Homogeneous Rings Research Articles

Modified method of round Gaussian rings. Application to the two-planetary problem

A scheme of the modified method of round Gaussian rings, designed to study the secular evolution of orbits in systems consisting of a central star and two planets, is presented. The reason for the secular evolution of the nodes and inclinations of the orbits of the planets is their mutual gravitational attraction. The orbits of the planets are modeled by homogeneous round Gaussian rings, to which the masses, sizes and angles of inclination of the orbits, as well as orbital angular momenta of the planets, are transferred. The method takes into account the fact that, in general, the ascending nodes of the orbits may not coincide. The mutual gravitational energy of the rings 𝑊𝑚𝑢𝑡 is represented as a series in the quadratic approximation in powers of small inclination angles. Using this function 𝑊𝑚𝑢𝑡, a closed system of four differential equations describing the secular evolution of the planets’ orbits is composed. The solution to the equations is obtained in finite analytic form, which simplifies the interpretation of the investigated planetary motions. The method was tested on the example of the Sun-Jupiter-Saturn system; for it, in particular, the difference in the longitudes of the nodes of the orbits of Jupiter and Saturn was calculated as a function of time. New approach is also used to study the precession of nodes in the exoplanetary system K2-36; graphs of all unknown quantities are obtained. It has been established that in the course of evolution the mutual inclination angle of the orbits remains constant, and the librations of the orbits in the inclination angle and in the motion of the nodes occur synchronously.

Multiple Sound Scattering by Combinations of Cylindrically Symmetric and Linearly Invariant Anomalies

A number of previous papers have used the coupled-mode method to assess three-dimensional scattering by cylindrically symmetric anomalies (seamounts, hills) or anomalies which are invariant in a horizontal direction (wedges, ridges). This paper makes an extension to combinations of these two anomaly types. The upper and lower depth boundaries of the anomalies may be flat or irregular, and the sound source may be anywhere in the medium. After a discretization of the anomalies of the two types with laterally homogeneous rings and strips, respectively, an adaptation of the coupled-mode method yields the solution of the pertinent Helmholtz equation. The adaptation involves a combination of Fourier-series summations to handle the ring anomalies and adaptive wavenumber integrations to handle the strip structure. For each anomaly, recursively computed reflection matrices relate the expansion coefficients for incoming and outgoing normal modes. Iterative solution of a linear equation system for the amplitudes of the scattered cylindrical waves from the ring anomalies, involving formulas for transformation between plane and cylindrical waves, yields an expansion of the field. Related expansions allow isolation of partial waves, multiply scattered among the anomalies. The paper includes examples from underwater acoustics and atmospheric acoustics.

Emergence of diverse patterns driven by molecular motors in the motility assay.

Actomyosin contractility originating from interactions between F-actin and myosin motors in the actin cytoskeleton generates mechanical forces and drives a wide range of cellular processes including cell migration and cytokinesis. To probe the interactions between F-actin and myosin motors, the myosin motility assay has been popularly employed, which consists of myosin heads attached to a glass surface and F-actins gliding on the surface via interactions with the heads. Several experiments have shown that F-actins move in a collective fashion due to volume-exclusion effects between neighboring F-actins. Furthermore, Computational models have shown how changes in key parameters lead to diverse pattern formation in motility assay. However, in most of the computational models, myosin motors were implicitly considered by applying a constant propulsion force to filaments to reduce computational cost. This simplification limits the physiological relevance of the insights provided by the models and potentially leads to artifacts. In this study, we employed an agent-based computational model for the motility assay with explicit immobile motors interacting with filaments. We rigorously account for the kinetics of myosin motors including the force-velocity relationship for walking and the binding and unbinding behaviors. We probed the effects of the length, rigidity, and concentration of filaments and repulsive strength on collective movements and pattern formation. It was found that four distinct types of structures-homogeneous networks, flocks, bands, and rings-emerged as a result of collisions between gliding filaments. We further analyzed the frequency and morphology of these structures and the curvature, alignment, and rotational motions of filaments. Our study provides better insights into the origin and properties of patterns formed by gliding filaments beyond what was shown before.

Levelness versus nearly Gorensteinness of homogeneous rings

Levelness and nearly Gorensteinness are well-studied properties of graded rings as a generalized notion of Gorensteinness. In this paper, we compare the strength of these properties. For any Cohen-Macaulay homogeneous affine semigroup ring R, we give a necessary condition for R to be non-Gorenstein and nearly Gorenstein in terms of the h-vector of R and we show that if R is nearly Gorenstein with Cohen-Macaulay type 2, then it is level. We also show that if Cohen-Macaulay type is more than 2, there are 2-dimensional counterexamples. Moreover, we characterize nearly Gorensteinness of Stanley-Reisner rings of low-dimensional simplicial complexes.

