Late-time Solutions Research Articles

A pulse-decay method for low (matrix) permeability analyses of granular rock media

Abstract. Nanodarcy level permeability measurements of porous media, such as nano-porous mudrocks, are frequently conducted with gas invasion methods into granular-sized samples with short diffusion lengths and thereby reduced experimental duration; however, these methods lack rigorous solutions and standardized experimental procedures. For the first time, we resolve this by providing an integrated technique (termed gas permeability technique, GPT) with coupled theoretical development, experimental procedures, and data interpretation workflow. Three exact mathematical solutions for transient and slightly compressible spherical flow, along with their asymptotic solutions, are developed for early- and late-time responses. Critically, one late-time solution is for an ultra-small gas-invadable volume, important for a wide range of practical usages. Developed to be applicable to different sample characteristics (permeability, porosity, and mass) in relation to the storage capacity of experimental systems, these three solutions are evaluated from essential considerations of error difference between exact and approximate solutions, optimal experimental conditions, and experimental demonstration of mudrocks and molecular-sieve samples. Moreover, a practical workflow of solution selection and data reduction to determine permeability is presented by considering samples with different permeability and porosity under various granular sizes. Overall, this work establishes a rigorous, theory-based, rapid, and versatile gas permeability measurement technique for tight media at sub-nanodarcy levels.

Three-dimensional buoyant hydraulic fractures: finite-volume release

In impermeable media, a hydraulic fracture can continue expanding even without additional fluid injection if its volume exceeds the limiting volume of a hydrostatically loaded radial fracture. This limit depends on the mechanical properties of the surrounding solid and the density contrast between the fluid and the solid. We show that two dimensionless numbers characterize self-sustained fracture growth. The first is a buoyancy factor that compares the total released volume to the volume of a hydrostatically loaded radial fracture to determine whether buoyant growth occurs. The second number is the dimensionless viscosity of a radial fracture when buoyant effects become of order one. Notably, this dimensionless viscosity depends on the rate at which the fluid volume is released, indicating that both the total volume and release history impact self-sustained buoyant growth. We identify six well-defined propagation histories based on these two dimensionless numbers. Their growth evolves between distinct limiting regimes of radial and buoyant propagation, resulting in different fracture shapes. Notably, our findings reveal two growth rates depending on the dominant energy dissipation mechanism (viscous flow versus fracture creation) in the fracture head. For finite values of material toughness, the toughness-dominated limit represents a late-time solution for all fractures in growth rate and head shape (possibly reached only at a very late time). The viscosity-dominated limit can appear at intermediate times. Our three-dimensional simulations confirm the predicted scalings. This contribution highlights the importance of the entire propagation and release history for accurate analysis of buoyant hydraulic fractures.

Effective dark energy through spin-gravity coupling

We investigate cosmological scenarios with spin-gravity coupling. In particular, due to the spin of the baryonic and dark matter particles and its coupling to gravity, they probe an effective spin-dependent metric, which can be calculated semi-classically in the Mathisson-Papapetrou-Tulczyjew-Dixon formalism. Hence, the usual field equations give rise to modified Friedmann equations, in which the extra terms can be identified as an effective dark-energy sector. Additionally, we obtain an effective interaction between the matter and dark-energy sectors. In the case where the spin-gravity coupling switches off, we recover standard ΛCDM cosmology. We perform a dynamical system analysis and we find a matter-dominated point that can describe the matter era, and a stable late-time solution corresponding to acceleration and dark-energy domination. For small values of the spin coupling parameter, deviations from ΛCDM concordance scenario are small, however for larger values they can be brought to the desired amount, leading to different dark-energy equation-of-state parameter behavior, as well as to different transition redshift from acceleration to deceleration. Finally, we confront the model predictions with Hubble function data.

