Asymptotic normalization coefficients and astrophysical factors
International Nuclear Information System (INIS)
Mukhamedzhanov, A.M.; Azhari, A.; Clark, H.L.; Gagliardi, C.A.; Lui, Y.-W.; Sattarov, A.; Trache, L.; Tribble, R.E.; Burjan, V.; Kroha, V.; Carstoiu, F.
2000-01-01
The S factor for the direct capture reaction 7 Be(p,γ) 8 B can be found at astrophysical energies from the asymptotic normalization coefficients (ANC's) which provide the normalization of the tails of the overlap functions for 8 B → 7 Be + p. Peripheral transfer reactions offer a technique to determine these ANC's. Using this technique, the 10 B( 7 Be, 8 B) 9 Be and 14 N( 7 Be, 8 B) 13 C reactions have been used to measure the asymptotic normalization coefficient for 7 Be(p, γ) 8 B. These results provide an indirect determination of S 17 (0). Analysis of the existing 9 Be(p, γ) 10 B experimental data within the framework of the R-matrix method demonstrates that experimentally measured ANC's can provide a reasonable determination of direct radiative capture rates. (author)
Asymptotic normalization coefficients for 10B→9Be+p
International Nuclear Information System (INIS)
Mukhamedzhanov, A.M.; Clark, H.L.; Gagliardi, C.A.; Lui, Y.; Trache, L.; Tribble, R.E.; Xu, H.M.; Zhou, X.G.; Burjan, V.; Cejpek, J.; Kroha, V.; Carstoiu, F.
1997-01-01
The differential cross sections for the reactions 9 Be( 10 B, 10 B) 9 Be and 9 Be( 10 B, 9 Be) 10 B have been measured at an incident energy of 100 MeV. The elastic scattering data have been used to determine the optical model parameters for the 9 Be+ 10 B system at this energy. These parameters are then used in distorted-wave Born approximation (DWBA) calculations to predict the cross sections of the 9 Be( 10 B, 9 Be) 10 B proton exchange reaction, populating the ground and low-lying states in 10 B. By normalizing the theoretical DWBA proton exchange cross sections to the experimental ones, the asymptotic normalization coefficients (ANC's), defining the normalization of the tail of the 10 B bound state wave functions in the two-particle channel 9 Be+p, have been found. The ANC for the virtual decay 10 B(g.s.)→ 9 Be+p will be used in an analysis of the 10 B( 7 Be, 8 B) 9 Be reaction to extract the ANC's for 8 B→ 7 Be +p. These ANC's determine the normalization of the 7 Be(p,γ) 8 B radiative capture cross section at very low energies, which is crucially important for nuclear astrophysics. copyright 1997 The American Physical Society
Asymptotic normalization coefficients, nuclear vertex constants and nuclear astrophysics problems
International Nuclear Information System (INIS)
Yarmukhamedov, R.; Artemov, S.V.; Igamov, S.B.; Burtebaev, N.; Peterson, R.J.
2007-01-01
Full text: We will review the results of a comprehensive analysis of the experimental astrophysical S- factors S(E) for the t(α, γ ) 7 Li, 3 He(α, γ) 7 Be, 7 Be(p, γ) 8 B, 12 C(p , γ) 13 N and 13 C(p,γ) 14 N reactions at extremely low energies, performed within a three-sided collaboration (Uzbekistan-Kazakhstan-USA). In the analysis, the new experimental data for the 12 C(p, γ) 13 N reaction are also included, as measured with the accelerator UKP-2-1 at the Institute of Nuclear Physics in Kazakhstan. The analysis is carried out within the framework of a new two-body potential approach and the R-matrix method, taking into account information about the asymptotic normalization coefficient (ANC) (or the respective nuclear vertex constant for virtual decay of the residual nuclei into two fragments of the initial states of the aforesaid reactions, which belong to the fundamental nuclear constants). Nowadays ANC's are obtained from analysis of peripheral one nucleon transfer reactions by method combining dispersion theory and DWBA (CM). It is shown that ANC can be also reliably obtained from analysis of proton capture reactions at astrophysical energies by new modified two-body potential method where the CM is used. A comparative analysis of the results obtained by different authors in the framework of different methods is also done
Indirect Techniques in Nuclear Astrophysics. Asymptotic Normalization Coefficient and Trojan Horse
International Nuclear Information System (INIS)
Mukhamedzhanov, A.M.; Blokhintsev, L.D.; Brown, S.
2007-01-01
We address two important indirect techniques, the asymptotic normalization coefficient (ANC) and the Trojan Horse (TH) methods. We discuss the application of the ANC technique to determine the astrophysical factor for the 13 C(α, n) 16 O reaction which is one of the neutron generators for the s processes in AGB stars. The TH method is a unique indirect technique allowing one to measure astrophysical S factors for rearrangement reactions down to astrophysically relevant energies. We derive equations connecting the cross sections for the binary direct and resonant reactions determined from the indirect TH reactions to direct cross sections measurements
International Nuclear Information System (INIS)
Yarmukhamedov, R.; Baye, D.
2011-01-01
Explicit relations between the effective-range expansion and the nuclear vertex constant or asymptotic normalization coefficient (ANC) for the virtual decay B→A+a are derived for an arbitrary orbital momentum together with the corresponding location condition for the (A+a) bound-state energy. They are valid both for the charged case and for the neutral case. Combining these relations with the standard effective-range function up to order six makes it possible to reduce to two the number of free effective-range parameters if an ANC value is known from experiment. Values for the scattering length, effective range, and form parameter are determined in this way for the 16 O+p, α+t, and α+ 3 He collisions in partial waves where a bound state exists by using available ANCs deduced from experiments. The resulting effective-range expansions for these collisions are valid up to energies larger than 5 MeV.
Astrophysical S factor for 13C(p,γ)14N and asymptotic normalization coefficients
International Nuclear Information System (INIS)
Mukhamedzhanov, A.M.; Azhari, A.; Gagliardi, C.A.; Sattarov, A.; Tang, X.; Trache, L.; Tribble, R.E.; Burjan, V.; Kroha, V.
2002-01-01
We reanalyze the 13 C(p,γ) 14 N radiative capture reaction within the R-matrix approach. The low-energy astrophysical S factor has important contributions from both resonant and onresonant captures. The normalization of the nonresonant component of the transition to a particular 14 N bound state is expressed in terms of the asymptotic normalization coefficient (ANC). In the analysis we use the experimental ANC's inferred from the 13 C( 14 N, 13 C) 14 N and 13 C( 3 He,d) 14 N reactions. The fits of the calculated S factors to the experimental data are sensitive to the ANC values and are used to test the extracted ANC's. We find that for transitions to all the states in 14 N, except the third excited state, the ANC's determined from the transfer reactions provide the best fit. The astrophysical factor we obtain, S(0)=7.7±1.1 keV b, is in excellent agreement with previous results
Indirect techniques in nuclear astrophysics. Asymptotic normalization coefficient and trojan horse
International Nuclear Information System (INIS)
Mukhamedzhanov, A.M.; Gagliardi, C.A.; Pirlepesov, F.; Trache, L.; Tribble, R.E.; Blokhintsev, L.D.; Brown, B.A.; Nunes, F.M.; Burjan, V.; Kroha, V.; Cherubini, S.; Pizzone, R.G.; Romano, S.; Spitaleri, C.; Tumino, A.; Irgaziev, B.F.; Tang, X.D.
2006-01-01
Owing to the presence of the Coulomb barrier at astrophysically relevant kinetic energies it is very difficult, or sometimes impossible, to measure astrophysical reaction rates in the laboratory. That is why different indirect techniques are being used along with direct measurements. Here we address two important indirect techniques, the asymptotic normalization coefficient (ANC) and the Trojan Horse (TH) methods. We discuss the application of the ANC technique for calculation of the astrophysical processes in the presence of subthreshold bound states, in particular, two different mechanisms are discussed: direct capture to the subthreshold state and capture to the low-lying bound states through the subthreshold state, which plays the role of the subthreshold resonance. The ANC technique can also be used to determine the interference sign of the resonant and nonresonant (direct) terms of the reaction amplitude. The TH method is unique indirect technique allowing one to measure astrophysical rearrangement reactions down to astrophysically relevant energies. We explain why there is no Coulomb barrier in the sub-process amplitudes extracted from the TH reaction. The expressions for the TH amplitude for direct and resonant cases are presented. (orig.)
On the determination of the vertex constants and asymptotic normalization coefficients
International Nuclear Information System (INIS)
Blokhintsev, L.D.; Yeremenko, V.O.
2006-01-01
Full text: The nuclear vertex constant (VC) G abc is the on-shell matrix element of the virtual decay (or synthesis) of a composite system into fragments b and c: a↔ b+c. It is proportional to the asymptotic normalization coefficient (ANC) of the wave function of the system a in the b+c channel. VC's and ANC's are important nuclear characteristics. They determine the cross sections of low-energy nuclear reactions with charged particles, in particular, of the peripheral astrophysical nuclear reactions [1]. There are different methods to obtain information on the values of VC's and ANC's, either from the analysis of experimental data or by calculating them using approaches of nuclear structure theory. Some of these methods are described in the review article [2]. In the given work, the new method of determining VC's is suggested, which makes use both of the experimental information and of the analytical properties of the scattering amplitudes. We consider two integrals over k of the partial wave amplitude f l (k) of the elastic b+c scattering in the complex k plane, k being the relative momentum of b and c. In the first integral (I 1 ) f l (k) is integrated along the real k axis where its values could be in principle taken from the phase-shift analysis of the corresponding data. The integration path of the second integral (I 2 ) is chosen along the dynamical cut of f l (k), which is situated on the positive imaginary k semi-axis. The integrand of I 2 is the discontinuity of f l (k)on this cut. Its explicit form follows from the analytical properties of f l (k). If there exists the bound state a with the angular momentum l in the b+c system, then, according to the Cauchy theorem, the sum I 1 +I 2 is equal to 2πi res f 1 (k), where res f 1 (k) is the residue of f l (k) at the pole corresponding to the binding energy of a in the b+c channel. This residue is expressed directly in terms of the sought-for VC G abc [2]. The integration limits of I 1 and I 2 are infinite
Sub-Coulomb 3He transfer and its use to extract three-particle asymptotic normalization coefficients
Avila, M. L.; Baby, L. T.; Belarge, J.; Keeley, N.; Kemper, K. W.; Koshchiy, E.; Kuchera, A. N.; Rogachev, G. V.; Rusek, K.; Santiago-Gonzalez, D.
2018-01-01
Data for the 13C(6Li,t )16O reaction, obtained in inverse kinematics at a 13C incident energy of 7.72 MeV, are presented. A distorted wave Born approximation (DWBA) analysis was used to extract spectroscopic factors and asymptotic normalization coefficients (ANCs) for the 〈" close="〉6Li∣3He +3H 〉">16O∣13C +3He overlaps, subject to the assumption of a fixed ANCs as a function of various inputs to the DWBA calculations was explored. The extracted ANCs were found to vary as a cubic function of the radius of the potential well binding the transferred 3He to the 13C core while the spectroscopic factors varied as a quartic function of the radius. The ANC values could be determined to within a factor of two for this system.
International Nuclear Information System (INIS)
Timofeyuk, N.K.; Johnson, R.C.; Descouvemont, P.
2005-01-01
In this talk, relation between proton and neutron Asymptotic Normalization Coefficients (ANCs) for light mirror nuclei will be discussed. This relation follows from charge symmetry of nucleon-nucleon interactions and is given by a simple approximate analytical formula which involves proton and neutron separation energies, charges of residual nuclei and the range of their strong interaction with the last nucleon. This relation is valid both for particle-bound mirror nuclear levels and for mirror pairs in which one of the levels is a narrow resonance. In the latter case, the width of this resonance is related to the ANC of its mirror particle-stable analog. Our theoretical study of mirror ANCs for several light nuclei within a framework of microscopic two-, three- and four-cluster models, have shown that the ratio of mirror ANCs changes as predicted by the simple approximate analytical formula. We will also compare the results from our microscopic calculations to the predictions of the single-particle model and discuss mirror symmetry of spectroscopic factors and single-particle ANCs. (author)
International Nuclear Information System (INIS)
Timofeyuk, N.K.; Johnson, R.C.; Descouvemont, P.
2006-01-01
It has been realised recently that charge symmetry of the nucleon-nucleon interaction leads to a certain relation between Asymptotic Normalization Coefficients (ANCs) in mirror-conjugated one-nucleon overlap integrals. This relation can be approximated by a simple analytical formula that involves mirror neutron and proton separation energies, the core charge and the range of the strong nucleon-core interaction. We perform detailed microscopic multi-channel cluster model calculations and compare their predictions to the simple analytical formula as well as to calculations within a single-particle model in which mirror symmetry in potential wells and spectroscopic factors are assumed. The validity of the latter assumptions is verified on the basis of microscopic cluster model calculations. For mirror pairs in which one of the states is above the proton decay threshold, a link exists between the proton partial width and the ANC of the mirror neutron. This link is given by an approximate analytical formula similar to that for a bound-bound mirror pair. We compare predictions of this formula to the results of microscopic cluster model calculations. Mirror symmetry in ANCs can be used to predict cross sections for proton capture at stellar energies using neutron ANCs measured with stable or ''less radioactive'' beams. (orig.)
Czech Academy of Sciences Publication Activity Database
Tang, X.; Azhari, A.; Gagliardi, C. A.; Mukhamedzhanov, A. M.; Pirlepesov, F.; Trache, L.; Tribble, R. E.; Burjan, Václav; Kroha, Václav; Carstoiu, F.
č. 67 (2003), s. 015804-1 - 015804-9 ISSN 0556-2813 R&D Projects: GA ČR GA202/01/0709; GA MŠk ME 385; GA AV ČR KSK1048102 Institutional research plan: CEZ:AV0Z1048901 Keywords : S factor * asymptotic normalization coefficient Subject RIV: BG - Nuclear, Atomic and Molecular Physics, Colliders Impact factor: 2.708, year: 2003
Czech Academy of Sciences Publication Activity Database
Mukhamedzhanov, A. M.; Azhari, A.; Burjan, Václav; Gagliardi, C. A.; Kroha, Václav; Sattarov, A.; Tang, X.; Trache, L.; Tribble, R. E.
2003-01-01
Roč. 725, č. 725 (2003), s. 279-294 ISSN 0375-9474 R&D Projects: GA ČR GA202/01/0709; GA MŠk ME 385 Institutional research plan: CEZ:AV0Z1048901 Keywords : radiative capture reaction * asymptotic normalization coefficient Subject RIV: BG - Nuclear, Atomic and Molecular Physics, Colliders Impact factor: 1.761, year: 2003
Czech Academy of Sciences Publication Activity Database
Mukhamedzhanov, A. M.; Azhari, A.; Burjan, Václav; Gagliardi, C. A.; Kroha, Václav; Sattarov, A.; Tang, X.; Trache, L.; Tribble, R. E.
2003-01-01
Roč. 725, č. 22 (2003), s. 279-294 ISSN 0375-9474 R&D Projects: GA ČR GA202/01/0709; GA MŠk ME 385 Institutional research plan: CEZ:AV0Z1048901 Keywords : radiative capture reaction * asymptotic normalization coefficient Subject RIV: BG - Nuclear, Atomic and Molecular Physics, Colliders Impact factor: 1.761, year: 2003
International Nuclear Information System (INIS)
Guo Bing; Li Zhihong
2007-01-01
The angular distribution of the 13 C(d,p) 14 C reaction is reanalysed using the Johnson-Soper approach. The squared asymptotic normalization coefficient (ANC) of virtual decay 14 C→ 13 C + n is then derived to be 21.4 ± 5.0 fm -1 . The squared ANC and spectroscopic factor (SF) of 14 O→ 13 N + p are extracted to be 30.4 ± 7.1 fm -1 and 1.94 ± 0.45, respectively. The astrophysical S-factors and reaction rates of 13 N(p, γ) 14 O are determined from the ANC of 14 O→ 13 N + p using the R-matrix approach. (authors)
Asymptotic normalization coefficients for 14N+p→15O and the astrophysical S factor for 14N(p,γ)15O
International Nuclear Information System (INIS)
Mukhamedzhanov, A.M.; Gagliardi, C.A.; Pirlepesov, F.; Tribble, R.E.; Bem, P.; Burjan, V.; Kroha, V.; Novak, J.; Piskor, S.; Simeckova, E.; Vincour, J.; Brown, B.A.; Nunes, F.M.
2003-01-01
The 14 N(p,γ) 15 O reaction, which controls energy production in the CNO cycle, has contributions from both resonance and direct captures to the ground and excited states. The overall normalization of the direct captures is defined by the corresponding asymptotic normalization coefficients (ANCs). Especially important is the ANC for the subthreshold state in 15 O at -0.504 keV since direct capture through this state dominates the reaction rate at stellar energies. In order to determine the ANCs for 14 N+p→ 15 O, the 14 N( 3 He,d) 15 O proton transfer reaction has been measured at an incident energy of 26.3 MeV. Angular distributions for proton transfer to the ground and five excited states were obtained. ANCs were then extracted from comparison to both distorted-wave Born approximation and coupled-channels Born approximation calculations. Using these ANCs, we calculated the astrophysical factor and reaction rates for 14 N(p,γ) 15 O. Our analysis favors a low value for the astrophysical factor
International Nuclear Information System (INIS)
Igamov, S.B.; Yarmukhamedov, R.
2007-01-01
A modified two-body potential approach is proposed for determination of both the asymptotic normalization coefficient (ANC) (or the respective nuclear vertex constant (NVC)) for the A+a->B (for the virtual decay B->A+a) from an analysis of the experimental S-factor for the peripheral direct capture a+A->B+γ reaction and the astrophysical S-factor, S(E), at low experimentally inaccessible energy regions. The approach proposed involves two additional conditions which verify the peripheral character of the considered reaction and expresses S(E) in terms of the ANC. The connection between NVC (ANC) and the effective range parameters for Aa-scattering is derived. To test this approach we reanalyse the precise experimental astrophysical S-factors for t+α->Li7+γ reaction at energies E= Li7(g.s.), α+t->Li7(0.478 MeV) and of S(E) at E=<50 keV. These ANC values have been used for getting information about the ''indirect'' measured values of the effective range parameters and the p-wave phase shift for αt-scattering in the energy range of 100-bar E-bar 180 keV
International Nuclear Information System (INIS)
Mukhamedzhanov, A. M.; Gagliardi, C. A.; Goldberg, V. Z.; Plunkett, A.; Trache, L.; Tribble, R. E.; Bem, P.; Burjan, V.; Hons, Z.; Kroha, V.; Mrazek, J.; Novak, J.; Piskor, S.; Simeckova, E.; Vesely, F.; Vincour, J.; La Cognata, M.; Pizzone, R. G.; Romano, S.; Spitaleri, C.
2008-01-01
The 15 N(p,γ) 16 O reaction provides a path from the CN cycle to the CNO bi-cycle and CNO tri-cycle. The measured astrophysical factor for this reaction is dominated by resonant capture through two strong J π =1 - resonances at E R =312 and 962 keV and direct capture to the ground state. Asymptotic normalization coefficients (ANCs) for the ground and seven excited states in 16 O were extracted from the comparison of experimental differential cross sections for the 15 N( 3 He,d) 16 O reaction with distorted-wave Born approximation calculations. Using these ANCs and proton and α resonance widths determined from an R-matrix fit to the data from the 15 N(p,α) 12 C reaction, we carried out an R-matrix calculation to obtain the astrophysical factor for the 15 N(p,γ) 16 O reaction. The results indicate that the direct capture contribution was previously overestimated. We find the astrophysical factor to be S(0)=36.0±6.0 keV b, which is about a factor of 2 lower than the presently accepted value. We conclude that for every 2200±300 cycles of the main CN cycle one CN catalyst is lost due to this reaction
Czech Academy of Sciences Publication Activity Database
McCleskey, M.; Mukhamedzhanov, A. M.; Trache, L.; Tribble, R. E.; Banu, A.; Eremenko, V.; Goldberg, V. Z.; Lui, Y. W.; McCleskey, E.; Roeder, B. T.; Spiridon, A.; Carstoiu, F.; Burjan, Václav; Hons, Zdeněk; Thompson, I. J.
2014-01-01
Roč. 89, č. 4 (2014), 044605 ISSN 0556-2813 R&D Projects: GA MŠk(CZ) LH11001 Institutional support: RVO:61389005 Keywords : capture reactions * cross-section * asymptotic normalization coefficient Subject RIV: BG - Nuclear, Atomic and Molecular Physics, Colliders Impact factor: 3.733, year: 2014
International Nuclear Information System (INIS)
Al-Abdullah, T.; Carstoiu, F.; Chen, X.; Clark, H. L.; Fu, C.; Gagliardi, C. A.; Lui, Y.-W.; Mukhamedzhanov, A.; Tabacaru, G.; Tokimoto, Y.; Trache, L.; Tribble, R. E.
2010-01-01
The production of 22 Na in ONe novae can be influenced by the 22 Mg(p,γ) 23 Al reaction. To investigate this reaction rate at stellar energies, we have determined the asymptotic normalization coefficient (ANC) for 22 Mg+p→ 23 Al through measurements of the ANCs in the mirror nuclear system 22 Ne+n→ 23 Ne. The peripheral neutron-transfer reactions 13 C( 12 C, 13 C) 12 C and 13 C( 22 Ne, 23 Ne) 12 C were studied. The identical entrance and exit channels of the first reaction make it possible to extract independently the ground-state ANC in 13 C. Our experiment gives C p 1/2 2 ( 13 C)=2.24±0.11 fm -1 , which agrees with the value obtained from several previous measurements. The weighted average for all the obtained C p 1/2 2 is 2.31±0.08 fm -1 . This value is adopted to be used in obtaining the ANCs in 23 Ne. The differential cross sections for the reaction 13 C( 22 Ne, 23 Ne) 12 C leading to the J π =5/2 + and 1/2 + states in 23 Ne have been measured at 12 MeV/u. Optical model parameters for use in the DWBA calculations were obtained from measurements of the elastic scatterings 22 Ne+ 13 C and 22 Ne+ 12 C. The extracted ANC for the ground state in 23 Ne, C d 5/2 2 =0.86±0.08±0.12 fm -1 , is converted to its corresponding value in 23 Al using mirror symmetry to give C d 5/2 2 ( 23 Al)=(4.63±0.77)x10 3 fm -1 . The astrophysical S factor S(0) for the 22 Mg(p,γ) reaction was determined to be 0.96±0.11 keV b. The consequences for nuclear astrophysics are discussed.
Trinucleon asymptotic normalization constants including Coulomb effects
International Nuclear Information System (INIS)
Friar, J.L.; Gibson, B.F.; Lehman, D.R.; Payne, G.L.
1982-01-01
Exact theoretical expressions for calculating the trinucleon S- and D-wave asymptotic normalization constants, with and without Coulomb effects, are presented. Coordinate-space Faddeev-type equations are used to generate the trinucleon wave functions, and integral relations for the asymptotic norms are derived within this framework. The definition of the asymptotic norms in the presence of the Coulomb interaction is emphasized. Numerical calculations are carried out for the s-wave NN interaction models of Malfliet and Tjon and the tensor force model of Reid. Comparison with previously published results is made. The first estimate of Coulomb effects for the D-wave asymptotic norm is given. All theoretical values are carefully compared with experiment and suggestions are made for improving the experimental situation. We find that Coulomb effects increase the 3 He S-wave asymptotic norm by less than 1% relative to that of 3 H, that Coulomb effects decrease the 3 He D-wave asymptotic norm by approximately 8% relative to that of 3 H, and that the distorted-wave Born approximation D-state parameter, D 2 , is only 1% smaller in magnitude for 3 He than for 3 H due to compensating Coulomb effects
Generalized heat kernel coefficients for a new asymptotic expansion
International Nuclear Information System (INIS)
Osipov, Alexander A.; Hiller, Brigitte
2003-01-01
The method which allows for asymptotic expansion of the one-loop effective action W = lndetA is formulated. The positively defined elliptic operator A = U + M2 depends on the external classical fields taking values in the Lie algebra of the internal symmetry group G. Unlike the standard method of Schwinger - DeWitt, the more general case with the nongenerate mass matrix M = diag(m1, m2, ...) is considered. The first coefficients of the new asymptotic series are calculated and their relationship with the Seeley - DeWitt coefficients is clarified
Asymptotic normalization coefficients in nuclear astrophysics
Czech Academy of Sciences Publication Activity Database
Kroha, Václav; Azhari, A.; Bém, Pavel; Burjan, Václav; Gagliardi, C. A.; Mukhamedzhanov, A. M.; Novák, Jan; Piskoř, Štěpán; Šimečková, Eva; Tang, X.; Trache, L.; Tribble, R. E.; Vincour, Jiří
2003-01-01
Roč. 719, - (2003), s. 119C-122C ISSN 0375-9474 R&D Projects: GA ČR GA202/01/0709; GA AV ČR KSK1048102 Institutional research plan: CEZ:AV0Z1048901 Keywords : S-factor * C-13(p,gamma)N-14 * Be-9(p, gamma)B-10 Subject RIV: BG - Nuclear, Atomic and Molecular Physics, Colliders Impact factor: 1.761, year: 2003
International Nuclear Information System (INIS)
Igamov, S.B.; Yarmukhamedov, R.
2007-01-01
Full text: The 7 Be(p,γ) 8 B reaction rate given by in terms of the zero-energy astrophysical S-factor S(0) is one of the main input data in the solar neutrino problem because the high energy neutrinos are produced via the decay 8 B→ 7 Be+e + + n e . This quantity is determined by both extrapolating the measured absolute cross sections σexp (E) (or equivalently its experimental S-factors S exp (E) ) to solar energies (≅ 25 keV) and the theoretical predictions. Despite the steady and impressive progress in our understanding of this reaction have been made in last years in measurements S exp (E) at extremely low energies and the theoretical predictions S(E) at solar energies (E≤25 keV), ambiguities (up to about 35%) associated with prediction for S(0) however still exist, and it may considerably influence the predictions of the standard solar model. In this work the modified two - body potential approach is applied for a new analysis of the highly precise experimental astrophysical S-factors for the direct capture 7 Be(p, γ) 8 B reaction at E≤400 keV and 1000≤E≤1200 keV to obtain 'indirectly measured' values both of the asymptotic normalization coefficient (ANC) for the p+ 7 Be→ 8 B and of S(E) at E≤115 keV, including E=0. In this approach S(E) is expressed in the terms of ANC C Aα;lj 2 but not in the terms of the usual spectroscopic factor Z Aα;lj , which is related to the ANC C Aα;l. j as Z aα;lj =C Aα;lj 2 /b lj 2 , where b lj is the single-particle ANC for the wave function of the bound 8 B( 7 Be+p) state calculated within the shell model using the phenomenological Woods-Saxon potential with the geometric parameters (a radius r o and a diffuseness a). The approach allows one to remove the model dependence of the calculated direct on S(E) on the geometric parameters r o and a both for the two-body bound ( 7 Be+p) state and the p 7 Be- scattering state in minimum. The analysis of the experimental S exp (E) is performed by verifying values of
The least weighted squares II. Consistency and asymptotic normality
Czech Academy of Sciences Publication Activity Database
Víšek, Jan Ámos
2002-01-01
Roč. 9, č. 16 (2002), s. 1-28 ISSN 1212-074X R&D Projects: GA AV ČR KSK1019101 Grant - others:GA UK(CR) 255/2000/A EK /FSV Institutional research plan: CEZ:AV0Z1075907 Keywords : robust regression * consistency * asymptotic normality Subject RIV: BA - General Mathematics
Quantum local asymptotic normality and other questions of quantum statistics
Kahn, Jonas
2008-01-01
This thesis is entitled Quantum Local Asymptotic Normality and other questions of Quantum Statistics ,. Quantum statistics are statistics on quantum objects. In classical statistics, we usually start from the data. Indeed, if we want to predict the weather, and can measure the wind or the
Energy Technology Data Exchange (ETDEWEB)
McCleskey, M; Mukhamedzhanov, A M; Trache, L; Tribble, R E; Banu, A; Eremenko, V; Goldberg, V Z; Lui, Y W; McCleskey, E; Roeder, B T; Spiridon, A; Carstoiu, F; Burjan, V; Hons, Z; Thompson, I J
2014-04-17
The ^{14}C + n <--> ^{15}C system has been used as a test case in the evaluation of a new method to determine spectroscopic factors that uses the asymptotic normalization coefficient (ANC). The method proved to be unsuccessful for this case. As part of this experimental program, the ANCs for the ^{15}C ground state and first excited state were determined using a heavy-ion neutron transfer reaction as well as the inverse kinematics (d,p) reaction, measured at the Texas A&M Cyclotron Institute. The ANCs were used to evaluate the astrophysical direct neutron capture rate on ^{14}C, which was then compared with the most recent direct measurement and found to be in good agreement. A study of the ^{15}C SF via its mirror nucleus ^{15}F and a new insight into deuteron stripping theory are also presented.
Lq-perturbations of leading coefficients of elliptic operators: Asymptotics of eigenvalues
Directory of Open Access Journals (Sweden)
Vladimir Kozlov
2006-01-01
Full Text Available We consider eigenvalues of elliptic boundary value problems, written in variational form, when the leading coefficients are perturbed by terms which are small in some integral sense. We obtain asymptotic formulae. The main specific of these formulae is that the leading term is different from that in the corresponding formulae when the perturbation is small in L∞-norm.
Sharp Spectral Asymptotics and Weyl Formula for Elliptic Operators with Non-smooth Coefficients
Energy Technology Data Exchange (ETDEWEB)
Zielinski, Lech [Universite Paris 7 (D. Diderot), Institut de Mathematiques de Paris-Jussieu UMR9994 (France)
1999-09-15
The aim of this paper is to give the Weyl formula for eigenvalues of self-adjoint elliptic operators, assuming that first-order derivatives of the coefficients are Lipschitz continuous. The approach is based on the asymptotic formula of Hoermander''s type for the spectral function of pseudo differential operators having Lipschitz continuous Hamiltonian flow and obtained via a regularization procedure of nonsmooth coefficients.
Sharp Spectral Asymptotics and Weyl Formula for Elliptic Operators with Non-smooth Coefficients
International Nuclear Information System (INIS)
Zielinski, Lech
1999-01-01
The aim of this paper is to give the Weyl formula for eigenvalues of self-adjoint elliptic operators, assuming that first-order derivatives of the coefficients are Lipschitz continuous. The approach is based on the asymptotic formula of Hoermander''s type for the spectral function of pseudo differential operators having Lipschitz continuous Hamiltonian flow and obtained via a regularization procedure of nonsmooth coefficients
Asymptotic normalization coefficients in nuclear astrophysics an structure
Czech Academy of Sciences Publication Activity Database
Gagliardi, C. A.; Azhari, A.; Burjan, Václav; Carstoiu, F.; Kroha, Václav; Mukhamedzhanov, A. M.; Sattarov, A.; Tang, X.; Trache, L.; Tribble, R. E.
2002-01-01
Roč. 15, 1/2 (2002), s. 69-73 ISSN 1434-6001 R&D Projects: GA MŠk ME 385; GA ČR GA202/01/0709 Keywords : cross-section measurements * optical-model * S-factor * breakup * B-8 * halo * coulomb * Be-7 Subject RIV: BG - Nuclear, Atomic and Molecular Physics, Colliders Impact factor: 1.657, year: 2002
A simple approximation to the bivariate normal distribution with large correlation coefficient
Albers, Willem/Wim; Kallenberg, W.C.M.
1994-01-01
The bivariate normal distribution function is approximated with emphasis on situations where the correlation coefficient is large. The high accuracy of the approximation is illustrated by numerical examples. Moreover, exact upper and lower bounds are presented as well as asymptotic results on the
A Review on asymptotic normality of sums of associated random ...
African Journals Online (AJOL)
Association between random variables is a generalization of independence of these random variables. This concept is more and more commonly used in current trends in any research elds in Statistics. In this paper, we proceed to a simple, clear and rigorous introduction to it. We will present the fundamental asymptotic ...
Orlov, Yu. V.; Irgaziev, B. F.; Nabi, Jameel-Un
2017-08-01
A new algorithm for the asymptotic nuclear coefficients calculation, which we call the Δ method, is proved and developed. This method was proposed by Ramírez Suárez and Sparenberg (arXiv:1602.04082.) but no proof was given. We apply it to the bound state situated near the channel threshold when the Sommerfeld parameter is quite large within the experimental energy region. As a result, the value of the conventional effective-range function Kl(k2) is actually defined by the Coulomb term. One of the resulting effects is a wrong description of the energy behavior of the elastic scattering phase shift δl reproduced from the fitted total effective-range function Kl(k2) . This leads to an improper value of the asymptotic normalization coefficient (ANC) value. No such problem arises if we fit only the nuclear term. The difference between the total effective-range function and the Coulomb part at real energies is the same as the nuclear term. Then we can proceed using just this Δ method to calculate the pole position values and the ANC. We apply it to the vertices 4He+12C ↔16O and 3He+4He↔7Be . The calculated ANCs can be used to find the radiative capture reaction cross sections of the transfers to the 16O bound final states as well as to the 7Be.
Ma, Rubao; Xu, Weichao; Zhang, Yun; Ye, Zhongfu
2014-01-01
This paper investigates the robustness properties of Pearson's rank-variate correlation coefficient (PRVCC) in scenarios where one channel is corrupted by impulsive noise and the other is impulsive noise-free. As shown in our previous work, these scenarios that frequently encountered in radar and/or sonar, can be well emulated by a particular bivariate contaminated Gaussian model (CGM). Under this CGM, we establish the asymptotic closed forms of the expectation and variance of PRVCC by means of the well known Delta method. To gain a deeper understanding, we also compare PRVCC with two other classical correlation coefficients, i.e., Spearman's rho (SR) and Kendall's tau (KT), in terms of the root mean squared error (RMSE). Monte Carlo simulations not only verify our theoretical findings, but also reveal the advantage of PRVCC by an example of estimating the time delay in the particular impulsive noise environment.
Integral relations for the asymptotic normalization of the triton
International Nuclear Information System (INIS)
Kim, Y.E.; Sander, C.; Tubis, A.
1976-01-01
Lehman and Gibson have recently derived an integral relation for C/sub t/, the normalization of the n-d tail of the triton wave function. We give (1) a concise alternative derivation of the Lehman-Gibson result, and (2) an explicit evaluation of C/sub t/ in momentum space for the case in which the two-body interaction is not purely local or purely separable. This evaluation in general involves a five dimensional integration
A note on asymptotic normality in the thermodynamic limit at low densities
DEFF Research Database (Denmark)
Jensen, J.L.
1991-01-01
We consider a continuous statistical mechanical system with a pair interaction in a region λ tending to infinity. For low densities asymptotic normality of the canonical statistic is proved, both in the grand canonical ensemble and in the canonical ensemble. The results are illustrated through...
Afrika Statistika ISSN 2316-090X Asymptotic normality of non ...
African Journals Online (AJOL)
We solved an open problem arising in mentioned paper. The asymptotic normality of the estimator is established. As an ... population with continuous density (pdf) f(x) at a point x on a given probability space. (Ω, A, P). The FGT .... In (1) h = h(n) is a positive nonrandom sequences of real numbers tending to zero as n tends to ...
