Weak Inhomogeneity Research Articles

Anomalous dispersion, superluminality, and instabilities in two-flavor theories with local non-Hermitian mass mixing

Pseudo-Hermitian field theories possess a global continuous “similarity” symmetry, interconnecting the theories with the same physical particle content and an identical mass spectrum. In their regimes with real spectra, within this family of similarity transformations, there is a map from the non-Hermitian theory to its Hermitian similarity partner. We promote the similarity transformation to a local symmetry, which requires the introduction of a new vector similarity field as a connection in the similarity space of non-Hermitian theories. In the case of non-Hermitian two-flavor scalar or fermion mixing and by virtue of a novel IR/UV mixing effect, the effect of inhomogeneous non-Hermiticity then reveals itself via anomalous dispersion, instabilities, and superluminal group velocities at very high momenta, thus setting an upper bound on the particle momentum propagating through inhomogeneous backgrounds characterized by Lagrangians with non-Hermitian mass matrices. Such a non-Hermitian extension of the Standard Model of particle physics, encoded in a weak inhomogeneity of the non-Hermitian part of the fermion mass matrix, may nevertheless provide us with a low-energy particle spectrum consistent with experimentally observed properties. Published by the American Physical Society 2024

Inertial range scaling of inhomogeneous turbulence

We investigate how inhomogeneity influences the $k^{-5/3}$ inertial range scaling of turbulent kinetic energy spectra (with $k$ the wavenumber). For weak statistical inhomogeneity, the energy spectrum can be described as an equilibrium spectrum plus a perturbation. Theoretical arguments suggest that this latter contribution scales as $k^{-7/3}$ . This prediction is assessed using direct numerical simulations of three-dimensional Kolmogorov flow.

Individual tooth segmentation in human teeth images using pseudo edge-region obtained by deep neural networks

In human teeth images taken outside the oral cavity with a general optical camera, it is difficult to segment individual tooth due to common obstacles such as weak edges, intensity inhomogeneities and strong light reflections. In this work, we propose a method for segmenting individual tooth in human teeth images. The key to this method is to obtain pseudo edge-region using deep neural networks. After an additional step to obtain initial contours for each tooth region, the individual tooth is segmented by applying active contour models. We also present a strategy using existing model-based methods for labeling the data required for neural network training.

Mathematical modeling of diagnostics of residual stresses in a layered medium

The work is devoted to the use of mathematical modeling in the framework of the problems of non-destructive testing of structural materials. A mathematical formulation of a three-dimensional problem of diagnostics for elastic layered medium is constructed, which makes it possible to determine the spatial distribution of residual stresses from the values of displacements measured on the surface of a layered half-space, which arose as a result of a specially initiated wave process. Under the assumption of weak inhomogeneity and anisotropy of the layers, a transition is made to a linearized (which is ill-posed) problem, the procedure for solving which is constructed using the method of stationary basic processes. As an example, the case of diagnosing a one-dimensional (depending only on the distance to the surface) distribution of residual stresses is considered.

Thresholdless stochastic particle heating by a single wave.

Stochastic heating is a well-known mechanism through which magnetized particles may be energized by low-frequency electromagnetic waves. In its simplest version, under spatially homogeneous conditions, it is known to be operative only above a threshold in the normalized wave amplitude, which may be a demanding requisite in actual scenarios, severely restricting its range of applicability. In this paper we show, by numerical simulations supported by inspection of the particle Hamiltonian, that allowing for even a very weak spatial inhomogeneity completely removes the threshold, trading the requirement upon the wave amplitude with a requisite upon the duration of the interaction between the wave and particle. The thresholdless chaotic mechanism considered here is likely to be applicable to other inhomogeneous systems.

Multipole theory of optical spatial dispersion in crystals

Natural optical activity is the paradigmatic example of an effect originating in the weak spatial inhomogeneity of the electromagnetic field on the atomic scale. In molecules, such effects are well described by the multipole theory of electromagnetism, where the coupling to light is treated semiclassically beyond the electric-dipole approximation. That theory has two shortcomings: it is limited to bounded systems, and its building blocks -the multipole transition moments- are origin dependent. In this work, we recast the multipole theory in a translationally-invariant form that remains valid for crystals. Working in the independent-particle approximation, we introduce "intrinsic" multipole transition moments that are origin independent and transform covariantly under gauge transformations of the Bloch eigenstates. Electric-dipole transitions are given by the interband Berry connection, while magnetic-dipole and electric-quadrupole transitions are described by matrix generalizations of the intrinsic magnetic moment and quantum metric. In addition to multipole-like terms, the response of crystals at first order in the wavevector of light contains band-dispersion terms that have no counterpart in molecular theories. The full response is broken down into magnetoelectric and quadrupolar parts, which can be isolated in the static limit where electric and magnetic fields become decoupled. The rotatory-strength sum rule for crystals is found to be equivalent to the topological constraint for a vanishing chiral magnetic effect in equilibrium, and the formalism is validated by numerical tight-binding calculations.

