We make use of supersymmetric quantum mechanics (SUSY QM) to find three sets of conditions under which the problem of a planar quantum pendulum becomes analytically solvable. The analytic forms of the pendulum's eigenfuntions make it possible to find analytic expressions for observables of interest, such as the expectation values of the angular momentum squared and of the orientation and alignment cosines as well as of the eigenenergy. Furthermore, we find that the topology of the intersections of the pendulum's eigenenergy surfaces can be characterized by a single integer index whose values correspond to the sets of conditions under which the analytic solutions to the quantum pendulum problem exist.
{"title":"Supersymmetry and eigensurface topology of the planar quantum pendulum","authors":"B. Schmidt, B. Friedrich","doi":"10.3389/fphy.2014.00037","DOIUrl":"https://doi.org/10.3389/fphy.2014.00037","url":null,"abstract":"We make use of supersymmetric quantum mechanics (SUSY QM) to find three sets of conditions under which the problem of a planar quantum pendulum becomes analytically solvable. The analytic forms of the pendulum's eigenfuntions make it possible to find analytic expressions for observables of interest, such as the expectation values of the angular momentum squared and of the orientation and alignment cosines as well as of the eigenenergy. Furthermore, we find that the topology of the intersections of the pendulum's eigenenergy surfaces can be characterized by a single integer index whose values correspond to the sets of conditions under which the analytic solutions to the quantum pendulum problem exist.","PeriodicalId":49264,"journal":{"name":"Frontiers of Physics in China","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.3389/fphy.2014.00037","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69647210","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Equatorial spread-F ionospheric plasma irregularities on the night-side, commonly called equatorial plasma bubbles (EPB), include electron density variations over a wide range of spatial scales. Here we focus on intermediate-scale structures ranging from 100 m to 10 km, which play an important role in the evolution of EPBs. High-resolution CHAMP magnetic field measurements sampled along north-south track at 50 Hz are interpreted in terms of diamagnetic effect for illustrating the details of electron density variations. We provide the first comprehensive study on intermediate-scale density structures associated with EPBs, covering a whole solar cycle from 2000 to 2010. The large number of detected events, almost 9000, allows us to draw a detailed picture of the plasma fine structure. The occurrence of intermediate-scale events is strongly favoured by high solar flux. During times of F10.7 < 100 sfu practically no events were observed. The longitudinal distribution of our events with respect to season or local time agrees well with that of the EPBs, qualifying the fine structure as a common feature, but the occurrence rates are smaller by a factor of 4 during the period 2000-2005. Largest amplitude electron density variations appear at the poleward boundaries of plasma bubbles. Above the dip-equator recorded amplitudes are small and fall commonly below our resolution. Events can generally be found at local times between 19 and 24 LT, with a peak lasting from 20 to 22 LT. The signal spectrum can be approximated by a power law. Over the frequency range 1 – 25 Hz we observe spectral indices between -1.4 and -2.6 with peak occurrence rates around -1.9. There is a weak dependence observed of the spectral index on local time. Towards later hours the spectrum becomes shallower. Similarly for the latitude dependence, there is a preference of shallower spectra for latitudes poleward of the ionisation anomaly crest. Our data suggest that the generation of small plasma structure
{"title":"Systematic study of intermediate-scale structures of equatorial plasma irregularities in the ionosphere based on CHAMP observations","authors":"H. Lühr, C. Xiong, Jaeheung Park, J. Rauberg","doi":"10.3389/fphy.2014.00015","DOIUrl":"https://doi.org/10.3389/fphy.2014.00015","url":null,"abstract":"Equatorial spread-F ionospheric plasma irregularities on the night-side, commonly called equatorial plasma bubbles (EPB), include electron density variations over a wide range of spatial scales. Here we focus on intermediate-scale structures ranging from 100 m to 10 km, which play an important role in the evolution of EPBs. High-resolution CHAMP magnetic field measurements sampled along north-south track at 50 Hz are interpreted in terms of diamagnetic effect for illustrating the details of electron density variations. We provide the first comprehensive study on intermediate-scale density structures associated with EPBs, covering a whole solar cycle from 2000 to 2010. The large number of detected events, almost 9000, allows us to draw a detailed picture of the plasma fine structure. The occurrence of intermediate-scale events is strongly favoured by high solar flux. During times of F10.7 < 100 sfu practically no events were observed. The longitudinal distribution of our events with respect to season or local time agrees well with that of the EPBs, qualifying the fine structure as a common feature, but the occurrence rates are smaller by a factor of 4 