The radial slump of a gravity current in a confined porous layer

The flow of a gravity current widely occurs in many geophysical, environmental and industrial processes. We focus on the overlooked process of radial slump of a gravity current in confined porous layers, which is related to the post-injection flow dynamics of many subsurface displacement processes, initiated by fluid injection through vertical wells. Specifically, we describe the time evolution of the interface shape and location of the propagating front, governed by a second-order nonlinear partial differential equation (PDE). By solving a nonlinear eigenvalue problem, we identify a self-similar solution to describe the dynamics of confined flows at early times, when the interface attaches to both the top and bottom boundaries of the porous layer. As time progresses, the flow gradually becomes unconfined, as gravity-driven slump causes the interface to detach from one boundary; the interface evolution at late times is then described by a self-similar solution of a nonlinear diffusion equation. Time transition from the early-time confined towards late-time unconfined self-similar solutions is also verified by comparing the self-similar solutions and numerical solutions of the governing PDE for both the interface shape and the frontal location. Interestingly, two special vertical locations have also been identified where the best agreement appears between the PDE numerical solutions and the early-time self-similar solutions for the interface shape, which is a novel feature of the radial flow, and the degree of agreement is not impacted by the time evolution.

Dynamical analysis of logarithmic energy–momentum squared gravity

We perform the dynamical system analysis of a cosmological model in the energy–momentum squared gravity (EMSG) of the form f ( T μ ν T μ ν ) = α ln ( λ T μ ν T μ ν ) , which is known as energy–momentum log gravity (EMLG). In particular, we show that the analytical cosmological solution of EMLG presented by Akarsu et al. (Eur. Phys. J. C 79:846, 2019) is a future attractor. It includes new terms in the right-hand side of the Einstein field equations, which yield constant inertial mass density and provide a dynamical dark energy with a density passing below zero at large redshifts, accommodating a mechanism for screening Λ in the past for α < 0 , suggested for alleviating some cosmological tensions. We show that the second law of thermodynamics requires α ≤ 0 that allows the screening mechanism to take place. We also show that the model gives rise to an entire class of new stable late-time solutions with H → ( Λ + 2 α ) / 3 as a → ∞ , where the new term is due to the constant effective inertial mass density that arises from EMLG contribution of dust, whereas H → Λ / 3 as a → ∞ in the Λ CDM model. We also show the existence of new interesting features and trajectories that are absent in Λ CDM with or without spatial curvature.

Qualitative study of Lyra cosmologies with spatial curvature

We investigate the spatially curved Friedmann–Robertson–Walker space–time with Lyra geometry model. The cosmological solutions are studied by using dynamical system methodology to explore the universe evolution in the model. The constructed autonomous system has been explored to extract the physically viable cosmological solutions by studying the behavior of eigenvalues at the fixed points of the system. Late-time attractor solution corresponding to the accelerated expansion exist in the model and thus, the model may explain the late-time accelerating expansion of universe. The model is also composed of deceleration to acceleration transition with Λ cold dark matter evolution at late-times. The evolution of cosmological parameters like deceleration parameter , effective equation of state parameter, total matter density and role of energy conditions with scale factor have been studied along with statefinder diagnostic to explain the universe evolution in the model. By dynamical system analysis, it has been observed that the displacement field plays a dominant role during the early times and, the universe is dominated by stiff matter like component. Implications of bouncing behavior in the model with role of energy conditions and continuity equation have been discussed in detail along with their physical consequences. • Lyra geometry model with FRW metric having spatial curvature is investigated. • Dynamical system method has been used to extract the cosmic dynamics of model. • The model explains late-time accelerating evolution of universe. • Cosmological parameters are studied by integrating the dynamical variables. • We illustrate that the fixed point corresponding to radiation phase is absent.

No-go guide for late-time solutions to the Hubble tension: Matter perturbations

The Hubble tension seems to be a crisis with $\sim5\sigma$ discrepancy between the most recent local distance ladder measurement from type Ia supernovae calibrated by Cepheids and the global fitting constraint from the cosmic microwave background data. To narrow down the possible late-time solutions to the Hubble tension, we have used in a recent study [Phys. Rev. D 105, L021301 (2022)] an improved inverse distance ladder method calibrated by the absolute measurements of the Hubble expansion rate at high redshifts from the cosmic chronometer data, and found no appealing evidence for new physics at the late time beyond the $\Lambda$CDM model characterized by a parametrization based on the cosmic age. In this paper, we further investigate the perspective of this improved inverse distance ladder method by including the late-time matter perturbation growth data. Independent of the dataset choices, model parametrizations, and diagnostic quantities ($S_8$ and $S_{12}$), the new physics at the late time beyond the $\Lambda$CDM model is strongly disfavored so that the previous late-time no-go guide for the Hubble tension is further strengthened.