Asymptotic normality of kernel estimator of $\\psi$-regression function for functional ergodic data
Laksaci ALI; Benziadi Fatima; Gheriballak Abdelkader
2016-01-01
In this paper we consider the problem of the estimation of the $\\psi$-regression function when the covariates take values in an infinite dimensional space. Our main aim is to establish, under a stationary ergodic process assumption, the asymptotic normality of this estimate.
International Nuclear Information System (INIS)
Lomnitz-Adler, J.; Brink, D.M.
1976-01-01
A generating function for the eigenvalues of the RGM Normalization Kernel is expressed in terms of the diagonal matrix elements of thw GCM Overlap Kernel. An asymptotic expression for the eigenvalues is obtained by using the Method of Steepest Descent. (Auth.)
Shahshahani, Behzad M.; Landgrebe, David A.
1992-01-01
The effect of additional unlabeled samples in improving the supervised learning process is studied in this paper. Three learning processes. supervised, unsupervised, and combined supervised-unsupervised, are compared by studying the asymptotic behavior of the estimates obtained under each process. Upper and lower bounds on the asymptotic covariance matrices are derived. It is shown that under a normal mixture density assumption for the probability density function of the feature space, the combined supervised-unsupervised learning is always superior to the supervised learning in achieving better estimates. Experimental results are provided to verify the theoretical concepts.
Fisher information and asymptotic normality in system identification for quantum Markov chains
International Nuclear Information System (INIS)
Guta, Madalin
2011-01-01
This paper deals with the problem of estimating the coupling constant θ of a mixing quantum Markov chain. For a repeated measurement on the chain's output we show that the outcomes' time average has an asymptotically normal (Gaussian) distribution, and we give the explicit expressions of its mean and variance. In particular, we obtain a simple estimator of θ whose classical Fisher information can be optimized over different choices of measured observables. We then show that the quantum state of the output together with the system is itself asymptotically Gaussian and compute its quantum Fisher information, which sets an absolute bound to the estimation error. The classical and quantum Fisher information are compared in a simple example. In the vicinity of θ=0 we find that the quantum Fisher information has a quadratic rather than linear scaling in output size, and asymptotically the Fisher information is localized in the system, while the output is independent of the parameter.
Confidence bounds for normal and lognormal distribution coefficients of variation
Steve Verrill
2003-01-01
This paper compares the so-called exact approach for obtaining confidence intervals on normal distribution coefficients of variation to approximate methods. Approximate approaches were found to perform less well than the exact approach for large coefficients of variation and small sample sizes. Web-based computer programs are described for calculating confidence...
Energy Technology Data Exchange (ETDEWEB)
Prior, C R [Cambridge Univ. (UK). Dept. of Applied Mathematics and Theoretical Physics
1977-06-27
Angular momentum in axisymmetric space-times is investigated. The conclusions lead to a general definition suitable for all asymptotically-flat spaces which is valid both at infinity and on the event horizon of a black hole. This first paper restricts attention to considerations at infinity. Working in terms of the spin coefficient formalism, the field equations are solved asymptotically at large distances and the definition is evaluated. A conservation law is derived and finally the effect on the angular momentum of a supertranslation of the coordinates is discussed.
Determination of rolling resistance coefficient based on normal tyre stiffness
Rykov, S. P.; Tarasuyk, V. N.; Koval, V. S.; Ovchinnikova, N. I.; Fedotov, A. I.; Fedotov, K. V.
2018-03-01
The purpose of the article is to develop analytical dependence of wheel rolling resistance coefficient based on the mathematical description of normal tyre stiffness. The article uses the methods of non-holonomic mechanics and plane section methods. The article shows that the abscissa of gravity center of tyre stiffness expansion by the length of the contact area is the shift of normal road response. It can be used for determining rolling resistance coefficient. When determining rolling resistance coefficient using ellipsis and power function equations, one can reduce labor costs for testing and increase assessment accuracy.
The least weighted squares I. The asymptotic linearity of normal equations
Czech Academy of Sciences Publication Activity Database
Víšek, Jan Ámos
2002-01-01
Roč. 9, č. 15 (2002), s. 31-58 ISSN 1212-074X R&D Projects: GA AV ČR KSK1019101 Grant - others:GA UK(CZ) 255/2002/A EK /FSV Institutional research plan: CEZ:AV0Z1075907 Keywords : the least weighted squares * robust regression * asymptotic normality and representation Subject RIV: BA - General Mathematics
Asymptotic Normality of the Optimal Solution in Multiresponse Surface Mathematical Programming
Díaz-García, José A.; Caro-Lopera, Francisco J.
2015-01-01
An explicit form for the perturbation effect on the matrix of regression coeffi- cients on the optimal solution in multiresponse surface methodology is obtained in this paper. Then, the sensitivity analysis of the optimal solution is studied and the critical point characterisation of the convex program, associated with the optimum of a multiresponse surface, is also analysed. Finally, the asymptotic normality of the optimal solution is derived by the standard methods.
Coefficient of restitution of sports balls: A normal drop test
International Nuclear Information System (INIS)
Haron, Adli; Ismail, K A
2012-01-01
Dynamic behaviour of bodies during impact is investigated through impact experiment, the simplest being a normal drop test. Normally, a drop test impact experiment involves measurement of kinematic data; this includes measurement of incident and rebound velocity in order to calculate a coefficient of restitution (COR). A high speed video camera is employed for measuring the kinematic data where speed is calculated from displacement of the bodies. Alternatively, sensors can be employed to measure speeds, especially for a normal impact where there is no spin of the bodies. This paper compares experimental coefficients of restitution (COR) for various sports balls, namely golf, table tennis, hockey and cricket. The energy loss in term of measured COR and effects of target plate are discussed in relation to the material and construction of these sports balls.
International Nuclear Information System (INIS)
Paris, R.B.; Wood, A.D.
1984-11-01
The asymptotic expansions of solutions of a class of linear ordinary differential equations of arbitrary order n, containing a factor zsup(m) multiplying the lower order derivatives, are investigated for large values of z in the complex plane. Four classes of solutions are considered which exhibit the following behaviour as /z/ → infinity in certain sectors: (i) solutions whose behaviour is either exponentially large or algebraic (involving p ( < n) algebraic expansions), (ii) solutions which are exponentially small (iii) solutions with a single algebraic expansion and (iv) solutions which are even and odd functions of z whenever n+m is even. The asymptotic expansions of these solutions in a full neigbourhood of the point at infinity are obtained by means of the theory of the solutions in the case m=O developed in a previous paper
Study of apparent diffusion coefficient value in the normal breastq
International Nuclear Information System (INIS)
Cai Shifeng
2007-01-01
Objective: To investigate the differences of apparent diffusion coefficient (ADC) value in normal breasts and to evaluate the correlation between ADC value and corresponding histology. Methods: Sixty-two normal breasts including 42 normal breasts of 42 patients with unilateral lesions and 20 normal breasts of 10 volunteers were studied. The ADC value of all 62 normal breasts were calculated when b value was given from 1000 to 0 s/mm 2 , 1000 to 500 s/mm 2 and 500 to 0 s/mm 2 . The MRI features of 60 normal breasts were classified into 3 types (dense, lobular-speckled, degenerative types) according to Wolf's classification and histology. Results: DWI and ADC images were different in 3 types of normal breasts because of different histologic structures. The mean ADC value of the dense type breasts was (1.70 ± 0.37) x 10 -3 mm 2 /s, the lobular-speckled type was (1.93 ± 0.46) x 10 -3 mm 2 /s and the degenerative type was (1.18 ± 0.65) x 10 -3 mm 2 /s (F=12.998, P=0.000). There were no significant differences between the dense type and the lobular-speckled type (F=2.167, P=0.147), but significant differences between the dense type and the degenerative type, the lobular-speckled type and the degenerate type (F=5.593 and 19.128; P=0.029 and 0.000). When b value decreased, the ADC value of the dense type and the lobular-speckled type increased correspondingly, but the degenerative type didn't increase apparently. Conclusion: ADC value was influenced by histologic structures in normal breasts and also was influenced by b value in the dense type and lobular-speckled type breasts. (authors)
A New Family of Consistent and Asymptotically-Normal Estimators for the Extremal Index
Directory of Open Access Journals (Sweden)
Jose Olmo
2015-08-01
Full Text Available The extremal index (θ is the key parameter for extending extreme value theory results from i.i.d. to stationary sequences. One important property of this parameter is that its inverse determines the degree of clustering in the extremes. This article introduces a novel interpretation of the extremal index as a limiting probability characterized by two Poisson processes and a simple family of estimators derived from this new characterization. Unlike most estimators for θ in the literature, this estimator is consistent, asymptotically normal and very stable across partitions of the sample. Further, we show in an extensive simulation study that this estimator outperforms in finite samples the logs, blocks and runs estimation methods. Finally, we apply this new estimator to test for clustering of extremes in monthly time series of unemployment growth and inflation rates and conclude that runs of large unemployment rates are more prolonged than periods of high inflation.
Asymptotic Normality of the Maximum Pseudolikelihood Estimator for Fully Visible Boltzmann Machines.
Nguyen, Hien D; Wood, Ian A
2016-04-01
Boltzmann machines (BMs) are a class of binary neural networks for which there have been numerous proposed methods of estimation. Recently, it has been shown that in the fully visible case of the BM, the method of maximum pseudolikelihood estimation (MPLE) results in parameter estimates, which are consistent in the probabilistic sense. In this brief, we investigate the properties of MPLE for the fully visible BMs further, and prove that MPLE also yields an asymptotically normal parameter estimator. These results can be used to construct confidence intervals and to test statistical hypotheses. These constructions provide a closed-form alternative to the current methods that require Monte Carlo simulation or resampling. We support our theoretical results by showing that the estimator behaves as expected in simulation studies.
Confidence bounds and hypothesis tests for normal distribution coefficients of variation
Steve Verrill; Richard A. Johnson
2007-01-01
For normally distributed populations, we obtain confidence bounds on a ratio of two coefficients of variation, provide a test for the equality of k coefficients of variation, and provide confidence bounds on a coefficient of variation shared by k populations.
Rates of convergence and asymptotic normality of curve estimators for ergodic diffusion processes
J.H. van Zanten (Harry)
2000-01-01
textabstractFor ergodic diffusion processes, we study kernel-type estimators for the invariant density, its derivatives and the drift function. We determine rates of convergence and find the joint asymptotic distribution of the estimators at different points.
Energy Technology Data Exchange (ETDEWEB)
Ablinger, J.; Hasselhuhn, A.; Schneider, C. [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation (RISC); Bluemlein, J.; Freitas, A. de [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Wissbrock, F. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation (RISC); IHES, Bures-sur-Yvette (France)
2017-05-15
Starting at 3-loop order, the massive Wilson coefficients for deep-inelastic scattering and the massive operator matrix elements describing the variable flavor number scheme receive contributions of Feynman diagrams carrying quark lines with two different masses. In the case of the charm and bottom quarks, the usual decoupling of one heavy mass at a time no longer holds, since the ratio of the respective masses, η=m{sup 2}{sub c}/m{sup 2}{sub b}∝1/10, is not small enough. Therefore, the usual variable flavor number scheme (VFNS) has to be generalized. The renormalization procedure in the two-mass case is different from the single mass case derived earlier (I. Bierenbaum, J: Bluemlein, S. Klein, 2009). We present the moments N=2,4 and 6 for all contributing operator matrix elements, expanding in the ratio η. We calculate the analytic results for general values of the Mellin variable N in the flavor non-singlet case, as well as for transversity and the matrix element A{sup (3)}{sub gq}. We also calculate the two-mass scalar integrals of all topologies contributing to the gluonic operator matrix element A{sub gg}. As it turns out, the expansion in η is usually inapplicable for general values of N. We therefore derive the result for general values of the mass ratio. From the single pole terms we derive, now in a two-mass calculation, the corresponding contributions to the 3-loop anomalous dimensions. We introduce a new general class of iterated integrals and study their relations and present special values. The corresponding functions are implemented in computer-algebraic form.
Directory of Open Access Journals (Sweden)
J. Ablinger
2017-08-01
Full Text Available Starting at 3-loop order, the massive Wilson coefficients for deep-inelastic scattering and the massive operator matrix elements describing the variable flavor number scheme receive contributions of Feynman diagrams carrying quark lines with two different masses. In the case of the charm and bottom quarks, the usual decoupling of one heavy mass at a time no longer holds, since the ratio of the respective masses, η=mc2/mb2∼1/10, is not small enough. Therefore, the usual variable flavor number scheme (VFNS has to be generalized. The renormalization procedure in the two-mass case is different from the single mass case derived in [1]. We present the moments N=2,4 and 6 for all contributing operator matrix elements, expanding in the ratio η. We calculate the analytic results for general values of the Mellin variable N in the flavor non-singlet case, as well as for transversity and the matrix element Agq(3. We also calculate the two-mass scalar integrals of all topologies contributing to the gluonic operator matrix element Agg. As it turns out, the expansion in η is usually inapplicable for general values of N. We therefore derive the result for general values of the mass ratio. From the single pole terms we derive, now in a two-mass calculation, the corresponding contributions to the 3-loop anomalous dimensions. We introduce a new general class of iterated integrals and study their relations and present special values. The corresponding functions are implemented in computer-algebraic form.
Ramírez Suárez, O. L.; Sparenberg, J.-M.
2017-09-01
We introduce a simplified effective-range function for charged nuclei, related to the modified K matrix but differing from it in several respects. Negative-energy zeros of this function correspond to bound states. Positive-energy zeros correspond to resonances and "echo poles" appearing in elastic-scattering phase-shifts, while its poles correspond to multiple-of-π phase shifts. Padé expansions of this function allow one to parametrize phase shifts on large energy ranges and to calculate resonance and bound-state properties in a very simple way, independently of any potential model. The method is first tested on a d -wave 12C+α potential model. It is shown to lead to a correct estimate of the subthreshold-bound-state asymptotic normalization constant (ANC) starting from the elastic-scattering phase shifts only. Next, the 12C+α experimental p -wave and d -wave phase shifts are analyzed. For the d wave, the relatively large error bars on the phase shifts do not allow one to improve the ANC estimate with respect to existing methods. For the p wave, a value agreeing with the 12C(6Li,d )16O transfer-reaction measurement and with the recent remeasurement of the 16Nβ -delayed α decay is obtained, with improved accuracy. However, the method displays two difficulties: the results are sensitive to the Padé-expansion order and the simplest fits correspond to an imaginary ANC, i.e., to a negative-energy "echo pole," the physical meaning of which is still debatable.
Shin, Hyun Kyung; Choi, Bongsik; Talkner, Peter; Lee, Eok Kyun
2014-12-01
Based on the generalized Langevin equation for the momentum of a Brownian particle a generalized asymptotic Einstein relation is derived. It agrees with the well-known Einstein relation in the case of normal diffusion but continues to hold for sub- and super-diffusive spreading of the Brownian particle's mean square displacement. The generalized asymptotic Einstein relation is used to analyze data obtained from molecular dynamics simulations of a two-dimensional soft disk fluid. We mainly concentrated on medium densities for which we found super-diffusive behavior of a tagged fluid particle. At higher densities a range of normal diffusion can be identified. The motion presumably changes to sub-diffusion for even higher densities.
2009-01-01
Abstract A kernel estimator of the conditional quantile is defined for a scalar response variable given a covariate taking values in a semi-metric space. The approach generalizes the median?s L1-norm estimator. The almost complete consistency and asymptotic normality are stated. correspondance: Corresponding author. Tel: +33 320 964 933; fax: +33 320 964 704. (Lemdani, Mohamed) (Laksaci, Ali) mohamed.lemdani@univ-lill...
Astrophysical S factor C-13(p,gamma)N-14 and asymptotic normalization coefficients
Czech Academy of Sciences Publication Activity Database
Mukhamedzhanov, A. M.; Azhari, A.; Burjan, Václav; Gagliardi, C. A.; Kroha, Václav; Sattarov, A.; Tang, X.; Trache, L.; Tribble, R. E.
2002-01-01
Roč. 66, č. 2 (2002), s. 027602 ISSN 0556-2813 R&D Projects: GA MŠk ME 385; GA ČR GA202/01/0709 Keywords : thermonuclear reaction-rates Subject RIV: BG - Nuclear, Atomic and Molecular Physics, Colliders Impact factor: 2.848, year: 2002
Indirect techniques in nuclear astrophysics. Asymptotic normalization coefficient and Trojan Horse
Czech Academy of Sciences Publication Activity Database
Mukhamedzhanov, A. M.; Blokhintsev, L.D.; Brown, S.; Burjan, Václav; Kroha, Václav
2007-01-01
Roč. 787, - (2007), 321C-328C ISSN 0375-9474 Institutional research plan: CEZ:AV0Z10480505 Keywords : VERTEX CONSTANT * S-factor Subject RIV: BE - Theoretical Physics Impact factor: 3.096, year: 2007
Czech Academy of Sciences Publication Activity Database
Gagliardi, C. A.; Azhari, A.; Burjan, Václav; Carstoiu, F.; Kroha, Václav; Mukhamedzhanov, A. M.; Tang, X.; Trache, L.; Tribble, R. E.
2001-01-01
Roč. 688, - (2001), s. 536c-538c ISSN 0375-9474 R&D Projects: GA ČR GA202/01/0709; GA MŠk ME 385; GA AV ČR KSK1048102 Subject RIV: BG - Nuclear, Atomic and Molecular Physics, Colliders Impact factor: 2.074, year: 2001
Asymptotic normalization coefficients from direct transfer reactions and astrophysical S factors
Czech Academy of Sciences Publication Activity Database
Gagliardi, C. A.; Azhari, A.; Bém, Pavel; Burjan, Václav; Carstoiu, F.; Cejpek, Jan; Clark, H. L.; Kroha, Václav; Lui, Z. W.; Mukhamedzhanov, A. M.; Novák, Jan; Piskoř, Štěpán; Sattarov, A.; Šimečková, Eva; Tang, X.; Trache, L.; Tribble, R. E.; Vincour, Jiří
2001-01-01
Roč. 682, - (2001), s. 369C-374C ISSN 0375-9474 R&D Projects: GA ČR GA202/01/0709; GA AV ČR KSK1048102 Subject RIV: BG - Nuclear, Atomic and Molecular Physics, Colliders Impact factor: 2.074, year: 2001
Asymptotic normalization coefficients from the (14)C(d,p)(15)C reaction
Czech Academy of Sciences Publication Activity Database
Mukhamedzhanov, A.; Burjan, Václav; Gulino, M.; Hons, Zdeněk; Kroha, Václav; McCleskey, M.; Mrázek, Jaromír; Nguyen, N.; Nunes, FM.; Piskoř, Štěpán; Romano, S.; Sergi, M. L.; Spitaleri, C.; Tribble, R. E.
2011-01-01
Roč. 84, č. 2 (2011), 024616/1-024616/6 ISSN 0556-2813 R&D Projects: GA MŠk LC07050; GA ČR GAP203/10/0310 Institutional research plan: CEZ:AV0Z10480505 Keywords : NUCLEI Subject RIV: CA - Inorganic Chemistry Impact factor: 3.308, year: 2011
Energy Technology Data Exchange (ETDEWEB)
Behring, A.; Bluemlein, J.; Freitas, A. de [Deutsches Elektronen Synchrotron, DESY, Zeuthen (Germany); Bierenbaum, I. [Universitaet Hamburg, II. Institut fuer Theoretische Physik, Hamburg (Germany); Klein, S. [RWTH Aachen University, Institut fuer Theoretische Teilchenphysik und Kosmologie, Aachen (Germany); Wissbrock, F. [Deutsches Elektronen Synchrotron, DESY, Zeuthen (Germany); Johannes Kepler University, Research Institute for Symbolic Computation (RISC), Linz (Austria); IHES, Bures-sur-Yvette (France)
2014-09-15
We calculate the logarithmic contributions to the massive Wilson coefficients for deep-inelastic scattering in the asymptotic region Q{sup 2} >> m{sup 2} to 3-loop order in the fixed flavor number scheme and present the corresponding expressions for the massive operator matrix elements needed in the variable flavor number scheme. Explicit expressions are given in Mellin N-space. (orig.)
Confidence bounds and hypothesis tests for normal distribution coefficients of variation
Steve P. Verrill; Richard A. Johnson
2007-01-01
For normally distributed populations, we obtain confidence bounds on a ratio of two coefficients of variation, provide a test for the equality of k coefficients of variation, and provide confidence bounds on a coefficient of variation shared by k populations. To develop these confidence bounds and test, we first establish that estimators based on Newton steps from n-...
2015-01-01
The recent availability of high frequency data has permitted more efficient ways of computing volatility. However, estimation of volatility from asset price observations is challenging because observed high frequency data are generally affected by noise-microstructure effects. We address this issue by using the Fourier estimator of instantaneous volatility introduced in Malliavin and Mancino 2002. We prove a central limit theorem for this estimator with optimal rate and asymptotic variance. An extensive simulation study shows the accuracy of the spot volatility estimates obtained using the Fourier estimator and its robustness even in the presence of different microstructure noise specifications. An empirical analysis on high frequency data (U.S. S&P500 and FIB 30 indices) illustrates how the Fourier spot volatility estimates can be successfully used to study intraday variations of volatility and to predict intraday Value at Risk. PMID:26421617
Sandberg, Mattias
2015-01-07
The Monte Carlo (and Multi-level Monte Carlo) finite element method can be used to approximate observables of solutions to diffusion equations with log normal distributed diffusion coefficients, e.g. modelling ground water flow. Typical models use log normal diffusion coefficients with H¨older regularity of order up to 1/2 a.s. This low regularity implies that the high frequency finite element approximation error (i.e. the error from frequencies larger than the mesh frequency) is not negligible and can be larger than the computable low frequency error. This talk will address how the total error can be estimated by the computable error.
Energy Technology Data Exchange (ETDEWEB)
Zielinski, Lech [Universite du Littoral, LMPA (France)], E-mail: lech.zielinski@lmpa.univ-littoral.fr
2002-06-15
Let A=A{sub 0}+v(x) where A{sub 0} is a second-order uniformly elliptic self-adjoint operator in R{sup d} and v is a real valued polynomially growing potential. Assuming that v and the coefficients of A{sub 0} are Hoelder continuous, we study the asymptotic behaviour of the counting function N(A,{lambda}) ({lambda}{sup {yields}}{infinity}) with the remainder estimates depending on the regularity hypotheses. Our strongest regularity hypotheses involve Lipschitz continuity and give the remainder estimate N(A,{lambda})O({l_brace}{lambda}{r_brace}{sup -{mu}}), where {mu} may take an arbitrary value strictly smaller than the best possible value known in the smooth case. In particular, our results are obtained without any hypothesis on critical points of the potential.
Sandberg, Mattias
2015-01-01
log normal diffusion coefficients with H¨older regularity of order up to 1/2 a.s. This low regularity implies that the high frequency finite element approximation error (i.e. the error from frequencies larger than the mesh frequency) is not negligible
Litniewski, Marek; Gorecki, Jerzy
2011-06-28
We have performed intensive computer simulations of the irreversible annihilation reaction: A + A → C + C and of the trapping reaction: A + B → C + B for a variety of three-dimensional fluids composed of identical spherical particles. We have found a significant difference in the asymptotic behavior of the rate coefficients for these reactions. Both the rate coefficients converge to the same value with time t going to infinity but the convergence rate is different: the O(t(-1/2)) term for the annihilation reaction is higher than the corresponding term for the trapping reaction. The simulation results suggest that ratio of the terms is a universal quantity with the value equal to 2 or slightly above. A model for the annihilation reaction based on the superposition approximation predicts the difference in the O(t(-1/2)) terms, but overestimates the value for the annihilation reaction by about 30%. We have also performed simulations for the dimerization process: A + A → E, where E stands for a dimer. The dimerization decreases the reaction rate due to the decrease in the diffusion constant for A. The effect is successfully predicted by a simple model.
Fino, Peter; Lockhart, Thurmon E
2014-04-11
This study investigated the relationship of required coefficient of friction to gait speed, obstacle height, and turning strategy as participants walked around obstacles of various heights. Ten healthy, young adults performed 90° turns around corner pylons of four different heights at their self selected normal, slow, and fast walking speeds using both step and spin turning strategies. Kinetic data was captured using force plates. Results showed peak required coefficient of friction (RCOF) at push off increased with increased speed (slow μ=0.38, normal μ=0.45, and fast μ=0.54). Obstacle height had no effect on RCOF values. The average peak RCOF for fast turning exceeded the OSHA safety guideline for static COF of μ>0.50, suggesting further research is needed into the minimum static COF to prevent slips and falls, especially around corners. Copyright © 2014 Elsevier Ltd. All rights reserved.
Directory of Open Access Journals (Sweden)
Young Han Lee
2013-01-01
Full Text Available A bandwidth extension (BWE algorithm from wideband to superwideband (SWB is proposed for a scalable speech/audio codec that uses modified discrete cosine transform (MDCT coefficients as spectral parameters. The superwideband is first split into several subbands that are represented as gain parameters and normalized MDCT coefficients in the proposed BWE algorithm. We then estimate normalized MDCT coefficients of the wideband to be fetched for the superwideband and quantize the fetch indices. After that, we quantize gain parameters by using relative ratios between adjacent subbands. The proposed BWE algorithm is embedded into a standard superwideband codec, the SWB extension of G.729.1 Annex E, and its bitrate and quality are compared with those of the BWE algorithm already employed in the standard superwideband codec. It is shown from the comparison that the proposed BWE algorithm relatively reduces the bitrate by around 19% with better quality, compared to the BWE algorithm in the SWB extension of G.729.1 Annex E.
DEFF Research Database (Denmark)
Franco, Antonio; Trapp, Stefan
2008-01-01
The sorption of organic electrolytes to soil was investigated. A dataset consisting of 164 electrolytes, composed of 93 acids, 65 bases, and six amphoters, was collected from literature and databases. The partition coefficient log KOW of the neutral molecule and the dissociation constant pKa were...... calculated by the software ACD/Labs®. The Henderson-Hasselbalch equation was applied to calculate dissociation. Regressions were developed to predict separately for the neutral and the ionic molecule species the distribution coefficient (Kd) normalized to organic carbon (KOC) from log KOW and pKa. The log...... KOC of strong acids (pKa correlated to these parameters. The regressions derived for weak acids and bases (undissociated at environmental pH) were similar. The highest sorption was found for strong bases (pKa > 7.5), probably due to electrical interactions. Nonetheless, their log KOC...
Optical measurement of isolated canine lung filtration coefficients at normal hematocrits.
Klaesner, J W; Pou, N A; Parker, R E; Finney, C; Roselli, R J
1997-12-01
In this study, lung filtration coefficient (Kfc) values were measured in eight isolated canine lung preparations at normal hematocrit values using three methods: gravimetric, blood-corrected gravimetric, and optical. The lungs were kept in zone 3 conditions and subjected to an average venous pressure increase of 10.24 +/- 0.27 (SE) cmH2O. The resulting Kfc (ml . min-1 . cmH2O-1 . 100 g dry lung wt-1) measured with the gravimetric technique was 0.420 +/- 0.017, which was statistically different from the Kfc measured by the blood-corrected gravimetric method (0.273 +/- 0.018) or the product of the reflection coefficient (sigmaf) and Kfc measured optically (0. 272 +/- 0.018). The optical method involved the use of a Cellco filter cartridge to separate red blood cells from plasma, which allowed measurement of the concentration of the tracer in plasma at normal hematocrits (34 +/- 1.5). The permeability-surface area product was measured using radioactive multiple indicator-dilution methods before, during, and after venous pressure elevations. Results showed that the surface area of the lung did not change significantly during the measurement of Kfc. These studies suggest that sigmafKfc can be measured optically at normal hematocrits, that this measurement is not influenced by blood volume changes that occur during the measurement, and that the optical sigmafKfc agrees with the Kfc obtained via the blood-corrected gravimetric method.
Apparent diffusion coefficients of normal uterus in premenopausal women with 3 T MRI
International Nuclear Information System (INIS)
Kuang, F.; Chen, Z.; Zhong, Q.; Fu, L.; Ma, M.
2013-01-01
Aim: To investigate the apparent diffusion coefficient (ADC) values of the normal uterine cervical zonal structures (cervical epithelium, the junctional zone, and myometrium) during different phases of the menstrual cycle among premenopausal women in different age groups. Materials and methods: Seventy healthy women, who were divided into three age groups (group A, 24 women in their twenties; group B, 23 women in their thirties; group C, 23 women in their forties), underwent 3 T magnetic resonance imaging (MRI) with T2-weighted and diffusion-weighted imaging (DWI) during the mid-proliferative and the mid-secretory phases. Results: The ADC values of each cervical zonal structure were significantly different from one another (p 0.05). Conclusion: ADC values of normal cervical epithelium and the junctional zone change with different phases of the menstrual cycle, which should be taken into consideration when early cervical disease is detected, when monitoring treatment response, and differentiating early tumour recurrence
Self-normalizing multiple-echo technique for measuring the in vivo apparent diffusion coefficient
International Nuclear Information System (INIS)
Perman, W.H.; Gado, M.; Sandstrom, J.C.
1989-01-01
This paper presents work to develop a new technique for quantitating the in vivo apparent diffusion/perfusion coefficient (ADC) by obtaining multiple data points from only two images with the capability to normalize the data from consecutive images, thus minimizing the effect of interimage variation. Two multiple-echo (six-to eight-echo) cardiac-gated images are obtained, one without and one with additional diffusion/perfusion encoding gradients placed about the 180 RF pulses of all but the first echo. Since the first echoes of both images have identical pulse sequence parameters, variations in signal intensity-between the first echoes represent image-to-image variation. The signal intensities of the subsequent echoes with additional diffusion/perfusion encoding gradients are then normalized by using the ratio of the first-echo signal intensities
International Nuclear Information System (INIS)
Garcia-Sanchez, L.; Konoplev, A.V.
2009-01-01
Radionuclide wash-off is the transport of activity by flowing water over the soil surface (runoff). To complete existing reviews on long-term removal rates, this paper focuses on short-term wash-off fluxes, quantified in the literature by soil-runoff transfer factors called normalized liquid and solid entrainment coefficients (noted K l *, K s *). Compiled data concerned essentially 137 Cs and 90 Sr wash-off measured under simulated rainfalls on small experimental plots after Chernobyl fallout in the exclusion zone. K l * and K s * values span approximately one order of magnitude. Their validity is limited to a season, and their representativeness is limited by restricted studied situations, notably dominant unsoluble forms in fallout, light soils and intense rainfalls. Formulas based on a simplified representation of the soil-runoff system were proposed to generalize the existing values for other conditions. However, their implementation requires a more systematic compilation of the available information, including decisive influence factors such as the fraction of exchangeable form, distribution coefficient, suspended matter enrichment ratio. Entrainment coefficients K l * and K s * were mathematically related to the transfer function approach. The proposed relationships proved their complementarity in terms of time support and captured fluctuations. Both approaches should be used in assessments to estimate average fluxes and their variability.
International Nuclear Information System (INIS)
Tsili, A.C.; Argyropoulou, M.I.; Tzarouchi, L.; Dalkalitsis, N.; Koliopoulos, G.; Paraskevaidis, E.; Tsampoulas, K.
2012-01-01
Objectives: To assess the apparent diffusion coefficient (ADC) changes of the normal uterine zones among reproductive women during the menstrual cycle. Methods: The study included 101 women of reproductive age, each with regular cycle and normal endometrium/myometrium, as proved on histopathology or MR imaging examination. Diffusion-weighted (DW) imaging was performed along the axial plane, using a single shot, multi-slice spin-echo planar diffusion pulse sequence and b-values of 0 and 800 s/mm 2 . The mean and standard deviation of the ADC values of normal endometrium/myometrium were calculated for menstrual, proliferative and secretory phase. Analysis of variance followed by the least significant difference test was used for statistical analysis. Results: The ADC values of the endometrium were different in the three phases of the menstrual cycle (menstrual phase: 1.25 ± 0.27; proliferative phase: 1.39 ± 0.20; secretory phase: 1.50 ± 0.18) (F: 9.64, p: 0.00). Statistical significant difference was observed among all groups (p 0.05). Conclusions: A wide variation of ADC values of normal endometrium and myometrium is observed during different phases of the menstrual cycle.
International Nuclear Information System (INIS)
Naganawa, Shinji; Sato, Chiho; Ishigaki, Takeo; Kumada, Hisashi; Miura, Shunichi; Takizawa, Osamu
2005-01-01
A relation between apparent diffusion coefficient (ADC) values and tumor cellular density has been reported. The purpose of this study was to measure the ADC values of cervical cancers in the uterus and compare them with those of normal cervical tissues, and to test whether ADC could differentiate between normal and malignant cervical tissues in the uterus. Twelve consecutive female patients with cervical cancer of the uterus and ten female patients with other pelvic abnormalities were included in this study. ADC was measured at 1.5 T with b-factors of 0, 300 and 600 s/mm 2 using single-shot echo-planar diffusion-weighted imaging and a parallel imaging technique. The mean ADC value of cervical cancer lesions was 1.09±0.20 x 10 -3 mm 2 /s, and that of normal cervix tissue was 1.79±0.24 x 10 -3 mm 2 /s (P<0.0001). In nine patients treated by chemotherapy and/or radiation therapy, the mean ADC value of the cervical cancer lesion increased significantly after therapy (P<0.001). The present study showed, with a small number of patients, that ADC measurement has a potential ability to differentiate between normal and cancerous tissue in the uterine cervix. Further study is necessary to determine the accuracy of ADC measurement in monitoring the treatment response. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Tsili, A.C., E-mail: a_tsili@yahoo.gr [Department of Clinical Radiology, University Hospital of Ioannina (Greece); Argyropoulou, M.I., E-mail: margyrop@cc.uoi.gr [Department of Clinical Radiology, University Hospital of Ioannina (Greece); Tzarouchi, L., E-mail: ltzar@cc.uoi.gr [Department of Clinical Radiology, University Hospital of Ioannina (Greece); Dalkalitsis, N., E-mail: ndalkal@cc.uoi.gr [Department of Obstetrics and Gynaecology, University Hospital of Ioannina (Greece); Koliopoulos, G., E-mail: georgekoliopoulos@yahoo.com [Department of Obstetrics and Gynaecology, University Hospital of Ioannina (Greece); Paraskevaidis, E., E-mail: eparaske@cc.uoi.gr [Department of Obstetrics and Gynaecology, University Hospital of Ioannina (Greece); Tsampoulas, K., E-mail: ctsampou@uoi.gr [Department of Clinical Radiology, University Hospital of Ioannina (Greece)
2012-08-15
Objectives: To assess the apparent diffusion coefficient (ADC) changes of the normal uterine zones among reproductive women during the menstrual cycle. Methods: The study included 101 women of reproductive age, each with regular cycle and normal endometrium/myometrium, as proved on histopathology or MR imaging examination. Diffusion-weighted (DW) imaging was performed along the axial plane, using a single shot, multi-slice spin-echo planar diffusion pulse sequence and b-values of 0 and 800 s/mm{sup 2}. The mean and standard deviation of the ADC values of normal endometrium/myometrium were calculated for menstrual, proliferative and secretory phase. Analysis of variance followed by the least significant difference test was used for statistical analysis. Results: The ADC values of the endometrium were different in the three phases of the menstrual cycle (menstrual phase: 1.25 {+-} 0.27; proliferative phase: 1.39 {+-} 0.20; secretory phase: 1.50 {+-} 0.18) (F: 9.64, p: 0.00). Statistical significant difference was observed among all groups (p < 0.05). The ADC values of the normal myometrium were different in the three phases of the menstrual cycle (menstrual phase: 1.91 {+-} 0.35; proliferative phase: 1.72 {+-} 0.27; secretory phase: 1.87 {+-} 0.28) (F: 3.60, p: 0.03). Statistical significant difference was observed between menstrual and proliferative phase and between proliferative and secretory phase (p < 0.05). No significant difference was noted between menstrual and secretory phase (p > 0.05). Conclusions: A wide variation of ADC values of normal endometrium and myometrium is observed during different phases of the menstrual cycle.
