Spin Geometry Research Articles

Inferring the iron K emissivity profiles of accretion discs irradiated by extended coronae

ABSTRACT One of the most promising methods to measure the spin of an accreting black hole is fitting the broad iron K$\alpha$ line in the X-ray spectrum. The line profile also depends on the geometry of the hard X-ray emitting corona. To put constraints on the black hole spin and corona geometry, it is essential to understand how do they affect the iron K$\alpha$ line emissivity profile. In this work, we present calculations of the illumination and the iron K$\alpha$ emissivity profiles performed with the Monte Carlo GR radiative transfer code monk. We focus on distinction between the illumination and emissivity profiles, which is in most previous studies neglected. We show that especially for the case of black hole X-ray binaries (BHXRBs), the difference is very large. For active galactic nuclei (AGNs), the emissivity profile has a more similar shape as the illumination profile, but it is notably steeper in the innermost region within a few gravitational radii. We find out that the different behaviour between AGN and BHXRB discs is due to the different energy spectra of the illuminating radiation. This suggests that the emissivity profile of the iron K$\alpha$ line cannot be determined by black hole spin and corona geometry alone and the energy spectrum of the illuminating radiation has to be taken into account. We also examined the effect of including the self-irradiation, and find it to be more important than the corona emission in BHXRBs.

Design and optimization of THz coupling in zirconia MAS rotors for dynamic nuclear polarization NMR

We present 3D electromagnetic simulations of the coupling of a 250 GHz beam to the sample in a 380 MHz DNP NMR spectrometer. To obtain accurate results for magic angle spinning (MAS) geometries, we first measured the complex dielectric constants of zirconia, sapphire, and the sample matrix material (DNP juice) from room temperature down to cryogenic temperatures and from 220 to 325 GHz with a VNA and up to 1 THz with a THz TDS system. Simulations of the coupling to the sample were carried out with the ANSYS HFSS code as a function of the rotor wall material (zirconia or sapphire), the rotor wall thickness, and the THz beam focusing (lens or no lens). For a zirconia rotor, the B1 field in the sample was found to be strongly dependent on the rotor wall thickness, which is attributed to the high refractive index of zirconia. The optimum thickness of the wall is likely due to a transmission maximum but is offset from the thickness predicted by a simple calculation for a flat slab of the wall material. The B1 value was found to be larger for a sapphire rotor than for a zirconia rotor for all cases studied. The results found in this work provide new insights into the coupling of THz radiation to the sample and should lead to improved designs of future DNP NMR instrumentation.

Recent advances of preparing structure-enhanced conductive yarns to control their performance in potential applications

There has been a recent transition from conventional textiles to smart and electronic textiles, mostly due to the rise of wearable technology. Functional yarns have been created to fulfil the varied application needs in various environments. Conductive yarns have attracted considerable interest because of their exceptional softness, comfort, and diverse capabilities, such as electromagnetic shielding and soft sensors. This paper presents a comprehensive examination of spinning techniques utilized for the production of conductive yarns, incorporating a range of conductive additives, conductive fabrics, and conventional electrical elements. The text emphasizes that the performance of conductive yarns is significantly affected by their structure, which is dictated by the geometrical configurations of their elements, and the spinning geometry, commonly known as the twisted triangle. The performance of conductive yarns is primarily determined by the concentration of conductive components in their structure. Moreover, this paper examines the possible uses of conductive fabrics in several technical domains. The mentioned applications encompass antistatic packaging, heating elements, wearable electronics, smart membrane technology, data storage and transmission, sensors, actuators, and protection against electromagnetic interference and electrostatic discharge. Conductive textiles possess a versatile character that presents a wide range of opportunities for progress in multiple industries. To summarize, this review thoroughly examines the spinning methods used to create conductive yarns, with a particular focus on the significance of yarn structure in influencing their performance. Furthermore, it emphasizes the wide range of technological applications in which conductive textiles can be utilized.

