Ring Geometry Research Articles

Ground-State Properties and Phase Separation of Binary Mixtures in Mesoscopic Ring Lattices.

We investigated the spatial phase separation of the two components forming a bosonic mixture distributed in a four-well lattice with a ring geometry. We studied the ground state of this system, described by means of a binary Bose–Hubbard Hamiltonian, by implementing a well-known coherent-state picture which allowed us to find the semi-classical equations determining the distribution of boson components in the ring lattice. Their fully analytic solutions, in the limit of large boson numbers, provide the boson populations at each well as a function of the interspecies interaction and of other significant model parameters, while allowing to reconstruct the non-trivial architecture of the ground-state four-well phase diagram. The comparison with the L-well () phase diagrams highlights how increasing the number of wells considerably modifies the phase diagram structure and the transition mechanism from the full-mixing to the full-demixing phase controlled by the interspecies interaction. Despite the fact that the phase diagrams for share various general properties, we show that, unlike attractive binary mixtures, repulsive mixtures do not feature a transition mechanism which can be extended to an arbitrary lattice of size L.

Photonic reservoir computer using speckle in multimode waveguide ring resonators.

Photonic reservoir computers (RC) come in single mode ring and multimode array geometries. We propose and simulate a photonic RC architecture using speckle in a multimode waveguide ring resonator that requires neither the ultra-high-speed analog-digital conversion nor the spatial light modulator used in other designs. We show that the equations for propagation around a multimode (MM) ring resonator along with an optical nonlinearity, and optical feedback can be cast exactly in the standard RC form with speckle mixing performing the pseudo-random matrix multiplications. The hyperparameters are the outcoupling efficiency, the nonlinearity saturation intensity, the input bias, and the waveguide properties. In particular, the number of waveguide modes is a measure of the number of effective neurons in the RC. Simulations show a ring using a strongly guiding 50-µm planar waveguide gives 206 effective neurons and excellent predictions of Mackey-Glass waveforms for a broad range of the hyperparameters, while a weakly guiding MM 200-µm diameter fiber gives 4,238 effective neurons and excellent predictions of chaotic solutions of the Kuramoto-Sivashinsky equation. We discuss physical realizations for implementing the system with a chip-scale device or with discrete components and a MM optical fiber.

Architecture-Promoted Biomechanical Performance-Tuning of Tissue-Engineered Constructs for Biological Intervertebral Disc Replacement.

Background: Biological approaches to intervertebral disc (IVD) restoration and/or regeneration have become of increasing interest. However, the IVD comprises a viscoelastic system whose biological replacement remains challenging. The present study sought to design load-sharing two-component model systems of circular, nested, concentric elements reflecting the nucleus pulposus and annulus fibrosus. Specifically, we wanted to investigate the effect of architectural design variations on (1) model system failure loads when testing the individual materials either separately or homogeneously mixed, and (2) also evaluate the potential of modulating other mechanical properties of the model systems. Methods: Two sets of softer and harder biomaterials, 0.5% and 5% agarose vs. 0.5% agarose and gelatin, were used for fabrication. Architectural design variations were realized by varying ring geometries and amounts while keeping the material composition across designs comparable. Results: Variations in the architectural design, such as lamellar width, number, and order, combined with choosing specific biomaterial properties, strongly influenced the biomechanical performance of IVD constructs. Biomechanical characterization revealed that the single most important parameter, in which the model systems vastly exceeded those of the individual materials, was failure load. The model system failure loads were 32.21- and 84.11-fold higher than those of the agarose materials and 55.03- and 2.14-fold higher than those of the agarose and gelatin materials used for system fabrication. The compressive strength, dynamic stiffness, and viscoelasticity of the model systems were always in the range of the individual materials. Conclusions: Relevant architecture-promoted biomechanical performance-tuning of tissue-engineered constructs for biological IVD replacement can be realized by slight modifications in the design of constructs while preserving the materials’ compositions. Minimal variations in the architectural design can be used to precisely control structure–function relations for IVD constructs rather than choosing different materials. These fundamental findings have important implications for efficient tissue-engineering of IVDs and other load-bearing tissues, as potential implants need to withstand high in situ loads.