Helical polymers for dissymmetric circularly polarized light imaging.

Control of the spin angular momentum (SAM) carried in a photon provides a technologically attractive element for next-generation quantum networks and spintronics1-5. However, the weak optical activity and inhomogeneity of thin films from chiral molecular crystals result in high noise and uncertainty in SAM detection. Brittleness of thin molecular crystals represents a further problem for device integration and practical realization of chiroptical quantum devices6-10. Despite considerable successes with highly dissymmetric optical materials based on chiral nanostructures11-13, the problem of integration of nanochiral materials with optical device platforms remains acute14-16. Here we report a simple yet powerful method to fabricate chiroptical flexible layers via supramolecular helical ordering of conjugated polymer chains. Their multiscale chirality and optical activity can be varied across the broad spectral range by chiral templating with volatile enantiomers. After template removal, chromophores remain stacked in one-dimensional helical nanofibrils producing a homogeneous chiroptical layer with drastically enhanced polarization-dependent absorbance, leading to well-resolved detection and visualization of SAM. This study provides a direct path to scalable realization of on-chip detection of the spin degree of freedom of photons necessary for encoded quantum information processing and high-resolution polarization imaging.

Curvature-induced pseudogauge fields from time-dependent geometries in graphene

The massless Dirac equation is studied in curved spacetime on the (2+1)-dimensional graphene sheet in time-dependent geometries. Emergent pseudogauge fields are found both in the adiabatic regime and, for high-frequency periodic geometries, in the nonadiabatic regime for a generic Friedmann-Lema\^itre-Robertson-Walker metric in Fermi normal coordinates. The former extends the conventionally understood homogeneous pseudogauge field to include weak temporal inhomogeneities. The latter, through the usage of Floquet theory, represents a new class of emergent pseudogauge field and is argued to potentially provide a condensed matter realization of cosmological high-frequency geometries.

Magnetic Helicity Fluxes from Triple Correlators

Fluxes of the magnetic helicity density play an important role in large-scale turbulent dynamos, allowing the growth of large-scale magnetic fields while overcoming catastrophic quenching. We show here, analytically, how several important types of magnetic helicity fluxes can arise from terms involving triple correlators of fluctuating fields in the helicity density evolution equation. For this, we assume incompressibility and weak inhomogeneity, and use a quasi-normal closure approximation: fourth-order correlators are replaced by products of second-order ones, and the effect of the fourth-order cumulants on the evolution of the third moments is modeled by a strong damping term. First, we show how a diffusive helicity flux, until now only measured in simulations, arises from the triple correlation term. This is accompanied by what we refer to as a random advective flux, which predominantly transports magnetic helicity along the gradients of the random fields. We also find that a new helicity flux contribution, in some aspects similar to that first proposed by Vishniac, can arise from the triple correlator. This contribution depends on the gradients of the random magnetic and kinetic energies along the large-scale vorticity, and thus arises in any rotating, stratified system, even if the turbulence is predominantly non-helical. It can source a large-scale dynamo by itself while spatially transporting magnetic helicity within the system.

SIMULATION OF TWO-COMPONENT POWDER MOLDING MELTING UNDER VACUUM SINTERING CONDITIONS

Vacuum sintering of metal powders under controlled heating conditions belongs to the traditional powder technologies employed to obtain dense composite materials. Despite the long history of studies on sintering processes, modeling in this area remains relevant since it provides deeper understanding of the associated physical phenomena. In the present work, we studied a two-component powder pressing system melting model based on the multiphase filtration theory that takes into account the differences in the melting temperatures of the components. The appearance of the liquid phase was modeled by introducing a melting temperature interval. An algorithm for the numerical realization of the model was developed. Employing a titanium-aluminum as an example, we demonstrate that even a temperature field with weak inhomogeneity can cause an inhomogeneous velocity field and redistribution of the fusible component.

