Archimedean Spiral Research Articles

Sharp acoustic vortex focusing by Fresnel-spiral zone plates

We report the optimal focusing of acoustic vortex beams by using flat lenses based on a Fresnel-spiral diffraction grating. The flat lenses are designed by spiral-shaped Fresnel zone plates composed of one or several arms. The constructive and destructive interferences of the diffracted waves by the spiral grating result in sharp acoustic vortex beams, following the focal laws obtained in analogy with the Fresnel zone plate lenses. In addition, we show that the number of arms determines the topological charge of the vortex, allowing the precise manipulation of the acoustic wave field by flat lenses. The experimental results in the ultrasonic regime show excellent agreement with the theory and full-wave numerical simulations. A comparison with beam focusing by Archimedean spirals also showing vortex focusing is given. The results of this work may have potential applications for particle trapping, ultrasound therapy, imaging, or underwater acoustic transmitters.

Corrigendum: Digitizing Tablet and Fahn–Tolosa–Marín Ratings of Archimedes Spirals have Comparable Minimum Detectable Change in Essential Tremor

Within the original published version of the Brief Report, “Digitizing Tablet and Fahn–Tolosa–Marin Ratings of Archimedes Spirals have Comparable Minimum Detectable Change in Essential Tremor,” the heading of the first column in Table 1 contained an additional label of "(cm)". The editorial office of Tremor and Other Hyperkinetic Movements has corrected the error and as of April 30, 2018 the column heading features only the appropriate information on all versions of the article.

Corrigendum: Digitizing Tablet and Fahn-Tolosa-Marín Ratings of Archimedes Spirals have Comparable Minimum Detectable Change in Essential Tremor.

[This corrects the article DOI: 10.7916/D89S20H7.].

Using spiral chain models for study of nanoscroll structures

Molecular nanoribbons with different chemical structures can form scrolled packings possessing outstanding properties and application perspectives due to their morphology. Here, we propose a simplified two-dimensional model of the molecular chain that allows us to describe the molecular nanoribbon's scrolled packings of various structures as a spiral packaging chain. The model allows us to obtain the possible stationary states of single-layer nanoribbon scrolls of graphene, graphane, fluorographene, fluorographane (graphene hydrogenated on one side and fluorinated on the other side), graphone ${\mathrm{C}}_{4}\mathrm{H}$ (graphene partially hydrogenated on one side), and fluorographone ${\mathrm{C}}_{4}\mathrm{F}$. The obtained states and the states of the scrolls found through all-atomic models coincide with good accuracy. We show the stability of scrolled packings and calculate the dependence of energy, the number of coils, and the inner and outer radius of the scrolled packing on the nanoribbon length. It is shown that a scrolled packing is the most energetically favorable conformation for nanoribbons of graphene, graphane, fluorographene, and fluorographane at large lengths. A double-scrolled packing when the nanoribbon is symmetrically rolled into a scroll from opposite ends is more advantageous for longer length nanoribbons of graphone and fluorographone. We show the possibility of the existence of scrolled packings for nanoribbons of fluorographene and the existence of two different types of scrolls for nanoribbons of fluorographane, which correspond to the left and right Archimedean spirals of the chain model. The simplicity of the proposed model allows us to consider the dynamics of molecular nanoribbon scrolls of sufficiently large lengths and at sufficiently large time intervals.

Two-Dimensional Model of Scrolled Packings of Molecular Nanoribbons

A simplified model of the in-plane molecular chain, allowing the description of folded and scrolled packings of molecular nanoribbons of different structures, is proposed. Using this model, possible steady states of single-layer nanoribbons scrolls of graphene, graphane, fluorographene, and fluorographane (graphene hydrogenated on the one side and fluorinated on the other side) are obtained. Their stability is demonstrated and their energy is calculated as a function of the nanoribbon length. It is shown that the scrolled packing is the most energetically favorable nanoribbon conformation at long lengths. The existences of scrolled packings for fluorographene nanoribbons and the existence of two different scroll types corresponding to left- and right-hand Archimedean spirals for fluorographane nanoribbons in the chain model are shown for the first time. The simplicity of the proposed model makes it possible to consider the dynamics of scrolls of rather long molecular nanoribbons at long enough time intervals.

