Weak Limit Research Articles

Synsedimentary Compaction of Peat Under the Load of Alluvial System Sediments in the Most Basin (Czech Republic, Lower Miocene): From Weak Compaction to Strong Local Deformation of Clastics and Peat

Alluvial systems affected by peat layer compaction of a variable degree are studied all over the world, especially in areas of large river deltas and coastal plains. Ordinarily studied Holocene peat accumulations do not reach thicknesses of more than 6–10 m. This paper documents four ancient alluvial systems affected by peat compaction during the Lower Miocene in large exposures of open-cast lignite mines within the Most Basin, Czech Republic. Field observations and the study of 3000 borehole sections showed a clear dependence of the thickness and composition of the underlying peat on the scale of the accommodation space for loading by younger alluvial sediments. If the underlying partly compacted peat was tens to hundreds of meters in thickness, significant deformations of the peat appeared during its loading, leading up to the formation of growth faults. In such cases, missing parts of the coal seams were also observed below the alluvial systems. Especially borehole data showed that a linear correlation exists between the thickness of the alluvial sediments and the maximum instantaneous available compaction capacity of the underlying peat.

Deflection angle and quasi-periodic oscillations of extended gravitational decoupled black hole solution

Abstract In weak field limits, we compute the deflection angle of gravitational decoupling extended black hole Solution black hole solution. We obtained the Gaussian optical curvature by examining the null geodesic equations with the help of Gauss–Bonnet theorem. We also looked into the deflection angle of light by black hole in weak field limits with the use of the Gibbons Werner method. We verify the graphical behaviour of the black hole after determining the deflection angle of light. Additionally, in the presence of the plasma medium, we also determine the deflection angle of the light and examine the graphical behaviour. Further, we compute the Einstein ring via gravitational decoupling extended black hole solution. We also compute the quasi-periodic oscillations and discuss their graphical behaviour.

Investigating the weak gravitational lensing in Starobinsky–Bel–Robinson gravity black hole

This paper is motivated to study the weak gravitational lensing of the black hole in the context of Starobinsky–Bel–Robinsion gravity. We deduce the deflection angle of light in the weak field limits. For this purpose, we find the Gaussian curvature and apply the Gauss–Bonnet theorem. We also investigate the deflection angle at which light is deflected by a plasma medium. Furthermore, we analyze the graphical behavior of the deflection angle in the framework of SBR gravity. We also calculate the energy extracted from the black hole in SBR gravity, Einstein ring, and lens equation in the non-plasma and plasma framework. We conclude this study with a discussion of how light beams behave when they approach such a four-dimensional black hole by calculating the deflection angle.

Interaction-Driven Instabilities in the Random-Field XXZ Chain.

Despite enormous efforts devoted to the study of the many-body localization (MBL) phenomenon, the nature of the high-energy behavior of the Heisenberg spin chain in a strong random magnetic field is lacking consensus. Here, we take a step back by exploring the weak interaction limit starting from the Anderson localized (AL) insulator. Through shift-invert diagonalization, we find that, below a certain disorder threshold h^{*}, weak interactions necessarily lead to an ergodic instability, whereas at strong disorder the AL insulator directly turns into MBL, in agreement with a simple interpretation of the avalanche theory for restoration of ergodicity. We further map the phase diagram for the generic XXZ model in the disorder h-interaction Δ plane. Taking advantage of the total magnetization conservation, our results unveil the remarkable behavior of the spin-spin correlation functions: in the regime indicated as MBL by standard observables, their exponential decay undergoes an inversion of orientation ξ_{z}>ξ_{x}. We find that the longitudinal length ξ_{z} is a key quantity for capturing ergodic instabilities, as it increases with system size near the thermal phase, in sharp contrast to its transverse counterpart.