Adaptive weighted curvature-based active contour for ultrasonic and 3T/5T MR image segmentation

Image segmentation is a complex and core technique for disease diagnosis or image-guided surgery in the medical image domain. However, low-quality images, such as images with weak edges and intensity inhomogeneities, may bring considerable challenges for radiologists. In this paper, we propose an adaptive weighted curvature-based active contour model by coupling heat kernel convolution and adaptively weighted high-order total variation for medical image segmentation to improve diagnosis effectiveness. To reduce the computational complexity, the heat kernel convolution operation is applied to approximate the perimeter of a segmentation curve. In addition, the weighted parameter included in the high-order total variation term can be automatically evaluated based on an adaptive input image to emphasize local structures and increase segmentation accuracy. Since the proposed method is a smoothing optimization model, the alternating direction method of multipliers is introduced to translate the original problems into several easily solvable subproblems. The numerical experimental results on ultrasonic and 3T/5T MRI datasets demonstrate that the proposed model is quite efficient and robust compared with several traditional segmentation methods.

Inhomogeneity of microstructure and mechanical properties in compression-type bulk formed specimens

The effect of elongation and spreading in a material on strain and microstructure inhomogeneity during compression-type bulk forming processes was investigated to improve the strain homogeneity of the materials. For systematic investigation, four different compression-type forming processes, namely wire flat rolling, plate flat rolling, wire caliber rolling, and uniaxial compression, were compared. Strain inhomogeneity and macroscopic shear bands (MSBs) were clearly observed during the compression-type bulk forming processes based on a comparative study on the shape change, effective strain and hardness distributions, and microstructural evolution in twinning-induced plasticity steel. The flat-rolled wire had the largest strain inhomogeneity, followed by the caliber-rolled wire, compressed specimen, and flat-rolled plate in the listed order. The inhomogeneity of the strain distribution along the horizontal direction tended to increase with the pure spreading during the forming process. Meanwhile, the inhomogeneity of the strain distribution along the vertical direction increased with decreasing elongation during the process. Therefore, a small pure spreading and large elongation of the specimen result in more homogeneous and higher quality products in the compression-type bulk forming process. For instance, the flat-rolled plate exhibited weak MSBs and low strain inhomogeneity because of the small pure spreading and large elongation during the forming process.

Phoretic self-propulsion of a slightly inhomogeneous disc

In two dimensions, the problem governing a homogeneous phoretic swimmer of circular cross-section is ill-posed because of the logarithmic divergence associated with a purely diffusive solute transport. We address here the well-posed problem that is devised by introducing a slight inhomogeneity in the interfacial chemical activity. With the radial symmetry being perturbed, phoretic motion is animated by diffusio-osmosis. Solute advection, associated with that motion, becomes comparable to diffusion at large distances. The singular problem associated with that scale disparity is analysed using matched asymptotic expansions for arbitrary values of the Damköhler number $\textit {Da}$ and the intrinsic Péclet number $\textit {Pe}$ . Asymptotic matching provides an implicit equation for the particle velocity in terms of these two parameters. The velocity exhibits a non-trivial dependence upon the sign $M$ of the slip coefficient. For $M=-1$ , we observe the appearance of several solutions beyond a $\textit {Da}$ -dependent critical value of $\textit {Pe}$ . We also address the respective limits of small and large $\textit {Da}$ for fixed $\textit {Pe}$ and arbitrary inhomogeneity, and illuminate their linkage to the limit of weak inhomogeneity.

Trans-dimensional imaging of the random inhomogeneity structure in the southern Ryukyu arc, Japan

SUMMARY The seismic velocity structure of the lithosphere shows various inhomogeneities over a wide range of scales, and such inhomogeneity causes complex seismic waves above a few hertz due to multiple scattering. Medium around active volcanoes and large faults tends to show strong random inhomogeneity in relatively small areas. For a more precise understanding of such random velocity inhomogeneities, it is necessary to estimate their detailed spatial variation without smoothing constraints. This study introduces a trans-dimensional approach for the 3-D imaging of random inhomogeneity using the reversible jump Markov chain Monte Carlo (rjMCMC) method, and set the number of structural parameters and their spatial layout as unknown parameters. Since the scale dependence of the random inhomogeneity is related to the frequency dependence of seismic wave scattering, the covariance matrix of the likelihood function was defined to be non-diagonal so that residuals at different frequencies in each ray path are correlated. A synthetic test showed this covariance matrix worked adequately for estimating parameters of a power-law-type spectrum of random inhomogeneity. Analysis of seismic data at the southern Ryukyu arc in the southwest Japan found anomalies with strong and weak inhomogeneities. A strongly inhomogeneous band with a width of 20–30 km was distributed in the Okinawa Trough at depths of 0–20 km. In part of this area, magma intrusions and associated complex structures have been detected by a seismic reflection survey. The scale of the structures discussed in this study is almost the same with that discussed in the reflection survey. The rjMCMC-based analysis made it possible to compare random inhomogeneities with the structural variations estimated by the deterministic seismic reflection survey. Since analyses of scattered seismic waves can examine much greater depths than seismic reflection surveys, further comparisons between the two methods in the shallow crust could provide useful insights for detailed interpretation of complex structures at deeper depth.

