase transition in pores of a saturated porous medium. The model takes into account the difference in specific volume between ice and water which causes structural changes in the porous medium. Describing details of heat, phase, and structure dynamics, the model contributes to a deeper understanding of phenomena in upper soil layers subjected to either seasonal conditions or climate changes. Governing multi-physics system of equations includes the conservation of mass, momentum and energy at the pore level and includes the anisotropic Allen–Cahn equation for tracking the position of ice during nucleation and growth inside the pores. The model provides space–time behavior of key quantities and describes the interaction of growing ice with pore geometry and surrounding grains. The governing system of equations is solved by the finite-element method to provide several qualitative computational studies of the ice growth inside a porous structure.

Application of Computer Big Data Modeling Based on Lagrangian Mathematical Equation in the Village Cultural Industry Model

Abstract To understand the Lagrangian mathematical equation, the author proposes an application study of big data modeling in the village cultural industry model. The author takes 20 traditional villages in Beijing as the object, and through crawling relevant Internet cultural and tourism big data, using the theory of tourism consumer behavior, from the aspects of consumer motivation behavior, food, housing, shopping, and other experience behavior, consumer evaluation behavior, and consumer space-time behavior, carry out targeted content analysis, aggregation analysis, etc, fully reveal the behavioral portrait of tourists in Beijing’s traditional villages. The results show that the overall tourism experience of Beijing’s traditional villages is good, but the development level is quite different, the cultural and tourism supply pattern of “some have boutiques, some have highlights, and the overall influence is weak” is presented to improve the overall level. At the same time, the computer big data based on tourists’ feedback can reasonably reveal the inherent characteristics and problems of traditional village tourism, which is innovative in the current situation where village tourism data is difficult to obtain.

Experimental investigation of turbulent counter-rotating Taylor–Couette flows for radius ratio η = 0.1

Turbulent Taylor–Couette flow between two concentric independently rotating cylinders with a radius ratio of $\eta = 0.1$ is studied experimentally. While the scope is to study the counter-rotating cases between both cylinders, the radial and azimuthal velocity components are recorded at different horizontal planes with high-speed particle image velocimetry. The parametric study considered a set of different shear Reynolds numbers in the range of $20\,000 \leq Re_s \leq 1.31 \times 10^5$ , with different rotation ratios of $-0.06 \leq \mu \leq +0.008$ . The observed flow fields had a clear dependence on the rotation ratio, where flow patterns evolved with a more pronounced axial dependence. The angular momentum transport is computed as a result of the recorded flow fields and given by a quasi-Nusselt number. The dependence of the Nusselt number on the different rotation ratios shows a maximum for the low counter-rotating case and $\mu _{max}$ is found between $-0.011 < \mu _{max} < -0.0077$ . The Nusselt number decreases for stronger counter-rotation until a minimum is reached, where it tends to increase again for higher counter-rotation rates. The space–time behaviour of the turbulent flow showed the existence of patterns propagating from the inner region towards the outer region for all studied counter-rotating cases. In addition, patterns have been found that tend to propagate from the outer region towards the inner region with a novel character at high counter-rotation cases. These patterns enhance the angular momentum transport where a second maximum in the transport mechanism has to be expected.

Backpackers' Order and Visit Length in an Urban World Heritage Destination: an Analysis Using Ordered Logit and Linear Models

Described as a group of independent travelers with flexible itineraries and without substantial time constraints, backpackers constitute one of the tourist segments that has drawn the attention of many researchers around the world. However, little is known about how this segment of travelers behaves in destinations from a space–time perspective. The purpose of this study is to examine the relevance of the order and visit length on backpackers' space–time behavior in an urban world heritage destination. Using geographic information system (GIS) software, the sequence and the length of the visit were identified. To analyze the order of the places visited, we used the ordered logit method and to study the duration dimension a multivariate equation, estimated by OLS with heteroskedasticity robust errors, was selected. The results showed that no variable in particular influences the order of the places visited in any of the parishes simultaneously, reinforcing the underlying randomness in relation to the order in which destination parishes are visited. Length of stay is mostly influenced by factors related to mobility conditions as well as factors exogenous to tourists' decision-making capacity.

Pointwise space-time estimates of compressible Oldroyd-B model

In this paper, we investigate pointwise space-time behavior of the compressible Oldroyd-B model in R3 based on Green's function method. We first give the representations of two Green's matrices in the Fourier space: one is a 7×7 matrix for the compressible part and the other is a 6×6 matrix for the incompressible part. Then by using high-medium-low frequency analysis together with real analysis and Fourier analysis we get the pointwise estimates for each entry in these Green's matrices. Finally, we deal with the nonlinear problem and obtain the pointwise space-time description of the solution. It shows that the fluid density ρ, momentum m and the symmetric tensor of constrains T obey the generalized Huygens' principle as the compressible Navier-Stokes equations. As a byproduct, we extend L2-estimate in [47] to Lp-estimate with p>1. Moreover, the decay of T is faster than those of (ρ,m), which also refine the result in [47].

Geometrization of string cloud spacetime in general relativity

<abstract><p>The purpose of the article is to analyze the behavior of spacetime using a string cloud energy-momentum tensor $ \mathcal{T} $ having string cloud fluid density $ \rho $ and string tension $ \lambda $, named <italic>relativistic string cloud spacetime</italic>. We obtain some results for string cloud spacetime with a divergence-free matter tensor and a diminishing space matter tensor. Next, we discuss some curvature characteristics, such as conformally flat, Ricci semi-symmetric and pseudo-Ricci-symmetric, for relativistic string cloud spacetime. In addition, we gain a condition that coincides with the equation of state for the cloud of geometric strings in Ricci semi-symmetric string cloud spacetime.</p></abstract>

Green's function and pointwise behaviors of the one-dimensional modified Vlasov-Poisson-Boltzmann system

The pointwise space-time behaviors of the Green's function and the global solution to the modified Vlasov- Poisson-Boltzmann (mVPB) system in one-dimensional space are studied in this paper. It is shown that, the Green's function admits the diffusion wave, the Huygens's type sound wave, the singular kinetic wave and the remainder term decaying exponentially in space-time. These behaviors are similar to the Boltzmann equation (Liu and Yu in Comm. Pure Appl. Math. 57: 1543-1608, 2004). Furthermore, we establish the pointwise space-time nonlinear diffusive behaviors of the global solution to the nonlinear mVPB system in terms of the Green's function.

Pointwise space–time estimates for compressible Navier–Stokes equations for a reacting mixture

AbstractIn this paper, we consider the pointwise space–time behaviors of solutions for the dynamic combustion of compressible reactive mixture. The pointwise estimates of global solutions are established in the whole space by using the Green's function method. These estimates also show the wave propagation of the solution. As a by‐product, the ‐norm decay rates of the solution are achieved.

Green’s Function and the Pointwise Behaviors of the Vlasov-Poisson-Fokker-Planck System

The pointwise space-time behaviors of the Green’s function and the global solution to the Vlasov-Poisson-Fokker-Planck (VPFP) system in three dimensional space are studied in this paper. It is shown that the Green’s function consists of the diffusion waves decaying exponentially in time but algebraically in space, and the singular kinetic waves which become smooth for all (t, x, v) when t > 0. Furthermore, we establish the pointwise space-time behaviors of the global solution to the nonlinear VPFP system when the initial data is not necessarily smooth in terms of the Green’s function.