Warped Geometry Research Articles

Kinematical signatures: Distinguishing between warps and radial flows

Increasing evidence shows that warped disks are common, challenging the methods used to model their velocity fields. Molecular line emission of these disks is characterized by a twisted pattern, similar to the signal from radial flows, complicating the study of warped disk kinematics. Previous attempts to model these features have encountered difficulties in distinguishing between the underlying kinematics of different disks. This study aims to advance gas kinematics modeling capabilities by extending the Extracting Disk Dynamics ( eddy ) package to include warped geometries and radial flows. We assess the performance of eddy in recovering input parameters for scenarios involving warps, radial flows, and combinations of the two. Additionally, we provide a basis to break the visual degeneracy between warped disks and radial flow, establishing a criterion to distinguish them. We extended the eddy package to handle warped geometries by including a parametric prescription of a warped disk and a ray-casting algorithm to account for the surface self-obscuration arising from the 3D to 2D projection. The effectiveness of the tool was tested using the radiative transfer code RADMC3D generating synthetic models for disks with radial flows, warped disks, and warped disks with radial flows. We demonstrate the efficacy of our tool in accurately recovering the geometrical parameters of systems, particularly in data with sufficient angular resolution. Importantly, we observe minimal impact from thermal noise levels typical in Atacama Large Millimeter/submillimeter Array (ALMA) observations. Furthermore, our findings reveal that fitting an incorrect model type produces characteristic residual signatures, which serve as kinematic criteria for disk classification. Characterizing gas kinematics requires careful consideration of twisted motions. While our model provides insights into disk geometries, caution is needed when interpreting parameters in regions with complex kinematics or low-resolution data. Future ALMA baseline observations should help clarify warped disk kinematics.

Moduli dynamics in effective nested warped geometry in four dimensions and some cosmological implications

We analyze the effective four-dimensional dynamics of the extra-dimensional moduli fields in curved braneworlds having nested warping, with particular emphasis on the doubly warped model which is interesting in the light of current collider constraints on the mass of the Kaluza-Klein graviton. The presence of a non-zero brane cosmological constant (Ω) naturally induces an effective moduli potential in the four-dimensional action, which shows distinct features in dS (Ω > 0) and AdS (Ω < 0) branches. For the observationally interesting case of dS 4-branes, a metastable minimum in the potential arises along the first modulus, with no minima along the higher moduli. The underlying nested geometry also leads to interesting separable forms of the non-canonical kinetic terms in the Einstein frame, where the brane curvature directly impacts the kinetic properties of only the first modulus. The non-canonicity of the scenario has been illustrated via an explicit computation of the field space curvature. We subsequently explore the ability of curved multiply warped geometries to drive inflation with an in-built exit mechanism, by considering predominant slow roll along each modular direction on a case-by-case basis. We find slow roll on top of the metastable plateau along the first modular direction to be the most viable scenario, with the higher-dimensional moduli parametrically tuning the height of the potential without significant impact on the inflationary observables. On the other hand, while slow roll along the higher moduli can successfully inflate the background and eventually lead to an exit, consistency with observations seemingly requires unphysical hierarchies among the extra-dimensional radii, thus disfavouring such scenarios.

Semi-Symmetric Metric Connections and Homology of CR-Warped Product Submanifolds in a Complex Space Form Admitting a Concurrent Vector Field

In this paper, we conduct a thorough study of CR-warped product submanifolds in a Kaehler manifold, utilizing a semi-symmetric metric connection within the framework of warped product geometry. Our analysis yields fundamental and noteworthy results that illuminate the characteristics of these submanifolds. Additionally, we investigate the implications of our findings on the homology of these submanifolds, offering insights into their topological properties. Notably, we present a compelling proof demonstrating that, under a specific condition, stable currents cannot exist for these warped product submanifolds. Our research outcomes contribute significant knowledge concerning the stability and behavior of CR-warped product submanifolds equipped with a semi-symmetric metric connection. Furthermore, this work establishes a robust groundwork for future explorations and advancements in this particular field of study.

Localized structures in three-field models: Geometrically constrained configurations and the first-order framework

This work deals with models described by three real scalar fields in one spatial dimension. We study the case where two of the three fields engender kinematical modifications, which respond as geometrical constrictions, that can be used to change the center and/or the tails of the kinklike configurations. An important advantage of our procedure is the construction of a method for the obtention of first-order differential equations that solve the equations of motion and give rise to stable localized structures. We illustrate the general procedure investigating several distinct examples, and suggesting some possibilities of applications of practical use, in particular, to the case of domain walls and skyrmions in magnetic material, collisions of kinks and to deal with braneworld scenarios having a warped five-dimensional anti de Sitter geometry, with a single extra dimension of infinite extent.

