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Journal articles on the topic 'Circular domain'

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Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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1

Cowburn, R. P., D. K. Koltsov, A. O. Adeyeye, M. E. Welland, and D. M. Tricker. "Single-Domain Circular Nanomagnets." Physical Review Letters 83, no. 5 (August 2, 1999): 1042–45. http://dx.doi.org/10.1103/physrevlett.83.1042.

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2

Vasconcelos, Giovani L. "Generalization of the Schwarz–Christoffel mapping to multiply connected polygonal domains." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470, no. 2166 (June 8, 2014): 20130848. http://dx.doi.org/10.1098/rspa.2013.0848.

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A generalization of the Schwarz–Christoffel mapping to multiply connected polygonal domains is obtained by making a combined use of two preimage domains, namely, a rectilinear slit domain and a bounded circular domain. The conformal mapping from the circular domain to the polygonal region is written as an indefinite integral whose integrand consists of a product of powers of the Schottky-Klein prime functions, which is the same irrespective of the preimage slit domain, and a prefactor function that depends on the choice of the rectilinear slit domain. A detailed derivation of the mapping formula is given for the case where the preimage slit domain is the upper half-plane with radial slits. Representation formulae for other canonical slit domains are also obtained but they are more cumbersome in that the prefactor function contains arbitrary parameters in the interior of the circular domain.

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3

Shur, V. Ya, M. S. Kosobokov, A. V. Makaev, and D. K. Kuznetsov. "Light-induced ordering of nanodomains in lithium tantalate as a result of multiple scanning by IR laser irradiation." Journal of Applied Physics 133, no. 1 (January 7, 2023): 014105. http://dx.doi.org/10.1063/5.0128980.

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The ordering of a light-induced structure of isolated circular ferroelectric nanodomains was discovered in lithium tantalate crystals under multiple scanning by infrared laser irradiation. The effect was considered as domain arising and growth under the action of alternating in sign pyroelectric field arising during sample heating and subsequent cooling. The circular domains appeared due to 1D to 2D shape transformation after the second scan and grew during subsequent scanning by merging with arising domains accompanied by shape restoration. The ordering of the domain pattern during multiple scanning characterized by an increase in the peak of the autocorrelation function was attributed to domain interaction. This mechanism was confirmed by computer simulation using the kinetic approach based on the analogy between the growth of domains and crystals. It was demonstrated that the quasi-regular pattern of one-size circular domains could be created by scanning with shift. The discovered domain ordering effect is similar to that in magnetic materials.

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4

Bird, M. D., and C. R. Steele. "Separated Solution Procedure for Bending of Circular Plates With Circular Holes." Applied Mechanics Reviews 44, no. 11S (November 1, 1991): S27—S35. http://dx.doi.org/10.1115/1.3121366.

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A separated solution procedure is presented for the two-dimensional bi-harmonic equation on circular domains with circular holes and arbitrary boundary conditions. The solutions use the traditional trigonometric Fourier series on the boundaries with a power series decay into the domain. The interaction of the boundaries is expressed simply and exactly resulting in quick processing time. The only simplification made is the use of a finite number of terms in the boundary conditions.

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5

Parihar, Manoj S., Ananjan Basu, and Shiban K. Koul. "Transient analysis of reconfigurable polarization antenna." International Journal of Microwave and Wireless Technologies 5, no. 4 (February 18, 2013): 521–27. http://dx.doi.org/10.1017/s175907871300007x.

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Time-domain characterization of a microstrip patch antenna with circular corner truncation to achieve polarization reconfigurability is presented. By applying zero bias, forward bias, and reverse bias to the four PIN diodes, the antenna can radiate with linear polarization (LP), right hand circular polarization (RHCP), and left hand circular polarization (LHCP). The circular cuts reduce centre-frequency shift from linear to circularly polarized states, compared with conventional straight cuts. Time-domain simulation and measurement are carried out to show the switching characteristics of the proposed antenna, and it is established that satisfactory switching speed can be obtained using a simple low-cost driver circuit.

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6

DeLillo, T. K., T. A. Driscoll, A. R. Elcrat, and J. A. Pfaltzgraff. "Radial and circular slit maps of unbounded multiply connected circle domains." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 464, no. 2095 (March 18, 2008): 1719–37. http://dx.doi.org/10.1098/rspa.2008.0006.

