Circular Lattices Research Articles

Wrapped processes on circular lattices for planar directions

This paper introduces a class of stochastic processes making jumps around the circle. These circular processes are the wrapped versions of the Poisson, the negative binomial, the binomial processes and of extensions thereof obtained by compounding with a secondary frequency distribution. Their prevailing application is for modeling planar motions. These processes can be weakly stationary, can have uniform stationary distribution, can have independent or stationary circular increments. Their autocovariance functions, one-dimensional trigonometric moments and wrapped distributions are obtained. For the wrapped Poisson process, it is shown that the formula for the one-dimensional distribution can be obtained either by discrete Fourier transform or by wrapping the Poisson distribution around the circle and by simplifying it with the generalized hyperbolic function. Some numerical illustrations and comparisons are provided.

Long ties accelerate noisy threshold-based contagions.

In widely used models of biological contagion, interventions that randomly rewire edges (generally making them 'longer') accelerate spread. However, recent work has argued that highly clustered, rather than random, networks facilitate the spread of threshold-based contagions, such as those motivated by myopic best response for adoption of new innovations, norms and products in games of strategic complement. Here we show that minor modifications to this model reverse this result, thereby harmonizing qualitative facts about how network structure affects contagion. We analyse the rate of spread over circular lattices with rewired edges and show that having a small probability of adoption below the threshold probability is enough to ensure that random rewiring accelerates the spread of a noisy threshold-based contagion. This conclusion is verified in simulations of empirical networks and remains valid with partial but frequent enough rewiring and when adoption decisions are reversible but infrequently so, as well as in high-dimensional lattice structures.

Manufacturability and deformation studies on a novel metallic lattice structure fabricated by Selective Laser Melting

Additive Manufacturing of metallic lattice structures has been well-researched and adopted in the biomedical and aerospace sectors. The reason is that these structures with tailored mechanical properties are worthy candidates for applications requiring lightweighting and energy absorption characteristics. In this paper, we propose a new unit cell that, by repetition in three directions, forms a lattice that can reduce the stress concentrations between the struts and enable smoother deformations compared to conventional structures and circular unit cell-based lattices. The designs were fabricated by Selective Laser Melting of the commercial Ti–6Al–4V alloy. It was found that the manufacturability of the novel cells was excellent, and the structure was found to perform better in terms of compressive yield strength and have almost similar energy absorption characteristics to the BCC lattices.

A comparative study of the fatigue behavior of Ti‐6Al‐4V circular lattices using numerical and experimental methods

AbstractLattice materials are a subset of cellular solids with a periodic microstructure and are of interest in a number of applications because of their potential weight‐saving properties. In this study, circular lattices are machined out of plates made of Ti‐6Al‐4V and fatigue tested to generate an S–N curve. These results are compared to a FEM with fatigue data based on MIL‐HDBK‐5H. A good agreement with the FEM was found, suggesting that the fatigue life of lattices can be modeled without specifically detailed fatigue data. The model accurately predicted the point of failure in most of the lattice specimens and was within 4% of the scatter band. Fractographic analysis showed significant shear features in the fracture surfaces, indicating a rapid shear fracture is likely the dominant mode of failure. Finally, the relationship between equivalent stress and relative density was determined using a variety of optimization schemes.

Inverse modeling of circular lattices via orbit response measurements in the presence of degeneracy

The number and relative placement of BPMs and steerers with respect to the quadrupoles in a circular lattice can lead to degeneracy in the context of inverse modeling of accelerator optics. Further, the measurement uncertainties introduced by beam position monitors can propagate by the inverse modeling process in ways that prohibit the successful estimation of model errors. In this contribution, the influence of BPM and steerer placement on the conditioning of the inverse problem is studied. An analytical version of the Jacobian, linking the quadrupole gradient errors along with BPM and steerer gain errors with the orbit response matrix, is derived. It is demonstrated that this analytical version of the Jacobian can be used in place of the numerically obtained Jacobian during the fitting procedure. The approach is first tested with simulations and the findings are verified by measurement data taken on SIS18 synchrotron at GSI. The results are crosschecked with the standard numerical Jacobian approach. The quadrupole errors causing tune discrepancies observed at SIS18 are identified.