Machine Learning-Based Models for the Estimation of the Energy Consumption in Metal Forming Processes

This research provides an insight on the performances of machine learning (ML)-based algorithms for the estimation of the energy consumption in metal forming processes and is applied to the radial-axial ring rolling process. To define the mutual influence between ring geometry, process settings, and ring rolling mill geometries with the resulting energy consumption, measured in terms of the force integral over the processing time (FIOT), FEM simulations have been implemented in the commercial SW Simufact Forming 15. A total of 380 finite element simulations with rings ranging from 650 mm < DF < 2000 mm have been implemented and constitute the bulk of the training and validation datasets. Both finite element simulation settings (input), as well as the FI (output), have been utilized for the training of eight machine learning models, implemented with Python scripts. The results allow defining that the Gradient Boosting (GB) method is the most reliable for the FIOT prediction in forming processes, being its maximum and average errors equal to 9.03% and 3.18%, respectively. The trained ML models have been also applied to own and literature experimental cases, showing a maximum and average error equal to 8.00% and 5.70%, respectively, thus proving once again its reliability.

Controlling the breakup of toroidal liquid films on solid surfaces

The breakup of a slender filament of liquid driven by surface tension is a classical fluid dynamics stability problem that is important in many situations where fine droplets are required. When the filament is resting on a flat solid surface which imposes wetting conditions the subtle interplay with the fluid dynamics makes the instability pathways and mode selection difficult to predict. Here, we show how controlling the static and dynamic wetting of a surface can lead to repeatable switching between a toroidal film of an electrically insulating liquid and patterns of droplets of well-defined dimensions confined to a ring geometry. Mode selection between instability pathways to these different final states is achieved by dielectrophoresis forces selectively polarising the dipoles at the solid-liquid interface and so changing both the mobility of the contact line and the partial wetting of the topologically distinct liquid domains. Our results provide insights into the wetting and stability of shaped liquid filaments in simple and complex geometries relevant to applications ranging from printing to digital microfluidic devices.

Ammonia optical gas sensing based on graphene-covered silicon microring resonators: A design space exploration

This paper discusses the design space exploration for an ammonia optical gas sensor based on a silicon microring resonator that is covered by graphene. A comparative analysis of the transmittance sensitivity of its fundamental quasi-TE and quasi-TM modes is presented. Results show that a large fraction of the fundamental quasi-TM mode’s electrical energy is propagating outside the waveguide, which makes this geometry more sensitive to ammonia induced changes in Fermi energy of graphene. The overall transmittance intensity difference, for the fundamental quasi-TE mode is less than 1 ​dB, independent of ring radius, when the ammonia gas concentration is varied from 0.5 to 1000 ​ppm. For the fundamental quasi-TM mode, results show that a ring radius ~8.4 ​μm can provide critical coupling condition and lead to >20 ​dB modulation of transmittance intensity when the ammonia gas concentration is varied from 0.5 to 1000 ​ppm. Overall, proper selection of mode excitation as well as ring geometry is essential to attain practical sensitivity.

Electronic properties of graphene quantum ring with wedge disclination

We study the energy spectrum and persistent current of charge carriers confined in a graphene quantum ring geometry of radius $R$ and width $w$ subjected to a magnetic flux. We consider the case where the crystal symmetry is locally modified by replacing a hexagon by a pentagon, square, heptagon or octagon. To model this type of defect we include appropriate boundary conditions for the angular coordinate. The electrons are confined to a finite width strip in radial direction by setting infinite mass boundary conditions at the edges of the strip. The solutions are expressed in terms of Hankel functions and their asymptotic behavior allows to derive quantized energy levels in the presence of an energy gap. We also investigate the persistent currents that appear in the quantum ring and how wedge disclination influences different quantum transport quantities.

A possible way to explicitly account for different molecular geometries with an equation of state