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Infinite product formulae for conformally mapping an unbounded multiply connected circle domain to an unbounded canonical radial or circular slit domain, or to domains with both radial and circular slit boundary components are derived and implemented numerically and graphically. The formulae are generated by analytic continuation with the reflection principle. Convergence of the infinite products is proved for domains with sufficiently well-separated boundary components. Some recent progress in the numerical implementation of infinite product mapping formulae is presented.

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7

Crowdy, Darren. "The Schwarz–Christoffel mapping to bounded multiply connected polygonal domains." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 461, no. 2061 (June 23, 2005): 2653–78. http://dx.doi.org/10.1098/rspa.2005.1480.

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A formula for the generalized Schwarz–Christoffel mapping from a bounded multiply connected circular domain to a bounded multiply connected polygonal domain is derived. The theory of classical Schottky groups is employed. The formula for the derivative of the mapping function contains a product of powers of Schottky–Klein prime functions associated with a Schottky group relevant to the circular pre-image domain. The formula generalizes, in a natural way, the known mapping formulae for simply and doubly connected polygonal domains.

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8

Groemer, H. "Stability Theorems for Convex Domains of Constant Width." Canadian Mathematical Bulletin 31, no. 3 (September 1, 1988): 328–37. http://dx.doi.org/10.4153/cmb-1988-048-3.

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AbstractIt is known that among all plane convex domains of given constant width Reuleaux triangles have minimal and circular discs have maximal area. Some estimates are given concerning the following associated stability problem: If K is a convex domain of constant width w and if the area of K differs at most ∊ from the area of a Reuleaux triangle or a circular disc of width w, how close (in terms of the Hausdorff distance) is K to a Reuleaux triangle or a circular disc? Another result concerns the deviation of a convex domain M of diameter d from a convex domain of constant width if the perimeter of M is close to πd.

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9

Luca, Elena, and Darren G. Crowdy. "A transform method for the biharmonic equation in multiply connected circular domains." IMA Journal of Applied Mathematics 83, no. 6 (July 6, 2018): 942–76. http://dx.doi.org/10.1093/imamat/hxy030.

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Abstract A new transform approach for solving mixed boundary value problems for the biharmonic equation in simply and multiply connected circular domains is presented. This work is a sequel to Crowdy (2015, IMA J. Appl. Math., 80, 1902–1931) where new transform techniques were developed for boundary value problems for Laplace’s equation in circular domains. A circular domain is defined to be a domain, which can be simply or multiply connected, having boundaries that are a union of circular arc segments. The method provides a flexible approach to finding quasi-analytical solutions to a wide range of problems in fluid dynamics and plane elasticity. Three example problems involving slow viscous flows are solved in detail to illustrate how to apply the method; these concern flow towards a semicircular ridge, a translating and rotating cylinder near a wall as well as in a channel geometry.

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10

Li, Ai-jun, Yong Liu, and Zuo-rui Lyu. "Analysis of water wave interaction with a submerged quarter-circular breakwater using multipole method." Proceedings of the Institution of Mechanical Engineers, Part M: Journal of Engineering for the Maritime Environment 234, no. 4 (March 24, 2020): 846–60. http://dx.doi.org/10.1177/1475090220910594.

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This article studies water wave interaction with a submerged quarter-circular breakwater based on potential theory and multipole expansion method. The obliquely and normally incident waves are independently considered. The series solution of velocity potential in the external fluid domain is expressed through the multipole expansions, while the series solution of velocity potential in the quarter-circular internal fluid domain is obtained through the separation of variables. Then, the unknown coefficients in the series solutions are determined by matching the boundary conditions between external and internal fluid domains. The calculation methods for the reflection and transmission coefficients of the submerged quarter-circular breakwater as well as the horizontal and vertical wave forces on the breakwater are presented. The wave forces acting on the submerged breakwater with a seaside quarter-circular-arc and that with a leeside quarter-circular-arc are compared. The hydrodynamic quantities of the submerged quarter-circular breakwater are also compared with those of the submerged semi-circular breakwater. In addition, the effects of breakwater radius, incident frequency, and incident angle on the hydrodynamic quantities of the quarter-circular breakwater are clarified. Valuable results for practical engineering application are drawn.

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11

Wang, Zhengpeng, Peter S. Hall, James R. Kelly, and Peter Gardner. "Wideband Frequency-Domain and Space-Domain Pattern Reconfigurable Circular Antenna Array." IEEE Transactions on Antennas and Propagation 65, no. 10 (October 2017): 5179–89. http://dx.doi.org/10.1109/tap.2017.2740969.