The h-vectors of the edge rings of a special family of graphs

The h-vectors of homogeneous rings are one of the most important invariants that often reflect ring-theoretic properties. On the other hand, there are a few examples of edge rings of graphs whose h-vectors are explicitly computed. In this paper, we compute the h-vector of a special family of graphs, by using the technique of initial ideals and the associated simplicial complex.

The exact solution of annular sandwich plate undercoated with radial-FGM subjected to radial pressure or transverse load

This study aims to derive the exact stretching and bending solutions of the radially FGM annular sandwich plate subjected to either radial pressure or transverse load. The radially FGM annular sandwich plate consists of two homogeneous rings and an FGM-undercoated layer with uniform Poisson’s ratio and radially graded Young’s modulus based on the power function. Although the radially FGM annular sandwich plate is nonhomogeneous, the stretching and bending problems can be analyzed separately based on the elastic plate theory. Then the exact solution corresponding to the power-law graded FGM can be evaluated by solving the simultaneous equations of the boundary and continuous conditions. The theoretical results are validated through the comparison with the finite element solutions. When degenerated, our results coincide with those of the homogeneous annular plate in the literature, making the obtained solutions reliable. Using the radial-FGM as the undercoated layer makes the strains and stresses smoothly continuous at the interfaces of the layers. The effects of the material index on mechanical behavior are under investigation.

Water wave cloaking using a floating composite plate

The trajectory of surface gravity waves in the potential flow regime is affected by the gravitational acceleration, water density and sea bed depth. Although the gravitational acceleration and water density are approximately constant, the effect of water depth on surface gravity waves exponentially decreases as the water depth increases. In shallow water, cloaking an object from surface waves by varying the sea bed topography is possible, however, as the water depth increases, cloaking becomes a challenge because there is no physical parameter to be engineered and subsequently affects the wave propagation. In order to create an omnidirectional cylindrical cloaking device for finite-depth/deep-water waves, we propose an elastic composite plate that floats on the surface around a to-be-cloaked cylinder. The composite plate is made of axisymmetric, homogeneous and isotropic annular thin rings which provide adjustable degrees of freedom to engineer and affect the wave propagation. We first develop a pseudo-spectral method to efficiently determine the wave solution for a floating composite plate. Next, we optimise the physical parameters of the plate (i.e. flexural rigidity and mass of every ring) using an evolutionary algorithm to minimise the energy of scattered waves from the object and therefore cloak the inner cylinder from incident waves. We show that the optimised cloak reduces the energy of scattered waves as high as 99 % for the target wave number. We quantify the effectiveness of our cloak with different parameters of the plate and show that varying the flexural rigidity is essential to control wave propagation and the cloaking structure needs to be at least made of four rings with a radius of at least three times of the cloaked region. We quantify the wave drift force exerted on the structures and show that the optimised plate reduces the exerted force by 99.9 %. The proposed cloak, due to its structural simplicity and effectiveness in reducing the wave drift force, may have potential applications in cloaking offshore structures from water waves.

Nitrogen-Embedded Multi-Resonance Heteroaromatics with Prolonged Homogeneous Hexatomic Rings.

Nitrogen-containing polycyclic heteroaromatics have exhibited fascinating multi-resonance (MR) characteristics for efficient narrowband emission, but strategies to bathochromic shift their emissions while maintaining the narrow bandwidths remain exclusive. Here, homogeneous hexatomic rings are introduced into nitrogen-embedded MR skeletons to prolong the π-conjugation length for low-energy electronic transitions while retaining the non-bonding character of the remaining parts. The proof-of-the-concept emitters exhibit near unity photoluminescence quantum yields with peaks at 598 nm and 620 nm and small full-width-at-half-maximums of 28 nm and 31 nm, respectively. Optimal organic light-emitting diodes exhibit a high external quantum efficiency of 18.2 %, negligible efficiency roll-off, and ultra-long lifetime with negligible degradation at an initial luminance of 10 000 cd m-2 after 94 hours.

