Exterior Region Research Articles

Compact objects admitting Finch–Skea symmetry in [formula omitted] gravity

This paper investigates the viability and stability of anisotropic compact stars in the framework of f(R,T2) theory (R is the Ricci scalar and T2=TτυTτυ). In this perspective, we use Finch–Skea symmetry and consider different f(R,T2) models to examine physical characteristics of compact stars. We match interior spacetime with the exterior region to find the values of unknown constants. Further, we analyze the behavior of several physical quantities such as effective matter variables, energy bounds, anisotropic factor and equation of state parameters in the interior of Vela X-1, SAX J 1808.4-3658, Her X-1 and PSR J0348+0432 stars. The equilibrium state of these compact stars is examined through the Tolman–Oppenheimer–Volkoff equation and their stability is checked by causality condition, Herrera cracking approach and adiabatic index. It is found that all the required conditions are fulfilled for the considered models. We can conclude that more viable and stable compact stars are obtained in this modified theory.

The response mechanism of pressure fluctuation to the unsteady heat release in a strong rotating environment

The response mechanism of the pressure fluctuation to the unsteady heat release rate at the ‘unsteady’ combustion state in a strong rotating environment was investigated using a stratified vortex-tube combustor via a large eddy simulation method. Results show that the peak amplitude of heat release fluctuation at the ‘unsteady’ state is just 2.8 × 106 W/m3 and the peak amplitude of pressure fluctuation is always within 3000 Pa based on the vortex-tube configuration, indicating a weak fluctuation degree. The unsteady heat release does not bring about a higher momentum flux fluctuation due to quick momentum damping in the rotating reactive environment. The pressure fluctuation does not relate closely to the momentum flux and its fluctuation; this is due to the effect of the centrifugal force caused by rotating behavior. After splitting the momentum flux into the different components, we found that the tangential component acts in reverse to that of the radial and axial directions in the exterior region. Viz., the pressure increases when the tangential momentum flux increases in the exterior region but decreases when the radial and axial components increase. The laminarization of the fluid suppresses the fluctuations in the radial and axial directions only, therefore the uneven attenuation of the momentum flux fluctuation in different directions is the dominant cause of the enlarged pressure fluctuation in the ‘unsteady’ burning state. Moreover, we find that the pressure fluctuation degree is also closely related to the centrifugal weight coefficient. When this coefficient is far away from zero, the centrifugal effect will become obvious, and vice versa.

Traversable wormholes with double layer thin shells in quadratic gravity

In quadratic gravity, the junction conditions are six in number and permit the appearance of double layer thin shells. Double layers arise typically in theories with dipoles, i.e., two opposite charges, such as electromagnetic theories, and appear exceptionally in gravitational theories, which are theories with a single charge. We explore this property of the existence of double layers in quadratic gravity to find and study traversable wormholes in which the two domains of the wormhole interior region, where the throat is located, are matched to two vacuum domains of the exterior region via the use of two double layer thin shells. The quadratic gravity we use is essentially given by a R+alpha R^2 Lagrangian, where R is the Ricci scalar of the spacetime and alpha is a coupling constant, plus a matter Lagrangian. The null energy condition, or NEC for short, is tested for the whole wormhole spacetime. The analysis shows that the NEC is satisfied for the stress-energy tensor of the matter in the whole wormhole interior region, notably at the throat, and is satisfied for some of the stress–energy tensor components of the matter at the double layer thin shell, but is not satisfied for some other components, namely, the double layer stress–energy distribution component, at the thin shell. This seems to mean that the NEC is basically impossible, or at least very hard, to be satisfied when double layer thin shells are present. Single layer thin shells are also admitted within the theory, and we present thin shell traversable wormholes, i.e., wormholes without interior, with a single layer thin shell at the throat for which the corresponding stress–energy tensor satisfies the NEC, that are asymmetric, i.e., with two different vacuum domains of the exterior region joined at the wormhole throat.

