Geometric Origin Research Articles

Tectonic evolution of the Zagros foreland basin since Early Cretaceous, SW Iran: Regional tectonic implications from subsidence analysis

• Basement palaeo-highs exert major impact on the basin's subsidence history. • Architecture of the Zagros foreland dramatically changed during the Cretaceous. • NE-SW deep-seated basement faults were intensively re-activated during the Turonian . • N-S deep seated basement faults were re-activated during the last 20 Ma. Subsidence analysis of 42 exploration wells in the Zagros foreland basin indicates the tectonic evolution of the basin since Early Cretaceous. The impact of inherited basement structures on the basin evolution is documented in this study. Subsidence maps show that the architecture of the basin dramatically changed during the Cretaceous. In the Central Zagros, the Hercynian palaeo-high (i.e. Wadi Al Batin palaeo-high), which affected sedimentation until the Early Cretaceous time gradually disappeared and the South Pars palaeo-high within the central Persian Gulf started to show more impact on sedimentation. The palaeo-highs in the Zagros basement have different geometrical characteristics and origin. The Hercynian and South Pars are wide-wavelength palaeo-highs with a regional-scale impact on subsidence. In contrast, the Hendijan, Kharg-Mish and Kazerun palaeo-highs with different orientations and quite smaller wavelengths show different impact on the subsidence pattern. These kinds of palaeo-highs could be related to re-activation of pre-existing basement faults. Whereas South Pars and Hercynian paleo highs are possibly related to thermal expansion or contraction of the crust. The Hendijan and Kharg-Mish palaeo-highs with the NE-SW orientation were intensively re-activated during Turonian time. On the contrary, the Kazerun Fault with the N-S orientation became more active and considerably influenced sedimentation during the last 20 Ma. Selective re-activation of deep-seated faults might have taken place as a result of changes in the orientation of the far-field stress in the region. Understanding the complexities of inherited structures and their impact on reservoir characteristics can support future exploration activities in the Zagros foreland basin.

Elliptic classes, McKay correspondence and theta identities

We revisit the construction of elliptic class given by Borisov and Libgober for singular algebraic varieties. Assuming torus action we adjust the theory to the equivariant local situation. We study theta function identities having a geometric origin. In the case of quotient singularities {mathbb {C}}^n/G, where G is a finite group the theta identities arise from McKay correspondence. The symplectic singularities are of special interest. The Du Val surface singularity A_n leads to a remarkable formula.

Scalar field unification of interacting viscous dark fluid from a geometrical scalar–tensor theory of gravity

We investigate, in the framework of a recently introduced new class of invariant geometrical scalar-tensor theory of gravity, the possibility that a viscous dark fluid can be described in a unified manner by a single scalar field. Thus we developed a model in which both the metric tensor and the scalar field have geometrical origin. The scalar field is characterized by a non-canonical kinetic term and the scalar viscosity of the dark fluid appears as soon the kinetic energy of the scalar field is no longer canonical. The scalar viscosity is considered as a function of the Hubble and the deceleration parameters. To illustrate the formalism we have considered two cases: a constant and a thermodynamic equation of state parameters. In the both cases we obtain analytic representations for the scalar field and their respective potentials. We delimit free parameters by comparing with some Planck 2018 results.

Intensity and Polarization of Radiation Emerging from Rotating Accretion Disc with Increasing Height

We consider the radiation emission in continuum and spectral lines from rotating accretion disc with the progressive increasing height. It is known that for the plane accretion disc with homogeneous atmosphere the wave electric field E is perpendicular to the plane between line of sight n and the normal to the disc N. For the expanding accretion disc the wave electric field from every inclined cone-like part with given azimuthal angle φ has direction perpendicular to the plane between n and local normal N′ to the inclined surface. This behaviour is the consequence of homogeneity of inclined atmosphere and has purely geometrical origin. The geometrical consideration shows that the position angles of polarized radiation in the right and left parts relative to plane (nN) of the inclined accretion disc have opposite values. Therefore, for inclined accretion disc the integral continuum radiation has the usual polarization angle perpendicular to the plane (nN), but smaller degree of polarization and less alongated along the normal N than that for the plane accretion disc. For spectral line, due to the Doppler effect, the polarization (position) angles have opposite signs for the red and blue wings. Such behaviour is frequently observed in Hα-radiation.

