Real Space Research Articles

Effect of local fractional derivatives on Riemann curvature tensor

In this paper, we give a main example indicating the ineffectiveness of the local fractional derivatives on the Riemann curvature tensor that is a common tool in calculating curvature of a Riemannian manifold. For this, first we introduce a general local fractional derivative operator that involves the mostly used ones in the literature as conformable, alternative, truncated M− and V−fractional derivatives. Then, according to this general operator, a particular Riemannian metric on the real affine space Rn that is different from the Euclidean one is defined. In conclusion, our main example states that the Riemann curvature tensor of Rn endowed with this particular metric is identically 0, that is, one is locally isometric to Euclidean space.

Intermittency in the not-so-smooth elastic turbulence.

Elastic turbulence is the chaotic fluid motion resulting from elastic instabilities due to the addition of polymers in small concentrations at very small Reynolds ( ) numbers. Our direct numerical simulations show that elastic turbulence, though a low phenomenon, has more in common with classical, Newtonian turbulence than previously thought. In particular, we find power-law spectra for kinetic energy E(k) ~ k-4 and polymeric energy Ep(k) ~ k-3/2, independent of the Deborah (De) number. This is further supported by calculation of scale-by-scale energy budget which shows a balance between the viscous term and the polymeric term in the momentum equation. In real space, as expected, the velocity field is smooth, i.e., the velocity difference across a length scale r, δu ~ r but, crucially, with a non-trivial sub-leading contribution r3/2 which we extract by using the second difference of velocity. The structure functions of second difference of velocity up to order 6 show clear evidence of intermittency/multifractality. We provide additional evidence in support of this intermittent nature by calculating moments of rate of dissipation of kinetic energy averaged over a ball of radius r, εr, from which we compute the multifractal spectrum.

Exact calculus for s-Holder subgradients in Banach spaces

We give in this paper some useful calculus results related to the s-H$\ddot{o}$lder subdifferential of extended-real valued functions defined on arbitrary real Banach spaces.

Large anomalous Hall conductivity induced by spin chirality fluctuation in an ultraclean frustrated antiferromagnet PdCrO2

Magnetic frustration, realized in the special geometrical arrangement of localized spins, often promotes topologically nontrivial spin textures in the real space and induces significantly large unconventional Hall responses. This spin Berry curvature effect in itinerant frustrated magnets mainly works with a static spin order, limiting the effective temperature range below the magnetic transition temperature and yielding the typical anomalous Hall conductivity below ~ 103 Ω−1cm−1. Here we show that an ultraclean triangular-lattice antiferromagnet PdCrO2 exhibits a large anomalous Hall conductivity up to ~ 106 Ω−1cm−1 in the paramagnetic state, which is maintained far above the Neel temperature (TN) up to ~ 4TN. The reported enhancement of anomalous Hall response above TN is attributed to the skew scattering of highly mobile Pd electrons to fluctuating but locally-correlated Cr spins with a finite spin chirality. Our findings point at an alternative route to realizing high-temperature giant anomalous Hall responses, exploiting magnetic frustration in the ultraclean regime.

Inverse Synthetic Aperture Radar Imaging of Space Targets Using Wideband Pseudo-Noise Signals with Low Peak-to-Average Power Ratio

With the number of new satellites increasing dramatically, comprehensive space surveillance is becoming increasingly important. Therefore, high-resolution inverse synthetic aperture radar (ISAR) imaging of satellites can provide an in-situ assessment of the satellites. This paper demonstrates that pseudo-noise signals can also be used for satellite imaging, in addition to classical linear frequency-modulated chirp signals. Pseudo-noise transmission signals offer the advantage of very low cross-correlation values. This, for instance, enables the possibility of a system with multiple channels transmitting instantaneously. Furthermore, it can significantly reduce signal interference with other systems operating in the same frequency spectrum, which is of particular interest for high-bandwidth, high-power systems such as satellite imaging radars. A new routine has been introduced to generate a wideband pseudo-noise signal with a peak-to-average power ratio (PAPR) similar to that of a chirp signal. This is essential for applications where the transmit signal power budget is sharply limited by the high-power amplifier. The paper presents both theoretical descriptions and analysis of the generated pseudo-noise signal as well as the results of an imaging measurement of a real space target using the introduced pseudo-noise signals.

