Dual Circle Research Articles

The bubble of nothing under T-duality

The bubble of nothing is a solution to Einstein’s equations where a circle shrinks and pinches off smoothly. As such, it is one of the simplest examples of a dynamical cobordism to nothing. We take a first step in studying how this solution transforms under T-duality in bosonic string theory. Applying Buscher’s rules reveals that the dual solution features a singular, strongly coupled core, with a circle blowing-up rather than pinching off. This naive approach to T-duality solely accounts for the zero-modes of the fields after dimensional reduction on the circle. For this reason, we argue that this is not the full picture that the T-dual solution should depend non-trivially on the dual circle. We point out evidence to this effect both in the gravity description and on the worldsheet. A more complete description of the T-dual object would require a full-fledged sigma model for the bubble of nothing. Nevertheless, inspired by similar examples in the literature, we detail one possible scenario where the stringy bubble of nothing is mediated by closed string tachyon condensation and we discuss its T-duality.

Camera calibration using the dual double-contact property of circles

To mitigate the influence of the relative positional relationship between circles on camera calibration, this study explores the double contact of dual circles with dual circular points. We demonstrate that one of the generalized eigenvectors of two dual circles corresponds to the line passing through their respective centers. Moreover, we establish a methodology to identify this line from the three generalized eigenvectors and show that, regardless of the positional arrangement of the three co-planar circles, the image of the circular points can be constructed by calculating the image of this line. Consequently, the applicability of circles as calibration templates is expanded, enabling the development of a novel optimization technique for fitting circular images with enhanced calibration precision.

On dynamical gaskets generated by rational maps, Kleinian groups, and Schwarz reflections

According to the Circle Packing Theorem, any triangulation of the Riemann sphere can be realized as a nerve of a circle packing. Reflections in the dual circles generate a Kleinian group H H whose limit set is a generalized Apollonian gasket Λ H \Lambda _H . We design a surgery that relates H H to a rational map g g whose Julia set J g \mathcal {J}_g is (non-quasiconformally) homeomorphic to Λ H \Lambda _H . We show for a large class of triangulations, however, the groups of quasisymmetries of Λ H \Lambda _H and J g \mathcal {J}_g are isomorphic and coincide with the corresponding groups of self-homeomorphisms. Moreover, in the case of H H , this group is equal to the group of Möbius symmetries of Λ H \Lambda _H , which is the semi-direct product of H H itself and the group of Möbius symmetries of the underlying circle packing. In the case of the tetrahedral triangulation (when Λ H \Lambda _H is the classical Apollonian gasket), we give a quasiregular model for the above actions which is quasiconformally equivalent to g g and produces H H by a David surgery. We also construct a mating between the group and the map coexisting in the same dynamical plane and show that it can be generated by Schwarz reflections in the deltoid and the inscribed circle.

Universal platform for accurately damage-free mapping of sEVs cargo information

SEVs (small extracellular vesicles) contents signatures appear to mirror pathological changes of diseases, and mapping sEVs contents profile is a promising approach for non-invasive diagnosis of the disease. Herein, we propose a universal system for accurately and damage-freely mapping of sEVs content profile using dual-recognition triggered CHA (catalytic hairpin assembly) and DNAzyme based signal amplification strategy. After immunoassay based capture of CD63 positive sEVs by anti-CD63 lgG coated on the surface of polystyrene plates, probes are incubated with fixed sEVs to penetrate sEVs membrane and act to sense sEVs contents. In detection step, integrated CHA and DNAzyme based strategy is initiated by released initiator from capture probe after recognizing targets, forming a dual circle signal recycling process, realizing signal amplification for high sensitivity. Given the attractive analytical features that i) a universal platform for indistinctive sEVs nucleic acids and protein molecules detection; ii) high sensitivity derived from dual circle signal recycling process; iii) enzyme-free characteristic of integrated CHA and DNAzyme minimizes the interference to sEVs biological activity; iv) mapping of sEVs contents profiles indicates a brand-new strategy for non-invasive diagnosis of the disease, the present approach shows great promise for analyzing additional different analytes in clinical and experimental researches.

