Статті в журналах: "Dispersion functions"

1

Percival, D. J., and P. A. Robinson. "Generalized plasma dispersion functions." Journal of Mathematical Physics 39, no. 7 (July 1998): 3678–93. http://dx.doi.org/10.1063/1.532460.

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2

Robinson, P. A. "Relativistic plasma dispersion functions." Journal of Mathematical Physics 27, no. 5 (May 1986): 1206–14. http://dx.doi.org/10.1063/1.527127.

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3

Camacho, J. "Thermodynamic functions for Taylor dispersion." Physical Review E 48, no. 3 (September 1, 1993): 1844–49. http://dx.doi.org/10.1103/physreve.48.1844.

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4

Ideguchi, Shinsuke, Yuichi Tashiro, Takuya Akahori, Keitaro Takahashi, and Dongsu Ryu. "FARADAY DISPERSION FUNCTIONS OF GALAXIES." Astrophysical Journal 792, no. 1 (August 14, 2014): 51. http://dx.doi.org/10.1088/0004-637x/792/1/51.

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5

Katsuura, Hidefumi. "Dispersion points and continuous functions." Topology and its Applications 28, no. 3 (April 1988): 233–40. http://dx.doi.org/10.1016/0166-8641(88)90044-2.

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6

Melrose, D. B., J. I. Weise, and J. McOrist. "Relativistic quantum plasma dispersion functions." Journal of Physics A: Mathematical and General 39, no. 27 (June 21, 2006): 8727–40. http://dx.doi.org/10.1088/0305-4470/39/27/011.

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7

Robinson, P. A. "Relativistic and nonrelativistic plasma dispersion functions." Journal of Mathematical Physics 30, no. 11 (November 1989): 2484–87. http://dx.doi.org/10.1063/1.528528.

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8

Pernal, Katarzyna, and Krzysztof Szalewicz. "Third-order dispersion energy from response functions." Journal of Chemical Physics 130, no. 3 (January 21, 2009): 034103. http://dx.doi.org/10.1063/1.3058477.

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9

Dubrovskii, V. G. "Dispersion of scale-invariant size-distribution functions." Technical Physics Letters 43, no. 5 (May 2017): 413–15. http://dx.doi.org/10.1134/s1063785017050029.

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10

LUO, Q., and D. B. MELROSE. "Approximate plasma dispersion functions at relativistic temperatures." Journal of Plasma Physics 70, no. 6 (December 2004): 709–18. http://dx.doi.org/10.1017/s0022377804002867.

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11

Arteaga, Daniel, Renaud Parentani, and Enric Verdaguer. "Retarded Green Functions and Modified Dispersion Relations." International Journal of Theoretical Physics 44, no. 10 (October 2005): 1665–89. http://dx.doi.org/10.1007/s10773-005-8888-z.

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12

Swanson, D. G. "Exact and moderately relativistic plasma dispersion functions." Plasma Physics and Controlled Fusion 44, no. 7 (June 19, 2002): 1329–47. http://dx.doi.org/10.1088/0741-3335/44/7/320.

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13

Essa, Khaled S. M., and Maha S. El-Otaify. "Atmospheric vertical dispersion in moderate winds with eddy diffusivities as power law functions." Meteorologische Zeitschrift 17, no. 1 (February 26, 2008): 13–18. http://dx.doi.org/10.1127/0941-2948/2007/0238.

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14

Fernandez-Ponce, J. M., S. C. Kochar, and J. Muñoz-Perez. "Partial Orderings of Distributions Based on Right-Spread Functions." Journal of Applied Probability 35, no. 1 (March 1998): 221–28. http://dx.doi.org/10.1239/jap/1032192565.

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In this paper we introduce a quantile dispersion measure. We use it to characterize different classes of ageing distributions. Based on the quantile dispersion measure, we propose a new partial ordering for comparing the spread or dispersion in two probability distributions. This new partial ordering is weaker than the well known dispersive ordering and it retains most of its interesting properties.