Kaniadakis-holographic dark energy: observational constraints and global dynamics

ABSTRACT We investigate Kaniadakis-holographic dark energy by confronting it with observations. We perform a Markov Chain Monte Carlo analysis using cosmic chronometers, supernovae type Ia, and Baryon Acoustic Oscillations data. Concerning the Kaniadakis parameter, we find that it is constrained around zero, namely around the value in which Kaniadakis entropy recovers standard Bekenstein-Hawking one. Additionally, for the present matter density parameter $\Omega _m^{(0)}$, we obtain a value slightly smaller compared to ΛCDM scenario. Furthermore, we reconstruct the evolution of the Hubble, deceleration, and jerk parameters extracting the deceleration-acceleration transition redshift as $z_T = 0.86^{+0.21}_{-0.14}$. Finally, performing a detailed local and global dynamical system analysis, we find that the past attractor of the Universe is the matter-dominated solution, while the late-time stable solution is the dark-energy-dominated one.

No-go guide for the Hubble tension: Late-time solutions

The Hubble tension, if not caused by any systematics, could be relieved or even resolved from modifying either the early-time or late-time Universe. The early-time modifications are usually in tension with either galaxy clustering or galaxy lensing constraints. The late-time modifications are also in conflict with the constraint from the inverse distance ladder, which, however, is weakened by the dependence on a sound-horizon prior and some particular approximation for the late-time expansion history. To achieve a more general no-go argument for the late-time scenarios, we propose to use a global parametrizationbased on the cosmic age (PAge) to consistently use the cosmic chronometers data beyond the Taylor expansion domain and without the input of a sound-horizon prior. Both the early-time and late-time scenarios are therefore largely ruled out, indicating the possible ways out of the Hubble tension from either exotic modifications of our concordance Universe or some unaccounted systematics.

Modeling of early- and late-time countercurrent spontaneous imbibition in porous media: A semi-analytical approach

Countercurrent spontaneous imbibition (SI) is an important flow mechanism to recover oil in water-wet porous media through capillarity. Experimental imbibition tests conducted in core samples show that oil recovery as a function of time occurs in a characteristic S-shaped curve, which describes the infinite-acting and the boundary-dominated regime. Although several dimensionless time groups have been proposed to model countercurrent SI in porous media, they fail to properly scale the results, causing inaccurate estimates of oil recovery. In this work, we present a new approach, using a hybrid solution, to model countercurrent SI for oil-water systems dominated by capillary forces. The infinite-acting regime is modeled by an early-time solution using a new dimensionless time group, which enables the correct scaling of imbibition results onto a universal single curve. To model the boundary-dominated regime, we introduce a late-time solution derived as a function of a characteristic distribution of saturation to estimate the flow behavior after the imbibing fluid reaches the no-flow boundary. The novelty of the model is that it enables the accurate estimation of fluid imbibition under the boundary-dominated regime, a flow condition critical to evaluate the true potential of countercurrent SI driven by capillarity for oil recovery in porous media. We verified the model against numerical simulations under a wide range of flow conditions relevant in water-oil systems, and used experimental data reported in the literature to validate our model. The solution presented provides an accurate approach to model countercurrent SI, which could be extended for dynamic conditions and the modeling of the flow of fluids in fractured media.

\U0001d4a9-field cosmology in hyperbolic field space: stability and general solutions

We study the dynamics of a cosmological model with a perfect fluid and \U0001d4a9 fields on a hyperbolic field space interacting via a symmetric potential. We list all late-time solutions, investigate their stability and briefly discuss predictions of the theory. Moreover, for the case of two scalar fields and an exponential potential we prove that the field equations are Liouville integrable and we provide for the first time the general solution for a region of the parameter space.