Indentation of suspended two-dimensional solids: The signatures of geometrical and material nonlinearity

The material characterization of ultra-thin solid sheets, including two-dimensional materials like graphene, is often performed through indentation tests on a flake suspended over a hole in a substrate. While this ‘suspended indentation’ is a convenient means of measuring properties such as the stretching (two-dimensional) modulus of such materials, experiments on ostensibly similar systems have reported very different material properties. In this paper, we present a modelling study of this indentation process assuming elastic behaviour. In particular, we investigate the possibility that the reported differences may arise from different geometrical parameters and/or non-Hookean deformations, which lead to the system exploring nonlinearities with geometrical or material origins.

Geometric Origin of the Tennis Racket Effect.

The tennis racket effect is a geometric phenomenon which occurs in a free rotation of a three-dimensional rigid body. In a complex phase space, we show that this effect originates from a pole of a Riemann surface and can be viewed as a result of the Picard-Lefschetz formula. We prove that a perfect twist of the racket is achieved in the limit of an ideal asymmetric object. We give upper and lower bounds to the twist defect for any rigid body, which reveals the robustness of the effect. A similar approach describes the Dzhanibekov effect in which a wing nut, spinning around its central axis, suddenly makes a half-turn flip around a perpendicular axis and the monster flip, an almost impossible skateboard trick.

Cosmological applications of F(R,T) gravity with dynamical curvature and torsion

We investigate the cosmological applications of Myrzakulov $F(R,T)$ gravity. In this theory ones uses a specific but non-special connection, and thus both curvature and torsion are dynamical fields related to gravity. We introduce a parametrization that quantifies the deviation of curvature and torsion scalars form their corresponding values obtained using the special Levi-Civita and Weitzenb{\"{o}}ck connections, and we extract the cosmological field equations following the mini-super-space procedure. Even for the simple case where the action of the theory is linear in $R$ and $T$, we find that the Friedmann equations contain new terms of geometrical origin, reflecting the non-special connection. Applying the theory at late times we find that we can acquire the thermal history of the universe, where dark energy can be quintessence-like or phantom-like, or behave exactly as a cosmological constant and thus reproducing $\Lambda$CDM cosmology. Furthermore, we show that these features are obtained for other Lagrangian choices, too. Finally, early-time application leads to the de Sitter solution, as well as to an inflationary realization with the desired scale-factor evolution.

The variable radio counterpart of Swift J1858.6-0814

ABSTRACT Swift J1858.6-0814 is a transient neutron star X-ray binary discovered in 2018 October. Multiwavelength follow-up observations across the electromagnetic spectrum revealed many interesting properties, such as erratic flaring on minute time-scales and evidence for wind outflows at both X-ray and optical wavelengths, strong and variable local absorption, and an anomalously hard X-ray spectrum. Here, we report on a detailed radio observing campaign consisting of one observation at 5.5/9 GHz with the Australia Telescope Compact Array, and nine observations at 4.5/7.5 GHz with the Karl G. Jansky Very Large Array. A radio counterpart with a flat to inverted radio spectrum is detected in all observations, consistent with a compact jet being launched from the system. Swift J1858.6-0814 is highly variable at radio wavelengths in most observations, showing significant variability when imaged on 3-to-5-min time-scales and changing up to factors of 8 within 20 min. The periods of brightest radio emission are not associated with steep radio spectra, implying they do not originate from the launching of discrete ejecta. We find that the radio variability is similarly unlikely to have a geometric origin, be due to scintillation, or be causally related to the observed X-ray flaring. Instead, we find that it is consistent with being driven by variations in the accretion flow propagating down the compact jet. We compare the radio properties of SwiftJ1858.6-0814 with those of Eddington-limited X-ray binaries with similar X-ray and optical characteristics, but fail to find a match in radio variability, spectrum, and luminosity.

