Simple Superpositions Research Articles

No general relation between phase vortices and orbital angular momentum

Simple superpositions of Laguerre–Gauss beams illustrate, counterintuitively, the difference between two quantities that are commonly conflated: the component of orbital angular momentum ⟨l⟩ in the propagation direction z, and the total topological charge S, which is the algebraic sum of the charges of vortices piercing any plane perpendicular to z. The examples illustrate two contrasting situations: ⟨l⟩ = 0, S ≠ 0, and ⟨l⟩ ≠ 0, S = 0. In the second situation, not only is the total charge zero but also there are no vortices in the infinite half-space beyond the beam waist plane z = 0.

MCPANet: Multiscale Cross-Position Attention Network for Retinal Vessel Image Segmentation

Accurate medical imaging segmentation of the retinal fundus vasculature is essential to assist physicians in diagnosis and treatment. In recent years, convolutional neural networks (CNN) are widely used to classify retinal blood vessel pixels for retinal blood vessel segmentation tasks. However, the convolutional block receptive field is limited, simple multiple superpositions tend to cause information loss, and there are limitations in feature extraction as well as vessel segmentation. To address these problems, this paper proposes a new retinal vessel segmentation network based on U-Net, which is called multi-scale cross-position attention network (MCPANet). MCPANet uses multiple scales of input to compensate for image detail information and applies to skip connections between encoding blocks and decoding blocks to ensure information transfer while effectively reducing noise. We propose a cross-position attention module to link the positional relationships between pixels and obtain global contextual information, which enables the model to segment not only the fine capillaries but also clear vessel edges. At the same time, multiple scale pooling operations are used to expand the receptive field and enhance feature extraction. It further reduces pixel classification errors and eases the segmentation difficulty caused by the asymmetry of fundus blood vessel distribution. We trained and validated our proposed model on three publicly available datasets, DRIVE, CHASE, and STARE, which obtained segmentation accuracy of 97.05%, 97.58%, and 97.68%, and Dice of 83.15%, 81.48%, and 85.05%, respectively. The results demonstrate that the proposed method in this paper achieves better results in terms of performance and segmentation results when compared with existing methods.

A perspective on intelligent design of engineered materials and structures by interface mechanics

Engineering design of materials and structures has evolved radically from earliest employment of single phase materials with a focus on optimization of geometric shapes to recent multiphase materials with tactful integration and assembly in both geometric shapes and material domains. In these recent design concepts and strategies, the interfaces are crucial and leveraged to achieve properties and functionalities surpassing those of individual material/phase components and/or their simple superpositions. This perspective focuses on the underpinned interface mechanics view in which insights are essential to understand fundamentals of integration, tailoring and assembly of multiphase materials with diverse geometric layouts. The view also provides insights to enable creations of intelligent new design concepts and approaches of materials and structures capable of being readily manufactured with current technologies. Selected examples of engineered materials and structures enabled by either solid-solid or solid-liquid interactions are provided to highlight the driving role of interface mechanics in designs and to outlook the associated future opportunities and challenges.

In-situ Switchback Formation in the Expanding Solar Wind

Abstract Recent near-Sun solar-wind observations from Parker Solar Probe have found a highly dynamic magnetic environment, permeated by abrupt radial-field reversals, or “switchbacks.” We show that many features of the observed turbulence are reproduced by a spectrum of Alfvénic fluctuations advected by a radially expanding flow. Starting from simple superpositions of low-amplitude outward-propagating waves, our expanding-box compressible magnetohydrodynamic simulations naturally develop switchbacks because (i) the normalized amplitude of waves grows due to expansion and (ii) fluctuations evolve toward spherical polarization (i.e., nearly constant field strength). These results suggest that switchbacks form in situ in the expanding solar wind and are not indicative of impulsive processes in the chromosphere or corona.

P.302 Healthy women who use oral contraceptives show lower brain serotonin 4 receptor binding relative to nonusers

Critical state field profiles and thermomagnetic instabilities are studied in two kinds of three-dimensional nanostructured superconductors. We find that the critical state field profiles in some simple bi-layer systems are not simple superpositions of critical states in the two layers. Competition between the divergence of the local field at the edges of the film and the shielding by the neighboring layer makes novel critical state field profiles. We also studied flux avalanches in shifted strip arrays (SSAs) with layer numbers up to six. Various forms of avalanches either perpendicular or parallel to the strip are observed when the overlap between strips in neighboring layers is large. We also find that introduction of asymmetry in various forms to SSA affects the shape of flux avalanches sensitively.

Simple Wave-Optical Superpositions as Prime Number Sieves.