Different molecular geometries are determinant to condensed phases structures, and to the thermodynamic behavior. To take into consideration the nonsphericity in the development of equations of state, molecules have been taken either as chains of spherical segments or sets of nonspherical segments. In this work, we model molecules as single anisotropic particles, introducing a general Hard Nonspherical Segment (HNS) reference term, which can, in principle, be used within the framework of the Statistical Associating Fluid Theory (SAFT), once coupled with an appropriate association term. The resulting model explicitly accounts for different molecular geometries. Variants of the HNS reference term for ellipsoids, cylinders, and spherocylinders were applied to calculate vapor-liquid equilibrium of carbon dioxide, benzene, toluene, n-perfluoroalkanes (CF4, C2F6, C3F8), and n-alkanes (from methane to octane). We have shown that, in general, our approach of modeling molecules as nonspherical particles yield better results than a comparable equation of state for which molecules are taken as chains of spherical segments. Furthermore, the fitted parameters lead to physically sound geometrical models; for instance, the oblate geometry of the aromatic rings was inferred from vapor-liquid equilibrium data upon fitting the model parameters. We show that the adjusted aspect ratios of the ellipsoidal and spherocylindrical particles can be correlated with the acentric factor of their respective molecules, adding evidence that the degree of nonsphericity of molecules is indeed somehow captured by the acentric factor. State-of-the-art equations of state such as PC-SAFT and SAFT-VR Mie still give better results, and the level of complexity in their formulation may justify it. Therefore, we believe that the proposed methodology with nonspherical segments is promising, but has space for further improvement.

Chimeras on a social-type network

We consider a social-type network of coupled phase oscillators. Such a network consists of an active core of mutually interacting elements, and of a flock of passive units, which follow the driving from the active elements, but otherwise are not interacting. We consider a ring geometry with a long-range coupling, where active oscillators form a fluctuating chimera pattern. We show that the passive elements are strongly correlated. This is explained by negative transversal Lyapunov exponents.

A reinforcement learning approach to rare trajectory sampling

Very often when studying non-equilibrium systems one is interested in analysing dynamical behaviour that occurs with very low probability, so called rare events. In practice, since rare events are by definition atypical, they are often difficult to access in a statistically significant way. What are required are strategies to ‘make rare events typical’ so that they can be generated on demand. Here we present such a general approach to adaptively construct a dynamics that efficiently samples atypical events. We do so by exploiting the methods of reinforcement learning (RL), which refers to the set of machine learning techniques aimed at finding the optimal behaviour to maximise a reward associated with the dynamics. We consider the general perspective of dynamical trajectory ensembles, whereby rare events are described in terms of ensemble reweighting. By minimising the distance between a reweighted ensemble and that of a suitably parametrised controlled dynamics we arrive at a set of methods similar to those of RL to numerically approximate the optimal dynamics that realises the rare behaviour of interest. As simple illustrations we consider in detail the problem of excursions of a random walker, for the case of rare events with a finite time horizon; and the problem of a studying current statistics of a particle hopping in a ring geometry, for the case of an infinite time horizon. We discuss natural extensions of the ideas presented here, including to continuous-time Markov systems, first passage time problems and non-Markovian dynamics.

Analytical and Numerical Model of Aluminum Alloy Swaging Ring Design to Study the Effect on the Sealing for Piping Systems

In various fields of engineering, the assembly and repair of hydraulic installations are accomplished by joining the pipes. In such applications, the ring swaging method is used to connect the fittings to the pipes by means of a hydraulic hand tool. The basis to develop a swaging tool relies on the knowledge of the design parameter that influence plastic deformation of the swaging ring. In addition to build control over the design parameters, it is necessary to join pipes under severe conditions such as cryogenic vacuum and constrained space which require an intact sealing. In this study, the effect of swaging ring designs on sealing and strength has been examined and different swaging methods have been investigated by finite element modeling methods. Based on the obtained results, the analysis methodology of ring swaging and the characteristic impact of swaging ring design on the sealing of pipe connection are shown. The prime novelty of the study is to report the impact of swaging ring design and geometry on sealing efficiency of the pipe connection. The results of the study open new avenues for the development of efficient tools for designing swaging rings. Doi: 10.28991/cej-2021-03091641 Full Text: PDF

Effects of terminal biphenyl ring geometry on the photophysical properties of closo-o-carboranyl–anthracene dyads

Four anthracene-based closo-o-carboranyl compounds bearing phenyl or biphenyl substituents at C10 were prepared to establish a design strategy for enhancing the solution- and solid-state emissive properties.

A Comparative study by TCAD Simulation for two different planar n-on-p silicon particle detectors with different guard ring implant type

In this paper, we compare two multi-guard ring geometries for n-on-p silicon particle detectors for high luminosity applications. One structure has p-type guard rings while the other has n-type guard rings with p-stop isolation between n+ implants. The pre-irradiation performance of the guard ring structures are studied as a function of oxide charge. It is found that for both structures, there is a value of oxide charge for which the breakdown voltage is maximum. The post-irradiation performance of the structures are evaluated with simulations up to a radiation fluence of 1×10+16 neq/cm2 using an existing three-level trap model for p-type FZ silicon. TCAD simulation has been used to simulate I-V characteristics, charge carrier concentration, electric field, and potential distribution.

