Spiral Point Research Articles

An optimization method for flexural bearing design for high-stroke high-frequency applications

A method for optimization of a high-stroke, high-frequency flexural bearing was completed. The main goal was to design a flexural bearing system as the energy restoration component of a one kW free piston linear engine alternator (LEA) operating at 90 Hz and maximum targeted displacement of 22 mm. Defined electricity output of 1 kW, with more than 30% efficiency, required engine operation under high speed and high stroke conditions. Under such challenging stroke and frequency requirements, a method of design was required to select between a wide range of parameters in flexural bearing design. A parametric CAD model was prepared and used in the optimization package of a finite element analysis (FEA) software. Four main parameters of flexural bearing geometry were identified and included the outer diameter, thickness, number of arms, and sweep angle of spiral cuts. Other design parameters including spiral gap width, shape factor and spiral start points angle were shown to be less important compared to these four main parameters in primary design and were examined separately. A neural network algorithm was used to investigate the interactions and effects of design parameters. The sensitivity of each parameter on output criteria such as maximum stress and natural frequency was examined and design charts developed. Methods for further modification of the spiral curve at end points were introduced to reduce the maximum stress level by up to 20%. Several steel alloys and a titanium-based alloy were identified as proper material candidates for high cycle applications and the final designed spring was manufactured and tested to validate the FEA results of axial stiffness and strain level throughout the flexure arms. The percent of the flexure’s moving mass was estimated to be 29% with FEA analysis and compared well with the experimental value of 31%. The stress/strain results of the FEA analysis matched with the experimental results – within ±5%.

Spiral Tool Path Generation Method on Mesh Surfaces Guided by Radial Curves

This paper presents a new spiral smoothing method to generate smooth curved tool paths directly on mesh surfaces. Spiral tool paths are preferable for computer numerical control (CNC) milling, especially for high-speed machining. At present, most spiral tool path generation methods aim mainly for pocketing, and a few methods for machining complex surface also suffer from some inherent problems, such as selection of projecting direction, preprocessing of complex offset contours, easily affected by the mesh or mesh deformation. To address the limitations, a new spiral tool path method is proposed, in which the radial curves play a key role as the guiding curves for spiral tool path generation. The radial curve is defined as one on the mesh surface that connects smoothly one point on the mesh surface and its boundary. To reduce the complexity of constructing the radial curves directly on the mesh surface, the mesh surface is first mapped onto a circular region. In this region, the radial lines, starting from the center, are planned and then mapped inversely onto the mesh surface, thereby forming the desired radial curves. By traversing these radial curves using the proposed linear interpolation method, a polyline spiral is generated, and then, the unfavorable overcuts and undercuts are identified and eliminated by supplementing additional spiral points. Spline-based technique of rounding the corners is also discussed to smooth the polyline spiral, thereby obtaining a smooth continuous spiral tool path. This method is able to not only greatly simplify the construction of radial curves and spiral tool path but also to have the ability of processing and smoothing complex surfaces. Experimental results are presented to validate the proposed method.

Flow structure and heat transfer characteristics of a dimpled wedge channel with a bleed hole in dimple at different orientations and locations

In this study, the heat transfer and friction factor characteristics of a dimpled surface with a bleed hole in the converge channel is studied using a numerical method. The converge angle of the channel is approximately 12.7°. The installation angle of the bleed hole ranges from −30° to 30°. The diameter of the bleed hole is 0.5 mm. The Reynolds number of the main flow is between 8500 and 60,000. The mass flow rate of each bleed hole is 0.5% of the total mass flow rate at the inlet. A dimple without a bleed hole is used as the Baseline. It is found that the bleed hole significantly destroys the low-speed-recirculation. The area of reverse region decreases and the strength of secondary vortex increases as the installation angle increases. The spiral point and reattachment line are also changed as the installation angle changes. This is more distinct for a bleed hole at α = 30°. The primary vortex and spiral point are almost invisible. Two regions with a high turbulent kinetic energy and a high Nusselt number are found. The area-averaged Nu number ratios increase as the installation angle increases. The thermal performance is also improved by the bleed hole.