Raman Scattering Polarization and Single Spinon Identification in Two-Dimensional Kitaev Quantum Spin Liquids

Perfect deporalization of the Loudon-Fleury inelastic visible-light scattering in the Kitaev honeycomb model is well known. Though it happens in Heisenberg Kagome and triangular antiferromagnets as well, yet we prove it to be of geometric origin rather than peculiar to quantum spin liquids. A Kitaev spin liquid in the square planar geometry indeed exhibits polarized Raman spectra containing defferent symmetry species, each brought by symmetry-compatible spinon geminate excitations, i.e. arising from symmetry-compatible direct-product representations made of double-valued irreducible representations of mediating-spinon-belonging gauged $\bm{k}$-point symmetry groups. We combine a standard point-symmetry-group analysis of the Raman vertex in the real space and an elaborate projective-symmetry-group analysis of Raman-scattering-mediating Majorana spinons in the reciprocal space to identify emergent spinons singly.

Modeling of a Spherical Tokamak as an Extended Neutron Source Using ASTRA and MCNP

Fast neutrons can perform two functions that are critical to the nuclear power industry: breed fissile material from fertile material and burn minor actinides in spent fuel. The fusion reaction in a fusion reactor between deuterium and tritium nuclei yields an alpha particle and a neutron with 14.5-MeV energy. These neutrons can easily convert fertile material (such as 238U and 232Th) into fissile material (such as 239Pu and 233U) and destroy minor actinides (Pu, Np, Am, and Cm) present in the spent nuclear fuel and significantly reduce its radiotoxicity. However, each neutron generated implies one tritium consumed and tritium is generated by nuclear reactions between a neutron and lithium nuclei. Therefore, neutron economy becomes a crucial issue and an adequate neutronic modeling of the neutron source becomes critical. In this article, the Automatic System for TRansport Analysis (ASTRA) and Monte Carlo N-Particle (MCNP) codes are used in conjunction to characterize the neutron flux coming out of a low-aspect-ratio tokamak machine. ASTRA is first used to determine temperature and density profiles within the plasma volume and MCNP is used to evaluate the neutron flux. Since the simulation of an extended neutron source with complex geometry such as the confined plasma inside the tokamak is difficult, steps are taken to simplify the geometry by defining two simple sources, a cylindrical wall and a disk, which should have similar neutron emission distributions to the volumetric source. This reduction is done using a preprocessing Monte Carlo algorithm to establish probability density functions of neutron emission for the cylindrical wall as a function of the height and for the disk as a function of the radius, based on the emission characteristics of the extended source. The results that compare the neutron flux leaving a volume for four different configurations of neutron sources (isotropic source at the geometrical origin, ring source at the plasma geometrical center, cylindrical wall source, and distributed multipoint source) are presented. It is found that the processing of the two simple sources has a higher computational cost in terms of both processing time and random number consumption.

Heronian Friezes

Abstract Motivated by computational geometry of point configurations on the Euclidean plane, and by the theory of cluster algebras of type $A$, we introduce and study Heronian friezes, the Euclidean analogues of Coxeter’s frieze patterns. We prove that a generic Heronian frieze possesses the glide symmetry (hence is periodic) and establish the appropriate version of the Laurent phenomenon. For a closely related family of Cayley–Menger friezes, we identify an algebraic condition of coherence, which all friezes of geometric origin satisfy. This yields an unambiguous propagation rule for coherent Cayley–Menger friezes, as well as the corresponding periodicity results.

Geometric dark matter

The dark matter, needed for various phenomena ranging from flat rotation curves to structure formation, seems to be not only neutral and long-living but also highly secluded from the ordinary matter. Here we show that, metric-affine gravity, which involves metric tensor and affine connection as two independent fields, dynamically reduces, in its minimal form, to the usual gravity plus a massive vector field. The vector, which interacts with only the quarks, leptons and gravity, is neutral and long-living (longer than the age of the Universe) when its mass range is 9.4 MeV < MY < 28.4 MeV. Its scattering cross section from nucleons, which is some 60 orders of magnitude below the current bounds, is too small to facilitate direct detection of the dark matter. This property provides an explanation for whys and hows of dark matter searches. We show that due to its geometrical origin the Yμ does not couple to scalars and gauge bosons. It couples only to fermions. This very feature of the Yμ makes it fundamentally different than all the other vector dark matter candidates in the literature. The geometrical dark matter we present is minimal and self-consistent not only theoretically but also astrophysically in that its feebly interacting nature is all that is needed for its longevity.

