Scalar Energy Research Articles

Scalar field solutions and energy bounds for modeling spatial oscillations in Schwarzschild black holes based on the Regge–Wheeler equation

This text discusses the behavior of solutions and the energy stability within Schwarzschild spacetimes, with a particular emphasis on the behavior of massless scalar fields under the influence of a non-rotating and spherically symmetric black hole. The stability of solutions in the proximity of the event horizon of black holes in general relativity remains an open question, especially given the difficulties introduced by minor perturbations that may resemble Kerr solutions. To address this, this work explores a simplified model, including massless scalar fields, to better understand perturbation behaviors around black holes under the Schwarzschild approach. We depart from Richard Price’s work in connection with how scalar, electromagnetic, and gravitational fields behave. The tortoise coordinate transformation is considered to set the stage for numerical solutions to the wave equations. Afterward, we explore energy estimates, which are used to gauge stability and wave behavior over time. Our analysis reveals that the time evolution of the energy does not exceed twice its initial value. Further and under the assumption of initial conditions in L2−spaces, we obtain an exponential decreasing behavior in the energy time evolution. A question to continue exploring is how perturbations in L2 in the initial conditions that introduce Kerr solutions as a second-order effect in the linearized equations perturb this obtained exponential decay.

Resummation of local and non-local scalar self energies via the Schwinger–Dyson equation in de Sitter spacetime

Resummation of local and non-local scalar self energies via the Schwinger–Dyson equation in de Sitter spacetime

On The Determination Of Conditional Statistics Along Gradient Trajectories At The Turbulent/Non-Turbulent Interface Of Jet Flows.

Conditional sampling and averaging are valuable techniques for discerning and quantifying notable regions within turbulent flows. These methods have been particularly prevalent in experimental and numerical investigations of turbulent shear flows. Conditional statistics effectively analyze the dynamics and characteristics of turbulent flows, offering insights into transitional behaviors and distinct features within these regimes. This approach is instrumental in studying turbulent shear flows, such as jets or mixing layers, where a well-defined zone separates the turbulent core from the non-turbulent surrounding fluid. This zone, known as the Turbulent/Non-Turbulent Interface (TNTI), plays a crucial role in various phenomenological changes, including the transfer of mass, momentum, and scalar fluxes. While statistics in jet flows are often reported along the radial direction for a given downstream position, this method can obscure the underlying physical processes. Scalar dissipation rate, transport, or turbulent kinetic energy involve velocity or concentration gradients at the flow interface. To date, the impact of sampling direction on conditional statistics within jet flows has not yet been thoroughly discussed. This study focuses on determining gradient trajectories at the interface of turbulent flows. Gradient trajectories have been used to explore structures in turbulent flows, proving effective in analyzing homogeneous shear turbulence. This study introduces a methodology for sampling conditional data by computing gradient trajectories intersecting the TNTI. The primary objective is to verify whether sampling statistics along the gradient of scalar concentration provide a more detailed understanding of the processes occurring near the TNTI. The methodology involves computing a field of gradient trajectories from concentration fields obtained through Planar Laser-Induced Fluorescence (PLIF) in a N2/N2 jet with Re = 2900. Conditional statistics at the TNTI of a jet flow along the gradient trajectory for a given downstream position are calculated and reported. The paper aims to compare conditional statistics along gradient trajectories with those obtained along radial and normal directions at the TNTI. It is expected that gradient trajectory statistics align more closely with normal direction statistics near the interface and diverge as it gets into the jet or coflow fluid.

Suggestions of decreasing dark energy from supernova and BAO data

The potential energy from a time-dependent scalar field provides a possible explanation for the observed cosmic acceleration. In this paper, we investigate how data from supernova and bary acoustic oscillation surveys constrain the possible evolution of a single scalar field over the period of time (roughly half the age of the universe) for which these data are available. Taking a linear approximation to the scalar potential V(ϕ) = V 0 + V 1 ϕ around the present value, a likelihood analysis appears to significantly prefer models with a decreasing potential energy at present, with approximately 99.99 % of the exp(-χ 2/2) distribution having V 1 > 0 in a convention where ϕ̇ ≤ 0 at present. The models favoured by the distribution typically have an order one decrease 〈|Range[V(ϕ(t))]/V(t 0)|〉 ≈ 0.36 in the scalar potential energy over the time frame corresponding to z < 2. According to the likelihood analysis, the ΛCDM model with no variation in dark energy appears to be significantly disfavoured in the context of the linear potential model, but this should be interpreted cautiously since model selection criteria that make use of Δχ 2 while ignoring parameter space volumes still favour ΛCDM. Working with a second order approximation to the potential, the supernova data can be fit well for a wide range of possible potentials, including models where the universe has already stopped accelerating.