2010 August 1–2 Sympathetic Eruptions. II. Magnetic Topology of the MHD Background Field

Abstract Using a potential field source-surface (PFSS) model, we recently analyzed the global topology of the background coronal magnetic field for a sequence of coronal mass ejections (CMEs) that occurred on 2010 August 1–2. Here we repeat this analysis for the background field reproduced by a magnetohydrodynamic (MHD) model that incorporates plasma thermodynamics. As for the PFSS model, we find that all three CME source regions contain a coronal hole (CH) that is separated from neighboring CHs by topologically very similar pseudo-streamer structures. However, the two models yield very different results for the size, shape, and flux of the CHs. We find that the helmet-streamer cusp line, which corresponds to a source-surface null line in the PFSS model, is structurally unstable and does not form in the MHD model. Our analysis indicates that, generally, in MHD configurations, this line instead consists of a multiple-null separator passing along the edge of disconnected-flux regions. Some of these regions are transient and may be the origin of the so-called streamer blobs. We show that the core topological structure of such blobs is a three-dimensional “plasmoid” consisting of two conjoined flux ropes of opposite handedness, which connect at a spiral null point of the magnetic field. Our analysis reveals that such plasmoids also appear in pseudo-streamers on much smaller scales. These new insights into the coronal magnetic topology provide some intriguing implications for solar energetic particle events and for the properties of the slow solar wind.

Simulation of Spiral Waves and Point Sources in Atrial Fibrillation with Application to Rotor Localization.

Cardiac simulations play an important role in studies involving understanding and investigating the mechanisms of cardiac arrhythmias. Today, studies of arrhythmogenesis and maintenance are largely being performed by creating simulations of a particular arrhythmia with high accuracy comparable to the results of clinical experiments. Atrial fibrillation (AF), the most common arrhythmia in the United States and many other parts of the world, is one of the major field where simulation and modeling is largely used. AF simulations not only assist in understanding its mechanisms but also help to develop, evaluate and improve the computer algorithms used in electrophysiology (EP) systems for ablation therapies. In this paper, we begin with a brief overeview of some common techniques used in simulations to simulate two major AF mechanisms - spiral waves (or rotors) and point (or focal) sources. We particularly focus on 2D simulations using Nygren et al.'s mathematical model of human atrial cell. Then, we elucidate an application of the developed AF simulation to an algorithm designed for localizing AF rotors for improving current AF ablation therapies. Our simulation methods and results, along with the other discussions presented in this paper is aimed to provide engineers and professionals with a working-knowledge of application-specific simulations of spirals and foci.

A numerical analysis on forming limits during spiral and concentric single point incremental forming

Sheet metal forming is one of the major manufacturing industries, which are building numerous parts for aerospace, automotive and medical industry. Due to the high demand in vehicle industry and environmental regulations on less fuel consumption on other hand, researchers are innovating new methods to build these parts with energy efficient sheet metal forming process instead of conventionally used punch and die to form the parts to achieve the lightweight parts. One of the most recognized manufacturing process in this category is Single Point Incremental Forming (SPIF). SPIF is the die-less sheet metal forming process in which the single point tool incrementally forces any single point of sheet metal at any process time to plastic deformation zone. In the present work, finite element method (FEM) is applied to analyze the forming limits of high strength low alloy steel formed by single point incremental forming (SPIF) by spiral and concentric tool path. SPIF numerical simulations were model with 24 and 29 mm cup depth, and the results were compare with Nakajima results obtained by experiments and FEM. It was found that the cup formed with Nakajima tool failed at 24 mm while cups formed by SPIF surpassed the limit for both depths with both profiles. It was also notice that the strain achieved in concentric profile are lower than that in spiral profile.

A Predator-prey Model with Predator Population Saturation

In this article, a new predator-prey model having predator saturation is proposed. The model resembles a classical Rosenzweig-MacArthur type model, but comes with an added function, the population saturation function of the predator. This function of the predator population is a factor in the predator fertility term in the model. Consequently the model behaves better than the Rosenzweig-MacArthur model since all solutions are bounded within the population quadrant. An invariant region arises where the Poincare-Bendixon theorem can be applied. In most cases there is but a single critical value, either an attracting spiral point suggesting a stable population pair or an unstable node, resulting in a unique limit cycle. This model is fully described and an analysis of the stability of critical values is provided. The robustness of the model is demonstrated based on the classification of Gunawardena [8].

Spiral-shells and nascent bipolar outflow in CIT 6: hints for an eccentric-orbit binary?