Comparison of supercontinuum spectral widths in CCl4-core PCF with square and circular lattices in the claddings

In this study, we demonstrate the ability to generate a broad supercontinuum (SC) spectrum with a low peak power of square (S-PCF) and circular (C-PCF) lattice photonic crystal fibers with hollow-core infiltrated with carbon tetrachloride (CCl4). The dispersion and nonlinear characteristics have been numerically analyzed in detail and compared to select the optimal structures for SC generation and evaluate the SC generation efficiency for each PCF. With four optimal proposed structures, the all-normal dispersion of square PCF (#SF1) is found to be flatter and smaller. This results in its SC bandwidth reaching 901 nm at 1.095 μm pumping wavelength which is broader than that of circular PCF (#CF1) (768 nm at 0.98 μm wavelength) despite the lower nonlinear coefficient and higher confinement loss. For the anomalous dispersion regime, #CF2 fiber provides a wider SC spectrum (1753.1 nm) with a peak power of 10 kW compared to #SF2 (1689.6 nm) with a peak power of 13.75 kW thanks to the higher nonlinear coefficient and smaller confinement loss. With the higher nonlinearity of CCl4, the proposed fibers can be a new generation of optical fibers, suitable for low peak power all-fiber optical systems replacing glass core fibers.

Estimation of the Space–Time Spectrum of Waves Based on Circular Measuring Gratings

In this paper, a method for estimating the spectra of wave processes based on a special type of measuring lattices, which are a set of rotating and static sensors, called “circular,” is developed. A method for correcting spectra estimated on the basis of discrete digital series obtained from circular lattice sensors is described. Spectra estimates are based on the multidimensional maximum entropy method. The data of test calculations for several types of circular lattices are presented as applied to wave processes in the form of harmonics distorted by white noise. The effectiveness of the proposed method for correcting spectra is shown. The general principles of using circular lattices for estimating the spectra of wave processes with the help of sensors located on rotating satellites are outlined. The possibility of using this approach for estimating the spectra of wave processes using sensors installed on micro- and nanosatellites is discussed.

Comparison of effective mode area and confinement loss of chloroform-core photonic crystal fibers with circular and hexagonal lattices

In this research, new circular and hexagonal photonic crystal fibers (PCFs) filled with chloroform have been designed considering the difference in air hole diameters to optimize the characteristics of the fiber simultaneously. Effective mode area and confinement loss of five PCFs with optimal dispersion have been further studied to find the fiber with a great application value for supercontinuum generation (SCG). Generally, circular PCFs are dominant over hexagonal lattices because of their small effective mode area, low loss, and small dispersion. #CF1 fiber with a lattice constant (Ʌ) of 1.0 μm and filling factor (d1/Ʌ) of 0.65 has an all-normal dispersion with a low value of -1.623 ps/nm/km, a small effective mode area of 1.43 µm2, and a low loss of 2.472 dB/m at 0.945 µm. The effective mode area and confinement loss of #CF2 (Ʌ = 1.0 µm, d1/Ʌ = 0.7) are the smallest of proposed PCFs. #HF1 fiber (Ʌ = 1.0 µm, d1/Ʌ = 0.5) has a very flat dispersion curve in the 1-2 µm wavelength range and a rather small effective mode area. These are the most optimal fibers for two types of lattices, which are very suitable for near-infrared SCG.

Circular accelerator lattices with skew quadrupoles

Circular accelerator lattices are usually confined in the horizontal plane. Optics design does not rely on the orbit in the vertical direction. Here we propose a circular accelerator lattice in which the orbit moves in both horizontal and vertical directions. Having another degree of freedom, flexibility of the optics increases with less constraints of the orbit, e.g. a zero momentum compaction factor lattice without reverse bending magnets or a negative dispersion function. As a possible application of the concept, a collider ring arc of a muon collider facility is illustrated.

Theoretical investigation of two-dimensional sub-wavelength structures fabricated by multi-beam surface plasmon interference lithography

In this study, multi-beam surface plasmon (SP) interference lithography was theoretically proposed and demonstrated to fabricate periodic two-dimensional sub-wavelength structures. The lithography structures were based on an attenuated total reflection prism used to excite the SPs using a 442 nm laser. Circular lattices with periods of 166 and 288 nm were successfully obtained via three- and six-beam SP interference lithography, respectively; these lattices exhibited an identical feature size of 96 nm. Square dot arrays with a 177 nm period and 88.5 nm spot size were obtained by four-beam SP interference lithography. The proposed lithography technology has a simple structure and is economical; further, it may provide an effective method for the fabrication of two-dimensional sub-wavelength structures.

Entanglement of Two Disjoint Intervals in Conformal Field Theory and the 2D Coulomb Gas on a Lattice.

In the conformal field theories given by the Ising and Dirac models, when the system is in the ground state, the moments of the reduced density matrix of two disjoint intervals and of its partial transpose have been written as partition functions on higher genus Riemann surfaces with Z_{n} symmetry. We show that these partition functions can be expressed as the grand canonical partition functions of the two-dimensional two component classical Coulomb gas on certain circular lattices at specific values of the coupling constant.