Composition operators on the algebra of Dirichlet series

The algebra of Dirichlet series A(C+)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {A}({{\\mathbb {C}}}_+)$$\\end{document} consists on those Dirichlet series convergent in the right half-plane C+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathbb {C}}}_+$$\\end{document} and which are also uniformly continuous there. This algebra was recently introduced by Aron, Bayart, Gauthier, Maestre, and Nestoridis. We describe the symbols Φ:C+→C+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Phi :{{\\mathbb {C}}}_+\\rightarrow {{\\mathbb {C}}}_+$$\\end{document} giving rise to bounded composition operators CΦ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C_{\\Phi }$$\\end{document} in A(C+)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {A}({{\\mathbb {C}}}_+)$$\\end{document} and denote this class by GA\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {G}_{\\mathcal {A}}$$\\end{document}. We also characterise when the operator CΦ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C_{\\Phi }$$\\end{document} is compact in A(C+)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {A}({{\\mathbb {C}}}_+)$$\\end{document}. As a byproduct, we show that the weak compactness is equivalent to the compactness for CΦ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C_{\\Phi }$$\\end{document}. Next, the closure under the local uniform convergence of several classes of symbols of composition operators in Banach spaces of Dirichlet series is discussed. We also establish a one-to-one correspondence between continuous semigroups of analytic functions {Φt}\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\{\\Phi _t\\}$$\\end{document} in the class GA\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {G}_{\\mathcal {A}}$$\\end{document} and strongly continuous semigroups of composition operators {Tt}\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\{T_t\\}$$\\end{document}, Ttf=f∘Φt\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_tf=f\\circ \\Phi _t$$\\end{document}, f∈A(C+)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f\\in \\mathcal {A}({{\\mathbb {C}}}_+)$$\\end{document}. We conclude providing examples showing the differences between the symbols of bounded composition operators in A(C+)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {A}({{\\mathbb {C}}}_+)$$\\end{document} and the Hardy spaces of Dirichlet series Hp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {H}^p$$\\end{document} and H∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {H}^{\\infty }$$\\end{document}.

Effects of non-commutative geometry on black hole properties

In this study, we investigate the signatures of a non-commutative black hole solution. Initially, we calculate the thermodynamic properties of the system, including entropy, heat capacity, and Hawking radiation. For the latter quantity, we employ two distinct methods: surface gravity and the topological approach. Additionally, we examine the emission rate and remnant mass within this context. Remarkably, the lifetime of the black hole, after reaching its final state due to the evaporation process, is expressed analytically up to a grey-body factor. We estimate the lifetime for specific initial and final mass configurations. Also, we analyze the tensorial quasinormal modes using the 6th-order WKB method. Finally, we study the deflection angle, i.e., gravitational lensing, in both the weak and strong deflection limits.

On the Convergence of the Drainage Network with Branching

The Drainage Network is a system of coalescing random walks, exhibiting long-range dependence before coalescence, introduced by Gangopadhyay, Roy, and Sarkar [14]. Coletti, Fontes, and Dias [5] proved its convergence to the Brownian Web under diffusive scaling. In this work, we introduce a perturbation of the system allowing branching of the random walks with low probabilities varying with the scaling parameter. When the branching probability is inversely proportional to the scaling parameter, we show that this drainage network with branching consists of a tight family such that any weak limit point contains a Brownian Net. We conjecture that the limit is indeed the Brownian Net.

The de Broglie-Einstein-Rosen gravitational wave

de Broglie gravitational waves are solutions of the linearized Einstein's field equations in vacuum, with intriguing properties. They are axially symmetric and have an effective mass, which is responsible for longitudinal effects that are absent in standard gravity waves. Moreover, they represent a classical realization of a form of dynamics proposed for quantum particles by de Broglie one hundred years ago. In this paper we will show that this perturbation field can be obtained, apart from a proportionality constant, in the weak field limit of a particular Einstein-Rosen field, which we call the de Broglie-Einstein-Rosen wave. Some properties of this exact solution are also discussed.

Thermal fluctuations, deflection angle, and greybody factor of a high-dimensional Schwarzschild black hole in scalar–tensor–vector gravity

In this study, we examined the thermal fluctuations, deflection angle, and greybody factor of a high-dimensional Schwarzschild black hole in scalar–tensor–vector gravity (STVG). We calculated some thermodynamic quantities related to the correction of the black hole entropy caused by thermal fluctuations and discussed the effect of the correction parameters on these quantities. By analyzing the changes in the corrected specific heat, we found that thermal fluctuations made the small black hole more stable. It is worth noting that the STVG parameter did not affect the thermodynamic stability of this black hole. Additionally, by utilizing the Gauss–Bonnet theorem, the deflection angle was obtained in the weak field limit, and the effects of the two parameters on the results were visualized. Finally, we calculated the bounds on the greybody factor of a massless scalar field. We observed that as the STVG parameter around the black hole increased, the weak deflection angle became larger, and more scalar particles can reach infinity. However, the spacetime dimension has the opposite effect on the STVG parameter on the weak deflection angle and greybody factor.

Fluctuation-dissipation theorem and entanglement dynamics in one-dimensional low-density Jaynes-Cummings Hubbard model after a quench.