Impact of cooling rate on mechanical properties and failure mechanism of sandstone under thermal–mechanical coupling effect

High geo-temperature is one of the inevitable geological disasters in deep engineering such as resource extraction, space development, and energy utilization. One of the key issues is to understand the mechanical properties and failure mechanism of high-temperature rock disturbed by low-temperature airflow after excavation. Therefore, the experimental and numerical investigation were carried out to study the impact of cooling rate on mechanical properties and failure mechanism of high temperature sandstone. First, uniaxial compression experiments of high temperature sandstone at different real-time cooling rates were carried out to study the mechanical properties and failure modes. The experimental results indicate that the cooling rate has a significant effect on the mechanical properties and failure modes of sandstone. The peak strain, peak stress, and elastic modulus decrease with an increase in cooling rate, and the fragmentation degree after failure increases gradually. Moreover, the equivalent numerical model of heterogeneous sandstone was established using particle flow code (PFC) to reveal the failure mechanism. The results indicate that the sandstone is dominated by intragrain failure in the cooling stage, the number of microcracks is exponentially related to the cooling rate, and the higher the cooling rate, the more cracks are concentrated in the exterior region. Under axial loading, the tensile stress is mostly distributed along the radial direction, and the damage in the cooling stage is mostly due to the fracture of the radial bond. In addition, axial loading, temperature gradient and thermal stress mismatch between adjacent minerals are the main reasons for the damage of sandstone in the cooling stage. Moreover, the excessive temperature gradient in the exterior region of the sandstone is the main reason for the damage concentration in this region.

Simulating the dynamics of dispersal and dispersal ability in fragmented populations with mate-finding Allee effects.

We consider the spatial propagation and genetic evolution of model populations comprising multiple subpopulations, each distinguished by its own characteristic dispersal rate. Mate finding is modeled in accord with the assumption that reproduction is based on random encounters between pairs of individuals, so that the frequency of interbreeding between two subpopulations is proportional to the product of local population densities of each. The resulting nonlinear growth term produces an Allee effect, whereby reproduction rates are lower in sparsely populated areas; the distribution of dispersal rates that evolves is then highly dependent upon the population's initial spatial distribution. In a series of numerical test cases, we consider how these dynamics affect lattice-like arrangements of population fragments, and investigate how a population's initial fragmentation determines the dispersal rates that evolve as a habitat is colonized. First, we consider a case where initial population fragments coincide with habitat islands, within which death rates differ from those that apply outside; the presence of inhospitable exterior regions exaggerates Allee effect-driven reductions in dispersal ability. We then examine how greater distances separating adjacent population fragments lead to more severe reductions in dispersal ability. For populations of a fixed initial magnitude, fragmentation into smaller, denser patches leads not only to greater losses of dispersal ability, but also helps ensure the population's long-term persistence, emphasizing the trade-offs between the benefits and risks of rapid dispersal under Allee effects. Next, simulations of well-established populations disrupted by localized depopulation events illustrate how mate-finding Allee effects and spatial heterogeneity can drive a population's dispersal ability to evolve either downward or upward depending on conditions, highlighting a qualitative distinction between population fragmentation and habitat heterogeneity. A final test case compares populations that are fragmented across multiple scales, demonstrating how differences in the relative scales of micro- and macro-level fragmentation can lead to qualitatively different evolutionary outcomes.

On local energy decay for solutions of the Benjamin–Ono equation

We consider the long time dynamics of large solutions to the Benjamin–Ono equation. Using virial techniques, we describe regions of space where every solution in a suitable Sobolev space must decay to zero along sequences of times. Moreover, in the case of exterior regions, we prove complete decay for any sequence of times. The remaining regions not treated here are essentially the strong dispersion and soliton regions.

Tutorial on vibration and sound

Over the years I have written many tutorials on vibroacoustics. This tutorial summarizes much of the material in those articles, starting with structural flexural vibrations and how they radiate sound. I explain structural modes of vibration, how they sum into structural mobilities, and how to use infinite plate theory to estimate the means of those mobilities. I also show that as structural damping increases, the mobilities of finite structures converge to that of an infinite structure. Next, you will see how structural flexural waves radiate sound into adjacent acoustic spaces. The radiated sound power may be normalized to a nondimensional radiation efficiency. Next we will examine fluid loading effects on structures, including loading from exterior and internal acoustic regions. I will show how exterior heavy fluid loading (from water) significantly mass loads and radiation damps structural vibrations. I will also show how internal air cavities can stiffen low order structural modes, and in some cases cause coupled oscillator behavior when structural and cavity mode resonance frequencies coincide. Finally, I will explore the fundamentals of sound transmission loss through structural barriers. My complete tutorial series on vibroacoustics is available at hambricacoustics.com.

