Relevant bibliographies by topics / Bipolar coordinates

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Bipolar coordinates'

Author: Grafiati
Published: 4 June 2025
Last updated: 15 July 2025

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Journal articles on the topic "Bipolar coordinates"

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Nelson, David. "BIPOLAR COORDINATES AND PLOTTERS*." PRIMUS 4, no. 1 (1994): 77–83. http://dx.doi.org/10.1080/10511979408965735.

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Huang, Zhu, and John P. Boyd. "Chebyshev–Fourier spectral methods in bipolar coordinates." Journal of Computational Physics 295 (August 2015): 46–64. http://dx.doi.org/10.1016/j.jcp.2015.03.062.

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Li, Chenglong, Jinbei Wei, Jianxiong Han, et al. "Efficient deep-blue OLEDs based on phenanthro[9,10-d]imidazole-containing emitters with AIE and bipolar transporting properties." Journal of Materials Chemistry C 4, no. 42 (2016): 10120–29. http://dx.doi.org/10.1039/c6tc03923e.

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Yu, Hua, Ya-jing Meng, Xiao-jing Li, et al. "Common and distinct patterns of grey matter alterations in borderline personality disorder and bipolar disorder: voxel-based meta-analysis." British Journal of Psychiatry 215, no. 01 (2019): 395–403. http://dx.doi.org/10.1192/bjp.2019.44.

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BackgroundWhether borderline personality disorder (BPD) and bipolar disorder are the same or different disorders lacks consistency.AimsTo detect whether grey matter volume (GMV) and grey matter density (GMD) alterations show any similarities or differences between BPD and bipolar disorder.MethodWeb-based publication databases were searched to conduct a meta-analysis of all voxel-based studies that compared BPD or bipolar disorder with healthy controls. We included 13 BPD studies (395 patients with BPD and 415 healthy controls) and 47 bipolar disorder studies (2111 patients with bipolar disorder and 3261 healthy controls). Peak coordinates from clusters with significant group differences were extracted. Effect-size signed differential mapping meta-analysis was performed to analyse peak coordinates of clusters and thresholds (P< 0.005, uncorrected). Conjunction analyses identified regions in which disorders showed common patterns of volumetric alteration. Correlation analyses were also performed.ResultsPatients with BPD showed decreased GMV and GMD in the bilateral medial prefrontal cortex network (mPFC), bilateral amygdala and right parahippocampal gyrus; patients with bipolar disorder showed decreased GMV and GMD in the bilateral medial orbital frontal cortex (mOFC), right insula and right thalamus, and increased GMV and GMD in the right putamen. Multi-modal analysis indicated smaller volumes in both disorders in clusters in the right medial orbital frontal cortex. Decreased bilateral mPFC in BPD was partly mediated by patient age. Increased GMV and GMD of the right putamen was positively correlated with Young Mania Rating Scale scores in bipolar disorder.ConclusionsOur results show different patterns of GMV and GMD alteration and do not support the hypothesis that bipolar disorder and BPD are on the same affective spectrum.Declaration of interestNone.
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Rajamouli, Boddula, and Vaidyanthan Sivakumar. "Effect of carbazole functionalization with a spacer moiety in the phenanthroimidazole bipolar ligand in a europium(iii) complex on its luminescence properties: combined experimental and theoretical study." New Journal of Chemistry 41, no. 3 (2017): 1017–27. http://dx.doi.org/10.1039/c6nj03014a.

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A carbazole functionalized phenanthroimidazole based bipolar ligand consisting of a β-diketonate Eu(iii) complex shows efficient energy transfer and QE (11.5%) with appropriate CIE color coordinates (x = 0.66, y = 0.33).
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Rajamouli, B., C. S. Dwaraka Viswanath, S. Giri, C. K. Jayasankar, and V. Sivakumar. "Carbazole functionalized new bipolar ligand for monochromatic red light-emitting europium(iii) complex: combined experimental and theoretical study." New Journal of Chemistry 41, no. 8 (2017): 3112–23. http://dx.doi.org/10.1039/c6nj03947b.

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Complete energy transfer observed from carbazole functionalized bipolar ligand as well as β-diketonate to Eu(iii) ion and Eu(iii) complex shows efficient PLQE (41.4%) with appropriate CIE color coordinates (x = 0.64, y = 0.36).
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Chen, Huanyang, and C. T. Chan. "“Cloaking at a distance” from folded geometries in bipolar coordinates." Optics Letters 34, no. 17 (2009): 2649. http://dx.doi.org/10.1364/ol.34.002649.