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15

Fernandez-Ponce, J. M., S. C. Kochar, and J. Muñoz-Perez. "Partial Orderings of Distributions Based on Right-Spread Functions." Journal of Applied Probability 35, no. 01 (March 1998): 221–28. http://dx.doi.org/10.1017/s0021900200014819.

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In this paper we introduce a quantile dispersion measure. We use it to characterize different classes of ageing distributions. Based on the quantile dispersion measure, we propose a new partial ordering for comparing the spread or dispersion in two probability distributions. This new partial ordering is weaker than the well known dispersive ordering and it retains most of its interesting properties.

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16

MELROSE, D. B. "Generalized Trubnikov functions for unmagnetized plasmas." Journal of Plasma Physics 62, no. 2 (August 1999): 249–53. http://dx.doi.org/10.1017/s0022377899007898.

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A class of relativistic dispersion functions for unmagnetized thermal plasmas is defined by generalizing functions first defined by Trubnikov in 1958. Recursion relations are derived that allow one to generate explicit expressions for the class of functions in terms of the relativistic plasma dispersion function T(z, ρ) introduced by Godfrey et al. in 1975. These functions are relevant to the description of the response of a weakly mangetized, highly relativistic, thermal plasma.

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17

Perepelkin, E. E., B. I. Sadovnikov, N. G. Inozemtseva, and I. I. Aleksandrov. "Dispersion chain of Vlasov equations." Journal of Statistical Mechanics: Theory and Experiment 2022, no. 1 (January 1, 2022): 013205. http://dx.doi.org/10.1088/1742-5468/ac4515.

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Abstract On the basis of the Vlasov chain of equations, a new infinite dispersion chain of equations is obtained for the distribution functions of mixed higher order kinematical values. In contrast to the Vlasov chain, the dispersion chain contains distribution functions with an arbitrary set of kinematical values and has a tensor form of writing. For the dispersion chain, new equations for mixed Boltzmann functions and the corresponding chain of conservation laws for fluid dynamics are obtained. The probability is proved to be a constant value for a particle to belong the region where the quasi-probability density is negative (Wigner function).

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18

Pennison, Garland, Bret Webb, Ioannis Gidaris, and Jamie Padgett. "PREDICTING COASTAL ROADWAY DAMAGE USING MODIFIED DISPERSION FUNCTIONS." Coastal Engineering Proceedings, no. 36 (December 30, 2018): 5. http://dx.doi.org/10.9753/icce.v36.structures.5.

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Empirical dispersion functions appear to reasonably predict damage risks for coastal roadways subjected to coastal storm surge and wave hazards. County Road 257 (CR 257) in Brazoria County, Texas had significant damage at various locations during Hurricane Ike in September 2008. Cumulative peak hourly water surface elevation, wave period, and current velocity output from a hindcast ADCIRC+SWAN model was assessed using modified celerity dispersion functions relative to measured distance between road and shoreline. These intensity measures provide a strongly correlated model for predicting likelihood of road damage.

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19

Andrinopoulos, Lampros, Nicholas D. M. Hine, and Arash A. Mostofi. "Calculating dispersion interactions using maximally localized Wannier functions." Journal of Chemical Physics 135, no. 15 (October 21, 2011): 154105. http://dx.doi.org/10.1063/1.3647912.

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20

Vandas, Marek, and Petr Hellinger. "Linear dispersion properties of ring velocity distribution functions." Physics of Plasmas 22, no. 6 (June 2015): 062107. http://dx.doi.org/10.1063/1.4922073.

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21

Abid, Rahma, Célestin C. Kokonendji, and Afif Masmoudi. "Geometric dispersion models with real quadratic v-functions." Statistics & Probability Letters 145 (February 2019): 197–204. http://dx.doi.org/10.1016/j.spl.2018.09.010.