Двумерная модель рулонных упаковок молекулярных нанолент

AbstractA simplified model of the in-plane molecular chain, allowing the description of folded and scrolled packings of molecular nanoribbons of different structures, is proposed. Using this model, possible steady states of single-layer nanoribbons scrolls of graphene, graphane, fluorographene, and fluorographane (graphene hydrogenated on the one side and fluorinated on the other side) are obtained. Their stability is demonstrated and their energy is calculated as a function of the nanoribbon length. It is shown that the scrolled packing is the most energetically favorable nanoribbon conformation at long lengths. The existences of scrolled packings for fluorographene nanoribbons and the existence of two different scroll types corresponding to left- and right-hand Archimedean spirals for fluorographane nanoribbons in the chain model are shown for the first time. The simplicity of the proposed model makes it possible to consider the dynamics of scrolls of rather long molecular nanoribbons at long enough time intervals.

Review of the Functions of Archimedes' Spiral Metallic Nanostructures.

Here, we have reviewed some typical plasmonic structures based on Archimedes’ spiral (AS) architectures, which can produce polarization-sensitive focusing phenomenon and generate plasmonic vortices (PVs) carrying controllable orbital angular momentum (OAM) because of the relation between the incident polarized states and the chiralities of the spiral structures. These features can be used to analyze different circular polarization states, which has been one of the rapidly developing researching topics in nanophotonics in recent years. Many investigations demonstrate that the multifunctional spiral-based plasmonic structures are excellent choices for chiral selection and generating the transmitted field with well-defined OAM. The circular polarization extinction ratio, as an evaluation criterion for the polarization selectivity of a designed structure, could be effectively improved by properly modulating the parameters of spiral structures. Such functional spiral plasmonic nanostructures are promising for applications in analyzing circular polarization light, full Stokes vector polarimetric sensors, near-field imaging, and so on.

Analytical design of Archimedean spiral coils used in inductive power transfer for electric vehicles application

The inductive power transfer (IPT) systems have been drawing much attention in the wide variety of industrial and automotive electric power applications such as battery chargers in automated guided vehicles and electric vehicles (EVs) these days. At the heart of this IPT system are two mutually coupled coils also known as charging pad. Among different existing charging pads, circular charging pad is the most widely adopted charging pad for stationary charging of EV. This is mainly due to ease of manufacturing, symmetric coupling profile, ease of experimental characterization and its non-directional characteristics which ensure simplicity of use by a driver. Circular charging pads consist of coils in the form of Archimedean spirals. For the design of Archimedean spiral, i.e., calculation of number of turns, outer and inner diameter, air gap between primary and secondary coil is often done using finite element analysis software (FEA). However, FEA simulations are complicated and may require a significant number of iterations before achieving the final design goals and therefore are time-consuming. Therefore, the aim of this paper is to formulate simple analytical expressions to design Archimedean spiral from given electrical parameters. An analytical expression for self-inductance as well mutual inductance has been presented. Analytical expressions have been validated using five different coil-pairs fabricated for the same electrical parameters. Usefulness and limitations of the analytical expressions have been discussed.

Momentum Vortices on Pairs Production by Two Counter-Rotating Fields

Multiphoton pair production is investigated by focusing on the momentum structures of produced pairs in the polarization plane for the two circularly polarized fields. Upon the momentum spectra, different from the concentric rings with the familiar Ramsey interference fringes for the same handedness, however, the obvious vortex structures are found constituted by the Archimedean spirals for two opposite handedness fields. The underlying physical reasons are analyzed and discussed. It is also found that the vortex patterns are sensitive to the relative carrier envelope phase, the time delay, and the handedness of two fields, which can be used to detect the applied laser field characteristics as a probe way.