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12

Kuryliak, Andriy, and Oleh Skaskiv. "Wiman’s Type Inequality in Multiple-Circular Domain." Axioms 10, no. 4 (December 17, 2021): 348. http://dx.doi.org/10.3390/axioms10040348.

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In the paper we prove for the first time an analogue of the Wiman inequality in the class of analytic functions f∈A0p(G) in an arbitrary complete Reinhard domain G⊂Cp, p∈N represented by the power series of the form f(z)=f(z1,⋯,zp)=∑‖n‖=0+∞anzn with the domain of convergence G. We have proven the following statement: If f∈Ap(G) and h∈Hp, then for a given ε=(ε1,…,εp)∈R+p and arbitrary δ>0 there exists a set E⊂|G| such that ∫E∩Δεh(r)dr1⋯drpr1⋯rp<+∞ and for all r∈Δε∖E we have Mf(r)≤μf(r)(h(r))p+12lnp2+δh(r)lnp2+δ{μf(r)h(r)}∏j=1p(lnerjεj)p−12+δ. Note, that this assertion at p=1,G=C,h(r)≡const implies the classical Wiman–Valiron theorem for entire functions and at p=1, the G=D:={z∈C:|z|<1},h(r)≡1/(1−r) theorem about the Kővari-type inequality for analytic functions in the unit disc D; p>1 implies some Wiman’s type inequalities for analytic functions of several variables in Cn×Dk, n,k∈Z+,n+k∈N.

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13

Kazakova, O., M. Hanson, A. M. Blixt, and B. Hjörvarsson. "Domain structure of circular and ring magnets." Journal of Magnetism and Magnetic Materials 258-259 (March 2003): 348–51. http://dx.doi.org/10.1016/s0304-8853(02)01057-0.

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14

Kuznetsov, V. O. "Polarization and Circular Truncation of a Domain." Journal of Mathematical Sciences 217, no. 1 (July 7, 2016): 108–13. http://dx.doi.org/10.1007/s10958-016-2959-y.

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15

ALEXANDER, JAMES C., ANDREW J. BERNOFF, ELIZABETH K. MANN, J. ADIN MANN, JACOB R. WINTERSMITH, and LU ZOU. "Domain relaxation in Langmuir films." Journal of Fluid Mechanics 571 (January 4, 2007): 191–219. http://dx.doi.org/10.1017/s0022112006003326.

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We report on theoretical studies of molecularly thin Langmuir films on the surface of a quiescent subfluid and qualitatively compare the results to both new and previous experiments. The film covers the entire fluid surface, but domains of different phases are observed. In the absence of external forcing, the compact domains tend to relax to circles, driven by a line tension at the phase boundaries. When stretched (by a transient applied stagnation-point flow or by stirring), a compact domain elongates, creating a bola consisting of two roughly circular reservoirs connected by a thin tether. This shape will then relax slowly to the minimum-energy configuration of a circular domain. The tether is never observed to rupture, even when it is more than a hundred times as long as it is wide. We model these experiments by taking previous descriptions of the full hydrodynamics, identifying the dominant effects via dimensional analysis, and reducing the system to a more tractable form. The result is a free boundary problem for an inviscid Langmuir film whose motion is driven by the line tension of the domain and damped by the viscosity of the subfluid. Using this model we derive relaxation rates for perturbations of a uniform strip and a circular patch. We also derive a boundary integral formulation which allows an efficient numerical solution of the problem. Numerically this model replicates the formation of a bola and the subsequent relaxation observed in the experiments. Finally, we suggest physical properties of the system (such as line tension) that can be deduced by comparison of the theory and numerical simulations to the experiment. Two movies are available with the online version of the paper.

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16

Kurakin, L. G., and I. V. Ostrovskaya. "On the Stability of the System of Thomson’s Vortex $n$-Gon and a Moving Circular Cylinder." Nelineinaya Dinamika 18, no. 5 (2022): 0. http://dx.doi.org/10.20537/nd221217.

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The linearization matrix and the quadratic part of the Hamiltonian of the problem are studied. As a result, the parameter space of the problem is divided into the instability area and the area of linear stability where nonlinear analysis is required. In the case $n=2,3$ two domains of linear stability are found. In the case $n=4,5,6$ there is just one domain. In the case $n\geqslant 7$ the studied solution is unstable for any value of the problem parameters. The obtained results in the limiting case as $a\to\infty$ agree with the known results for the model of point vortices outside the circular domain.

