Compressible potential flows around round bodies: Janzen–Rayleigh expansion inferences

The subsonic, compressible, potential flow around a hypersphere can be derived using the Janzen–Rayleigh expansion (JRE) of the flow potential in even powers of the incident Mach number ${\mathcal {M}}_\infty$ . JREs were carried out with terms polynomial in the inverse radius $r^{-1}$ to high orders in two dimensions, but were limited to order ${\mathcal {M}}_\infty ^{4}$ in three dimensions. We derive general JRE formulae for arbitrary order, adiabatic index and dimension. We find that powers of $\ln (r)$ can creep into the expansion, and are essential in the three-dimensional (3-D) sphere beyond order ${\mathcal {M}}_\infty ^{4}$ . Such terms are apparently absent in the 2-D disk, as we verify up to order ${\mathcal {M}}_\infty ^{100}$ , although they do appear in other dimensions (e.g. at order ${\mathcal {M}}_\infty ^{2}$ in four dimensions). An exploration of various 2-D and 3-D bodies suggests a topological connection, with logarithmic terms emerging when the flow is simply connected. Our results have additional physical implications. They are used to improve the hodograph-based approximation for the flow in front of a sphere. The symmetry-axis velocity profiles of axisymmetric flows around different prolate spheroids are approximately related to each other by a simple, Mach-independent scaling.

Embeddings of integrable models in supergravity and their perturbative stability

We discuss the perturbative stability of an AdS 3 non-supersymmetric solution of the type-IIB supergravity, whose internal geometry is given by the direct product of a round three-sphere and two λ-deformed factors based on the coset CFTs SU(2)/U(1) and SL(2, ℝ)/SO(1,1). This solution admits a two-dimensional parametric space spanned by the inverse radius of the AdS 3 and the deformation parameter λ. Reality of the background imposes restrictions on the values of these parameters. Further limitations on the values of the inverse radius and the parameter λ arise after requiring the stability of the solution. Our approach relies on the study of scalar perturbations around the AdS 3 vacuum of a three-dimensional effective theory. This reveals the existence of a region in the parametric space where the Breitenlohner-Freedman bound is not violated.

Vortical Effects for Free Fermions on Anti-De Sitter Space-Time

Here, we study a quantum fermion field in rigid rotation at finite temperature on anti-de Sitter space. We assume that the rotation rate Ω is smaller than the inverse radius of curvature ℓ−1, so that there is no speed of light surface and the static (maximally-symmetric) and rotating vacua coincide. This assumption enables us to follow a geometric approach employing a closed-form expression for the vacuum two-point function, which can then be used to compute thermal expectation values (t.e.v.s). In the high temperature regime, we find a perfect analogy with known results on Minkowski space-time, uncovering curvature effects in the form of extra terms involving the Ricci scalar R. The axial vortical effect is validated and the axial flux through two-dimensional slices is found to escape to infinity for massless fermions, while for massive fermions, it is completely converted into the pseudoscalar density −iψ¯γ5ψ. Finally, we discuss volumetric properties such as the total scalar condensate and the total energy within the space-time and show that they diverge as [1−ℓ2Ω2]−1 in the limit Ω→ℓ−1.

Global properties of the conformal manifold for S-fold backgrounds

We study a one-parameter family of $$ \mathcal{N} $$ N = 2 anti-de Sitter vacua with U(1)2 symmetry of gauged four-dimensional maximal supergravity, with dyonic gauge group [SO(6) × SO(1, 1)] ⋉ ℝ12. These backgrounds are known to correspond to Type IIB S-fold solutions with internal manifold of topology S1 × S5. The family of AdS4 vacua is parametrized by a modulus χ. Although χ appears non-compact in the four-dimensional supergravity, we show that this is just an artefact of the four-dimensional description. We give the 10-dimensional geometric interpretation of the modulus and show that it actually has periodicity of $$ \frac{2\pi }{T} $$ 2 π T , which is the inverse radius of S1. We deduce this by providing the explicit D = 10 uplift of the family of vacua as well as computing the entire modulus-dependent Kaluza-Klein spectrum as a function of χ. At the special values χ = 0 and χ = $$ \frac{\pi }{T} $$ π T , the symmetry enhances according to U(1)2 → U(2), giving rise however to inequivalent Kaluza-Klein spectra. At χ = $$ \frac{\pi }{T} $$ π T , this realizes a bosonic version of the “space invaders” scenario with additional massless vector fields arising from formerly massive fields at higher Kaluza-Klein levels.