during the period 2000-2005. Largest amplitude electron density variations appear at the poleward boundaries of plasma bubbles. Above the dip-equator recorded amplitudes are small and fall commonly below our resolution. Events can generally be found at local times between 19 and 24 LT, with a peak lasting from 20 to 22 LT. The signal spectrum can be approximated by a power law. Over the frequency range 1 – 25 Hz we observe spectral indices between -1.4 and -2.6 with peak occurrence rates around -1.9. There is a weak dependence observed of the spectral index on local time. Towards later hours the spectrum becomes shallower. Similarly for the latitude dependence, there is a preference of shallower spectra for latitudes poleward of the ionisation anomaly crest. Our data suggest that the generation of small plasma structure","PeriodicalId":49264,"journal":{"name":"Frontiers of Physics in China","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.3389/fphy.2014.00015","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69647198","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We determined many functional representations of interparticle interactions between water molecules, all of which reproduce the experimentally measured density-temperature relation at 1 bar with an accuracy better than obtained by previous models. Numerous similar descriptions of pair interactions will be discovered increasingly in the coming years, which will help us to understand why solid water has polymorphic structures and why liquid water has a large number of anomalies. We used a self-consistent Ornstein-Zernike approximation (SCOZA) with a potential given by multi-Yukawa terms. Because any smooth potential function can be fitted by multi-Yukawa terms, the method can be applied to various types of fluids. We also present a new simple fitting technique that makes the application of the SCOZA to any type of liquid much easier compared to a conventional Yukawa fit. Our new SCOZA fitting technique is among the most useful methods for determining the pair interaction between molecules of any liquid, and the potential will be helpful in improving realistic models.
{"title":"Interparticle interactions between water molecules","authors":"M. Yasutomi","doi":"10.3389/fphy.2014.00064","DOIUrl":"https://doi.org/10.3389/fphy.2014.00064","url":null,"abstract":"We determined many functional representations of interparticle interactions between water molecules, all of which reproduce the experimentally measured density-temperature relation at 1 bar with an accuracy better than obtained by previous models. Numerous similar descriptions of pair interactions will be discovered increasingly in the coming years, which will help us to understand why solid water has polymorphic structures and why liquid water has a large number of anomalies. We used a self-consistent Ornstein-Zernike approximation (SCOZA) with a potential given by multi-Yukawa terms. Because any smooth potential function can be fitted by multi-Yukawa terms, the method can be applied to various types of fluids. We also present a new simple fitting technique that makes the application of the SCOZA to any type of liquid much easier compared to a conventional Yukawa fit. Our new SCOZA fitting technique is among the most useful methods for determining the pair interaction between molecules of any liquid, and the potential will be helpful in improving realistic models.","PeriodicalId":49264,"journal":{"name":"Frontiers of Physics in China","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.3389/fphy.2014.00064","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69647367","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Antiprotons have been proposed as possible particles for radiotherapy; over the past years, the renewed interest in the potential biomedical relevance led to an increased research activity. It is the aim of this review to deliver a comprehensive overview regarding the evidence accumulated so far, analysing the background and depicting the current status of antiprotons in radiotherapy. A literature search has been conducted, including major scientific and commercial databases. All articles and a number of relevant conference abstracts published in the respective field have been included in this systematic review. The physical basis of antiproton radiotherapy is complex; however, the characterisation of the energy deposition profile supports its potential use in radiotherapy. Also the dosimetry improved considerably over the past few years. Regarding the biological properties, data on the effects on cells are presented; however, definite conclusions regarding the relative biological effectiveness cannot be made at the moment and radiobiological evidence of enhanced effectiveness remains scarce. In addition, there is new evidence supporting the potential imaging properties, for example for online dose verification. Clinical settings which might profit from the use of antiprotons have been further tracked. Judging from the evidence available so far, clinical constellations requiring optimal sparing in the entrance region of the beam and re-irradiations might profit most from antiproton radiotherapy. While several open questions remain to be answered, first steps towards a thorough characterisation of this interesting modality have been made.