Minkowski Space from Quantum Mechanics

Penrose’s Spin Geometry Theorem is extended further, from SU(2) and E(3) (Euclidean) to E(1, 3) (Poincaré) invariant elementary quantum mechanical systems. The Lorentzian spatial distance between any two non-parallel timelike straight lines of Minkowski space, considered to be the centre-of-mass world lines of E(1, 3)-invariant elementary classical mechanical systems with positive rest mass, is expressed in terms of E(1, 3)-invariant basic observables, viz. the 4-momentum and the angular momentum of the systems. An analogous expression for E(1, 3)-invariant elementary quantum mechanical systems in terms of the basic quantum observables in an abstract, algebraic formulation of quantum mechanics is given, and it is shown that, in the classical limit, it reproduces the Lorentzian spatial distance between the timelike straight lines of Minkowski space with asymptotically vanishing uncertainty. Thus, the metric structure of Minkowski space can be recovered from quantum mechanics in the classical limit using only the observables of abstract quantum mechanical systems.

The Relativistic Spin Precession in the Compact Double Neutron Star System PSR J1946+2052

Abstract We observe systematic profile changes in the visible pulsar of the compact double neutron star system PSR J1946+2052 using observations with the Five-hundred-meter Aperture Spherical radio Telescope (FAST). The interpulse of PSR J1946+2052 changed from a single-peak to a double-peak shape from 2018–2021. We attribute this evolution as the result of the relativistic spin precession of the pulsar. With the high sensitivity of FAST, we also measure significant polarization for the first time, allowing us to model this with the precessional rotating vector model. Assuming, to the first order, a circular hollow-cone-like emission beam pattern and taking the validity of general relativity (GR), we derive the binary’s orbital inclination angle ( 63 ∘ − 3 ∘ + 5 ∘ ) and pulsar’s spin geometry. The pulsar’s spin vector and the orbital angular momentum vector are found to be only slightly misaligned ( 0. ∘ 21 − 0. ∘ 10 + 0. ∘ 28 ). The quoted uncertainties do not reflect the systematic uncertainties introduced by our model assumptions. By simulating future observations of profile and polarization evolution, we estimate that we could constrain the precession rate within a 43% uncertainty in 9 yr. Hence, we suggest that the system’s profile evolution could be combined with precise pulsar timing to test GR in the future.

Non-compactness results for the spinorial Yamabe-type problems with non-smooth geometric data

Let (M,g,σ) be an m-dimensional closed spin manifold, with a fixed Riemannian metric g and a fixed spin structure σ; let S(M) be the spinor bundle over M. The spinorial Yamabe-type problems address the solvability of the following equationDgψ=f(x)|ψ|g2m−1ψ,ψ:M→S(M),x∈M where Dg is the associated Dirac operator and f:M→R is a given function. The study of such nonlinear equation is motivated by its important applications in Spin Geometry: when m=2, a solution corresponds to a conformal isometric immersion of the universal covering M˜ into R3 with prescribed mean curvature f; meanwhile, for general dimensions and f≡constant≠0, a solution provides an upper bound estimate for the Bär-Hijazi-Lott invariant.The aim of this paper is to establish non-compactness results related to the spinorial Yamabe-type problems. Precisely, concrete analysis is made for two specific models on the manifold (Sm,g) where the solution set of the spinorial Yamabe-type problem is not compact: 1). the geometric potential f is constant (say f≡1) with the background metric g being a Ck perturbation of the canonical round metric gSm, which is not conformally flat somewhere on Sm; 2). f is a perturbation from constant and is of class C2, while the background metric g≡gSm.

Scalar Curvature Rigidity of Warped Product Metrics

We show scalar-mean curvature rigidity of warped products of round spheres of dimension at least 2 over compact intervals equipped with strictly log-concave warping functions. This generalizes earlier results of Cecchini-Zeidler to all dimensions. Moreover, we show scalar curvature rigidity of round spheres of dimension at least 3 with two antipodal points removed. This resolves a problem in Gromov's ''Four Lectures'' in all dimensions. Our arguments are based on spin geometry.

Algebra environments II. Algebra homomorphisms and derivations

Algebra environments provide requisites for studying objects of interest in operator algebra theory, group representation theory, spin geometry, Clifford analysis, and several variable operator theory. The concept is analyzed by developing an algebraic geometry approach. Specific algebraic sets, called structure manifolds of algebra environments, and their Zariski tangent spaces are introduced and described by using as critical tools derivations on algebras. Structure manifolds of tensor environments in particular yield spaces of algebra homomorphisms. Consequently, such spaces could be investigated as algebraic manifolds. Related issues include characterizations of their Zariski tangent spaces and of derivations that preserve algebra homomorphisms.