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17

Neradovskaya, E. A., M. M. Neradovskiy, V. V. Fedorovyh, A. P. Turygin, V. Ya Shur, A. L. Kholkin, and I. L. Ivleva. "Polarization reversal by tip of scanning probe microscope in SBN." KnE Materials Science 1, no. 1 (October 12, 2016): 115. http://dx.doi.org/10.18502/kms.v1i1.572.

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<p>We present the results of experimental study of the influence of initial domain state on the shape and size of isolated domains created by the conductive tip of scanning probe microscope during local polarization reversal in relaxor ferroelectric strontium barium niobate doped with nickel and cerium. The domain radius was found to increase with increasing voltage and time and depend on the initial polarization direction. Circular domains of the opposite sign were found to appear due to polarization backswitching. The obtained results can be used for practical applications of domain and domain wall engineering in ferroelectrics.</p>

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18

Qi, Hui, Jing Guo, and Jie Yang. "The Ground Motion of Isosceles Triangular Hill in Right-Angle Plane Impacted by SH-Wave." Applied Mechanics and Materials 121-126 (October 2011): 2363–66. http://dx.doi.org/10.4028/www.scientific.net/amm.121-126.2363.

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The analytical solution to the problem of the scattering of SH-wave by isosceles triangular hill in right-angle plane is given by using the methods of complex function and multiple coordinate. Firstly, the solution region is divided into two domains, where domain I involves isosceles triangular hill and a semi-circular bottom, domain II involves a semi-circular hollow in right-angle plane. And a standing wave function is constructed which satisfies the zero-stress conditions at the triangular wedges. In domain II, the scattering wave functions which satisfy the stress free boundary conditions at the free surfaces for the right-angle plane are constructed. Secondly, based on the conditions of the displacement continuity and stress continuity at the “common border” in the domains, a series of infinite algebraic equations are given and solved by truncation. Finally, some examples for amplitude of displacement on the surface are given. Numerical results show that amplitude of displacement on the surface is influenced by isosceles triangular hill.

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19

Sakajo, Takashi. "Equation of motion for point vortices in multiply connected circular domains." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465, no. 2108 (June 10, 2009): 2589–611. http://dx.doi.org/10.1098/rspa.2009.0070.

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The paper gives the equation of motion for N point vortices in a bounded planar multiply connected domain inside the unit circle that contains many circular obstacles, called the circular domain. The velocity field induced by the point vortices is described in terms of the Schottky–Klein prime function associated with the circular domain. The explicit representation of the equation enables us not only to solve the Euler equations through the point-vortex approximation numerically, but also to investigate the interactions between localized vortex structures in the circular domain. As an application of the equation, we consider the motion of two point vortices with unit strength and of opposite signs. When the multiply connected domain is symmetric with respect to the real axis, the motion of the two point vortices is reduced to that of a single point vortex in a multiply connected semicircle, which we investigate in detail.

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20

ALIASKARISOHI, S., P. TIERNO, P. DHAR, Z. KHATTARI, M. BLASZCZYNSKI, and TH M. FISCHER. "On the diffusion of circular domains on a spherical vesicle." Journal of Fluid Mechanics 654 (May 11, 2010): 417–51. http://dx.doi.org/10.1017/s0022112010000650.

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Tracking the motion of lipid domains on a vesicle is a rheological technique allowing the measurement of surface shear viscosities of vesicular lipid phases. The ratio of surface to bulk viscosity defines a viscous length scale. Hydrodynamic interactions split the motion of the domains into different modes of diffusion. The measurability of surface shear viscosities from any mode of diffusion is limited to viscous length scales between the radius of the domains and the radius of the vesicle. The measurability of the surface shear viscosity results from the sensitivity of the diffusion to surface shear viscosities and from sufficient spatial resolution to resolve the diffusive motion. Switching between the various modes of diffusion is a trade between sensitivity gained and resolution lost by the hydrodynamic interactions leaving the measurability unchanged. Measurability drops with the number of domains making single-domain rheology the best technique to measure surface shear viscosities. Ultimately confinement of the domains to small vesicles renders measurements of surface rheological properties with domain-tracking rheology impossible. Experiments on domains in vesicles of a mixture of dioleoylphosphatidylcholine (DOPC), dipalmytoylphosphatidylcholin (DPPC) and cholesterol (Chol) exhibit diffusion that is entirely controlled by dissipation into the water. The diffusion is suppressed compared to the diffusion of isolated domains in a flat membrane due to confinement to the curved vesicle and by hydrodynamic interactions between the domains. Effects of surface shear viscosity can be neglected.