Probing Magnetic Defects in Ultra-Scaled Nanowires with Optically Detected Spin Resonance in Nitrogen-Vacancy Center in Diamond.

Magnetic nanowires (NWs) are essential building blocks of spintronics devices as they offer tunable magnetic properties and anisotropy through their geometry. While the synthesis and compositional control of NWs have seen major improvements, considerable challenges remain for the characterization of local magnetic features at the nanoscale. Here, we demonstrate nonperturbative field distribution mapping in ultrascaled magnetic nanowires with diameters down to 6 nm by scanning nitrogen-vacancy magnetometry. This enables localized, minimally invasive magnetic imaging with sensitivity down to 3 μT Hz-1/2. The imaging reveals the presence of weak magnetic inhomogeneities inside in-plane magnetized nanowires that are largely undetectable with standard metrology and can be related to local fluctuations of the NWs' saturation magnetization. In addition, the strong magnetic field confinement in the nanowires allows for the study of the interaction between the stray magnetic field and the nitrogen-vacancy sensor, thus clarifying the contrasting formation mechanisms for technologically relevant magnetic nanostructures.

Refined fundamental parameters of Canopus from combined near-IR interferometry and spectral energy distribution

Context. Canopus, the brightest and closest yellow supergiant to our Solar System, offers a unique laboratory for understanding the physics of evolved massive stars. Aims. We aim at quantitatively exploring a large space of fundamental parameters of Canopus based on the combined analysis of its spectral energy distribution (SED) and optical-IR long baseline interferometry. Methods. We use the most recent high resolution near-IR data from the VLTI focal beam combiners PIONIER (H and K bands) and AMBER (K band), together with precise spectrophotometric measures that cover the SED of Canopus, from the UV to the IR, taken from ground and space observatories. Results. The accurate and precise PIONIER data allowed us to simultaneously measure the angular diameter and the limb darkening (LD) profile using different analytical laws. We found that the power-law LD, being also in agreement with predictions from stellar atmosphere models, reproduces the interferometric data well. For this model we measured an angular diameter of 7.184 ± 0.0017 ± 0.029 mas and an LD coefficient of 0.1438 ± 0.0015, which are respectively ≳5 and ~15−25 more precise than in our previous A&A paper on Canopus from 2008. From a dedicated analysis of the interferometric data, we also provide new constraints on the putative presence of weak surface inhomogeneities. Additionally, we analyzed the SED in a innovative way by simultaneously fitting the reddening-related parameters and the stellar effective temperature and gravity. We find that a model based on two effective temperatures is much better at reproducing the whole SED, from which we derived several parameters, including a new bolometric flux estimate: fbol = (59.22 ± 2.45) × 10−6 erg cm−2 s−1. We were also able to estimate the stellar mass from these measurements, and it is shown to be in agreement with additional predictions from evolutionary models, from which we inferred the age of Canopus as well. Conclusions. The Canopus angular diameter and LD measured in this work with PIONIER are the most precise to date, with a direct impact on several related fundamental parameters. Moreover, thanks to our joint analysis, we were able to determine a set of fundamental parameters that simultaneously reproduces both high-precision interferometric data and a good quality SED and, at the same time, agrees with stellar evolution models. This refined set of fundamental parameters constitutes a careful balance between the different methodologies used, providing invaluable observationally based constraints to models of stellar structure and evolution, which still present difficulties in simulating stars such as Canopus in detail.