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22

Robinson, P. A. "Relativistic plasma dispersion functions: Series, integrals, and approximations." Journal of Mathematical Physics 28, no. 5 (May 1987): 1203–5. http://dx.doi.org/10.1063/1.527515.

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23

Canterle, Diego Ramos, and Fábio Mariano Bayer. "Variable dispersion beta regressions with parametric link functions." Statistical Papers 60, no. 5 (February 13, 2017): 1541–67. http://dx.doi.org/10.1007/s00362-017-0885-9.

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24

Obcemea, Ceferino H. "Free energy and dispersion forces via response functions." International Journal of Quantum Chemistry 31, no. 1 (January 1987): 113–17. http://dx.doi.org/10.1002/qua.560310113.

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25

Köken, Reşit, Tevfik Demir, Tolga Altuğ Şen, Ahmet Afşin Kundak, Osman Öztekin, and Faruk Alpay. "The relationship between P-wave dispersion and diastolic functions in diabetic children." Cardiology in the Young 20, no. 2 (March 12, 2010): 133–37. http://dx.doi.org/10.1017/s104795110999031x.

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AbstractObjectiveThe aim of this study was to investigate the relations between the P-wave dispersion and diastolic functions in type 1 diabetic children.PatientsA total of 33 diabetic patients without any cardiovascular disease, with a mean age of 12.3 plus or minus 4.2 years, and 29 healthy controls, with a mean age of 10.4 plus or minus 3.9 years were enrolled for this study. Left and right ventricular functions were assessed by using standard pulsed-wave Doppler echocardiography. P-wave dispersion was calculated by measuring minimum and maximum P-wave duration values on the surface electrocardiogram.ResultsFor the diabetic patients, P-wave maximum duration and dispersion was found to be significantly increased compared with healthy controls. Likewise, mitral A velocity and A velocity time integral was significantly increased while the isovolumic contraction time was significantly higher in the diabetics. In tricuspid valve measurements, however, A velocity time integral was found to be significantly higher, whereas the deceleration time was significantly lower in the diabetics. No relation was found between the left ventricle diastolic functions and duration of diabetes, HbA1c levels and P-wave dispersion in the diabetic children. No correlation was found between the diastolic functions and P-wave minimum, maximum duration, and dispersion for all the participants.ConclusionIn type-1 diabetic children, the diastolic functions of both the ventricles were observed to be affected negatively together. Diabetes might be causing the prolongation of P-wave dispersion, but there was no relationship between the diastolic functions and P-wave dispersion in the diabetic children.

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26

Essink, Sebastian, Verena Hormann, Luca R. Centurioni, and Amala Mahadevan. "Can We Detect Submesoscale Motions in Drifter Pair Dispersion?" Journal of Physical Oceanography 49, no. 9 (September 2019): 2237–54. http://dx.doi.org/10.1175/jpo-d-18-0181.1.

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AbstractA cluster of 45 drifters deployed in the Bay of Bengal is tracked for a period of four months. Pair dispersion statistics, from observed drifter trajectories and simulated trajectories based on surface geostrophic velocity, are analyzed as a function of drifter separation and time. Pair dispersion suggests nonlocal dynamics at submesoscales of 1–20 km, likely controlled by the energetic mesoscale eddies present during the observations. Second-order velocity structure functions and their Helmholtz decomposition, however, suggest local dispersion and divergent horizontal flow at scales below 20 km. This inconsistency cannot be explained by inertial oscillations alone, as has been reported in recent studies, and is likely related to other nondispersive processes that impact structure functions but do not enter pair dispersion statistics. At scales comparable to the deformation radius LD, which is approximately 60 km, we find dynamics in agreement with Richardson’s law and observe local dispersion in both pair dispersion statistics and second-order velocity structure functions.