Normalized glandular dose (DgN) coefficients for flat-panel CT breast imaging
International Nuclear Information System (INIS)
Thacker, Samta C; Glick, Stephen J
2004-01-01
The development of new digital mammography techniques such as dual-energy imaging, tomosynthesis and CT breast imaging will require investigation of optimal camera design parameters and optimal imaging acquisition parameters. In optimizing these acquisition protocols and imaging systems it is important to have knowledge of the radiation dose to the breast. This study presents a methodology for estimating the normalized glandular dose to the uncompressed breast using the geometry proposed for flat-panel CT breast imaging. The simulation uses the GEANT 3 Monte Carlo code to model x-ray transport and absorption within the breast phantom. The Monte Carlo software was validated for breast dosimetry by comparing results of the normalized glandular dose (DgN) values of the compressed breast to those reported in the literature. The normalized glandular dose was then estimated for a range of breast diameters from 10 cm to 18 cm using an uncompressed breast model with a homogeneous composition of adipose and glandular tissue, and for monoenergetic x-rays from 10 keV to 120 keV. These data were fit providing expressions for the normalized glandular dose. Using these expressions for the DgN coefficients and input variables such as the diameter, height and composition of the breast phantom, the mean glandular dose for any spectra can be estimated. A computer program to provide normalized glandular dose values has been made available online. In addition, figures displaying energy deposition maps are presented to better understand the spatial distribution of dose in CT breast imaging
Speech Emotion Recognition Based on Power Normalized Cepstral Coefficients in Noisy Conditions
Directory of Open Access Journals (Sweden)
M. Bashirpour
2016-09-01
Full Text Available Automatic recognition of speech emotional states in noisy conditions has become an important research topic in the emotional speech recognition area, in recent years. This paper considers the recognition of emotional states via speech in real environments. For this task, we employ the power normalized cepstral coefficients (PNCC in a speech emotion recognition system. We investigate its performance in emotion recognition using clean and noisy speech materials and compare it with the performances of the well-known MFCC, LPCC, RASTA-PLP, and also TEMFCC features. Speech samples are extracted from the Berlin emotional speech database (Emo DB and Persian emotional speech database (Persian ESD which are corrupted with 4 different noise types under various SNR levels. The experiments are conducted in clean train/noisy test scenarios to simulate practical conditions with noise sources. Simulation results show that higher recognition rates are achieved for PNCC as compared with the conventional features under noisy conditions.
Energy Technology Data Exchange (ETDEWEB)
Žerovnik, Gašper, E-mail: gasper.zerovnik@ijs.si [Jožef Stefan Institute, Jamova cesta 39, SI-1000 Ljubljana (Slovenia); Trkov, Andrej, E-mail: andrej.trkov@ijs.si [Jožef Stefan Institute, Jamova cesta 39, SI-1000 Ljubljana (Slovenia); Smith, Donald L., E-mail: donald.l.smith@anl.gov [Argonne National Laboratory, 1710 Avenida del Mundo, Coronado, CA 92118-3073 (United States); Capote, Roberto, E-mail: roberto.capotenoy@iaea.org [NAPC–Nuclear Data Section, International Atomic Energy Agency, PO Box 100, Vienna-A-1400 (Austria)
2013-11-01
Inherently positive parameters with large relative uncertainties (typically ≳30%) are often considered to be governed by the lognormal distribution. This assumption has the practical benefit of avoiding the possibility of sampling negative values in stochastic applications. Furthermore, it is typically assumed that the correlation coefficients for comparable multivariate normal and lognormal distributions are equivalent. However, this ideal situation is approached only in the linear approximation which happens to be applicable just for small uncertainties. This paper derives and discusses the proper transformation of correlation coefficients between both distributions for the most general case which is applicable for arbitrary uncertainties. It is seen that for lognormal distributions with large relative uncertainties strong anti-correlations (negative correlations) are mathematically forbidden. This is due to the asymmetry that is an inherent feature of these distributions. Some implications of these results for practical nuclear applications are discussed and they are illustrated with examples in this paper. Finally, modifications to the ENDF-6 format used for representing uncertainties in evaluated nuclear data libraries are suggested, as needed to deal with this issue.
International Nuclear Information System (INIS)
Žerovnik, Gašper; Trkov, Andrej; Smith, Donald L.; Capote, Roberto
2013-01-01
Inherently positive parameters with large relative uncertainties (typically ≳30%) are often considered to be governed by the lognormal distribution. This assumption has the practical benefit of avoiding the possibility of sampling negative values in stochastic applications. Furthermore, it is typically assumed that the correlation coefficients for comparable multivariate normal and lognormal distributions are equivalent. However, this ideal situation is approached only in the linear approximation which happens to be applicable just for small uncertainties. This paper derives and discusses the proper transformation of correlation coefficients between both distributions for the most general case which is applicable for arbitrary uncertainties. It is seen that for lognormal distributions with large relative uncertainties strong anti-correlations (negative correlations) are mathematically forbidden. This is due to the asymmetry that is an inherent feature of these distributions. Some implications of these results for practical nuclear applications are discussed and they are illustrated with examples in this paper. Finally, modifications to the ENDF-6 format used for representing uncertainties in evaluated nuclear data libraries are suggested, as needed to deal with this issue
Asymptotics of bivariate generating functions with algebraic singularities
Greenwood, Torin
Flajolet and Odlyzko (1990) derived asymptotic formulae the coefficients of a class of uni- variate generating functions with algebraic singularities. Gao and Richmond (1992) and Hwang (1996, 1998) extended these results to classes of multivariate generating functions, in both cases by reducing to the univariate case. Pemantle and Wilson (2013) outlined new multivariate ana- lytic techniques and used them to analyze the coefficients of rational generating functions. After overviewing these methods, we use them to find asymptotic formulae for the coefficients of a broad class of bivariate generating functions with algebraic singularities. Beginning with the Cauchy integral formula, we explicity deform the contour of integration so that it hugs a set of critical points. The asymptotic contribution to the integral comes from analyzing the integrand near these points, leading to explicit asymptotic formulae. Next, we use this formula to analyze an example from current research. In the following chapter, we apply multivariate analytic techniques to quan- tum walks. Bressler and Pemantle (2007) found a (d + 1)-dimensional rational generating function whose coefficients described the amplitude of a particle at a position in the integer lattice after n steps. Here, the minimal critical points form a curve on the (d + 1)-dimensional unit torus. We find asymptotic formulae for the amplitude of a particle in a given position, normalized by the number of steps n, as n approaches infinity. Each critical point contributes to the asymptotics for a specific normalized position. Using Groebner bases in Maple again, we compute the explicit locations of peak amplitudes. In a scaling window of size the square root of n near the peaks, each amplitude is asymptotic to an Airy function.
Thompson, P. M.; Stein, G.
1980-01-01
The behavior of the closed loop eigenstructure of a linear system with output feedback is analyzed as a single parameter multiplying the feedback gain is varied. An algorithm is presented that computes the asymptotically infinite eigenstructure, and it is shown how a system with high gain, feedback decouples into single input, single output systems. Then a synthesis algorithm is presented which uses full state feedback to achieve a desired asymptotic eigenstructure.
Directory of Open Access Journals (Sweden)
Phillip Burgers
Full Text Available For a century, researchers have used the standard lift coefficient C(L to evaluate the lift, L, generated by fixed wings over an area S against dynamic pressure, ½ρv(2, where v is the effective velocity of the wing. Because the lift coefficient was developed initially for fixed wings in steady flow, its application to other lifting systems requires either simplifying assumptions or complex adjustments as is the case for flapping wings and rotating cylinders.This paper interprets the standard lift coefficient of a fixed wing slightly differently, as the work exerted by the wing on the surrounding flow field (L/ρ·S, compared against the total kinetic energy required for generating said lift, ½v(2. This reinterpreted coefficient, the normalized lift, is derived from the work-energy theorem and compares the lifting capabilities of dissimilar lift systems on a similar energy footing. The normalized lift is the same as the standard lift coefficient for fixed wings, but differs for wings with more complex motions; it also accounts for such complex motions explicitly and without complex modifications or adjustments. We compare the normalized lift with the previously-reported values of lift coefficient for a rotating cylinder in Magnus effect, a bat during hovering and forward flight, and a hovering dipteran.The maximum standard lift coefficient for a fixed wing without flaps in steady flow is around 1.5, yet for a rotating cylinder it may exceed 9.0, a value that implies that a rotating cylinder generates nearly 6 times the maximum lift of a wing. The maximum normalized lift for a rotating cylinder is 1.5. We suggest that the normalized lift can be used to evaluate propellers, rotors, flapping wings of animals and micro air vehicles, and underwater thrust-generating fins in the same way the lift coefficient is currently used to evaluate fixed wings.
Burgers, Phillip; Alexander, David E.
2012-01-01
For a century, researchers have used the standard lift coefficient CL to evaluate the lift, L, generated by fixed wings over an area S against dynamic pressure, ½ρv 2, where v is the effective velocity of the wing. Because the lift coefficient was developed initially for fixed wings in steady flow, its application to other lifting systems requires either simplifying assumptions or complex adjustments as is the case for flapping wings and rotating cylinders. This paper interprets the standard lift coefficient of a fixed wing slightly differently, as the work exerted by the wing on the surrounding flow field (L/ρ·S), compared against the total kinetic energy required for generating said lift, ½v2. This reinterpreted coefficient, the normalized lift, is derived from the work-energy theorem and compares the lifting capabilities of dissimilar lift systems on a similar energy footing. The normalized lift is the same as the standard lift coefficient for fixed wings, but differs for wings with more complex motions; it also accounts for such complex motions explicitly and without complex modifications or adjustments. We compare the normalized lift with the previously-reported values of lift coefficient for a rotating cylinder in Magnus effect, a bat during hovering and forward flight, and a hovering dipteran. The maximum standard lift coefficient for a fixed wing without flaps in steady flow is around 1.5, yet for a rotating cylinder it may exceed 9.0, a value that implies that a rotating cylinder generates nearly 6 times the maximum lift of a wing. The maximum normalized lift for a rotating cylinder is 1.5. We suggest that the normalized lift can be used to evaluate propellers, rotors, flapping wings of animals and micro air vehicles, and underwater thrust-generating fins in the same way the lift coefficient is currently used to evaluate fixed wings. PMID:22629326
Burgers, Phillip; Alexander, David E
2012-01-01
For a century, researchers have used the standard lift coefficient C(L) to evaluate the lift, L, generated by fixed wings over an area S against dynamic pressure, ½ρv(2), where v is the effective velocity of the wing. Because the lift coefficient was developed initially for fixed wings in steady flow, its application to other lifting systems requires either simplifying assumptions or complex adjustments as is the case for flapping wings and rotating cylinders.This paper interprets the standard lift coefficient of a fixed wing slightly differently, as the work exerted by the wing on the surrounding flow field (L/ρ·S), compared against the total kinetic energy required for generating said lift, ½v(2). This reinterpreted coefficient, the normalized lift, is derived from the work-energy theorem and compares the lifting capabilities of dissimilar lift systems on a similar energy footing. The normalized lift is the same as the standard lift coefficient for fixed wings, but differs for wings with more complex motions; it also accounts for such complex motions explicitly and without complex modifications or adjustments. We compare the normalized lift with the previously-reported values of lift coefficient for a rotating cylinder in Magnus effect, a bat during hovering and forward flight, and a hovering dipteran.The maximum standard lift coefficient for a fixed wing without flaps in steady flow is around 1.5, yet for a rotating cylinder it may exceed 9.0, a value that implies that a rotating cylinder generates nearly 6 times the maximum lift of a wing. The maximum normalized lift for a rotating cylinder is 1.5. We suggest that the normalized lift can be used to evaluate propellers, rotors, flapping wings of animals and micro air vehicles, and underwater thrust-generating fins in the same way the lift coefficient is currently used to evaluate fixed wings.
Zhu, Y H; Song, S P; Luo, W; Elias, P M; Man, M Q
2011-01-01
Studies have demonstrated that some cutaneous biophysical properties vary with age, gender and body sites. However, the characteristics of the skin friction coefficient in different genders and age groups have not yet been well established. In the present study, we assess the skin friction coefficient in a larger Chinese population. A total of 633 subjects (300 males and 333 females) aged 0.15-79 years were enrolled. A Frictiometer FR 770 and Corneometer CM 825 (C&K MPA 5) were used to measure the skin friction coefficient and stratum corneum hydration, respectively, on the dorsal surface of the hand, the forehead and the canthus. In the females, the maximum skin friction coefficients on both the canthus and the dorsal hand skin were observed around the age of 40 years. In the males, the skin friction coefficient on the dorsal hand skin gradually increased from 0 to 40 years of age, and changed little afterward. Skin friction coefficients on some body sites were higher in females than in age-matched males in some age groups. On the canthus and the dorsal hand skin of females, a positive correlation was found between skin friction coefficient and stratum corneum hydration (p skin friction coefficient was positively correlated with stratum corneum hydration on the forehead and the dorsal hand skin (p skin friction coefficient varies with age, gender and body site, and positively correlates with stratum corneum hydration on some body sites. Copyright © 2010 S. Karger AG, Basel.
Journal Afrika Statistika ISSN 0852-0305 Asymptotic representation ...
African Journals Online (AJOL)
Asymptotic representation theorems for poverty indices ... Statistical asymptotic laws for these indices, particularly asymptotic normality, on which statistical inference on the ... population of individuals, each of which having a random income or ...
Zarzycki, R.; Linden, van der E.; Sagis, L.M.C.; Venema, P.; Babuchowski, A.
2004-01-01
Abstract This paper illustrates how rheo-optical techniques may be utilized to determine the first normal stress coefficient for an exopolysaccharide (EPS) produced by the Lactobacillus delbrueckii ssp. bulgaricus LY03, which is widely used in yoghurt production. In this technique both shear stress,
Kiessling, Michael Karl-Heinz
2017-10-01
Let z\\in C, let σ ^2>0 be a variance, and for N\\in N define the integrals E_N^{}(z;σ ) := {1/σ } \\int _R\\ (x^2+z^2) e^{-{1/2σ^2 x^2}}{√{2π }}/dx \\quad if N=1, {1/σ } \\int _{R^N} \\prod \\prod \\limits _{1≤ k1. These are expected values of the polynomials P_N^{}(z)=\\prod _{1≤ n≤ N}(X_n^2+z^2) whose 2 N zeros ± i X_k^{}_{k=1,\\ldots ,N} are generated by N identically distributed multi-variate mean-zero normal random variables {X_k}N_{k=1} with co-variance {Cov}_N^{}(X_k,X_l)=(1+σ ^2-1/N)δ _{k,l}+σ ^2-1/N(1-δ _{k,l}). The E_N^{}(z;σ ) are polynomials in z^2, explicitly computable for arbitrary N, yet a list of the first three E_N^{}(z;σ ) shows that the expressions become unwieldy already for moderate N—unless σ = 1, in which case E_N^{}(z;1) = (1+z^2)^N for all z\\in C and N\\in N. (Incidentally, commonly available computer algebra evaluates the integrals E_N^{}(z;σ ) only for N up to a dozen, due to memory constraints). Asymptotic evaluations are needed for the large- N regime. For general complex z these have traditionally been limited to analytic expansion techniques; several rigorous results are proved for complex z near 0. Yet if z\\in R one can also compute this "infinite-degree" limit with the help of the familiar relative entropy principle for probability measures; a rigorous proof of this fact is supplied. Computer algebra-generated evidence is presented in support of a conjecture that a generalization of the relative entropy principle to signed or complex measures governs the N→ ∞ asymptotics of the regime iz\\in R. Potential generalizations, in particular to point vortex ensembles and the prescribed Gauss curvature problem, and to random matrix ensembles, are emphasized.
International Nuclear Information System (INIS)
Meyer, P.
1978-01-01
After having established the renormalization group equations and the possibilities of fixed points for the effective coupling constants the non abelian gauge theories are shown to have the property of asymptotic freedom. These results are applied to the colour gauge group of the strong interactions of quarks and gluons. The behavior of the moments of the structure functions of the deep inelastic scattering of leptons on nucleons (scaling and its logarithmic violations) is then deduced with using the Wilson's operator product expansion [fr
Pachhai, S.; Masters, G.; Laske, G.
2017-12-01
Earth's normal-mode spectra are crucial to studying the long wavelength structure of the Earth. Such observations have been used extensively to estimate "splitting coefficients" which, in turn, can be used to determine the three-dimensional velocity and density structure. Most past studies apply a non-linear iterative inversion to estimate the splitting coefficients which requires that the earthquake source is known. However, it is challenging to know the source details, particularly for big events as used in normal-mode analyses. Additionally, the final solution of the non-linear inversion can depend on the choice of damping parameter and starting model. To circumvent the need to know the source, a two-step linear inversion has been developed and successfully applied to many mantle and core sensitive modes. The first step takes combinations of the data from a single event to produce spectra known as "receiver strips". The autoregressive nature of the receiver strips can then be used to estimate the structure coefficients without the need to know the source. Based on this approach, we recently employed a neighborhood algorithm to measure the splitting coefficients for an isolated inner-core sensitive mode (13S2). This approach explores the parameter space efficiently without any need of regularization and finds the structure coefficients which best fit the observed strips. Here, we implement a Bayesian approach to data collected for earthquakes from early 2000 and more recent. This approach combines the data (through likelihood) and prior information to provide rigorous parameter values and their uncertainties for both isolated and coupled modes. The likelihood function is derived from the inferred errors of the receiver strips which allows us to retrieve proper uncertainties. Finally, we apply model selection criteria that balance the trade-offs between fit (likelihood) and model complexity to investigate the degree and type of structure (elastic and anelastic
Werner, Charles L.; Wegmueller, Urs; Small, David L.; Rosen, Paul A.
1994-01-01
Terrain slopes, which can be measured with Synthetic Aperture Radar (SAR) interferometry either from a height map or from the interferometric phase gradient, were used to calculate the local incidence angle and the correct pixel area. Both are required for correct thematic interpretation of SAR data. The interferometric correlation depends on the pixel area projected on a plane perpendicular to the look vector and requires correction for slope effects. Methods for normalization of the backscatter and interferometric correlation for ERS-1 SAR are presented.
Algebraic polynomials with random coefficients
Directory of Open Access Journals (Sweden)
K. Farahmand
2002-01-01
Full Text Available This paper provides an asymptotic value for the mathematical expected number of points of inflections of a random polynomial of the form a0(ω+a1(ω(n11/2x+a2(ω(n21/2x2+…an(ω(nn1/2xn when n is large. The coefficients {aj(w}j=0n, w∈Ω are assumed to be a sequence of independent normally distributed random variables with means zero and variance one, each defined on a fixed probability space (A,Ω,Pr. A special case of dependent coefficients is also studied.
International Nuclear Information System (INIS)
Makai, M.; Kalya, Z.; Nemes, I.; Pos, I.; Por, G.
2007-01-01
Moderator temperature coefficient of reactivity is not monitored during fuel cycles in WWER reactors, because it is not very easy or impossible to measure it without disturbing the normal operation. Two new methods were tested in our WWER type nuclear power plant to try methodologies, which enable to measure that important to safety parameter during the fuel cycle. One is based on small perturbances, and only small changes are requested in operation, the other is based on noise methods, which means it is without interference with reactor operation. Both method is new that aspects that they uses the plant computer data(VERONA) based signals calculated by C P ORCA diffusion code (Authors)
Stark resonances: asymptotics and distributional Borel sum
International Nuclear Information System (INIS)
Caliceti, E.; Grecchi, V.; Maioli, M.
1993-01-01
We prove that the Stark effect perturbation theory of a class of bound states uniquely determines the position and the width of the resonances by Distributional Borel Sum. In particular the small field asymptotics of the width is uniquely related to the large order asymptotics of the perturbation coefficients. Similar results apply to all the ''resonances'' of the anharmonic and double well oscillators. (orig.)
A method for summing nonalternating asymptotic series
International Nuclear Information System (INIS)
Kazakov, D.I.
1980-01-01
A method for reconstructing a function from its nonalternating asymptotic series is proposed. It can also be applied when only a limited number of coefficients and their high order asymptotic behaviour are known. The method is illustrated by examples of the ordinary simple integral simulating a functional integral in a theory with degenerate minimum and of the double-well unharmonic oscillator
Lebovici, Andrei; Sfrangeu, Silviu A; Feier, Diana; Caraiani, Cosmin; Lucan, Ciprian; Suciu, Mihai; Elec, Florin; Iacob, Gheorghita; Buruian, Mircea
2014-05-10
We tested the feasibility of a simple method for assessment of prostate cancer (PCa) aggressiveness using diffusion-weighted magnetic resonance imaging (MRI) to calculate apparent diffusion coefficient (ADC) ratios between prostate cancer and healthy prostatic tissue. The requirement for institutional review board approval was waived. A set of 20 standardized core transperineal saturation biopsy specimens served as the reference standard for placement of regions of interest on ADC maps in tumorous and normal prostatic tissue of 22 men with PCa (median Gleason score: 7; range, 6-9). A total of 128 positive sectors were included for evaluation. Two diagnostic ratios were computed between tumor ADCs and normal sector ADCs: the ADC peripheral ratio (the ratio between tumor ADC and normal peripheral zone tissue, ADC-PR), and the ADC central ratio (the ratio between tumor ADC and normal central zone tissue, ADC-CR). The performance of the two ratios in detecting high-risk tumor foci (Gleason 8 and 9) was assessed using the area under the receiver operating characteristic curve (AUC). Both ADC ratios presented significantly lower values in high-risk tumors (0.48 ± 0.13 for ADC-CR and 0.40 ± 0.09 for ADC-PR) compared with low-risk tumors (0.66 ± 0.17 for ADC-CR and 0.54 ± 0.09 for ADC-PR) (p performance (ADC-CR AUC = 0.77, sensitivity = 82.2%, specificity = 66.7% and ADC-PR AUC = 0.90, sensitivity = 93.7%, specificity = 80%) than stand-alone tumor ADCs (AUC of 0.75, sensitivity = 72.7%, specificity = 70.6%) for identifying high-risk lesions. The ADC ratio as an intrapatient-normalized diagnostic tool may be better in detecting high-grade lesions compared with analysis based on tumor ADCs alone, and may reduce the rate of biopsies.
Chaumoitre, K; Colavolpe, N; Shojai, R; Sarran, A; D' Ercole, C; Panuel, M
2007-01-01
To assess the use of diffusion-weighted magnetic resonance imaging (DW-MRI) in the evaluation of the fetal kidney and to estimate age-dependent changes in the apparent diffusion coefficient (ADC) of normal and pathological fetal kidneys. DW-MRI was performed on a 1.5-T machine at 23-38 gestational weeks in 51 pregnant women in whom the fetal kidneys were normal and in 10 whose fetuses had renal pathology (three with suspected nephropathy, three with renal tract dilatation, one with unilateral renal venous thrombosis, and three with twin-twin transfusion syndrome (TTTS)). The ADC was measured in an approximately 1-cm2 region of interest within the renal parenchyma. ADC values in normal renal parenchyma ranged from 1.1 to 1.8 10(-3) mm2 s-1. There was no significant age-dependent change in the ADC of normal kidneys. In cases of nephropathy, the ADC value was not always pathological but an ADC map could show abnormal findings. In cases of dilatation, the ADC value was difficult to determine when the dilatation was huge. In cases of TTTS, the ADC of the donor twin was higher than that of the recipient twin and the difference seemed to be related to the severity of the syndrome. Evaluation of the ADC for fetal kidneys is feasible. Fetal measurement of the ADC value and ADC maps may be useful tools with which to explore the fetal kidney when used in conjunction with current methods. DW-MR images, ADC value and ADC map seem to be useful in cases of suspected nephropathy (hyperechoic kidneys), dilated kidney and vascular pathology (renal venous thrombosis, TTTS). Copyright (c) 2006 ISUOG.
Czech Academy of Sciences Publication Activity Database
Tang, X. D.; Azhari, A.; FU, CB.; Gagliardi, C. A.; Mukhamedzhanov, A. M.; Pirlepesov, F.; Trache, L.; Tribble, R. E.; Burjan, Václav; Kroha, Václav; Carstoiu, F.; Irgaziev, BF.
2004-01-01
Roč. 69, č. 5 (2004), 055807 ISSN 0556-2813 R&D Projects: GA ČR GA202/01/0709; GA MŠk ME 385 Institutional research plan: CEZ:AV0Z1048901 Keywords : coupled-channels calculations * cross-section Subject RIV: BG - Nuclear, Atomic and Molecular Physics, Colliders Impact factor: 3.125, year: 2004
Czech Academy of Sciences Publication Activity Database
Mukhamedzhanov, A. M.; Bém, Pavel; Burjan, Václav; Gagliardi, C. A.; Irgaziev, BF.; Kroha, Václav; Novák, Jan; Piskoř, Štěpán; Šimečková, Eva; Tribble, R. E.; Veselý, František; Vincour, Jiří
2006-01-01
Roč. 73, č. 3 (2006), 035806 ISSN 0556-2813 R&D Projects: GA MŠk ME 643; GA AV ČR KSK1048102; GA ČR GA202/05/0302 Institutional research plan: CEZ:AV0Z1048901 Keywords : shell nuclei * S-factor * scattering Subject RIV: BG - Nuclear, Atomic and Molecular Physics, Colliders Impact factor: 3.327, year: 2006
Czech Academy of Sciences Publication Activity Database
Mukhamedzhanov, A. M.; Bém, Pavel; Brown, BA.; Burjan, Václav; Gagliardi, C. A.; Kroha, Václav; Novák, Jan; Nunes, FM.; Paskor, S.; Pirlepesov, F.; Šimečková, Eva; Trible, RE.; Vincour, Jiří
2003-01-01
Roč. 67, č. 6 (2003), s. -065804 ISSN 0556-2813 R&D Projects: GA AV ČR KSK1048102 Keywords : thermonuclear reaction-rates * nuclear shell-model Subject RIV: BG - Nuclear, Atomic and Molecular Physics, Colliders Impact factor: 2.708, year: 2003
Czech Academy of Sciences Publication Activity Database
Mukhamedzhanov, A. M.; Bém, Pavel; Burjan, Václav; Gagliardi, C. A.; Goldberg, V.Z.; Hons, Zdeněk; La Cognata, M.; Kroha, Václav; Mrázek, Jaromír; Novák, Jan; Piskoř, Štěpán; Pizzone, R. G.; Plunkett, A.; Romano, S.; Šimečková, Eva; Spitareli, C.; Trache, L.; Tribble, R. E.; Veselý, František; Vincour, Jiří
2008-01-01
Roč. 78, č. 1 (2008), 015804/1-015804/8 ISSN 0556-2813 R&D Projects: GA ČR GA202/05/0302; GA MŠk LC07050 Institutional research plan: CEZ:AV0Z10480505 Keywords : ANC Subject RIV: BG - Nuclear, Atomic and Molecular Physics, Colliders Impact factor: 3.124, year: 2008
International Nuclear Information System (INIS)
Lebovici, Andrei; Sfrangeu, Silviu A; Feier, Diana; Caraiani, Cosmin; Lucan, Ciprian; Suciu, Mihai; Elec, Florin; Iacob, Gheorghita; Buruian, Mircea
2014-01-01
We tested the feasibility of a simple method for assessment of prostate cancer (PCa) aggressiveness using diffusion-weighted magnetic resonance imaging (MRI) to calculate apparent diffusion coefficient (ADC) ratios between prostate cancer and healthy prostatic tissue. The requirement for institutional review board approval was waived. A set of 20 standardized core transperineal saturation biopsy specimens served as the reference standard for placement of regions of interest on ADC maps in tumorous and normal prostatic tissue of 22 men with PCa (median Gleason score: 7; range, 6–9). A total of 128 positive sectors were included for evaluation. Two diagnostic ratios were computed between tumor ADCs and normal sector ADCs: the ADC peripheral ratio (the ratio between tumor ADC and normal peripheral zone tissue, ADC-PR), and the ADC central ratio (the ratio between tumor ADC and normal central zone tissue, ADC-CR). The performance of the two ratios in detecting high-risk tumor foci (Gleason 8 and 9) was assessed using the area under the receiver operating characteristic curve (AUC). Both ADC ratios presented significantly lower values in high-risk tumors (0.48 ± 0.13 for ADC-CR and 0.40 ± 0.09 for ADC-PR) compared with low-risk tumors (0.66 ± 0.17 for ADC-CR and 0.54 ± 0.09 for ADC-PR) (p < 0.001) and had better diagnostic performance (ADC-CR AUC = 0.77, sensitivity = 82.2%, specificity = 66.7% and ADC-PR AUC = 0.90, sensitivity = 93.7%, specificity = 80%) than stand-alone tumor ADCs (AUC of 0.75, sensitivity = 72.7%, specificity = 70.6%) for identifying high-risk lesions. The ADC ratio as an intrapatient-normalized diagnostic tool may be better in detecting high-grade lesions compared with analysis based on tumor ADCs alone, and may reduce the rate of biopsies
Asymptotic numbers, asymptotic functions and distributions
International Nuclear Information System (INIS)
Todorov, T.D.
1979-07-01
The asymptotic functions are a new type of generalized functions. But they are not functionals on some space of test-functions as the distributions of Schwartz. They are mappings of the set denoted by A into A, where A is the set of the asymptotic numbers introduced by Christov. On its part A is a totally-ordered set of generalized numbers including the system of real numbers R as well as infinitesimals and infinitely large numbers. Every two asymptotic functions can be multiplied. On the other hand, the distributions have realizations as asymptotic functions in a certain sense. (author)
Khalil, Nagi
2018-04-01
The homogeneous cooling state (HCS) of a granular gas described by the inelastic Boltzmann equation is reconsidered. As usual, particles are taken as inelastic hard disks or spheres, but now the coefficient of normal restitution α is allowed to take negative values , which is a simple way of modeling more complicated inelastic interactions. The distribution function of the HCS is studied at the long-time limit, as well as intermediate times. At the long-time limit, the relevant information of the HCS is given by a scaling distribution function , where the time dependence occurs through a dimensionless velocity c. For , remains close to the Gaussian distribution in the thermal region, its cumulants and exponential tails being well described by the first Sonine approximation. In contrast, for , the distribution function becomes multimodal, its maxima located at , and its observable tails algebraic. The latter is a consequence of an unbalanced relaxation–dissipation competition, and is analytically demonstrated for , thanks to a reduction of the Boltzmann equation to a Fokker–Plank-like equation. Finally, a generalized scaling solution to the Boltzmann equation is also found . Apart from the time dependence occurring through the dimensionless velocity, depends on time through a new parameter β measuring the departure of the HCS from its long-time limit. It is shown that describes the time evolution of the HCS for almost all times. The relevance of the new scaling is also discussed.
Asymptotic expansions for high-contrast linear elasticity
Poveda, Leonardo A.; Huepo, Sebastian; Calo, Victor M.; Galvis, Juan
2015-01-01
We study linear elasticity problems with high contrast in the coefficients using asymptotic limits recently introduced. We derive an asymptotic expansion to solve heterogeneous elasticity problems in terms of the contrast in the coefficients. We study the convergence of the expansion in the H1 norm. © 2015 Elsevier B.V.
Asymptotic expansions for high-contrast linear elasticity
Poveda, Leonardo A.
2015-03-01
We study linear elasticity problems with high contrast in the coefficients using asymptotic limits recently introduced. We derive an asymptotic expansion to solve heterogeneous elasticity problems in terms of the contrast in the coefficients. We study the convergence of the expansion in the H1 norm. © 2015 Elsevier B.V.
Asymptotically Safe Dark Matter
DEFF Research Database (Denmark)
Sannino, Francesco; Shoemaker, Ian M.
2015-01-01
We introduce a new paradigm for dark matter (DM) interactions in which the interaction strength is asymptotically safe. In models of this type, the coupling strength is small at low energies but increases at higher energies, and asymptotically approaches a finite constant value. The resulting...... searches are the primary ways to constrain or discover asymptotically safe dark matter....
Seo, Na Jin; Armstrong, Thomas J; Drinkaus, Philip
2009-01-01
This study compares two methods for estimating static friction coefficients for skin. In the first method, referred to as the 'tilt method', a hand supporting a flat object is tilted until the object slides. The friction coefficient is estimated as the tangent of the angle of the object at the slip. The second method estimates the friction coefficient as the pull force required to begin moving a flat object over the surface of the hand, divided by object weight. Both methods were used to estimate friction coefficients for 12 subjects and three materials (cardboard, aluminium, rubber) against a flat hand and against fingertips. No differences in static friction coefficients were found between the two methods, except for that of rubber, where friction coefficient was 11% greater for the tilt method. As with previous studies, the friction coefficients varied with contact force and contact area. Static friction coefficient data are needed for analysis and design of objects that are grasped or manipulated with the hand. The tilt method described in this study can easily be used by ergonomic practitioners to estimate static friction coefficients in the field in a timely manner.
Estimating varying coefficients for partial differential equation models.
Zhang, Xinyu; Cao, Jiguo; Carroll, Raymond J
2017-09-01
Partial differential equations (PDEs) are used to model complex dynamical systems in multiple dimensions, and their parameters often have important scientific interpretations. In some applications, PDE parameters are not constant but can change depending on the values of covariates, a feature that we call varying coefficients. We propose a parameter cascading method to estimate varying coefficients in PDE models from noisy data. Our estimates of the varying coefficients are shown to be consistent and asymptotically normally distributed. The performance of our method is evaluated by a simulation study and by an empirical study estimating three varying coefficients in a PDE model arising from LIDAR data. © 2017, The International Biometric Society.
Litjens, G.J.S.; Hambrock, T.; Hulsbergen-van de Kaa, C.A.; Barentsz, J.O.; Huisman, H.J.
2012-01-01
Purpose: To determine the interpatient variability of prostate peripheral zone (PZ) apparent diffusion coefficient (ADC) and its effect on the assessment of prostate cancer aggressiveness. Materials and Methods: The requirement for institutional review board approval was waived. Intra- and
Asymptotic and geometrical quantization
International Nuclear Information System (INIS)
Karasev, M.V.; Maslov, V.P.
1984-01-01
The main ideas of geometric-, deformation- and asymptotic quantizations are compared. It is shown that, on the one hand, the asymptotic approach is a direct generalization of exact geometric quantization, on the other hand, it generates deformation in multiplication of symbols and Poisson brackets. Besides investigating the general quantization diagram, its applications to the calculation of asymptotics of a series of eigenvalues of operators possessing symmetry groups are considered
Asymptotics and Borel summability
Costin, Ovidiu
2008-01-01
Incorporating substantial developments from the last thirty years into one resource, Asymptotics and Borel Summability provides a self-contained introduction to asymptotic analysis with special emphasis on topics not covered in traditional asymptotics books. The author explains basic ideas, concepts, and methods of generalized Borel summability, transseries, and exponential asymptotics. He provides complete mathematical rigor while supplementing it with heuristic material and examples, so that some proofs may be omitted by applications-oriented readers.To give a sense of how new methods are us
Burgers, Phillip; Alexander, David E.