In one-dimensional low-density Jaynes-Cummings Hubbard (JCH) models [Phys. Rev. E 106, 064107 (2022)2470-004510.1103/PhysRevE.106.064107], we proved that the eigenstate thermalization hypothesis (ETH) is valid when the tunneling strength and coupling strength are of the same order. Surprisingly, at the weak tunneling limit, we observed that the entanglement entropy and scaling law of kinetic energy operators also exhibit obvious quantum chaotic properties, this is an unexpected result. To substantiate these findings, we further discuss their nonequilibrium dynamics in this paper. Our analysis reveals that when the model is a weak tunneling limit after the quench and the initial state is an equilibrium state of chaos, the system reaches an equilibrium state. This observation supports the conclusion that the low-density JCH model at the weak tunneling limit is nonintegrable, corroborating our previous results [Phys. Rev. E 106, 064107 (2022)2470-004510.1103/PhysRevE.106.064107]. Additionally, by discussing the validity of the fluctuation-dissipation theorem (FDT) and the evolution behavior of entanglement entropy and fidelity, we numerically demonstrate the differences between the one-dimensional low-density JCH model and general nonintegrable systems. Specifically, in the low-density JCH model, when the Hamiltonian after the quench is integrable, the validity of FDT depends on the thermal behavior of the initial Hamiltonian, and a metastable state is observed during the evolution of entanglement entropy. Our research presents an an intriguing and unique nonintegrable model, enriching the current understanding of nonintegrable systems.

Geodesics structure and deflection angle of electrically charged black holes in gravity with a background Kalb–Ramond field

This article investigates the geodesic structure and deflection angle of charged black holes in the presence of a nonzero vacuum expectation value background of the Kalb–Ramond field. Topics explored include null and timelike geodesics, energy extraction by collisions, and the motion of charged particles. The photon sphere radius is calculated and plotted to examine the effects of both the black hole charge (Q) and the Lorentz-violating parameter (b) on null geodesics. The effective potential for timelike geodesics is analyzed, and second-order analytical orbits are derived. We further show that the combined effects of Lorentz-violating parameter and electric charge can mimic a Kerr black hole spin parameter up to its maximum values, i.e., a/M∼1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a/M \\sim 1$$\\end{document} thus suggesting that the current precision of measurements of highly spinning black hole candidates may not rule out the effect of Lorentz-violating parameter. The center of mass energy of colliding particles is also considered, demonstrating a decrease with increasing Lorentz-violating parameter. Circular orbiting particles of charged particles are discovered, with the minimum radius for a stable circular orbit decreasing as both b and Q increase. Results show that this circular orbit is particularly sensitive to changes in the Lorentz-violating parameter. Additionally, a timelike particle trajectory is demonstrated as a consequence of the combined effects of parameters b and Q. Finally, the light deflection angle is analyzed using the weak field limit approach to determine the Lorentz-breaking effect, employing the Gauss–Bonnet theorem for computation. Findings are visualized with appropriate plots and thoroughly discussed.

Probing the weak limit of magnetocrystalline anisotropy through a spin‒flop transition in the van der Waals antiferromagnet CrPS4

The influence of magnetocrystalline anisotropy (MCA) on antiferromagnetism is elucidated through the characterization of the spin‒flop transition. However, due to a lack of suitable candidates for investigation, a detailed understanding of the preservation of the spin‒flop transition in the presence of low MCA energy remains elusive. In this study, we introduce CrPS4, which is a two-dimensional van der Waals antiferromagnet, as an ideal system to explore the exceedingly weak limit of the thermally-evolved MCA energy. By employing a uniaxially anisotropic spin model and fitting it to the experimental magnetic properties, we quantify the MCA energy and identify the discernible spin configurations in different magnetic phases. Notably, even at the limit of extremely weak MCA, with a mere 0.12% of the interlayer antiferromagnetic exchange interaction at T = 33 K, which is slightly below the Néel temperature (TN) of 38 K, the spin‒flop transition remains intact. We further establish a direct correlation between the visualized spin arrangements and the progressive reversal of magnetic torque induced by rotating magnetic fields. This analysis reveals the essential role of MCA in antiferromagnetism, thus extending our understanding to previously undetected limits and providing valuable insights for the development of spin-processing functionalities based on van der Waals magnets.