Exact Analytic Solution for a Ballistic Orbiting Wind

Abstract Much theoretical and observational work has been done on stellar winds within binary systems. We present a new solution for a ballistic wind launched from a source in a circular orbit. The solution is that of a single wind—no second wind is included in the system and the shocks that arise are those due to the orbiting wind interacting with itself. Our method emphasizes the curved streamlines in the corotating frame, where the flow is steady-state, allowing us to obtain an exact solution for the mass density at all pre-shock locations. Assuming an initially isotropic wind, fluid elements launched from the interior hemisphere of the wind will be the first to cross other streamlines, resulting in a spiral structure bounded by two shock surfaces. Streamlines from the outer wind hemisphere later intersect these shocks as well. An analytic solution is obtained for the geometry of the two shock surfaces. Although the inner and outer shock surfaces asymptotically trace Archimedean spirals, our tail solution suggests many crossings where the shocks overlap, beyond which the analytic solution cannot be continued. Our solution can be readily extended to an initially anisotropic wind.

Digitizing Tablet and Fahn–Tolosa–Marı´n Ratings of Archimedes Spirals have Comparable Minimum Detectable Change in Essential Tremor

Digitizing Tablet and Fahn–Tolosa–Marı´n Ratings of Archimedes Spirals have Comparable Minimum Detectable Change in Essential Tremor

Embroidered archimedean spiral electrodes for contactless prosthetic control.

With continuous advancements on active prosthetics the detection of the user's intention becomes the new technological bottleneck. While electromyography (EMG) is widely used to detect individual muscular contributions, sweat and relative sensor movements degrade the quality of the signal over time. In this paper, we bypass the problems created with the skin contact analyzing the muscular activation with Archimedean Spiral (AS) electrodes. We compare traditional EMG electrodes with AS electrodes, stacked up in textile embroidered layers to improve their functionality, and eventually adding a layer of cloth/silicon between the electrodes and the human skin to ascertain the feasibility of the method. We use n=9 volunteers to perform a loaded wrist extension and record signals from the extensor digitorum muscle group. We evaluate the amplitude and noise from all results and conclude that the AS electrode is capable of detecting muscular activation without touching the skin. As part of a low-cost prosthetic initiative, this EMG alternative can be potentially embedded to the prosthetic socket to improve usage and reduce adaptation problems.

Visualisation of upper limb activity using spirals: A new approach to the assessment of daily prosthesis usage.

Background:Current outcome measures used in upper limb myoelectric prosthesis studies include clinical tests of function and self-report questionnaires on real-world prosthesis use. Research in other cohorts has questioned both the validity of self-report as an activity assessment tool and the relationship between clinical functionality and real-world upper limb activity. Previously,1 we reported the first results of monitoring upper limb prosthesis use. However, the data visualisation technique used was limited in scope.Study Design:Methodology development.Objectives:To introduce two new methods for the analysis and display of upper limb activity monitoring data and to demonstrate the potential value of the approach with example real-world data.Methods:Upper limb activity monitors, worn on each wrist, recorded data on two anatomically intact participants and two prosthesis users over 1 week. Participants also filled in a diary to record upper limb activity. Data visualisation was carried out using histograms, and Archimedean spirals to illustrate temporal patterns of upper limb activity.Results:Anatomically intact participants’ activity was largely bilateral in nature, interspersed with frequent bursts of unilateral activity of each arm. At times when the prosthesis was worn prosthesis users showed very little unilateral use of the prosthesis (≈20–40 min/week compared to ≈350 min/week unilateral activity on each arm for anatomically intact participants), with consistent bias towards the intact arm throughout. The Archimedean spiral plots illustrated participant-specific patterns of non-use in prosthesis users.Conclusion:The data visualisation techniques allow detailed and objective assessment of temporal patterns in the upper limb activity of prosthesis users.Clinical relevanceActivity monitoring offers an objective method for the assessment of upper limb prosthesis users’ (PUs) activity outside of the clinic. By plotting data using Archimedean spirals, it is possible to visualise, in detail, the temporal patterns of upper limb activity. Further work is needed to explore the relationship between traditional functional outcome measures and real-world prosthesis activity.