Analytical expressions for pulse profile of neutron stars in plasma environments

We present an analytical study of light curves of slowly rotating radio pulsars with emphasis on the chromatic effects derived from the presence of a plasma environment; analyzing the effects of the compactness, the metric model, and the electronic plasma density profile. After doing a numerical integration of the trajectories and luminosity curves of pulsars for different spherically symmetric metrics representing the exterior region of the pulsar, we generalize the approximate Beloborodov formula in order to include plasma corrections, obtaining simple analytical expressions for the trajectories and the observed flux and significantly simplifying the calculation of the pulse profiles by a drastic reduction of their computational cost. We study the errors committed by our approximation, comparing the numerical and analytical procedures. We also show how to use the new formalism to model the flux coming from different emission caps, not necessarily circular or antipodal and including the case of ring-shaped hot spots. Finally, we extend the classification introduced by Beloborodov to the case of two distinguishable, non-antipodal, finite size emission caps, showing the respective classification maps and some of the characteristic pulse profiles.

The gravitational field outside a spatially compact stationary source in a generic fourth-order theory of gravity

By applying the symmetric and trace-free formalism in terms of the irreducible Cartesian tensors, the metric for the external gravitational field of a spatially compact stationary source is provided in F(X, Y, Z) gravity, a generic fourth-order theory of gravity, where X := R is Ricci scalar, Y := RμνRμν is Ricci square, and Z := RμνρσRμνρσ is Riemann square. A new type of gauge condition is proposed so that the linearized gravitational field equations of F(X, Y, Z) gravity are greatly simplified, and then, the stationary metric in the region exterior to the source is derived. In the process of applying the result, integrations are performed only over the domain occupied by the source. The multipole expansion of the metric potential in F(X, Y, Z) gravity for a spatially compact stationary source is also presented. In the expansion, the corrections of F(X, Y, Z) gravity to General Relativity are Yukawa-like ones, dependent on two characteristic lengths. Two additional sets of mass-type source multipole moments appear in the corrections and the salient feature characterizing them is that the integrations in their expressions are always modulated by a common radial factor related to the source distribution.

Peridynamic elastic waves in two-dimensional unbounded domains: Construction of nonlocal Dirichlet-type absorbing boundary conditions

The focus of this paper is on application of peridynamics (PD) to propagation of elastic waves in unbounded domains. We construct absorbing boundary conditions (ABCs) derived from a semi-analytical solution of the PD governing equation at the exterior region. This solution is made up of a finite series of plane waves, as fundamental solutions (modes), which satisfy the PD dispersion relations. The modes are adjusted to transmit the energy from the interior region (near field) to the exterior region (far field). The corresponding unknown coefficients of the series are found in terms of the displacement field at a layer of points adjacent to the absorbing boundary. This is accomplished through a collocation procedure at subregions (clouds) around each absorbing point. The proposed ABCs offer appealing advantages, which facilitate their application to PD. They are of Dirichlet-type, hence their implementation is relatively simple as no derivatives of the field variables are required. They are constructed in the time and space domains and thus application of Fourier and Laplace transforms, cumbersome for nonlocal models, is not required. At the discrete level, the modes satisfy the same numerical dispersion relations of the near field, which makes the far-field solution compatible with that of the near field. We scrutinize the performance of the proposed ABCs through several examples. Our investigation shows that the proposed ABCs perform stably in time with an appropriate level of accuracy even in problems characterized by highly-dispersive propagating waves, including crack propagation in semi-unbounded brittle solids.

Axionic and nonaxionic electrodynamics in plane and circular geometry

Various aspects of axion electrodynamics in the presence of a homogeneous and isotropic dielectric medium are discussed. First, we consider the ``antenna-like'' property of a planar dielectric surface in axion electrodynamics, elaborating on the treatment given earlier on this topic by Millar et al. [J. Cosmol. Astropart. Phys. 01 (2017) 061.]. We calculate the electromagnetic energy transmission coefficient for a dielectric plate, and compare with the conventional expression in ordinary electrodynamics. Second, we consider the situation where the medium exterior to the plate, assumed elastic, is ``bent back'' and glued together, so that we obtain a circular dielectric string in which the waves can propagate clockwise or counterclockwise. As will be shown, a stationary wave pattern is permitted by the formalism, and we show how the amplitudes for the two counterpropagating waves can be found. Third, as a special case, by omitting axions for a moment, we analyze the Casimir effect for the string, showing its similarity as well as its difference from the Casimir effect of a scalar field for a piecewise uniform string [I. Brevik and H. B. Nielsen, Phys. Rev. D 41, 1185 (1990).]. Finally, including axions again we analyze the enhancement of the surface-generated electromagnetic radiation near the center of a cylindrical haloscope, where the interior region is a vacuum and the exterior region a high refractive index medium. This enhancement is caused by the curvature of the boundary, and is mathematically a consequence of the behavior of the Hankel function of the second kind for small arguments. A simple estimate shows that enhancement may be quite significant, and can therefore be of experimental interest. The presence of an absorber in the center and the possibility of adopting it to search for axions with mass in the THz region, and possibly the GHz region too, is also discussed. This proposal is suggested as an alternative to the reflector arrangement in a similar arrangement recently discussed by Liu et al. [, Phys. Rev. Lett. 128, 131801 (2022).].