Algorithms for split equality variational inequality and fixed point problems

ABSTRACT This study presents algorithms for addressing split equality variational inequality and fixed point problems in real Hilbert spaces that are inertial-like subgradient extragradient and inertial-like Tseng extragradient, respectively. We prove that the resulting sequences of the proposed algorithms converge strongly to solutions of the problem provided that the underlying mappings are quasi-monotone, uniformly continuous and quasi-nonexpansive mappings under some mild conditions. Furthermore, numerical experiments are shown to demonstrate the effectiveness of our techniques.

Missing Wedge Completion via Unsupervised Learning with Coordinate Networks.

Cryogenic electron tomography (cryoET) is a powerful tool in structural biology, enabling detailed 3D imaging of biological specimens at a resolution of nanometers. Despite its potential, cryoET faces challenges such as the missing wedge problem, which limits reconstruction quality due to incomplete data collection angles. Recently, supervised deep learning methods leveraging convolutional neural networks (CNNs) have considerably addressed this issue; however, their pretraining requirements render them susceptible to inaccuracies and artifacts, particularly when representative training data is scarce. To overcome these limitations, we introduce a proof-of-concept unsupervised learning approach using coordinate networks (CNs) that optimizes network weights directly against input projections. This eliminates the need for pretraining, reducing reconstruction runtime by 3-20× compared to supervised methods. Our in silico results show improved shape completion and reduction of missing wedge artifacts, assessed through several voxel-based image quality metrics in real space and a novel directional Fourier Shell Correlation (FSC) metric. Our study illuminates benefits and considerations of both supervised and unsupervised approaches, guiding the development of improved reconstruction strategies.

Group-Invariant Max Filtering

AbstractGiven a real inner product space V and a group G of linear isometries, we construct a family of G-invariant real-valued functions on V that we call max filters. In the case where $$V={\mathbb {R}}^d$$ V = R d and G is finite, a suitable max filter bank separates orbits, and is even bilipschitz in the quotient metric. In the case where $$V=L^2({\mathbb {R}}^d)$$ V = L 2 ( R d ) and G is the group of translation operators, a max filter exhibits stability to diffeomorphic distortion like that of the scattering transform introduced by Mallat. We establish that max filters are well suited for various classification tasks, both in theory and in practice.

An interpolation result for A_1 weights with applications to fractional Poincaré inequalities

We characterize the real interpolation space between weighted \(L^1\) and \(W^{1,1}\) spaces on arbitrary domains different from \(\mathbb{R}^n\), when the weights are positive powers of the distance to the boundary multiplied by an \(A_1\) weight. As an application of this result we obtain weighted fractional Poincaré inequalities with sharp dependence on the fractional parameter \(s\) (for \(s\) close to 1) and show that they are equivalent to a weighted Poincaré inequality for the gradient.

Atomic-Scale Tracking Topological Phase Transition Dynamics of Polar Vortex-Antivortex Pairs.

Non-trivial topological structures, such as vortex-antivortex (V-AV) pairs, have garnered significant attention in the field of condensed matter physics. However, the detailed topological phase transition dynamics of V-AV pairs, encompassing behaviors like self-annihilation, motion, and dissociation, have remained elusive in real space. Here, we employ polar V-AV pairs as a model system and track their transition pathways with atomic-scale resolution, facilitated by in situ (scanning) transmission electron microscopy and phase field simulations. Our investigation reveals that polar vortices and antivortices can stably coexist as bound pairs at room temperature, and their polarization decreases with heating. No dissociation behavior is observed between the V-AV phase at room temperature and the paraelectric phase at high temperature. However, the application of electric fields can promote the approach of vortex and antivortex cores, ultimately leading to their annihilation near the interface. Revealing the transition process mediated by polar V-AV pairs at the atomic scale, particularly the role of polar antivortex, provides us new insights into understanding the topological phases of matter and their topological phase transitions. Moreover, the detailed exploration of the dynamics of polar V-AV pairs under thermal and electrical fields lays a solid foundation for their potential applications in electronic devices. This article is protected by copyright. All rights reserved.