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Khomasuridze, N. "Solution of some elasticity boundary value problems in bipolar coordinates." Acta Mechanica 189, no. 3-4 (2007): 207–24. http://dx.doi.org/10.1007/s00707-006-0388-6.

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Alaci, Stelian, Florina-Carmen Ciornei, and Ionut-Cristian Romanu. "Stress State in an Eccentric Elastic Ring Loaded Symmetrically by Concentrated Forces." Mathematics 10, no. 8 (2022): 1314. http://dx.doi.org/10.3390/math10081314.

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The stress state from an eccentric ring made of an elastic material symmetrically loaded on the outer boundary by concentrated forces is deduced. The analytical results are obtained using the Airy stress function expressed in bipolar coordinates. The elastic potential corresponding to the same loading but for a compact disk is first written in bipolar coordinates, then expanded in Fourier series, and after that, an auxiliary potential of a convenient form is added to it in order to impose boundary conditions. Since the inner boundary is unloaded, boundary conditions may be applied directly to the total potential. A special focus is on the number of terms from Fourier expansion of the potential in bipolar coordinates corresponding to the compact disk as this number influences the sudden increase if the coefficients from the final form of the total potential. Theoretical results are validated both by using finite element software and experimentally through the photoelastic method, for which a device for sample loading was designed and constructed. Isochromatic fields were considered for the photoelastic method. Six loading cases for two different geometries of the ring were studied. For all the analysed cases, an excellent agreement between the analytical, numerical and experimental results was achieved. Finally, for all the situations considered, the stress concentration effect of the inner hole was analytically determined. It should be mentioned that as the eccentricity of the inner hole decreases, the integrals from the relations of the total elastic potential present a diminishing convergence in the vicinity of the inner boundary.
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Alexanyan, R., L. Harutunyan, and A. Sedrakyan. "FLAT PROBLEM FOR OUTSIDE A CIRCULAR SEGMENT." Slovak international scientific journal, no. 80 (February 12, 2024): 34–37. https://doi.org/10.5281/zenodo.10651872.

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A plane problem of circular segment with mixed boundary condition is considered. On the border of thecircular segment normal and shear stresses given, and normal stress and shear displacement of the boundary aregiven on theother part. With the stress function and Fourier integrals in the bipolar system of coordinates theproblem solved is closed. A particular case is considered.
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Dissertations / Theses on the topic "Bipolar coordinates"

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Masa, Font Roser. "Efectivitat d’un programa d’activitat física i dieta coordinat entre Atenció Primària i Salut Mental, per a modificar els factors de risc cardiovascular en pacients amb esquizofrènia, trastorn bipolar o trastorn esquizoafectiu." Doctoral thesis, Universitat Autònoma de Barcelona, 2017. http://hdl.handle.net/10803/457519.

