Arbitrary Arrangement Research Articles

Absorptive coding metasurface for further radar cross section reduction

Lossless coding metasurfaces and metamaterial absorbers have been widely used for radar cross section (RCS) reduction and stealth applications, which merely depend on redirecting electromagnetic wave energy into various oblique angles or absorbing electromagnetic energy, respectively. Here, an absorptive coding metasurface capable of both the flexible manipulation of backward scattering and further wideband bistatic RCS reduction is proposed. The original idea is carried out by utilizing absorptive elements, such as metamaterial absorbers, to establish a coding metasurface. We establish an analytical connection between an arbitrary absorptive coding metasurface arrangement of both the amplitude and phase and its far-field pattern. Then, as an example, an absorptive coding metasurface is demonstrated as a nonperiodic metamaterial absorber, which indicates an expected better performance of RCS reduction than the traditional lossless coding metasurface and periodic metamaterial-absorber. Both theoretical analysis and full-wave simulation results show good accordance with the experiment.

Generating Focused 3D Perfect Vortex Beams By Plasmonic Metasurfaces

AbstractPerfect vortex (PV) beams possessing annular intensity profiles independent of topological charges promise significant advances in particle manipulation, fiber communication, and quantum optics. The PV beam is typically generated from the Fourier transformation of the Bessel–Gauss beam. However, the conventional method to produce PV beams requires a series of bulky optical components, which greatly increases the system complexity and also hinders the photonic device integration. Here, plasmonic metasurfaces made of rectangular‐hole nanoantennas as integrated beam converters are designed and demonstrated to generate focused 3D PV beams in a broad wavelength range, by combining the phase profiles of axicon, spiral phase plate, and Fourier transform lens simultaneously based on the Pancharatnam–Berry phase. It is demonstrated that the PV beam structures can be adjusted by varying several control parameters in the metasurface design. Moreover, multiple PV beams with arbitrary arrangement and topological charges are also produced. These results have the promising potential for enabling new types of compact optical devices for tailoring complex light beams and advancing metasurface‐based functional integrated photonic chips.

Clustering-induced self-propulsion of isotropic autophoretic particles.

Self-diffusiophoretic particles exploit local concentration gradients of a solute species in order to self-propel at the micron scale. While an isolated chemically- and geometrically-isotropic particle cannot swim, we show that it can achieve self-propulsion through interactions with other individually-non-motile particles by forming geometrically-anisotropic clusters via phoretic and hydrodynamic interactions. This result identifies a new route to symmetry-breaking for the concentration field and to self-propulsion, that is not based on an anisotropic design, but on the collective dynamics of identical and homogeneous active particles. Using full numerical simulations as well as theoretical modelling of the clustering process, the statistics of the propulsion properties are obtained for arbitrary initial arrangement of the particles. The robustness of these results to thermal noise, and more generally the effect of Brownian motion of the particles, is also discussed.

Heavy hyperplanes in multiarrangements and their freeness

Only few categories of free arrangements are known in which Terao's conjecture holds. One of such categories consists of $3$-arrangements with unbalanced Ziegler restrictions. In this paper, we generalize this result to arbitrary dimensional arrangements in terms of flags by introducing unbalanced multiarrangements. For that purpose, we generalize several freeness criterions for simple arrangements, including Yoshinaga's freeness criterion, to unbalanced multiarrangements.

Technique for Simulation of Black Sea Circulation with Increased Resolution in the Area of the IO RAS Polygon

A numerical technique is presented for simulating the hydrophysical fields of the Black Sea on a variable-step grid with refinement in the area of IO RAS polygon. Model primitive equations are written in spherical coordinates with an arbitrary arrangement of poles. In order to increase the horizontal resolution of the coastal zone in the area of the IO RAS polygon in the northeastern part of the sea near Gelendzhik, one of the poles is placed at a land point (38.35° E, 44.75° N). The model horizontal resolution varies from 150 m in the area of the IO RAS polygon to 4.6 km in the southwestern part of the Black Sea. The numerical technique makes it possible to simulate a large-scale structure of Black Sea circulation as well as the meso- and submesoscale dynamics of the coastal zone. In order to compute the atmospheric forcing, the results of the regional climate model WRF with a resolution of about 10 km in space and 1 h in time are used. In order to demonstrate the technique, Black Sea hydrophysical fields for 2011–2012 and a passive tracer transport representing self-cleaning of Gelendzhik Bay in July 2012 are simulated.