Undrained stability of dual tunnels in layered soils with different strength

The stability of dual circle tunnels buried in layered soils with different shear strengths was investigated by using finite element limit analysis (FELA). The emphasis of this study is in quantitating that the existing tunnels affects the newly-built one, and design suggestions have been provided especially in the optimum location of construction. By imposing a FELA modelling, the variation trends of undrained bearing capacity with different influential factors, including the horizontal distance, vertical distance, the thickness of the top layer, the shear strength ratio of the layered soil, were further investigated. It is concluded that there exists an inclination-fixed worst-band, in which there would be a worst undrained stability once the bottom tunnel was constructed in the band. It is interested that the inclination seems constant by varying several factors but the horizontal distance would be changed with the soil properties. In addition, three patterns of collapse were summarized.

Polarization- and Frequency-Reconfigurable Patch Antenna Using Gravity-Controlled Liquid Metal

This letter presents a reconfigurable antenna that uses gravity to control the self-circulation of liquid metal (LM), thereby realizing an adaptive reconstruction method. Then the polydimethylsiloxane (PDMS) structure with a square ring channel is loaded on the microstrip antenna, and the contact position between the liquid metal and the patch is controlled by gravity, which provides conditions for reconfiguration. The antenna has four reconfigurable frequency bands, which can be switched between the dual circle polarization (left- and right-hand circular polarization) mode and the linear polarization (LP) mode without additional mechanical adjustment structures, radio frequency circuits or related components. The measured results show that the proposed antenna has −10 dB impedance band of 1.2-1.6 GHz, 2.5-2.75 GHz, 4.2-4.55 GHz and 5-5.4 GHz and peak gain of 3.6 dBi, 5.07 dBi, 2.68 dBi and 3.25 dBi within passband, which agree well with the simulated results.

Homotopy versus isotopy: Spheres with duals in 4-manifolds

Dave Gabai recently proved a smooth 4-dimensional “light bulb theorem” in the absence of 2-torsion in the fundamental group. We extend his result to 4-manifolds with arbitrary fundamental group by showing that an invariant of Mike Freedman and Frank Quinn gives the complete obstruction to “homotopy implies isotopy” for embedded 2-spheres which have a common geometric dual. The invariant takes values in an F2-vector space generated by elements of order 2 in the fundamental group and has applications to unknotting numbers and pseudoisotopy classes of self-diffeomorphisms. Our methods also give an alternative approach to Gabai’s theorem using various maneuvers with Whitney disks and a fundamental isotopy between surgeries along dual circles in an orientable surface.

Optimization study on high-temperature corrosion prevention of the water wall of a 1000 MW dual circle tangential boiler during operation

High-temperature corrosion of boiler water wall is one of the major factors that affect safe and economic operation of large thermal generator sets. For the high-temperature corrosion of right and left water walls of a domestic 1000 MW dual circle tangential boiler during trial operation, this paper studies impact on high-temperature corrosion of water walls from burner height–width ratio and secondary air nozzle swing angle respectively through Fluent numerical simulation. Simulation results show that a burner combination mode with a small height–width ratio shall be used during actual operation of the boiler. In addition, when the secondary air nozzle is swung upward by 15°, the CO concentration at the place close to the wall surface in the combustion zone is less than 3% with adequate oxygen content, which can reduce high-temperature corrosion risk of water walls.

Combined effects of yaw and tilt angles of separated overfire air on the combustion characteristics in a 1,000 MW coal-fired boiler: A numerical study

Separated overfire air (SOFA) is typically employed in coal-fired boilers with air staged technology to sustain lower NOX emission, and SOFA nozzle angles are crucial adjustment parameters. In this work, the combined effects of SOFA yaw and tilt angles on combustion characteristics were numerically investigated for a 1,000 MW dual circle tangentially coal-fired boiler. Numerical results show that the forward increase of the SOFA yaw angle from 0° brings about the enlarged SOFA tangential circle and the gradual appearance of bimodal high-temperature zones at furnace exit. With further tuning SOFA tilt angles vertically, the bimodal high-temperature zones would separate to the two halves of the furnace, inducing a more severe deviation of gas temperature. Besides, the gas residual rotating momentum is strengthened as SOFA yaw angles forward increase, resulting in the enhancement of traction effect in the upper furnace as well as the rise of flame. However, the gas velocity deviation is somewhat eliminated as SOFA rotates reversely. No matter that the SOFA yaw angle increases forward or reversely, the coal burnout would deteriorate with the overly enlarged SOFA tangential circles. Tuning SOFA yaw and tilt angles, respectively, at 5° and 0° can simultaneously guarantee lower CO and NOX emissions.