Nitrogen‐Embedded Multi‐Resonance Heteroaromatics with Prolonged Homogeneous Hexatomic Rings

AbstractNitrogen‐containing polycyclic heteroaromatics have exhibited fascinating multi‐resonance (MR) characteristics for efficient narrowband emission, but strategies to bathochromic shift their emissions while maintaining the narrow bandwidths remain exclusive. Here, homogeneous hexatomic rings are introduced into nitrogen‐embedded MR skeletons to prolong the π‐conjugation length for low‐energy electronic transitions while retaining the non‐bonding character of the remaining parts. The proof‐of‐the‐concept emitters exhibit near unity photoluminescence quantum yields with peaks at 598 nm and 620 nm and small full‐width‐at‐half‐maximums of 28 nm and 31 nm, respectively. Optimal organic light‐emitting diodes exhibit a high external quantum efficiency of 18.2 %, negligible efficiency roll‐off, and ultra‐long lifetime with negligible degradation at an initial luminance of 10 000 cd m−2 after 94 hours.

Fabrication and evaluation of negative axicons for ultrashort pulsed laser applications

We report on the fabrication and evaluation of a sharp tip negative axicon paving the way for applications in high-power ultrashort pulsed laser systems. The negative axicon is manufactured by applying a two-step all laser-based process chain consisting of ultrashort pulsed laser ablation and CO2 laser polishing finishing the component in less than 5 minutes. The finalized negative axicon reveals a surface roughness of 18 nm, fulfilling optical quality. Two measurement setups, including the ultrashort pulsed laser itself, are used to evaluate the formation of Bessel beams in detail. By applying a focusing lens behind the negative axicon, well-developed Bessel beams are generated while their lengths depend on the distance between the negative axicon and the lens. Furthermore, the diameter of the Bessel beams increase strongly with the propagation distance. By adding a second focusing lens, Bessel beams are generated at its focal position, being almost invariant of its position. Hence, the typical Bessel beam intensity distribution is observed over an entire moving range of this second lens of 300 mm. While these Bessel beams show superior quality in terms of sharp peaks with homogeneous concentric rings, only minor deviations in intensity and diameter are observed over the moving range.

Spontaneous emergence of Josephson junctions in homogeneous rings of single-crystal Sr2RuO4

The chiral p-wave order parameter in Sr2RuO4 would make it a special case amongst the unconventional superconductors. A consequence of this symmetry is the possible existence of superconducting domains of opposite chirality. At the boundary of such domains, the locally suppressed condensate can produce an intrinsic Josephson junction. Here, we provide evidence of such junctions using mesoscopic rings, structured from Sr2RuO4 single crystals. Our order parameter simulations predict such rings to host stable domain walls across their arms. This is verified with transport experiments on loops, with a sharp transition at 1.5 K, which show distinct critical current oscillations with periodicity corresponding to the flux quantum. In contrast, loops with broadened transitions at around 3 K are void of such junctions and show standard Little–Parks oscillations. Our analysis demonstrates the junctions are of intrinsic origin and makes a compelling case for the existence of superconducting domains.

Multiple underwater sound scattering by cylindrically symmetric anomalies.

A number of previous papers have treated scattering by a single cylindrically symmetric anomaly, such as a seamount, in an otherwise laterally homogeneous medium. The present paper makes an extension to several anomalies, including multiple scattering among them, and to sound sources within a horizontal anomaly region. Each anomaly is modeled as a sequence of laterally homogeneous rings. Reflection (or scattering) matrices, recursively computed by an initial outward marching step, relate the expansion coefficients for incoming and outgoing normal modes. Expressing the scattered waves from each anomaly as incoming waves on the other anomalies, with a standard approach to multiple scattering problems, a linear equation system appears for the amplitudes of these scattered waves. This equation system is solved iteratively, with a physical interpretation of the iterates as partial waves. An inward marching step, stabilized by the stored reflection matrices to incorporate the inner boundary conditions, finally yields the interior field for each anomaly. It follows by wavefield reciprocity that the reflection matrices are symmetric. As a consequence, the mentioned partial waves satisfy the reciprocity principle individually.

Prime and homogeneous rings and algebras

Prime and homogeneous rings and algebras

Prime and Homogeneous Rings and Algebras

Let ℳ be a structure of a signature Σ. For any ordered tuple $$ \overline{a}=\left({a}_1,\dots, {a}_{\mathrm{n}}\right) $$ of elements of ℳ, $$ {\mathrm{tp}}^{\mathcal{M}}\left(\overline{a}\right) $$ denotes the set of formulas θ(x1, …, xn) of a first-order language over Σ with free variables x1, . . . , xn such that $$ \mathcal{M}\left|=\theta \left({a}_1,\dots, {a}_n\right)\right. $$. A structure ℳ is said to be strongly ω-homogeneous if, for any finite ordered tuples $$ \overline{a} $$ and $$ \overline{b} $$ of elements of ℳ, the coincidence of $$ {\mathrm{tp}}^{\mathcal{M}}\left(\overline{a}\right) $$ and $$ {\mathrm{tp}}^{\mathrm{M}}\left(\overline{b}\right) $$ implies that these tuples are mapped into each other (componentwise) by some automorphism of the structure ℳ. A structure ℳ is said to be prime in its theory if it is elementarily embedded in every structure of the theory Th (ℳ). It is proved that the integral group rings of finitely generated relatively free orderable groups are prime in their theories, and that this property is shared by the following finitely generated countable structures: free nilpotent associative rings and algebras, free nilpotent rings and Lie algebras. It is also shown that finitely generated non-Abelian free nilpotent associative algebras and finitely generated non-Abelian free nilpotent Lie algebras over uncountable fields are strongly ω-homogeneous.