Relativistic massive and massless scalar fields bound to the Bumblebee gravity's black hole

In this letter, we examine massive and massless scalar quasibound states bound in the static spherically symmetric black hole solution of the Einstein-Bumblebee space-time. We start with constructing the governing relativistic fields' dynamical equation, i.e. the Klein-Gordon equation, component by component. With the help of the ansatz of separation of variables, we find the exact solution of the angular part in terms of Spherical Harmonics while the radial exact solution is discovered in terms of the Confluent Heun function. The quantization of the quasibound state is done by applying the polynomial condition of the Confluent Heun function that reveals a complex-valued energy levels expression for the case of massive scalar, where the real part is the scalar particle's energy and the imaginary part represents the quasibound state's decay. And for a massless scalar, a pure imaginary energy levels is obtained. The quasibound states, thus, describe decaying relativistic states bound in the black hole's gravitational potential well. At the end, we investigate the Hawking radiation of the static Bumblebee black hole's horizon by deriving and investigating the radiation distribution function.

Dynamical system analysis of scalar field cosmology in coincident f(Q) gravity

In this article, we investigate scalar field cosmology in the coincident f(Q) gravity formalism. We calculate the motion equations of f(Q) gravity under the flat Friedmann-Lemaître-Robertson-Walker background in the presence of a scalar field. We consider a non-linear f(Q) model, particularly f(Q) = − Q + α Q n , which is nothing but a polynomial correction to the Symmetric Teleparallel Equivalent to General Relativity (STEGR) case. Further, we assumed two well-known specific forms of the potential function, specifically the exponential from V(ϕ) = V 0 e −β ϕ and the power-law form V(ϕ) = V 0 ϕ −k . We employ some phase-space variables and transform the cosmological field equations into an autonomous system. We calculate the critical points of the corresponding autonomous systems and examine their stability behaviors. We discuss the physical significance corresponding to the exponential case for parameter values n = 2 and n = − 1 with β = 1, and n = − 1 with β=3 . Moreover, we discuss the same corresponding to the power-law case for the parameter value n = − 2 and k = 0.16. We also analyze the behavior of corresponding cosmological parameters such as scalar field and dark energy density, deceleration, and the effective equation of state parameter. Corresponding to the exponential case, we find that the results obtained for the parameter constraints in Case III is better among all three cases, and that represents the evolution of the Universe from a decelerated stiff era to an accelerated de-Sitter era via matter-dominated epoch. Further, in the power-law case, we find that all trajectories exhibit identical behavior, representing the evolution of the Universe from a decelerated stiff era to an accelerated de-Sitter era. Lastly, we conclude that the exponential case shows better evolution as compared to the power-law case.

Direct measurement of the inertial-convective subrange above ocean surface waves

The −5/3 power law over the inertial subrange of the turbulence kinetic energy spectrum is one of the most well-known concepts in fluid physics. Obukhov and Corrsin extended the original hypothesis to a passive tracer, leading to the concept of an inertial-convective subrange. These postulates have been empirically validated in the atmospheric turbulence over land but have not been comprehensively studied in the marine air flow. During a recent oceanic campaign, the platform FLIP was deployed with an array of sensors to measure the perturbation wind velocity, temperature, and water vapor. Using these data, a previous study found that Kolmogorov's hypothesized −5/3 was not universally valid over the ocean. Here, we continue that work to analyze the spectrum of temperature and water vapor to empirically evaluate the theoretical extension by Obukhov-Corrsin. For temperature, the observed spectra were too noisy for thorough analysis; our conjecture for the source of noise and its implications for near-surface observations of atmospheric turbulence are discussed. For water vapor, we found strong agreement with the previous analysis of the kinetic energy spectrum. These findings corroborate (1) the theoretical notion of the scalar energy dissipation subrange driven by the inertial motions in the marine boundary layer and (2) evidence for non-Kolmogorov turbulence in the high Reynolds flow immediately above ocean waves. Our analysis shows a strong relationship with distance from the wavy surface; using linear extrapolation, we find that divergence from −5/3 persists in the lowest 25 m of the atmosphere.