Two Separate Circles With Same-Radius: Projective Geometric Properties and Applicability in Camera Calibration

In the domain of computer vision, camera calibration is a key step in recovering the two-dimensional Euclidean structure. Circles are considered important image features similar to points, lines, and conics. In this paper, a novel linear calibration method is proposed using two separate same-radius (SSR) circles as the calibration pattern. We show that the distinct pair of dual circles encodes three lines, two of which are parallel to each other and perpendicular to the remaining line. When any two coplanar or parallel circles degenerate to SSR circles, a solution can be found to recover another pair of parallel lines based on the geometric properties of the SSR circles. Using the vanishing points obtained as the key helper for determining the imaged circular points and the orthogonal vanishing points, we deduce the constraints on the image of the absolute conic (IAC) and then employ it for complete camera calibration. Furthermore, a closed-form solution for the extrinsic parameters can be obtained based on the projective invariance of the conic dual to the circular points. Evaluations based on simulated and real data confirmed the effectiveness and feasibility of the proposed algorithms.

The topological cyclic homology of the dual circle

We give a new proof of a result of Lazarev, that the dual of the circle S+1 in the category of spectra is equivalent to a strictly square-zero extension as an associative ring spectrum. As an application, we calculate the topological cyclic homology of DS1 and rule out a Koszul-dual reformulation of the Novikov conjecture.

Towards the design of effective freehand gestural interaction for interactive TV

As interactive devices become pervasive, people are beginning to looking for more advanced interaction with televisions in the living room. Interactive television has the potential to offer a very engaging experience. But most common user tasks are still challenging with such systems, such as menu selection or text input. And little work has been done on understanding and sup-porting the effective design of freehand interaction with an TV in the living room. In this paper, we perform two studies investi-gating freehand gestural interaction with a consumer level sensor, which is suitable for TV scenarios. In the first study, we inves-tigate a range of design factors for tiled layout menu selection, including wearable feedback, push gesture depth, target size and position in motor space. The results show that tactile and audio feedback have no significant effect on performance and prefer-ence, and these results inform potential designs for high selection performance. In the second study, we investigate a common TV user task of text input using freehand gesture. We design and evaluate two virtual keyboard layouts and three freehand selec-tion methods. Results show that ease of use and error tolerance can be both achieved using a text entry method utilizing a dual circle layout and an expanding target selection technique. Finally, we propose design guidelines for effective, usable and com-fortable freehand gestural interaction for interactive TV based on the findings.

No Benefit After THA Performed With Computer-assisted Cup Placement: 10-year Results of a Randomized Controlled Study.

Computer-assisted surgery (CAS) for cup placement has been developed to improve the functional results and to reduce the dislocation rate and wear after total hip arthroplasty (THA). Previously published studies demonstrated radiographic benefits of CAS in terms of implant position, but whether these improvements result in clinically important differences that patients might perceive remains largely unknown. We hypothesized that THA performed with CAS would improve 10-year patient-reported outcomes measured by validated scoring tools, reduce acetabular polyethylene wear as measured using a validated radiological method, and increase survivorship. Sixty patients operated on for a THA between April 2004 and April 2005 were randomized into two groups using either the CAS technique or a conventional technique for cup placement. All patient candidates for a THA with the diagnosis of primary arthritis or avascular necrosis were eligible for the CAS procedure and randomly assigned to the CAS group by the Hospital Informatics Department with use of a systematic sampling method. The patients assigned to the freehand cup placement group were matched for sex, age within 5 years, pathological condition, operatively treated side, and body mass index within 3 points. All patients were operated on through an anterolateral approach (patient in the supine position) using cementless implants. In the CAS group, a specific surgical procedure using an imageless cup positioning computer-based navigation system was performed. There were 16 men and 14 women in each group; mean age was 62 years (range, 24-80 years), and mean body mass index was 25 ± 3 kg/m(2). No patient was lost to followup at 10 years, but five patients have died (two in the CAS group and three in the control group). At the 10-year followup, an independent observer blinded to the type of technique performed patients' evaluation. Cup positioning was evaluated postoperatively using a CT scan in the two groups with results previously published. At 10 years, we assessed subjective functional outcome and quality of life using validated questionnaires (SF-12, Harris hip score [HHS], Hip injury and Osteoarthritis Outcome Score). Wear rate was then evaluated on standardized radiographs using a previously validated semiautomated computer analogic measurement method (dual circle method). Complications and survivorship were compared between groups. With our available sample size, this study had 80% power to detect a difference of 4 points out of 100 on the HHS at the p < 0.05 level. With the numbers available, we found we found no differences between groups regarding HSS at last followup 95.3 ± 5.9 points (CAS group) versus 96.2 ± 4.5 points, a mean difference of 0.9 points (95% confidence interval [CI], -4.3 to 4.6; p = 0.6). There was no difference between the groups in terms of the mean (± SD) acetabular linear wear at 10 years. The mean wear was 0.71 ± 0.6 mm in the CAS group versus 0.77 ± 0.52 mm in the control group, a mean difference of 0.06 mm (95% CI, -0.1 to 0.2; p = 0.54). With the numbers available, there was no difference between the CAS group and the conventional THA groups in terms of survivorship free from aseptic loosening (100%; 95% CI, 100%-95%, versus 100%; 95% CI, 100%-94%; p = 0.3). Our observations suggest that CAS used for cup placement does not confer any substantial advantage in function, wear rate, or survivorship at 10 years after THA. Because CAS is associated with added costs and surgical time, future studies need to identify what clinically relevant advantages it offers, if any, to justify its continued use in THA. Level II, therapeutic study.