Hidden Real Topology and Unusual Magnetoelectric Responses in Two-Dimensional Antiferromagnets.

Recently, the real topology has been attracting widespread interest in two dimensions (2D). Here, based on first-principles calculations and theoretical analysis, the monolayer Cr2Se2O (ML-CrSeO) is revealed as the first material example of a 2D antiferromagnetic (AFM) real Chern insulator (RCI) with topologically protected corner states. Unlike previous RCIs, it is found that the real topology of the ML-CrSeO is rooted in one certain mirror subsystem of the two spin channels, and cannot be directly obtained from all the valence bands in each spin channel as commonly believed. In particular, due to antiferromagnetism, the corner modes in ML-CrSeO exhibit strong corner-contrasted spin polarization, leading to spin-corner coupling (SCC). This SCC enables a direct connection between spin space and real space. Consequently, large and switchable net magnetization can be induced in the ML-CrSeO nanodisk by electrostatic means, such as potential step and in-plane electric field, and the corresponding magnetoelectric responses behave like a sign function, distinguished from that of the conventional multiferroic materials. This work considerably broadens the candidate range of RCI materials, and opens up a new direction for topo-spintronics and 2D AFM materialsresearch.

Fermi Surface Spin Texture and Topological Superconductivity in Spin-Orbit Free Noncollinear Antiferromagnets.

We explore the relationship among the magnetic ordering in real space, the resulting spin texture on the Fermi surface, and the related superconducting gap structure in noncollinear antiferromagnetic metals without spin-orbit coupling. Via a perturbative approach, we show that noncollinear magnetic ordering in a metal can generate momentum-dependent spin texture on its Fermi surface, even in the absence of spin-orbit coupling, if the metal has more than three sublattices in its magnetic unit cell. Thus, our theory naturally extends the idea of altermagnetism to noncollinear spin structures. When superconductivity is developed in a magnetic metal, as the gap-opening condition is strongly constrained by the spin texture, the nodal structure of the superconducting state is also enforced by the magnetism-induced spin texture. Taking the noncollinear antiferromagnet on the kagome lattice as a representative example, we demonstrate how the Fermi surface spin texture induced by noncollinear antiferromagnetism naturally leads to odd-parity spin-triplet superconductivity with nontrivial topological properties.

Average Degree of the Essential Variety

AbstractThe essential variety is an algebraic subvariety of dimension 5 in real projective space $$\mathbb R\mathrm P^{8}$$ R P 8 which encodes the relative pose of two calibrated pinhole cameras. The 5-point algorithm in computer vision computes the real points in the intersection of the essential variety with a linear space of codimension 5. The degree of the essential variety is 10, so this intersection consists of 10 complex points in general. We compute the expected number of real intersection points when the linear space is random. We focus on two probability distributions for linear spaces. The first distribution is invariant under the action of the orthogonal group $$\textrm{O}(9)$$ O ( 9 ) acting on linear spaces in $$\mathbb R\mathrm P^{8}$$ R P 8 . In this case, the expected number of real intersection points is equal to 4. The second distribution is motivated from computer vision and is defined by choosing 5 point correspondences in the image planes $$\mathbb R\mathrm P^2\times \mathbb R\mathrm P^2$$ R P 2 × R P 2 uniformly at random. A Monte Carlo computation suggests that with high probability the expected value lies in the interval $$(3.95 - 0.05,\ 3.95 + 0.05)$$ ( 3.95 - 0.05 , 3.95 + 0.05 ) .

Convergence Results for History-Dependent Variational Inequalities

We consider a history-dependent variational inequality in a real Hilbert space, for which we recall an existence and uniqueness result. We associate this inequality with a gap function, together with two additional problems: a nonlinear equation and a minimization problem. Then, we prove that solving these problems is equivalent to solving the original history-dependent variational inequality. Next, we state and prove a convergence criterion, i.e., we provide necessary and sufficient conditions which guarantee the convergence of a sequence of functions to the solution of the considered inequality. Based on the equivalence above, we deduce various consequences that present some interest on their own, and, moreover, we obtain convergence results for the two additional problems considered. Finally, we apply our abstract results to the study of an inequality problem in solid mechanics. It concerns the study of a viscoelastic constitutive law with long memory and unilateral constraints, for which we deduce a convergence result and provide the corresponding mechanical interpretations.