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27

Bodin, T., M. Sambridge, H. Tkalčić, P. Arroucau, K. Gallagher, and N. Rawlinson. "Transdimensional inversion of receiver functions and surface wave dispersion." Journal of Geophysical Research: Solid Earth 117, B2 (February 2012): n/a. http://dx.doi.org/10.1029/2011jb008560.

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28

Shenghong Liu, Le-Wei Li, Mook-Seng. "Circular Chiroferrite Waveguides: Dispersion Curves and Dyadic Green's Functions." Electromagnetics 21, no. 6 (September 2001): 467–83. http://dx.doi.org/10.1080/027263401750399543.

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29

Castejon, F., and S. S. Pavlov. "The exact plasma dispersion functions in the complex region." Nuclear Fusion 48, no. 5 (April 7, 2008): 054003. http://dx.doi.org/10.1088/0029-5515/48/5/054003.

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30

GUSTAFSON, DAVID. "MODELING ROOT ZONE DISPERSION: A COMEDY OF ERROR FUNCTIONS." Chemical Engineering Communications 73, no. 1 (November 1988): 77–94. http://dx.doi.org/10.1080/00986448808940435.

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31

Dinda, P. Tchofo, K. Nakkeeran, and A. B. Moubissi. "Optimized Hermite-gaussian ansatz functions for dispersion-managed solitons." Optics Communications 187, no. 4-6 (January 2001): 427–33. http://dx.doi.org/10.1016/s0030-4018(00)01135-4.

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32

Chow, Kwok W. "Theta Functions and the Dispersion Relations of Periodic Waves." Journal of the Physical Society of Japan 62, no. 6 (June 15, 1993): 2007–11. http://dx.doi.org/10.1143/jpsj.62.2007.

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33

Kniehl, Bernd A., and Alberto Sirlin. "Dispersion relations for vacuum-polarization functions in electroweak physics." Nuclear Physics B 371, no. 1-2 (March 1992): 141–48. http://dx.doi.org/10.1016/0550-3213(92)90232-z.

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34

Babiano, Armando, Claude Basdevant, and Robert Sadourny. "Structure Functions and Dispersion Laws in Two-Dimensional Turbulence." Journal of the Atmospheric Sciences 42, no. 9 (May 1985): 941–49. http://dx.doi.org/10.1175/1520-0469(1985)042<0941:sfadli>2.0.co;2.

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35

Vlad, Marcel Ovidiu. "Persistent distribution functions for the dispersion of structured populations." Mathematical Biosciences 87, no. 2 (December 1987): 173–98. http://dx.doi.org/10.1016/0025-5564(87)90073-3.

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36

Nordli, Håkon, Torfinn Taxt, Gunnar Moen, and Renate Grüner. "Voxel-specific brain arterial input functions from dynamic susceptibility contrast MRI and blind deconvolution in a group of healthy males." Acta Radiologica 51, no. 3 (April 2010): 334–43. http://dx.doi.org/10.3109/02841850903536094.

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Background: Arterial input functions may differ between brain regions due to delay and dispersion effects in the vascular supply network. Unless corrected for, these differences may degrade quantitative estimations of cerebral blood flow in dynamic susceptibility contrast magnetic resonance perfusion imaging (DSC-MRI). Purpose: To investigate in a healthy population ( n=44) the properties of voxel-specific arterial input functions that were obtained using a recently published blind estimation approach. Material and Methods: The voxel-specific arterial input functions were qualitatively and quantitatively assessed, through visual inspection or by comparing time-to-peak (delays) and peak amplitude (dispersion) values between eight regions of the brain. Furthermore, they were compared to arterial input functions selected manually in the middle cerebral artery (MCA), where normally no delay or dispersion of the contrast agent was expected. Results: The estimated voxel-specific arterial input functions varied between brain regions. Differences in delays and dispersion were larger within one brain region among all participants than between regions in one participant. A good correlation was typically found between the estimated voxel-specific arterial input functions and the manually selected arterial input functions in the MCA region. Conclusion: Given knowledge of neurovascular anatomy, the current blind approach seemingly produced reasonable estimates of voxel-specific arterial input functions. In addition to potentially reducing quantification errors in DSC-MRI, these user-independent voxel-specific arterial input functions could be useful for visualizing abnormal blood supply patterns in patients.