Nested warped geometry in a non-flat braneworld scenario

We generalize nested multiply warped braneworld models by incorporating non-zero brane curvature caused by an effective cosmological constant Omega induced on the 3-branes. Starting with the doubly warped model, we first analyze the case where the maximally warped brane is identified as the visible brane. For Omega <0, resolution of the gauge hierarchy problem imposes a small upper bound on |Omega |, and can possibly lead to positivity of all the 3-brane tensions. For Omega >0, the latter is not possible but the tuning of the cosmological constant to its tiny observed value is linked to the tuning of the extra dimensional moduli close to the inverse Planck length, justifying the original flat brane approximation. In both regimes, we study the dependence of the scale-clustering of the pair of TeV-branes on the brane cosmological constant and hence its potential role in generating a fermion mass hierarchy between these branes. Identifying the near-maximally warped brane as the visible brane instead opens up regions in the parameter space that allow positive 3-brane tensions for both anti de Sitter and de Sitter branes, subject to non-trivial constraints on the warping parameters. We conclude by generalizing the key results to arbitrary n-fold nested warped braneworlds.

Constraining the Evolution of the Unstable Accretion Disk in SMC X-1 with NICER

Neutron star high-mass X-ray binaries with superorbital modulations in luminosity host warped inner accretion disks that occult the neutron star during precession. In SMC X-1, the instability in the warped disk geometry causes superorbital period “excursions”: times of instability when the superorbital period decreases from its typical value of 55 to ∼40 days. Disk instability makes SMC X-1 an ideal system in which to investigate the effects of variable disk geometry on the inner accretion flow. Using the high-resolution spectral and timing capabilities of the Neutron Star Interior Composition Explorer, we examined the high state of four different superorbital cycles of SMC X-1 to search for changes in spectral shape and connections to the unstable disk geometry. We performed pulse phase-averaged and phase-resolved spectroscopy to closely compare the changes in spectral shape and any cycle-to-cycle variations. While some parameters, including the photon index and absorbing column density, show slight variations with superorbital phase, these changes are most evident during the intermediate state of the superorbital cycle. Few spectral changes are observed within the high state of the superorbital cycle, possibly indicating the disk instability does not significantly change SMC X-1's accretion process.

Entanglement entropy in internal spaces and Ryu-Takayanagi surfaces

We study minimum area surfaces associated with a region, R, of an internal space. For example, for a warped product involving an asymptotically AdS space and an internal space K, the region R lies in K and the surface ends on ∂R. We find that the result of Graham and Karch can be avoided in the presence of warping, and such surfaces can sometimes exist for a general region R. When such a warped product geometry arises in the IR from a higher dimensional asymptotic AdS, we argue that the area of the surface can be related to the entropy arising from entanglement of internal degrees of freedom of the boundary theory. We study several examples, including warped or direct products involving AdS2, or higher dimensional AdS spaces, with the internal space, K = Rm, Sm; Dp brane geometries and their near horizon limits; and several geometries with a UV cut-off. We find that such RT surfaces often exist and can be useful probes of the system, revealing information about finite length correlations, thermodynamics and entanglement. We also make some preliminary observations about the role such surfaces can play in bulk reconstruction, and their relation to subalgebras of observables in the boundary theory.

Photon rings around warped black holes

The black hole photon ring is a prime target for upcoming space-based VLBI missions seeking to image the fine structure of astrophysical black holes. The classical Lyapunov exponents of the corresponding nearly bound null geodesics control the quasinormal ringing of a perturbed black hole as it settles back down to equilibrium, and they admit a holographic interpretation in terms of quantum Ruelle resonances of the microstate dual to the Kerr black hole. Recent work has identified a number of emergent symmetries related to the intricate self-similar structure of the photon ring. Here, we explore this web of interrelated phenomena in an exactly soluble example that arises as an approximation to the near-extremal Kerr black hole. The self-dual warped AdS3 geometry has a photon ring as well as isometries and an exactly calculable quasinormal mode (QNM) spectrum. We show explicitly that the geometric optics approximation reproduces the eikonal limit of the exact scalar QNM spectrum, as well as the approximate ‘near-ring’ wavefunctions. The isometries are directly related to the emergent conformal symmetry of the photon ring in black hole images but are distinct from a recently discussed conformal symmetry of the eikonal QNM spectrum. The equivalence of the classical QNM spectrum—and thus the photon ring—to the quantum Ruelle resonances in the context of a spacetime with a putative holographic dual suggests that the photon ring of a warped black hole is indeed part of the black hole hologram.