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Els pacients amb trastorn mental sever tenen una major prevalença de factors de risc cardiovascular i una menor esperança de vida. El control de l’obesitat i el sedentarisme en pot reduir la morbi-mortalitat. Per tant, són necessàries intervencions dirigides a la disminució de pes i/o a l’augment del nivell d’activitat física en aquesta població. Aquesta tesi recull els resultats principals de l’estudi CAPiCOR, assaig clínic aleatoritzat que avalua l’efectivitat d’una intervenció educativa centrada en la dieta i l’activitat física amb la finalitat de modificar estils de vida com la quantitat d’activitat física i l’hàbit dietètic i el seu efecte sobre el metabolisme en variables com l’índex de massa corporal i el perímetre de cintura. També es vol avaluar l’efectivitat en el canvi d‘altres factors de risc cardiovascular com la pressió arterial i paràmetres analítics (colesterol, triglicèrids,...) i el seu impacte sobre la qualitat de vida. Es van reclutar 332 pacients ambulatoris de 8 Centres de Salut Mental de Barcelona amb diagnòstic d’esquizofrènia, trastorn esquizoafectiu o trastorn bipolar en tractament amb medicació antipsicòtica, que van ser assignats aleatòriament al grup intervenció (n=169) o al grup control (n=163). Els pacients del grup intervenció van participar en un programa educatiu d’activitat física (centrat en caminar amb podòmetres) i dieta (coneixements bàsics sobre hàbits dietètics sans) amb dues sessions a la setmana durant 12 setmanes. Les variables van ser avaluades cegament als 0, 3, 6 i 12 mesos: nivell d’activitat física (qüestionari IPAQ), índex de massa corporal, perímetre de cintura, hàbit dietètic (qüestionari PREDIMED), pressió arterial, paràmetres de laboratori (colesterol, triglicèrids i glucosa) i qualitat de vida (SF-36). L’estudi CAPiCOR demostra que els pacients amb trastorn mental sever que van participar en el programa d’activitat física i dieta van augmentar de forma significativa el seu nivell d'activitat física setmanal als 3 mesos d'iniciar la intervenció. Aquesta millora però, deixà de ser significativa als 6 i als 12 mesos. A més, l'augment en la quantitat d’activitat física no es va traduir en cap moment en una millora en la resta de variables avaluades: paràmetres físics i analítics, hàbits dietètics o qualitat de vida. La manca de resultats favorables a nivell antropomètric i analític podria ser deguda a diversos factors, segons la literatura consultada. Calen intervencions de major intensitat i, sobretot, de major duració, així com un seguiment acurat al llarg del temps. S’ha de tenir en compte que els pacients inclosos en el nostre estudi tenien una mitjana d’aproximadament 15 anys des del moment del diagnòstic de la seva patologia mental, per la qual cosa els estils de vida poc saludables estan molt arrelats i són difícils de modificar amb una intervenció de 3 mesos de duració. Tot i així, cal destacar la importància de tractar-se d’un estudi multicèntric, amb una grandària mostral molt superior a la majoria d’estudis que trobem a la literatura i amb un elevat percentatge de seguiment a les visites de control. Aquest estudi aporta la base per a dissenyar noves intervencions amb les modificacions necessàries. De cara al futur s’haurien de plantejar intervencions des del moment del diagnòstic amb consells d’eficàcia provada i programes flexibles i atractius, amb seguiment a llarg termini, que incloguin modificacions del comportament per tal d’augmentar la participació i l’adherència dels pacients i aconseguir un canvi en els estils de vida i en el metabolisme d’aquesta població.<br>Patients with a severe mental disorder have a high prevalence of cardiovascular risk factors and a decreased life expectancy. Control of obesity and sedentary lifestyle can reduce the morbidity and mortality. Therefore, interventions aimed at decreasing the weight and / or increasing the level of physical activity in this population are necessary. This thesis includes the main results of the CAPiCOR study, a randomized clinical trial that evaluates the effectiveness of an educational intervention focused on diet and physical activity in order to modify lifestyles such as the amount of physical activity and The dietary habit and its effect on metabolism in variables such as the body mass index and the waist circumference. We also want to evaluate the effectiveness in the change of other cardiovascular risk factors such as blood pressure and analytical parameters (cholesterol, triglycerides…) and their impact on quality of life. 332 outpatient patients were recruited from 8 mental healthcare centers of Barcelona with a diagnosis of schizophrenia, schizoaffective disorder or bipolar disorder in treatment with an antipsychotic drug, randomized to the intervention group (n = 169) or the control group (n = 163). The patients in the intervention group participated in an educational program of physical activity (focused on walking with pedometers) and diet (basic knowledge about healthy dietary habits) with two sessions per week for 12 weeks. The variables were blindly evaluated at 0, 3, 6 and 12 months: level of physical activity (IPAQ questionnaire), body mass index, waist circumference, dietary habit (PREDIMED questionnaire), blood pressure, laboratory parameters (cholesterol, triglycerides and glucose) and quality of life (SF-36). The CAPiCOR study shows that patients with severe mental disorders who participated in the physical activity and diet program significantly increased their level of weekly physical activity after 3 months of initiating the intervention. This improvement, however, was no less significant at 6 and 12 months. In addition, the increase in the amount of physical activity did not translate at any moment in an improvement in the other evaluated variables: physical and analytical parameters, dietary habits or quality of life. The lack of favorable results at the anthropometric and analytical level could be due to several factors, according to the literature consulted. Interventions of greater intensity and, above all, longer, as well as careful monitoring over time, are needed. It has to be taken into account that the patients included in our study had an average of approximately 15 years from the moment of the diagnosis of their mental pathology, so unhealthy lifestyles are deeply rooted and are difficult to modify with an intervention of 3 months of duration. Even so, it is worth mentioning the importance of being a multicenter study, with a sample size much higher than most studies found in literature and with a high percentage of follow-up in the control visits. This study provides the basis for designing new interventions with the necessary modifications. In the face of the future, interventions should be considered from the moment of diagnosis with proven efficacy councils and flexible and attractive programs, with long-term follow-up, which include behavioral modifications in order to increase the participation and adherence of patients and achieve a change in the lifestyles and metabolism of this population.
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Machynia, Adam. "Application of translational addition theorems to electrostatic and magnetostatic field analysis for systems of circular cylinders." 2012. http://hdl.handle.net/1993/5291.