{"title":"A systematic review of antiproton radiotherapy","authors":"M. Bittner, A. Grosu, N. Wiedenmann, J. Wilkens","doi":"10.3389/fphy.2013.00037","DOIUrl":"https://doi.org/10.3389/fphy.2013.00037","url":null,"abstract":"Antiprotons have been proposed as possible particles for radiotherapy; over the past years, the renewed interest in the potential biomedical relevance led to an increased research activity. It is the aim of this review to deliver a comprehensive overview regarding the evidence accumulated so far, analysing the background and depicting the current status of antiprotons in radiotherapy. A literature search has been conducted, including major scientific and commercial databases. All articles and a number of relevant conference abstracts published in the respective field have been included in this systematic review. The physical basis of antiproton radiotherapy is complex; however, the characterisation of the energy deposition profile supports its potential use in radiotherapy. Also the dosimetry improved considerably over the past few years. Regarding the biological properties, data on the effects on cells are presented; however, definite conclusions regarding the relative biological effectiveness cannot be made at the moment and radiobiological evidence of enhanced effectiveness remains scarce. In addition, there is new evidence supporting the potential imaging properties, for example for online dose verification. Clinical settings which might profit from the use of antiprotons have been further tracked. Judging from the evidence available so far, clinical constellations requiring optimal sparing in the entrance region of the beam and re-irradiations might profit most from antiproton radiotherapy. While several open questions remain to be answered, first steps towards a thorough characterisation of this interesting modality have been made.","PeriodicalId":49264,"journal":{"name":"Frontiers of Physics in China","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.3389/fphy.2013.00037","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69647152","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Grothendieck's dessins d'enfants arise with ever-increasing frequency in many areas of 21st century mathematical physics. In this paper, we review the connections between dessins and the theory of Hecke groups. Focussing on the restricted class of highly symmetric dessins corresponding to the so-called Archimedean solids, we apply this theory in order to provide a means of computing representatives of the associated conjugacy classes of Hecke subgroups in each case. The aim of this paper is to demonstrate that dessins arising in mathematical physics can point to new and hitherto unexpected directions for further research. In addition, given the particular ubiquity of many of the dessins corresponding to the Archimedean solids, the hope is that the computational results of this paper will prove useful in the further study of these objects in mathematical physics contexts.
{"title":"Hecke Groups, Dessins d'Enfants, and the Archimedean Solids","authors":"Yang-Hui He, James Read","doi":"10.3389/fphy.2015.00091","DOIUrl":"https://doi.org/10.3389/fphy.2015.00091","url":null,"abstract":"Grothendieck's dessins d'enfants arise with ever-increasing frequency in many areas of 21st century mathematical physics. In this paper, we review the connections between dessins and the theory of Hecke groups. Focussing on the restricted class of highly symmetric dessins corresponding to the so-called Archimedean solids, we apply this theory in order to provide a means of computing representatives of the associated conjugacy classes of Hecke subgroups in each case. The aim of this paper is to demonstrate that dessins arising in mathematical physics can point to new and hitherto unexpected directions for further research. In addition, given the particular ubiquity of many of the dessins corresponding to the Archimedean solids, the hope is that the computational results of this paper will prove useful in the further study of these objects in mathematical physics contexts.","PeriodicalId":49264,"journal":{"name":"Frontiers of Physics in China","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.3389/fphy.2015.00091","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69647521","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
ADSORPTION OF LEAD (II) IONS BY ORGANOSILICATE NANOPOROUS MATERIALS Larry Keith Isaacs Old Dominion University, 2007 Director: Dr. Mujde Erten-Unal As-synthesized organosilicate nanoporous (OSNP) materials HMS (hexagonal mesoporous structure) and MCM-41 were used as adsorbents for removal of lead (II) ions in laboratory batch and column studies. Mesoporous organosilicates were prepared from tetraethylorthosilicate (TEOS) and either an ionic (cetyltrimethyl-ammonium) or neutral (dodecylamine) surfactant. Batch reaction distribution coefficients for MCM-41 were Kd = 51.5 L/g (SD 26.3) at 24 h and KD = 73.7 L/g (SD = 40.5) at 7 d. OSNP lead (II) ion adsorption increased from pH = 3 until pH ca. 7.5 after which a sharp decrease in adsorption was noted. OSNP materials reflected a dependence on ionic strength consistent with an outer-sphere complexation and electrostatic bonding mechanism. Lead (II) ion adsorption behavior in seven matrix batch solutions was not effective possibly due to soluble complexes that were formed that prevented adsorption and precipitation. There was no difference in the