Nonorientability-induced PT phase transition in ladder lattices

We study parity-time (PT) phase transitions in the energy spectra of ladder lattices caused by the interplay between non-orientability and non-Hermitian PT symmetry. The energy spectra show level crossings in circular ladder lattices with increasing on-site energy gain-loss because of the orientability of a normal strip. However, the energy levels show PT phase transitions in PT-symmetric Moebius ladder lattices due to the non-orientability of a Moebius strip. In order to understand the level crossings of PT symmetric phases, we generalize the rotational transformation using a complex rotation angle. We also study the modification of resonant tunneling induced by a sharply twisted interface in PT-symmetric ladder lattices. Finally, we find that the perfect transmissions at the zero energy are recovered at the exceptional points of the PT-symmetric system due to the self-orthogonal states.

Analysis of dispersion characteristics of solid-core PCFs with different types of lattice in the claddings, infiltrated with ethanol

In this paper, we propose three solid-core photonic crystal fibers based on silica, with hexagonal, circular and square lattices as a cladding, composed of 8 rings of air-holes surrounding the core, infiltrated with ethanol. Using a commercial software we simulated the light propagation in these structures. The size of the air-holes was from 1 µm to 4 µm. We have shown that the fibers with the hexagonal lattices are optimal for supercontinuum generation since their dispersion characteristics are flat and the smallest.

Comparison between optimal configuration algorithms of fiber phased array

Optical fiber phased array can be used in high-power laser beam combination, lidar and other areas. The configuration of the optical fiber array is different from the microwave phased array, which has periodic problems that affect the energy intensity distribution of the main lobe. Starting from the physical model, in this paper we establish a theoretical model of optical phased array antenna array based on a set of concentric circular ring lattices, and propose a theory of the rapid synthesis of randomly configured interference field strengths through using analytical continuation method and Fourier transform method. The problem of sampling bandwidth and sampling number that should be paid attention to in the numerical simulation of discrete sampling are discussed, and the problem of quickly realizing the numerical simulation of multi-beam interference field is solved. Genetic algorithm and particle swarm algorithm for optimizing the configuration of optical phased array antennas are investigated with different populations. The convergence speeds and optimization efficiencies of the two algorithms are compared and analyzed. It is demonstrated that the peak side-lobe ratio PSR can be achieved to be better than 0.270 by the genetic algorithm optimized configuration array under the real fabricate parameter. The proposed method is expected to be used in the actual optical phased array antenna configuration to guide the optimal design of the antenna with low side lobes, and the proposed model is also expected to provide a certain reference value for the study of optimizing the non-differentiable objective function.

Laser-writing of ring-shaped waveguides in BGO crystal for telecommunication band.

We report on the fabrication of ring-shaped waveguides operating at the telecommunication band in a cubic Bi4Ge3O12 (BGO) crystal by using technique of femtosecond laser writing. In the regions of laser written tracks in BGO crystal, positive refractive index is induced, resulting in so-called Type I configuration. The modal profiles are within the designed track cladding with ring-shaped geometries, which are analogous to circular optical lattices. The homogenous guidance along both TE and TM polarizations has been obtained at telecommunication wavelength of 1.55 μm. Both straight and S-curved waveguiding structures have been produced with ring-shaped configurations. This work paves the way to fabricate complex photonic networks for telecommunications by using ring-shaped waveguides in compact chips.

New edge magnetoplasmon interference like photovoltage oscillations and their amplitude enhancement in the presence of an antidot lattice

We present new photovoltage oscillation in a pure two dimensional electron gas (2DEG) and in the presence of circular or semicircular antidot lattices. Results were interpreted as EMPs-like photovoltage oscillations. We observed and explained the photovoltage oscillation amplitude enhancement in the presence of an antidot lattice with regard to the pure 2DEG. The microwave frequency excitation range is 139 – 350 GHz. The cyclotron and magnetoplasmon resonances take place in the magnetic field range 0.4 – 0.8 T. This original experimental condition allows edge magnetoplasmons EMPs interference like observation at low magnetic field, typically B < Bc where Bc is the magnetic field at which the cyclotron resonance takes place. The different oscillation periods observed and their microwave frequency dependence were discussed. For 139 and 158 GHz microwave excitation frequencies, a unique EMPs-like interference period was found in the presence of antidots whereas two periods were extracted for 295 or 350 GHz. An explanation of this effect is given taking account of strong electron interaction with antidot at low magnetic field. Indeed, electrons involved in EMPs like phenomenon interact strongly with antidots when electron cyclotron orbits are larger than or comparable to the antidot diameter.