Numerical Modeling of Marine Circulation, Pollution Assessment and Optimal Ship Routes

Methods and technology have been developed to solve a wide range of problems in the dynamics of sea currents and to assess their “impact” on objects in the marine environment. Technology can be used for monitoring and forecasting sea currents, for solving the problems of minimizing risks and analyzing marine disasters associated with the choice of the optimal course of the ship, and assessing the pollution of coastal zones, etc. The technology includes a numerical model of marine circulation with improved resolution of coastal zones, a method for solving the inverse problem of contamination of the sea with a passive impurity, and a variational algorithm for constructing the optimal trajectory of the vessel. The methods and technology are illustrated by solving problems of Baltic Sea dynamics. The model of sea dynamics is governed by primitive equations that are solved on a grid with an improved resolution of the selected coastal zone—in this case, the Gulf of Finland. The equations of the model are formulated in a bipolar orthogonal coordinate system with an arbitrary arrangement of poles and the sigma coordinate in the vertical direction. An increase in the horizontal resolution of the allocated zone is achieved due to the displacement of the north pole in the vicinity of the city of St. Petersburg. A class of dangerous technogenic situations and natural phenomena (sea accidents, which can be investigated with the help of the proposed methodology), includes tanker accidents in the case of a possible collision with a stationary object (with “dynamic danger”) or a moving object (including another ship), accidents on oil-producing platforms and oil pipelines, and coastal pollution.

Flowrate Determination for Arbitrary Multipath Arrangement Based on Generalized Inverse of Matrix

As a widely used method in flow measurement, Gaussian quadrature is traditionally applied to determine the flowrate with multiple acoustic paths. However, it is only available to parallel path arrangement and the path position cannot be customized by users because of the nature of numerical integration principle. Accuracy of flowrate determination is greatly restricted meanwhile. In this paper, a new method based on generalized inverse of matrix (GIM) is proposed to work out the flowrate in arbitrary multipath arrangement. With an integrable model of flow distribution established, the GIM method will find the optimal weights and achieve highly accurate flowrate. Three perfect profile assumptions, including Jacobi, optimal weighted integration for circular sections, and typical power-law profile, are, respectively, adopted in this paper to explore the performance of GIM. Its effects are at first experimentally validated in parallel path arrangement of Gauss–Jacobi on a commercially available ultrasonic flowmeter. Then, four representative types that Gaussian quadrature is not feasible to are studied via numerical simulation, including a parallel and three crossed path arrangements. Performance of the proposed GIM method is verified under straight pipe, single bend, and double bend with an expander as well as on eight installation angles. Results reveal that GIM is applicable to accurate flowrate determination for arbitrary multipath arrangement and crossed paths could provide high determination accuracy and good robustness even under complicated flow field.

Thermophoretic Tweezers for Low-Power and Versatile Manipulation of Biological Cells.

Optical manipulation of biological cells and nanoparticles is significantly important in life sciences, early disease diagnosis, and nanomanufacturing. However, low-power and versatile all-optical manipulation has remained elusive. Herein, we have achieved light-directed versatile thermophoretic manipulation of biological cells at an optical power 100-1000 times lower than that of optical tweezers. By harnessing the permittivity gradient in the electric double layer of the charged surface of the cell membrane, we succeed at the low-power trapping of suspended biological cells within a light-controlled temperature gradient field. Furthermore, through dynamic control of optothermal potentials using a digital micromirror device, we have achieved arbitrary spatial arrangements of cells at a resolution of ∼100 nm and precise rotation of both single and assemblies of cells. Our thermophoretic tweezers will find applications in cellular biology, nanomedicine, and tissue engineering.

Efficient Evaluation of Earth Return Impedances of Arbitrary Conductor Arrangements With a Horizontally Multilayered Soil

The evaluation of the earth return mutual impedance of arbitrary conductor arrangements with a horizontally multilayered nonmagnetic soil is of great significance when the electromagnetic compatibility is concerned. To evaluate the earth return impedance accurately and efficiently, a semianalytical approach is proposed in this paper. With the proposed approach, the expression of the earth return impedance, which includes a complex highly oscillatory integrand, is divided into two parts, i.e., the definite and the tail integral. The definite integral is evaluated by using the moment technique and the tail integral is evaluated by using the exponential integrals with an asymptotic integrand. The numerical examples show that the proposed algorithm can evaluate the earth return impedance with various parameters and arbitrary conductor arrangements accurately and efficiently and the required computational time of the proposed approach is almost independent of the geometric and electric parameters.