Fast and Fourier: extreme mass ratio inspiral waveforms in the frequency domain

Extreme Mass Ratio Inspirals (EMRIs) are one of the key sources for future space-based gravitational wave interferometers. Measurements of EMRI gravitational waves are expected to determine the characteristics of their sources with sub-percent precision. However, their waveform generation is challenging due to the long duration of the signal and the high harmonic content. Here, we present the first ready-to-use Schwarzschild eccentric EMRI waveform implementation in the frequency domain for use with either graphics processing units (GPUs) or central processing units (CPUs). We present the overall waveform implementation and test the accuracy and performance of the frequency domain waveforms against the time domain implementation. On GPUs, the frequency domain waveform takes in median 0.044 s to generate and is twice as fast to compute as its time domain counterpart when considering massive black hole masses ≥2×106M⊙ and initial eccentricities e0 > 0.2. On CPUs, the median waveform evaluation time is 5 s, and it is five times faster in the frequency domain than in the time domain. Using a sparser frequency array can further speed up the waveform generation, reaching up to 0.3 s. This enables us to perform, for the first time, EMRI parameter inference with fully relativistic waveforms on CPUs. Future EMRI models, which encompass wider source characteristics (particularly black hole spin and generic orbit geometries), will require significantly more harmonics. Frequency domain models will be essential analysis tools for these astrophysically realistic and important signals.

Magnetic dimeric metal-porphyrin rings mechanically bonded around carbon nanotubes: the role of nanotube defects modulating magnetic properties.

Carbon nanotubes constitute an excellent option to connect molecular nanomagnets (MNMs) to solid-state devices, allowing the electrical control of the molecule spin state. The main challenge in this area is to obtain stable nanohybrid structures that preserve the magnetic properties and functionality of the molecule. One of the strategies developed to build these structures combining MNMs and carbon nanotubes involves the encapsulation of the nanotube within magnetic organic macrocycle(s), leading to magnetic mechanically interlocked derivatives of carbon nanotubes (mMINTs). Recently, mMINTs with dimeric metal-porphyrin rings containing Cu2+ or Co2+ attached to carbon nanotubes have been synthesized. Different structural and spectroscopic techniques confirm that the metal centers in both mMINTs preserve the coordination sphere and structure of the free macrocycles, with only small deviations from the square planar geometry. However, different magnetic behaviors are observed depending on the metal. The Cu derivative has well-preserved spin geometry, with quantum coherence times on the microsecond scale, as in the free molecule (τ = 25 μs). In contrast, the continuous-wave electron paramagnetic resonance (EPR) spectrum measured on the Co derivative does not show any clear contribution from Co, although EXAFS unambiguously shows the presence of Co2+. In order to understand this different magnetic behavior, we studied mMINTs by means of periodic DFT calculations. The analysis of the optimized geometries, the spin density of the free macrocycles and the mMINTs, the adsorption energies, the extension of the charge transfer between the macrocycle and the nanotube and the density of states reveals a stronger macrocycle-nanotube interaction for the Co-mMINT. Our results point to carbon vacancies in the nanotubes as responsible for the different macrocycle-nanotube interaction and the observed loss of the Co2+ EPR signal in the Co-mMINT.

Too small to fail: characterizing sub-solar mass black hole mergers with gravitational waves

The detection of a sub-solar mass black hole could yield dramatic new insights into the nature of dark matter and early-Universe physics, as such objects lack a traditional astrophysical formation mechanism. Gravitational waves allow for the direct measurement of compact object masses during binary mergers, and we expect the gravitational-wave signal from a low-mass coalescence to remain within the LIGO frequency band for thousands of seconds. However, it is unclear whether one can confidently measure the properties of a sub-solar mass compact object and distinguish between a sub-solar mass black hole or other exotic objects. To this end, we perform Bayesian parameter estimation on simulated gravitational-wave signals from sub-solar mass black hole mergers to explore the measurability of their source properties. We find that the LIGO/Virgo detectors during the O4 observing run would be able to confidently identify sub-solar component masses at the threshold of detectability; these events would also be well-localized on the sky and may reveal some information on their binary spin geometry. Further, next-generation detectors such as Cosmic Explorer and the Einstein Telescope will allow for precision measurement of the properties of sub-solar mass mergers and tighter constraints on their compact-object nature.