Charged dilatonic spacetimes in string theory

We construct and study general static, spherically symmetric, magnetically charged solutions in Einstein-Maxwell-dilaton gravity in four dimensions. That is, taking Einstein gravity coupled to a U(1) gauge field and a massless dilaton — e.g., the action in the low-energy limit of string theory or Kaluza-Klein reduction — with arbitrary dilaton coupling, we build a three-parameter family of objects characterized by their mass, charge, and dilaton flux, generalizing the well known Garfinkle-Horowitz-Strominger black hole. We analyze the near-extremal and near-horizon behavior in detail, finding new warped geometries. In a particular limit, where the geometry reduces to the recently discovered customizable AdS2 × S2 of Einstein-Maxwell-dilaton gravity, we compute the static s-wave linearized solutions and characterize the anabasis relating the horizon perturbations to their nonlinear completions within our generalized family of spacetimes.

Spin-2 Kaluza-Klein scattering in a stabilized warped background

Scattering amplitudes involving massive spin-2 particles typically grow rapidly with energy. In this paper we demonstrate that the anomalous high-energy growth of the scattering amplitudes cancel for the massive spin-2 Kaluza-Klein modes arising from compactified five-dimensional gravity in a stabilized warped geometry. Generalizing previous work, we show that the two sum rules which enforce the cancellations between the contributions to the scattering amplitudes coming from the exchange of the (massive) radion and those from the exchange of the tower of Goldberger-Wise scalar states (admixtures of the original gravitational and scalar fields of the theory) still persist in the case of the warping which would be required to produce the hierarchy between the weak and Planck scales in a Randall-Sundrum model. We provide an analytic proof of one combination of these generalized scalar sum rules and show how the sum rule depends on the Einstein equations determining the background geometry and the mode-equations and normalization of the tower of physical scalar states. Finally, we provide a consistent and self-contained derivation of the equations governing the physical scalar modes, and we list, in appendixes, the full set of sum rules ensuring proper high-energy growth of all $2\ensuremath{\rightarrow}2$ massive spin-2 scattering amplitudes.

A thermodynamic framework for additive manufacturing of crystallizing polymers, Part II: Simulation of the printing of a stent

We use the theory developed by [43] to simulate in Abaqus the printing of a drug-eluting bioresorbable stent (BRS), which is used to treat a stenosed renal artery, by fused deposition modeling (FDM). The stent is assumed to be printed using a semi-crystalline polylactic acid (PLA). We control the process parameters to architect the microstructure of the stent such that the stent has an amorphous glassy phase on a crystalline backbone, which would ensure sufficient strength along with the regulated release of the drug into the bloodstream. Through this simulation, we highlight those regions in the stent geometry that should adhere to strict quality control requirements during the fabrication process. In this regard, it is observed that a preexisting crack at the core of the third layer has a very high tendency to propagate along the ‘r’ or ‘z’ direction, whereas a preexisting crack at the core of the second layer has a very high tendency to propagate along the ‘r’ direction, thus increasing the probability of an intra-layer delamination process during service. Similarly, the stent has a high chance of inter-layer delamination between the second and third layers by the mode-I mechanism for cracking. Moreover, the final cup-like warped geometry of the stent could injure the arterial wall during deployment by balloon expansion and also during service, thus increasing the risk of neointimal hyperplasia.

Dimeric tetrabromo-p-quinodimethanes: synthesis and structural/electronic properties.

Despite their great potential as molecular building blocks for organic synthesis, tetrabromo-p-quinodimethanes (TBQs) are a relatively unknown family of compounds. Herein, we showcase a series of five derivatives incorporating two tetrabromo-anthraquinodimethane (TBAQ) units linked by π-conjugated spacers of different nature and length. The resulting dimers TBQ1-5 are fully characterised by means of thorough spectroscopic measurements and theoretical calculations. Interestingly, owing to the steric hindrance imposed by the four bulky bromine atoms, the TBAQ fragments adopt a characteristically warped geometry, somehow resemblant of a butterfly, and the novel dimers show a complex NMR pattern with signal splittings. To ascertain whether dynamic processes regarding fluxional inversion of the butterfly configurations are involved, first-principles calculations assessing the interconversion energy barriers are performed. Three possible stereoisomers are predicted involving two diastereomers, thus accounting for the observed NMR spectra. The rotational freedom of the TBAQ units around the π-conjugated linker influences the structural and electronic properties of TBQ1-5 and modulates the electronic communication between the terminal TBAQ moieties. The role of the linker on the electronic properties is investigated by Raman and UV-vis spectroscopies, theoretical calculations and UV-vis measurements at low temperature. TBQ1-5 are of interest as less-explored structural building precursors for a variety of scientific areas. Finally, the sublimation, self-assembly and reactivity on Au(111) of TBQ3 is assessed.