Study of decoupled gravastars in energy–momentum squared gravity

In this paper, we generate an exact anisotropic gravastar model using gravitational decoupling technique through minimal geometric deformation in the framework of f(ℜ,T2) gravity. This novel model explains an ultra-compact stellar configuration whose internal region is smoothly matched to the exterior region. The developed stellar model satisfies some of the essential characteristics of a physically acceptable model such as a positive monotonically decreasing profile of energy density from the center to the boundary and monotonically decreasing behavior of the pressure. The anisotropic factor and Schwarzschild spacetime follows physically acceptable behavior. We find that all the energy bounds are satisfied except strong energy condition inside the ultra-compact stellar structure for the coupling constant of this theory, which is compatible with the regularity condition.

Proportioning, Carbonation, Performance Assessment, and Application of Reactive Magnesium Oxide Cement–Based Composites with Superplasticizers

Formulation of highly workable reactive magnesium oxide (MgO) cement (RMC)–based composites is critical to their wider adoption in the construction industry. Yet, the performance of the binder with the presence of chemical admixtures is not well understood. This study assessed the influence of polycarboxylate ether (PCE)–based superplasticizers on the hydration and carbonation kinetics of RMC. Its application was also demonstrated. RMC-based composites were prepared with conventional aggregates, superplasticizers to aid workability, and fibers to control cracking induced by volume changes under both hydration and carbonation. Two carbonation methods were utilized: 20% CO2 in a carbonation chamber and CO2 in an enclosed plastic bag to emulate a low-technology carbonation process. Highly workable RMC-based mortar mixes were achieved with a superplasticizer content of 2% by weight, despite the presence of 0.2% by volume polyethylene microfibers. The admixtures slowed down the hydration rate and altered the morphology of the hydration product. Compressive strength of 32.7 MPa was attained after 7 days under 20% CO2 in a carbonation chamber compared with 15.6 MPa under carbonation inside the plastic bag condition. The crystalline carbonation products within the exterior regions were dominated by nesquehonite. A significantly reduced carbonation level was observed within the interior regions due to the formation of the carbonation products and the resulting pore refinement within the exterior regions. Also, the PE fibers provided a crack control mechanism, and their failure mode was characterized by pullout. The finalized mix was successfully applied for the construction of a large-scale architectural structure.

Doubling of Asymptotically Flat Half-spaces and the Riemannian Penrose Inequality

Building on previous works of Bray, of Miao, and of Almaraz, Barbosa, and de Lima, we develop a doubling procedure for asymptotically flat half-spaces (M, g) with horizon boundary Sigma subset M and mass min {mathbb {R}}. If 3le dim (M)le 7, (M, g) has non-negative scalar curvature, and the boundary partial M is mean-convex, we obtain the Riemannian Penrose-type inequality m≥12nn-1|Σ|ωn-1n-2n-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} m\\ge \\left( \\frac{1}{2}\\right) ^{\\frac{n}{n-1}}\\,\\left( \\frac{|\\Sigma |}{\\omega _{n-1}}\\right) ^{\\frac{n-2}{n-1}} \\end{aligned}$$\\end{document}as a corollary. Moreover, in the case where partial M is not totally geodesic, we show how to construct local perturbations of (M, g) that increase the scalar curvature. As a consequence, we show that equality holds in the above inequality if and only if the exterior region of (M, g) is isometric to a Schwarzschild half-space. Previously, these results were only known in the case where dim (M)=3 and Sigma is a connected free boundary hypersurface.

Wearable and Washable MnO2-Zn Battery Packaged by Vacuum Sealing.

Batteries are used in all types of electronic devices from conventional to advanced devices. Currently, batteries are evolving in the direction of extremely personalized yarn- or textile-structured textronic systems. However, the absence of a protective layer on such batteries is a critical limitation to their practical use. In this study, we developed a wearable and washable MnO2-Zn textile battery that maintains its electrochemical capacity under various external environmental conditions through a vacuum-sealed packaging. The packaged textile battery was fabricated by vacuuming a polymer envelope containing the battery, followed by heat sealing with a vacuum packaging machine. The interior and exterior regions of the textile battery are completely separated by the packaging sheath to preclude leakage and intrusion of substances. The resulting packaged textile battery exhibits stable capacity retention performance under varying temperature and humidity; mechanical deformations due to bending, twisting, rubbing, and pressing; and several mechanical, chemical, and their combined washing cycles. On the basis of these demonstrations, we expect that our vacuum-packaged textile battery will offer new possibilities for practical and convenient use of textronics.