Magnetic Characterization of Unsymmetrical Coil Pairs Using Archimedean Spirals for Wider Misalignment Tolerance in IPT Systems

Resonant inductive power transfer (RIPT) is gaining popularity for wireless charging applications of future electric transportation. A fundamental challenge of implementing an RIPT system for wireless power transfer is the coupling variation between the primary and secondary coils, due to misalignment, while parking the car over the primary coil. Thus, it is desirable to have a coil pair, which is least sensitive to misalignments, to ensure efficient power transfer over a wide operating area, and to enable ease of use. The operating area of a coil pair is limited by the existence of a magnetic null in its coupling profile. For circular charging pads, employing a symmetrical Archimedean spiral, a magnetic null occurs at a misalignment distance equal to approximately 40% of the pad diameter (or about 70% of the coil diameter), irrespective of the air gap. In this paper, five diverse unsymmetrical coil pairs have been investigated, to find the coil pair least sensitive to misalignments. For unsymmetrical coil pairs, the position of the magnetic null shifts with the change in separation between the coils. By operating the primary and secondary pads at a distinct separation, the null position can be shifted further away from the center of the coils. This, in turn, increases the effective area, over which a given amount of power can be transferred to the load. After investigating the unsymmetrical coil pairs, it was found that the outer radius of the secondary coil should be kept equal to the outer radius of the primary coil, and inner radius of the secondary coil should be maintained greater than the inner radius of the primary coil, to obtain the best coupling profile.

Interlocked archimedean spirals for conversion of planar rigid panels into locally flexible panels with stiffness control

We present a relief cutting method to turn rigid planar surfaces into flexible ones using meander patterns that consist of interlocked Archimedean spirals. We have developed an approach to obtain all possible such 2D meander patterns with a set of simple remeshing processes. Our algorithm can be applied to any polygonal mesh to produce 2D meander patterns. Since these meander patterns are obtained by remeshing processes, we can control the local properties of the pattern with intensity of images to obtain different stiffness values in different regions. This approach provides a simple interface to construct desired patterns.

Rapid isolation of blood plasma using a cascaded inertial microfluidic device.

Blood, saliva, mucus, sweat, sputum, and other biological fluids are often hindered in their ability to be used in point-of-care (POC) diagnostics because their assays require some form of off-site sample pre-preparation to effectively separate biomarkers from larger components such as cells. The rapid isolation, identification, and quantification of proteins and other small molecules circulating in the blood plasma from larger interfering molecules are therefore particularly important factors for optical blood diagnostic tests, in particular, when using optical approaches that incur spectroscopic interference from hemoglobin-rich red blood cells (RBCs). In this work, a sequential spiral polydimethylsiloxane (PDMS) microfluidic device for rapid (∼1 min) on-chip blood cell separation is presented. The chip utilizes Dean-force induced migration via two 5-loop Archimedean spirals in series. The chip was characterized in its ability to filter solutions containing fluorescent beads and silver nanoparticles and further using blood solutions doped with a fluorescent protein. Through these experiments, both cellular and small molecule behaviors in the chip were assessed. The results exhibit an average RBC separation efficiency of ∼99% at a rate of 5.2 × 106 cells per second while retaining 95% of plasma components. This chip is uniquely suited for integration within a larger point-of-care diagnostic system for the testing of blood plasma, and the use of multiple filtering spirals allows for the tuning of filtering steps, making this device and the underlying technique applicable for a wide range of separation applications.

Electron Vortices in Femtosecond Multiphoton Ionization.

Multiphoton ionization of potassium atoms with a sequence of two counter-rotating circularly polarized femtosecond laser pulses produces vortex-shaped photoelectron momentum distributions in the polarization plane describing Archimedean spirals. The pulse sequences are produced by polarization shaping and the three-dimensional photoelectron distributions are tomographically reconstructed from velocity map imaging measurements. We show that perturbative ionization leads to electron vortices with c_{6} rotational symmetry. A change from c_{6} to c_{4} rotational symmetry of the vortices is demonstrated for nonperturbative interaction.