We encode the sequence of prime numbers into simple superpositions of identical waves, mimicking the archetypal prime number sieve of Eratosthenes. The primes are identified as zeros accompanied by phase singularities in a physically generated wave field for integer valued momenta. Similarly, primes are encoded in the diffraction pattern from a simple single aperture and in the harmonics of a single vibrating resonator. Further, diffraction physics connections to number theory reveal how to encode all Gaussian primes, twin primes, and how to construct wave fields with amplitudes equal to the divisor function at integer spatial frequencies. Remarkably, all of these basic diffraction phenomena reveal that the naturally irregular sequence of primes can arise from trivially ordered wave superpositions.

Critical states and thermomagnetic instabilities in three-dimensional nanostructured superconductors

Critical state field profiles and thermomagnetic instabilities are studied in two kinds of three-dimensional nanostructured superconductors. We find that the critical state field profiles in some simple bi-layer systems are not simple superpositions of critical states in the two layers. Competition between the divergence of the local field at the edges of the film and the shielding by the neighboring layer makes novel critical state field profiles. We also studied flux avalanches in shifted strip arrays (SSAs) with layer numbers up to six. Various forms of avalanches either perpendicular or parallel to the strip are observed when the overlap between strips in neighboring layers is large. We also find that introduction of asymmetry in various forms to SSA affects the shape of flux avalanches sensitively.

ABC‐Type meso‐Triaryl‐Substituted Subporphyrins

AbstractABC‐Type subporphyrins 5a–5h, which bear three different meso‐aryl substituents, were rationally synthesized by condensation of AB‐type tripyrranes and aroyl chlorides. ABC‐Type subporphyrins 5i and 5j were synthesized by Pd‐catalyzed amination reaction of 4‐bromophenyl subporphyrins 5e and 5h, respectively. Comparative studies on these ABC‐type subporphyrins with A3‐type subporphyrins and A2B‐type subporphyrins revealed that substituent effects are mostly simple superpositions of individual substituents but cooperative effects are recognized for subporphyrins which bear both electron‐donating and electron‐withdrawing substituents. Despite extensive attempts, enantiomeric separation of B‐methoxy ABC‐type subporphyrins was unsuccessful, whereas B‐phenylated ABC‐type subporphyrins were separated to pure enantiomers. Separated enantiomers showed weak but distinct CD signals reflecting the chiral clockwise/anticlockwise arrangements of the meso‐aryl substituents. These results suggest facile racemization through SN1‐type heterolysis of the B–OMe bond in solution.

About linear superpositions of special exact solutions of Nizhnik-Veselov-Novikov equation

General scheme for calculations via Zakharov and Manakov ∂̄-dressing method of exact solutions, nonstationary and stationary, of Nizhnik-Veselov-Novikov (NVN) equation in the forms of simple nonlinear and linear superpositions of arbitrary number N of exact special solutions u(n), n = 1,..., N is presented. Simple nonlinear superpositions are given up to a constant by the sums of solutions u(n) and calculated by ∂̄-dressing of the first auxiliary linear problem with nonzero asymptotic values of potential at infinity. It is remarkable that in the zero limit of asymptotic values of potential simple nonlinear superpositions convert in to linear ones in the form of the sums of special solutions u(n). It is shown that the sums u = u(kl) + ...+ u(km), 1 ≤ k1 < k2 < ... < km ≤ N of arbitrary subsets of these N solutions are also exact solutions of NVN equation. The obtained results are illustrated in detail by hyperbolic version of NVN equation, i. e. by NVN-II equation. The presented exact solutions include as superpositions of special line solitons and also superpositions of plane wave type singular periodic solutions.

About simple nonlinear and linear superpositions of special exact solutions of Veselov-Novikov equation

New exact solutions, nonstationary and stationary, of Veselov-Novikov (VN) equation in the forms of simple nonlinear and linear superpositions of arbitrary number N of exact special solutions u(n), n = 1, …, N are constructed via Zakharov and Manakov \documentclass[12pt]{minimal}\begin{document}$\overline{\partial }$\end{document}∂¯-dressing method. Simple nonlinear superpositions are represented up to a constant by the sums of solutions u(n) and calculated by \documentclass[12pt]{minimal}\begin{document}$\overline{\partial }$\end{document}∂¯-dressing on nonzero energy level of the first auxiliary linear problem, i.e., 2D stationary Schrödinger equation. It is remarkable that in the zero energy limit simple nonlinear superpositions convert to linear ones in the form of the sums of special solutions u(n). It is shown that the sums \documentclass[12pt]{minimal}\begin{document}$u= u^{(k_1)}+\ldots + u^{(k_m)}$\end{document}u=u(k1)+...+u(km), 1 ⩽ k1 &amp;lt; k2 &amp;lt; … &amp;lt; km ⩽ N of arbitrary subsets of these solutions are also exact solutions of VN equation. The presented exact solutions include as superpositions of special line solitons and also superpositions of plane wave type singular periodic solutions. By construction these exact solutions represent also new exact transparent potentials of 2D stationary Schrödinger equation and can serve as model potentials for electrons in planar structures of modern electronics.