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Analytic solutions to the static and stationary boundary value field problems relative to an arbitrary configuration of parallel cylinders are obtained by using translational addition theorems for scalar Laplacian polar functions, to express the field due to one cylinder in terms of the polar coordinates of the other cylinders such that the boundary conditions can be imposed at all the cylinder surfaces. The constants of integration in the field expressions of all the cylinders are obtained from a truncated infinite matrix equation. Translational addition theorems are available for scalar cylindrical and spherical wave functions but such theorems are not directly available for the general solution of the Laplace equation in polar coordinates. The purpose of deriving these addition theorems and applying them to field problems involving systems of cylinders is to obtain exact analytic solutions with controllable accuracies, thereby, yielding benchmark solutions to validate other approximate numerical methods.
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Book chapters on the topic "Bipolar coordinates"

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Farouki, Rida T., and Hwan Pyo Moon. "Bipolar and Multipolar Coordinates." In The Mathematics of Surfaces IX. Springer London, 2000. http://dx.doi.org/10.1007/978-1-4471-0495-7_21.

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Mindlin, Raymond D. "Gravitational Stresses in Bipolar Coordinates." In The Collected Papers of Raymond D. Mindlin Volume I. Springer New York, 1989. http://dx.doi.org/10.1007/978-1-4613-8865-4_14.

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Clerc, Louis. "Defining Finland’s Cultural Diplomacy from Postwar to Cold War." In Palgrave Macmillan Series in Global Public Diplomacy. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-12205-7_2.

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AbstractCultural diplomacy, as a dimension of the state’s cultural and foreign policy, refers to specific actions planned, coordinated or organized by central public institutions, aiming to support the objectives of the state. But the objectives of any state’s policy are rarely an object of domestic consensus: they might be disputed in society, and different emphases might be found even inside the state’s organizational frame. An important starting point in our search for Finland’s cultural diplomacy is thus to find the various reasons for which Finnish administrators would engage in and develop a cultural diplomacy. Discussing these elements in the context of the Cold War, one has to consider both the weight of the bipolar divide on any policy undertaken by the Finnish state, as well as the local context. Arguments in favor of state-led cultural outreach overseas showed a certain consistency over the three decades studied here, with concerns expressed immediately after the war and continuing up to the 1970s. This continuity was also the result of continuities in personnel, with roughly the same individuals dealing with international cultural relations inside the Finnish civil service. They developed a number of rationales for cultural diplomacy, between supporting Finland’s foreign policy in a difficult geopolitical situation, modernizing Finnish society through curated foreign examples and an opening up to global cultural trends, promoting a new image of the country abroad, supporting trade or participating in the work of international organizations.
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Waleffe, Fabian. "Points, Lines, Planes, etc." In Vector and Complex Calculus. Oxford University PressOxford, 2025. http://dx.doi.org/10.1093/oso/9780198927839.003.0007.

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Abstract Introduces the position (or radius) vector. Discusses cartesian, cylindrical and spherical coordinates. Investigates vector equations of lines and planes and their intersection. Introduces some coordinate systems beyond those three basic systems, including bipolar coordinates.
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"Bipolar Coordinate RCWA Computational Examples and Case Studies." In Computational Methods for Electromagnetic and Optical Systems. CRC Press, 2016. http://dx.doi.org/10.1201/9781439891285-12.

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Gupta, Sudhiranjan, and Rakeshwar S. Guleria. "The Role of Brain-Derived Neurotrophic Factor in Psychiatric Disorders." In Old Protein New Medicine-Brain-Derived Neurotrophic Factor [Working Title]. IntechOpen, 2023. http://dx.doi.org/10.5772/intechopen.112567.