Computerized spiral analysis using the iPad

BackgroundDigital analysis of writing and drawing has become a valuable research and clinical tool for the study of upper limb motor dysfunction in patients with essential tremor, Parkinson’s disease, dystonia, and related disorders. We developed a validated method of computerized spiral analysis of hand-drawn Archimedean spirals that provides insight into movement dynamics beyond subjective visual assessment using a Wacom graphics tablet. While the Wacom tablet method provides robust data, more widely available mobile technology platforms exist. New methodWe introduce a novel adaptation of the Wacom-based method for the collection of hand-drawn kinematic data using an Apple iPad. This iPad-based system is stand-alone, easy-to-use, can capture drawing data with either a finger or capacitive stylus, is precise, and potentially ubiquitous. ResultsThe iPad-based system acquires position and time data that is fully compatible with our original spiral analysis program. All of the important indices including degree of severity, speed, presence of tremor, tremor amplitude, tremor frequency, variability of pressure, and tightness are calculated from the digital spiral data, which the application is able to transmit. Comparison with existing methodWhile the iPad method is limited by current touch screen technology, it does collect data with acceptable congruence compared to the current Wacom-based method while providing the advantages of accessibility and ease of use. ConclusionsThe iPad is capable of capturing precise digital spiral data for analysis of motor dysfunction while also providing a convenient, easy-to-use modality in clinics and potentially at home.

A novel spiral trajectory for damage component recovery with cold spray

Cold spray is widely applied for the dimensional recovery of damaged parts and components due to the advantages in avoiding local melting, depressing thermal stress and oxidation, and high bonding strength. In this work, a novel trajectory applicable to cold spray for repairing damaged workpiece was proposed for the purpose of improving productivity and reducing cost in machinery work. The Archimedean spiral was chosen as the basis for building this novel trajectory due to the constant distance between two successive turns. This novel trajectory was composed of two symmetrical Archimedean spirals adapted to the damage contour by scaling method. Nozzle speed at each target point was compensated based on the corresponding crater depth. With this novel trajectory, the experimental validation of an Al5056 coating depositing on a damaged Al2027A substrate was conducted. The results showed that the damaged workpiece was perfectly repaired and the coating had good quality in terms of porosity and bonding strength. Therefore, cold spray with the spiral trajectory and adapted nozzle speed is an effective way to repair damage components. Comparing with the round-trip trajectory, Archimedean spiral trajectory is able to significantly save process duration as well as consumption of powder and spray system energy, which leads to the increase of spray efficiency.

Dynamic scan control in STEM: spiral scans

AbstractScanning transmission electron microscopy (STEM) has emerged as one of the foremost techniques to analyze materials at atomic resolution. However, two practical difficulties inherent to STEM imaging are: radiation damage imparted by the electron beam, which can potentially damage or otherwise modify the specimen and slow-scan image acquisition, which limits the ability to capture dynamic changes at high temporal resolution. Furthermore, due in part to scan flyback corrections, typical raster scan methods result in an uneven distribution of dose across the scanned area. A method to allow extremely fast scanning with a uniform residence time would enable imaging at low electron doses, ameliorating radiation damage and at the same time permitting image acquisition at higher frame-rates while maintaining atomic resolution. The practical complication is that rastering the STEM probe at higher speeds causes significant image distortions. Non-square scan patterns provide a solution to this dilemma and can be tailored for low dose imaging conditions. Here, we develop a method for imaging with alternative scan patterns and investigate their performance at very high scan speeds. A general analysis for spiral scanning is presented here for the following spiral scan functions: Archimedean, Fermat, and constant linear velocity spirals, which were tested for STEM imaging. The quality of spiral scan STEM images is generally comparable with STEM images from conventional raster scans, and the dose uniformity can be improved.