2012-01-01
For a century, researchers have used the standard lift coefficient C(L) to evaluate the lift, L, generated by fixed wings over an area S against dynamic pressure, ½ρv(2), where v is the effective velocity of the wing. Because the lift coefficient was developed initially for fixed wings in steady flow, its application to other lifting systems requires either simplifying assumptions or complex adjustments as is the case for flapping wings and rotating cylinders.This paper interprets the standar...
Asymptotic Solutions of Serial Radial Fuel Shuffling
Directory of Open Access Journals (Sweden)
Xue-Nong Chen
2015-12-01
Full Text Available In this paper, the mechanism of traveling wave reactors (TWRs is investigated from the mathematical physics point of view, in which a stationary fission wave is formed by radial fuel drifting. A two dimensional cylindrically symmetric core is considered and the fuel is assumed to drift radially according to a continuous fuel shuffling scheme. A one-group diffusion equation with burn-up dependent macroscopic coefficients is set up. The burn-up dependent macroscopic coefficients were assumed to be known as functions of neutron fluence. By introducing the effective multiplication factor keff, a nonlinear eigenvalue problem is formulated. The 1-D stationary cylindrical coordinate problem can be solved successively by analytical and numerical integrations for associated eigenvalues keff. Two representative 1-D examples are shown for inward and outward fuel drifting motions, respectively. The inward fuel drifting has a higher keff than the outward one. The 2-D eigenvalue problem has to be solved by a more complicated method, namely a pseudo time stepping iteration scheme. Its 2-D asymptotic solutions are obtained together with certain eigenvalues keff for several fuel inward drifting speeds. Distributions of the neutron flux, the neutron fluence, the infinity multiplication factor kinf and the normalized power are presented for two different drifting speeds.
Lattimore, Tor; Hutter, Marcus
2011-01-01
Artificial general intelligence aims to create agents capable of learning to solve arbitrary interesting problems. We define two versions of asymptotic optimality and prove that no agent can satisfy the strong version while in some cases, depending on discounting, there does exist a non-computable weak asymptotically optimal agent.
Kim, Jin You; Suh, Hie Bum; Kang, Hyun Jung; Shin, Jong Ki; Choo, Ki Seok; Nam, Kyung Jin; Lee, Seok Won; Jung, Young Lae; Bae, Young Tae
2016-05-01
The purpose of this study was to investigate prospectively whether the apparent diffusion coefficients (ADCs) of both breast cancer and normal fibroglandular tissue vary with the menstrual cycle and menopausal status. Institutional review board approval was obtained, and informed consent was obtained from each participant. Fifty-seven women (29 premenopausal, 28 postmenopausal) with newly diagnosed breast cancer underwent diffusion-weighted imaging twice (interval 12-20 days) before surgery. Two radiologists independently measured ADC of breast cancer and normal contralateral breast tissue, and we quantified the differences according to the phases of menstrual cycle and menopausal status. With normal fibroglandular tissue, ADC was significantly lower in postmenopausal than in premenopausal women (P = 0.035). In premenopausal women, ADC did not differ significantly between proliferative and secretory phases in either breast cancer or normal fibroglandular tissue (P = 0.969 and P = 0.519, respectively). In postmenopausal women, no significant differences were found between ADCs measured at different time intervals in either breast cancer or normal fibroglandular tissue (P = 0.948 and P = 0.961, respectively). The within-subject variability of the ADC measurements was quantified using the coefficient of variation (CV) and was small: the mean CVs of tumor ADC were 2.90 % (premenopausal) and 3.43 % (postmenopausal), and those of fibroglandular tissue ADC were 4.37 % (premenopausal) and 2.55 % (postmenopausal). Both intra- and interobserver agreements were excellent for ADC measurements, with intraclass correlation coefficients in the range of 0.834-0.974. In conclusion, the measured ADCs of breast cancer and normal fibroglandular tissue were not affected significantly by menstrual cycle, and the measurements were highly reproducible both within and between observers.
Albuja, Antonella A.; Scheeres, Daniel J.
2015-02-01
The Yarkovsky-O'Keefe-Radzvieskii-Paddack (YORP) effect has been well studied for asteroids. This paper develops an analytic solution to find the normal emission YORP component for a single facet. The solution presented here does not account for self-shadowing or self-heating. The YORP coefficient for all facets can be summed together to find the total coefficient of the asteroid. The normal emission component of YORP has been shown to be the most important for asteroids and it directly affects the rate of change of the asteroid's spin period. The analytical solution found is a sole function of the facet's geometry and the obliquity of the asteroid. This solution is universal for any facet and its orientation. The behaviour of the coefficient is analysed with this analytical solution. The closed-form solution is used to find the total YORP coefficient for the asteroids Apollo and 1998 ML14 whose shape models are composed of different numbers of facets. The results are then compared to published results and those obtained through numerical quadrature for validation.
Block Empirical Likelihood for Longitudinal Single-Index Varying-Coefficient Model
Directory of Open Access Journals (Sweden)
Yunquan Song
2013-01-01
Full Text Available In this paper, we consider a single-index varying-coefficient model with application to longitudinal data. In order to accommodate the within-group correlation, we apply the block empirical likelihood procedure to longitudinal single-index varying-coefficient model, and prove a nonparametric version of Wilks’ theorem which can be used to construct the block empirical likelihood confidence region with asymptotically correct coverage probability for the parametric component. In comparison with normal approximations, the proposed method does not require a consistent estimator for the asymptotic covariance matrix, making it easier to conduct inference for the model's parametric component. Simulations demonstrate how the proposed method works.
Numerical algorithms for uniform Airy-type asymptotic expansions
N.M. Temme (Nico)
1997-01-01
textabstractAiry-type asymptotic representations of a class of special functions are considered from a numerical point of view. It is well known that the evaluation of the coefficients of the asymptotic series near the transition point is a difficult problem. We discuss two methods for computing
Conformal Phase Diagram of Complete Asymptotically Free Theories
DEFF Research Database (Denmark)
Pica, Claudio; Ryttov, Thomas A.; Sannino, Francesco
2017-01-01
function. We provide the general conditions that the beta function coefficients must abide for the theory to be completely asymptotically free while simultaneously possessing an infrared stable fixed point. We also uncover special trajectories in coupling space along which some couplings are both...... asymptotically safe and infrared conformal....
Kashchenko, Sergey A.
2016-12-01
The dynamics of second-order equations with nonlinear delayed feedback and a large coefficient of a delayed equation is investigated using asymptotic methods. Based on special methods of quasi-normal forms, a new construction is elaborated for obtaining the main terms of asymptotic expansions of asymptotic residual solutions. It is shown that the dynamical properties of the above equations are determined mostly by the behavior of the solutions of some special families of parabolic boundary value problems. A comparative analysis of the dynamics of equations with the delayed feedback of three types is carried out.
Asymptotic Parachute Performance Sensitivity
Way, David W.; Powell, Richard W.; Chen, Allen; Steltzner, Adam D.
2006-01-01
In 2010, the Mars Science Laboratory mission will pioneer the next generation of robotic Entry, Descent, and Landing systems by delivering the largest and most capable rover to date to the surface of Mars. In addition to landing more mass than any other mission to Mars, Mars Science Laboratory will also provide scientists with unprecedented access to regions of Mars that have been previously unreachable. By providing an Entry, Descent, and Landing system capable of landing at altitudes as high as 2 km above the reference gravitational equipotential surface, or areoid, as defined by the Mars Orbiting Laser Altimeter program, Mars Science Laboratory will demonstrate sufficient performance to land on 83% of the planet s surface. By contrast, the highest altitude landing to date on Mars has been the Mars Exploration Rover at 1.3 km below the areoid. The coupling of this improved altitude performance with latitude limits as large as 60 degrees off of the equator and a precise delivery to within 10 km of a surface target, will allow the science community to select the Mars Science Laboratory landing site from thousands of scientifically interesting possibilities. In meeting these requirements, Mars Science Laboratory is extending the limits of the Entry, Descent, and Landing technologies qualified by the Mars Viking, Mars Pathfinder, and Mars Exploration Rover missions. Specifically, the drag deceleration provided by a Viking-heritage 16.15 m supersonic Disk-Gap-Band parachute in the thin atmosphere of Mars is insufficient, at the altitudes and ballistic coefficients under consideration by the Mars Science Laboratory project, to maintain necessary altitude performance and timeline margin. This paper defines and discusses the asymptotic parachute performance observed in Monte Carlo simulation and performance analysis and its effect on the Mars Science Laboratory Entry, Descent, and Landing architecture.
Asymptotical representation of discrete groups
International Nuclear Information System (INIS)
Mishchenko, A.S.; Mohammad, N.
1995-08-01
If one has a unitary representation ρ: π → U(H) of the fundamental group π 1 (M) of the manifold M then one can do may useful things: 1. To construct a natural vector bundle over M; 2. To construct the cohomology groups with respect to the local system of coefficients; 3. To construct the signature of manifold M with respect to the local system of coefficients; and others. In particular, one can write the Hirzebruch formula which compares the signature with the characteristic classes of the manifold M, further based on this, find the homotopy invariant characteristic classes (i.e. the Novikov conjecture). Taking into account that the family of known representations is not sufficiently large, it would be interesting to extend this family to some larger one. Using the ideas of A.Connes, M.Gromov and H.Moscovici a proper notion of asymptotical representation is defined. (author). 7 refs
ASYMPTOTICS OF a PARTICLES TRANSPORT PROBLEM
Directory of Open Access Journals (Sweden)
Kuzmina Ludmila Ivanovna
2017-11-01
Full Text Available Subject: a groundwater filtration affects the strength and stability of underground and hydro-technical constructions. Research objectives: the study of one-dimensional problem of displacement of suspension by the flow of pure water in a porous medium. Materials and methods: when filtering a suspension some particles pass through the porous medium, and some of them are stuck in the pores. It is assumed that size distributions of the solid particles and the pores overlap. In this case, the main mechanism of particle retention is a size-exclusion: the particles pass freely through the large pores and get stuck at the inlet of the tiny pores that are smaller than the particle diameter. The concentrations of suspended and retained particles satisfy two quasi-linear differential equations of the first order. To solve the filtration problem, methods of nonlinear asymptotic analysis are used. Results: in a mathematical model of filtration of suspensions, which takes into account the dependence of the porosity and permeability of the porous medium on concentration of retained particles, the boundary between two phases is moving with variable velocity. The asymptotic solution to the problem is constructed for a small filtration coefficient. The theorem of existence of the asymptotics is proved. Analytical expressions for the principal asymptotic terms are presented for the case of linear coefficients and initial conditions. The asymptotics of the boundary of two phases is given in explicit form. Conclusions: the filtration problem under study can be solved analytically.
International Nuclear Information System (INIS)
Pogosian, S.
1981-01-01
It is known that in the grand canonical ensemble (for the case of small density of particles) the fluctuations (approximately mod(Λ)sup(1/2)) in the particle number have an asymptotic normal distribution as Λ→infinity. A similar statement holds for the distribution of the particle number in a bounded domain evaluated with respect to the limiting Gibbs distribution. The author obtains an asymptotic expansion in the local limit theorem for the particle number in the grand canonical ensemble, by using the asymptotic expansion of the grand canonical partition function. The coefficients of this expansion are not constants but depend on the form of the domain Λ. More precisely, they are constant up to a correction which is small (for large Λ). The author obtains an explicit form for the second term of the asymptotic expansion in the local limit theorem for the particle number, and also gets the first correction terms for the coefficients of this expansion. (Auth.)
International Nuclear Information System (INIS)
Todorov, T.D.
1980-01-01
The set of asymptotic numbers A as a system of generalized numbers including the system of real numbers R, as well as infinitely small (infinitesimals) and infinitely large numbers, is introduced. The detailed algebraic properties of A, which are unusual as compared with the known algebraic structures, are studied. It is proved that the set of asymptotic numbers A cannot be isomorphically embedded as a subspace in any group, ring or field, but some particular subsets of asymptotic numbers are shown to be groups, rings, and fields. The algebraic operation, additive and multiplicative forms, and the algebraic properties are constructed in an appropriate way. It is shown that the asymptotic numbers give rise to a new type of generalized functions quite analogous to the distributions of Schwartz allowing, however, the operation multiplication. A possible application of these functions to quantum theory is discussed
Asymptotic freedom without guilt
International Nuclear Information System (INIS)
Ma, E.
1979-01-01
The notion of asymptotic freedom in quantum chromodynamics is explained on general physical grounds, without invoking the formal arguments of renormalizable quantum field theory. The related concept of quark confinement is also discussed along the same line. 5 references
International Nuclear Information System (INIS)
Fornasa, Francesca; Montemezzi, Stefania
2012-01-01
Background: Diffusion-weighted magnetic resonance imaging (DWI) is increasingly used in the diagnosis of endometrial disease. No complete knowledge, however, exists yet of the influence of physiology on the endometrial apparent diffusion coefficient (ADC) values on which DWI is based. Purpose: To establish whether the ADC values measured with DWI in the endometrium of healthy reproductive-aged women significantly vary from the early proliferative to the periovulatory phase of the menstrual cycle and between the fundus and the isthmus of the uterus. Material and Methods: In 17 women the endometrial ADC values measured on the fifth menstrual day, both at the fundus and at the isthmus of the uterus, were compared to the values obtained on the 14th day before the subsequent cycle. In 81 women (menstrual day: fifth through 21st) the endometrial ADC values measured at the fundus were compared to the values obtained at the isthmus of the uterus. All examinations were performed with a 1.5 T magnet (b values: 0 and 800 mm/s 2 ). The results were analyzed by means of Student's t-test per paired data. Results: The endometrial ADC values measured on the fifth day of the menstrual cycle were lower than those obtained in the periovulatory phase both at the fundus (mean 0.923 vs. 1.256 x 10 - 3 mm 2 /s) and at the isthmus (mean 1.297 vs. 1.529 x 10 - 3 mm 2 /s) of the uterus. The endometrial ADC values measured at the fundus of the uterus were lower than those obtained at the isthmus (mean 1.132 vs. 1.420 x 10 - 3 mm 2 /s) through the menstrual cycle. All these differences were highly significant (P < 0.001) at statistical analysis. Conclusion: Physiological variations occurring in endometrial ADC values of healthy women should be considered by the radiologists when interpreting DWI examinations in patients with endometrial disease
Asymptotic Theory for Regressions with Smoothly Changing Parameters
DEFF Research Database (Denmark)
Hillebrand, Eric Tobias; Medeiros, Marcelo C.; Xu, Junyue
We derive asymptotic properties of the quasi maximum likelihood estimator of smooth transition regressions when time is the transition variable. The consistency of the estimator and its asymptotic distribution are examined. It is shown that the estimator converges at the usual square-root-of-T rate...... and has an asymptotically normal distribution. Finite sample properties of the estimator are explored in simulations. We illustrate with an application to US inflation and output data....
Asymptotic theory for regressions with smoothly changing parameters
DEFF Research Database (Denmark)
Hillebrand, Eric; Medeiros, Marcelo; Xu, Junyue
2013-01-01
We derive asymptotic properties of the quasi maximum likelihood estimator of smooth transition regressions when time is the transition variable. The consistency of the estimator and its asymptotic distribution are examined. It is shown that the estimator converges at the usual pT-rate and has...... an asymptotically normal distribution. Finite sample properties of the estimator are explored in simulations. We illustrate with an application to US inflation and output data....
Large time asymptotics of solutions of the equations of principal chiral field
International Nuclear Information System (INIS)
Sukhanov, V.V.
1990-01-01
Asymptotic behaviour of solutions of the equations of principal chiral field when one of the arguments tends to infinity is investigated. Asymptotics of solutions of the corresponding spectral problem is investigated as well. explicit formulas are constructed which connect the coefficients of the asymptotic decomposition of the potential with the data of the corresponding inverse problem by means of a birational transformation
Quasi-extended asymptotic functions
International Nuclear Information System (INIS)
Todorov, T.D.
1979-01-01
The class F of ''quasi-extended asymptotic functions'' is introduced. It contains all extended asymptotic functions as well as some new asymptotic functions very similar to the Schwartz distributions. On the other hand, every two quasiextended asymptotic functions can be multiplied as opposed to the Schwartz distributions; in particular, the square delta 2 of an asymptotic function delta similar to Dirac's delta-function, is constructed as an example
International Nuclear Information System (INIS)
Dewar, R. L.
1995-01-01
A large part of physics consists of learning which asymptotic methods to apply where, yet physicists are not always taught asymptotics in a systematic way. Asymptotology is given using an example from aerodynamics, and a rent Phys. Rev. Letter Comment is used as a case study of one subtle way things can go wrong. It is shown that the application of local analysis leads to erroneous conclusions regarding the existence of a continuous spectrum in a simple test problem, showing that a global analysis must be used. The final section presents results on a more sophisticated example, namely the WKBJ solution of Mathieu equation. 13 refs., 2 figs
Asymptotic expansions for the Gaussian unitary ensemble
DEFF Research Database (Denmark)
Haagerup, Uffe; Thorbjørnsen, Steen
2012-01-01
Let g : R ¿ C be a C8-function with all derivatives bounded and let trn denote the normalized trace on the n × n matrices. In Ref. 3 Ercolani and McLaughlin established asymptotic expansions of the mean value ¿{trn(g(Xn))} for a rather general class of random matrices Xn, including the Gaussian U...
Asymptotics for the minimum covariance determinant estimator
Butler, R.W.; Davies, P.L.; Jhun, M.
1993-01-01
Consistency is shown for the minimum covariance determinant (MCD) estimators of multivariate location and scale and asymptotic normality is shown for the former. The proofs are made possible by showing a separating ellipsoid property for the MCD subset of observations. An analogous property is shown
International Nuclear Information System (INIS)
Priola, Adriano Massimiliano; Priola, Sandro Massimo; Gned, Dario; Veltri, Andrea; Giraudo, Maria Teresa
2018-01-01
To prospectively evaluate usefulness of the apparent diffusion coefficient (ADC) in differentiating anterior mediastinal lymphoma from nonsuppressing normal thymus on chemical-shift MR, and to look at the relationship between patient age and ADC. Seventy-three young subjects (25 men, 48 women; age range, 9-29 years), who underwent chemical-shift MR and diffusion-weighted MR were divided into a normal thymus group (group A, 40 subjects), and a lymphoma group (group B, 33 patients). For group A, all subjects had normal thymus with no suppression on opposed-phase chemical-shift MR. Two readers measured the signal intensity index (SII) and ADC. Differences in SII and ADC between groups were tested using t-test. ADC was correlated with age using Pearson correlation coefficient. Mean SII±standard deviation was 2.7±1.8% for group A and 2.2±2.4% for group B, with no significant difference between groups (P=.270). Mean ADC was 2.48±0.38 x 10 -3 mm 2 /s for group A and 1.24±0.23 x 10 -3 mm 2 /s for group B. A significant difference between groups was found (P<.001), with no overlap in range. Lastly, significant correlation was found between age and ADC (r=0.935, P<.001) in group A. ADC of diffusion-weighted MR is a noninvasive and accurate parameter for differentiating lymphoma from nonsuppressing thymus on chemical-shift MR in young subjects. (orig.)
DEFF Research Database (Denmark)
Litim, Daniel F.; Sannino, Francesco
2014-01-01
We study the ultraviolet behaviour of four-dimensional quantum field theories involving non-abelian gauge fields, fermions and scalars in the Veneziano limit. In a regime where asymptotic freedom is lost, we explain how the three types of fields cooperate to develop fully interacting ultraviolet ...
Cristallini, Achille
2016-07-01
A new and intriguing machine may be obtained replacing the moving pulley of a gun tackle with a fixed point in the rope. Its most important feature is the asymptotic efficiency. Here we obtain a satisfactory description of this machine by means of vector calculus and elementary trigonometry. The mathematical model has been compared with experimental data and briefly discussed.
Adubeiro, Nuno; Nogueira, Maria Luísa; Nunes, Rita G; Ferreira, Hugo Alexandre; Ribeiro, Eduardo; La Fuente, José Maria Ferreira
Determining optimal b-value pair for differentiation between normal and prostate cancer (PCa) tissues. Forty-three patients with diagnosis or PCa symptoms were included. Apparent diffusion coefficient (ADC) was estimated using minimum and maximum b-values of 0, 50, 100, 150, 200, 500s/mm2 and 500, 800, 1100, 1400, 1700 and 2000s/mm2, respectively. Diagnostic performances were evaluated when Area-under-the-curve (AUC)>95%. 15 of the 35 b-values pair surpassed this AUC threshold. The pair (50, 2000s/mm2) provided the highest AUC (96%) with ADC cutoff 0.89×10- 3 mm 2 /s, sensitivity 95.5%, specificity 93.2% and accuracy 94.4%. The best b-value pair was b=50, 2000s/mm2. Copyright © 2017 Elsevier Inc. All rights reserved.
Cookbook asymptotics for spiral and scroll waves in excitable media.
Margerit, Daniel; Barkley, Dwight
2002-09-01
Algebraic formulas predicting the frequencies and shapes of waves in a reaction-diffusion model of excitable media are presented in the form of four recipes. The formulas themselves are based on a detailed asymptotic analysis (published elsewhere) of the model equations at leading order and first order in the asymptotic parameter. The importance of the first order contribution is stressed throughout, beginning with a discussion of the Fife limit, Fife scaling, and Fife regime. Recipes are given for spiral waves and detailed comparisons are presented between the asymptotic predictions and the solutions of the full reaction-diffusion equations. Recipes for twisted scroll waves with straight filaments are given and again comparisons are shown. The connection between the asymptotic results and filament dynamics is discussed, and one of the previously unknown coefficients in the theory of filament dynamics is evaluated in terms of its asymptotic expansion. (c) 2002 American Institute of Physics.
Asymptotics of relativistic spin networks
International Nuclear Information System (INIS)
Barrett, John W; Steele, Christopher M
2003-01-01
The stationary phase technique is used to calculate asymptotic formulae for SO(4) relativistic spin networks. For the tetrahedral spin network this gives the square of the Ponzano-Regge asymptotic formula for the SU(2) 6j-symbol. For the 4-simplex (10j-symbol) the asymptotic formula is compared with numerical calculations of the spin network evaluation. Finally, we discuss the asymptotics of the SO(3, 1) 10j-symbol
Mixed normal inference on multicointegration
Boswijk, H.P.
2009-01-01
Asymptotic likelihood analysis of cointegration in I(2) models, see Johansen (1997, 2006), Boswijk (2000) and Paruolo (2000), has shown that inference on most parameters is mixed normal, implying hypothesis test statistics with an asymptotic 2 null distribution. The asymptotic distribution of the
Asymptotic distribution of products of sums of independent random ...
Indian Academy of Sciences (India)
integrable random variables (r.v.) are asymptotically log-normal. This fact ... the product of the partial sums of i.i.d. positive random variables as follows. .... Now define ..... by Henan Province Foundation and Frontier Technology Research Plan.
Variationally Asymptotically Stable Difference Systems
Directory of Open Access Journals (Sweden)
Goo YoonHoe
2007-01-01
Full Text Available We characterize the h-stability in variation and asymptotic equilibrium in variation for nonlinear difference systems via n∞-summable similarity and comparison principle. Furthermore we study the asymptotic equivalence between nonlinear difference systems and their variational difference systems by means of asymptotic equilibria of two systems.
Perturbed asymptotically linear problems
Bartolo, R.; Candela, A. M.; Salvatore, A.
2012-01-01
The aim of this paper is investigating the existence of solutions of some semilinear elliptic problems on open bounded domains when the nonlinearity is subcritical and asymptotically linear at infinity and there is a perturbation term which is just continuous. Also in the case when the problem has not a variational structure, suitable procedures and estimates allow us to prove that the number of distinct crtitical levels of the functional associated to the unperturbed problem is "stable" unde...
Model Hadron asymptotic behaviour
International Nuclear Information System (INIS)
Kralchevsky, P.; Nikolov, A.
1983-01-01
The work is devoted to the problem of solving a set of asymptotic equations describing the model hardon interaction. More specifically an interactive procedure consisting of two stages is proposed and the first stage is exhaustively studied here. The principle of contracting transformations has been applied for this purpose. Under rather general and natural assumptions, solutions in a series of metric spaces suitable for physical applications have been found. For each of these spaces a solution with unique definiteness is found. (authors)
On asymptotic analysis of spectral problems in elasticity
Directory of Open Access Journals (Sweden)
S.A. Nazarov
Full Text Available The three-dimensional spectral elasticity problem is studied in an anisotropic and inhomogeneous solid with small defects, i.e., inclusions, voids, and microcracks. Asymptotics of eigenfrequencies and the corresponding elastic eigenmodes are constructed and justified. New technicalities of the asymptotic analysis are related to variable coefficients of differential operators, vectorial setting of the problem, and usage of intrinsic integral characteristics of defects. The asymptotic formulae are developed in a form convenient for application in shape optimization and inverse problems.
Extended asymptotic functions - some examples
International Nuclear Information System (INIS)
Todorov, T.D.
1981-01-01
Several examples of extended asymptotic functions of two variables are given. This type of asymptotic functions has been introduced as an extension of continuous ordinary functions. The presented examples are realizations of some Schwartz distributions delta(x), THETA(x), P(1/xsup(n)) and can be multiplied in the class of the asymptotic functions as opposed to the theory of Schwartz distributions. The examples illustrate the method of construction of extended asymptotic functions similar to the distributions. The set formed by the extended asymptotic functions is also considered. It is shown, that this set is not closed with respect to addition and multiplication
International Nuclear Information System (INIS)
O'Flynn, Elizabeth A.M.; Morgan, Veronica A.; Giles, Sharon L.; de Souza, Nandita M.
2012-01-01
To establish the reproducibility of apparent diffusion coefficient (ADC) measurements in normal fibroglandular breast tissue and to assess variation in ADC values with phase of the menstrual cycle and menopausal status. Thirty-one volunteers (13 premenopausal, 18 postmenopausal) underwent magnetic resonance twice (interval 11-22 days) using diffusion-weighted MRI. ADC total and a perfusion-insensitive ADC high (omitting b = 0) were calculated. Reproducibility and inter-observer variability of mean ADC values were assessed. The difference in mean ADC values between the two phases of the menstrual cycle and the postmenopausal breast were evaluated. ADC total and ADC high showed good reproducibility (r% = 17.6, 22.4). ADC high showed very good inter-observer agreement (kappa = 0.83). The intraclass correlation coefficients (ICC) were 0.93 and 0.91. Mean ADC values were significantly lower in the postmenopausal breast (ADC total 1.46 ± 0.3 x 10 -3 mm 2 /s, ADC high 1.33 ± 0.3 x 10 -3 mm 2 /s) compared with the premenopausal breast (ADC total 1.84 ± 0.26 x 10 -3 mm 2 /s, ADC high 1.77 ± 0.26 x 10 -3 mm 2 /s; both P total P = 0.2, ADC high P = 0.24) or between postmenopausal women taking or not taking oestrogen supplements (ADC total P = 0.6, ADC high P = 0.46). ADC values in fibroglandular breast tissue are reproducible. Lower ADC values within the postmenopausal breast may reduce diffusion-weighted contrast and have implications for accurately detecting tumours. (orig.)
Energy Technology Data Exchange (ETDEWEB)
O' Flynn, Elizabeth A.M.; Morgan, Veronica A.; Giles, Sharon L. [Cancer Research UK and ESPSRC Cancer Imaging Centre, Clinical Magnetic Resonance Group, Surrey (United Kingdom); deSouza, Nandita M. [Royal Marsden NHS Foundation Trust, Clinical Magnetic Resonance Group, Institute of Cancer Research, Surrey (United Kingdom)
2012-07-15
To establish the reproducibility of apparent diffusion coefficient (ADC) measurements in normal fibroglandular breast tissue and to assess variation in ADC values with phase of the menstrual cycle and menopausal status. Thirty-one volunteers (13 premenopausal, 18 postmenopausal) underwent magnetic resonance twice (interval 11-22 days) using diffusion-weighted MRI. ADC{sub total} and a perfusion-insensitive ADC{sub high} (omitting b = 0) were calculated. Reproducibility and inter-observer variability of mean ADC values were assessed. The difference in mean ADC values between the two phases of the menstrual cycle and the postmenopausal breast were evaluated. ADC{sub total} and ADC{sub high} showed good reproducibility (r% = 17.6, 22.4). ADC{sub high} showed very good inter-observer agreement (kappa = 0.83). The intraclass correlation coefficients (ICC) were 0.93 and 0.91. Mean ADC values were significantly lower in the postmenopausal breast (ADC{sub total} 1.46 {+-} 0.3 x 10{sup -3} mm{sup 2}/s, ADC{sub high} 1.33 {+-} 0.3 x 10{sup -3} mm{sup 2}/s) compared with the premenopausal breast (ADC{sub total} 1.84 {+-} 0.26 x 10{sup -3} mm{sup 2}/s, ADC{sub high} 1.77 {+-} 0.26 x 10{sup -3} mm{sup 2}/s; both P < 0.001). No significant difference was seen in ADC values in relation to menstrual cycle (ADC{sub total} P = 0.2, ADC{sub high} P = 0.24) or between postmenopausal women taking or not taking oestrogen supplements (ADC{sub total} P = 0.6, ADC{sub high} P = 0.46). ADC values in fibroglandular breast tissue are reproducible. Lower ADC values within the postmenopausal breast may reduce diffusion-weighted contrast and have implications for accurately detecting tumours. (orig.)
Song, Yong Sub; Choi, Seung Hong; Park, Chul-Kee; Yi, Kyung Sik; Lee, Woong Jae; Yun, Tae Jin; Kim, Tae Min; Lee, Se-Hoon; Kim, Ji-Hoon; Sohn, Chul-Ho; Park, Sung-Hye; Kim, Il Han; Jahng, Geon-Ho; Chang, Kee-Hyun
2013-01-01
The purpose of this study was to differentiate true progression from pseudoprogression of glioblastomas treated with concurrent chemoradiotherapy (CCRT) with temozolomide (TMZ) by using histogram analysis of apparent diffusion coefficient (ADC) and normalized cerebral blood volume (nCBV) maps. Twenty patients with histopathologically proven glioblastoma who had received CCRT with TMZ underwent perfusion-weighted imaging and diffusion-weighted imaging (b = 0, 1000 sec/mm(2)). The corresponding nCBV and ADC maps for the newly visible, entirely enhancing lesions were calculated after the completion of CCRT with TMZ. Two observers independently measured the histogram parameters of the nCBV and ADC maps. The histogram parameters between the true progression group (n = 10) and the pseudoprogression group (n = 10) were compared by use of an unpaired Student's t test and subsequent multivariable stepwise logistic regression analysis to determine the best predictors for the differential diagnosis between the two groups. Receiver operating characteristic analysis was employed to determine the best cutoff values for the histogram parameters that proved to be significant predictors for differentiating true progression from pseudoprogression. Intraclass correlation coefficient was used to determine the level of inter-observer reliability for the histogram parameters. The 5th percentile value (C5) of the cumulative ADC histograms was a significant predictor for the differential diagnosis between true progression and pseudoprogression (p = 0.044 for observer 1; p = 0.011 for observer 2). Optimal cutoff values of 892 × 10(-6) mm(2)/sec for observer 1 and 907 × 10(-6) mm(2)/sec for observer 2 could help differentiate between the two groups with a sensitivity of 90% and 80%, respectively, a specificity of 90% and 80%, respectively, and an area under the curve of 0.880 and 0.840, respectively. There was no other significant differentiating parameter on the nCBV histograms. Inter
International Nuclear Information System (INIS)
Bailin, D.
1974-01-01
It is proved that the characteristic power deviations from scaling of the theories which are not asymptotically free should be detectable in the N.A.L. muon experiments. The Yukawa theories here considered have SU(3) non-singlet structure function moments varying as a power of -q 2 , namely (-q 2 ) at power -p. The maximum value of p is determined to be 2/3:SU3 and 1:SU2. The outstanding question is whether the Yukawa theories considered do in fact have fixed points satisfying the inequalities, and thus simultaneous (non-trivial) zeroes of β(g) and β(lambda) have to be found
High frequency asymptotic methods
International Nuclear Information System (INIS)
Bouche, D.; Dessarce, R.; Gay, J.; Vermersch, S.
1991-01-01
The asymptotic methods allow us to compute the interaction of high frequency electromagnetic waves with structures. After an outline of their foundations with emphasis on the geometrical theory of diffraction, it is shown how to use these methods to evaluate the radar cross section (RCS) of complex tri-dimensional objects of great size compared to the wave-length. The different stages in simulating phenomena which contribute to the RCS are reviewed: physical theory of diffraction, multiple interactions computed by shooting rays, research for creeping rays. (author). 7 refs., 6 figs., 3 insets
Asymptotic Safety Guaranteed in Supersymmetry
Bond, Andrew D.; Litim, Daniel F.
2017-11-01
We explain how asymptotic safety arises in four-dimensional supersymmetric gauge theories. We provide asymptotically safe supersymmetric gauge theories together with their superconformal fixed points, R charges, phase diagrams, and UV-IR connecting trajectories. Strict perturbative control is achieved in a Veneziano limit. Consistency with unitarity and the a theorem is established. We find that supersymmetry enhances the predictivity of asymptotically safe theories.
Robust methods and asymptotic theory in nonlinear econometrics
Bierens, Herman J
1981-01-01
This Lecture Note deals with asymptotic properties, i.e. weak and strong consistency and asymptotic normality, of parameter estimators of nonlinear regression models and nonlinear structural equations under various assumptions on the distribution of the data. The estimation methods involved are nonlinear least squares estimation (NLLSE), nonlinear robust M-estimation (NLRME) and non linear weighted robust M-estimation (NLWRME) for the regression case and nonlinear two-stage least squares estimation (NL2SLSE) and a new method called minimum information estimation (MIE) for the case of structural equations. The asymptotic properties of the NLLSE and the two robust M-estimation methods are derived from further elaborations of results of Jennrich. Special attention is payed to the comparison of the asymptotic efficiency of NLLSE and NLRME. It is shown that if the tails of the error distribution are fatter than those of the normal distribution NLRME is more efficient than NLLSE. The NLWRME method is appropriate ...
Asymptotic series and functional integrals in quantum field theory
International Nuclear Information System (INIS)
Shirkov, D.V.