Structural and Dynamical Characteristics of Short-Chain Branched Ring Polymer Melts at Interface under Shear Flow

We present a detailed analysis of the interfacial chain structure and dynamics of confined polymer melt systems under shear over a wide range of flow strengths using atomistic nonequilibrium molecular dynamics simulations, paying particular attention to the rheological influence of the closed-loop ring geometry and short-chain branching. We analyzed the interfacial slip, characteristic molecular mechanisms, and deformed chain conformations in response to the applied flow for linear, ring, short-chain branched (SCB) linear, and SCB ring polyethylene melts. The ring topology generally enlarges the interfacial chain dimension along the neutral direction, enhancing the dynamic friction of interfacial chains moving against the wall in the flow direction. This leads to a relatively smaller degree of slip () for the ring-shaped polymers compared with their linear analogues. Furthermore, short-chain branching generally resulted in more compact and less deformed chain structures via the intrinsically fast random motions of the short branches. The short branches tend to be oriented more perpendicular (i.e., aligned in the neutral direction) than parallel to the backbone, which is mostly aligned in the flow direction, thereby enhancing the dynamic wall friction of the moving interfacial chains toward the flow direction. These features afford a relatively lower and less variation in in the weak-to-intermediate flow regimes. Accordingly, the interfacial SCB ring system displayed the lowest among the studied polymer systems throughout these regimes owing to the synergetic effects of ring geometry and short-chain branching. On the contrary, the structural disturbance exerted by the highly mobile short branches promotes the detachment of interfacial chains from the wall at strong flow fields, which results in steeper increasing behavior of the interfacial slip for the SCB polymers in the strong flow regime compared to the pure linear and ring polymers.

Producing flow in racetrack atom circuits by stirring

We present a study of how macroscopic flow can be produced in Bose-Einstein condensate confined in a "racetrack" potential by stirring with a wide rectangular barrier. This potential consists of two half-circle channels separated by straight channels of length $L$ and is a ring potential if $L=0$. We present the results of a large set of simulations where racetrack condensates stirred with a barrier under varying conditions of barrier height, stir speed, racetrack geometry, and temperature. We found that stirring was readily able to produce circulation in ring and non-ring geometries but that the exact amount of flow produced was complicated. We therefore also studied the mechanism by which flow was produced in the stirring process. We found that circulation was induced by the swap of a vortex/anti-vortex pair that was initially created by backflow of the condensate in the region of depressed density by the barrier. When the barrier strength reached a critical value a number of these vortex-swap events occurred in rapid succession so that flow speed of the circulation produced was enough to exceed the stir speed of the barrier. Flow that was initially localized in the vortices involved in the vortex swap was converted into macroscopic flow around the racetrack by pairs of disturbances each generated during the vortex swap. Each pair consisted of a vortex/anti-vortex pair moving in the anti-stir direction and a compression wave moving in the stir direction. This picture of the mechanism for making flow will enable the design of stirring schedules that create a desired amount of flow.

Comparison between Specialized Quadrature Rules for Method of Moments with NURBS Modelling Applied to Periodic Multilayer Structures

A comparison between Ma-Rokhlin-Wandzura (MRW) and double exponential (DE) quadrature rules for numerical integration of method of moments (MoM) matrix entries with singular behavior is presented for multilayer periodic structures. Non Uniform Rational B-Splines (NURBS) modelling of the layout surfaces is implemented to provide high-order description of the geometry. The comparison is carried out in order to show that quadrature rule is more suitable for MoM matrix computation in terms of sampling, accuracy of computation of MoM matrix, and CPU time consumption. The comparison of CPU time consumption shows that the numerical integration with MRW samples is roughly 15 times faster than that numerical integration using DE samples for results with similar accuracies. These promising results encourage to carry out a comparison with results obtained in previous works where a specialized approach for the specific analysis of split rings geometries was carried out. This previous approach uses spectral MoM version with specific entire domain basis function with edge singularities defined on split ring geometry. Thus, the previous approach provides accurate results with low CPU time consumption to be compared. The comparison shows that CPU time consumption obtained by MRW samples is similar to the CPU time consumption required by the previous work of specific analysis of split rings geometries. The fact that similar CPU time consumptions are obtained by MRW quadrature rules for modelling of general planar geometries and by the specialized approach for split ring geometry provides an assessment for the usage of the MRW quadrature rules and NURBS modelling. This fact provides an efficient tool for analysis of reflectarray elements with general planar layout geometries, which is suitable for reflectarray designs under local periodicity assumption where a huge number of periodic multilayer structures have to be analyzed.