Corneal Biomechanical Properties in Varying Severities of Myopia

Purpose: To investigate corneal biomechanical response parameters in varying degrees of myopia and their correlation with corneal geometrical parameters and axial length.Methods: In this prospective cross-sectional study, 172 eyes of 172 subjects, the severity degree of myopia was categorized into mild, moderate, severe, and extreme myopia. Cycloplegic refraction, corneal tomography using Pentacam HR, corneal biomechanical assessment using Corvis ST and Ocular Response Analyser (ORA), and ocular biometry using IOLMaster 700 were performed for all subjects. A general linear model was used to compare biomechanical parameters in various degrees of myopia, while central corneal thickness (CCT) and biomechanically corrected intraocular pressure (bIOP) were considered as covariates. Multiple linear regression was used to investigate the relationship between corneal biomechanical parameters with spherical equivalent (SE), axial length (AXL), bIOP, mean keratometry (Mean KR), and CCT.Results: Corneal biomechanical parameters assessed by Corvis ST that showed significant differences among the groups were second applanation length (AL2, p = 0.035), highest concavity radius (HCR, p < 0.001), deformation amplitude (DA, p < 0.001), peak distance (PD, p = 0.022), integrated inverse radius (IR, p < 0.001) and DA ratio (DAR, p = 0.004), while there were no significant differences in the means of pressure-derived parameters of ORA between groups. Multiple regression analysis showed all parameters of Corvis ST have significant relationships with level of myopia (SE, AXL, Mean KR), except AL1 and AL2. Significant biomechanical parameters showed progressive reduction in corneal stiffness with increasing myopia (either with greater negative SE or greater AXL), independent of IOP and CCT. Also, corneal hysteresis (CH) or ability to dissipate energy from the ORA decreased with increasing level of myopia.Conclusions: Dynamic corneal response assessed by Corvis ST shows evidence of biomechanical changes consistent with decreasing stiffness with increasing levels of myopia in multiple parameters. The strongest correlations were with highest concavity parameters where the sclera influence is maximal.

Repeatability and comparison of new Corvis ST parameters in normal and keratoconus eyes

To evaluate the repeatability of corneal biomechanical parameters in normal and keratoconus eyes, and explore factors that affects the repeatability, and further assess the diagnostic ability of new parameters. Seventy-seven keratoconus eyes of 47 patients and 77 right eyes of 77 normal subjects were recruited in current study. All participants received three repeated measurements with 2 to 5 minutes interval. The interclass correlation coefficient (ICC), Cronbach’ α and repeatability coefficient (RC) were evaluated. The liner regression analysis was used to identify factors that affect the repeatability, and linear mixed effects model was performed to compare the parameters differences. The receiver operating characteristic (ROC) curve was used to evaluate the diagnostic ability of new parameters. Eighteen parameters in normal eyes and twenty-two parameters in keratoconus eyes showed excellent repeatability (ICC ≥ 0.90). Age, axial measurement (AL), spherical equivalent, astigmatism, gender, mean keratometry (Kmean), intraocular pressure (IOP) and central corneal thickness (CCT) could affect the repeatability of new Corvis ST parameters. Compared with normal eyes, the Ambrósio’s Relational Thickness horizontal (ARTh), biomechanical corrected IOP (bIOP), stiffness parameter at first applanation (SP A1) were low and the Max Inverse Radius, deformation amplitude (DA) Ratio Max [2 mm], Pachy Slope, DA Ratio Max [1 mm], Integrated Radius and Corvis Biomechanical Index (CBI) were high in keratoconus eyes (All P < 0.05). Both ARTh and CBI had high Youden index (0.870), and the corresponding cut-off values were 379.29 and 0.44. The repeatability of Corvis ST parameters was acceptable both in normal and keratoconus eyes, and new parameters could effectively diagnose keratoconus eyes from normal eyes.