Moduli stabilization with bulk scalar in nested doubly warped braneworld model

We examine the modulus stabilization mechanism of a warped geometry model with nested warping. Such a model with multiple moduli is known to offer a possible resolution of the fermion mass hierarchy problem in the Standard Model. A six dimensional doubly warped braneworld model under consideration admits two distinct moduli, with the associated warp factors dynamically generating different physical mass scales on four 3-branes. In order to address the hierarchy problem related to the Higgs mass, both moduli need to be stabilized around their desired values without any extreme fine tuning of parameters. We show that it is possible to stabilize them simultaneously due to the appearence of an effective 4D moduli potential, which is generated by a single massive bulk scalar field having non-zero VEVs frozen on the 3-branes. This gives rise to two scalar radions, one of which has mass slightly below {mathcal {O}}(TeV) and couplings to SM fields proportional to the inverse of its {mathcal {O}}(TeV) VEV, and the other has nearly {mathcal {O}}(M_{Pl}) mass and interactions with SM fields suppressed by the Planck scale. We also discuss how the entire mechanism can possibly be understood from a purely gravitational point of view, with higher curvature f(R) contributions in the bulk automatically providing a scalar degree of freedom that can serve as the stabilizing field in the Einstein frame.

Continuum spectra from warped dimensions

Using a five dimensional (5D) warped model with two branes along the extra dimension, we study the Green's functions for gauge bosons with a mass gap mg=ρ/2 and a continuum for s>mg2. We find that the Green's functions exhibit poles in the second Riemann sheet of the complex s plane, denoting the existence of broad resonances. The positivity of the spectral functions is also analyzed. Finally, it is shown how the Green's functions can modify some Standard Model processes in pp collisions.

Correction of mould cavity geometry for warpage compensation

Warpage is one of the most challenging defects occurring in plastic injection moulded parts. Various approaches to overcome this issue have been proposed in the literature, but they all provide only partial solutions to the problem. This paper proposes a new method for the compensation and minimisation of warpage. The method is based on Mould Cavity (MC) correction. In contrast to other similar methods, here the MC correction is accomplished through a direct comparison of the local deviations of the warped part’s geometry to the desired geometry of the part. Modifying the MC shape accordingly yields parts with a lower shape discrepancy from the desired geometry compared to the nonadjusted shape. The key novelty of the paper is the development of software that iteratively adjusts the MC shape to minimise local deviations. In every iteration, the warped part is compared to the desired geometry in order to compute local deviations between both geometries. Computation is done first by determining the point normal vector of the warped geometry mesh and its piercing point through desired geometry mesh. Second, distance between the base point and the piercing point is calculated. After all local deviations are determined, the MC geometry is adjusted accordingly. Two case studies demonstrate the method’s capabilities. In the first case we present a curved thin-walled plate part. The maximum warpage value of 0.005 mm (0.7% of the initial maximum warpage) was reached after three iterations of MC geometry correction and remained stable afterwards. In the second case the method was tested on the box-shaped part. The maximum warpage dropped from initial 0.711 mm to 0.066 mm after three iterations.

Radion dynamics, heavy Kaluza–Klein resonances and gravitational waves

In this paper, we study the confinement/deconfinement phase transition of the radion field in a warped model with a polynomial bulk potential. The backreaction of the radion on the metric is taken into account by using the superpotential formalism, while the radion effective potential is obtained from a novel formulation which can incorporate the backreaction. The phase transition leads to a stochastic gravitational wave background that depends on the energy scale of the first Kaluza–Klein resonance, [Formula: see text]. This work completes previous studies in the following aspects: (i) we detail the evaluation of the radion spectrum; (ii) we report on the mismatches between the thick wall approximation and the numerical bounce solution; (iii) we include a suppression factor in the spectrum of sound waves accounting for their finite lifetime; and (iv) we update the bound on [Formula: see text] in view of the O3 LIGO and Virgo data. We find that the forthcoming gravitational wave interferometers can probe scenarios where [Formula: see text], while the O3-run bounds rule out warped models with [Formula: see text] exhibiting an extremely strong confinement/deconfinement phase transition.