Analysis of the lasing characteristics of InGaAs/GaAs WGM microlasers

We present an analysis of spectral and threshold characteristics of InGaAs/GaAs quantum well-dot microdisk laser operated under cw current injection at room temperature without external cooling. The experimental values of the threshold current for the disk and ring microlasers are compared. We observe that the threshold current can be significantly decreased in devices with large diameters (more than 30 μm) by using the ring geometry.

Excluding possible sites of high-energy emission in 3C 84

ABSTRACT The FR-I galaxy 3C 84, that is identified with the misaligned blazar NGC 1275, is well known as one of the very few radio galaxies emitting gamma-rays in the TeV range. Yet, the gamma-ray emission region cannot be pinpointed and the responsible mechanisms are still unclear. We calculate the optical absorption depth of high-energy photons in the broad-line region of 3C 84 depending on their energy and distance to the central black hole. Based on these calculations, a lower limit on the distance of the emission region from the central black hole can be derived. These lower limits are estimated for two broad-line region geometries (shell and ring) and two states of the source, the low state in 2016 October–December and a flare state in 2017 January. For the shell geometry, we can place the emission region outside the Ly α radius. For the ring geometry and the low flux activity, the minimal distance between the black hole, and the gamma-ray emission region is close to the Ly α radius. In the case of the flaring state (ring geometry), the results are not conclusive. Our results exclude the region near the central black hole as the origin of the gamma-rays detected by Fermi–LAT and Major Atmospheric Gamma-Ray Imaging Cherenkov. With these findings, we can constrain the theoretical models of acceleration mechanisms and compare the possible emission region to the source’s morphology resolved by radio images from the Very Long Baseline Array.

Majorana end states in an interacting quantum wire

We propose and investigate a simple one-dimensional model for a single-channel quantum wire hosting electrons that interact repulsively and are subject to a significant spin-orbit interaction. We show that an external Zeeman magnetic field, applied at the right angle to the Rashba spin-orbit axis, drives the wire into a correlated spin-density wave state with gapped spin and gapless charge excitations. By computing the ground-state degeneracies of the model with either (anti-)periodic or open boundary conditions, we conclude that the correlated spin-density state realizes a gapless symmetry-protected topological phase, as the ground state is unique in the ring geometry while it is two-fold degenerate in the wire with open boundaries. Microscopically the two-fold degeneracy is found to be protected by the conservation of the magnetization parity. Open boundaries induce localized zero-energy (midgap) states which are described, at the special Luther-Emery point of the model, by Majorana fermions. We find that spin densities at the open ends of the wire exhibit unusual long-ranged correlations despite the fact that all correlations in the bulk of the wire decay in a power-law or exponential fashion. Our study exposes the crucial importance of the long-ranged string operator needed to implement the correct commutation relations between spin densities at different points in the wire. Along the way we rederive the low-energy theory of Galilean-invariant electron systems in terms of current operators.

Hjelmslev's geometry of reality

During the first half of the 20th century the Danish geometer Johannes Hjelmslev developed what he called a geometry of reality. It was presented as an alternative to the idealized Euclidean paradigm that had recently been completed by Hilbert. Hjelmslev argued that his geometry of reality was superior to the Euclidean geometry both didactically, scientifically and in practice: Didactically, because it was closer to experience and intuition, in practice because it was in accordance with the real geometrical drawing practice of the engineer, and scientifically because it was based on a smaller axiomatic basis than Hilbertian Euclidean geometry but still included the important theorems of ordinary geometry. In this paper, I shall primarily analyze the scientific aspect of Hjelmslev's new approach to geometry that gave rise to the so-called Hjelmslev (incidence) geometry or ring geometry.