Maxwell equations in curved space-time: non-vanishing magnetic field in pure electrostatic systems

Solutions of the Maxwell equations for electrostatic systems with manifestly vanishing electric currents in the curved space-time for stationary metrics are shown to exhibit a non-vanishing magnetic field of pure geometric origin. In contrast to the conventional magnetic field of the Earth it can not be screened away by a magnetic shielding. As an example of practical significance we treat electrostatic systems at rest on the rotating Earth and derive the relevant geometric magnetic field. We comment on its impact on the ultimate precision searches of the electric dipole moments of ultracold neutrons and of protons in all electric storage rings.

Tunable Layer Circular Photogalvanic Effect in Twisted Bilayers.

We develop a general theory of the layer circular photogalvanic effect (LCPGE) in quasi-two-dimensional chiral bilayers, which refers to the appearance of a polarization-dependent, out-of-plane static dipole moment induced by circularly polarized light. We elucidate the geometric origin of the LCPGE as two types of interlayer coordinate shift weighted by the quantum metric tensor and the Berry curvature, respectively. As a concrete example, we calculate the LCPGE in twisted bilayer graphene, and find that it exhibits a resonance peak whose frequency can be tuned from visible to infrared as the twisting angle varies. The LCPGE thus provides a promising route toward frequency-sensitive, circularly polarized light detection, particularly in the infrared range.

A parsec-scale wobbling jet in the high-synchrotron peaked blazar PG 1553+113

Context. The detection of quasi-periodic variability in active galactic nuclei in general, and in blazars in particular, is key to our understanding of the origin and nature of these objects as well as their cosmological evolution. PG 1553+113 is the first blazar showing an approximately two-year quasi-periodic pattern in its γ-ray light curve, which is also revealed at optical frequencies. Aims. Such quasi-periodicity might have a geometrical origin, possibly related to the precessing nature of the jet, or could be intrinsic to the source and related to pulsational accretion flow instabilities. In this work we investigate and characterise the high-resolution radio emission properties of PG 1553+113 on parsec scales in order to differentiate between these different physical scenarios. Methods. We monitored the source with the very long baseline array (VLBA) at 15, 24, and 43 GHz during an entire cycle of γ-ray activity in the period 2015–2017, with a cadence of about 2 months, both in total and polarised intensity. We constrained the jet position angle across the different observing epochs by investigating the total intensity ridge lines. Results. We find a core-dominated source with a limb-brightened jet structure extending for ∼1.5 mas in the northeast direction whose position angle varies in time in the range ∼40°−60°. No clear periodic pattern can be recognized in the VLBA light curves during 2015–2017 or in the 15 GHz Owens Valley Radio Observatory light curve during the period 2008–2018. The core region polarisation percentage varies in the range ∼1−4%, and the polarisation angle varies from being roughly parallel to roughly transverse to the jet axis. We estimate a rotation measure value in the core region of ∼−1.0 ± 0.4 × 104 rad m−2. The brightness temperature (TB) is found to decrease as the frequency increases with an intrinsic value of ∼1.5 × 1010 K and the estimated Doppler factor is ∼1.4. Conclusions. Although the jet wobbling motion indicates that geometrical effects can produce an enhanced emission through the Doppler boosting modulation, additional mechanisms are required in order to account for the quasi-periodic variability patterns observed in γ rays. The intrinsic TB value indicates that the total energy in the core region is dominated by the magnetic field.

Higgs inflation in complex geometrical scalar-tensor theory of gravity

We derive a Higgs inflationary model in the context of a complex geometrical scalar-tensor theory of gravity. In this model the Higgs inflaton scalar field has geometrical origin playing the role of the Weyl scalar field in the original non-riemannian background geometry. The energy scale enough to generate inflation from the Higgs energy scale is achieved due to the compatibility of the theory with its background complex Weyl-integrable geometry. We found that for a number of e-foldings $N=63$, a nearly scale invariant spectrum for the inflaton is obtained with an spectral index $n_s\simeq 0.9735$ and a scalar to tensor ratio $r\simeq 0.01$, which are in agreement with Planck observational data.