Modular Equalities for Complex Reflection Arrangements

We compute the combinatorial Aomoto-Betti numbers $\beta_p(\mathcal{A})$ of a complex reflection arrangement. When $\mathcal{A}$ has rank at least $3$, we find that $\beta_p(\mathcal{A})\le 2$, for all primes $p$. Moreover, $\beta_p(\mathcal{A})=0$ if $p>3$, and $\beta_2(\mathcal{A})\ne 0$ if and only if $\mathcal{A}$ is the Hesse arrangement. We deduce that the multiplicity $e_d(\mathcal{A})$ of an order $d$ eigenvalue of the monodromy action on the first rational homology of the Milnor fiber is equal to the corresponding Aomoto-Betti number, when $d$ is prime. We give a uniform combinatorial characterization of the property $e_d(\mathcal{A})\ne 0$, for $2\le d\le 4$. We completely describe the monodromy action for full monomial arrangements of rank $3$ and $4$. We relate $e_d(\mathcal{A})$ and $\beta_p(\mathcal{A})$ to multinets, on an arbitrary arrangement.

Evacuating two robots from multiple unknown exits in a circle

We study a robot evacuation problem in a circle. Assume that k exits are arranged on a unit circle. Two autonomous mobile robots are placed on the circle and in arbitrary positions. The robots can travel with maximum speed of 1 and can communicate wirelessly at any time and distance. They also have a map of the domain, including exits, but do not have knowledge of their own initial locations on the circle, rather they only know their relative distance. The goal of the evacuation problem is to give an algorithm for the two robots to reach an exit (not necessarily the same), which also minimizes the time until an exit is found, in the worst case.We consider two variants of the evacuation problem depending on whether or not the two robots have control over their initial distance. When the initial distance of the robots is part of the input (i.e. no control), we show that simple algorithms exist which achieve optimal worst case evacuation times for the cases where the robots begin colocated with an arbitrary arrangement of the exits; and when the exits are either colocated or evenly spaced, with arbitrary starting positions of the robots. We also give upper and lower bounds on the problem with arbitrary arrangement of exits and starting positions of the robots. For the problem where robots can choose their initial distance (with knowledge of, but not control over the distribution of exits), we propose a natural family of algorithms parameterized by the maximum distance between any two exits and analyse their cost.

Analysis of rectangular cracks in elastic bodies

The solution of Volterra dislocation is derived in an infinite elastic body. Stress components are Cauchy singular at dislocation location. The stress field is utilized to construct integral equations for rectangular cracks with arbitrary arrangement in the body. The solution to integral equations is used to determine stress intensity factors on the crack edges. Numerical results are presented for a rectangular crack under various loads. Furthermore, interaction between two cracks, having a line of symmetry, is studied.

Equivariant cohomology and the Varchenko–Gelfand filtration

The cohomology of the configuration space of n points in R3 is isomorphic to the regular representation of the symmetric group, which acts by permuting the points. We give a new proof of this fact by showing that the cohomology ring is canonically isomorphic to the associated graded of the Varchenko–Gelfand filtration on the cohomology of the configuration space of n points in R1. Along the way, we give a presentation of the equivariant cohomology ring of the R3 configuration space with respect to a circle acting on R3 via rotation around a fixed line. We extend our results to the settings of arbitrary real hyperplane arrangements (the aforementioned theorems correspond to the braid arrangement) as well as oriented matroids.

Piecewise-planar Reconstruction of Multi-room Interiors with Arbitrary Wall Arrangements

Reconstructing the as-built architectural shape of building interiors has emerged in recent years as an important and challenging research problem. An effective approach must be able to faithfully ...

Piecewise‐planar Reconstruction of Multi‐room Interiors with Arbitrary Wall Arrangements

AbstractReconstructing the as‐built architectural shape of building interiors has emerged in recent years as an important and challenging research problem. An effective approach must be able to faithfully capture the architectural structures and separate permanent components from clutter (e.g. furniture), while at the same time dealing with defects in the input data. For many applications, higher‐level information on the environment is also required, in particular the shape of individual rooms. To solve this ill‐posed problem, state‐of‐the‐art methods assume constrained input environments with a 2.5D or, more restrictively, a Manhattan‐world structure, which significantly restricts their applicability in real‐world settings. We present a novel pipeline that allows to reconstruct general 3D interior architectures, significantly increasing the range of real‐world architectures that can be reconstructed and labeled by any interior reconstruction method to date. Our method finds candidate permanent components by reasoning on a graph‐based scene representation, then uses them to build a 3D linear cell complex that is partitioned into separate rooms through a multi‐label energy minimization formulation. We demonstrate the effectiveness of our method by applying it to a variety of real‐world and synthetic datasets and by comparing it to more specialized state‐of‐the‐art approaches.