Strong-coupling dynamics and entanglement in de Sitter space

We use holography to study the dynamics of a strongly-coupled gauge theory in four-dimensional de Sitter space with Hubble rate H. The gauge theory is non-conformal with a characteristic mass scale M. We solve Einstein’s equations numerically and determine the time evolution of homogeneous gauge theory states. If their initial energy density is high compared with H4 then the early-time evolution is well described by viscous hydrodynamics with a non-zero bulk viscosity. At late times the dynamics is always far from equilibrium. The asymptotic late-time state preserves the full de Sitter symmetry group and its dual geometry is a domain-wall in AdS5. The approach to this state is characterised by an emergent relation of the form mathcal{P} = w ℰ that is different from the equilibrium equation of state in flat space. The constant w does not depend on the initial conditions but only on H/M and is negative if the ratio H/M is close to unity. The event and the apparent horizons of the late-time solution do not coincide with one another, reflecting its non-equilibrium nature. In between them lies an “entanglement horizon” that cannot be penetrated by extremal surfaces anchored at the boundary, which we use to compute the entanglement entropy of boundary regions. If the entangling region equals the observable universe then the extremal surface coincides with a bulk cosmological horizon that just touches the event horizon, while for larger regions the extremal surface probes behind the event horizon.

Five-dimensional Brans–Dicke compactified universe dominated by a varying speed of light

We extend the model of a 5D Brans–Dicke gravity theory reduced to 4D through the presence of a hypersurface-orthogonal space-like killing vector field in the underlying 5D spacetime by including a varying speed of light. The resulting model is characterized by the presence of two scalar fields. We focus on late-time power law solutions which emerge in general when scalar fields couple to spacetime curvature and do not contradict the SNIa astrophysical data. Analytic solutions in 4-dimensions are derived and late-time accelerated expansion was found. The universe is dominated by dark energy, free from phantom field and is characterized by a decaying energy matter density, decaying scalar fields, and a decreasing celerity of light. The model is confronted with astrophysical observations and is found to fit these data.

A radial differential pressure decay method with micro-plug samples for determining the apparent permeability of shale matrix

We propose a radial differential pressure decay (RDPD) method to measure the apparent permeability in shale matrix. The experimental design extends the upper limit of pressure in conventional methods. The experimental error caused by the dispersiveness of sample size and the irregularity of particle shape is reduced by utilizing precisely prepared micro-plug samples with highly uniform diameters, and the reliability of the result is improved substantially. The late-time approximate solution for cylindrical samples based on the experimental configuration is presented for data interpretation and verified with the numerical simulation. The experiments based on shale matrix samples are demonstrated. The results reveal that the RDPD method can capture a differential pressure decay curve precisely, which can be closely fitted through the late-time solution. It also has great potential for various tight porous media. This method sets the stage for the accurate investigation of gas transport mechanisms in tight porous media in future work.

A stable finite-difference time-domain scheme for local time-stepping on an adaptive mesh

Physical effects driven by strong electromagnetic fields often occur in regions of highly localized fields on a scattering object. Unfortunately, the most common numerical technique for simulating time-domain electromagnetics, known as Finite-Difference Time-Domain (FDTD), is ill-equipped to handle such problems. A common solution to capture physics across many spatial scales is to use an adaptive mesh, which resolves temporal or spatial features exactly when and where they are needed, avoiding extra computation in space-time regions where it is unnecessary. We present a minimal modification to the FDTD algorithm that allows for a stable late-time solution to Maxwell's equations on an adaptive mesh with a Courant-Friedrichs-Levy limit of 5/6. An emphasis is placed on creating a simple, flexible, and easy to understand algorithm. The algorithm is implemented in 1D, 2D and 3D for geometries which are dynamic or possess large disparities in spatial or temporal scales. An example is presented which demonstrates the use of the algorithm in a resonant dielectric disc with a small slot.

The role of natural fractures of finite double-porosity aquifers on diffusive leakage of brine during geological storage of CO2

The diffusive leakage rate (DLR) of brine from a finite fractured aquifer into intact overlying and underlying layers during geosequestration of carbon dioxide is modeled using a two-dimensional radial domain. To handle the interaction between aquifer and caprock or overlying layer (underlying layer), continuities of pressures and fluid fluxes are taken into account at the aquifer-caprock interface. In order to solve this problem, Laplace transform and finite Hankel transform are adopted. The early-time and late-time solutions for DLR of brine from a double-porosity aquifer are also examined using the developed general solution. The solutions are used to analyze DLR from the fractured aquifer into overlying formation and the average pressures in the fractured aquifer and the caprock during injection and post injection periods. Variations of DLR and the average pressures in the fractured aquifer and the caprock with the double-porosity parameters are characterized. It is shown that DLR of brine and the average pressures in the aquifer and the caprock are sensitive to double-porosity parameters during CO2 injection when ratio of the horizontal fracture to the caprock permeabilities (kfh1D) is small. However, they remain practically insensitive to double-porosity parameters for a large kfh1D. The results also confirm that DLR of brine reaches to a fixed pseudo-steady state value at late times during CO2 injection. In addition, the post injection DLR for low to moderate values of kfh1D is found to be negligible while for high value of kfh1D DLR is more evident. These results find applications in geological storage of CO2 in fractured saline aquifers.