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21

Goto, S., and S. Hayashi. "Proximal to distal cell communication in the Drosophila leg provides a basis for an intercalary mechanism of limb patterning." Development 126, no. 15 (August 1, 1999): 3407–13. http://dx.doi.org/10.1242/dev.126.15.3407.

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Proximodistal patterning in the Drosophila leg is elaborated from the circular arrangement of the proximal domain expressing escargot and homothorax, and the distal domain expressing Distal-less that are allocated during embryogenesis. The distal domain differentiates multiply segmented distal appendages by activating additional genes such as dachshund. Secreted signaling molecules Wingless and Decapentaplegic, expressed along the anterior-posterior compartment boundary, are required for activation of Distal-less and dachshund and repression of homothorax in the distal domain. However, whether Wingless and Decapentaplegic are sufficient for the circular pattern of gene expression is not known. Here we show that a proximal gene escargot and its activator homothorax regulate proximodistal patterning in the distal domain. Clones of cells expressing escargot or homothorax placed in the distal domain induce intercalary expression of dachshund in surrounding cells and reorient planar cell polarity of those cells. Escargot and homothorax-expressing cells also sort out from other cells in the distal domain. We suggest that inductive cell communication between the proximodistal domains, which is maintained in part by a cell-sorting mechanism, is the cellular basis for an intercalary mechanism of the proximodistal axis patterning of the limb.

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22

Green, Christopher C., and Giovani L. Vasconcelos. "Multiple steadily translating bubbles in a Hele-Shaw channel." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470, no. 2163 (March 8, 2014): 20130698. http://dx.doi.org/10.1098/rspa.2013.0698.

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Analytical solutions are constructed for an assembly of any finite number of bubbles in steady motion in a Hele-Shaw channel. The solutions are given in the form of a conformal mapping from a bounded multiply connected circular domain to the flow region exterior to the bubbles. The mapping is written as the sum of two analytic functions—corresponding to the complex potentials in the laboratory and co-moving frames—that map the circular domain onto respective degenerate polygonal domains. These functions are obtained using the generalized Schwarz–Christoffel formula for multiply connected domains in terms of the Schottky–Klein prime function. Our solutions are very general in that no symmetry assumption concerning the geometrical disposition of the bubbles is made. Several examples for various bubble configurations are discussed.

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23

Kotani, Yoshinori, Yasunori Senba, Kentaro Toyoki, David Billington, Hiroyuki Okazaki, Akira Yasui, Wakana Ueno, et al. "Realization of a scanning soft X-ray microscope for magnetic imaging under high magnetic fields." Journal of Synchrotron Radiation 25, no. 5 (August 2, 2018): 1444–49. http://dx.doi.org/10.1107/s1600577518009177.

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For the purpose of imaging element- and shell-specific magnetic distributions under high magnetic fields, a scanning soft X-ray microscope has been developed at beamline BL25SU, SPring-8, Japan. The scanning X-ray microscope utilizes total electron yield detection of absorbed circularly polarized soft X-rays in order to observe magnetic domains through the X-ray magnetic circular dichroism effect. Crucially, this system is equipped with an 8 T superconducting magnet. The performance and features of the present system are demonstrated by magnetic domain observations of the fractured surface of a Nd14.0Fe79.7Cu0.1B6.2sintered magnet.

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24

Coupet, Bernard, Yifei Pan, and Alexandre Sukhov. "On proper holomorphic mappings from domains with T-action." Nagoya Mathematical Journal 154 (1999): 57–72. http://dx.doi.org/10.1017/s0027763000025307.

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AbstractWe describe the branch locus of a proper holomorphic mapping between two smoothly bounded pseudoconvex domains of finite type in under the assumption that the first domain admits a transversal holomorphic action of the unit circle. As an application we show that any proper holomorphic self-mapping of a smoothly bounded pseudoconvex complete circular domain of finite type in is biholomorphic.

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25

Kim, Chang-Su, and Sang-Uk Lee. "Fractal Coding of Video Sequence by Circular Prediction Mapping." Fractals 05, supp01 (April 1997): 75–88. http://dx.doi.org/10.1142/s0218348x97000656.

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We propose a novel algorithm for fractal video sequence coding, based on the Circular Prediction Mapping (CPM), in which each range block is approximated by a domain block in the circularly previous frame. In our approach, the size of the domain block is set to be same as that of the range block for exploiting the high temporal correlation between the adjacent frames, while most other fractal coders use the domain block larger than the range block. Therefore the domain-range mapping in the CPM becomes similar to the block matching algorithm in the motion compensation techniques, and the advantages from this similarity are discussed. Also the modified collage theorem, which yields better prediction method for the CPM than the conventional collage theorem, is provided by linear systematic analysis. The computer simulation results on real video-conferencing image sequences demonstrate that the average compression ratios ranging from 60 to 70 can be obtained with good subjective quality.