Quantum Physics as Dynamic Space-Time Differential Calculus

For the first time, a unified quantum metric system has been developed analytically without any artifacts, such as m, s, and kg without measurements at all. Energy diagrams of Feynman are replaced by calculations of relative spacetime differentials. The main constants of quantum physics are, in fact, the dynamic gradients of the normal, halfnormal, log-normal and truncated normal distribution of the inverse radius of the pulsating spiral. Quantum physics as a whole is a logarithmically compressed two-dimensional image of the three-dimensional motion of wave fronts.

Comparison of corneal dynamic parameters and tomographic measurements using Scheimpflug imaging in keratoconus

AimTo compare the diagnostic ability of corneal tomography and corneal dynamic response measurements in normal and keratoconus eyes.MethodsConsecutive patients with grade II–III keratoconus and age-matched normal subjects were recruited. Corneal imaging was performed using Pentacam (Oculus Optikgeräte, Wetzlar, Germany) and Corvis (Oculus Optikgeräte). A beta version of Corvis software was used with three additional parameters: maximal change of arc length, deformation amplitude (DA) ratio 1 and DA ratio 2. Diagnostic ability of both devices to differentiate normal and keratoconus eyes was evaluated using receiver-operating characteristic (ROC) curves. The areas under the ROC curve (AUC) and partial AUC (pAUC) for specificity ≥80% for each parameter of Corvis and final D value of Belin/Ambrosio Enhanced Ectasia Display (BAD) were compared.ResultsForty-two eyes of 42 patients (21 patients with keratoconus and 21 normal subjects) were included. Both groups were age matched (p=0.760). The ROC analysis showed that the final D value of BAD had the highest AUC (0.994) and pAUC (0.194). Maximum inverse radius had the highest AUC (0.954) but a relatively lower pAUC (0.158), while DA ratio 2 had the second highest AUC (0.946) together with the highest pAUC (0.177) among Corvis parameters. There was no significant difference between AUC and pAUC of BAD compared with those of DA ratio 1 (p≥0.162) and DA ratio 2 (p≥0.208).ConclusionsThe results of our study suggest that Corvis measurements have the potential to differentiate keratoconus and normal eyes. The diagnostic ability of novel parameters on Corvis was comparable to Pentacam.

Operational Restrictions on Morphing of Quasi-Geometric 4D Physical Spaces

Since a hierarchical notion of dimension is needed to ensure that a virtual, indirect orthogonality of dimensions is maintained in higher-dimensional spatial structures, a generic function for furling and unfurling of the fourth dimension in four-dimensional (4D) spatial structures is proposed. The furling allows three extra dimensions (above the regular three) in a 6D algebraic structure to be represented as a single fourth dimension and thus effectively facilitates morphing of the 4D spacetime into its dual 4D timespace. The effect of the furling of the extra three dimensions resembles that of compactification proposed by Kaluza-Klein theory yet without curling of the furled dimension. The furling supports reexpansion of stringy space into yet another dimension and so enables mapping of radius R (of a closed string being squeezed beyond its minimal radius) into an inverse radius 1/R, which was attributed to string duality, but is shown as due to duality of the 4D spatial structures of spacetime and timespace. Mathematically, it may appear as if further squeezing of the minimal string morphs it into an expanding pointletlike energy bubble so that the stringy spacetime reexpands in a new direction/dimension located within the bubbly dual timespace. So vibrating string is a mirror image of an energy bubblet, both of which do represent the same stringlet. By analogy, particle cast in spacetime could appear mathematically as having a mirror image (or its superpartner) cast in the dual timespace.

Scale effects for strength, ductility, and toughness in “brittle” materials

Decreasing scales effectively increase nearly all important mechanical properties of at least some “brittle” materials below 100 nm. With an emphasis on silicon nanopillars, nanowires, and nanospheres, it is shown that strength, ductility, and toughness all increase roughly with the inverse radius of the appropriate dimension. This is shown experimentally as well as on a mechanistic basis using a proposed dislocation shielding model. Theoretically, this collects a reasonable array of semiconductors and ceramics onto the same field using fundamental physical parameters. This gives proportionality between fracture toughness and the other mechanical properties. Additionally, this leads to a fundamental concept of work per unit fracture area, which predicts the critical event for brittle fracture. In semibrittle materials such as silicon, this can occur at room temperature when the scale is sufficiently small. When the local stress associated with dislocation nucleation increases to that sufficient to break bonds, an instability occurs resulting in fracture.