Grain boundary segregation predicted by quantum-accurate segregation spectra but not by classical models

In alloys, solute segregation at grain boundaries is classically attributed to three driving forces: a high solution enthalpy, a high size mismatch, and a high difference in interfacial energy. These effects are generally cast into a single scalar segregation energy and used to predict grain boundary solute enrichment or depletion. This approach neglects the physics of segregation at many competing grain boundary sites, and can also miss electronic effects that are energetically significant to the problem. In this paper, we demonstrate that such driving forces cannot explain, nor thus predict, segregation in some alloys. Using quantum-accurate segregation spectra that have recently become available for some polycrystalline alloys, we predict strong segregation for gold in aluminum, a solvent-solute combination that does not conform to classical driving forces. Our experiments confirm these predictions and reveal gold enrichment at grain boundaries that is two orders of magnitude over the bulk lattice solute concentration.

Stability and moduli space of generalized Ricci solitons

The generalized Einstein–Hilbert action is an extension of the classic scalar curvature energy and Perelman’s F-functional which incorporates a closed three-form. The critical points are known as generalized Ricci solitons, which arise naturally in mathematical physics, complex geometry, and generalized geometry. Through a delicate analysis of the group of generalized gauge transformations, and implementing a novel connection, we give a simple formula for the second variation of this energy which generalizes the Lichnerowicz operator in the Einstein case. As an application we show that all Bismut-flat manifolds are linearly stable critical points, and admit nontrivial deformations arising from Lie theory. Furthermore, this leads to extensions of classic results of Koiso [1–4] and Podesta, Spiro, Kröncke [5–8] to the moduli space of generalized Ricci solitons. To finish we classify deformations of the Bismut-flat structure on S3 and show that some are integrable while others are not.

Exact analytical quasibound states of a scalar particle around a Reissner-Nordström black hole

In this paper, we investigate behavior of massive and massless scalar particle around a static spherically symmetric charged black hole—so called Reissner-Nordström black hole in 3+1 dimension. We successfully discover a novel exact analytical quasibound states' wave functions and energy levels by solving the covariant Klein-Gordon wave equation. The quasibound state has complex-valued energy E=ER+iEI where the real part ER can be interpreted as the scalar particle's energy while the imaginary part represents the decay. We also discuss the Hawking radiation from the apparent horizon of Reissner-Nordström black hole which can be calculated using the scalar particle's wave function. In principle, this study could provide the possibility for laboratory testing of effects whose nature is absolutely related with quantum effects in gravity.

Simultaneous measurements of kinetic and scalar energy spectrum time evolution in the Richtmyer–Meshkov instability upon reshock

The Richtmyer–Meshkov instability (Richtmyer, Commun. Pure Appl. Maths, vol. 13, issue 2, 1960, pp. 297–319; Meshkov, Fluid Dyn., vol. 4, issue 5, 1972, pp. 101–104) of a twice-shocked gas interface is studied using both high spatial resolution single-shot (SS) and lower spatial resolution, time-resolved, high-speed (HS) simultaneous planar laser-induced fluorescence and particle image velocimetry in the Wisconsin Shock Tube Laboratory's vertical shock tube. The initial condition (IC) is a shear layer with broadband diffuse perturbations at the interface between a helium–acetone mixture and argon. This IC is accelerated by a shock of nominal strength Mach number $M = 1.75$ , and then accelerated again by the transmitted shock that reflects off the end wall of the tube. An ensemble of experiments is analysed after reshock while the interface mixing width grows linearly with time. The kinetic and scalar energy spectra and the terms of their evolution equation are calculated and compared between SS and HS experiments. The inertial range scaling of the scalar power spectrum is found to follow Gibson's relation (Gibson, Phys. Fluids, vol. 11, issue 11, 1968, pp. 2316–2327) as a function of Schmidt number when the effective turbulent Schmidt number is used in place of the material Schmidt number that controls equilibrium scaling. Further, the spatially integrated scalar flux follows similar behaviour observed for the kinetic energy in large eddy simulation studies by Zeng et al. (Phys. Fluids, vol. 30, issue 6, 2018, 064106) while the spatially varying scalar flux exhibits back scatter along the centre of the mixing layer and forward energy transfer in the spike and bubble regions.