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26

LI Jia, 李佳, 盛业华 SHENG Ye-hua, 张卡 ZHANG Ka, and 段平 DUAN Ping. "Image matching of variable circular domain compass features." Optics and Precision Engineering 22, no. 5 (2014): 1339–46. http://dx.doi.org/10.3788/ope.20142205.1339.

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27

Hong, Dae-Ki, Cheol-Hee Park, Min-Chul Ju, Kyu-Jung Youn, Sun-Do Jun, and Jin-Woong Cho. "SNR estimation in frequency domain using circular correlation." Electronics Letters 38, no. 25 (2002): 1693. http://dx.doi.org/10.1049/el:20021178.

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28

May, A., P. A. Firby, and A. P. Bassom. "Diffusion driven instability in an inhomogeneous circular domain." Mathematical and Computer Modelling 29, no. 4 (February 1999): 53–66. http://dx.doi.org/10.1016/s0895-7177(99)00039-4.

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29

Murzin, Alexey G. "Probable circular permutation in the flavin-binding domain." Nature Structural Biology 5, no. 2 (February 1998): 101. http://dx.doi.org/10.1038/nsb0298-101.

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30

Sarode, Tanuja, Devishree Pillai, Shalmalee Pokale, and Tejashri Prabhu. "Image Encryption in Transform Domain using Circular Shift." International Journal of Computer Applications 140, no. 11 (April 15, 2016): 19–23. http://dx.doi.org/10.5120/ijca2016909493.

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31

Gander, Martin J., and Yingxiang Xu. "Optimized Schwarz methods with nonoverlapping circular domain decomposition." Mathematics of Computation 86, no. 304 (May 17, 2016): 637–60. http://dx.doi.org/10.1090/mcom/3127.

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32

Berre, M. Le, D. Leduc, E. Ressayre, and A. Tallet. "Striped and circular domain walls in the DOPO." Journal of Optics B: Quantum and Semiclassical Optics 1, no. 1 (January 1, 1999): 153–60. http://dx.doi.org/10.1088/1464-4266/1/1/027.

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33

Yin, Yuan, Yangsen Li, Ruizong Lin, Zhiwei Liu, Benzhao Fu, Guo Huang, and Hongjie Zhang. "Study on effect of boundary conditions on simulation of wind flow in mountainous area." Journal of Physics: Conference Series 2280, no. 1 (June 1, 2022): 012018. http://dx.doi.org/10.1088/1742-6596/2280/1/012018.

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Abstract The simulation analysis of wind flow in mountainous area can assist the design of the transmission line. The conventional square computational domain is not conducive for the condition of different wind directions. In this paper, a circular computational domain is proposed for the solution of wind flow in mountainous area in the condition of different wind directions. A square computational domain and a circular one are used to solve the wind flow around the standard hill model. The simulation accuracy of the circular computational domain is verified by the wind profiles at the windward slope, the top of the slope and the leeward slope.

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34

Crowdy, Darren, and Jonathan Marshall. "Analytical formulae for the Kirchhoff–Routh path function in multiply connected domains." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 461, no. 2060 (June 23, 2005): 2477–501. http://dx.doi.org/10.1098/rspa.2005.1492.

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Explicit formulae for the Kirchhoff–Routh path functions (or Hamiltonians) governing the motion of N -point vortices in multiply connected domains are derived when all circulations around the holes in the domain are zero. The method uses the Schottky–Klein prime function to find representations of the hydrodynamic Green's function in multiply connected circular domains. The Green's function is then used to construct the associated Kirchhoff–Routh path function. The path function in more general multiply connected domains then follows from a transformation property of the path function under conformal mapping of the canonical circular domains. Illustrative examples are presented for the case of single vortex motion in multiply connected domains.

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35

Rojas, David, and Pedro J. Torres. "Bifurcation of relative equilibria generated by a circular vortex path in a circular domain." Discrete & Continuous Dynamical Systems - B 25, no. 2 (2020): 749–60. http://dx.doi.org/10.3934/dcdsb.2019265.

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36

El mokhtari, Karim, Serge Reboul, Georges Stienne, Jean Bernard Choquel, Benaissa Amami, and Mohammed Benjelloun. "An IMM Filter Defined in the Linear-Circular Domain, Application to Maneuver Detection with Heading Only." Mathematical Problems in Engineering 2018 (November 6, 2018): 1–14. http://dx.doi.org/10.1155/2018/3531075.