We present the essential results pointed out in a recently published paper, Kim et al. 2015, Astrophys. J., 814, 61. The carbon star CIT 6 reveals evidences for a binary in a high-resolution CO line emission map of its circumstellar envelope taken with the Submillimeter Array. The morphology of the outflow described by the spiral-shell pattern, bipolar (or possibly multipolar) outflow, one-sided interarm gaps, and double spiral feature point to a plausible scenario that CIT 6 is a binary system in an eccentric orbit with the mass losing star evolving from the AGB.

GAS DYNAMICS IN THE MILKY WAY: A LOW PATTERN SPEED MODEL

ABSTRACT We present gas flow models for the Milky Way based on high-resolution grid-based hydrodynamical simulations. The basic galactic potential we use is from an N-body model constrained by the density of red clump giants in the Galactic bulge. We augment this potential with a nuclear bulge, two pairs of spiral arms, and additional mass at the bar end to represent the long bar component. With this combined model we can reproduce many features in the observed ( ) diagram with a bar pattern speed of and a spiral pattern speed of . The shape and kinematics of the nuclear ring, Bania’s Clump 2, the Connecting arm, the Near and Far 3 kpc arms, the Molecular Ring, and the spiral arm tangent points in our simulations are comparable to those in the observations. Our results imply that a low pattern speed model for the bar in our Milky Way reproduces the observations for a suitable Galactic potential. Our best model gives a better match to the ( ) diagram than previous high pattern speed hydrodynamical simulations.

A preliminary investigation towards automated computation of Multiparametric strain Z-Score in dilated cardiomyopathy using navigator-gated spiral DENSE MRI and radial point interpolation method

A preliminary investigation towards automated computation of Multiparametric strain Z-Score in dilated cardiomyopathy using navigator-gated spiral DENSE MRI and radial point interpolation method

Resolution enhancement of optical scanning holography with a spiral modulated point spread function

In optical scanning holography, one pupil produces a spherical wave and another produces a plane wave. They interfere with each other and result in a fringe pattern for scanning a three-dimensional object. The resolution of the hologram reconstruction is affected by the point spread function (PSF) of the optical system. In this paper, we modulate the PSF by a spiral phase plate, which significantly enhances the lateral and depth resolution. We explain the theory for such resolution enhancement and show simulation results to verify the efficacy of the approach.

A Novel Dynamic Secret key Generation for an Efficient Image Encryption Algorithm

<p>Today, the security of digital images is considered more and more essential and a strong secret key plays a major role in the image encryption. In this paper, a novel method for generating dynamic non-linear secret keys for a symmetric block cipher using XOR-operation is proposed. The dynamic non-linear secret keys generation is based on a combination of logistic and piecewise chaotic map methods with a new automatic creation of initial seed values. The automatic initial seed values creation depends on the development of a novel strategy for seeds creation based on sunflower spiral points. The experimental results indicate that the proposed key generator algorithm has the advantage of large key space with a safety protection of brute force attack. Therefore, the performance analysis of image encryption reveals a correlation coefficient of about (-0.0001) and entropy greater than (7.9978). Furthermore, the results show high security for encryption based on strong dynamic secret key properties.</p>

Offset between stellar spiral arms and gas arms of the Milky Way

Spiral arms shown by different components may not be spatially coincident, which can constrain formation mechanisms of spiral structure in a galaxy. We reassess the spiral arm tangency directions in the Milky Way through identifying the bump features in the longitude plots of survey data for infrared stars, radio recombination lines (RRLs), star formation sites, CO, high density regions in clouds, and HI. The bump peaks are taken as indications for arm tangencies, which are close to the real density peaks near the spiral arm tangency point but often have $\sim$ 1$^\circ$ offset to the interior of spiral arms. The arm tangencies identified from the longitudes plots for RRLs, HII regions, methanol masers, CO, high density gas regions, and HI gas appear nearly the same Galactic longitude, and therefore there is no obvious offset for spiral arms traced by different gas components. However, we find obvious displacements of 1.3$^\circ-$ 5.8$^\circ$ between gaseous bump peaks from the directions of the maximum density of old stars near the tangencies of the Scutum-Centaurus Arm, the northern part of the Near 3 kpc Arm, and maybe also the Sagittarius Arm. The offsets between the density peaks of gas and old stars for spiral arms are comparable with the arm widths, which is consistent with expectations for quasi-stationary density wave in our Galaxy.