Introducing nonlinear, multivariate ‘Predictor Surfaces’ for quantitative modeling of chemical systems with higher-order, coupled predictor variables

Innovations in chemometrics are required for studies of chemical systems which are governed by nonlinear responses to chemical parameters and/or interdependencies (coupling) among these parameters. Conventional and linear multivariate models have limited use for quantitative and qualitative investigations of such systems because they are based on the assumption that the measured data are simple superpositions of several input parameters. ‘Predictor Surfaces’ were developed for studies of more chemically complex systems such as biological materials in order to ensure accurate quantitative analyses and proper chemical modeling for in-depth studies of such systems. Predictor Surfaces are based on approximating nonlinear multivariate model functions by multivariate Taylor expansions which inherently introduce the required coupled and higher-order predictor variables.As proof-of-principle for the Predictor Surfaces’ capabilities, an application from environmental analytical chemistry was chosen. Microalgae cells are known to sensitively adapt to changes in environmental parameters such as pollution and/or nutrient availability and thus have potential as novel in situ sensors for environmental monitoring. These adaptations of the microalgae cells are reflected in their chemical signatures which were then acquired by means of FT-IR spectroscopy. In this study, the concentrations of three nutrients, namely inorganic carbon and two nitrogen containing ions, were chosen. Biological considerations predict that changes in nutrient availability produce a nonlinear response in the cells’ biomass composition; it is also known that microalgae need certain nutrient mixes to thrive. The nonlinear Predictor Surfaces were demonstrated to be more accurate in predicting the values of these nutrients’ concentrations than principal component regression. For qualitative chemical studies of biological systems, the Predictor Surfaces themselves are a novel tool as they visualize nonlinearities and more importantly the coupling among predictor variables. Thus, they can serve as a novel tool for studies in bioanalytical chemistry, biology, and ecology.

Thermal decomposition of polymer mixtures of PVC, PET and ABS containing brominated flame retardant: Formation of chlorinated and brominated organic compounds

The thermal decomposition of various mixtures of acrylonitrile butadiene styrene copolymer (ABS), ABS containing brominated epoxy resin flame retardant and Sb2O3, poly(ethylene terephthalate) (PET) and poly(vinyl chloride) (PVC) has been studied in order to clarify the reactions between the components of mixed polymers. More than 40 halogen-containing molecules have been identified among the pyrolysis products of mixed samples. Brominated and chlorinated aromatic esters were detected from the mixtures containing PET and halogen-containing polymers. A series of chlorinated, brominated and mixed chlorinated and brominated phenols and bisphenol A molecules have been identified among the pyrolysis products of polymer mixtures containing flame retarded ABS and PVC. It was established that the decomposition rate curves (DTG) of the mixtures were not simple superpositions of the individual components indicating interactions between the decomposition reactions of the polymer components. The maximal rate of thermal decomposition of both ABS and PET decreases significantly if the mixture contains brominated epoxy flame retardant and Sb2O3 synergist. The dehydrochlorination rate of PVC is enhanced in the presence of ABS or PET.

Arrival times, complex potentials, and decoherent histories

We address a number of aspects of the arrival time problem defined using a complex potential of step function form. We concentrate on the limit of a weak potential, in which the resulting arrival time distribution function is closely related to the quantum-mechanical current. We first consider the analagous classical arrival time problem involving an absorbing potential, and this sheds some light on certain aspects of the quantum case. In the quantum case, we review the path decomposition expansion (PDX), in which the propagator is factored across a surface of constant time, so is very useful for potentials of step function form. We use the PDX to derive the usual scattering wave functions and the arrival time distribution function. This method gives a direct and geometrically appealing account of known results (but also points the way to how they can be extended to more general complex potentials). We use these results to carry out a decoherent histories analysis of the arrival time problem, taking advantage of a recently demonstrated connection between pulsed measurements and complex potentials. We obtain very simple and plausible expressions for the class operators (describing the amplitudes for crossing the origin during intervals of time) and show that decoherence of histories is obtained for a wide class of initial states (such as simple wave packets and superpositions of wave packets). We find that the decoherent histories approach gives results with a sensible classical limit that are fully compatible with standard results on the arrival time problem. We also find some interesting connections between backflow and decoherence.