Fourier transform-based post-processing drift compensation and calibration method for scanning probe microscopy

Scanning probe microscopy (SPM) is ubiquitous in nanoscale science allowing the observation of features in real space down to the angstrom resolution. The scanning nature of SPM, wherein a sharp tip rasters the surface during which a physical setpoint is maintained via a control feedback loop, often implies that the image is subject to drift effects, leading to distortion of the resulting image. While there are in-operando methods to compensate for the drift, correcting the residual linear drift in obtained images is often neglected. In this paper, we present a reciprocal space-based technique to compensate the linear drift in atomically-resolved scanning probe microscopy images without distinction of the fast and slow scanning directions; furthermore this method does not require the set of SPM images obtained for the different scanning directions. Instead, the compensation is made possible by the a priori knowledge of the lattice parameters. The method can also be used to characterize and calibrate the SPM instrument.

A step towards 6D WAXD tensor tomography.

X-ray scattering/diffraction tensor tomography techniques are promising methods to acquire the 3D texture information of heterogeneous biological tissues at micrometre resolution. However, the methods suffer from a long overall acquisition time due to multi-dimensional scanning across real and reciprocal space. Here, a new approach is introduced to obtain 3D reciprocal information of each illuminated scanning volume using mathematic modeling, which is equivalent to a physical scanning procedure for collecting the full reciprocal information required for voxel reconstruction. The virtual reciprocal scanning scheme was validated by a simulated 6D wide-angle X-ray diffraction tomography experiment. The theoretical validation of the method represents an important technological advancement for 6D diffraction tensor tomography and a crucial step towards pervasive applications in the characterization of heterogeneous materials.

Gate-Tunable Asymmetric Quantum Dots in Graphene-Based Heterostructures: Pure Valley Polarization and Confinement

We explore the possibility of attaining valley-dependent tunnelling and confinement using proximity-induced spin-orbit couplings (SOCs) in graphene-based heterostructures. We consider gate-tunable asymmetric quantum dots (AQDs) on graphene heterostructures and exhibiting a C3v and/or C6v symmetry. By employing a tight-binding model, we explicitly reveal a pure valley confinement and valley signal in AQDs by streaming the valley local density, leading to valley-charge separation in real space. The confinement of the valley quasi-bound states is sensitive to the locally induced SOCs and to the spatial distribution of the induced AQDs; it is also robust against on-site disorder. The adopted process of attaining a pure valley-Hall conductivity and confinement with zero charge currents is expected to provide more options towards valley-dependent electron optics.

Spin-orbit coupled Hubbard skyrmions

When the material phases exhibit topological quantum numbers, they host defects protected by the nontrivial topology. Magnetic skyrmions are such “quantized” objects, and although many of them are metals, they had been most likely treated in theories as purely classical spin states. Here, we show that the electrons described by the Hubbard model with strong spin-orbit couplings can exhibit various nano- or flake-size skyrmions in their ground state. Importantly, the conducting electrons forming Fermi pockets themselves carry textured magnetic moments in both real and momentum space and on top of that possess Chern numbers in their energy bands. This quantum and conducting skyrmion is related to small skyrmions observed in atomic-layered compounds. We clarify how the effective magnetic interactions and magnetic anisotropies are tied to the spin-orbit coupling, and how they influence the stability of skyrmions beyond the phenomenology. Published by the American Physical Society 2024

Preferences, risk neutrality and risk-sensitive MDPs

Preferences, risk neutrality and risk-sensitive MDPs

Quantum-Acoustical Drude Peak Shift.

Quantum acoustics-a recently developed framework parallel to quantum optics-establishes a nonperturbative and coherent treatment of the electron-phonon interaction in real space. The quantum-acoustical representation reveals a displaced Drude peak hiding in plain sight within the venerable Fröhlich model: the optical conductivity exhibits a finite frequency maximum in the far-infrared range and the dc conductivity is suppressed. Our results elucidate the origin of the high-temperature absorption peaks in strange or bad metals, revealing that dynamical lattice disorder steers the system towards a non-Drude behavior.