batch adsorption performance of MCM-41 and HMS. Column designs were optimized by response surface methods. OSNP material/sand media head loss at a superficial velocity = 0.49 m/h increased 28.1% compared with sand only media. At column break through, defined as Ce/Co = 0.5, MCM-41/sand media Kd = 46.2 L/g and sand only Kd = 0.04 L/g. There was significant evidence to warrant rejection of the claim that the variances in Kd were equal (P < 0.001, n = 12). Adsorption capacity in columns with synthetic adsorbates at Ce/Co = 0.50 were HMS = 0.013 mmol/g (2.74 mg/g) at 0.6 m3/m2 h and MCM-41 = 0.071 mmol/g (14.63 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. mg/g) at 2.1 m3/m2 h. For a stormwater treated by single pass column filtration, MCM41 lead (II) ion adsorption at Ce/Co = 0.50 was 0.028 mmol/g (5.88 mg/g) and sand only = 2.83E-05 mmol/g (0.01 mg/g). Water molecule ionization by metal cations decreased influent pH, combined with deprotonation of MCM-41 during adsorption of lead (II) ions, caused a decrease in pH sufficient to change column adsorption performance. The declining rate sand filtration cost for a 100 m2 unit in 2007 dollars was estimated at $31,600, however this did not include the cost for MCM-41 adsorbent materials, which are not available commercially. Adsorbent life cycle was calculated at 2.6 years. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Copyright, 2007, by Larry Keith Isaacs, All Rights Reserved. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. This dissertation is dedicated to my wife Marsha who has been forever patient and to our children for their constant encouragement. Reproduced with permission of the copyright owner. Further reproduction prohibited without permiss
{"title":"Adsorption of Lead (II) Ions by Organosilicate Nanoporous Materials","authors":"L. Isaacs","doi":"10.25777/FPHY-GM74","DOIUrl":"https://doi.org/10.25777/FPHY-GM74","url":null,"abstract":"ADSORPTION OF LEAD (II) IONS BY ORGANOSILICATE NANOPOROUS MATERIALS Larry Keith Isaacs Old Dominion University, 2007 Director: Dr. Mujde Erten-Unal As-synthesized organosilicate nanoporous (OSNP) materials HMS (hexagonal mesoporous structure) and MCM-41 were used as adsorbents for removal of lead (II) ions in laboratory batch and column studies. Mesoporous organosilicates were prepared from tetraethylorthosilicate (TEOS) and either an ionic (cetyltrimethyl-ammonium) or neutral (dodecylamine) surfactant. Batch reaction distribution coefficients for MCM-41 were Kd = 51.5 L/g (SD 26.3) at 24 h and KD = 73.7 L/g (SD = 40.5) at 7 d. OSNP lead (II) ion adsorption increased from pH = 3 until pH ca. 7.5 after which a sharp decrease in adsorption was noted. OSNP materials reflected a dependence on ionic strength consistent with an outer-sphere complexation and electrostatic bonding mechanism. Lead (II) ion adsorption behavior in seven matrix batch solutions was not effective possibly due to soluble complexes that were formed that prevented adsorption and precipitation. There was no difference in the batch adsorption performance of MCM-41 and HMS. Column designs were optimized by response surface methods. OSNP material/sand media head loss at a superficial velocity = 0.49 m/h increased 28.1% compared with sand only media. At column break through, defined as Ce/Co = 0.5, MCM-41/sand media Kd = 46.2 L/g and sand only Kd = 0.04 L/g. There was significant evidence to warrant rejection of the claim that the variances in Kd were equal (P < 0.001, n = 12). Adsorption capacity in columns with synthetic adsorbates at Ce/Co = 0.50 were HMS = 0.013 mmol/g (2.74 mg/g) at 0.6 m3/m2 h and MCM-41 = 0.071 mmol/g (14.63 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. mg/g) at 2.1 m3/m2 h. For a stormwater treated by single pass column filtration, MCM41 lead (II) ion adsorption at Ce/Co = 0.50 was 0.028 mmol/g (5.88 mg/g) and sand only = 2.83E-05 mmol/g (0.01 mg/g). Water molecule ionization by metal cations decreased influent pH, combined with deprotonation of MCM-41 during adsorption of lead (II) ions, caused a decrease in pH sufficient to change column adsorption performance. The declining rate sand filtration cost for a 100 m2 unit in 2007 dollars was estimated at $31,600, however this did not include the cost for MCM-41 adsorbent materials, which are not available commercially. Adsorbent life cycle was calculated at 2.6 years. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Copyright, 2007, by Larry Keith Isaacs, All Rights Reserved. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. This dissertation is dedicated to my wife Marsha who has been forever patient and to our children for their constant encouragement. Reproduced with permission of the copyright owner. Further reproduction prohibited without permiss","PeriodicalId":49264,"journal":{"name":"Frontiers of Physics in China","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2007-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69253471","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Frontiers of Physics 1998, Proceedings of the Intl Mtg","authors":"S. Chia, D. Bradley","doi":"10.1142/4583","DOIUrl":"https://doi.org/10.1142/4583","url":null,"abstract":"","PeriodicalId":49264,"journal":{"name":"Frontiers of Physics in China","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2000-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"63995523","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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