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Brain derived neurotrophic factor (BDNF) is one of the most extensively studied and widespread growth factors in the brain. BDNF and its receptors are the critical factors having multipotent impact on the central nervous system (CNS). The biological function of BDNF primarily mediated by two receptors, tropomyosin receptor kinase B (TrkB) receptor and p75 neurotrophin receptor. BDNF contributes a pivotal role in neuronal and glial development, modulation and maintaining overall synaptic plasticity of the brain; therefore, widely involved in psychiatric diseases. Current hypotheses indicates that abnormal BDNF level, a vital condition for psychiatric and neurodegeneration diseases are mainly due to the disruption of the BDNF-associated signaling cascades. It is, therefore, crucial to understand how BDNF coordinate the psychiatric diseases in the brain. This review begins with the history of BDNF and its biology in brain homeostasis and focuses on several aspects of BDNF signaling. In addition, the review addresses the impact of BDNF level in diverse neuropsychiatric disorders including major depressive disorder, schizophrenia, bipolar disorder, post-traumatic stress disorder and, possible biological mechanisms of BDNF that may shed new insight for future therapeutic use and drug development.
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Batista, Sharon M., and Joseph Z. Lux. "A Biopsychosocial Approach to Psychiatric Consultation in Persons with HIV and AIDS." In Handbook of AIDS Psychiatry. Oxford University Press, 2010. http://dx.doi.org/10.1093/oso/9780195372571.003.0006.

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For persons with HIV and AIDS, a thorough and comprehensive assessment has far-reaching implications not only for compassionate, competent, and coordinated care but also for adherence to medical treatment and risk reduction, as well as public health. Primary physicians, HIV specialists, as well as psychiatrists and other mental health professionals can play an important role in preventing the spread of HIV infection. Psychiatric disorders are associated with inadequate adherence to risk reduction, medical care, and antiretroviral therapy. While adherence to medical care for most medical illnesses has major meaning to patients, loved ones, and families, adherence to medical care for HIV and AIDS has major implications for reduction of HIV transmission and prevention of emergence of drug-resistant HIV viral strains (Cohen and Chao, 2008). Many persons with HIV and AIDS have psychiatric disorders (Stoff et al., 2004) and can benefit from psychiatric consultation and care. The rates of HIV infection are also higher among persons with serious mental illness (Blank et al., 2002), indicating a bidirectional relationship. Some persons with HIV and AIDS have no psychiatric disorder, while others have a multiplicity of complex psychiatric disorders that are responses to illness or treatments or are associated with HIV/AIDS (such as HIV-associated dementia) or multimorbid medical illnesses and treatments (such as hepatitis C, cirrhosis, end-stage liver disease, HIV nephropathy, end-stage renal disease, anemia, coronary artery disease, and cancer). Persons with HIV and AIDS may also have multimorbid psychiatric disorders that are co-occurring and may be unrelated to HIV (such as posttraumatic stress disorder, or PTSD, schizophrenia, and bipolar disorder). The complexity of AIDS psychiatric consultation is illustrated in an article (Freedman et al., 1994) with the title “Depression, HIV Dementia, Delirium, Posttraumatic Stress Disorder (or All of the Above).” Comprehensive psychiatric evaluations can provide diagnoses, inform treatment, and mitigate anguish, distress, depression, anxiety, and substance use in persons with HIV and AIDS. Furthermore, thorough and comprehensive assessment is crucial because HIV has an affinity for brain and neural tissue and can cause central nervous system (CNS) complications even in healthy seropositive individuals. Because of potential CNS complications as well as the multiplicity of other severe and complex medical illnesses in persons with HIV and AIDS (Huang et al., 2006), every person who is referred for a psychiatric consultation needs a full biopsychosocial evaluation.
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Conference papers on the topic "Bipolar coordinates"

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Zhang, Xuefei, Niancheng Zhou, Qianggang Wang, et al. "A Distributed Coordinated Control Strategy for Unbalanced Voltage Suppression in Bipolar DC Microgrids with Flexible ZIP Load." In 2024 International Conference on Smart Energy Systems and Technologies (SEST). IEEE, 2024. http://dx.doi.org/10.1109/sest61601.2024.10694140.

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Tamura, Poohsan N. "Optical 3-Dimensional Digital Data Acquisition Using Far-field Approximation." In Machine Vision. Optica Publishing Group, 1985. http://dx.doi.org/10.1364/mv.1985.wb3.

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Li, W., N. Fan, and C. Yang. "The Study for Algorithm of Linear Interpolation Based on Bipolar Coordinates." In 2010 International Conference on Intelligent Computation Technology and Automation (ICICTA). IEEE, 2010. http://dx.doi.org/10.1109/icicta.2010.165.