1979-01-01
Investigations of the methods for analyzing ultra-violet and infrared asymptotics in the quantum field theory (QFT) have been reviewed. A powerful method of the QFT analysis connected with the group property of renormalized transformations has been created at the first stage. The result of the studies of the second period is the constructive solution of the problem of outgoing the framework of weak coupling. At the third stage of studies essential are the asymptotic series and functional integrals in the QFT, which are used for obtaining the asymptotic type of the power expansion coefficients in the coupling constant at high values of the exponents for a number of simple models. Further advance to higher values of the coupling constant requires surmounting the difficulties resulting from the asymptotic character of expansions and a constructive application in the region of strong coupling (g >> 1)
Bao, Shixing; Watanabe, Yoshiyuki; Takahashi, Hiroto; Tanaka, Hisashi; Arisawa, Atsuko; Matsuo, Chisato; Wu, Rongli; Fujimoto, Yasunori; Tomiyama, Noriyuki
2018-05-31
This study aimed to determine whether whole-tumor histogram analysis of normalized cerebral blood volume (nCBV) and apparent diffusion coefficient (ADC) for contrast-enhancing lesions can be used to differentiate between glioblastoma (GBM) and primary central nervous system lymphoma (PCNSL). From 20 patients, 9 with PCNSL and 11 with GBM without any hemorrhagic lesions, underwent MRI, including diffusion-weighted imaging and dynamic susceptibility contrast perfusion-weighted imaging before surgery. Histogram analysis of nCBV and ADC from whole-tumor voxels in contrast-enhancing lesions was performed. An unpaired t-test was used to compare the mean values for each type of tumor. A multivariate logistic regression model (LRM) was performed to classify GBM and PCNSL using the best parameters of ADC and nCBV. All nCBV histogram parameters of GBMs were larger than those of PCNSLs, but only average nCBV was statistically significant after Bonferroni correction. Meanwhile, ADC histogram parameters were also larger in GBM compared to those in PCNSL, but these differences were not statistically significant. According to receiver operating characteristic curve analysis, the nCBV average and ADC 25th percentile demonstrated the largest area under the curve with values of 0.869 and 0.838, respectively. The LRM combining these two parameters differentiated between GBM and PCNSL with a higher area under the curve value (Logit (P) = -21.12 + 10.00 × ADC 25th percentile (10 -3 mm 2 /s) + 5.420 × nCBV mean, P histogram analysis of nCBV and ADC combined can be a valuable objective diagnostic method for differentiating between GBM and PCNSL.
Barral, M; Soyer, P; Ben Hassen, W; Gayat, E; Aout, M; Chiaradia, M; Rahmouni, A; Luciani, A
2013-04-01
To evaluate reproducibility and variations in apparent diffusion coefficient (ADC) measurement in normal pancreatic parenchyma at 1.5- and 3.0-Tesla and determine if differences may exist between the four pancreatic segments. Diffusion-weighted MR imaging of the pancreas was performed at 1.5-Tesla in 20 patients and at 3.0-Tesla in other 20 patients strictly matched for gender and age using the same b values (0, 400 and 800s/mm(2)). Two independent observers placed regions of interest within the four pancreatic segments to measure ADC at both fields. Intra- and inter-observer agreement in ADC measurement was assessed using Bland-Altman analysis and comparison between ADC values obtained at both fields using non-parametrical tests. There were no significant differences in ADC between repeated measurements and between ADC obtained at 1.5-Tesla and those at 3.0-Tesla. The 95% limits of intra-observer agreement between ADC were 2.3%-22.7% at 1.5-Tesla and 1%-24.2% at 3.0-Tesla and those for inter-observer agreement between 1.9%-14% at 1.5-Tesla and 8%-25% at 3.0-Tesla. ADC values were similar in all pancreatic segments at 3.0-T whereas the tail had lower ADC at 1.5-Tesla. ADC measurement conveys high degrees of intra- and inter-observer reproducibility. ADC have homogeneous distribution among the four pancreatic segments at 3.0-Tesla. Copyright © 2012 Éditions françaises de radiologie. Published by Elsevier Masson SAS. All rights reserved.
More asymptotic safety guaranteed
Bond, Andrew D.; Litim, Daniel F.
2018-04-01
We study interacting fixed points and phase diagrams of simple and semisimple quantum field theories in four dimensions involving non-Abelian gauge fields, fermions and scalars in the Veneziano limit. Particular emphasis is put on new phenomena which arise due to the semisimple nature of the theory. Using matter field multiplicities as free parameters, we find a large variety of interacting conformal fixed points with stable vacua and crossovers inbetween. Highlights include semisimple gauge theories with exact asymptotic safety, theories with one or several interacting fixed points in the IR, theories where one of the gauge sectors is both UV free and IR free, and theories with weakly interacting fixed points in the UV and the IR limits. The phase diagrams for various simple and semisimple settings are also given. Further aspects such as perturbativity beyond the Veneziano limit, conformal windows, and implications for model building are discussed.
Asymptotically safe grand unification
Energy Technology Data Exchange (ETDEWEB)
Bajc, Borut [J. Stefan Institute,1000 Ljubljana (Slovenia); Sannino, Francesco [CP-Origins & the Danish IAS, University of Southern Denmark,Campusvej 55, DK-5230 Odense M (Denmark); Université de Lyon, France, Université Lyon 1, CNRS/IN2P3, UMR5822 IPNL,F-69622 Villeurbanne Cedex (France)
2016-12-28
Phenomenologically appealing supersymmetric grand unified theories have large gauge representations and thus are not asymptotically free. Their ultraviolet validity is limited by the appearance of a Landau pole well before the Planck scale. One could hope that these theories save themselves, before the inclusion of gravity, by generating an interacting ultraviolet fixed point, similar to the one recently discovered in non-supersymmetric gauge-Yukawa theories. Employing a-maximization, a-theorem, unitarity bounds, as well as positivity of other central charges we nonperturbatively rule out this possibility for a broad class of prime candidates of phenomenologically relevant supersymmetric grand unified theories. We also uncover candidates passing these tests, which have either exotic matter or contain one field decoupled from the superpotential. The latter class of theories contains a model with the minimal matter content required by phenomenology.
Renormalization group and asymptotic freedom
International Nuclear Information System (INIS)
Morris, J.R.
1978-01-01
Several field theoretic models are presented which allow exact expressions of the renormalization constants and renormalized coupling constants. These models are analyzed as to their content of asymptotic free field behavior through the use of the Callan-Symanzik renormalization group equation. It is found that none of these models possesses asymptotic freedom in four dimensions
Heavy flavor DIS Wilson coefficients in the asymptotic regime
Energy Technology Data Exchange (ETDEWEB)
Ablinger, J.; Schneider, C. [Linz Univ. (AT). Research Inst. for Symbolic Computation (RISC); Bierenbaum, I. [CSIC-Universitat de Valencia (Spain). Inst. de Fisica Corpuscular; Bluemlein, J.; Hasselhuhn, A.; Wissbrock, F. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Klein, S. [RWTH Aachen (Germany). Inst. fuer Theoretische Teilchenphysik und Kosmologie
2010-07-15
We report on results for the heavy flavor contributions to F{sub 2}(x,Q{sup 2}) in the limit Q{sup 2}>>m{sup 2} at NNLO. By calculating the massive 3-loop operator matrix elements, we account for all but the power suppressed terms in m{sup 2}/Q{sup 2}. Recently, the calculation of fixed Mellin moments of all 3-loop massive operator matrix elements has been finished. We present new all-N results for the O(n{sub f})-terms, thereby confirming the corresponding parts of the 3-loop anomalous dimensions. Additionally, we report on first genuine 3-loop results of the ladder-type diagrams for general values of the Mellin variable N. (orig.)
On some asymptotic relations in the Boltzmann-Enskog model
International Nuclear Information System (INIS)
Sadovnikov, B.I.; Inozemtseva, N.G.
1977-04-01
The coefficients in the tsup(-3/2) asymptotics of the time autocorrelation functions are successively determined in the framework of the non-linear Boltzmann-Enskog model. The left and right eigenfunction systems are constructed for the Boltzmann-Enskog operator
Asymptotic behaviour of Feynman integrals
International Nuclear Information System (INIS)
Bergere, M.C.
1980-01-01
In these lecture notes, we describe how to obtain the asymptotic behaviour of Feynman amplitudes; this technique has been already applied in several cases, but the general solution for any kind of asymptotic behaviour has not yet been found. From the mathematical point of view, the problem to solve is close to the following problem: find the asymptotic expansion at large lambda of the integral ∫...∫ [dx] esup(-LambdaP[x]) where P[x] is a polynomial of several variables. (orig.)
Asymptotic structure of isolated systems
International Nuclear Information System (INIS)
Schmidt, B.G.
1979-01-01
The main methods to formulate asymptotic flatness conditions are introduced and motivation and basic ideas are emphasized. Any asymptotic flatness condition proposed up to now describes space-times which behave somehow like Minkowski space, and a very explicit exposition of the structure at infinity of Minkowski space is given. This structure is used to describe the asymptotic behaviour of fields on Minkowski space in a frame-dependent way. The definition of null infinity for curved space-time according to Penrose is given and attempts to define spacelike infinity are outlined. The conformal bundle approach to the formulation of asymptotic behaviour is described and its relation to null and spacelike infinity is given, as far as known. (Auth.)
Nonminimal hints for asymptotic safety
Eichhorn, Astrid; Lippoldt, Stefan; Skrinjar, Vedran
2018-01-01
In the asymptotic-safety scenario for gravity, nonzero interactions are present in the ultraviolet. This property should also percolate into the matter sector. Symmetry-based arguments suggest that nonminimal derivative interactions of scalars with curvature tensors should therefore be present in the ultraviolet regime. We perform a nonminimal test of the viability of the asymptotic-safety scenario by working in a truncation of the renormalization group flow, where we discover the existence of an interacting fixed point for a corresponding nonminimal coupling. The back-coupling of such nonminimal interactions could in turn destroy the asymptotically safe fixed point in the gravity sector. As a key finding, we observe nontrivial indications of stability of the fixed-point properties under the impact of nonminimal derivative interactions, further strengthening the case for asymptotic safety in gravity-matter systems.
Generating asymptotically plane wave spacetimes
International Nuclear Information System (INIS)
Hubeny, Veronika E.; Rangamani, Mukund
2003-01-01
In an attempt to study asymptotically plane wave spacetimes which admit an event horizon, we find solutions to vacuum Einstein's equations in arbitrary dimension which have a globally null Killing field and rotational symmetry. We show that while such solutions can be deformed to include ones which are asymptotically plane wave, they do not posses a regular event horizon. If we allow for additional matter, such as in supergravity theories, we show that it is possible to have extremal solutions with globally null Killing field, a regular horizon, and which, in addition, are asymptotically plane wave. In particular, we deform the extremal M2-brane solution in 11-dimensional supergravity so that it behaves asymptotically as a 10-dimensional vacuum plane wave times a real line. (author)
New Inference Procedures for Semiparametric Varying-Coefficient Partially Linear Cox Models
Directory of Open Access Journals (Sweden)
Yunbei Ma
2014-01-01
Full Text Available In biomedical research, one major objective is to identify risk factors and study their risk impacts, as this identification can help clinicians to both properly make a decision and increase efficiency of treatments and resource allocation. A two-step penalized-based procedure is proposed to select linear regression coefficients for linear components and to identify significant nonparametric varying-coefficient functions for semiparametric varying-coefficient partially linear Cox models. It is shown that the penalized-based resulting estimators of the linear regression coefficients are asymptotically normal and have oracle properties, and the resulting estimators of the varying-coefficient functions have optimal convergence rates. A simulation study and an empirical example are presented for illustration.
Polynomial Asymptotes of the Second Kind
Dobbs, David E.
2011-01-01
This note uses the analytic notion of asymptotic functions to study when a function is asymptotic to a polynomial function. Along with associated existence and uniqueness results, this kind of asymptotic behaviour is related to the type of asymptote that was recently defined in a more geometric way. Applications are given to rational functions and…
Caustics, counting maps and semi-classical asymptotics
International Nuclear Information System (INIS)
Ercolani, N M
2011-01-01
This paper develops a deeper understanding of the structure and combinatorial significance of the partition function for Hermitian random matrices. The coefficients of the large N expansion of the logarithm of this partition function, also known as the genus expansion (and its derivatives), are generating functions for a variety of graphical enumeration problems. The main results are to prove that these generating functions are, in fact, specific rational functions of a distinguished irrational (algebraic) function, z 0 (t). This distinguished function is itself the generating function for the Catalan numbers (or generalized Catalan numbers, depending on the choice of weight of the parameter t). It is also a solution of the inviscid Burgers equation for certain initial data. The shock formation, or caustic, of the Burgers characteristic solution is directly related to the poles of the rational forms of the generating functions. As an intriguing application, one gains new insights into the relation between certain derivatives of the genus expansion, in a double-scaling limit, and the asymptotic expansion of the first Painlevé transcendent. This provides a precise expression of the Painlevé asymptotic coefficients directly in terms of the coefficients of the partial fractions expansion of the rational form of the generating functions established in this paper. Moreover, these insights point towards a more general program relating the first Painlevé hierarchy to the higher order structure of the double-scaling limit through the specific rational structure of generating functions in the genus expansion. The paper closes with a discussion of the relation of this work to recent developments in understanding the asymptotics of graphical enumeration. As a by-product, these results also yield new information about the asymptotics of recurrence coefficients for orthogonal polynomials with respect to exponential weights, the calculation of correlation functions for certain
Caustics, counting maps and semi-classical asymptotics
Ercolani, N. M.
2011-02-01
This paper develops a deeper understanding of the structure and combinatorial significance of the partition function for Hermitian random matrices. The coefficients of the large N expansion of the logarithm of this partition function, also known as the genus expansion (and its derivatives), are generating functions for a variety of graphical enumeration problems. The main results are to prove that these generating functions are, in fact, specific rational functions of a distinguished irrational (algebraic) function, z0(t). This distinguished function is itself the generating function for the Catalan numbers (or generalized Catalan numbers, depending on the choice of weight of the parameter t). It is also a solution of the inviscid Burgers equation for certain initial data. The shock formation, or caustic, of the Burgers characteristic solution is directly related to the poles of the rational forms of the generating functions. As an intriguing application, one gains new insights into the relation between certain derivatives of the genus expansion, in a double-scaling limit, and the asymptotic expansion of the first Painlevé transcendent. This provides a precise expression of the Painlevé asymptotic coefficients directly in terms of the coefficients of the partial fractions expansion of the rational form of the generating functions established in this paper. Moreover, these insights point towards a more general program relating the first Painlevé hierarchy to the higher order structure of the double-scaling limit through the specific rational structure of generating functions in the genus expansion. The paper closes with a discussion of the relation of this work to recent developments in understanding the asymptotics of graphical enumeration. As a by-product, these results also yield new information about the asymptotics of recurrence coefficients for orthogonal polynomials with respect to exponential weights, the calculation of correlation functions for certain
Energy Technology Data Exchange (ETDEWEB)
Sukhanov, V V [Leningradskij Gosudarstvennyj Univ., Leningrad (USSR)
1990-07-01
Asymptotic behaviour of solutions of the equations of principal chiral field when one of the arguments tends to infinity is investigated. Asymptotics of solutions of the corresponding spectral problem is investigated as well. explicit formulas are constructed which connect the coefficients of the asymptotic decomposition of the potential with the data of the corresponding inverse problem by means of a birational transformation.
Heat Kernel Asymptotics of Zaremba Boundary Value Problem
Energy Technology Data Exchange (ETDEWEB)
Avramidi, Ivan G. [Department of Mathematics, New Mexico Institute of Mining and Technology (United States)], E-mail: iavramid@nmt.edu
2004-03-15
The Zaremba boundary-value problem is a boundary value problem for Laplace-type second-order partial differential operators acting on smooth sections of a vector bundle over a smooth compact Riemannian manifold with smooth boundary but with discontinuous boundary conditions, which include Dirichlet boundary conditions on one part of the boundary and Neumann boundary conditions on another part of the boundary. We study the heat kernel asymptotics of Zaremba boundary value problem. The construction of the asymptotic solution of the heat equation is described in detail and the heat kernel is computed explicitly in the leading approximation. Some of the first nontrivial coefficients of the heat kernel asymptotic expansion are computed explicitly.
The unusual asymptotics of three-sided prudent polygons
International Nuclear Information System (INIS)
Beaton, Nicholas R; Guttmann, Anthony J; Flajolet, Philippe
2010-01-01
We have studied the area-generating function of prudent polygons on the square lattice. Exact solutions are obtained for the generating function of two-sided and three-sided prudent polygons, and a functional equation is found for four-sided prudent polygons. This is used to generate series coefficients in polynomial time, and these are analysed to determine the asymptotics numerically. A careful asymptotic analysis of the three-sided polygons produces a most surprising result. A transcendental critical exponent is found, and the leading amplitude is not quite a constant, but is a constant plus a small oscillatory component with an amplitude approximately 10 -8 times that of the leading amplitude. This effect cannot be seen by any standard numerical analysis, but it may be present in other models. If so, it changes our whole view of the asymptotic behaviour of lattice models. (fast track communication)
Extensions to the coupling coefficient calculations for muon telescopes
Energy Technology Data Exchange (ETDEWEB)
Baker, C P; Humble, J E [Tasmania Univ., Sandy Bay (Australia). Dept. of Physics; Duldig, M L [Dept. of the Arts, Sport, the Environment, Tourism and Territories, Hobart (Australia). Antarctic Div.
1989-01-01
The calculation of coupling coefficients for muon telescopes has previously used interpolation from a limited set of asymptotic directions of arrival of primary particles. Furthermore, these calculations have not incorporated curvature of the atmosphere and thus diverge from the true response at zenith angles greater than about 75 degrees. The necessary extensions to calculate coupling coefficients at arbitrary zenith angles are given, including an improved method of incorporating the asymptotic directions of the primary particles. It is shown, using this method, that certain coupling coefficients are highly sensitive to small changes in asymptotic directions for some telescope configurations. 10 refs., 1 fig., 3 tabs.
Extensions to the coupling coefficient calculations for muon telescopes
International Nuclear Information System (INIS)
Baker, C.P.; Humble, J.E.; Duldig, M.L.
1989-01-01
The calculation of coupling coefficients for muon telescopes has previously used interpolation from a limited set of asymptotic directions of arrival of primary particles. Furthermore, these calculations have not incorporated curvature of the atmosphere and thus diverge from the true response at zenith angles greater than about 75 degrees. The necessary extensions to calculate coupling coefficients at arbitrary zenith angles are given, including an improved method of incorporating the asymptotic directions of the primary particles. It is shown, using this method, that certain coupling coefficients are highly sensitive to small changes in asymptotic directions for some telescope configurations. 10 refs., 1 fig., 3 tabs
Asymptotic conditions and conserved quantities
International Nuclear Information System (INIS)
Koul, R.K.
1990-01-01
Two problems have been investigated in this dissertation. The first one deals with the relationship between stationary space-times which are flat at null infinity and stationary space-times which are asymptotic flat at space-like infinity. It is shown that the stationary space-times which are asymptotically flat, in the Penrose sense, at null infinity, are asymptotically flat at space-like infinity in the Geroch sense and metric at space like infinity is at least C 1 . In the converse it is shown that the stationary space-times which are asymptotically flat at space like infinity, in the Beig sense, are asymptotically flat at null infinity in the Penrose sense. The second problem addressed deals with the theories of arbitrary dimensions. The theories treated are the ones which have fiber bundle structure, outside some compact region. For these theories the criterion for the choice of the background metric is specified, and the boundary condition for the initial data set (q ab , P ab ) is given in terms of the background metric. Having these boundary conditions it is shown that the symplectic structure and the constraint functionals are well defined. The conserved quantities associated with internal Killing vector fields are specified. Lastly the energy relative to a fixed background and the total energy of the theory have been given. It is also shown that the total energy of the theory is independent of the choice of the background
Asymptotic strength of thermal pulses in the helium shell burning
Energy Technology Data Exchange (ETDEWEB)
Fujimoto, M Y [Niigata Univ. (Japan); Sugimoto, D
1979-03-01
Secular growth in the strength of the recurrent thermal pulses of helium shell burning is discussed for the purpose of determining its asymptotic strength. It is shown that the pulse grows stronger if the helium zone has been cooled more before the initiation of the pulse. The secular growth of the pulse is related with the increasing degree of cooling. Thermal pulses are computed for an initial model corresponding to the maximum possible cooling, i.e., for a model in which the steady-state entropy distribution was realized in the helium zone. Such thermal pulses are shown to give an upper bound to the asymptotic strength, which is close enough to the asymptotic strength itself for relatively large core masses. Numerical results are given for the core mass of 1.07 M sub(sun), for which the asymptotic strength is found to be 9 x 10/sup 6/ L sub(sun). Thermal pulses are also computed for an initial model which has been cooled artificially more than the steady-state model. The first pulse results in a much greater strength than in the normal model, but a later pulse approaches the normal asymptotic value. Such models are also discussed in relation to the shell flashes on accreting white dwarfs.
Asymptotic analysis and boundary layers
Cousteix, Jean
2007-01-01
This book presents a new method of asymptotic analysis of boundary-layer problems, the Successive Complementary Expansion Method (SCEM). The first part is devoted to a general comprehensive presentation of the tools of asymptotic analysis. It gives the keys to understand a boundary-layer problem and explains the methods to construct an approximation. The second part is devoted to SCEM and its applications in fluid mechanics, including external and internal flows. The advantages of SCEM are discussed in comparison with the standard Method of Matched Asymptotic Expansions. In particular, for the first time, the theory of Interactive Boundary Layer is fully justified. With its chapter summaries, detailed derivations of results, discussed examples and fully worked out problems and solutions, the book is self-contained. It is written on a mathematical level accessible to graduate and post-graduate students of engineering and physics with a good knowledge in fluid mechanics. Researchers and practitioners will estee...
Integrable theories that are asymptotically CFT
Evans, J M; Jonathan M Evans; Timothy J Hollowood
1995-01-01
A series of sigma models with torsion are analysed which generate their mass dynamically but whose ultra-violet fixed points are non-trivial conformal field theories -- in fact SU(2) WZW models at level k. In contrast to the more familiar situation of asymptotically free theories in which the fixed points are trivial, the sigma models considered here may be termed ``asymptotically CFT''. These theories have previously been conjectured to be quantum integrable; we confirm this by proposing a factorizable S-matrix to describe their infra-red behaviour and then carrying out a stringent test of this proposal. The test involves coupling the theory to a conserved charge and evaluating the response of the free-energy both in perturbation theory to one loop and directly from the S-matrix via the Thermodynamic Bethe Ansatz with a chemical potential at zero temperature. Comparison of these results provides convincing evidence in favour of the proposed S-matrix; it also yields the universal coefficients of the beta-func...
Asymptotic geometric analysis, part I
Artstein-Avidan, Shiri
2015-01-01
The authors present the theory of asymptotic geometric analysis, a field which lies on the border between geometry and functional analysis. In this field, isometric problems that are typical for geometry in low dimensions are substituted by an "isomorphic" point of view, and an asymptotic approach (as dimension tends to infinity) is introduced. Geometry and analysis meet here in a non-trivial way. Basic examples of geometric inequalities in isomorphic form which are encountered in the book are the "isomorphic isoperimetric inequalities" which led to the discovery of the "concentration phenomen
Asymptotically free SU(5) models
International Nuclear Information System (INIS)
Kogan, Ya.I.; Ter-Martirosyan, K.A.; Zhelonkin, A.V.
1981-01-01
The behaviour of Yukawa and Higgs effective charges of the minimal SU(5) unification model is investigated. The model includes ν=3 (or more, up to ν=7) generations of quarks and leptons and, in addition, the 24-plet of heavy fermions. A number of solutions of the renorm-group equations are found, which reproduce the known data about quarks and leptons and, due to a special choice of the coupling constants at the unification point are asymptotically free in all charges. The requirement of the asymptotical freedom leads to some restrictions on the masses of particles and on their mixing angles [ru
Asymptotic inference for jump diffusions with state-dependent intensity
Becheri, Gaia; Drost, Feico; Werker, Bas
2016-01-01
We establish the local asymptotic normality property for a class of ergodic parametric jump-diffusion processes with state-dependent intensity and known volatility function sampled at high frequency. We prove that the inference problem about the drift and jump parameters is adaptive with respect to
Asymptotics for Estimating Equations in Hidden Markov Models
DEFF Research Database (Denmark)
Hansen, Jørgen Vinsløv; Jensen, Jens Ledet
Results on asymptotic normality for the maximum likelihood estimate in hidden Markov models are extended in two directions. The stationarity assumption is relaxed, which allows for a covariate process influencing the hidden Markov process. Furthermore a class of estimating equations is considered...
Asymptotics of the QMLE for General ARCH(q) Models
DEFF Research Database (Denmark)
Kristensen, Dennis; Rahbek, Anders Christian
2009-01-01
-ARCH -- are derived. Strong consistency is established under the assumptions that the ARCH process is geometrically ergodic, the conditional variance function has a finite log-moment, and finite second moment of the rescaled error. Asymptotic normality of the estimator is established under the additional assumption...
Ruin problems and tail asymptotics
DEFF Research Database (Denmark)
Rønn-Nielsen, Anders
The thesis Ruin Problems and Tail Asymptotics provides results on ruin problems for several classes of Markov processes. For a class of diffusion processes with jumps an explicit expression for the joint Laplace transform of the first passage time and the corresponding undershoot is derived...
Asymptotic Expansions - Methods and Applications
International Nuclear Information System (INIS)
Harlander, R.
1999-01-01
Different viewpoints on the asymptotic expansion of Feynman diagrams are reviewed. The relations between the field theoretic and diagrammatic approaches are sketched. The focus is on problems with large masses or large external momenta. Several recent applications also for other limiting cases are touched upon. Finally, the pros and cons of the different approaches are briefly discussed. (author)
Naturalness of asymptotically safe Higgs
DEFF Research Database (Denmark)
Pelaggi, Giulio M.; Sannino, Francesco; Strumia, Alessandro
2017-01-01
that the scalars can be lighter than Λ. Although we do not have an answer to whether the Standard Model hypercharge coupling growth toward a Landau pole at around Λ ~ 1040GeV can be tamed by non-perturbative asymptotic safety, our results indicate that such a possibility is worth exploring. In fact, if successful...
Thermodynamics of asymptotically safe theories
DEFF Research Database (Denmark)
Rischke, Dirk H.; Sannino, Francesco
2015-01-01
We investigate the thermodynamic properties of a novel class of gauge-Yukawa theories that have recently been shown to be completely asymptotically safe, because their short-distance behaviour is determined by the presence of an interacting fixed point. Not only do all the coupling constants freeze...
Airy asymptotics: the logarithmic derivative and its reciprocal
International Nuclear Information System (INIS)
Kearney, Michael J; Martin, Richard J
2009-01-01
We consider the asymptotic expansion of the logarithmic derivative of the Airy function Ai'(z)/Ai(z), and also its reciprocal Ai(z)/Ai'(z), as |z| → ∞. We derive simple, closed-form solutions for the coefficients which appear in these expansions, which are of interest since they are encountered in a wide variety of problems. The solutions are presented as Mellin transforms of given functions; this fact, together with the methods employed, suggests further avenues for research.
Asymptotic functions and multiplication of distributions
International Nuclear Information System (INIS)
Todorov, T.D.
1979-01-01
Considered is a new type of generalized asymptotic functions, which are not functionals on some space of test functions as the Schwartz distributions. The definition of the generalized asymptotic functions is given. It is pointed out that in future the particular asymptotic functions will be used for solving some topics of quantum mechanics and quantum theory
Energy Technology Data Exchange (ETDEWEB)
Marklund, Mette [Parker Institute: Imaging Unit, Frederiksberg Hospital (Denmark)], E-mail: mm@frh.regionh.dk; Christensen, Robin [Parker Institute: Musculoskeletal Statistics Unit, Frederiksberg Hospital (Denmark)], E-mail: robin.christensen@frh.regionh.dk; Torp-Pedersen, Soren [Parker Institute: Imaging Unit, Frederiksberg Hospital (Denmark)], E-mail: stp@frh.regionh.dk; Thomsen, Carsten [Department of Radiology, Rigshospitalet, University of Copenhagen (Denmark)], E-mail: carsten.thomsen@rh.regionh.dk; Nolsoe, Christian P. [Department of Radiology, Koge Hospital (Denmark)], E-mail: cnolsoe@dadlnet.dk
2009-01-15
Purpose: To prospectively investigate the effect on signal intensity (SI) of healthy breast parenchyma on magnetic resonance mammography (MRM) when doubling the contrast dose from 0.1 to 0.2 mmol/kg bodyweight. Materials and methods: Informed consent and institutional review board approval were obtained. Twenty-five healthy female volunteers (median age: 24 years (range: 21-37 years) and median bodyweight: 65 kg (51-80 kg)) completed two dynamic MRM examinations on a 0.6 T open scanner. The inter-examination time was 24 h (23.5-25 h). The following sequences were applied: axial T2W TSE and an axial dynamic T1W FFED, with a total of seven frames. At day 1, an i.v. gadolinium (Gd) bolus injection of 0.1 mmol/kg bodyweight (Omniscan) (low) was administered. On day 2, the contrast dose was increased to 0.2 mmol/kg (high). Injection rate was 2 mL/s (day 1) and 4 mL/s (day 2). Any use of estrogen containing oral contraceptives (ECOC) was recorded. Post-processing with automated subtraction, manually traced ROI (region of interest) and recording of the SI was performed. A random coefficient model was applied. Results: We found an SI increase of 24.2% and 40% following the low and high dose, respectively (P < 0.0001); corresponding to a 65% (95% CI: 37-99%) SI increase, indicating a moderate saturation. Although not statistically significant (P = 0.06), the results indicated a tendency, towards lower maximal SI in the breast parenchyma of ECOC users compared to non-ECOC users. Conclusion: We conclude that the contrast dose can be increased from 0.1 to 0.2 mmol/kg bodyweight, if a better contrast/noise relation is desired but increasing the contrast dose above 0.2 mmol/kg bodyweight is not likely to improve the enhancement substantially due to the moderate saturation observed. Further research is needed to determine the impact of ECOC on the relative enhancement ratio, and further studies are needed to determine if a possible use of ECOC should be considered a compromising
International Nuclear Information System (INIS)
Marklund, Mette; Christensen, Robin; Torp-Pedersen, Soren; Thomsen, Carsten; Nolsoe, Christian P.
2009-01-01
Purpose: To prospectively investigate the effect on signal intensity (SI) of healthy breast parenchyma on magnetic resonance mammography (MRM) when doubling the contrast dose from 0.1 to 0.2 mmol/kg bodyweight. Materials and methods: Informed consent and institutional review board approval were obtained. Twenty-five healthy female volunteers (median age: 24 years (range: 21-37 years) and median bodyweight: 65 kg (51-80 kg)) completed two dynamic MRM examinations on a 0.6 T open scanner. The inter-examination time was 24 h (23.5-25 h). The following sequences were applied: axial T2W TSE and an axial dynamic T1W FFED, with a total of seven frames. At day 1, an i.v. gadolinium (Gd) bolus injection of 0.1 mmol/kg bodyweight (Omniscan) (low) was administered. On day 2, the contrast dose was increased to 0.2 mmol/kg (high). Injection rate was 2 mL/s (day 1) and 4 mL/s (day 2). Any use of estrogen containing oral contraceptives (ECOC) was recorded. Post-processing with automated subtraction, manually traced ROI (region of interest) and recording of the SI was performed. A random coefficient model was applied. Results: We found an SI increase of 24.2% and 40% following the low and high dose, respectively (P < 0.0001); corresponding to a 65% (95% CI: 37-99%) SI increase, indicating a moderate saturation. Although not statistically significant (P = 0.06), the results indicated a tendency, towards lower maximal SI in the breast parenchyma of ECOC users compared to non-ECOC users. Conclusion: We conclude that the contrast dose can be increased from 0.1 to 0.2 mmol/kg bodyweight, if a better contrast/noise relation is desired but increasing the contrast dose above 0.2 mmol/kg bodyweight is not likely to improve the enhancement substantially due to the moderate saturation observed. Further research is needed to determine the impact of ECOC on the relative enhancement ratio, and further studies are needed to determine if a possible use of ECOC should be considered a compromising
Asymptotic structure of isolated systems
International Nuclear Information System (INIS)
Beig, R.
1988-01-01
I discuss the general ideas underlying the subject of ''asymptotics'' in general relativity and describe the current status of the concepts resulting from these ideas. My main concern will be the problem of consistency. By this I mean the question as to whether the geometric assumptions inherent in these concepts are compatible with the dynamics of the theory, as determined by Einstein's equations. This rather strong bias forces me to leave untouched several issues related to asymptotics, discussed in the recent literature, some of which are perhaps thought equally, or more important, by other workers in the field. In addition I shall, for coherence of presentation, mainly consider Einstein's equations in vacuo. When attention is confined to small neighbourhoods of null and spacelike infinity, this restriction is not important, but is surely relevant for more global issues. (author)
Asymptotic freedom and Zweig's rule
International Nuclear Information System (INIS)
Appelquist, Th.
1977-01-01
Some theoretical aspects of applying short distance physics (asymptotic freedom) are discussed to prove the correctness of the quantum chromodynamics. Properties of new particles that depend only on short distance physics can be dealt with perturbatively. The new mesons are assumed to be CantiC bound states, where C is a new heavy quark. With this in mind some comments are made on the calculation of total widths for the direct decay of different CantiC states into ordinary hadrons
Asymptotics of the filtration problem for suspension in porous media
Directory of Open Access Journals (Sweden)
Kuzmina Ludmila Ivanovna
2015-01-01
Full Text Available The mechanical-geometric model of the suspension filtering in the porous media is considered. Suspended solid particles of the same size move with suspension flow through the porous media - a solid body with pores - channels of constant cross section. It is assumed that the particles pass freely through the pores of large diameter and are stuck at the inlet of pores that are smaller than the particle size. It is considered that one particle can clog only one small pore and vice versa. The particles stuck in the pores remain motionless and form a deposit. The concentrations of suspended and retained particles satisfy a quasilinear hyperbolic system of partial differential equations of the first order, obtained as a result of macro-averaging of micro-stochastic diffusion equations. Initially the porous media contains no particles and both concentrations are equal to zero; the suspension supplied to the porous media inlet has a constant concentration of suspended particles. The flow of particles moves in the porous media with a constant speed, before the wave front the concentrations of suspended and retained particles are zero. Assuming that the filtration coefficient is small we construct an asymptotic solution of the filtration problem over the concentration front. The terms of the asymptotic expansions satisfy linear partial differential equations of the first order and are determined successively in an explicit form. It is shown that in the simplest case the asymptotics found matches the known asymptotic expansion of the solution near the concentration front.
Asymptotic integration of differential and difference equations
Bodine, Sigrun
2015-01-01
This book presents the theory of asymptotic integration for both linear differential and difference equations. This type of asymptotic analysis is based on some fundamental principles by Norman Levinson. While he applied them to a special class of differential equations, subsequent work has shown that the same principles lead to asymptotic results for much wider classes of differential and also difference equations. After discussing asymptotic integration in a unified approach, this book studies how the application of these methods provides several new insights and frequent improvements to results found in earlier literature. It then continues with a brief introduction to the relatively new field of asymptotic integration for dynamic equations on time scales. Asymptotic Integration of Differential and Difference Equations is a self-contained and clearly structured presentation of some of the most important results in asymptotic integration and the techniques used in this field. It will appeal to researchers i...
Autcha Araveeporn
2013-01-01
This paper compares a Least-Squared Random Coefficient Autoregressive (RCA) model with a Least-Squared RCA model based on Autocorrelated Errors (RCA-AR). We looked at only the first order models, denoted RCA(1) and RCA(1)-AR(1). The efficiency of the Least-Squared method was checked by applying the models to Brownian motion and Wiener process, and the efficiency followed closely the asymptotic properties of a normal distribution. In a simulation study, we compared the performance of RCA(1) an...