Vision pose estimation from planar dual circles in a single image

A novel vision based pose estimation method for a single image with planar dual circles is addressed. We present a very simple formula to solve camera pose with a single circle, and then develop a fusion method to integrate solved poses of dual circles by using space geometry constraints. After that, a new definition of the difference quantity between two ellipses is proposed to evaluate reprojection errors of dual circles and determine the optimal and unique pose solution. Experiments with synthetic data and real images are carried out to validate the proposed method, and results show that the method has a high accuracy and good robustness.

Modeling the Occurrence and Methods of Reducing Thermal Deviations of Upper Furnace Heating Surfaces in a 1000 MW Dual Circle Tangential Firing Single Furnace Ultra-Supercritical Boiler

The FLUENT computational fluid dynamics software package was used to model outlet velocity and temperature inhomogeneity in a 1000 MW dual circle tangential firing single furnace ultra-supercritical boiler. These computations allowed a theoretical analysis of thermal deviations at the furnace outlet and suggested means of reducing such deviations. This work involved study of radiative and convective heat transfer of the upper furnace platen superheaters, the radiative–convective heating surfaces above the furnace nose and the convective heating surfaces in the horizontal flue. The results demonstrated that the radiant heat load of the heating surfaces of the platen superheaters is related to the sectional dimensions of the furnace and exhibits a bimodal distribution in the boiler modeled during this work. It was also determined that a large recirculation zone is formed in the central section of the horizontal flue owing to velocity superposition. After establishing the thermal load distribution characteristics and the causes of thermal deviations at the various heating surfaces, further modeling was performed to assess the extent to which thermal deviations could be reduced by decreasing residual rotation at the furnace outlet via horizontally swinging the over fire air (OFA). The effects of OFA swing angles on velocity and temperature inhomogeneity at the furnace outlet were subsequently analyzed, and an OFA swing of −10° was found to be optimal based on considerations of thermal deviations at the furnace outlet, the airflow field in the furnace, and safe operation of the boiler.

WE-G-BRF-07: Non-Circular Scanning Trajectories with Varian Developer Mode

Purpose: Cone-beam CT (CBCT) in image-guide radiation therapy (IGRT) typicallyacquires scan data via the circular trajectory of the linearaccelerator's (linac) gantry rotation. Though this lends itself toanalytic reconstruction algorithms like FDK, iterative reconstructionalgorithms allow for a broader range of scanning trajectories. Weimplemented a non-circular scanning trajectory with Varian's TrueBeamDeveloper Mode and performed some preliminary reconstructions toverify the geometry. Methods: We used TrueBeam Developer Mode to program a new scanning trajectorythat increases the field of view (FOV) along the gantry rotation axiswithout moving the patient. This trajectory consisted of moving thegantry in a circle, then translating the source and detector along theaxial direction before acquiring another circular scan 19 cm away fromthe first. The linear portion of the trajectory includes an additional4.5 cm above and below the axial planes of the source's circularrotation. We scanned a calibration phantom consisting of a lucite tubewith a spiral pattern of CT spots and used the maximum-likelihoodalgorithm to iteratively reconstruct the CBCT volume. Results: With the TrueBeam trajectory definition, we acquired projection dataof the calibration phantom using the previously described trajectory.We obtained a scan of the treatment couch for log normalization byscanning with the same trajectory but without the phantom present.Using the nominal geometric parameters reported in the projectionheaders with our iterative reconstruction algorithm, we obtained acorrect reconstruction of the calibration phantom. Conclusion: The ability to implement new scanning trajectories with the TrueBeamDeveloper Mode enables us access to a new parameter space for imagingwith CBCT for IGRT. Previous simulations and simple dual circle scanshave shown iterative reconstruction with non-circular trajectories canincrease the axial FOV with CBCT. Use of Developer Mode allowsexperimentally testing these and other new scanning trajectories. Support was provided in part by the University of Chicago Research Computing Center, Varian Medical Systems, and NIH Grants 1RO1CA120540, T32EB002103, S10 RR021039 and P30 CA14599. The contents of this work are solely the responsibility of the authors and do not necessarily represent the official views of the supporting organizations.