Minimal expansive systems and spiral points

It is known that if a compact metric space X admits a minimal expansive homeomorphism then X is totally disconnected. In this note we give a short proof of this result and we analyze its extension to expansive flows.

ENERGY DISSIPATION IN MAGNETIC NULL POINTS AT KINETIC SCALES

We use kinetic particle-in-cell and magnetohydrodynamic simulations supported by an observational dataset to investigate magnetic reconnection in clusters of null points in space plasma. The magnetic configuration under investigation is driven by fast adiabatic flux rope compression that dissipates almost half of the initial magnetic field energy. In this phase powerful currents are excited producing secondary instabilities, and the system is brought into a state of `intermittent turbulence' within a few ion gyro-periods. Reconnection events are distributed all over the simulation domain and energy dissipation is rather volume-filling. Numerous spiral null points interconnected via their spines form null lines embedded into magnetic flux ropes; null point pairs demonstrate the signatures of torsional spine reconnection. However, energy dissipation mainly happens in the shear layers formed by adjacent flux ropes with oppositely directed currents. In these regions radial null pairs are spontaneously emerging and vanishing, associated with electron streams and small-scale current sheets. The number of spiral nulls in the simulation outweighs the number of radial nulls by a factor of 5\---10, in accordance with Cluster observations in the Earth's magnetosheath. Twisted magnetic fields with embedded spiral null points might indicate the regions of major energy dissipation for future space missions such as Magnetospheric Multiscale Mission (MMS).

Hurricane maximum potential intensity equilibrium

This study presents a minimal model to examine the stability of the hurricane maximum potential intensity (MPI) equilibrium, based on the evolution of several hurricane fundamental scales. It is shown that this hurricane‐scale model contains MPI as an asymptotically stable spiral point under the wind‐induced surface heat exchange (WISHE) feedback mechanism. Furthermore, the hurricane development is characterized by two different time‐scales instead of a simple linear growth, as often assumed in previous studies. Inclusion of radiative cooling reduces the MPI limit, but the MPI equilibrium in general is structurally stable. In particular, radiative cooling will modify the basin of attraction of the MPI equilibrium and create a domain in the phase space of the hurricane scales such that a vortex would not develop if its initial condition falls within this domain. Potential mechanisms that can further unfold the stability of the MPI equilibrium will also be discussed.

Numerical Prediction of Flow Structure and Heat Enhancement with Different Dimple Depth

Aim at finding the relation between flow structure and heat enhancement, this paper change the dimple depth to print diameter from 0.06 to 0.3, with an interval of 0.02, and keep the print diameter constant. Through vortex structure analysis and Nu number integration, find out that: Vortex structure varies with dimple depth. Shallow depth dimple induces horseshoe vortex; middle depth dimple induces symmetric tornado-like vortex; deep depth dimple induces tornado-like vortex. Heat enhancement is closely related to vortex structure. Where spiral separation focus point exists, there the lowest Nu/Nu0 exists. Flow impingement at the windward side of dimple and new viscous layer generation at immediate plane after the dimple enhance heat transfer. The highest Nu/Nu0 exists in the sharp rearward dimple edge. From Fig 6, the deeper the dimple is, the higher the average Nu/Nu0 is, so does the pressure drop. But from 0.06 to 0.2 dimple, heat enhancement increased because of vortex structure changed. From 0.2 to 0.3 heat enhancement increased because of the increased area.

The Vortical Structures in the Rear Separation and Wake Produced by a Supersonic Micro-Ramp

The vortical structures in the rear separation and wake region produced by a micro-ramp that immersed in a supersonic turbulent boundary layer are investigated. The small scale separation close to the trailing edge was revealed and this confirms the previous experimental observation. Between the reverse region and surrounding fast moving flow, a three-dimensional shear layer was formed, and vortices are generated. By using vortex line method, the spiral points were illustrated as the cross-sections of the Ω-shaped vortices that follow the shape of the separation. The vortical structure was analogous to that in the wake region, where similar Ω-shaped vortex which follows the deficit region caused by the micro-ramp can be observed. Finally, the revealed flow topology was conceived new and beneficial to the studying of wall bounded turbulence which involves similar vortical structures but in a smaller scale, compared with the vortical pattern in the current micro-ramp wake.