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37

Meng, Weijuan, and Li-Yun Fu. "Numerical dispersion analysis of discontinuous Galerkin method with different basis functions for acoustic and elastic wave equations." GEOPHYSICS 83, no. 3 (May 1, 2018): T87—T101. http://dx.doi.org/10.1190/geo2017-0485.1.

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The discontinuous Galerkin method (DGM) has been applied to investigate seismic wave propagation recently. However, few studies have examined the dispersion property of DGM with different basis functions. Therefore, three common basis functions, Legendre polynomial, Lagrange polynomial with equidistant nodes, and Lagrange polynomial with Gauss-Lobatto-Legendre (GLL) nodes, are used for numerical approximation. The numerical dispersion and anisotropy numerical behavior of acoustic and elastic waves are compared, and the numerical errors of different order methods are analyzed. The result shows that the dispersion errors for all basis functions reduce generally with increasing interpolation orders, but with large differences in different directions. Specifically, the Legendre basis function and Lagrange basis function with GLL nodes have attractive advantages over the Lagrange polynomial with equidistant nodes for numerical computation. We verified the dispersion properties by theoretical and numerical analyses.

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38

Robinson, P. A., and D. L. Newman. "Approximation of the dielectric properties of Maxwellian plasmas: dispersion functions and physical constraints." Journal of Plasma Physics 40, no. 3 (December 1988): 553–66. http://dx.doi.org/10.1017/s0022377800013519.

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The dielectric properties of Maxwellian plasmas are approximated using both Padé approximants to the dispersion function and direct approximation of the distribution. Physical constraints on permissible approximations are discussed, and it is found that some previously published results can lead to predictions of qualitatively incorrect wave properties, including unphysical negative damping. Approximate dispersion functions for Maxwellian distributions are given explicitly, and some of the effects of these approximations on the resulting dispersion are discussed. The approximations discussed here are of use both in analytic work and in accelerating large-scale numerical computations.

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39

Ding, Qinxu, Yong Liu, Chunyan Miao, Fei Cheng, and Haihong Tang. "A Hybrid Bandit Framework for Diversified Recommendation." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 5 (May 18, 2021): 4036–44. http://dx.doi.org/10.1609/aaai.v35i5.16524.

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The interactive recommender systems involve users in the recommendation procedure by receiving timely user feedback to update the recommendation policy. Therefore, they are widely used in real application scenarios. Previous interactive recommendation methods primarily focus on learning users' personalized preferences on the relevance properties of an item set. However, the investigation of users' personalized preferences on the diversity properties of an item set is usually ignored. To overcome this problem, we propose the Linear Modular Dispersion Bandit (LMDB) framework, which is an online learning setting for optimizing a combination of modular functions and dispersion functions. Specifically, LMDB employs modular functions to model the relevance properties of each item, and dispersion functions to describe the diversity properties of an item set. Moreover, we also develop a learning algorithm, called Linear Modular Dispersion Hybrid (LMDH) to solve the LMDB problem and derive a gap-free bound on its n-step regret. Extensive experiments on real datasets are performed to demonstrate the effectiveness of the proposed LMDB framework in balancing the recommendation accuracy and diversity.

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40

Sert, Ahmet, Cem Gokcen, Ebru Aypar, and Dursun Odabas. "Effects of atomoxetine on cardiovascular functions and on QT dispersion in children with attention deficit hyperactivity disorder." Cardiology in the Young 22, no. 2 (August 25, 2011): 158–61. http://dx.doi.org/10.1017/s1047951111001211.