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In this article, we propose a multimodel filter for circular data. The so-called Circular Interacting Multimodel filter is derived in a Bayesian framework with the circular normal von Mises distribution. The aim of the proposed filter is to obtain the same performance in the circular domain as the classical IMM filter in the linear domain. In our approach, the mixing and fusion stages of the Circular Interacting Multimodel filter are, respectively, defined from the a priori and from the a posteriori circular distributions of the state angle knowing the measurements and according to a set of models. We propose in this article a set of circular models that will be used in order to detect the vehicle maneuvers from heading measurements. The Circular Interacting Multimodel filter performances are assessed on synthetic data and we show on real data a vehicle maneuver detection application.

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37

Baddoo, Peter J., and Darren G. Crowdy. "Periodic Schwarz–Christoffel mappings with multiple boundaries per period." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 475, no. 2228 (August 2019): 20190225. http://dx.doi.org/10.1098/rspa.2019.0225.

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We present an extension to the theory of Schwarz–Christoffel (S–C) mappings by permitting the target domain to be a single period window of a periodic configuration having multiple polygonal (straight-line) boundaries per period. Taking the arrangements to be periodic in the x -direction in an ( x , y )-plane, three cases are considered; these differ in whether the period window extends off to infinity as y → ± ∞, or extends off to infinity in only one direction ( y → + ∞ or y → − ∞), or is bounded. The preimage domain is taken to be a multiply connected circular domain. The new S–C mapping formulae are shown to be expressible in terms of the Schottky–Klein prime function associated with the circular preimage domains. As usual for an S–C map, the formulae are explicit but depend on a finite set of accessory parameters. The solution of this parameter problem is discussed in detail, and illustrative examples are presented to highlight the essentially constructive nature of the results.

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38

Gozdek, Agnieszka, Anna Stankiewicz-Drogoń, Jarosław Poznański, and Anna M. Boguszewska-Chachulska. "Circular dichroism analysis for multidomain proteins: studies of the irreversible unfolding of Hepatitis C virus helicase." Acta Biochimica Polonica 55, no. 1 (January 23, 2008): 57–66. http://dx.doi.org/10.18388/abp.2008_3201.

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The non-structural protein 3 (NS3) of Hepatitis C virus (HCV) is a bifunctional enzyme with RNA-dependent NTPase/RNA helicase and serine protease activities, and thus represents a promising target for anti-HCV therapy. These functions are performed by two distinct moieties; the N-terminal protease domain and the C-terminal helicase domain that further folds into three structural subdomains. To obtain lower molecular mass proteins suitable for nuclear magnetic resonance studies of helicase-inhibitor complexes, helicase domains 1, 2, and 1+2 devoid of a hydrophobic beta-loop were overexpressed and purified. Circular dichroism studies were carried out to confirm the secondary structure content and to determine thermodynamic parameters describing the stability of the proteins. Both thermal and GuHCl-induced unfolding experiments confirmed the multidomain organization of the helicase. The unfolding transition observed for domain 1+2 was in agreement with the model of two well-resolved successive steps corresponding to the independent unfolding of domains 1 and 2, respectively. In the case of the full-length helicase, the presence of domain 3 remarkably changed the transition profile, leading to fast and irreversible transformation of partially unfolded protein.

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39

Dmytryshyn, R. I. "On some of convergence domains of multidimensional S-fractions with independent variables." Carpathian Mathematical Publications 11, no. 1 (June 30, 2019): 54–58. http://dx.doi.org/10.15330/cmp.11.1.54-58.

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The convergence of multidimensional S-fractions with independent variables is investigated using the multidimensional generalization of the classical Worpitzky's criterion of convergence, the criterion of convergence of the branched continued fractions with independent variables, whose partial quotients are of the form $\frac{q_{i(k)}^{i_k}q_{i(k-1)}^{i_k-1}(1-q_{i(k-1)})z_{i(k)}}{1}$, and the convergence continuation theorem to extend the convergence, already known for a small domain (open connected set), to a larger domain. It is shown that the union of the intersections of the parabolic and circular domains is the domain of convergence of the multidimensional S-fraction with independent variables, and that the union of parabolic domains is the domain of convergence of the branched continued fraction with independent variables, reciprocal to it.