International Nuclear Information System (INIS)
Bachoc, Francois
2014-01-01
Covariance parameter estimation of Gaussian processes is analyzed in an asymptotic framework. The spatial sampling is a randomly perturbed regular grid and its deviation from the perfect regular grid is controlled by a single scalar regularity parameter. Consistency and asymptotic normality are proved for the Maximum Likelihood and Cross Validation estimators of the covariance parameters. The asymptotic covariance matrices of the covariance parameter estimators are deterministic functions of the regularity parameter. By means of an exhaustive study of the asymptotic covariance matrices, it is shown that the estimation is improved when the regular grid is strongly perturbed. Hence, an asymptotic confirmation is given to the commonly admitted fact that using groups of observation points with small spacing is beneficial to covariance function estimation. Finally, the prediction error, using a consistent estimator of the covariance parameters, is analyzed in detail. (authors)
Asymptotics for Associated Random Variables
Oliveira, Paulo Eduardo
2012-01-01
The book concerns the notion of association in probability and statistics. Association and some other positive dependence notions were introduced in 1966 and 1967 but received little attention from the probabilistic and statistics community. The interest in these dependence notions increased in the last 15 to 20 years, and many asymptotic results were proved and improved. Despite this increased interest, characterizations and results remained essentially scattered in the literature published in different journals. The goal of this book is to bring together the bulk of these results, presenting
Asymptotic Normality of Poly-T Densities with Bayesian Applications.
1987-10-01
Quincy Street University of Iowa Arlington, VA 22217-5000 Iowa City, IA 52242 Dr. Hans Crombag Dr. James A. Earles University of Leyden Air Force Human...Resources Lab Education Research Center Brooks AFB, TX 78235 Boerhaavelaan 2 2334 EN Leyden Dr. Kent Eaton The NETHERLANDS Army Research Institute...William L. Maloy San Diego, CA 92152-6800 Chief of Naval Education and Training Ms. Kathleen Moreno Naval Air Station Navy Personnel R&D Center Pensacola
Asymptotic solutions and spectral theory of linear wave equations
International Nuclear Information System (INIS)
Adam, J.A.
1982-01-01
This review contains two closely related strands. Firstly the asymptotic solution of systems of linear partial differential equations is discussed, with particular reference to Lighthill's method for obtaining the asymptotic functional form of the solution of a scalar wave equation with constant coefficients. Many of the applications of this technique are highlighted. Secondly, the methods and applications of the theory of the reduced (one-dimensional) wave equation - particularly spectral theory - are discussed. While the breadth of application and power of the techniques is emphasised throughout, the opportunity is taken to present to a wider readership, developments of the methods which have occured in some aspects of astrophysical (particularly solar) and geophysical fluid dynamics. It is believed that the topics contained herein may be of relevance to the applied mathematician or theoretical physicist interest in problems of linear wave propagation in these areas. (orig./HSI)
Numerical relativity and asymptotic flatness
International Nuclear Information System (INIS)
Deadman, E; Stewart, J M
2009-01-01
It is highly plausible that the region of spacetime far from an isolated gravitating body is, in some sense, asymptotically Minkowskian. However theoretical studies of the full nonlinear theory, initiated by Bondi et al (1962 Proc. R. Soc. A 269 21-51), Sachs (1962 Proc. R. Soc. A 270 103-26) and Newman and Unti (1962 J. Math. Phys. 3 891-901), rely on careful, clever, a priori choices of a chart (and tetrad) and so are not readily accessible to the numerical relativist, who chooses her/his chart on the basis of quite different grounds. This paper seeks to close this gap. Starting from data available in a typical numerical evolution, we construct a chart and tetrad which are, asymptotically, sufficiently close to the theoretical ones, so that the key concepts of the Bondi news function, Bondi mass and its rate of decrease can be estimated. In particular, these estimates can be expressed in the numerical relativist's chart as numerical relativity recipes.
Asymptotic twistor theory and the Kerr theorem
International Nuclear Information System (INIS)
Newman, Ezra T
2006-01-01
We first review asymptotic twistor theory with its real subspace of null asymptotic twistors: a five-dimensional CR manifold. This is followed by a description of the Kerr theorem (the identification of shear-free null congruences, in Minkowski space, with the zeros of holomorphic functions of three variables) and an asymptotic version of the Kerr theorem that produces regular asymptotically shear-free null geodesic congruences in arbitrary asymptotically flat Einstein or Einstein-Maxwell spacetimes. A surprising aspect of this work is the role played by analytic curves in H-space, each curve generating an asymptotically flat null geodesic congruence. Also there is a discussion of the physical space realizations of the two associated five- and three-dimensional CR manifolds
Asymptotic density and effective negligibility
Astor, Eric P.
In this thesis, we join the study of asymptotic computability, a project attempting to capture the idea that an algorithm might work correctly in all but a vanishing fraction of cases. In collaboration with Hirschfeldt and Jockusch, broadening the original investigation of Jockusch and Schupp, we introduce dense computation, the weakest notion of asymptotic computability (requiring only that the correct answer is produced on a set of density 1), and effective dense computation, where every computation halts with either the correct answer or (on a set of density 0) a symbol denoting uncertainty. A few results make more precise the relationship between these notions and work already done with Jockusch and Schupp's original definitions of coarse and generic computability. For all four types of asymptotic computation, including generic computation, we demonstrate that non-trivial upper cones have measure 0, building on recent work of Hirschfeldt, Jockusch, Kuyper, and Schupp in which they establish this for coarse computation. Their result transfers to yield a minimal pair for relative coarse computation; we generalize their method and extract a similar result for relative dense computation (and thus for its corresponding reducibility). However, all of these notions of near-computation treat a set as negligible iff it has asymptotic density 0. Noting that this definition is not computably invariant, this produces some failures of intuition and a break with standard expectations in computability theory. For instance, as shown by Hamkins and Miasnikov, the halting problem is (in some formulations) effectively densely computable, even in polynomial time---yet this result appears fragile, as indicated by Rybalov. In independent work, we respond to this by strengthening the approach of Jockusch and Schupp to avoid such phenomena; specifically, we introduce a new notion of intrinsic asymptotic density, invariant under computable permutation, with rich relations to both
Asymptotic safety, emergence and minimal length
International Nuclear Information System (INIS)
Percacci, Roberto; Vacca, Gian Paolo
2010-01-01
There seems to be a common prejudice that asymptotic safety is either incompatible with, or at best unrelated to, the other topics in the title. This is not the case. In fact, we show that (1) the existence of a fixed point with suitable properties is a promising way of deriving emergent properties of gravity, and (2) there is a sense in which asymptotic safety implies a minimal length. In doing so we also discuss possible signatures of asymptotic safety in scattering experiments.
Stable Parameter Estimation for Autoregressive Equations with Random Coefficients
Directory of Open Access Journals (Sweden)
V. B. Goryainov
2014-01-01
Full Text Available In recent yearsthere has been a growing interest in non-linear time series models. They are more flexible than traditional linear models and allow more adequate description of real data. Among these models a autoregressive model with random coefficients plays an important role. It is widely used in various fields of science and technology, for example, in physics, biology, economics and finance. The model parameters are the mean values of autoregressive coefficients. Their evaluation is the main task of model identification. The basic method of estimation is still the least squares method, which gives good results for Gaussian time series, but it is quite sensitive to even small disturbancesin the assumption of Gaussian observations. In this paper we propose estimates, which generalize the least squares estimate in the sense that the quadratic objective function is replaced by an arbitrary convex and even function. Reasonable choice of objective function allows you to keep the benefits of the least squares estimate and eliminate its shortcomings. In particular, you can make it so that they will be almost as effective as the least squares estimate in the Gaussian case, but almost never loose in accuracy with small deviations of the probability distribution of the observations from the Gaussian distribution.The main result is the proof of consistency and asymptotic normality of the proposed estimates in the particular case of the one-parameter model describing the stationary process with finite variance. Another important result is the finding of the asymptotic relative efficiency of the proposed estimates in relation to the least squares estimate. This allows you to compare the two estimates, depending on the probability distribution of innovation process and of autoregressive coefficients. The results can be used to identify an autoregressive process, especially with nonGaussian nature, and/or of autoregressive processes observed with gross
Numerical Asymptotic Solutions Of Differential Equations
Thurston, Gaylen A.
1992-01-01
Numerical algorithms derived and compared with classical analytical methods. In method, expansions replaced with integrals evaluated numerically. Resulting numerical solutions retain linear independence, main advantage of asymptotic solutions.
Mayer coefficients in two-dimensional Coulomb systems
International Nuclear Information System (INIS)
Speer, E.R.
1986-01-01
It is shown that, for neutral systems of particles of arbitrary charges in two dimensions, with hard cores, coefficients of the Mayer series for the pressure exist in the thermodynamic limit below certain thresholds in the temperature. The methods used here apply also to correlation functions and yield bounds on the asymptotic behavior of their Mayer coefficients
Asymptotic behaviour in field theory
Energy Technology Data Exchange (ETDEWEB)
Banerjee, H.
1980-07-01
Asymptotic behaviour in field theory has been studied and the anomalies are pointed out in two specific cases, (i) the infrared and fixed angle high energy behaviour in the non-trivial case of the 'box' amplitude in a scalar-scalar theory and (ii) high energy behaviour of a sixth order Yang-Mills diagram. A set of rules are presented for writing down the precise leading infrared behaviour of an arbitrary generalised ladder diagram (GLD) in QED. These rules are the final result of a detailed analysis of the relevant amplitudes in the Feynman parameter space. The connection between the infrared and fixed angle high energy limits of generalised ladder diagrams is explained. It is argued that the same set of rules yield the fixed angle high energy limit.
Exponential asymptotics of homoclinic snaking
International Nuclear Information System (INIS)
Dean, A D; Matthews, P C; Cox, S M; King, J R
2011-01-01
We study homoclinic snaking in the cubic-quintic Swift–Hohenberg equation (SHE) close to the onset of a subcritical pattern-forming instability. Application of the usual multiple-scales method produces a leading-order stationary front solution, connecting the trivial solution to the patterned state. A localized pattern may therefore be constructed by matching between two distant fronts placed back-to-back. However, the asymptotic expansion of the front is divergent, and hence should be truncated. By truncating optimally, such that the resultant remainder is exponentially small, an exponentially small parameter range is derived within which stationary fronts exist. This is shown to be a direct result of the 'locking' between the phase of the underlying pattern and its slowly varying envelope. The locking mechanism remains unobservable at any algebraic order, and can only be derived by explicitly considering beyond-all-orders effects in the tail of the asymptotic expansion, following the method of Kozyreff and Chapman as applied to the quadratic-cubic SHE (Chapman and Kozyreff 2009 Physica D 238 319–54, Kozyreff and Chapman 2006 Phys. Rev. Lett. 97 44502). Exponentially small, but exponentially growing, contributions appear in the tail of the expansion, which must be included when constructing localized patterns in order to reproduce the full snaking diagram. Implicit within the bifurcation equations is an analytical formula for the width of the snaking region. Due to the linear nature of the beyond-all-orders calculation, the bifurcation equations contain an analytically indeterminable constant, estimated in the previous work by Chapman and Kozyreff using a best fit approximation. A more accurate estimate of the equivalent constant in the cubic-quintic case is calculated from the iteration of a recurrence relation, and the subsequent analytical bifurcation diagram compared with numerical simulations, with good agreement
Asymptotic behaviour of pion-pion total cross-sections
International Nuclear Information System (INIS)
Greynat, David; Rafael, Eduardo de; Vulvert, Grégory
2014-01-01
We derive a sum rule which shows that the Froissart-Martin bound for the asymptotic behaviour of the ππ total cross sections at high energies, if modulated by the Lukaszuk-Martin coefficient of the leading log 2 s behaviour, cannot be an optimal bound in QCD. We next compute the total cross sections for π + π − , π ± π 0 and π 0 π 0 scattering within the framework of the constituent chiral quark model (CχQM) in the limit of a large number of colours N c and discuss their asymptotic behaviours. The same ππ cross sections are also discussed within the general framework of Large-N c QCD and we show that it is possible to make an Ansatz for the isospin I=1 and I=0 spectrum which satisfy the Froissart-Martin bound with coefficients which, contrary to the Lukaszuk-Martin coefficient, are not singular in the chiral limit and have the correct Large-N c counting. We finally propose a simple phenomenological model which matches the low energy behaviours of the σ π ± π 0 total (s) cross section predicted by the CχQM with the high energy behaviour predicted by the Large-N c Ansatz. The magnitude of these cross sections at very high energies is of the order of those observed for the pp and pp-bar scattering total cross sections
Asymptotics of Laplace-Dirichlet integrals
International Nuclear Information System (INIS)
Kozlov, S.M.
1990-01-01
Here we consider the problem of the asymptotic expansion of the Laplace-Dirichlet integral. In homogenization theory such an integral represents the energy, and in general depends on the cohomology class. Here the asymptotic behaviour of this integral is found. The full text will appear in Functional Analysis and Applications, 1990, No.2. (author). 3 refs
Wijsman Orlicz Asymptotically Ideal -Statistical Equivalent Sequences
Directory of Open Access Journals (Sweden)
Bipan Hazarika
2013-01-01
in Wijsman sense and present some definitions which are the natural combination of the definition of asymptotic equivalence, statistical equivalent, -statistical equivalent sequences in Wijsman sense. Finally, we introduce the notion of Cesaro Orlicz asymptotically -equivalent sequences in Wijsman sense and establish their relationship with other classes.
8. Asymptotically Flat and Regular Cauchy Data
Dain, Sergio
I describe the construction of a large class of asymptotically flat initial data with non-vanishing mass and angular momentum for which the metric and the extrinsic curvature have asymptotic expansions at space-like infinity in terms of powers of a radial coordinate. I emphasize the motivations and the main ideas behind the proofs.
Asymptotic inference in system identification for the atom maser.
Catana, Catalin; van Horssen, Merlijn; Guta, Madalin
2012-11-28
System identification is closely related to control theory and plays an increasing role in quantum engineering. In the quantum set-up, system identification is usually equated to process tomography, i.e. estimating a channel by probing it repeatedly with different input states. However, for quantum dynamical systems such as quantum Markov processes, it is more natural to consider the estimation based on continuous measurements of the output, with a given input that may be stationary. We address this problem using asymptotic statistics tools, for the specific example of estimating the Rabi frequency of an atom maser. We compute the Fisher information of different measurement processes as well as the quantum Fisher information of the atom maser, and establish the local asymptotic normality of these statistical models. The statistical notions can be expressed in terms of spectral properties of certain deformed Markov generators, and the connection to large deviations is briefly discussed.
Jingping Gu; Paula Hernandez-Verme
2009-01-01
In this paper, we propose a new semiparametric varying coefficient model which extends the existing semi-parametric varying coefficient models to allow for a time trend regressor with smooth coefficient function. We propose to use the local linear method to estimate the coefficient functions and we provide the asymptotic theory to describe the asymptotic distribution of the local linear estimator. We present an application to evaluate credit rationing in the U.S. credit market. Using U.S. mon...
Qi Gao; Jingping Gu; Paula Hernandez-Verme
2012-01-01
In this paper, we propose a new semiparametric varying coefficient model which extends the existing semi-parametric varying coefficient models to allow for a time trend regressor with smooth coefficient function. We propose to use the local linear method to estimate the coefficient functions and we provide the asymptotic theory to describe the asymptotic distribution of the local linear estimator. We present an application to evaluate credit rationing in the U.S. credit market. Using U.S. mon...
Asymptotics and Numerics of Polynomials Used in Tricomi and Buchholz Expansions of Kummer functions
J.L. López; N.M. Temme (Nico)
2010-01-01
textabstractExpansions in terms of Bessel functions are considered of the Kummer function ${}_1F_1(a;c,z)$ (or confluent hypergeometric function) as given by Tricomi and Buchholz. The coefficients of these expansions are polynomials in the parameters of the Kummer function and the asymptotic
Experimental tests of asymptotic freedom
International Nuclear Information System (INIS)
Bethke, S.
1996-09-01
Measurements which probe the energy dependence of α s , the coupling strength of the strong interaction, are reviewed. Jet counting in e + e - annihilation, combining results obtained in the centre of mass energy range from 22 to 133 GeV, provides direct evidence for an asymptotically free coupling, without the need to determine explicit values of α s . Recent results from jet production in e p and in p p collisions, obtained in single experiments spanning large ranges of momentum transfer, Q 2 , are in good agreement with the running of α s as predicted by QCD. Mass spectra of hadronic decays of τ-leptons are analysed to probe the running α s in the very low energy domain, 0.7 GeV 2 2 2 τ . An update of the world summary of measurements of α s (Q 2 ) consistently proves the energy dependence of α s and results in a combined average of α s (M Z 0 =0.118±0.006). (orig.)
On the asymptotic form of the recursion method basis vectors for periodic Hamiltonians
International Nuclear Information System (INIS)
O'Reilly, E.P.; Weaire, D.
1984-01-01
The authors present the first detailed study of the recursion method basis vectors for the case of a periodic Hamiltonian. In the examples chosen, the probability density scales linearly with n as n → infinity, whenever the local density of states is bounded. Whenever it is unbounded and the recursion coefficients diverge, different scaling behaviour is found. These findings are explained and a scaling relationship between the asymptotic forms of the recursion coefficients and basis vectors is proposed. (author)
Asymptotic Conservation Laws in Classical Field Theory
International Nuclear Information System (INIS)
Anderson, I.M.; Torre, C.G.
1996-01-01
A new, general, field theoretic approach to the derivation of asymptotic conservation laws is presented. In this approach asymptotic conservation laws are constructed directly from the field equations according to a universal prescription which does not rely upon the existence of Noether identities or any Lagrangian or Hamiltonian formalisms. The resulting general expressions of the conservation laws enjoy important invariance properties and synthesize all known asymptotic conservation laws, such as the Arnowitt-Deser-Misner energy in general relativity. copyright 1996 The American Physical Society
Asymptotic work distributions in driven bistable systems
International Nuclear Information System (INIS)
Nickelsen, D; Engel, A
2012-01-01
The asymptotic tails of the probability distributions of thermodynamic quantities convey important information about the physics of nanoscopic systems driven out of equilibrium. We apply a recently proposed method to analytically determine the asymptotics of work distributions in Langevin systems to an one-dimensional model of single-molecule force spectroscopy. The results are in excellent agreement with numerical simulations, even in the centre of the distributions. We compare our findings with a recent proposal for an universal form of the asymptotics of work distributions in single-molecule experiments.
An asymptotic model of seismic reflection from a permeable layer
Energy Technology Data Exchange (ETDEWEB)
Silin, D.; Goloshubin, G.
2009-10-15
Analysis of compression wave propagation in a poroelastic medium predicts a peak of reflection from a high-permeability layer in the low-frequency end of the spectrum. An explicit formula expresses the resonant frequency through the elastic moduli of the solid skeleton, the permeability of the reservoir rock, the fluid viscosity and compressibility, and the reservoir thickness. This result is obtained through a low-frequency asymptotic analysis of Biot's model of poroelasticity. A review of the derivation of the main equations from the Hooke's law, momentum and mass balance equations, and Darcy's law suggests an alternative new physical interpretation of some coefficients of the classical poroelasticity. The velocity of wave propagation, the attenuation factor, and the wave number, are expressed in the form of power series with respect to a small dimensionless parameter. The absolute value of this parameter is equal to the product of the kinematic reservoir fluid mobility and the wave frequency. Retaining only the leading terms of the series leads to explicit and relatively simple expressions for the reflection and transmission coefficients for a planar wave crossing an interface between two permeable media, as well as wave reflection from a thin highly-permeable layer (a lens). Practical applications of the obtained asymptotic formulae are seismic modeling, inversion, and at-tribute analysis.
Robust and bias-corrected estimation of the coefficient of tail dependence
DEFF Research Database (Denmark)
Dutang, C.; Goegebeur, Y.; Guillou, A.
2014-01-01
We introduce a robust and asymptotically unbiased estimator for the coefficient of tail dependence in multivariate extreme value statistics. The estimator is obtained by fitting a second order model to the data by means of the minimum density power divergence criterion. The asymptotic properties ...
The theory of asymptotic behaviour
International Nuclear Information System (INIS)
Ward, B.F.L.; Purdue Univ., Lafayette, IN
1978-01-01
The Green's functions of renormalizable quantum field theory are shown to violate, in general, Euler's theorem on homogeneous functions, that is to say, to violate naive dimensional analysis. The respective violations are established by explicit calculation with Feynman diagrams. These violations, when incorporated into the renormalization group, then provide the basis for an entirely new approach to asymptotic behaviour in renormalizable field theory. Specifically, the violations add new delta-function sources to the usual partial differential equations of the group when these equations are written in terms of the external momenta of the respective Green's functions. The effect of these sources is illustrated by studying the real part, Re GAMMA 6 (lambda p), of the six-point 1PI vertex of the massless scalar field with quartic self-coupling - the simplest of ranormalizable situations. Here, lambda p is symbolic for the six-momenta of GAMMA 6 . Briefly, it is found that the usual theory of characteristics is unable to satisfy the boundary condition attendant to the respective dimensional-analysis-violating sources. Thus, the method of characteristics is completely abandonded in favour of the method of separation of variables. A complete solution which satisfies the inhomogeneous group equation and all boundary conditions is then explicitly constructed. This solution possesses Laurent expansions in the scale lambda of its momentum arguments for all real values of lambda 2 except lambda 2 = 0. For |lambda 2 |→ infinity and |lambda 2 |→ 0, the solution's leading term in its respective Laurent series is proportional to lambda -2 . The limits lambda 2 →0sub(+) and lambda 2 →0sup(-) of lambda 2 ReGAMMA 6 are both nonzero and unequal. The value of the solution at lambda 2 = 0 is not simply related to the value of either of these limits. The new approach would appear to be operationally established
Asymptotic Likelihood Distribution for Correlated & Constrained Systems
Agarwal, Ujjwal
2016-01-01
It describes my work as summer student at CERN. The report discusses the asymptotic distribution of the likelihood ratio for total no. of parameters being h and 2 out of these being are constrained and correlated.
Asymptotic Poincare lemma and its applications
International Nuclear Information System (INIS)
Ziolkowski, R.W.; Deschamps, G.A.
1984-01-01
An asymptotic version of Poincare's lemma is defined and solutions are obtained with the calculus of exterior differential forms. They are used to construct the asymptotic approximations of multidimensional oscillatory integrals whose forms are commonly encountered, for example, in electromagnetic problems. In particular, the boundary and stationary point evaluations of these integrals are considered. The former is applied to the Kirchhoff representation of a scalar field diffracted through an aperture and simply recovers the Maggi-Rubinowicz-Miyamoto-Wolf results. Asymptotic approximations in the presence of other (standard) critical points are also discussed. Techniques developed for the asymptotic Poincare lemma are used to generate a general representation of the Leray form. All of the (differential form) expressions presented are generalizations of known (vector calculus) results. 14 references, 4 figures
EMC effect: asymptotic freedom with nuclear targets
International Nuclear Information System (INIS)
West, G.B.
1984-01-01
General features of the EMC effect are discussed within the framework of quantum chromodynamics as expressed via the operator product expansion and asymptotic freedom. These techniques are reviewed with emphasis on the target dependence. 22 references
Spectral asymptotic in the large coupling limit
Bruneau, V
2002-01-01
In this paper, we study a singular perturbation of an eigenvalues problem related to supra-conductor wave guides. Using boundary layer tools we perform a complete asymptotic expansion of the eigenvalues as the conductivity tends to $+\\infty$.
Large Deviations and Asymptotic Methods in Finance
Gatheral, Jim; Gulisashvili, Archil; Jacquier, Antoine; Teichmann, Josef
2015-01-01
Topics covered in this volume (large deviations, differential geometry, asymptotic expansions, central limit theorems) give a full picture of the current advances in the application of asymptotic methods in mathematical finance, and thereby provide rigorous solutions to important mathematical and financial issues, such as implied volatility asymptotics, local volatility extrapolation, systemic risk and volatility estimation. This volume gathers together ground-breaking results in this field by some of its leading experts. Over the past decade, asymptotic methods have played an increasingly important role in the study of the behaviour of (financial) models. These methods provide a useful alternative to numerical methods in settings where the latter may lose accuracy (in extremes such as small and large strikes, and small maturities), and lead to a clearer understanding of the behaviour of models, and of the influence of parameters on this behaviour. Graduate students, researchers and practitioners will find th...
Zhang, Juping; Yang, Chan; Jin, Zhen; Li, Jia
2018-07-14
In this paper, the correlation coefficients between nodes in states are used as dynamic variables, and we construct SIR epidemic dynamic models with correlation coefficients by using the pair approximation method in static networks and dynamic networks, respectively. Considering the clustering coefficient of the network, we analytically investigate the existence and the local asymptotic stability of each equilibrium of these models and derive threshold values for the prevalence of diseases. Additionally, we obtain two equivalent epidemic thresholds in dynamic networks, which are compared with the results of the mean field equations. Copyright © 2018 Elsevier Ltd. All rights reserved.
Partially linear varying coefficient models stratified by a functional covariate
Maity, Arnab
2012-10-01
We consider the problem of estimation in semiparametric varying coefficient models where the covariate modifying the varying coefficients is functional and is modeled nonparametrically. We develop a kernel-based estimator of the nonparametric component and a profiling estimator of the parametric component of the model and derive their asymptotic properties. Specifically, we show the consistency of the nonparametric functional estimates and derive the asymptotic expansion of the estimates of the parametric component. We illustrate the performance of our methodology using a simulation study and a real data application.
Asymptotic expansion of the Keesom integral
International Nuclear Information System (INIS)
Abbott, Paul C
2007-01-01
The asymptotic evaluation and expansion of the Keesom integral, K(a), is discussed at some length in Battezzati and Magnasco (2004 J. Phys. A: Math. Gen. 37 9677; 2005 J. Phys. A: Math. Gen. 38 6715). Here, using standard identities, it is shown that this triple integral can be reduced to a single integral from which the asymptotic behaviour is readily obtained using Laplace's method. (comment)
Composite asymptotic expansions and scaling wall turbulence.
Panton, Ronald L
2007-03-15
In this article, the assumptions and reasoning that yield composite asymptotic expansions for wall turbulence are discussed. Particular attention is paid to the scaling quantities that are used to render the variables non-dimensional and of order one. An asymptotic expansion is proposed for the streamwise Reynolds stress that accounts for the active and inactive turbulence by using different scalings. The idea is tested with the data from the channel flows and appears to have merit.
AGB [asymptotic giant branch]: Star evolution
International Nuclear Information System (INIS)
Becker, S.A.
1987-01-01
Asymptotic giant branch stars are red supergiant stars of low-to-intermediate mass. This class of stars is of particular interest because many of these stars can have nuclear processed material brought up repeatedly from the deep interior to the surface where it can be observed. A review of recent theoretical and observational work on stars undergoing the asymptotic giant branch phase is presented. 41 refs
Directory of Open Access Journals (Sweden)
S. A. Kaschenko
2014-01-01
Full Text Available We study the dynamics of finite-difference approximation on spatial variables of a logistic equation with delay and diffusion. It is assumed that the diffusion coefficient is small and the Malthusian coefficient is large. The question of the existence and asymptotic behavior of attractors was studied with special asymptotic methods. It is shown that there is a rich array of different types of attractors in the phase space: leading centers, spiral waves, etc. The main asymptotic characteristics of all solutions from the corresponding attractors are adduced in this work. Typical graphics of wave fronts motion of different structures are represented in the article.
Asymptotic behaviour of pion-pion total cross-sections
Energy Technology Data Exchange (ETDEWEB)
Greynat, David [Dipartimento di Scienze Fisiche, Universita di Napoli “Federico II”,Via Cintia, 80126 Napoli (Italy); Rafael, Eduardo de [Aix-Marseille Université, CNRS,CPT, UMR 7332, 13288 Marseille (France); Université de Toulon, CNRS,CPT, UMR 7332, 83957 La Garde (France); Vulvert, Grégory [Departament de Física Teórica, IFIC,CSIC - Universitat de València, Apt. Correus 22085, E-46071 València (Spain)
2014-03-24
We derive a sum rule which shows that the Froissart-Martin bound for the asymptotic behaviour of the ππ total cross sections at high energies, if modulated by the Lukaszuk-Martin coefficient of the leading log{sup 2} s behaviour, cannot be an optimal bound in QCD. We next compute the total cross sections for π{sup +}π{sup −}, π{sup ±}π{sup 0} and π{sup 0}π{sup 0} scattering within the framework of the constituent chiral quark model (CχQM) in the limit of a large number of colours N{sub c} and discuss their asymptotic behaviours. The same ππ cross sections are also discussed within the general framework of Large-N{sub c} QCD and we show that it is possible to make an Ansatz for the isospin I=1 and I=0 spectrum which satisfy the Froissart-Martin bound with coefficients which, contrary to the Lukaszuk-Martin coefficient, are not singular in the chiral limit and have the correct Large-N{sub c} counting. We finally propose a simple phenomenological model which matches the low energy behaviours of the σ{sub π{sup ±}π{sup 0total}}(s) cross section predicted by the CχQM with the high energy behaviour predicted by the Large-N{sub c} Ansatz. The magnitude of these cross sections at very high energies is of the order of those observed for the pp and pp-bar scattering total cross sections.
Directory of Open Access Journals (Sweden)
G. M. N’Guérékata
2018-01-01
Full Text Available The main aim of this paper is to investigate generalized asymptotical almost periodicity and generalized asymptotical almost automorphy of solutions to a class of abstract (semilinear multiterm fractional differential inclusions with Caputo derivatives. We illustrate our abstract results with several examples and possible applications.
On Parametric Gevrey Asymptotics for Some Cauchy Problems in Quasiperiodic Function Spaces
Directory of Open Access Journals (Sweden)
A. Lastra
2014-01-01
Full Text Available We investigate Gevrey asymptotics for solutions to nonlinear parameter depending Cauchy problems with 2π-periodic coefficients, for initial data living in a space of quasiperiodic functions. By means of the Borel-Laplace summation procedure, we construct sectorial holomorphic solutions which are shown to share the same formal power series as asymptotic expansion in the perturbation parameter. We observe a small divisor phenomenon which emerges from the quasiperiodic nature of the solutions space and which is the origin of the Gevrey type divergence of this formal series. Our result rests on the classical Ramis-Sibuya theorem which asks to prove that the difference of any two neighboring constructed solutions satisfies some exponential decay. This is done by an asymptotic study of a Dirichlet-like series whose exponents are positive real numbers which accumulate to the origin.
Directory of Open Access Journals (Sweden)
Xueli Song
2014-01-01
Full Text Available This paper researches global asymptotic stability of impulsive cellular neural networks with proportional delays and partially Lipschitz activation functions. Firstly, by means of the transformation vi(t=ui(et, the impulsive cellular neural networks with proportional delays are transformed into impulsive cellular neural networks with the variable coefficients and constant delays. Secondly, we provide novel criteria for the uniqueness and exponential stability of the equilibrium point of the latter by relative nonlinear measure and prove that the exponential stability of equilibrium point of the latter implies the asymptotic stability of one of the former. We furthermore obtain a sufficient condition to the uniqueness and global asymptotic stability of the equilibrium point of the former. Our method does not require conventional assumptions on global Lipschitz continuity, boundedness, and monotonicity of activation functions. Our results are generalizations and improvements of some existing ones. Finally, an example and its simulations are provided to illustrate the correctness of our analysis.
Fuel Temperature Coefficient of Reactivity
Energy Technology Data Exchange (ETDEWEB)
Loewe, W.E.
2001-07-31
A method for measuring the fuel temperature coefficient of reactivity in a heterogeneous nuclear reactor is presented. The method, which is used during normal operation, requires that calibrated control rods be oscillated in a special way at a high reactor power level. The value of the fuel temperature coefficient of reactivity is found from the measured flux responses to these oscillations. Application of the method in a Savannah River reactor charged with natural uranium is discussed.
A cardy formula for three-point coefficients or how the black hole got its spots
Energy Technology Data Exchange (ETDEWEB)
Kraus, Per [Department of Physics and Astronomy, University of California,Los Angeles, CA 90095 (United States); Maloney, Alexander [Physics Department, McGill University,Montréal, QC H3A 2T8 (Canada)
2017-05-31
Modular covariance of torus one-point functions constrains the three point function coefficients of a two dimensional CFT. This leads to an asymptotic formula for the average value of light-heavy-heavy three point coefficients, generalizing Cardy’s formula for the high energy density of states. The derivation uses certain asymptotic properties of one-point conformal blocks on the torus. Our asymptotic formula matches a dual AdS{sub 3} computation of one point functions in a black hole background. This is evidence that the BTZ black hole geometry emerges upon course-graining over a suitable family of heavy microstates.
Bridging asymptotic independence and dependence in spatial exbtremes using Gaussian scale mixtures
Huser, Raphaël
2017-06-23
Gaussian scale mixtures are constructed as Gaussian processes with a random variance. They have non-Gaussian marginals and can exhibit asymptotic dependence unlike Gaussian processes, which are asymptotically independent except in the case of perfect dependence. In this paper, we study the extremal dependence properties of Gaussian scale mixtures and we unify and extend general results on their joint tail decay rates in both asymptotic dependence and independence cases. Motivated by the analysis of spatial extremes, we propose flexible yet parsimonious parametric copula models that smoothly interpolate from asymptotic dependence to independence and include the Gaussian dependence as a special case. We show how these new models can be fitted to high threshold exceedances using a censored likelihood approach, and we demonstrate that they provide valuable information about tail characteristics. In particular, by borrowing strength across locations, our parametric model-based approach can also be used to provide evidence for or against either asymptotic dependence class, hence complementing information given at an exploratory stage by the widely used nonparametric or parametric estimates of the χ and χ̄ coefficients. We demonstrate the capacity of our methodology by adequately capturing the extremal properties of wind speed data collected in the Pacific Northwest, US.
Bridging asymptotic independence and dependence in spatial exbtremes using Gaussian scale mixtures
Huser, Raphaë l; Opitz, Thomas; Thibaud, Emeric
2017-01-01
Gaussian scale mixtures are constructed as Gaussian processes with a random variance. They have non-Gaussian marginals and can exhibit asymptotic dependence unlike Gaussian processes, which are asymptotically independent except in the case of perfect dependence. In this paper, we study the extremal dependence properties of Gaussian scale mixtures and we unify and extend general results on their joint tail decay rates in both asymptotic dependence and independence cases. Motivated by the analysis of spatial extremes, we propose flexible yet parsimonious parametric copula models that smoothly interpolate from asymptotic dependence to independence and include the Gaussian dependence as a special case. We show how these new models can be fitted to high threshold exceedances using a censored likelihood approach, and we demonstrate that they provide valuable information about tail characteristics. In particular, by borrowing strength across locations, our parametric model-based approach can also be used to provide evidence for or against either asymptotic dependence class, hence complementing information given at an exploratory stage by the widely used nonparametric or parametric estimates of the χ and χ̄ coefficients. We demonstrate the capacity of our methodology by adequately capturing the extremal properties of wind speed data collected in the Pacific Northwest, US.