Geodesic congruences in 5D warped Ellis–Bronnikov spacetimes

We study the timelike geodesic congruences in the generalised Ellis–Bronnikov spacetime (4D-GEB) and in recently proposed 5D model where a 4D-GEB is embedded in a warped geometry (5D-WGEB) and conduct a comparative study. Analytical expressions of ESR variables (for 4D geometries) are found which reveal the role of the wormhole parameter. In more general 4D and 5D scenarios geodesic equation, geodesic deviation equation and Raychaudhuri equations are solved numerically. The evolution of cross-sectional area of the congruences of timelike geodesics (orthogonal to the geodesic flow lines) projected on 2D-surfaces yield an interesting perspective and shows the effects of the wormhole parameter and growing/decaying warp factors. The presence of warping factor triggers rotation or accretion even in the absence of initial congruence rotation. The presence of rotation in the congruence is also found to be playing a crucial role which we discuss in detail.

Harmonic Function for 3D Warped Transition Geometry and Its Practical Use

A transition is typically required in irrigation canals, laboratory flumes and many other waterways. The warped type transition (WTT) is the preferred link structure between a small rectangular and relatively large trapezoidal channel section. However, the best method of determining the WTT geometry still requires evaluation. This paper provides an analytical function for the three-dimensional (3D) WTT geometry. This was achieved by solving a Dirichlet problem for Laplace’s equation. The boundary conditions in the problem were chosen based on guidelines and recommendations from earlier studies of transitions. Solving the problem analytically yields a harmonic function. The geometry given by this function guarantees a streamlined rectangular-trapezoidal link and avoids sharp corners. The streamlined transition would work to reduce flow separation and head loss. This paper contributes to the development of a new method for fabricating WTT with precision and repeatability. The harmonic function can generate geometrical data as essential input for laboratory-scale and field-scale WTTs and can aid in the construction of a three-dimensional model for use in computational fluid dynamic models.

Bending waves excited by irregular gas inflow along warps

ABSTRACT Gaia has revealed clear evidence of bending waves in the vertical kinematics of stars in the solar neighbourhood. We study bending waves in two simulations, one warped, with the warp due to misaligned gas inflow, and the other unwarped. We find slow, retrograde bending waves in both models, with the ones in the warped model having larger amplitudes. We also find fast, prograde bending waves. Prograde bending waves in the unwarped model are very weak, in agreement with the expectation that these waves should decay on short, approximately crossing, time-scales, due to strong winding. However, prograde bending waves are much stronger for the duration of the warped model, pointing to irregular gas inflow along the warp as a continuous source of excitation. We demonstrate that large-amplitude bending waves that propagate through the solar neighbourhood give rise to a correlation between the mean vertical velocity and the angular momentum, with a slope consistent with that found by Gaia. The bending waves affect populations of all ages, but the sharpest features are found in the young populations, hinting that short-wavelength waves are not supported by the older, kinematically hotter, populations. Our results demonstrate the importance of misaligned gas accretion as a recurrent source of vertical perturbations of disc galaxies, including in the Milky Way.

HANDHELD FISHEYE MULTICAMERA SYSTEM: SURVEYING MEANDERING ARCHITECTONIC SPACES IN OPEN-LOOP MODE – ACCURACY ASSESSMENT

Abstract. The task of digitalizing meandering complex spaces in 3D is a challenging one even with the most advanced instrumentation like lightweight terrestrial laser scanner or portable/wearable Mobile Mapping Systems (MMSs). The complexity and extension of architectonic spaces such as staircases, corridors and passages are such that the acquisition time using static devices becomes prohibitive and the accuracy using mobile devices gets affected by drift error leading to warped models or requiring abundant control measurements. This paper presents a photogrammetric portable fisheye multicamera solution for the 3D survey of complex areas that aims at being both handy and fast in the acquisition as well as more reliable ad accurate than common MMSs. The paper showcases a stress test conducted on five complex reconstruction trajectories selected from the meandering connection passages of Milan’s Cathedral. The tests are constructed as worst-case scenario to evaluate the accuracy and drift error amount of the proposed system in open-ended unconstrained paths. The results, though still suffering from moderate drift error, highlights the potential of the solution, especially in retaining the overall shape and orthogonality of the architectonic elements acquired.