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Chae, You Seong, Seung Hyun Lee, Hyun Min Oh, and Min Young Kim. "Coordinates tracking and augmented reality system using bipolar X-ray fluoroscopy and stereo vision for image-guided neurosurgery." In 2013 13th International Conference on Control, Automaton and Systems (ICCAS). IEEE, 2013. http://dx.doi.org/10.1109/iccas.2013.6703872.

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Eatock Taylor, R. "Forces on Pairs of Closely Spaced Unequal Circular Cylinders in an External Flow." In ASME 2011 30th International Conference on Ocean, Offshore and Arctic Engineering. ASMEDC, 2011. http://dx.doi.org/10.1115/omae2011-49194.

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The paper examines how interference effects between a pair of closely spaced cylinders influence the fluid forces acting on them in a low Keulegan Carpenter number regime. The forces are characterised by inertia coefficients, and the analysis is based on potential flow theory using a mapping based on bipolar coordinates. The analysis corresponds to the long wave limit. The dependence of the force coefficients on cylinder spacing and radius ratio is illustrated by contour plots, which might be used as design charts to determine the fluid forces on arbitrary configurations of the two cylinders. Results are also given for some representative geometries indicating the effects of wave diffraction on closely spaced vertical cylinders.
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Chen, Zhanfeng, Xiaoli Shen, Hao Ye, Sunting Yan, and Zhijiang Jin. "Surface Stress Analysis of Internally Corroded Pipes Under External Pressure." In ASME 2017 Pressure Vessels and Piping Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/pvp2017-66163.

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Corrosion often leads to the failure of transporting pipelines. The surface stresses on the corroded pipes are related to the failure pressure. In this paper, a double circular arc (DCA) model is developed to calculate the surface stress of the internal corroded pipes under external pressure. In addition, a critical corrosion ratio and a critical thickness-to-diameter ratio are presented to determine the location of the maximum stress. Based on the stress function method and bipolar coordinates, an analytical solution of the DCA model was obtained. And then the stress distributions on the internal and external surfaces of the corroded pipes were determined. Next, the equivalent and hoop stresses at several locations in the cross section of the corroded pipes were discussed. The calculated results were validated using finite element method (FEM). Results show that the maximum stresses vary from the internal surface to the external surface with the increase of the corrosion ratio or the thickness-to-diameter ratio. Our research provides a benchmark for approximate solutions to predict the failure pressure and assess the integrity of the corroded pipelines.
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Stephens, Lyndon S., and Mark A. Casemore. "Negative Stiffness Coefficients for Magnetic Actuators Using Laplace’s Equation." In ASME 1999 International Gas Turbine and Aeroengine Congress and Exhibition. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/99-gt-179.

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Magnetic bearings offer high speed and low power losses as compared to film riding and rolling element bearings. Significant efforts are underway to apply magnetic bearings to gas turbines and jet aircraft engines. Negative stiffness coefficients for magnetic actuators can have a significant impact on shaft rotordynamics. These coefficients are typically computed as the sensitivity of a magnetic force expression derived from a lumped parameter reluctance network. However, as the complexity of magnetic actuator designs increases, the reluctance network method may become impractical for, or even incapable of, coefficient determination. In this paper, an alternative method is presented for determination of negative stiffness coefficients for a large class of magnetic actuators. The method solves the Dirichlet boundary value problem (BVP) for the magnetomotive force (MMF) in the actuator air gap, subject to periodic boundary conditions that can be represented by Fourier series. A conformal transformation to bipolar coordinates is used that results in a BVP that is solvable using separation of variables. Negative stiffness coefficients are presented and the method is benchmarked against well-known solutions using the reluctance network method.
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Matyas, Alpar, and Botond Nagy. "Numerical study of bipolar coordinate Jeffery-Hamel flow." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2016). Author(s), 2017. http://dx.doi.org/10.1063/1.4992760.

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Chen, GuangJin, Yue Wang, Qian Liang, LinZhen Fan, ZiHao Wu, and ChenXi Wang. "Coordinated Control Strategy for Power Imbalance in Bipolar MMC-HVDC." In 2024 IEEE 7th International Electrical and Energy Conference (CIEEC）. IEEE, 2024. http://dx.doi.org/10.1109/cieec60922.2024.10583617.

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Li, Xialin, Li Guo, Zhen Guo, et al. "Coordinated control of multiple voltage balancers in a Bipolar DC microgrid." In 2017 IEEE Power & Energy Society General Meeting (PESGM). IEEE, 2017. http://dx.doi.org/10.1109/pesgm.2017.8274113.

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