Spacetime geometry of spin, polarization, and wavefunction collapse

To incorporate quantum nonlocality into general relativity, we propose that the preparation and measurement of a quantum system are simultaneous events. To make progress in realizing this proposal, we introduce a spacetime geometry that is endowed with particles which have no distinct points in their worldlines; we call these particles ‘pointons’. This new geometry recently arose in nonnoetherian algebraic geometry. We show that on such a spacetime, metrics are degenerate and tangent spaces have variable dimension. This variability then implies that pointons are spin-12 fermions that satisfy the Born rule, where a projective measurement of spin corresponds to an actual projection of tangent spaces of different dimensions. Furthermore, the 4-velocities of pointons are necessarily replaced by their Hodge duals, and this transfer from vector to pseudo-tensor introduces a free choice of orientation that we identify with electric charge. Finally, a simple composite model of electrons and photons results from the metric degeneracy, and from this we obtain a new ontological model of photon polarization.

Solutions of spinorial Yamabe-type problems on 𝑆^{𝑚}: Perturbations and applications

This paper is part of a program to establish the existence theory for the conformally invariant Dirac equation \[ D g ψ = f ( x ) | ψ | g 2 m − 1 ψ D_g\psi =f(x)|\psi |_g^{\frac 2{m-1}}\psi \] on a closed spin manifold ( M , g ) (M,g) of dimension m ≥ 2 m\geq 2 with a fixed spin structure, where f : M → R f:M\to \mathbb {R} is a given function. The study on such nonlinear equation is motivated by its important applications in Spin Geometry: when m = 2 m=2 , a solution corresponds to an isometric immersion of the universal covering M ~ \widetilde M into R 3 \mathbb {R}^3 with prescribed mean curvature f f ; meanwhile, for general dimensions and f ≡ c o n s t a n t f\equiv constant , a solution provides an upper bound estimate for the Bär-Hijazi-Lott invariant. Comparing with the existing issues, the aim of this paper is to establish multiple existence results in a new geometric context, which have not been considered in the previous literature. Precisely, in order to examine the dependence of solutions of the aforementioned nonlinear Dirac equations on geometrical data, concrete analyses are made for two specific models on the manifold ( S m , g ) (S^m,g) : the geometric potential f f is a perturbation from constant with g = g S m g=g_{S^m} being the canonical round metric; and f ≡ 1 f\equiv 1 with the metric g g being a perturbation of g S m g_{S^m} that is not conformally flat somewhere on S m S^m . The proof is variational: solutions of these problems are found as critical points of their corresponding energy functionals. The emphasis is that the solutions are always degenerate: they appear as critical manifolds of positive dimension. This is very different from most situations in elliptic PDEs and classical critical point theory. As corollaries of the existence results, multiple distinct embedded spheres in R 3 \mathbb {R}^3 with a common mean curvature are constructed, and furthermore, a strict inequality estimate for the Bär-Hijazi-Lott invariant on S m S^m , m ≥ 4 m\geq 4 , is derived, which is the first result of this kind in the non-locally-conformally-flat setting.

Noncommutativity and physics: a non-technical review

We give an overview of the applications of noncommutative geometry to physics. Our focus is entirely on the conceptual ideas, rather than on the underlying technicalities. Starting historically from the Heisenberg relations, we will explain how in general noncommutativity yields a canonical time evolution, while at the same time allowing for the coexistence of discrete and continuous variables. The spectral approach to geometry is then explained to encompass two natural ingredients: the line element and the algebra. The relation between these two is dictated by so-called higher Heisenberg relations, from which both spin geometry and non-abelian gauge theory emerges. Our exposition indicates some of the applications in physics, including Pati–Salam unification beyond the Standard Model, the criticality of dimension 4, second quantization and entropy.