Starting inflation from inhomogeneous initial conditions with momentum

We investigate the circumstances under which cosmic inflation can arise from very inhomogeneous initial conditions using numerical relativity simulations. Previous studies have not considered cases with non-zero momentum density due to technical challenges with solving the coupled Einstein constraint equations. Here we address these, introducing and comparing several different ways of constructing cosmological initial conditions with inhomogeneous scalar field and time derivative profiles. We evolve such initial conditions with large inhomogeneities in both single- and two-field inflationary models. We study cases where the initial gradient and kinetic energy are much larger than the inflationary energy scale, and black holes can form, as well as cases where the initial scalar potential energy is comparable, as in scenarios where inflation occurs at nearly Planckian densities, finding large-field inflation to be generally robust. We consider examples of initial conditions where a large scalar field velocity towards non-inflationary values would prevent inflation from occurring in the homogeneous case, finding that the addition of large gradients in the scalar field can actually dilute this effect, with the increased expansion and non-vanishing restoring force leading to inflation.

Hydrodynamic pressure and effective mixing length in vegetated free-flow region

Submerged vegetation acts as large-scale roughness element that changes flow structure and promotes flow subdivision, thereby affecting scalar transport and energy transfer in the river. This article explores vertical distributions of both the hydrodynamic pressure P D and effective mixing length L in vegetated free- flow region through flume experiments. Firstly, formulas have been proposed in the present study to calculate the P D and L values by some theoretical analyses. Then, we discuss the P D and L profiles under different vegetation density λ, submergence degree H/h v and mean bulk velocity U m conditions. The P D value is positive and attains its vertical maximum around the middle position of this region, indicating that shear turbulence promotes the upwards release of the hydro pressure. The vertical variation coefficient for P D is nearly 1.15 and independent of λ and U m in this study. The dimensionless L value varies little in the lower part of this region and increases linearly upwards in the upper part, reflecting vertical variation of shear turbulence movement. Since the vegetation density λ and submergence H/h v control turbulence coherent motion, the P D and L/(h o - h v) values change monotonically with them in this study. The high-velocity flow accelerates turbulence waves and promotes an increase in P D.

Predictability of passive scalar dispersion in atmospheric surface layers with urban‐like roughness: A large‐eddy simulations study

AbstractThe predictability of passive scalar dispersion is of both theoretical interest and practical importance, for example for high‐resolution numerical weather prediction and air quality modeling. However, the implications for the numerical modeling of urban areas remain relatively unexplored. Using obstacle‐resolving large‐eddy simulations (LES), we conducted twin experiments, with and without a velocity perturbation, to investigate how the presence of urban roughness affects error growth in streamwise velocity (u) and passive scalar (θ) fields, as well as the differences between error evolutions in u and θ fields. The predictability limit is characterized using the signal‐to‐noise ratio (SNR) as a continuous metric to indicate when error reaches saturation. The presence of urban roughness decreases of the passive scalar by around 20% compared to cases without them. The error statistics of θ indicate that urban roughness‐induced flow structures and different scalar source locations affect the scalar dispersion and relative fluctuations, which subsequently dictate the evolution of the SNR. Analysis of the passive scalar error energy (ϵθ2) budget indicates that the contributions from advective transport by the velocity and velocity error dominate. The error energy spectra of both u and θ exhibit a −5/3 slope in flat‐wall cases, but not in the presence of urban roughness, thereby highlighting the deviation from the assumption of locally isotropic turbulence. This study reveals that urban roughness can decrease the predictability of the passive scalar and destroy the similarity between the error statistics of the velocity and the passive scalar.

Rotation in vacuum and scalar background: Are there alternatives to Newman–Janis algorithm?

The Newman–Janis (NJ) algorithm is the standard approach to rotation in general relativity which, in vacuum, builds the Kerr metric from the Schwarzschild spacetime. Recently, we have shown that the same algorithm applied to the Papapetrou antiscalar spacetime produces a rotational metric devoid of horizons and ergospheres. Though exact in the scalar sector, this metric, however, satisfies the Einstein equations only asymptotically. We argue that this discrepancy between geometric and matter parts (essential only inside gravitational radius scale) is caused by the violation of the Hawking–Ellis energy conditions for the scalar energy–momentum tensor. The axial potential functions entering the metrics appear to be of the same form both in vacuum and scalar background, and they also coincide with the linearized Yang–Mills field, which might hint at their common nongravitational origin. As an alternative to the Kerr-type spacetimes produced by NJ algorithm we suggest the exact solution obtained by local rotational coordinate transformation from the Schwarzschild spacetime. Then, comparison with the Kerr-type metrics shows that the Lense–Thirring phenomenon might be treated as a coordinate effect, similar to the Coriolis force.