The Unruh state for massless fermions on Kerr spacetime and its Hadamard property

We give a rigorous definition of the Unruh state in the setting of massless Dirac fields on slowly rotating Kerr spacetimes. In the black hole exterior region, we show that it is asymptotically thermal at Hawking temperature on the past event horizon. Furthermore, we demonstrate that in the union of the exterior and interior regions, the Unruh state is pure and Hadamard. The main ingredients are the Hafner-Nicolas scattering theory, new microlocal estimates for characteristic Cauchy problems and criteria on the level of square-integrable solutions.

The growth or decay estimates for nonlinear wave equations with damping and source terms.

The spatial decay or growth behavior of a coupled nonlinear wave equation with damping and source terms is considered. By defining the wave equations in a cylinder or an exterior region, the spatial growth and decay estimates for the solutions are obtained by assuming that the boundary conditions satisfy certain conditions. We also show that the growth or decay rates are faster than those obtained by relevant literature. This kind of spatial behavior can be extended to a nonlinear system of viscoelastic type. In the case of decay, we also prove that the total energy can be bounded by known data.

Microstructure and flexural strength of C/HfC-ZrC-SiC composites prepared by reactive melt infiltration method

C/HfC-ZrC-SiC composites were fabricated via reactive melt infiltration (RMI) of the mixed HfSi2 and ZrSi2 alloys. The microstructure, infiltration behavior of the hybrid silicide alloys infiltrating C/C composites, and flexural strength of C/HfC-ZrC-SiC composites was studied. Inside composites, there were more Hf-rich (Hf, Zr)C phases distributed in the exterior region, while more SiC and Zr-rich (Zr, Hf)Si2 in the interior region. There was compositional segregation in (Hf, Zr)C, with the HfC content decreasing from the exterior region to interior region. The RMI process was performed at different temperatures to investigate the structural evolution, and a model for the reactive melt infiltration of the mixed HfSi2 and ZrSi2 alloys into C/C composites was established. Compared with C/HfC-SiC and C/ZrC-SiC prepared by same process, C/HfC-ZrC-SiC had the highest flexural strength of 247Mpa and 213Mpa after oxidation at 1200 ℃ for 15 min. Both the unoxidized and oxidized samples presented a pseudo-plastic fracture behavior.

Steady Two-Dimensional Conduction: Simple and Double Layer Potentials, Corner Singularities, and Induced Heat Flux

Abstract Two-dimensional steady-state heat conduction is possible outside closed boundaries on which two isothermal segments at different temperatures are separated by two adiabatic segments. Remarkably, previous research showed that the conduction shape factor for the region exterior to the boundary is equal to that for the interior region, despite the asymmetry and singularity of the boundary heat flux distributions. In this study, classical potential theory is used for the temperature and heat flux distributions as a combination of simple-layer and double-layer potentials, including the relationships between the values inside and outside the boundary curve. Isothermal boundaries exhibit an induced heat flux that varies from point-to-point on the boundary. The induced flux integrates to zero over each isothermal edge. Singularities of the heat flux are identified and resolved. Computations that validate the theory are provided for mixed boundary conditions on a disk and a square. Numerical fits to both the simple-layer and double-layer densities are given for the disk and the square. The analysis explains why the interior and exterior conduction shape factors are equal despite wildly differing heat flux distributions, and the results are compared to a previous study of this configuration. This paper also develops fundamental concepts of potential theory and can serve as a tutorial on the subject.

A Finite Element Method for Modeling Edge Effects in Composite Laminates with Different Ply Orientations

A finite element (FE) method is used for modeling edge effects in composite laminates with different ply orientations. Two types of three-dimensional isoperimetric FE methods have been used. One in the interior region has standard linear shape functions, while the other in the exterior region has special shape functions for which an exponential variation is derived using the perturbation technique. The exponential shape functions are introduced to an originally written FE program which uses special mesh generation and numerical integration, as well as other subroutines. The proposed FE solution is found to be in good agreement with the solutions available in the literature. KEYWORDS: Finite-element modeling, Perturbation technique, Laminated composites, Edge effect, Delamination