Effect of the chameleon scalar field on brane cosmological evolution

We have investigated a brane world model in which the gravitational field in the bulk is described both by a metric tensor and a minimally coupled scalar field. This scalar field is taken to be a chameleon with an appropriate potential function. The scalar field interacts with matter and there is an energy transfer between the two components. We find a late-time asymptotic solution which exhibits late-time accelerating expansion. We also show that the Universe recently crosses the phantom barrier without recourse to any exotic matter. We provide some thermodynamic arguments which constrain both the direction of energy transfer and dynamics of the extra dimension.

The asymptotic behavior of bouncing cosmological models in F(𝒢) gravity theory

We reconstruct [Formula: see text] gravity theory with an exponential scale factor to realize the bouncing behavior in the early universe and examine the asymptotic behavior of late-time solutions in this model. We propose an approach for the construction of asymptotic expansions of solutions of the Friedmann equations on the basis of Puiseux series.

Late-time cosmological evolution of a general class of f(mathsf{R},mathsf{T}) gravity with minimal curvature-matter coupling

In this work, we study the late-time cosmological solutions of f(mathsf{R},mathsf{T})=g(mathsf{R})+h(-mathsf{T}) models assuming that the conservation of the energy-momentum tensor (EMT) is violated. We perform our analysis through constructing an autonomous dynamical system for the equations of motion. We study the stability properties of solutions via considering linear perturbations about the related equilibrium points. Moreover, we parameterize the Lagrangian by introducing the parameters m(r) and n(s). These parameters which are constructed out of the functions g(mathsf{R}) and h(-mathsf{T}) play the main role in finding the late-time behavior of the solutions. We find that there exist, in general, three classes of solutions; all models with n>0 include a proper transition from a prolonged matter era to a de Sitter solution. Models with -0.5<n<0 and n'>1, for at least a root of equation n(s)=s-1, include an unphysical dark energy solution preceding an improper matter era. Finally, for n<-1/2 there is a transient accelerated expansion era with -1/2<w^mathrm{{(eff)}}<-1/3 before a de Sitter phase. For all cases, in order to have a long enough matter dominated epoch, the condition m'rightarrow 0^{+} for rlessapprox -1 must hold. We also show that models with a power law dependency i.e., f(mathsf{R},mathsf{T})=mathsf{R}^{beta }+(-mathsf{T})^{alpha } can be observationally motivating for mrightarrow 0^{+} and -0.024<alpha <0.02 and therefore could provide a suitable setting for later investigations.

Consequences of energy conservation violation: late time solutions of Lambda (mathsf{T}) mathsf{CDM} subclass of f(mathsf{R},mathsf{T}) gravity using dynamical system approach

Very recently, Josset and Perez (Phys. Rev. Lett. 118:021102, 2017) have shown that a violation of the energy-momentum tensor (EMT) could result in an accelerated expansion state via the appearance of an effective cosmological constant, in the context of unimodular gravity. Inspired by this outcome, in this paper we investigate cosmological consequences of a violation of the EMT conservation in a particular class of f(mathsf{R},mathsf{T}) gravity when only the pressure-less fluid is present. In this respect, we focus on the late time solutions of models of the type f(mathsf{R},mathsf{T})=mathsf{R}+beta Lambda (-mathsf{T}). As the first task, we study the solutions when the conservation of EMT is respected, and then we proceed with those in which violation occurs. We have found, provided that the EMT conservation is violated, that there generally exist two accelerated expansion solutions of which the stability properties depend on the underlying model. More exactly, we obtain a dark energy solution for which the effective equation of state depends on the model parameters and a de Sitter solution. We present a method to parametrize the Lambda (-mathsf{T}) function, which is useful in a dynamical system approach and has been employed in the model. Also, we discuss the cosmological solutions for models with Lambda (-mathsf{T})=8pi G(-mathsf{T})^{alpha } in the presence of ultra-relativistic matter.