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40

Endo, Yasushi, Yusuke Niimi, Ryoichi Nakatani, Yoshio Kawamura, and Masahiko Yamamoto. "Magnetic Properties of Various Thick Co-Fe Circular Dot Arrays." Solid State Phenomena 124-126 (June 2007): 879–82. http://dx.doi.org/10.4028/www.scientific.net/ssp.124-126.879.

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We have studied the magnetic properties of Co-Fe circular dot arrays with various thicknesses and diameters in order to determine the optimum thickness and diameter of these dot arrays with a single-domain state for the transmission of spin information. For the thickness of 10 nm, the magnetic state changes from a multi-domain state to a closure-domain state and further to a single-domain state with decreasing diameter. On the other hand, for the thickness of 30 nm and 50 nm, all magnetic states are in a vortex state, regardless of the diameter. From these results, it is found that the optimum thickness and diameter of Co-Fe circular dots with a single-domain state are, respectively, 10 nm and less than 100 nm.

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41

Viator, Robert, and Braxton Osting. "Steklov eigenvalues of reflection-symmetric nearly circular planar domains." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474, no. 2220 (December 2018): 20180072. http://dx.doi.org/10.1098/rspa.2018.0072.

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We consider Steklov eigenvalues of reflection-symmetric, nearly circular, planar domains. Treating such domains as perturbations of the disc, we obtain a second-order formal asymptotic estimate in the domain perturbation parameter. We conclude with a discussion of implications for isoperimetric inequalities. Namely, our results corroborate the results of Weinstock and Brock that state, respectively, that the disc is the maximizer for the area and perimeter constrained problems. They also support the result of Hersch, Payne and Schiffer that the product of the first two eigenvalues is maximal among all open planar sets of equal perimeter. In addition, our results imply that the disc is not the maximizer of the area constrained problems for higher even numbered Steklov eigenvalues, as suggested by previous numerical results.

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42

K, Santhi, and Anil Kumar M N. "Biometrics based Steganography using Circular Folding in DWT Domain." International Journal of Computer Applications 61, no. 10 (January 18, 2013): 47–51. http://dx.doi.org/10.5120/9968-4624.

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43

Aiyappan, S., Editha C. Jose, Ivy Carol B. Lomerio, and A. K. Nandakumaran. "Control problem on a rough circular domain and homogenization." Asymptotic Analysis 115, no. 1-2 (October 3, 2019): 19–46. http://dx.doi.org/10.3233/asy-191526.

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44

Gander, Martin J., and Yingxiang Xu. "Optimized Schwarz Methods for Circular Domain Decompositions with Overlap." SIAM Journal on Numerical Analysis 52, no. 4 (January 2014): 1981–2004. http://dx.doi.org/10.1137/130946125.

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45

Yan, Shefeng. "Robust Time-Domain Broadband Modal Beamforming for Circular Arrays." IEEE Transactions on Aerospace and Electronic Systems 56, no. 3 (June 2020): 1783–94. http://dx.doi.org/10.1109/taes.2019.2935598.

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46

Panda, G., A. Alvarez, P. Grant, and C. Cowan. "A transform domain circular convolution algorithm for adaptive filtering." IEEE Transactions on Acoustics, Speech, and Signal Processing 35, no. 8 (August 1987): 1217–20. http://dx.doi.org/10.1109/tassp.1987.1165264.

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47

Buchris, Yaakov, Israel Cohen, and Jacob Benesty. "Frequency-Domain Design of Asymmetric Circular Differential Microphone Arrays." IEEE/ACM Transactions on Audio, Speech, and Language Processing 26, no. 4 (April 2018): 760–73. http://dx.doi.org/10.1109/taslp.2018.2796844.

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48

Hoffmann, H., and F. Steinbauer. "Single domain and vortex state in ferromagnetic circular nanodots." Journal of Applied Physics 92, no. 9 (November 2002): 5463–67. http://dx.doi.org/10.1063/1.1510559.

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49

Guan, Shuguang, C. H. Lai, and G. W. Wei. "Fourier–Bessel analysis of patterns in a circular domain." Physica D: Nonlinear Phenomena 151, no. 2-4 (May 2001): 83–98. http://dx.doi.org/10.1016/s0167-2789(01)00223-8.

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50

Xie, Hongtu, Shaoying Shi, Junfa Mao, Daoxiang An, Fuhai Li, Zhimin Zhou, and Guoqian Wang. "Fast Time-domain Imaging Method for Bistatic Circular SAR." Journal of Physics: Conference Series 960 (January 2018): 012021. http://dx.doi.org/10.1088/1742-6596/960/1/012021.

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