A quantum kinematics for asymptotically flat gravity
Campiglia, Miguel; Varadarajan, Madhavan
2015-07-01
We construct a quantum kinematics for asymptotically flat gravity based on the Koslowski-Sahlmann (KS) representation. The KS representation is a generalization of the representation underlying loop quantum gravity (LQG) which supports, in addition to the usual LQG operators, the action of ‘background exponential operators’, which are connection dependent operators labelled by ‘background’ su(2) electric fields. KS states have, in addition to the LQG state label corresponding to one dimensional excitations of the triad, a label corresponding to a ‘background’ electric field that describes three dimensional excitations of the triad. Asymptotic behaviour in quantum theory is controlled through asymptotic conditions on the background electric fields that label the states and the background electric fields that label the operators. Asymptotic conditions on the triad are imposed as conditions on the background electric field state label while confining the LQG spin net graph labels to compact sets. We show that KS states can be realised as wave functions on a quantum configuration space of generalized connections and that the asymptotic behaviour of each such generalized connection is determined by that of the background electric fields which label the background exponential operators. Similar to the spatially compact case, the Gauss law and diffeomorphism constraints are then imposed through group averaging techniques to obtain a large sector of gauge invariant states. It is shown that this sector supports a unitary action of the group of asymptotic rotations and translations and that, as anticipated by Friedman and Sorkin, for appropriate spatial topology, this sector contains states that display fermionic behaviour under 2π rotations.
Asymptotic stability of a catalyst particle
DEFF Research Database (Denmark)
Wedel, Stig; Michelsen, Michael L.; Villadsen, John
1977-01-01
The catalyst asymptotic stability problem is studied by means of several new methods that allow accurate solutions to be calculated where other methods have given qualitatively erroneous results. The underlying eigenvalue problem is considered in three limiting situations Le = ∞, 1 and 0. These a......The catalyst asymptotic stability problem is studied by means of several new methods that allow accurate solutions to be calculated where other methods have given qualitatively erroneous results. The underlying eigenvalue problem is considered in three limiting situations Le = ∞, 1 and 0...
Directions for model building from asymptotic safety
Bond, Andrew D.; Hiller, Gudrun; Kowalska, Kamila; Litim, Daniel F.
2017-08-01
Building on recent advances in the understanding of gauge-Yukawa theories we explore possibilities to UV-complete the Standard Model in an asymptotically safe manner. Minimal extensions are based on a large flavor sector of additional fermions coupled to a scalar singlet matrix field. We find that asymptotic safety requires fermions in higher representations of SU(3) C × SU(2) L . Possible signatures at colliders are worked out and include R-hadron searches, diboson signatures and the evolution of the strong and weak coupling constants.
On the asymptotics of dimers on tori
Kenyon, Richard W.; Sun, Nike; Wilson, David B.
2013-01-01
We study asymptotics of the dimer model on large toric graphs. Let $\\mathbb L$ be a weighted $\\mathbb{Z}^2$-periodic planar graph, and let $\\mathbb{Z}^2 E$ be a large-index sublattice of $\\mathbb{Z}^2$. For $\\mathbb L$ bipartite we show that the dimer partition function on the quotient $\\mathbb{L}/(\\mathbb{Z}^2 E)$ has the asymptotic expansion $\\exp[A f_0 + \\text{fsc} + o(1)]$, where $A$ is the area of $\\mathbb{L}/(\\mathbb{Z}^2 E)$, $f_0$ is the free energy density in the bulk, and $\\text{fsc...
Extracting OPE coefficient of Konishi at four loops
Energy Technology Data Exchange (ETDEWEB)
Goncalves, Vasco [ICTP South American Institute for Fundamental Research Instituto de Fisica Teorica,UNESP, Universidad Estadual Paulista, Rua Dr. Bento T. Ferraz 271, 01140-070, Sao Paulo, SP (Brazil)
2017-03-15
In this short note we compute the OPE coefficient of two 20{sup ′} operators and the Konishi operator. To this end, we use the OPE decomposition of a four point function of four 20{sup ′} operators and the method of asymptotic expansions to compute the leading term, in the OPE limit, of all integrals contributing to the four point function.
Estimates of the Sampling Distribution of Scalability Coefficient H
Van Onna, Marieke J. H.
2004-01-01
Coefficient "H" is used as an index of scalability in nonparametric item response theory (NIRT). It indicates the degree to which a set of items rank orders examinees. Theoretical sampling distributions, however, have only been derived asymptotically and only under restrictive conditions. Bootstrap methods offer an alternative possibility to…
Quantum Non-Markovian Langevin Equations and Transport Coefficients
International Nuclear Information System (INIS)
Sargsyan, V.V.; Antonenko, N.V.; Kanokov, Z.; Adamian, G.G.
2005-01-01
Quantum diffusion equations featuring explicitly time-dependent transport coefficients are derived from generalized non-Markovian Langevin equations. Generalized fluctuation-dissipation relations and analytic expressions for calculating the friction and diffusion coefficients in nuclear processes are obtained. The asymptotic behavior of the transport coefficients and correlation functions for a damped harmonic oscillator that is linearly coupled in momentum to a heat bath is studied. The coupling to a heat bath in momentum is responsible for the appearance of the diffusion coefficient in coordinate. The problem of regression of correlations in quantum dissipative systems is analyzed
Asymptotic integration of a linear fourth order differential equation of Poincaré type
Directory of Open Access Journals (Sweden)
Anibal Coronel
2015-11-01
Full Text Available This article deals with the asymptotic behavior of nonoscillatory solutions of fourth order linear differential equation where the coefficients are perturbations of constants. We define a change of variable and deduce that the new variable satisfies a third order nonlinear differential equation. We assume three hypotheses. The first hypothesis is related to the constant coefficients and set up that the characteristic polynomial associated with the fourth order linear equation has simple and real roots. The other two hypotheses are related to the behavior of the perturbation functions and establish asymptotic integral smallness conditions of the perturbations. Under these general hypotheses, we obtain four main results. The first two results are related to the application of a fixed point argument to prove that the nonlinear third order equation has a unique solution. The next result concerns with the asymptotic behavior of the solutions of the nonlinear third order equation. The fourth main theorem is introduced to establish the existence of a fundamental system of solutions and to precise the formulas for the asymptotic behavior of the linear fourth order differential equation. In addition, we present an example to show that the results introduced in this paper can be applied in situations where the assumptions of some classical theorems are not satisfied.
DEFF Research Database (Denmark)
Vahdatirad, Mohammadjavad; Bayat, Mehdi; Andersen, Lars Vabbersgaard
2015-01-01
shear strength of clay. Normal and Sobol sampling are employed to provide the asymptotic sampling method to generate the probability distribution of the foundation stiffnesses. Monte Carlo simulation is used as a benchmark. Asymptotic sampling accompanied with Sobol quasi random sampling demonstrates......The mechanical responses of an offshore monopile foundation mounted in over-consolidated clay are calculated by employing a stochastic approach where a nonlinear p–y curve is incorporated with a finite element scheme. The random field theory is applied to represent a spatial variation for undrained...... an efficient method for estimating the probability distribution of stiffnesses for the offshore monopile foundation....
Derivative analyticity relations and asymptotic energies
International Nuclear Information System (INIS)
Fischer, J.
1976-01-01
On the basis of general principles of the S-matrix theory theorems are derived showing that derivative analyticity relations analogous to those of Bronzen, Kane and Sukhatme hold at asymptotic energies if the high-energy limits of certain physical quantities exist
Stationary solutions and asymptotic flatness I
International Nuclear Information System (INIS)
Reiris, Martin
2014-01-01
In general relativity, a stationary isolated system is defined as an asymptotically flat (AF) stationary spacetime with compact material sources. Other definitions that are less restrictive on the type of asymptotic could in principle be possible. Between this article and its sequel, we show that under basic assumptions, asymptotic flatness indeed follows as a consequence of Einstein's theory. In particular, it is proved that any vacuum stationary spacetime-end whose (quotient) manifold is diffeomorphic to R 3 minus a ball and whose Killing field has its norm bounded away from zero, is necessarily AF with Schwarzschildian fall off. The ‘excised’ ball would contain (if any) the actual material body, but this information is unnecessary to reach the conclusion. In this first article, we work with weakly asymptotically flat (WAF) stationary ends, a notion that generalizes as much as possible that of the AF end, and prove that WAF ends are AF with Schwarzschildian fall off. Physical and mathematical implications are also discussed. (paper)
Renormalization and asymptotic freedom in quantum gravity
International Nuclear Information System (INIS)
Tomboulis, E.T.
1984-01-01
The article reviews some recent attempts to construct satisfactory theories of quantum gravity within the framework of local, continuum field theory. Quantum gravity; the renormalization group and its fixed points; fixed points and dimensional continuation in gravity; and quantum gravity at d=4-the 1/N expansion-asymptotic freedom; are all discussed. (U.K.)
Supersymmetric asymptotic safety is not guaranteed
DEFF Research Database (Denmark)
Intriligator, Kenneth; Sannino, Francesco
2015-01-01
in supersymmetric theories, and use unitarity bounds, and the a-theorem, to rule it out in broad classes of theories. The arguments apply without assuming perturbation theory. Therefore, the UV completion of a non-asymptotically free susy theory must have additional, non-obvious degrees of freedom, such as those...
The asymptotic expansion method via symbolic computation
Navarro, Juan F.
2012-01-01
This paper describes an algorithm for implementing a perturbation method based on an asymptotic expansion of the solution to a second-order differential equation. We also introduce a new symbolic computation system which works with the so-called modified quasipolynomials, as well as an implementation of the algorithm on it.
The Asymptotic Expansion Method via Symbolic Computation
Directory of Open Access Journals (Sweden)
Juan F. Navarro
2012-01-01
Full Text Available This paper describes an algorithm for implementing a perturbation method based on an asymptotic expansion of the solution to a second-order differential equation. We also introduce a new symbolic computation system which works with the so-called modified quasipolynomials, as well as an implementation of the algorithm on it.
Large degree asymptotics of generalized Bessel polynomials
J.L. López; N.M. Temme (Nico)
2011-01-01
textabstractAsymptotic expansions are given for large values of $n$ of the generalized Bessel polynomials $Y_n^\\mu(z)$. The analysis is based on integrals that follow from the generating functions of the polynomials. A new simple expansion is given that is valid outside a compact neighborhood of the
Asymptotic Translation Length in the Curve Complex
Valdivia, Aaron D.
2013-01-01
We show that when the genus and punctures of a surface are directly proportional by some rational number the minimal asymptotic translation length in the curve complex has behavior inverse to the square of the Euler characteristic. We also show that when the genus is fixed and the number of punctures varies the behavior is inverse to the Euler characteristic.
Asymptotic inversion of the Erlang B formula
Leeuwaarden, van J.S.H.; Temme, N.M.
2008-01-01
The Erlang B formula represents the steady-state blocking probability in the Erlang loss model or M=M=s=s queue. We derive asymptotic expansions for the offered load that matches, for a given number of servers, a certain blocking probability. In addressing this inversion problem we make use of
Asymptotic analysis of the Forward Search
DEFF Research Database (Denmark)
Johansen, Søren; Nielsen, Bent
The Forward Search is an iterative algorithm concerned with detection of outliers and other unsuspected structures in data. This approach has been suggested, analysed and applied for regression models in the monograph Atkinson and Riani (2000). An asymptotic analysis of the Forward Search is made...
On iterative procedures of asymptotic inference
K.O. Dzhaparidze (Kacha)
1983-01-01
textabstractAbstract An informal discussion is given on performing an unconstrained maximization or solving non‐linear equations of statistics by iterative methods with the quadratic termination property. It is shown that if a miximized function, e.g. likelihood, is asymptotically quadratic, then
Asymptotic evolution of quantum Markov chains
Energy Technology Data Exchange (ETDEWEB)
Novotny, Jaroslav [FNSPE, CTU in Prague, 115 19 Praha 1 - Stare Mesto (Czech Republic); Alber, Gernot [Institut fuer Angewandte Physik, Technische Universitaet Darmstadt, D-64289 Darmstadt (Germany)
2012-07-01
The iterated quantum operations, so called quantum Markov chains, play an important role in various branches of physics. They constitute basis for many discrete models capable to explore fundamental physical problems, such as the approach to thermal equilibrium, or the asymptotic dynamics of macroscopic physical systems far from thermal equilibrium. On the other hand, in the more applied area of quantum technology they also describe general characteristic properties of quantum networks or they can describe different quantum protocols in the presence of decoherence. A particularly, an interesting aspect of these quantum Markov chains is their asymptotic dynamics and its characteristic features. We demonstrate there is always a vector subspace (typically low-dimensional) of so-called attractors on which the resulting superoperator governing the iterative time evolution of quantum states can be diagonalized and in which the asymptotic quantum dynamics takes place. As the main result interesting algebraic relations are presented for this set of attractors which allow to specify their dual basis and to determine them in a convenient way. Based on this general theory we show some generalizations concerning the theory of fixed points or asymptotic evolution of random quantum operations.
Infrared studies of asymptotic giant branch stars
International Nuclear Information System (INIS)
Willems, F.J.
1987-01-01
In this thesis studies are presented of asymptotic giant branch stars, which are thought to be an important link in the evolution of the galaxy. The studies were performed on the basis of data collected by the IRAS, the infrared astronomical satelite. 233 refs.; 33 figs.; 16 tabs
Asymptotic behaviour of firmly non expansive sequences
International Nuclear Information System (INIS)
Rouhani, B.D.
1993-04-01
We introduce the notion of firmly non expansive sequences in a Banach space and present several results concerning their asymptotic behaviour extending previous results and giving an affirmative answer to an open question raised by S. Reich and I. Shafir. Applications to averaged mappings are also given. (author). 16 refs
An asymptotic problem in renewal theory
Klamkin, M.S.; van Lint, J.H.
1972-01-01
A special problem in renewal theory is considered. The asymptotic behavior of the renewal function was studied by W. L. Smith. Here we show that his result with an exponentially small remainder term follows from a theorem of De Bruijn on Volterra integral equations.
Behavior of asymptotically electro-Λ spacetimes
Saw, Vee-Liem
2017-04-01
We present the asymptotic solutions for spacetimes with nonzero cosmological constant Λ coupled to Maxwell fields, using the Newman-Penrose formalism. This extends a recent work that dealt with the vacuum Einstein (Newman-Penrose) equations with Λ ≠0 . The results are given in two different null tetrads: the Newman-Unti and Szabados-Tod null tetrads, where the peeling property is exhibited in the former but not the latter. Using these asymptotic solutions, we discuss the mass loss of an isolated electrogravitating system with cosmological constant. In a universe with Λ >0 , the physics of electromagnetic (EM) radiation is relatively straightforward compared to those of gravitational radiation: (1) It is clear that outgoing EM radiation results in a decrease to the Bondi mass of the isolated system. (2) It is also perspicuous that if any incoming EM radiation from elsewhere is present, those beyond the isolated system's cosmological horizon would eventually arrive at the spacelike I and increase the Bondi mass of the isolated system. Hence, the (outgoing and incoming) EM radiation fields do not couple with Λ in the Bondi mass-loss formula in an unusual manner, unlike the gravitational counterpart where outgoing gravitational radiation induces nonconformal flatness of I . These asymptotic solutions to the Einstein-Maxwell-de Sitter equations presented here may be used to extend a raft of existing results based on Newman-Unti's asymptotic solutions to the Einstein-Maxwell equations where Λ =0 , to now incorporate the cosmological constant Λ .
Asymptotically Safe Standard Model via Vectorlike Fermions
Mann, R. B.; Meffe, J. R.; Sannino, F.; Steele, T. G.; Wang, Z. W.; Zhang, C.
2017-12-01
We construct asymptotically safe extensions of the standard model by adding gauged vectorlike fermions. Using large number-of-flavor techniques we argue that all gauge couplings, including the hypercharge and, under certain conditions, the Higgs coupling, can achieve an interacting ultraviolet fixed point.
Asymptotic symmetries, holography and topological hair
Mishra, Rashmish K.; Sundrum, Raman
2018-01-01
Asymptotic symmetries of AdS4 quantum gravity and gauge theory are derived by coupling the holographically dual CFT3 to Chern-Simons gauge theory and 3D gravity in a "probe" (large-level) limit. Despite the fact that the three-dimensional AdS4 boundary as a whole is consistent with only finite-dimensional asymptotic symmetries, given by AdS isometries, infinite-dimensional symmetries are shown to arise in circumstances where one is restricted to boundary subspaces with effectively two-dimensional geometry. A canonical example of such a restriction occurs within the 4D subregion described by a Wheeler-DeWitt wavefunctional of AdS4 quantum gravity. An AdS4 analog of Minkowski "super-rotation" asymptotic symmetry is probed by 3D Einstein gravity, yielding CFT2 structure (in a large central charge limit), via AdS3 foliation of AdS4 and the AdS3/CFT2 correspondence. The maximal asymptotic symmetry is however probed by 3D conformal gravity. Both 3D gravities have Chern-Simons formulation, manifesting their topological character. Chern-Simons structure is also shown to be emergent in the Poincare patch of AdS4, as soft/boundary limits of 4D gauge theory, rather than "put in by hand" as an external probe. This results in a finite effective Chern-Simons level. Several of the considerations of asymptotic symmetry structure are found to be simpler for AdS4 than for Mink4, such as non-zero 4D particle masses, 4D non-perturbative "hard" effects, and consistency with unitarity. The last of these in particular is greatly simplified because in some set-ups the time dimension is explicitly shared by each level of description: Lorentzian AdS4, CFT3 and CFT2. Relatedly, the CFT2 structure clarifies the sense in which the infinite asymptotic charges constitute a useful form of "hair" for black holes and other complex 4D states. An AdS4 analog of Minkowski "memory" effects is derived, but with late-time memory of earlier events being replaced by (holographic) "shadow" effects. Lessons
Asymptotic form of three-body (dtμ)+ and (ddμ)+ wave functions
International Nuclear Information System (INIS)
Kino, Y.; Shimamura, I.; Armour, E.A.G.; Kamimura, M.
1996-01-01
In order to investigate a discrepancy between existing literature values for the normalization constant in the asymptotic form of three-body wave functions for (DTμ) + , we report the results of a new calculation of the normalization constants for this system as well as the related system (DDμ) + . These were obtained by fitting to accurate variational wave functions with special care being taken to describe the long-range behavior. (orig.)
Calculation of anisotropic few-group constants in asymptotic cells: the code ANICELL
International Nuclear Information System (INIS)
Devenyi, A.
1985-10-01
The theoretical background of the ANICELL computer program together with a user's manual is presented. ANICELL is a nuclear reactor neutron transport code which solves the traditional asymptotic and the so-called tilted flux transport problems in one-dimensional cylindrical geometry using linearly anisotropic scattering. The method of solution used is the first flight collision probability technique. Few-group constants including radial and axial diffusion coefficients for the cell are also prepared by the program. (author)
Light rays in static spacetimes with critical asymptotic behavior: A variational approach
Directory of Open Access Journals (Sweden)
Valeria Luisi
2006-09-01
Full Text Available Let $mathcal{M}=mathcal{M}_{0}imes mathbb{R}$ be a Lorentzian manifold equipped with the static metric $langle cdot ,cdot angle _{z}=langle cdot ,cdot angle -eta (xdt^{2}$. The aim of this paper is investigating the existence of lightlike geodesics joining a point $z_{0}=(x_{0},t_{0}$ to a line $gamma ={ x_{1}} imes mathbb{R}$ when coefficient $eta $ has a quadratic asymptotic behavior by means of a variational approach.
Directory of Open Access Journals (Sweden)
Nicholas Scott Cardell
2013-05-01
Full Text Available Maximum entropy methods of parameter estimation are appealing because they impose no additional structure on the data, other than that explicitly assumed by the analyst. In this paper we prove that the data constrained GME estimator of the general linear model is consistent and asymptotically normal. The approach we take in establishing the asymptotic properties concomitantly identifies a new computationally efficient method for calculating GME estimates. Formulae are developed to compute asymptotic variances and to perform Wald, likelihood ratio, and Lagrangian multiplier statistical tests on model parameters. Monte Carlo simulations are provided to assess the performance of the GME estimator in both large and small sample situations. Furthermore, we extend our results to maximum cross-entropy estimators and indicate a variant of the GME estimator that is unbiased. Finally, we discuss the relationship of GME estimators to Bayesian estimators, pointing out the conditions under which an unbiased GME estimator would be efficient.
Cosmic censorship, persistent curvature and asymptotic causal pathology
International Nuclear Information System (INIS)
Newman, R.P.A.C.
1984-01-01
The paper examines cosmic censorship in general relativity theory. Conformally flat space-times; persistent curvature; weakly asymptotically simple and empty asymptotes; censorship conditions; and the censorship theorem; are all discussed. (U.K.)
Kartuzova, Olga; Kassemi, Mohammad
2015-01-01
A CFD model for simulating the self-pressurization of a large scale liquid hydrogen storage tank is utilized in this paper to model the MHTB self-pressurization experiment. The kinetics-based Schrage equation is used to account for the evaporative and condensi ng interfacial mass flows in this model. The effect of the accommodation coefficient for calculating the interfacial mass transfer rate on the tank pressure during tank selfpressurization is studied. The values of the accommodation coefficient which were considered in this study vary from 1.0e-3 to 1.0e-1 for the explicit VOF model and from 1.0e-4 to 1.0e-3 for the implicit VOF model. The ullage pressure evolutions are compared against experimental data. A CFD model for controlling pressure in cryogenic storage tanks by spraying cold liquid into the ullage is also presented. The Euler-Lagrange approach is utilized for tracking the spray droplets and for modeling the interaction between the droplets and the continuous phase (ullage). The spray model is coupled with the VOF model by performing particle tracking in the ullage, removing particles from the ullage when they reach the interface, and then adding their contributions to the liquid. Droplet-ullage heat and mass transfer are modeled. The flow, temperature, and interfacial mass flux, as well as droplets trajectories, size distribution and temperatures predicted by the model are presented. The ul lage pressure and vapor temperature evolutions are compared with experimental data obtained from the MHTB spray bar mixing experiment. The effect of the accommodation coefficient for calculating the interfacial and droplet mass transfer rates on the tank pressure during mixing of the vapor using spray is studied. The values used for the accommodation coefficient at the interface vary from 1.0e-5 to 1.0e-2. The droplet accommodation coefficient values vary from 2.0e-6 to 1.0e-4.
Callan-Symanzik equation and asymptotic freedom in the Marr-Shimamoto model
International Nuclear Information System (INIS)
Scarfone, Leonard M.
2010-01-01
The exactly soluble nonrelativistic Marr-Shimamoto model was introduced in 1964 as an example of the Lee model with a propagator and a nontrivial vertex function. An exactly soluble relativistic version of this model, known as the Zachariasen model, has been found to be asymptotically free in terms of coupling constant renormalization at an arbitrary spacelike momentum and on the basis of exact solutions of the Gell-Mann-Low equations. This is accomplished with conventional cut-off regularization by setting up the Yukawa and Fermi coupling constants at Euclidean momenta in terms of on mass-shell couplings and then taking the asymptotic limit. In view of this background, it may be expected that an investigation of the nonrelativistic Marr-Shimamoto theory may also exhibit asymptotic freedom in view of its manifest mathematical similarity to that of the Zachariasen model. To prove this point, the present paper prefers to examine asymptotic freedom in the nonrelativistic Marr-Shimamoto theory using the powerful concepts of the renormalization group and the Callan-Symanzik equation, in conjunction with the specificity of dimensional regularization and on-shell renormalization. This approach is based on calculations of the Callan-Symanzik coefficients and determinations of the effective coupling constants. It is shown that the Marr-Shimamoto theory is asymptotically free for dimensions D 3 occurring in periodic intervals over the range of 0< D<27 of particular interest. This differs from the original Lee model which has been shown by several authors, using these same concepts, to be asymptotically free only for D<4.
Wang, Rui; Li, Qiqiang
2016-01-01
We consider a class of second-order Emden-Fowler equations with positive and nonpositve neutral coefficients. By using the Riccati transformation and inequalities, several oscillation and asymptotic results are established. Some examples are given to illustrate the main results.
Dujardin, G. M.
2009-01-01
This paper deals with the asymptotic behaviour of the solutions of linear initial boundary value problems with constant coefficients on the half-line and on finite intervals. We assume that the boundary data are periodic in time and we investigate
Criteria for exponential asymptotic stability in the large of ...
African Journals Online (AJOL)
The purpose of this study is to provide necessary and sufficient conditions for exponential asymptotic stability in the large and uniform asymptotic stability of perturbations of linear systems with unbounded delays. A strong relationship is established between the two types of asymptotic stability. It is found that if the ...
The Asymptotic Safety Scenario in Quantum Gravity.
Niedermaier, Max; Reuter, Martin
2006-01-01
The asymptotic safety scenario in quantum gravity is reviewed, according to which a renormalizable quantum theory of the gravitational field is feasible which reconciles asymptotically safe couplings with unitarity. The evidence from symmetry truncations and from the truncated flow of the effective average action is presented in detail. A dimensional reduction phenomenon for the residual interactions in the extreme ultraviolet links both results. For practical reasons the background effective action is used as the central object in the quantum theory. In terms of it criteria for a continuum limit are formulated and the notion of a background geometry self-consistently determined by the quantum dynamics is presented. Self-contained appendices provide prerequisites on the background effective action, the effective average action, and their respective renormalization flows.
Asymptotic properties of a simple random motion
International Nuclear Information System (INIS)
Ravishankar, K.
1988-01-01
A random walker in R/sup N/ is considered. At each step the walker picks a point in R/sup N/ from a fixed finite set of destination points. Having chosen the point, the walker moves a fraction r (r < 1) of the distance toward the point along a straight line. Assuming that the successive destination points are chosen independently, it is shown that the asymptotic distribution of the walker's position has the same mean as the destination point distribution. An estimate is obtained for the fraction of time the walker stays within a ball centered at the mean value for almost every destination sequence. Examples show that the asymptotic distribution could have intricate structure
Asymptotic mass degeneracies in conformal field theories
International Nuclear Information System (INIS)
Kani, I.; Vafa, C.
1990-01-01
By applying a method of Hardy and Ramanujan to characters of rational conformal field theories, we find an asymptotic expansion for degeneracy of states in the limit of large mass which is exact for strings propagating in more than two uncompactified space-time dimensions. Moreover we explore how the rationality of the conformal theory is reflected in the degeneracy of states. We also consider the one loop partition function for strings, restricted to physical states, for arbitrary (irrational) conformal theories, and obtain an asymptotic expansion for it in the limit that the torus degenerates. This expansion depends only on the spectrum of (physical and unphysical) relevant operators in the theory. We see how rationality is consistent with the smoothness of mass degeneracies as a function of moduli. (orig.)
The Asymptotic Safety Scenario in Quantum Gravity
Directory of Open Access Journals (Sweden)
Niedermaier Max
2006-12-01
Full Text Available The asymptotic safety scenario in quantum gravity is reviewed, according to which a renormalizable quantum theory of the gravitational field is feasible which reconciles asymptotically safe couplings with unitarity. The evidence from symmetry truncations and from the truncated flow of the effective average action is presented in detail. A dimensional reduction phenomenon for the residual interactions in the extreme ultraviolet links both results. For practical reasons the background effective action is used as the central object in the quantum theory. In terms of it criteria for a continuum limit are formulated and the notion of a background geometry self-consistently determined by the quantum dynamics is presented. Self-contained appendices provide prerequisites on the background effective action, the effective average action, and their respective renormalization flows.
Asymptotic adaptive bipartite entanglement-distillation protocol
International Nuclear Information System (INIS)
Hostens, Erik; Dehaene, Jeroen; De Moor, Bart
2006-01-01
We present an asymptotic bipartite entanglement-distillation protocol that outperforms all existing asymptotic schemes. This protocol is based on the breeding protocol with the incorporation of two-way classical communication. Like breeding, the protocol starts with an infinite number of copies of a Bell-diagonal mixed state. Breeding can be carried out as successive stages of partial information extraction, yielding the same result: one bit of information is gained at the cost (measurement) of one pure Bell state pair (ebit). The basic principle of our protocol is at every stage to replace measurements on ebits by measurements on a finite number of copies, whenever there are two equiprobable outcomes. In that case, the entropy of the global state is reduced by more than one bit. Therefore, every such replacement results in an improvement of the protocol. We explain how our protocol is organized as to have as many replacements as possible. The yield is then calculated for Werner states
Optimization of Parameters of Asymptotically Stable Systems
Directory of Open Access Journals (Sweden)
Anna Guerman
2011-01-01
Full Text Available This work deals with numerical methods of parameter optimization for asymptotically stable systems. We formulate a special mathematical programming problem that allows us to determine optimal parameters of a stabilizer. This problem involves solutions to a differential equation. We show how to chose the mesh in order to obtain discrete problem guaranteeing the necessary accuracy. The developed methodology is illustrated by an example concerning optimization of parameters for a satellite stabilization system.
Theorems for asymptotic safety of gauge theories
Energy Technology Data Exchange (ETDEWEB)
Bond, Andrew D.; Litim, Daniel F. [University of Sussex, Department of Physics and Astronomy, Brighton (United Kingdom)
2017-06-15
We classify the weakly interacting fixed points of general gauge theories coupled to matter and explain how the competition between gauge and matter fluctuations gives rise to a rich spectrum of high- and low-energy fixed points. The pivotal role played by Yukawa couplings is emphasised. Necessary and sufficient conditions for asymptotic safety of gauge theories are also derived, in conjunction with strict no go theorems. Implications for phase diagrams of gauge theories and physics beyond the Standard Model are indicated. (orig.)
Mass loss on the Asymptotic Giant Branch
Zijlstra, Albert
2006-01-01
Mass loss on the Asymptotic Giant Branch provides the origin of planetary nebulae. This paper reviews several relevant aspects of AGB evolution: pulsation properties, mass loss formalisms and time variable mass loss, evidence for asymmetries on the AGB, binarity, ISM interaction, and mass loss at low metallicity. There is growing evidence that mass loss on the AGB is already asymmetric, but with spherically symmetric velocity fields. The origin of the rings may be in pulsational instabilities...
Asymptotic elastic energy in simple metals
International Nuclear Information System (INIS)
Khalifeh, J.M.
1983-07-01
The asymptotic form of the elastic binding energy ΔEsup(as)(R) between two Mg atoms in Al is expressed as a product of a lattice Green function and the dipole force tensor P. The quantity P is obtained by a nearly free electron model in which the impurity effect is introduced by a screened Ashcroft pseudopotential characterized by an excess charge ΔZ and a core radius rsub(j). (author)
Fields Institute International Symposium on Asymptotic Methods in Stochastics
Kulik, Rafal; Haye, Mohamedou; Szyszkowicz, Barbara; Zhao, Yiqiang
2015-01-01
This book contains articles arising from a conference in honour of mathematician-statistician Miklόs Csörgő on the occasion of his 80th birthday, held in Ottawa in July 2012. It comprises research papers and overview articles, which provide a substantial glimpse of the history and state-of-the-art of the field of asymptotic methods in probability and statistics, written by leading experts. The volume consists of twenty articles on topics on limit theorems for self-normalized processes, planar processes, the central limit theorem and laws of large numbers, change-point problems, short and long range dependent time series, applied probability and stochastic processes, and the theory and methods of statistics. It also includes Csörgő’s list of publications during more than 50 years, since 1962.
Asymptotic safety of gravity with matter
Christiansen, Nicolai; Litim, Daniel F.; Pawlowski, Jan M.; Reichert, Manuel
2018-05-01
We study the asymptotic safety conjecture for quantum gravity in the presence of matter fields. A general line of reasoning is put forward explaining why gravitons dominate the high-energy behavior, largely independently of the matter fields as long as these remain sufficiently weakly coupled. Our considerations are put to work for gravity coupled to Yang-Mills theories with the help of the functional renormalization group. In an expansion about flat backgrounds, explicit results for beta functions, fixed points, universal exponents, and scaling solutions are given in systematic approximations exploiting running propagators, vertices, and background couplings. Invariably, we find that the gauge coupling becomes asymptotically free while the gravitational sector becomes asymptotically safe. The dependence on matter field multiplicities is weak. We also explain how the scheme dependence, which is more pronounced, can be handled without changing the physics. Our findings offer a new interpretation of many earlier results, which is explained in detail. The results generalize to theories with minimally coupled scalar and fermionic matter. Some implications for the ultraviolet closure of the Standard Model or its extensions are given.
Translational friction coefficient of a permeable cylinder in a sheet of viscous fluid
Wiegel, F.W.
1979-01-01
The author calculates the translational friction coefficient and the translational diffusion coefficient of a permeable cylinder moving in a sheet of fluid which is embedded on both sides in a fluid of much lower viscosity. The result, which is an asymptotic expression valid in the limit of small
Rotational friction coefficient of a permeable cylinder in a viscous fluid
Wiegel, F.W.
1979-01-01
An exact expression is derived for the rotational friction coefficient of a cylinder of infinite length and constant permeability immersed in an incompressible viscous fluid. An asymptotic expression for the translational friction coefficient of a permeable cylinder moving in a sheet of viscous
Robust Stabilization of Nonlinear Systems with Uncertain Varying Control Coefficient
Directory of Open Access Journals (Sweden)
Zaiyue Yang
2014-01-01
Full Text Available This paper investigates the stabilization problem for a class of nonlinear systems, whose control coefficient is uncertain and varies continuously in value and sign. The study emphasizes the development of a robust control that consists of a modified Nussbaum function to tackle the uncertain varying control coefficient. By such a method, the finite-time escape phenomenon has been prevented when the control coefficient is crossing zero and varying its sign. The proposed control guarantees the asymptotic stabilization of the system and boundedness of all closed-loop signals. The control performance is illustrated by a numerical simulation.
Directory of Open Access Journals (Sweden)
J. Kalas
2012-01-01
Full Text Available The asymptotic behaviour for the solutions of a real two-dimensional system with a bounded nonconstant delay is studied under the assumption of instability. Our results improve and complement previous results by J. Kalas, where the sufficient conditions assuring the existence of bounded solutions or solutions tending to origin for $t$ approaching infinity are given. The method of investigation is based on the transformation of the considered real system to one equation with complex-valued coefficients. Asymptotic properties of this equation are studied by means of a suitable Lyapunov-Krasovskii functional and by virtue of the Wazewski topological principle.
Chiral symmetry breaking in asymptotically free and non-asymptotically free gauge theories
International Nuclear Information System (INIS)
Gusynin, V.P.; Miranskij, V.A.
1986-01-01
An essential distinction in the realization of the PCAC-dynamics in vector-like asymptotically free and non-asymptotically free (with a non-trival ultraviolet stable fixed point) gauge theories is revealed. For the latter theories an analytical expression for the condensate is obtained in the two-loop approximation and the arguments in support of a soft behaviour at small distances of composite operators are given. The problem of factorizing the low-energy region for the Wess-Zumino-Witten action is discussed
Fuel-to-cladding heat transfer coefficient into reactor fuel element
International Nuclear Information System (INIS)
Lassmann, K.