Diamond-kite adaptive quadrilateral meshing

We describe a family of quadrilateral meshes based on diamonds, rhombi with 60° and 120° angles, and kites with 60°, 90°, and 120° angles, that can be adapted to a local size function by local subdivision operations. Our meshes use a number of elements that is within a constant factor of the minimum possible for any mesh of bounded aspect ratio elements, graded by the same local size function, and is invariant under Laplacian smoothing. The vertices of our meshes form the centers of the circles in a pair of dual circle packings. The same vertex placement algorithm but a different mesh topology gives a pair of dual well-centered meshes adapted to the given size function.

Research on the elliptic aerodynamic field in a 1000 MW dual circle tangential firing single furnace ultra supercritical boiler

An IFA300 constant temperature anemometer system is adopted to perform cold air experiments on a scale model of a dual circle tangential firing single furnace ultra supercritical boiler to investigate the causes and influencing factors of jet deviation in the furnace, which is the main cause of the elliptical aerodynamic field. The elliptic aerodynamic field could cause heat imbalance in the burner zone, in which case high temperature corrosion and slagging might happen on the high-temperature furnace wall. Theoretical derivations and analysis have been carried out before any experimental studies, and an equation determining the influencing factors of the jet deviation has been established. The experimental results agree well with the equation. The jet deviation becomes more problematic when the velocity ratio of the impacting jet and the impacted jet increases from 0.85 to 1.30. A reduction in the distance from the impacting position to the root of the impacted jet also increases the jet deviation as well as the angle between the impacting jet and impacted jet. The results of the theoretical analysis and experiments provide some transformations within the boiler that could be adopted to avoid the formation of the oblique ellipse flow field.

Calculation of Dual Circle Closure Calibrations using Computer Spreadsheets

This technical note will detail a procedure for simultaneous calibration of two rotary devices by circle closure, along with the necessary calculations. These calculations can be implemented using ...

Analytic Torsion for Twisted De Rham Complexes

We define analytic torsion $\tau(X,\mathcal{E},H)\in \operatorname{det}H^{\bullet}(X,\mathcal{E},H)$ for the twisted de Rham complex, consisting of the spaces of differential forms on a compact oriented Riemannian manifold $X$ valued in a flat vector bundle $\mathcal{E}$, with a differential given by $\nabla^{\mathcal{E}}+H \land \cdot$, where $\nabla^{\mathcal{E}}$ is a flat connection on $\mathcal{E}$, $H$ is an odd-degree closed differential form on $X$, and $H^{\bullet}(X,\mathcal{E},H)$ denotes the cohomology of this $\mathbb{Z}_2$ graded complex. The definition uses pseudodifferential operators and residue traces. We show that when $\operatorname{dim} X$ is odd, $\tau(X, \mathcal{E},H)$ is independent of the choice of metrics on $X$ and $\mathcal{E}$ and of the representative $H$ in the cohomology class $[H]$. We define twisted analytic torsion in the context of generalized geometry and show that when $H$ is a 3-form, the deformation $H \mapsto H-dB$, where $B$ is a 2-form on $X$, is equivalent to deforming a usual metric $g$ to a generalized metric$ (g,B)$. We demonstrate some basic functorial properties. When $H$ is a top-degree form, we compute the torsion, define its simplicial counterpart, and prove an analogue of the Cheeger-Muller Theorem. We also study the twisted analytic torsion for $T$-dual circle bundles with integral 3-form fluxes.