The Atiyah-Singer Index Theorem for a Family of Fractional Dirac Operators on Spin Geometry

The Atiyah-Singer Index Theorem for a Family of Fractional Dirac Operators on Spin Geometry

Predictive Modeling of Yarn Quality at Ring Spinning Machine using Resilient Back Propagation Neural Networks

The final attenuation and twisting of fiber take place at ring spinning machine and hence its optimized performance is very crucial in terms of yarn quality. Drafting at ring spinning machine has a decisive effect on quality. There exist many influencing parameters in the spinning geometry that have to be optimized for manufacturing of quality yarn. The present research work was carried out to develop the Artificial neural networks (ANN) based prediction model for the polyester/cotton blended ring spun yarns by using these influencing parameters as inputs. ANN prediction model was developed using resilient backpropogation algorithm. Yarn quality parameters like yarn evenness, hairiness and tensile parameters were predicted. The low mean absolute error values for the yarn quality parameters proved that it is possible to predict the yarn quality on the basis of spinning geometry for cotton/polyester blended ring spun yarns using Resilient Back Propogation Neural Networks.

The interplay between spin states, geometries and biological activity of Fe(III) and Mn(II) complexes with thiosemicarbazone

Fe(III) and Mn(II) complexes with condensation product of thiosemicarbazide and 2-acetylthiazole (HL1, (E)-2-(1-(thiazol-2-yl)ethylidene)hydrazine-1-carbothioamide) have been synthesized and characterized by single-crystal X-ray diffraction, IR spectroscopy, and elemental analysis. In both complexes, the thiosemicarbazone ligand is coordinated in deprotonated form through the NNS donor set of atoms. However, while Fe(III) complex is in the doublet ground state with distorted octahedral geometry, the coordination environment around Mn(II) is distorted trigonal-prismatic, and the sextet state is found to be the ground state. DFT calculations were performed to rationalize spin state preferences, and continuous shape measure describes the deviation from ideal six-coordinated polyhedral geometries in the ground and excited states. Antimicrobial activity (against a panel of Gram-negative and Gram-positive bacteria, two yeast, and one fungal strain), brine shrimp assay, and DPPH radical scavenging activity of both complexes were evaluated, and these results relate to the electronic structure of the complexes.

Testing dynamical torsion effects on the charged black hole’s shadow, deflection angle and greybody with M87* and Sgr. A* from EHT

Poincaré Gauge’s theory of gravity is the most noteworthy alternative extension of general relativity that has a correspondence between spin and spacetime geometry. In this paper, we use Reissner–Nordstrom–de Sitter and anti-de Sitter solutions, where torsion τ is added as an independent field, to analyze the weak deflection angles αˆ of massive and null particles in finite distance regime. We then apply αˆ to determine the Einstein ring formation in M87* and Sgr. A* and determine that relative to Earth’s location from these black holes, massive torsion effects can provide considerable deviation, while the cosmological constant’s effect remains negligible. Furthermore, we also explore how the torsion parameter affects the shadow radius perceived by both static and co-moving (with cosmic expansion) observers in a Universe dominated by dark energy, matter, and radiation. Our findings indicate that torsion and cosmological constant parameters affect the shadow radius differently between observers in static and co-moving states. We also show how the torsion parameter affects the luminosity of the photonsphere by studying the shadow with infalling accretion. The calculation of the quasinormal modes, greybody bounds, and high-energy absorption cross-section are also affected by the torsion parameter considerably.

A Three-Dimensional Silicon-Diacetylene Porous Organic Radical Polymer

A Three-Dimensional Silicon-Diacetylene Porous Organic Radical Polymer

Three-Space from Quantum Mechanics

The spin geometry theorem of Penrose is extended from SU(2) to E(3) (Euclidean) invariant elementary quantum mechanical systems. Using the natural decomposition of the total angular momentum into its spin and orbital parts, the distance between the centre-of-mass lines of the elementary subsystems of a classical composite system can be recovered from their relative orbital angular momenta by E(3)-invariant classical observables. Motivated by this observation, an expression for the ‘empirical distance’ between the elementary subsystems of a composite quantum mechanical system, given in terms of E(3)-invariant quantum observables, is suggested. It is shown that, in the classical limit, this expression reproduces the a priori Euclidean distance between the subsystems, though at the quantum level it has a discrete character. ‘Empirical’ angles and 3-volume elements are also considered.