Rigid connections and $F$-isocrystals

An irreducible integrable connection $(E,\nabla)$ on a smooth projective complex variety $X$ is called rigid if it gives rise to an isolated point of the corresponding moduli space $\mathcal{M}_{\rm dR}(X)$. According to Simpson’s motivicity conjecture, irreducible rigid flat connections are of geometric origin, that is, arise as subquotients of a Gauss–Manin connection of a family of smooth projective varieties defined on an open dense subvariety of $X$. In this article we study mod-$p$ reductions of irreducible rigid connections and establish results which confirm Simpson’s prediction. In particular, for large $p$, we prove that $p$-curvatures of mod-$p$ reductions of irreducible rigid flat connections are nilpotent, and building on this result, we construct an $F$-isocrystalline realization for irreducible rigid flat connections. More precisely, we prove that there exist smooth models $X_R$ and $(E_R,\nabla_R)$ of $X$ and $(E,\nabla)$, over a finite-type ring $R$, such that for every Witt ring $W(k)$ of a finite field $k$ and every homomorphism $R \to W(k)$, the $p$-adic completion of the base change $(\widehat{E}_{W(k)},\widehat{\nabla}_{W(k)})$ on $\widehat{X}_{W(k)}$ represents an $F$-isocrystal. Subsequently, we show that irreducible rigid flat connections with vanishing $p$-curvatures are unitary. This allows us to prove new cases of the Grothendieck–Katz $p$-curvature conjecture. We also prove the existence of a complete companion correspondence for $F$-isocrystals stemming from irreducible cohomologically rigid connections.

On a geometric origin of the electric charge quantization

The field-line description of the electric field, proposed by Faraday, accepted by Maxwell and used by Dirac, is utilized here in order to try to understand the origin of the electric charge quantization. This origin could be the result of the discrete nature of the field lines in conjunction with the requirement for spherical symmetry of the field. Under the hypothesis that for elementary particles, the electric field is consisting of only a few field lines, the d-quark could be composed of four field lines, the u-quark of eight, and the electron of 12. The proton would also exhibit a 12 field line structure. For electrons and protons, such a structure could eventually be observed with the here proposed experimental techniques. New particles with charges 1/2e, 5/3e, and 2.5e would be allowed in this context.

Photoionization of C60: Effects of Correlation on Cross Sections and Angular Distributions of Valence Subshells.

Calculations of the photoionization cross section and asymmetry parameter, β, are performed at the density functional theory (DFT) and time-dependent density functional theory (TDDFT) levels for all 32 valence levels of C60. Accurate numerical results are obtained for the isolated molecule in icosahedral symmetry. A detailed analysis based on the comparison between the DFT and TDDFT results allows the identification of four types of resonances: the well-known confinement resonances of mainly geometrical origin, shape resonances native to the ionization channel, induced shape resonances, and autoionization resonances brought about by interchannel coupling, as well as their different prominence in cross section or asymmetry parameter. Generally, cross sections are enhanced at the TDDFT level, which includes contribution from the bound-state excitations from closed channels, neglected at the DFT level, and the effect persists even well above the highest ionization threshold. This effect is best seen in the total cross section, although not as dramatic as found from simpler models, probably due to the stiffer electronic structure inherent in the full molecular description. The effects of interchannel coupling on individual native resonances are rather less predictable, leading to both enhancement and decreases and often altering the details of the structure significantly. A comparison with the previous accurate total cross-sectional calculations, as well as with the available experimental data, is very good for cross sections but slightly inferior for β's. The results reported can serve as a reference to compare the effects of different environments on C60, as well as chemical substitution, notably endohedral fullerenes.

Shift vector as the geometric origin of beam shifts

Goos-Hanchen (GH) and Imbert-Fedorov (IF) shifts are lateral and transverse displacements of a wavepacket reflecting off a surface. A dramatic real-space manifestation of wavepacket phases, they have traditionally been analyzed in a model dependent fashion. Here we argue that GH and IF shifts admit a general geometrical description and arise from a gauge invariant geometric phase. In particular, we show GH/IF shifts can be naturally captured by a shift vector, analogous to the shift vector from shift currents in the bulk photovoltaic effect. Employing Wilson loops to visualize the scattering processes contributing to the shift vector, we separate the shift into an intrinsic (depends solely on the system bulk) and an extrinsic part. This enables to establish a clear model-independent link between symmetry and the presence/absence of intrinsic and extrinsic GH/IF shifts.