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AbstractBackgroundAtomoxetine is a central norepinephrine reuptake inhibitor used to treat attention deficit/hyperactivity disorder. The effects of atomoxetine on cardiovascular functions and QT dispersion in children with attention deficit/hyperactivity disorder have not been previously reported. The aim of this study was to analyse cardiovascular functions and QT dispersion on the surface electrocardiogram of children with attention deficit/hyperactivity disorder during atomoxetine therapy.MethodsA total of 40 children – with a mean age of 8.6 plus or minus 2.3 years and a median age of 11 years; ranged from 8 to 14 years – with attention deficit/hyperactivity disorder – with six girls and 34 boys – were included in the study. We recorded the mean systolic and diastolic blood pressure, heart rate, corrected QT interval, QT dispersion, and left ventricular systolic functions at baseline and 5 weeks after atomoxetine therapy.ResultsAtomoxetine decreased baseline mean systolic and diastolic blood pressure; baseline mean heart rate decreased; and baseline mean corrected QT interval and QT dispersion mildly increased. Atomoxetine decreased baseline mean ejection fraction and baseline mean shortening fraction.ConclusionThe results of our study suggest that atomoxetine does not cause clinically significant alterations in QT dispersion, systolic and diastolic blood pressure, heart rate, corrected QT interval, and left ventricular systolic functions during short-term treatment in children with attention deficit/hyperactivity disorder.

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41

Chapman, C. J. "The asymptotic theory of dispersion relations containing Bessel functions of imaginary order." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468, no. 2148 (September 26, 2012): 4008–23. http://dx.doi.org/10.1098/rspa.2012.0459.

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This paper presents a method of analysing wave-field dispersion relations in which Bessel functions of imaginary order occur. Such dispersion relations arise in applied studies in oceanography and astronomy, for example. The method involves the asymptotic theory developed by Dunster in 1990, and leads to simple analytical approximations containing only trigonometric and exponential functions. Comparisons with accurate numerical calculations show that the resulting approximations to the dispersion relation are highly accurate. In particular, the approximations are powerful enough to reveal the fine structure in the dispersion relation and so identify different wave regimes corresponding to different balances of physical processes. Details of the method are presented for the fluid-dynamical problem that stimulated this analysis, namely the dynamics of an internal ocean wave in the presence of an aerated surface layer; the method identifies and gives different approximations for the subcritical, supercritical and critical regimes. The method is potentially useful in a wide range of problems in wave theory and stability theory. A mathematical theme of the paper is that of the removable singularity.

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42

Kitazawa, Masakiyo, Atsuro Ikeda, and Masayuki Asakawa. "Dispersion relations of charmonia above Tc." EPJ Web of Conferences 175 (2018): 07006. http://dx.doi.org/10.1051/epjconf/201817507006.

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We study spectral properties of charmonia in the vector and pseudoscalar channels at nonzero momenta on quenched lattices focusing on the dispersion relation and the weight of the peak. The spectral functions of charmonia are studied by the maximum entropy method with the lattice Euclidean correlation functions on the anisotropic quenched lattices. The errors of the dispersion relations and the residues of the peak are analysed in the maximum entropy method. We find a significant increase of the masses of charmonia in medium. We also find that the functional form of the dispersion relations is not changed from that in the vacuum within the error even at T = 1:6Tc. Preprint number: J-PARC-TH-0111

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43

KENNETT, M. P., D. B. MELROSE, and Q. LUO. "Cyclotron effects on wave dispersion in pulsar plasmas." Journal of Plasma Physics 64, no. 4 (October 2000): 333–52. http://dx.doi.org/10.1017/s0022377800008862.