Buckling-mediated phase transitions in nano-electromechanical phononic waveguides

Acoustic signals in the megahertz to gigahertz regimes enable applications in phononic, electric and photonic circuitry. Hence, advancement in these multi-physics circuitries requires studying the transmission of elastic waves in micro/nano-electromechanical systems. Therefore, our work investigated the transmission of flexural waves in unidirectional phononic waveguides of coupled nano-electromechanical drumhead resonators. In particular, we studied the manipulation and tailoring of the transmission by thermal control of buckling within the waveguide. We showed—via experimental and computational evidence—that buckling tunes the frequency of transmission within the waveguide as determined by previous studies in literature. However, in our work, we demonstrated that excessive buckling stops the transmission in the fundamental (lowest frequency) passband of the waveguide, thus, inducing a phase transition in the waveguide leading to the absence of transmission in the respective frequency range. We computationally proved that this buckling-mediated phase transition necessitates the presence of weak inhomogeneities (∼5% variations) within the waveguide, which are inevitable in any fabrication process. In fact, these inhomogeneities are amplified due to buckling-residual stresses leading to structural aperiodicity that only affects the fundamental passband by converting the extended shapes of the transmission modes into localized shapes that prevent signal propagating throughout the waveguide.

Intrinsic Anomalous Hall Conductivity in a Nonuniform Electric Field.

We study how the intrinsic anomalous Hall conductivity is modified in two-dimensional crystals with broken time-reversal symmetry due to weak inhomogeneity of the applied electric field. Focusing on a clean noninteracting two-band system without band crossings, we derive the general expression for the Hall conductivity at small finite wave vector q to order q^{2}, which governs the Hall response to the second gradient of the electric field. Using the Kubo formula, we show that the answer can be expressed through the Berry curvature, Fubini-Study quantum metric, and the rank-3 symmetric tensor which is related to the quantum geometric connection and physically corresponds to the gauge-invariant part of the third cumulant of the position operator. We further compare our results with the predictions made within the semiclassical approach. By deriving the semiclassical equations of motion, we reproduce the result obtained from the Kubo formula in some limits. We also find, however, that the conventional semiclassical description in terms of the definite position and momentum of the electron is not fully consistent because of singular terms originating from the Heisenberg uncertainty principle. We thus present a clear example of a case when the semiclassical approach inherently suffers from the uncertainty principle, implying that it should be applied to systems in nonuniform fields with extra care.

Kinetic Modeling of Multiple Scattering of Acoustic Waves in Randomly Heterogeneous Flows

We study the propagation of sound waves in a three-dimensional, infinite ambient flow with weak random fluctuations of the mean particle velocity and speed of sound. We more particularly address the regime where the acoustic wavelengths are comparable to the correlation lengths of the weak inhomogeneities--the so-called weak coupling limit. The analysis is carried on starting from the linearized Euler equations and the convected wave equation with variable density and speed of sound, which can be derived from the nonlinear Euler equations. We use a multi-scale expansion of the Wigner distribution of a velocity potential associated to the waves to derive a radiative transfer equation describing the evolution of the angularly resolved wave action in space/time phase space. The latter experiences convection, refraction and scattering when it propagates through the heterogeneous ambient flow, although the overall wave action is conserved. The convection and refraction phenomena are accounted for by the convective part of the transport equation and depend on the smooth variations of the ambient quantities. The scattering phenomenon is accounted for by the collisional part of the transport equation and depends on the cross-power spectral densities of the fluctuations of the ambient quantities at the wavelength scales. The refraction, phase shift, spectral broadening, and multiple scattering effects of the high-frequency regimes described in various previous publications are thus encompassed by the proposed model. The overall derivation is based on the interpretation of spatial-temporal Wigner transforms in terms of semiclassical operators in their standard quantization.

Piercing the rainbow state: Entanglement on an inhomogeneous spin chain with a defect

The {\em rainbow state} denotes a set of valence bond states organized concentrically around the center of a spin 1/2 chain. It is the ground state of an inhomogeneous XX Hamiltonian and presents maximal violation of the area law of entanglement entropy. Here, we add a tunable exchange coupling constant at the center, $\gamma$, and show that it induces entanglement transitions of the ground state. At very strong inhomogeneity, the rainbow state survives for $0 \leq \gamma \leq 1$, while outside that region the ground state is a product of dimers. In the weak inhomogeneity regime the entanglement entropy satisfies a volume law, derived from CFT in curved spacetime, with an effective central charge that depends on the inhomogeneity parameter and $\gamma$. In all regimes we have found that the entanglement properties are invariant under the transformation $\gamma \longleftrightarrow 1 - \gamma$, whose fixed point $\gamma = \frac{1}{2}$ corresponds to the usual rainbow model. Finally, we study the robustness of non trivial topological phases in the presence of the defect.