Noise-based logic hyperspace with the superposition of [formula omitted] states in a single wire

In the introductory paper [L.B. Kish, Phys. Lett. A 373 (2009) 911], about noise-based logic, we showed how simple superpositions of single logic basis vectors can be achieved in a single wire. The superposition components were the N orthogonal logic basis vectors. Supposing that the different logic values have “on/off” states only, the resultant discrete superposition state represents a single number with N bit accuracy in a single wire, where N is the number of orthogonal logic vectors in the base. In the present Letter, we show that the logic hyperspace (product) vectors defined in the introductory paper can be generalized to provide the discrete superposition of 2 N orthogonal system states. This is equivalent to a multi-valued logic system with 2 2 N logic values per wire. This is a similar situation to quantum informatics with N qubits, and hence we introduce the notion of noise-bit. This system has major differences compared to quantum informatics. The noise-based logic system is deterministic and each superposition element is instantly accessible with the high digital accuracy, via a real hardware parallelism, without decoherence and error correction, and without the requirement of repeating the logic operation many times to extract the probabilistic information. Moreover, the states in noise-based logic do not have to be normalized, and non-unitary operations can also be used. As an example, we introduce a string search algorithm which is O ( M ) times faster than Grover's quantum algorithm (where M is the number of string entries), while it has the same hardware complexity class as the quantum algorithm.

Nano-nanocomposites: an emerging class of materials

We review some of our recent results on nano-nanocomposites (NNC), which may be defined as a random, bi-phasic nanodispersion, i.e., where the characteristic size of both phases present is in nanometers. This is a subset of the larger family of nanocomposites, which commonly consist of one phase nanodispersed in an extended matrix phase. Such systems afford the possibility of tuning their physico-chemical properties via a large number of parameters, which include the nature of the components, the composition, and the size and morphology of both the phases. In certain especially interesting situations, the properties of the NNC are not simple linear superpositions of the properties of the individual nanocrystalline species. The three such special cases that are reviewed here include: NNCs of II-VI semiconductors with different band gaps that show enhanced photoluminescence, photoconductivity, and non-linear optical properties; NNCs of a superconductor and a normal metal, whose properties are predominantly controlled by the superconducting proximity effect; Metal-metal NNCs that are actually nanoscale, phase-separated alloys of 'immiscible' metals.

Decoherence of multicomponent symmetrical superpositions of displaced quantum states

We study the decoherence of superpositions of displaced quantum states of the form (where |g⟩ is an arbitrary ‘fiducial’ state and is the usual displacement operator) within the framework of the standard master equation for a quantum damped or amplified harmonic oscillator interacting with a phase-insensitive (thermal) reservoir. We compare two simple measures of the degree of decoherence: the quantum purity and the height of the central interference peak of the Wigner function. We show that for N > 2 ‘mesoscopic’ components of the superposition, the decoherence process cannot be characterized by a single decoherence time. Therefore, we distinguish the ‘initial decoherence time’ and ‘final decoherence time’ and study their dependence on the parameters αk and N. We obtain approximate formulae for an arbitrary state |g⟩ and explicit exact expressions in the special case of |g⟩ = |m⟩, i.e., for (symmetrical) superpositions of displaced Fock states of occupation number m. We show that the superposition with a large number of components N and rich ‘internal structure’ (m ∼ |α|2) can be more robust against decoherence than simple superpositions of two coherent states (with m = 0), even if the initial decoherence times coincide. Also, we show how initial pure quantum superpositions are transformed into highly mixed and totally classical superpositions in the case of a phase-insensitive amplifier.

Decoherence of multicomponent and multimode generalizations of even/odd coherent states in thermal and phase reservoirs