A relativistic scalar model for fractional interaction between dark matter and gravity

Abstract In a series of recent papers we put forward a “fractional gravity”
framework striking an intermediate course between a modified gravity theory and an
exotic dark matter (DM) scenario, which envisages the DM component in virialized
halos to feel a non-local interaction mediated by gravity. The remarkable success
of this model in reproducing several aspects of DM phenomenology motivates us to
look for a general relativistic extension. Specifically, we propose a theory, dubbed
Relativistic Scalar Fractional Gravity or RSFG, in which the trace of the DM stressenergy tensor couples to the scalar curvature via a non-local operator constructed with
a fractional power of the d’Alembertian. We derive the field equations starting from
an action principle, and then we investigate their weak field limit, demonstrating that
in the Newtonian approximation the fractional gravity setup of our previous works is
recovered. We compute the first-order post-Newtonian parameter γ and its relation
with weak lensing, showing that although in RSFG the former deviates from its GR
values of unity, the latter is unaffected. We also perform a standard scalar-vectortensor-decomposition of RSFG in the weak field limit, to highlight that gravitational
waves propagate at the speed of light, though also an additional scalar mode becomes
dynamical. Finally, we derive the modified conservation laws of the DM stress energy
tensor in RSFG, showing that a new non-local force emerges, and hence that the DM
fluid deviates from the geodesic solutions of the field equations.

A generalized Dean–Kawasaki equation for an interacting Brownian gas in a partially absorbing medium

The Dean–Kawasaki (DK) equation is a stochastic partial differential equation (SPDE) for the global density ρ = N − 1 ∑ j = 1 N δ ( x − X j ( t ) ) of a gas of N over-damped Brownian particles, where X j ( t ) is the position of the j th particle. In the thermodynamic limit N → ∞ with weak pairwise interactions, the expectation ⟨ ρ ⟩ with respect to the white noise processes converges in distribution to the solution of a McKean–Vlasov (MV) equation. In this article, we use an encounter-based approach to derive a generalized DK equation for an interacting Brownian gas on the half-line with a partially absorbing boundary at x = 0 . Each particle is independently absorbed when its local time L j ( t ) at x = 0 exceeds a random threshold ℓ ^ j . The global density is now summed over the set of particles that have not yet been absorbed, and expectations are taken with respect to the Gaussian noise and the random thresholds ℓ ^ j . Assuming the DK equation has a well-defined mean-field limit, we derive the corresponding MV equation on the half-line. We illustrate the theory by (i) analysing stationary solutions for a Curie–Weiss (quadratic) interaction potential and a totally reflecting boundary; and (ii) calculating the effective rate of particle loss in the weak absorption limit. Extensions to finite intervals and partially absorbing traps are also considered.

Convergence of power sequences of operators via their stability

This paper is concerned with the convergence of power sequences and stability of Hilbert space operators, where “convergence” and “stability” are considered with respect to weak, strong and norm topologies. It is proved that an operator has a convergent power sequence if and only if it is a (not necessarily orthogonal) direct sum of an identity operator and a stable operator. This reduces the issue of convergence of the power sequence of an operator T to the study of stability of T. The question of when the limit of the power sequence is an orthogonal projection is investigated. Among operators sharing this property are hyponormal and contractive ones. In particular, a hyponormal or a contractive operator with no identity part is stable if and only if its power sequence is convergent. In turn, a unitary operator has a weakly convergent power sequence if and only if its singular-continuous part is weakly stable and its singular-discrete part is the identity. Characterizations of the convergence of power sequences and stability of subnormal operators are given in terms of semispectral measures.

Delta shock wave for ternary nonlinear chromatography equations as self-similar viscosity limit

In this paper, we investigate the existence and stability of the delta shock wave in ternary chromatography equations by the self-similar viscosity vanishing approach. Considering the appropriate initial values, we prove the existence of the self-similar solution for the corresponding Riemann problem of the ternary chromatography viscous equations. Furthermore, we rigorously demonstrate that the delta shock wave is the weak star limit of the self-similar solution as viscosity tends to disappear. The result implies that the structure of the delta shock wave is stable under the self-similar viscosity perturbation, which guarantees that the delta shock wave is a unique entropy solution. In addition, we present numerical simulations in agreement with the theoretical analysis.