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Dispersion in an intrinsically relativistic, one-dimensional, electron–positron pair plasma (a pulsar plasma) is treated exactly, generalizing earlier results that applied in the low-frequency limit and that neglected the cyclotron resonance. The general theory involves two additional relativistic plasma dispersion functions, evaluated at the normal and anomalous Doppler resonances. These two functions are associated with the non-gyrotropic and gyrotropic parts of the response respectively. The functions are evaluated for bell-type and Jüttner distributions. Wave dispersion is discussed for a non-gyrotropic pulsar plasma with a highly relativistic Alfvén speed. Emphasis is placed on crossings of the light line, defined in terms of the parallel phase velocity. Subluminal waves exist only for sufficiently small angles of propagation, and are confined to frequencies below about the mean gyrofrequency of the relativistic particles.

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44

Kęska, Adam. "AXIOMATIC DETERMINATION OF A CLASS OF ORDINAL VARIATION MEASURES." Studies in Logic, Grammar and Rhetoric 50, no. 1 (June 27, 2017): 45–65. http://dx.doi.org/10.1515/slgr-2017-0018.

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Abstract The article deals with the problem of the dispersion of ordinal variables. At first, it specifies the very concept of dispersion for this type of scale. Then some of the most known measures that fit to the concept of ordinal variation are recalled. They are constructed with two different types of statistical models: using loss functions and using distance functions. Finally, a new approach, which is the use of an axiomatic method for the construction of a dispersion measure, is proposed. Some relations and comparisons between different measures and between different approaches are shown.

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45

WANG, DONGDONG, and ZHENTING LIN. "A COMPARATIVE STUDY ON THE DISPERSION PROPERTIES OF HRK AND RK MESHFREE APPROXIMATIONS FOR KIRCHHOFF PLATE PROBLEM." International Journal of Computational Methods 09, no. 01 (March 2012): 1240015. http://dx.doi.org/10.1142/s0219876212400154.

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Dispersion analysis provides a rational way to examine the dynamic properties of numerical methods through comparing the numerical and continuum frequencies. In this paper a detailed comparative investigation is presented on the dispersion features of the Hermite reproducing kernel (HRK) and the conventional reproducing kernel (RK) meshfree methods for Kirchhoff plate problem with particular reference to the spatial discretizations. In the analysis the nodal variables of the semi-discretized meshfree Kirchhoff plate equations are assumed as harmonic wave functions to extract the numerical frequency. For the RK approximation, only the deflectional nodal variables are expressed by the harmonic wave functions, while unlike RK approximation, both deflectional and rotational nodal variables should be expressed by the harmonic wave functions for the HRK approximation. The dispersion analysis results uniformly evince that the HRK meshfree discretization has much smaller dispersion errors and performs superiorly compared to the conventional RK meshfree discretization for Kirchhoff plate problem.

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46

Krstovska, Danica, and Aleksandar Skeparovski. "Surface-state energies and wave functions in layered organic conductors." Zeitschrift für Naturforschung A 75, no. 11 (November 26, 2020): 987–98. http://dx.doi.org/10.1515/zna-2020-0223.

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AbstractWe have calculated and analyzed the surface-state energies and wave functions in quasi-two dimensional (Q2D) organic conductors in a magnetic field parallel to the surface. Two different forms for the electron energy spectrum are used in order to obtain more information on the elementary properties of surface states in these conductors. In addition, two mathematical approaches are implemented that include the eigenvalue and eigenstate problem as well as the quantization rule. We find significant differences in calculations of the surface-state energies arising from the specific form of the energy dispersion law. This is correlated with the different conditions needed to calculate the surface-state energies, magnetic field resonant values and the surface wave functions. The calculations reveal that the value of the coordinate of the electron orbit must be different for each state in order to numerically calculate the surface energies for one energy dispersion law, but it has the same value for each state for the other energy dispersion law. This allows to determine more accurately the geometric characteristics of the electron skipping trajectories in Q2D organic conductors. The possible reasons for differences associated with implementation of two distinct energy spectra are discussed. By comparing and analyzing the results we find that, when the energy dispersion law obtained within the tight-binding approximation is used the results are more relevant and reflect the Q2D nature of the organic conductors. This might be very important for studying the unique properties of these conductors and their wider application in organic electronics.