A novel proposal for enhancement of light extraction efficiency in WOLEDs based on optimized photonic crystal structures

In this paper we propose a framework to enhance light extraction efficiency in white organic light emitting diodes (WOLED) using photonic crystal (PhC) structures sandwiched between indium tin oxide (ITO, nITO=1.8+0.01i) and glass (nglass=1.51) substrate, according to the high refractive index contrast of these two layers almost 50% of the generated light inside WOLED gets trapped in the mentioned interface. The main purpose of this article is to suggest a method to intentionally optimize PhC structures to reduce total internal reflections (TIR) happening at ITO/glass interface. Here three different patterns are considered including rectangular, hexagonal and circular lattices. Using Finite Difference Time Domain (FDTD) method and the presented framework for choosing structural parameters the portion of 50% trapped light in ITO was reduced to 20% which is a large enhancement in extraction efficiency of WOLED. Also far-field results before and after adding PhCs are investigated.

Manipulation of magnetic state in nanostructures by perpendicular anisotropy and magnetic field

We investigate the transitions of spin configurations in ultrathin nanostructures by tuning the perpendicular anisotropy (Kz) and out-of-plane magnetic field (H), using the Monte Carlo simulation. It is revealed that enhancing the anisotropy Kz can drive the evolution of in-plane vortex state into intriguing saturated magnetization states under various H, such as the bubble domain state and quadruple-block-domain state etc. The spin configurations of these states exhibit remarkable H-dependence. In addition, the strong effects of geometry and size on the spin configurations of nanostructures are observed. In particular, a series of edged states occur in the circular disk-shaped lattices, and rich intricate saturated magnetization patterns appear in big lattices. It is suggested that the magnetic states can be manipulated by varying the perpendicular anisotropy, magnetic field, and geometry/size of the nanostructures. Furthermore, the stability (retention capacity) of the saturated magnetization states upon varying magnetic field is predicted, suggesting the potential applications of these saturated magnetization states in magnetic field-controlled data storages.

Stability bands for moving solitons in uniform and inhomogeneous damped ac-driven circular Toda lattices

Abstract By means of systematic simulations, we study the motion of discrete solitons in weakly dissipative Toda lattices (TLs) with periodic boundary conditions, resonantly driven by a spatially staggered time-periodic (ac) force. A complex set of alternating stability bands and instability gaps, including scattered isolated stability points, is revealed in the parametric plane of the soliton’s velocity and forcing amplitude for a given size of the circular lattice. The analysis is also reported for the circular TL including a single light- or heavymass defect. The stability chart as a whole shrinks and eventually disappears with the increase of the lattice’s size and strength of the mass defect. Qualitative explanations to these findings are proposed. We also report the dependence of the stability area on the initial position of the soliton, finding that the area is largest for some intersite position. For a pair of solitons traveling in opposite directions, there exist regimes where both solitons survive periodic collisions in small-size lattices.

Tunable Magnonic Spectra in Two‐Dimensional Magnonic Crystals with Variable Lattice Symmetry

AbstractTunable magnonic properties are demonstrated in two‐dimensional magnonic crystals in the form of artificial ferromagnetic nanodot lattices with variable lattice symmetry. An all‐optical time‐domain excitation and detection of the collective precessional dynamics is performed in the strongly magnetostatically coupled Ni80Fe20 (Py) circular dot lattices arranged in different lattice symmetry such as square, rectangular, hexagonal, honeycomb, and octagonal symmetry. As the symmetry changes from square to octagonal through rectangular, hexagonal and honeycomb, a significant variation in the spin wave spectra is observed. The single uniform collective mode in the square lattice splits in two distinct modes in the rectangular lattice and in three distinct modes in the hexagonal and octagonal lattices. However, in the honeycomb lattice a broad band of modes are observed. Micromagnetic simulations qualitatively reproduce the experimentally observed modes, and the simulated mode profiles reveal collective modes with different spatial distributions with the variation in the lattice symmetry determined by the magnetostatic field profiles. For the hexagonal lattice, the most intense peak shows a six‐fold anisotropy with the variation in the azimuthal angle of the external bias magnetic field. Analysis shows that this is due to the angular variation of the dynamical component of magnetization for this mode, which is directly influenced by the variation of the magnetostatic field on the elements in the hexagonal lattice. The observations are important for tunable and anisotropic propagation of spin waves in magnonic crystal based devices.