Axisymmetric Problem of Thermoplasticity for a Piecewise Homogeneous Ring

We develop an analytic approach to the determination and analysis of axisymmetric thermoplastic states in piecewise homogeneous rings subjected to nonstationary heating. The numerical analyses of the thermoplastic states of two- and three-layer annular plates are performed. An example of the problem of determination of compressive residual stresses in a plate subjected to local heating by a normal circular heat source illustrates the efficiency of the proposed approach in the case where the yield strength is a function of temperature.

Almost Gorenstein homogeneous rings and their h-vectors

In this paper, for the development of the study of almost Gorenstein graded rings, we discuss some relations between almost Gorensteinness of Cohen–Macaulay homogeneous rings and their h-vectors. Concretely, for a Cohen–Macaulay homogeneous ring R, we give a sufficient condition for R to be almost Gorenstein in terms of the h-vector of R (Theorem 3.1) and we also characterize almost Gorenstein homogeneous domains with small socle degrees in terms of the h-vector of R (Theorem 4.4). Moreover, we also provide the examples of almost Gorenstein homogeneous domains arising from lattice polytopes.

Thermovoltages under a non‐linear Seebeck coefficient

The thermovoltages in the case of a nonlinear absolute Seebeck‐coefficient S(T) of a material A are discussed up to the quadratic term in the expansion of S(T) for inhomogeneous (AB) as well as for homogeneous (AA) material rings. The quadratic term results in additional thermovoltages and in particular in a Benedicks effect, ΔuAA ∼ (ΔT)3, but only if there is a thermal asymmetry in the bisectional ring AA, too. The coefficients of the expansion of S(T) are calculated for the case that the quadratic term originates from the thermal expansion of a metallic material, using the Boltzmann–Fermi theory.

Analytical model of motion of turbulent vortex rings in an incompressible fluid

An analytical model describing the motion of vortex rings in an incompressible fluid is constructed. The model is valid both for homogeneous and inhomogeneous vortices buoyant in the gravity field, as well as for combined vortices. The expansion angle of a buoyant vortex is found from the characteristic parameters that define the flow rather than specified on the basis of experiments. Significant differences in the expansion angles of homogeneous and buoyant vortex rings are explained. The calculation results for the proposed model are compared with the results of laboratory experiments and data on the rise of the cloud produced by an atomic explosion.

Monolayer formation of hexagonal boron nitride on Ag(001)

The formation of monolayers from hexagonal boron nitride, h-BN, on the square Bravais lattice of a Ag(001) surface via chemical vapor deposition of borazine (HBNH)3 was investigated by X-ray photoelectron spectroscopy (XPS) and low energy electron diffraction (LEED). Due to the weak interaction between the h-BN monolayer and the Ag surface, there is no preferred orientation of the h-BN lattice. The h-BN-related hexagonal distributions of LEED spots transform into nearly homogeneous rings. The growth of h-BN on Ag(001) is the same as previously demonstrated for Ag(111), giving evidence that for weakly interacting transition metal surfaces the surface symmetry has no distinct impact on the h-BN growth.

Decomposition of monomial algebras: Applications and algorithms

Considering finite extensions K(A) K(B) of positive affine semigroup rings over a field K we have developed in (BEN) an algorithm to decompose K(B) as a direct sum of monomial ideals in K(A). By computing the regularity of homogeneous semigroup rings from the decomposition, we have confirmed the Eisenbud-Goto conjecture in a range of new cases not tractable by standard methods. Here we first illustrate this technique and its implementation in our Macaulay2 package MonomialAlgebras by computing the decomposition and the regularity step by step for an explicit example. We then focus on ring-theoretic properties of simplicial semigroup rings. From the characterizations given in (BEN), we develop and prove explicit algorithms testing various properties, including being Buchsbaum, Cohen- Macaulay, Gorenstein, normal, and seminormal. All algorithms are implemented in our Macaulay2 package.