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VV, Rumyantsev. "Dispersion of Electromagnetic Excitations in a Non-Ideal Microporous Lattice." Physical Science & Biophysics Journal 5, no. 2 (2021): 1–8. http://dx.doi.org/10.23880/psbj-16000182.

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We develop a numerical model for a defect-containing 2D lattice of microporous lattice with embedded ultracold atomic clusters (quantum dots). It is assumed that certain fractions of quantum dots and micropores are absent, which leads to transformation of polariton spectrum of the structure. The dispersion relations for polaritonic modes are derived as functions of defect concentrations and on this basis the band gap as well as the effective masses of lower and upper dispersion branch polaritons.

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BUHMANN, STEFAN YOSHI, STEFAN SCHEEL, HASSAN SAFARI, and DIRK-GUNNAR WELSCH. "DISPERSION FORCES AND DUALITY." International Journal of Modern Physics A 24, no. 08n09 (April 10, 2009): 1796–803. http://dx.doi.org/10.1142/s0217751x09045376.

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We formulate a symmetry principle on the basis of the duality of electric and magnetic fields and apply it to dispersion forces. Within the context of macroscopic quantum electrodynamics, we rigorously establish duality invariance for the free electromagnetic field in the presence of causal magnetoelectrics. Dispersion forces are given in terms of the Green tensor for the electromagnetic field and the atomic response functions. After discussing the behavior of the Green tensor under a duality transformation, we are able to show that Casimir forces on bodies in free space as well as local-field corrected Casimir–Polder and van der Waals forces are duality invariant.

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Huang, F., and F. Liu. "The time fractional diffusion equation and the advection-dispersion equation." ANZIAM Journal 46, no. 3 (January 2005): 317–30. http://dx.doi.org/10.1017/s1446181100008282.

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AbstractThe time fractional diffusion equation with appropriate initial and boundary conditions in an n-dimensional whole-space and half-space is considered. Its solution has been obtained in terms of Green functions by Schneider and Wyss. For the problem in whole-space, an explicit representation of the Green functions can also be obtained. However, an explicit representation of the Green functions for the problem in half-space is difficult to determine, except in the special cases α = 1 with arbitrary n, or n = 1 with arbitrary α. In this paper, we solve these problems. By investigating the explicit relationship between the Green functions of the problem with initial conditions in whole-space and that of the same problem with initial and boundary conditions in half-space, an explicit expression for the Green functions corresponding to the latter can be derived in terms of Fox functions. We also extend some results of Liu, Anh, Turner and Zhuang concerning the advection-dispersion equation and obtain its solution in half-space and in a bounded space domain.

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Du, Xunbai, Sina Dang, Yuzheng Yang, and Yingbin Chai. "The Finite Element Method with High-Order Enrichment Functions for Elastodynamic Analysis." Mathematics 10, no. 23 (December 4, 2022): 4595. http://dx.doi.org/10.3390/math10234595.

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Elastodynamic problems are investigated in this work by employing the enriched finite element method (EFEM) with various enrichment functions. By performing the dispersion analysis, it is confirmed that for elastodynamic analysis, the amount of numerical dispersion, which is closely related to the numerical error from the space domain discretization, can be suppressed to a very low level when quadric polynomial bases are employed to construct the local enrichment functions, while the amount of numerical dispersion from the EFEM with other types of enrichment functions (linear polynomial bases or first order of trigonometric functions) is relatively large. Consequently, the present EFEM with a quadric polynomial enrichment function shows more powerful capacities in elastodynamic analysis than the other considered numerical techniques. More importantly, the attractive monotonic convergence property can be broadly realized by the present approach with the typical two-step Bathe temporal discretization technique. Three representative numerical experiments are conducted in this work to verify the abilities of the present approach in elastodynamic analysis.

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