Meridional circulation streamlined

Time-dependent meridional circulation and differential rotation in radiative zones are central open issues in stellar evolution theory. We streamline this challenging problem using the “downward control principle” of atmospheric science, under a geostrophic f-plane approximation. We recover the known stellar physics result that the steady-state meridional circulation decays on the length scale proportional to N / f × Pr , assuming molecular viscosity is the dominant drag mechanism. Prior to steady-state, the meridional circulation and the zonal wind (= differential rotation) spread together via radiative diffusion, under thermal wind balance. The corresponding (fourth-order) hyperdiffusion process is reasonably well approximated by regular (second-order) diffusion on scales of order a pressure scale-height. We derive an inhomogeneous diffusion (equiv. advection-diffusion) equation for the zonal flow which admits closed-form time-dependent solutions in a finite depth domain, allowing for rapid prototyping of differential rotation profiles. In the weak drag limit, we find that the time to rotational steady-state can be longer than the Eddington-Sweet time and be instead determined by the longer drag time. Unless strong enough drag operates, the internal rotation of main-sequence stars may thus never reach a steady-state. Streamlined meridional circulation solutions provide leading-order internal rotation profiles for studying the role of fluid/MHD instabilities (or waves) in redistributing angular momentum in the radiative zones of stars. Despite clear geometrical limitations and simplifying assumptions, one might expect our thin-layer geostrophic approach to offer qualitatively useful results to understand deep meridional circulation in stars.

GUP corrected black holes with cloud of string

We investigate shadows, deflection angle, quasinormal modes (QNMs), and sparsity of Hawking radiation of the Schwarzschild string cloud black hole’s solution after applying quantum corrections required by the Generalised Uncertainty Principle (GUP). First, we explore the shadow’s behaviour in the presence of a string cloud using three alternative GUP frameworks: linear quadratic GUP (LQGUP), quadratic GUP (QGUP), and linear GUP. We then used the weak field limit approach to determine the effect of the string cloud and GUP parameters on the light deflection angle, with computation based on the Gauss–Bonnet theorem. Next, to compute the quasinormal modes of Schwarzschild string clouds incorporating quantum correction with GUP, we determine the effective potentials generated by perturbing scalar, electromagnetic and fermionic fields, using the sixth-order WKB approach in conjunction with the appropriate numerical analysis. Our investigation indicates that string and linear GUP parameters have distinct and different effects on QNMs. We find that the greybody factor increases due to the presence of string cloud while the linear GUP parameter shows the opposite. We then examine the radiation spectrum and sparsity in the GUP corrected black hole with the cloud of string framework, which provides additional information about the thermal radiation released by black holes. Finally, our inquiries reveal that the influence of the string parameter and the quadratic GUP parameter on various astrophysical observables is comparable, however the impact of the linear GUP parameter is opposite.

Enhanced Approaches to Gravitational Lensing: A Regular Charged Black Hole in Weak Field Limit

Gravitational lensing, an integral aspect of general relativity, profoundly impacts our understanding of black holes (BH’s). The presence of a centered singularity resulting from gravitational collapse is a fundamental characteristic of a BH Nonetheless, the exploitation of non-linear electrodynamics (NLED) divulges the emphatic concept of non-singularity. Our analysis primarily focuses on calculating the deflection angle in the weak field approximation, deliberately excluding the original spacetime configuration. The photon’s effective geometry is typically linked to NLED. Instead, a photon traverses an effective null geodesic that aligns with the geometry of a regular metric. The findings reveal an additional term in the deflection angle compared to the Reissner-Nordström (RN) metric, evidenced by a shifted positional displacement of the tertiary image associated with a regular BH This study succinctly encapsulates these findings, positioning them within the extensive terminology ambient to BH’s singularity and GL, thus edifying the scientific memoir with precise astrophysical insights.

Weak shock compaction on granular salt

This study conducted integrated experiments and computational modeling to investigate the speeds of a developing shock within granular salt and analyzed the effect of various impact velocities up to 245 m/s. Experiments were conducted on table salt utilizing a novel setup with a considerable bore length for the sample, enabling visualization of a moving shock wave. Experimental analysis using particle image velocimetry enabled the characterization of shock velocity and particle velocity histories. Mesoscale simulations further enabled advanced analysis of the shock wave’s substructure. In simulations, the shock front’s precursor was shown to have a heterogeneous nature, which is usually modeled as uniform in continuum analyses. The presence of force chains results in a spread out of the shock precursor over a greater ramp distance. With increasing impact velocity, the shock front thickness reduces, and the precursor of the shock front becomes less heterogeneous. Furthermore, mesoscale modeling suggests the formation of force chains behind the shock front, even under the conditions of weak shock. This study presents novel mesoscale simulation results on salt corroborated with data from experiments, thereby characterizing the compaction front speeds in the weak shock regime.