Analytic solutions of scalar field cosmology, mathematical structures for early inflation and late time accelerated expansion

We study the most general cosmological model with real scalar field which is minimally coupled to gravity. Our calculations are based on Friedmann–Lemaitre–Robertson–Walker (FLRW) background metric. Field equations consist of three differential equations. We switch independent variable from time to scale factor by change of variable {dot{a}}/a=H(a). Thus a new set of differential equations are analytically solvable with known methods. We formulate Hubble function, the scalar field, potential and energy density when one of them is given in the most general form. a(t) can be explicitly found as long as methods of integration techniques are available. We investigate the dynamics of the universe at early times as well as at late times in light of these formulas. We find mathematical machinery which turns on and turns off early accelerated expansion. On the other hand late time accelerated expansion is explained by cosmic domain walls. We have compared our results with recent observations of type Ia supernovae by considering the Hubble tension and absolute magnitude tension. Eighty-nine percent of present universe may consist of domain walls while rest is matter.

Dimensional regularization in quantum field theory with ultraviolet cutoff

In view of various field-theoretic reasons, in the present work, we study the question of if the usual dimensional regularization can be extended to quantum field theories with an ultraviolet cutoff (Poincare-breaking scale) in a way preserving all the properties of the dimensional regularization. And we find that it can indeed be. The resulting extension gives a framework in which the power-law and logarithmic divergences get detached to involve different scales. This new regularization scheme, the detached regularization as we call it, enables one to treat the power-law and logarithmic divergences differently and independently. We apply the detached regularization to the computation of the vacuum energy and to two well-known QFTs namely the scalar and spinor electrodynamics. As a case study, we consider Fujikawa's subtractive renormalization in the framework of the detached regularization, and show its effectiveness up to two loops by specializing to scalar self energy. We discuss various application areas of the detached regularization.

Dark Matter Searches with Top Quarks

Collider signatures with top quarks provide sensitive probes of dark matter (DM) production at the Large Hadron Collider (LHC). In this article, we review the results of DM searches in final states with top quarks conducted by the ATLAS and CMS Collaborations at the LHC, including the most recent results on the full LHC Run 2 dataset. We highlight the complementarity of DM searches in final states with top quarks with searches in other final states in the framework of various simplified models of DM. A reinterpretation of a DM search with top quarks in the context of an effective field theory description of scalar dark energy is also discussed. Finally, we give an outlook on the potential of DM searches with top quarks in LHC Run 3, at the high-luminosity LHC, and possible future colliders. In this context, we highlight new benchmark models that could be probed by existing and future searches as well as those that predict still-uncovered signatures of anomalous top-quark production and decays at the LHC.

Proposal of two parameters to evaluate in-situ apparent toughness of interphase in fiber reinforced ceramic matrix composites: Three-dimensional finite element simulations

Interphase structure characters such as single-layer interfacial thickness or number of multilayers may have a great influence on mechanical properties of continuous fibers reinforced ceramic matrix composites (CFRCMCs). However, the determination of the optimal interphase is still unclear for the complex microstructures of CFRCMCs. In this study, a novel Finite Element Method (FEM) -based numerical method considering mean scalar stiffness degradation and mean damage dissipation energy are proposed to quantitatively assess the effect of above structure characters on in-situ toughness of interphase. The proposed method has successfully applied on single pyrolytic carbon (PyC) layer and alternating silicon carbide/pyrolytic carbon (SiC-PyC) n multilayer systems. The results suggest that thicker PyC interphase will prone cause brittle fracture with lower toughness, whilst more layers with the same total thickness will improve fracture toughness for (SiC-PyC) n system. On the contrary, more layers with the same sublayer thickness will decrease in situ apparent fracture toughness. The proposed method explains well the previous contradictory experimental observations.

Loop correction to the scalar Casimir energy density and generation of topological mass due to a helix boundary condition in a scenario with Lorentz violation

In this paper, the effective potential approach in quantum field theory is used in order to investigate self-interaction loop correction to the Casimir energy density and generation of topological mass for both massless and massive real scalar fields. It is assumed that the scalar field obeys a helix boundary condition. In addition, it is also considered a CPT-even aether-type violation of the Lorentz symmetry. In the absence of the Lorentz violation, we obtain analytical expressions for the loop correction to the Casimir energy density and to the mass of the scalar field. The same expressions are also obtained assuming the Lorentz violation in each of the spacetime directions. We also show some graphs that exhibit how the loop correction and the Lorentz violation affect the Casimir energy density and the mass of the scalar field.