Superresolution using an acoustic vortex wave antenna

Acoustic waves, like their electromagnetic counterpart, exhibit a diffraction limit, which restricts the ability to resolve or generate fine structures in the pressure field. Previously proposed methods to overcome this limit, and therefore achieve superresolution, have mainly been limited to operating within the near-field region of the aperture. In this work, we describe how far-field superresolution can be achieved using shaped acoustic vortices, created by utilizing the topological diversity of an acoustic vortex wave antenna. Theoretical and numerical results will be presented for the design of an acoustic vortex wave antenna with arbitrary planar arrangement which is capable of generating superresolved far-field features in the radiated acoustic pressure. Variation of the antenna geometry enables different shaped acoustic vortex patterns to be achieved, which propagate from the near-field into the far-field through an arrangement of stable integer mode vortices. Despite the total aperture size being less than a wavelength in diameter, the proposed acoustic vortex wave antenna is shown to achieve far-field superresolution with feature sizes 4-9 times smaller than the resolution limit. Several examples will be presented and discussed in detail. [Work supported by the Office of Naval Research.]

Vibration analysis of thin circular plates with multiple openings by the assumed mode method

Circular plates with openings are used in many engineering structures, especially as swash bulkheads in cargo tanks of liquefied gas carriers. In this article, an approximate procedure is worked out for the vibration analysis of circular plates with different boundary conditions and a different number and size of openings with an arbitrary arrangement within the plate area. The assumed mode method, recently used in the vibration analysis of rectangular plates, is applied in this case. Following the basic idea, the effect of the openings is accounted for by subtracting the potential and kinetic energy of the cut-out plate parts corresponding to the total plate energies without openings. The procedure is illustrated with numerical examples related to the vibration analysis of annular plates and circular plates with openings. The results are evaluated through their comparison with an analytical and finite element method solution.

Optimized shapes of magnetic arrays for drug targeting applications

Arrays of permanent magnet elements have been utilized as light-weight, inexpensive sources for applying external magnetic fields in magnetic drug targeting applications, but they are extremely limited in the range of depths over which they can apply useful magnetic forces. In this paper, designs for optimized magnet arrays are presented, which were generated using an optimization routine to maximize the magnetic force available from an arbitrary arrangement of magnetized elements, depending on a set of design parameters including the depth of targeting (up to 50 mm from the magnet) and direction of force required. A method for assembling arrays in practice is considered, quantifying the difficulty of assembly and suggesting a means for easing this difficulty without a significant compromise to the applied field or force. Finite element simulations of in vitro magnetic retention experiments were run to demonstrate the capability of a subset of arrays to retain magnetic microparticles against flow. The results suggest that, depending on the choice of array, a useful proportion of particles (more than ) could be retained at flow velocities up to 100 mm s−1 or to depths as far as 50 mm from the magnet. Finally, the optimization routine was used to generate a design for a Halbach array optimized to deliver magnetic force to a depth of 50 mm inside the brain.

Extending the applicability of the Goldschmidt tolerance factor to arbitrary ionic compounds.

Crystal structure determination is essential for characterizing materials and their properties, and can be facilitated by various tools and indicators. For instance, the Goldschmidt tolerance factor (T) for perovskite compounds is acknowledged for evaluating crystal structures in terms of the ionic packing. However, its applicability is limited to perovskite compounds. Here, we report on extending the applicability of T to ionic compounds with arbitrary ionic arrangements and compositions. By focussing on the occupancy of constituent spherical ions in the crystal structure, we define the ionic filling fraction (IFF), which is obtained from the volumes of crystal structure and constituent ions. Ionic compounds, including perovskites, are arranged linearly by the IFF, providing consistent results with T. The linearity guides towards finding suitable unit cell and composition, thus tackling the main obstacle for determining new crystal structures. We demonstrate the utility of the IFF by solving the structure of three hydrides with new crystal structures.

Switchable friction enabled by nanoscale self-assembly on graphene.

Graphene monolayers are known to display domains of anisotropic friction with twofold symmetry and anisotropy exceeding 200%. This anisotropy has been thought to originate from periodic nanoscale ripples in the graphene sheet, which enhance puckering around a sliding asperity to a degree determined by the sliding direction. Here we demonstrate that these frictional domains derive not from structural features in the graphene but from self-assembly of environmental adsorbates into a highly regular superlattice of stripes with period 4–6 nm. The stripes and resulting frictional domains appear on monolayer and multilayer graphene on a variety of substrates, as well as on exfoliated flakes of hexagonal boron nitride. We show that the stripe-superlattices can be reproducibly and reversibly manipulated with submicrometre precision using a scanning probe microscope, allowing us to create arbitrary arrangements of frictional domains within a single flake. Our results suggest a revised understanding of the anisotropic friction observed on graphene and bulk graphite in terms of adsorbates.