Within the framework of the standard master equation for a quantum damped harmonic oscillator interacting with a phase-insensitive (thermal) reservoir, we study the decoherence of superpositions of displaced quantum states of the form \(\sum\nolimits_{k = 1}^N {c_k \hat D(\alpha _k )\left. {|g} \right\rangle } \), where |g〉 is an arbitrary “fiducial” state and \(\hat D(\alpha )\) is the usual displacement operator. We compare two simple measures of degree of decoherence — the quantum purity and the height of the central interference peak of the Wigner function. We show that for N > 2 components of the superposition, the decoherence process cannot be characterized by a single decoherence time if |α| ≫ 1. Therefore, we distinguish the “initial decoherence time” (IDT) and “final decoherence time” (FDT) and study their dependence on parameters α k and N. Explicit exact expressions are obtained in the special case of |g〉 = |m〉, i.e., for (symmetric) superpositions of displaced number states. We show that the superposition with a big number of components N and rich “internal structure” (m ∼ |α|2) can be more robust against decoherence than simple superpositions of two coherent states, even if the initial decoherence times coincide. Comparing the decoherence of n-mode superpositions of coherent states, we show that the FDT of initially factorized states can be significantly bigger than that of initially maximum entangled states with the same initial energy, especially if n ≫ 1. We compare the decoherence rates of even/odd superpositions of displaced number states |m, α〉± and photon-added coherent states |α, m〉± and show that their dependence on m is completely different. Finally, we find analytical expressions for the Wigner function and the time-dependent purity of even/odd coherent states in the case of phase damping. In this case, the IDT has the same dependence on the distance between the two components of the superposition as in the case of amplitude damping. However, the long-time behavior of the Wigner function is quite different, because the asymptotical stationary state is not a thermal one, but a strongly nonclassical (although highly mixed) state.

The mesoscale convection life cycle: Building block or prototype for large-scale tropical waves?

A cumulonimbus cloud may ascend and spawn its anvil cloud, precipitation, and downdrafts within an hour or so. This paper inquires why a similar progression of events (life cycle) is observed for tropical weather fluctuations with time scales of hours, days, and even weeks. Regressions using point data illustrate the characteristic unit of rain production: the mesoscale convective system (MCS), covering tens of kilometers and lasting several hours, with embedded convective rain cells. Meanwhile, averages over larger spatial areas indicate a self-similar progression from shallow to deep convection to stratiform anvils on many time scales. Synthetic data exercises indicate that simple superpositions of fixed-structure MCS life cycles (the Building Block hypothesis) cannot explain why longer period life cycles are similar. Rather, it appears that an MCS may be a small analogue or prototype of larger scale waves. Multiscale structure is hypothesized to occur via a Stretched Building Block conceptual model, in which the widths (durations) of zones of shallow, deep, and stratiform anvil clouds in MCSs are modulated by larger scale waves. Temperature ( T) and humidity ( q) data are examined and fed into an entraining plume model, in an attempt to elucidate their relative roles in these large-scale convection zone variations. T profile variations, with wavelengths shorter than troposphere depth, appear important for high-frequency ( ∼ 2–5-day period) convectively coupled waves, as density directly links convection (via buoyancy) and large-scale wave dynamics (via restoring force). Still, the associated q anomalies are several times greater than adiabatic, suggesting a strong amplification by shallow convective feedbacks. For lower frequency (intraseasonal) variability, q anomalies are considerably larger compared to T, and may be dominant.

Branches in the Spectral Flow of the Inhomogeneous Transfer Matrix for the XXZ Spin Chain

Branches such as bifurcations or multiple branches are observed in the flow of eigenvalues for the inhomogeneous transfer matrix of the XXZ spin chain. The spectral flow for the XXZ anisotropic parameter Δ is obtained by directly diagonalizing the transfer matrix in the regime: -1 ≤Δ≤1, where the inhomogeneous transfer matrix is real and symmetric. The branches are considered as novel spectral behaviors, which are not decomposed into simple superpositions of level crossings. We may call them level bifurcations . We also observe that no branches appear in the homogeneous case. The appearance of some of the branches are confirmed through the Bethe ansatz method.

Exact Connections of Warping Fields and Torsional Rigidities of Symmetric Composite Bars

Saint-Venant's torsion of symmetric cylindrical bars consisting of two or four homogeneous phases is studied. A symmetric section is meant that the cross section of the cylindrical bar possesses reflectional symmetry with respect to one or more axes. Each constituent region may have different shear modulus. The idea of the analysis is to superimpose suitably reflected potentials to obtain the torsion solution of the same composite section but with different moduli. For two-phase sections, we show that, if the warping fields for a given symmetric section with phase shear moduli μ1 and μ2 are known a priori, then the warping fields for the same configuration but with a different set of constituent moduli μ1 ′ and μ2 ′ are readily found through simple linear superpositions. Further, suppose that the torsional rigidities T(μ1,μ2) and T(μ1 ′,μ2 ′) for any two sets of phase moduli can be measured by some experimental tests or evaluated through numerical procedures, then the torsional rigidity for any other combinations of constituent moduli T(μ1 ′′,μ2 ′′) can be exactly determined without any recourse to the field solutions of governing differential equations. Similar procedures can be applied to a 4-phase symmetric section. But the coefficients of superposition are only found for a few branches. Specifically, we find that depending on the conditions of μ and μ′, admissible solutions can be divided into three categories. When the correspondence between the warping field is known to exist, a link between the torsional rigidities can be established as well.