QMC designs: Optimal order Quasi Monte Carlo integration schemes on the sphere

We study equal weight numerical integration, or Quasi Monte Carlo (QMC) rules, for functions in a Sobolev space H s ( S d ) \mathbb {H}^s( \mathbb {S}^d) with smoothness parameter s > d / 2 s > d/2 defined over the unit sphere S d \mathbb {S}^d in R d + 1 \mathbb {R}^{d+1} . Focusing on N N -point configurations that achieve optimal order QMC error bounds (as is the case for efficient spherical designs), we are led to introduce the concept of QMC designs: these are sequences of N N -point configurations X N X_N on S d \mathbb {S}^d such that the worst-case error satisfies sup f ∈ H s ( S d ) , ‖ f ‖ H s ≤ 1 | 1 N ∑ x ∈ X N f ( x ) − ∫ S d f ( x ) d σ d ( x ) | = O ( N − s / d ) , N → ∞ , \begin{equation*} \sup _{\substack {f \in \mathbb {H}^s( \mathbb {S}^d ), \\ \| f \|_{\mathbb {H}^s} \leq 1}} \Bigg | \frac {1}{N} \sum _{\mathbf {x} \in X_N} f( \mathbf {x} ) - \int _{\mathbb {S}^d} f( \mathbf {x} ) \, \mathrm {d} \sigma _d( \mathbf {x} ) \Bigg | = \mathcal {O}\big ( N^{-s/d} \big ), \qquad N \to \infty , \end{equation*} with an implied constant that depends on the H s ( S d ) \mathbb {H}^s( \mathbb {S}^d ) -norm, but is independent of N N . Here σ d \sigma _d is the normalized surface measure on S d \mathbb {S}^d . We provide methods for generation and numerical testing of QMC designs. An essential tool is an expression for the worst-case error in terms of a reproducing kernel for the space H s ( S d ) \mathbb {H}^s( \mathbb {S}^d ) with s > d / 2 s > d/2 . As a consequence of this and a recent result of Bondarenko et al. on the existence of spherical designs with appropriate number of points, we show that minimizers of the N N -point energy for this kernel form a sequence of QMC designs for H s ( S d ) \mathbb {H}^s( \mathbb {S}^d ) . Furthermore, without appealing to the Bondarenko et al. result, we prove that point sets that maximize the sum of suitable powers of the Euclidean distance between pairs of points form a sequence of QMC designs for H s ( S d ) \mathbb {H}^s( \mathbb {S}^d ) with s s in the interval ( d / 2 , d / 2 + 1 ) {(d/2,d/2+1)} . For such spaces there exist reproducing kernels with simple closed forms that are useful for numerical testing of optimal order Quasi Monte Carlo integration. Numerical experiments suggest that many familiar sequences of point sets on the sphere (equal area points, spiral points, minimal [Coulomb or logarithmic] energy points, and Fekete points) are QMC designs for appropriate values of s s . For comparison purposes we show that configurations of random points that are independently and uniformly distributed on the sphere do not constitute QMC designs for any s > d / 2 s>d/2 . If ( X N ) (X_N) is a sequence of QMC designs for H s ( S d ) \mathbb {H}^s( \mathbb {S}^d) , we prove that it is also a sequence of QMC designs for H s ′ ( S d ) \mathbb {H}^{s’}( \mathbb {S}^d) for all s ′ ∈ ( d / 2 , s ) s’\in (d/2,s) . This leads to the question of determining the supremum of such s s (here called the QMC strength of the sequence), for which we provide estimates based on computations for the aforementioned sequences.

A computational theory for spiral point vortices in multiply connected domains with slit boundaries

A spiral point vortex, which is a point vortex with a source-sink structure, appears when we consider a two-dimensional cross section of a straight vortex line with a uniform flow in its axial direction in three-dimensional space. In the present paper, we present a computational theory for the motion of spiral point vortices in two-dimensional exterior domains that contain multiple rectilinear line segments as boundaries, called slit domains. The theory consists of the evolution equation for spiral point vortices in multiply connected domains and a numerical procedure to construct conformal mappings from multiply connected domains with circular boundaries onto given slit domains. It is applicable to many flow problems arising in biofluids and environmental flows. As an example, we apply the theory to the flow problem of finding force-enhancing equilibria consisting of two spiral point vortices in a slit domain with two parallel plates in the presence of a uniform flow, which is a two-dimensional model of a wind-turbine with vertical blades.