1979-01-01
Models describing the fuel-to-cladding heat transfer coefficient in a reactor fuel element are reviewed critically. A new model is developed with contributions from solid, fluid and radiation heat transfer components. It provides a consistent description of the transition from an open gap to the contact case. Model parameters are easily available and highly independent of different combinations of material surfaces. There are no restrictions for fast transients. The model parameters are fitted to 388 data points under reactor conditions. For model verification another 274 data points of steel-steel and aluminium-aluminium interfaces, respectively, were used. The fluid component takes into account peak-to-peak surface roughnesses and, approximatively, also the wavelengths of surface roughnesses. For minor surface roughnesses normally prevailing in reactor fuel elements the model asymptotically yields Ross' and Stoute's model for the open gap, which is thus confirmed. Experimental contact data can be interpreted in very different ways. The new model differs greatly from Ross' and Stoute's contact term and results in better correlation coefficients. The numerical algorithm provides an adequate representation for calculating the fuel-to-cladding heat transfer coefficient in large fuel element structural analysis computer systems. (orig.) [de
Asymptotic problems for stochastic partial differential equations
Salins, Michael
Stochastic partial differential equations (SPDEs) can be used to model systems in a wide variety of fields including physics, chemistry, and engineering. The main SPDEs of interest in this dissertation are the semilinear stochastic wave equations which model the movement of a material with constant mass density that is exposed to both determinstic and random forcing. Cerrai and Freidlin have shown that on fixed time intervals, as the mass density of the material approaches zero, the solutions of the stochastic wave equation converge uniformly to the solutions of a stochastic heat equation, in probability. This is called the Smoluchowski-Kramers approximation. In Chapter 2, we investigate some of the multi-scale behaviors that these wave equations exhibit. In particular, we show that the Freidlin-Wentzell exit place and exit time asymptotics for the stochastic wave equation in the small noise regime can be approximated by the exit place and exit time asymptotics for the stochastic heat equation. We prove that the exit time and exit place asymptotics are characterized by quantities called quasipotentials and we prove that the quasipotentials converge. We then investigate the special case where the equation has a gradient structure and show that we can explicitly solve for the quasipotentials, and that the quasipotentials for the heat equation and wave equation are equal. In Chapter 3, we study the Smoluchowski-Kramers approximation in the case where the material is electrically charged and exposed to a magnetic field. Interestingly, if the system is frictionless, then the Smoluchowski-Kramers approximation does not hold. We prove that the Smoluchowski-Kramers approximation is valid for systems exposed to both a magnetic field and friction. Notably, we prove that the solutions to the second-order equations converge to the solutions of the first-order equation in an Lp sense. This strengthens previous results where convergence was proved in probability.
Lectures on the asymptotic theory of ideals
Rees, D
1988-01-01
In this book Professor Rees introduces and proves some of the main results of the asymptotic theory of ideals. The author's aim is to prove his Valuation Theorem, Strong Valuation Theorem, and Degree Formula, and to develop their consequences. The last part of the book is devoted to mixed multiplicities. Here the author develops his theory of general elements of ideals and gives a proof of a generalised degree formula. The reader is assumed to be familiar with basic commutative algebra, as covered in the standard texts, but the presentation is suitable for advanced graduate students. The work
Asymptotic density and the Ershov hierarchy
Downey, Rod; Jockusch, Carl; McNicholl, Timothy H.; Schupp, Paul
2013-01-01
We classify the asymptotic densities of the $\\Delta^0_2$ sets according to their level in the Ershov hierarchy. In particular, it is shown that for $n \\geq 2$, a real $r \\in [0,1]$ is the density of an $n$-c.e.\\ set if and only if it is a difference of left-$\\Pi_2^0$ reals. Further, we show that the densities of the $\\omega$-c.e.\\ sets coincide with the densities of the $\\Delta^0_2$ sets, and there are $\\omega$-c.e.\\ sets whose density is not the density of an $n$-c.e. set for any $n \\in \\ome...
Asymptotic freedom in extended conformal supergravities
International Nuclear Information System (INIS)
Fradkin, E.S.; Tseytlin, A.A.
1982-01-01
We present the calculation of the one-loop β-function in extended conformal supergravities. N = 1, 2, 3 theories (free or coupled to the Einstein supergravities) are found to the asymptotically free (like the N = 0 Weyl theory) while the N = 4 theory becomes finite under some plausible hypothesis. The results support the possibility to solve the problem of ghosts in these theories. The obtained sequence of SU(N) β-functions appears to be in remarkable correspondence with that for gauged O(N) supergravity theories. (orig.)
Asymptotically Free Natural Supersymmetric Twin Higgs Model
Badziak, Marcin; Harigaya, Keisuke
2018-05-01
Twin Higgs (TH) models explain the absence of new colored particles responsible for natural electroweak symmetry breaking (EWSB). All known ultraviolet completions of TH models require some nonperturbative dynamics below the Planck scale. We propose a supersymmetric model in which the TH mechanism is introduced by a new asymptotically free gauge interaction. The model features natural EWSB for squarks and gluino heavier than 2 TeV even if supersymmetry breaking is mediated around the Planck scale, and has interesting flavor phenomenology including the top quark decay into the Higgs boson and the up quark which may be discovered at the LHC.
Asymptotics with a positive cosmological constant II
Kesavan, Aruna; Ashtekar, Abhay; Bonga, Beatrice
2015-04-01
The study of isolated systems has been vastly successful in the context of vanishing cosmological constant, Λ = 0 . However, there is no physically useful notion of asymptotics for the universe we inhabit with Λ > 0 . This means that presently there is no fundamental understanding of gravitational waves in our own universe. The full non-linear framework is still under development, but some interesting results at the linearized level have been obtained. In particular, I will discuss the quadrupole formula for gravitational radiation and its implications.
Asymptotic behavior of monodromy singularly perturbed differential equations on a Riemann surface
Simpson, Carlos
1991-01-01
This book concerns the question of how the solution of a system of ODE's varies when the differential equation varies. The goal is to give nonzero asymptotic expansions for the solution in terms of a parameter expressing how some coefficients go to infinity. A particular classof families of equations is considered, where the answer exhibits a new kind of behavior not seen in most work known until now. The techniques include Laplace transform and the method of stationary phase, and a combinatorial technique for estimating the contributions of terms in an infinite series expansion for the solution. Addressed primarily to researchers inalgebraic geometry, ordinary differential equations and complex analysis, the book will also be of interest to applied mathematicians working on asymptotics of singular perturbations and numerical solution of ODE's.
Asymptotic behaviour of the scattering phase for non-trapping metrics
International Nuclear Information System (INIS)
Popov, G.S.
1982-01-01
The asymptotic behaviour of the scattering phase is considered at infinity for an elliptic, self-adjoint, second order differential operator H, defined either in Rsup(n) or in an unbounded domain Ω contains Rsup(n) with Dirichlet or Neumann boundary conditions. The operator H has the form H=- δsub(g)+hD+V where δsub(g) is the Laplace-Beltrami operator related to a Riemann metric g in anti Ω. Provided a non-trapping hypothesis is fulfilled and H coincides with the Laplace operator δ in a neighbourhood of infinity, an asymptotic development of the scattering phase s(lambda) is obtained for lambda → infinity. The first coefficients in this development are found
Asymptotic behavior of equilibrium states of reaction-diffusion systems with mass conservation
Chern, Jann-Long; Morita, Yoshihisa; Shieh, Tien-Tsan
2018-01-01
We deal with a stationary problem of a reaction-diffusion system with a conservation law under the Neumann boundary condition. It is shown that the stationary problem turns to be the Euler-Lagrange equation of an energy functional with a mass constraint. When the domain is the finite interval (0 , 1), we investigate the asymptotic profile of a strictly monotone minimizer of the energy as d, the ratio of the diffusion coefficient of the system, tends to zero. In view of a logarithmic function in the leading term of the potential, we get to a scaling parameter κ satisfying the relation ε : =√{ d } =√{ log κ } /κ2. The main result shows that a sequence of minimizers converges to a Dirac mass multiplied by the total mass and that by a scaling with κ the asymptotic profile exhibits a parabola in the nonvanishing region. We also prove the existence of an unstable monotone solution when the mass is small.
Dujardin, G. M.
2009-08-12
This paper deals with the asymptotic behaviour of the solutions of linear initial boundary value problems with constant coefficients on the half-line and on finite intervals. We assume that the boundary data are periodic in time and we investigate whether the solution becomes time-periodic after sufficiently long time. Using Fokas\\' transformation method, we show that, for the linear Schrödinger equation, the linear heat equation and the linearized KdV equation on the half-line, the solutions indeed become periodic for large time. However, for the same linear Schrödinger equation on a finite interval, we show that the solution, in general, is not asymptotically periodic; actually, the asymptotic behaviour of the solution depends on the commensurability of the time period T of the boundary data with the square of the length of the interval over. © 2009 The Royal Society.
Coulomb string tension, asymptotic string tension, and the gluon chain
Greensite, Jeff; Szczepaniak, Adam P.
2014-01-01
We compute, via numerical simulations, the non-perturbative Coulomb potential of pure SU(3) gauge theory in Coulomb gauge. We find that that the Coulomb potential scales nicely in accordance with asymptotic freedom, that the Coulomb potential is linear in the infrared, and that the Coulomb string tension is about four times larger than the asymptotic string tension. We explain how it is possible that the asymptotic string tension can be lower than the Coulomb string tension by a factor of four.
Numerical integration of asymptotic solutions of ordinary differential equations
Thurston, Gaylen A.
1989-01-01
Classical asymptotic analysis of ordinary differential equations derives approximate solutions that are numerically stable. However, the analysis also leads to tedious expansions in powers of the relevant parameter for a particular problem. The expansions are replaced with integrals that can be evaluated by numerical integration. The resulting numerical solutions retain the linear independence that is the main advantage of asymptotic solutions. Examples, including the Falkner-Skan equation from laminar boundary layer theory, illustrate the method of asymptotic analysis with numerical integration.
Local fields for asymptotic matching in multidimensional mode conversion
International Nuclear Information System (INIS)
Tracy, E. R.; Kaufman, A. N.; Jaun, A.
2007-01-01
The problem of resonant mode conversion in multiple spatial dimensions is considered. Using phase space methods, a complete theory is developed for constructing matched asymptotic expansions that fit incoming and outgoing WKB solutions. These results provide, for the first time, a complete and practical method for including multidimensional conversion in ray tracing algorithms. The paper provides a self-contained description of the following topics: (1) how to use eikonal (also known as ray tracing or WKB) methods to solve vector wave equations and how to detect conversion regions while following rays; (2) once conversion is detected, how to fit to a generic saddle structure in ray phase space associated with the most common type of conversion; (3) given the saddle structure, how to carry out a local projection of the full vector wave equation onto a local two-component normal form that governs the two resonantly interacting waves. This determines both the uncoupled dispersion functions and the coupling constant, which in turn determine the uncoupled WKB solutions; (4) given the normal form of the local two-component wave equation, how to find the particular solution that matches the amplitude, phase, and polarization of the incoming ray, to the amplitude, phase, and polarization of the two outgoing rays: the transmitted and converted rays
On maximal surfaces in asymptotically flat space-times
International Nuclear Information System (INIS)
Bartnik, R.; Chrusciel, P.T.; O Murchadha, N.
1990-01-01
Existence of maximal and 'almost maximal' hypersurfaces in asymptotically flat space-times is established under boundary conditions weaker than those considered previously. We show in particular that every vacuum evolution of asymptotically flat data for Einstein equations can be foliated by slices maximal outside a spatially compact set and that every (strictly) stationary asymptotically flat space-time can be foliated by maximal hypersurfaces. Amongst other uniqueness results, we show that maximal hypersurface can be used to 'partially fix' an asymptotic Poincare group. (orig.)
Asymptotic variance of grey-scale surface area estimators
DEFF Research Database (Denmark)
Svane, Anne Marie
Grey-scale local algorithms have been suggested as a fast way of estimating surface area from grey-scale digital images. Their asymptotic mean has already been described. In this paper, the asymptotic behaviour of the variance is studied in isotropic and sufficiently smooth settings, resulting...... in a general asymptotic bound. For compact convex sets with nowhere vanishing Gaussian curvature, the asymptotics can be described more explicitly. As in the case of volume estimators, the variance is decomposed into a lattice sum and an oscillating term of at most the same magnitude....
Directory of Open Access Journals (Sweden)
Uğur YALÇIN
2004-02-01
Full Text Available In this study, quasi-optical scattering of finite source electromagnetic waves from a dielectric coated cylindrical surface is analysed with Physical Optics (PO approach. A linear electrical current source is chosen as the finite source. Reflection coefficient of the cylindrical surface is derived by using Geometrical Theory of Diffraction (GTD. Then, with the help of this coefficient, fields scattered from the surface are obtained. These field expressions are used in PO approach and surface scattering integral is determined. Evaluating this integral asymptotically, fields reflected from the surface and surface divergence coefficient are calculated. Finally, results obtained in this study are evaluated numerically and effects of the surface impedance to scattered fields are analysed. The time factor is taken as j te? in this study.
Asymptotic distribution of ∆AUC, NRIs, and IDI based on theory of U-statistics.
Demler, Olga V; Pencina, Michael J; Cook, Nancy R; D'Agostino, Ralph B
2017-09-20
The change in area under the curve (∆AUC), the integrated discrimination improvement (IDI), and net reclassification index (NRI) are commonly used measures of risk prediction model performance. Some authors have reported good validity of associated methods of estimating their standard errors (SE) and construction of confidence intervals, whereas others have questioned their performance. To address these issues, we unite the ∆AUC, IDI, and three versions of the NRI under the umbrella of the U-statistics family. We rigorously show that the asymptotic behavior of ∆AUC, NRIs, and IDI fits the asymptotic distribution theory developed for U-statistics. We prove that the ∆AUC, NRIs, and IDI are asymptotically normal, unless they compare nested models under the null hypothesis. In the latter case, asymptotic normality and existing SE estimates cannot be applied to ∆AUC, NRIs, or IDI. In the former case, SE formulas proposed in the literature are equivalent to SE formulas obtained from U-statistics theory if we ignore adjustment for estimated parameters. We use Sukhatme-Randles-deWet condition to determine when adjustment for estimated parameters is necessary. We show that adjustment is not necessary for SEs of the ∆AUC and two versions of the NRI when added predictor variables are significant and normally distributed. The SEs of the IDI and three-category NRI should always be adjusted for estimated parameters. These results allow us to define when existing formulas for SE estimates can be used and when resampling methods such as the bootstrap should be used instead when comparing nested models. We also use the U-statistic theory to develop a new SE estimate of ∆AUC. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.
From asymptotic safety to dark energy
International Nuclear Information System (INIS)
Ahn, Changrim; Kim, Chanju; Linder, Eric V.
2011-01-01
We consider renormalization group flow applied to the cosmological dynamical equations. A consistency condition arising from energy-momentum conservation links the flow parameters to the cosmological evolution, restricting possible behaviors. Three classes of cosmological fixed points for dark energy plus a barotropic fluid are found: a dark energy dominated universe, which can be either accelerating or decelerating depending on the RG flow parameters, a barotropic dominated universe where dark energy fades away, and solutions where the gravitational and potential couplings cease to flow. If the IR fixed point coincides with the asymptotically safe UV fixed point then the dark energy pressure vanishes in the first class, while (only) in the de Sitter limit of the third class the RG cutoff scale becomes the Hubble scale.
Asymptotic theory of weakly dependent random processes
Rio, Emmanuel
2017-01-01
Presenting tools to aid understanding of asymptotic theory and weakly dependent processes, this book is devoted to inequalities and limit theorems for sequences of random variables that are strongly mixing in the sense of Rosenblatt, or absolutely regular. The first chapter introduces covariance inequalities under strong mixing or absolute regularity. These covariance inequalities are applied in Chapters 2, 3 and 4 to moment inequalities, rates of convergence in the strong law, and central limit theorems. Chapter 5 concerns coupling. In Chapter 6 new deviation inequalities and new moment inequalities for partial sums via the coupling lemmas of Chapter 5 are derived and applied to the bounded law of the iterated logarithm. Chapters 7 and 8 deal with the theory of empirical processes under weak dependence. Lastly, Chapter 9 describes links between ergodicity, return times and rates of mixing in the case of irreducible Markov chains. Each chapter ends with a set of exercises. The book is an updated and extended ...
Chiral fermions in asymptotically safe quantum gravity.
Meibohm, J; Pawlowski, J M
2016-01-01
We study the consistency of dynamical fermionic matter with the asymptotic safety scenario of quantum gravity using the functional renormalisation group. Since this scenario suggests strongly coupled quantum gravity in the UV, one expects gravity-induced fermion self-interactions at energies of the Planck scale. These could lead to chiral symmetry breaking at very high energies and thus to large fermion masses in the IR. The present analysis which is based on the previous works (Christiansen et al., Phys Rev D 92:121501, 2015; Meibohm et al., Phys Rev D 93:084035, 2016), concludes that gravity-induced chiral symmetry breaking at the Planck scale is avoided for a general class of NJL-type models. We find strong evidence that this feature is independent of the number of fermion fields. This finding suggests that the phase diagram for these models is topologically stable under the influence of gravitational interactions.
Asymptotic stability of steady compressible fluids
Padula, Mariarosaria
2011-01-01
This volume introduces a systematic approach to the solution of some mathematical problems that arise in the study of the hyperbolic-parabolic systems of equations that govern the motions of thermodynamic fluids. It is intended for a wide audience of theoretical and applied mathematicians with an interest in compressible flow, capillarity theory, and control theory. The focus is particularly on recent results concerning nonlinear asymptotic stability, which are independent of assumptions about the smallness of the initial data. Of particular interest is the loss of control that sometimes results when steady flows of compressible fluids are upset by large disturbances. The main ideas are illustrated in the context of three different physical problems: (i) A barotropic viscous gas in a fixed domain with compact boundary. The domain may be either an exterior domain or a bounded domain, and the boundary may be either impermeable or porous. (ii) An isothermal viscous gas in a domain with free boundaries. (iii) A h...
Asymptotic representation of relaxation oscillations in lasers
Grigorieva, Elena V
2017-01-01
In this book we analyze relaxation oscillations in models of lasers with nonlinear elements controlling light dynamics. The models are based on rate equations taking into account periodic modulation of parameters, optoelectronic delayed feedback, mutual coupling between lasers, intermodal interaction and other factors. With the aim to study relaxation oscillations we present the special asymptotic method of integration for ordinary differential equations and differential-difference equations. As a result, they are reduced to discrete maps. Analyzing the maps we describe analytically such nonlinear phenomena in lasers as multistability of large-amplitude relaxation cycles, bifurcations of cycles, controlled switching of regimes, phase synchronization in an ensemble of coupled systems and others. The book can be fruitful for students and technicians in nonlinear laser dynamics and in differential equations.
Asymptotically safe non-minimal inflation
Energy Technology Data Exchange (ETDEWEB)
Tronconi, Alessandro, E-mail: Alessandro.Tronconi@bo.infn.it [Dipartimento di Fisica e Astronomia and INFN, Via Irnerio 46,40126 Bologna (Italy)
2017-07-01
We study the constraints imposed by the requirement of Asymptotic Safety on a class of inflationary models with an inflaton field non-minimally coupled to the Ricci scalar. The critical surface in the space of theories is determined by the improved renormalization group flow which takes into account quantum corrections beyond the one loop approximation. The combination of constraints deriving from Planck observations and those from theory puts severe bounds on the values of the parameters of the model and predicts a quite large tensor to scalar ratio. We finally comment on the dependence of the results on the definition of the infrared energy scale which parametrises the running on the critical surface.
UV conformal window for asymptotic safety
Bond, Andrew D.; Litim, Daniel F.; Vazquez, Gustavo Medina; Steudtner, Tom
2018-02-01
Interacting fixed points in four-dimensional gauge theories coupled to matter are investigated using perturbation theory up to three loop order. It is shown how fixed points, scaling exponents, and anomalous dimensions are obtained as a systematic power series in a small parameter. The underlying ordering principle is explained and contrasted with conventional perturbation theory and Weyl consistency conditions. We then determine the conformal window with asymptotic safety from the complete next-to-next-to-leading order in perturbation theory. Limits for the conformal window arise due to fixed point mergers, the onset of strong coupling, or vacuum instability. A consistent picture is uncovered by comparing various levels of approximation. The theory remains perturbative in the entire conformal window, with vacuum stability dictating the tightest constraints. We also speculate about a secondary conformal window at strong coupling and estimate its lower limit. Implications for model building and cosmology are indicated.
Quantum defect theory and asymptotic methods
International Nuclear Information System (INIS)
Seaton, M.J.
1982-01-01
It is shown that quantum defect theory provides a basis for the development of various analytical methods for the examination of electron-ion collision phenomena, including di-electronic recombination. Its use in conjuction with ab initio calculations is shown to be restricted by problems which arise from the presence of long-range non-Coulomb potentials. Empirical fitting to some formulae can be efficient in the use of computer time but extravagant in the use of person time. Calculations at a large number of energy points which make no use of analytical formulae for resonance structures may be made less extravagant in computer time by the development of more efficient asymptotic methods. (U.K.)
Grassmann scalar fields and asymptotic freedom
Energy Technology Data Exchange (ETDEWEB)
Palumbo, F [INFN, Laboratori Nazionali di Frascati, Rome (Italy)
1996-03-01
The authors extend previous results about scalar fields whose Fourier components are even elements of a Grassmann algebra with given index of nilpotency. Their main interest in particle physics is related to the possibility that they describe fermionic composites analogous to the Copper pairs of superconductivity. The authors evaluate the free propagators for arbitrary index of nilpotency and they investigate a {phi}{sup 4} model to one loop. Due to the nature of the integral over even Grassmann fields such as a model exists for repulsive as well as attractive self interaction. In the first case the {beta}-function is equal to that of the ordinary theory, while in the second one the model is asymptotically free. The bare mass has a peculiar dependence on the cutoff, being quadratically decreasing/increasing for attractive/repulsive self interaction.
Asymptotic methods in mechanics of solids
Bauer, Svetlana M; Smirnov, Andrei L; Tovstik, Petr E; Vaillancourt, Rémi
2015-01-01
The construction of solutions of singularly perturbed systems of equations and boundary value problems that are characteristic for the mechanics of thin-walled structures are the main focus of the book. The theoretical results are supplemented by the analysis of problems and exercises. Some of the topics are rarely discussed in the textbooks, for example, the Newton polyhedron, which is a generalization of the Newton polygon for equations with two or more parameters. After introducing the important concept of the index of variation for functions special attention is devoted to eigenvalue problems containing a small parameter. The main part of the book deals with methods of asymptotic solutions of linear singularly perturbed boundary and boundary value problems without or with turning points, respectively. As examples, one-dimensional equilibrium, dynamics and stability problems for rigid bodies and solids are presented in detail. Numerous exercises and examples as well as vast references to the relevant Russi...
Asymptotic Sharpness of Bounds on Hypertrees
Directory of Open Access Journals (Sweden)
Lin Yi
2017-08-01
Full Text Available The hypertree can be defined in many different ways. Katona and Szabó introduced a new, natural definition of hypertrees in uniform hypergraphs and investigated bounds on the number of edges of the hypertrees. They showed that a k-uniform hypertree on n vertices has at most (nk−1$\\left( {\\matrix{n \\cr {k - 1} } } \\right$ edges and they conjectured that the upper bound is asymptotically sharp. Recently, Szabó verified that the conjecture holds by recursively constructing an infinite sequence of k-uniform hypertrees and making complicated analyses for it. In this note we give a short proof of the conjecture by directly constructing a sequence of k-uniform k-hypertrees.
Asymptotic safety, singularities, and gravitational collapse
International Nuclear Information System (INIS)
Casadio, Roberto; Hsu, Stephen D.H.; Mirza, Behrouz
2011-01-01
Asymptotic safety (an ultraviolet fixed point with finite-dimensional critical surface) offers the possibility that a predictive theory of quantum gravity can be obtained from the quantization of classical general relativity. However, it is unclear what becomes of the singularities of classical general relativity, which, it is hoped, might be resolved by quantum effects. We study dust collapse with a running gravitational coupling and find that a future singularity can be avoided if the coupling becomes exactly zero at some finite energy scale. The singularity can also be avoided (pushed off to infinite proper time) if the coupling approaches zero sufficiently rapidly at high energies. However, the evolution deduced from perturbation theory still implies a singularity at finite proper time.
Asymptotic limits of a statistical transport description
International Nuclear Information System (INIS)
Malvagi, F.; Levermore, C.D.; Pomraning, G.C.; Department of Mathematics, University of Arizona, Tucson, AZ 85721)
1989-01-01
We consider three different asymptotic limits of a model describing linear particle transport in a stochastic medium consisting of two randomly mixed immiscible fluids. These three limits are: (1) the fluid packets are small compared to the particle mean free path in the packet; (2) a small amount of large cross section fluid is admixed with a large amount of small cross section fluid; and (3) the angular dependence of the intensity (angular flux) is nearly isotropic. The first two limits reduce the underlying model, which consists of two coupled transport equations, to a single transport equation of the usual form. The third limit yields a two-equation diffusion approximation, and a boundary layer analysis gives boundary conditions for these two coupled diffusion equations
Charge exchange with ion excitation: asymptotic theory
International Nuclear Information System (INIS)
Ivakin, I.A.; Karbovanets, M.I.; Ostrovskii, V.N.
1987-01-01
There is developed an asymptotic (with respect to the large internuclear separation R) theory for computing the matrix element of the exchange interaction between states of quasimolecules, which is responsible for charge transfer with ion excitation: B + +A→B+A + *. A semiclassical approximation is used, which enables one to apply the theory to processes with the participation of multiply charged ions. The case of s--s transitions for excitation of the ion A + →A + *, where it is appropriate to take into account the distortion of the wave functions of the ion A + by the particle B, is treated separately. Calculations of cross sections and comparison with the results of experiments for He + --Cd and Ne + --Mg collisions at thermal energies are given. It is shown that it is impossible to explain the experimental data by the interaction of terms of the quasimolecules at large R only, and a possible mechanism for populating at small R is proposed
Methods in half-linear asymptotic theory
Directory of Open Access Journals (Sweden)
Pavel Rehak
2016-10-01
Full Text Available We study the asymptotic behavior of eventually positive solutions of the second-order half-linear differential equation $$ (r(t|y'|^{\\alpha-1}\\hbox{sgn} y''=p(t|y|^{\\alpha-1}\\hbox{sgn} y, $$ where r(t and p(t are positive continuous functions on $[a,\\infty$, $\\alpha\\in(1,\\infty$. The aim of this article is twofold. On the one hand, we show applications of a wide variety of tools, like the Karamata theory of regular variation, the de Haan theory, the Riccati technique, comparison theorems, the reciprocity principle, a certain transformation of dependent variable, and principal solutions. On the other hand, we solve open problems posed in the literature and generalize existing results. Most of our observations are new also in the linear case.
Lattice quantum gravity and asymptotic safety
Laiho, J.; Bassler, S.; Coumbe, D.; Du, D.; Neelakanta, J. T.
2017-09-01
We study the nonperturbative formulation of quantum gravity defined via Euclidean dynamical triangulations (EDT) in an attempt to make contact with Weinberg's asymptotic safety scenario. We find that a fine-tuning is necessary in order to recover semiclassical behavior. Such a fine-tuning is generally associated with the breaking of a target symmetry by the lattice regulator; in this case we argue that the target symmetry is the general coordinate invariance of the theory. After introducing and fine-tuning a nontrivial local measure term, we find no barrier to taking a continuum limit, and we find evidence that four-dimensional, semiclassical geometries are recovered at long distance scales in the continuum limit. We also find that the spectral dimension at short distance scales is consistent with 3 /2 , a value that could resolve the tension between asymptotic safety and the holographic entropy scaling of black holes. We argue that the number of relevant couplings in the continuum theory is one, once symmetry breaking by the lattice regulator is accounted for. Such a theory is maximally predictive, with no adjustable parameters. The cosmological constant in Planck units is the only relevant parameter, which serves to set the lattice scale. The cosmological constant in Planck units is of order 1 in the ultraviolet and undergoes renormalization group running to small values in the infrared. If these findings hold up under further scrutiny, the lattice may provide a nonperturbative definition of a renormalizable quantum field theory of general relativity with no adjustable parameters and a cosmological constant that is naturally small in the infrared.
Chen, Hua; Chen, Kun
2013-07-01
The distributions of coalescence times and ancestral lineage numbers play an essential role in coalescent modeling and ancestral inference. Both exact distributions of coalescence times and ancestral lineage numbers are expressed as the sum of alternating series, and the terms in the series become numerically intractable for large samples. More computationally attractive are their asymptotic distributions, which were derived in Griffiths (1984) for populations with constant size. In this article, we derive the asymptotic distributions of coalescence times and ancestral lineage numbers for populations with temporally varying size. For a sample of size n, denote by Tm the mth coalescent time, when m + 1 lineages coalesce into m lineages, and An(t) the number of ancestral lineages at time t back from the current generation. Similar to the results in Griffiths (1984), the number of ancestral lineages, An(t), and the coalescence times, Tm, are asymptotically normal, with the mean and variance of these distributions depending on the population size function, N(t). At the very early stage of the coalescent, when t → 0, the number of coalesced lineages n - An(t) follows a Poisson distribution, and as m → n, $$n\\left(n-1\\right){T}_{m}/2N\\left(0\\right)$$ follows a gamma distribution. We demonstrate the accuracy of the asymptotic approximations by comparing to both exact distributions and coalescent simulations. Several applications of the theoretical results are also shown: deriving statistics related to the properties of gene genealogies, such as the time to the most recent common ancestor (TMRCA) and the total branch length (TBL) of the genealogy, and deriving the allele frequency spectrum for large genealogies. With the advent of genomic-level sequencing data for large samples, the asymptotic distributions are expected to have wide applications in theoretical and methodological development for population genetic inference.
Asymptotic Method for Cladding Stress Evaluation in PCMI
International Nuclear Information System (INIS)
Kim, Hyungkyu; Kim, Jaeyong; Yoon, Kyungho; Lee, Kanghee; Kang, Heungseok
2014-01-01
A PCMI (Pellet Cladding Mechanical Interaction) failure was first reported in the GETR (General Electric Test Reactor) at Vacellitos in 1963, and such failures are still occurring. Since the high stress values in the cladding tube has been of a crucial concern in PCMI studies, there have been many researches on the stress analysis of a cladding tube pressed by a pellet. Typical works can be found in some references. It has often been assumed, however, that the cracks in the pellet were equally spaced and the pellet was a rigid body. In addition, the friction coefficient was arbitrarily chosen so that a slipping between the pellets and cladding tube could not be logically defined. Moreover, the stress intensification due to the sharp edge of a pellet fragment has never been realistically considered. These problems above drove us to launch a framework of a PCMI study particularly on stress analysis technology to improve the present analysis method incorporating the actual PCMI conditions such as the stress intensification, arbitrary distribution of the pellet cracks, material properties (esp. pellet) and slipping behavior of the pellet/cladding interface. As a first step of this work, this paper introduces an asymptotic method that was originally developed for a stress analysis in the vicinity of a sharp notch of a homogeneous body. The intrinsic reason for applying this method is to simulate the stress singularity that is expected to take place at the sharp edge of a pellet fragment due to cracking during irradiation. As a first attempt of this work, an eigenvalue problem is formulated in the case of adhered contact, and the generalized stress intensity factors are defined and evaluated. Although some works obviously remain to be accomplished, for the present framework on the PCMI analysis (e. g., slipping behaviour, contact force etc.), it was addressed that the asymptotic method can produce the stress values that cause the cladding tube failure in PCMI more
H. David Politzer, Asymptotic Freedom, and Strong Interaction
dropdown arrow Site Map A-Z Index Menu Synopsis H. David Politzer, Asymptotic Freedom, and Strong Interaction Resources with Additional Information H. David Politzer Photo Credit: California Institute of Technology H. David Politzer has won the 2004 Nobel Prize in Physics 'for the discovery of asymptotic freedom
Regge asymptotics of scattering with flavour exchange in QCD
International Nuclear Information System (INIS)
Kirschner, R.
1994-06-01
The contribution to the perturbative Regge asymptotics of the exchange of two reggeized fermions with opposite helicity is investigated. The methods of conformal symmetry known for the case of gluon exchange are extended to this case where double-logarithmic contributions dominate the asymptotics. The Regge trajectories at large momentum transfer are calculated. (orig.)
Error estimates in horocycle averages asymptotics: challenges from string theory
Cardella, M.A.
2010-01-01
For modular functions of rapid decay, a classical result connects the error estimate in their long horocycle average asymptotic to the Riemann hypothesis. We study similar asymptotics, for modular functions with not that mild growing conditions, such as of polynomial growth and of exponential growth
An asymptotic solution of large-N QCD
Directory of Open Access Journals (Sweden)
Bochicchio Marco
2014-01-01
Full Text Available We find an asymptotic solution for two-, three- and multi-point correlators of local gauge-invariant operators, in a lower-spin sector of massless large-N QCD, in terms of glueball and meson propagators, in such a way that the solution is asymptotic in the ultraviolet to renormalization-group improved perturbation theory, by means of a new purely field-theoretical technique that we call the asymptotically-free bootstrap, based on a recently-proved asymptotic structure theorem for two-point correlators. The asymptotically-free bootstrap provides as well asymptotic S-matrix amplitudes in terms of glueball and meson propagators. Remarkably, the asymptotic S-matrix depends only on the unknown particle spectrum, but not on the anomalous dimensions, as a consequence of the LS Z reduction formulae. Very many physics consequences follow, both practically and theoretically. In fact, the asymptotic solution sets the strongest constraints on any actual solution of large-N QCD, and in particular on any string solution.
An asymptotic formula of the divergent bilateral basic hypergeometric series
Morita, Takeshi
2012-01-01
We show an asymptotic formula of the divergent bilateral basic hypergeometric series ${}_1\\psi_0 (a;-;q,\\cdot)$ with using the $q$-Borel-Laplace method. We also give the limit $q\\to 1-0$ of our asymptotic formula.
Asymptotic representation theorems for poverty indices | Lo | Afrika ...
African Journals Online (AJOL)
Abstract. We set general conditions under which the general poverty index, which summarizes all the available indices, is asymptotically represented with some empirical processes. This representation theorem offers a general key, in most directions, for the asymptotic of the bulk of poverty indices and issues in poverty ...
Some asymptotic properties of functions holomorphic in tubular domains
International Nuclear Information System (INIS)
Zavialov, B.I.
1988-10-01
For the function holomorphic in curved tubular domain the connection between asymptotic behaviour of real part of its boundary value at a given point of base manifold and asymptotic behaviour of the whole function from the inside of this domain is studied. (author). 3 refs
Asymptotic time dependent neutron transport in multidimensional systems
International Nuclear Information System (INIS)
Nagy, M.E.; Sawan, M.E.; Wassef, W.A.; El-Gueraly, L.A.
1983-01-01
A model which predicts the asymptotic time behavior of the neutron distribution in multi-dimensional systems is presented. The model is based on the kernel factorization method used for stationary neutron transport in a rectangular parallelepiped. The accuracy of diffusion theory in predicting the asymptotic time dependence is assessed. The use of neutron pulse experiments for predicting the diffusion parameters is also investigated
Inverted hierarchy and asymptotic freedom in grand unified supersymmetric theories
International Nuclear Information System (INIS)
Aratyn, H.
1983-01-01
The interrelation between an inverted hierarchy mechanism and asymptotic freedom in supersymmetric theories is analyzed in two models for which we performed a detailed analysis of the effective potentials and effective couplings. We find it difficult to accommodate an inverted hierarchy together with asymptotic freedom for the matter-Yukawa couplings. (orig.)
Szegö Kernels and Asymptotic Expansions for Legendre Polynomials
Directory of Open Access Journals (Sweden)
Roberto Paoletti
2017-01-01
Full Text Available We present a geometric approach to the asymptotics of the Legendre polynomials Pk,n+1, based on the Szegö kernel of the Fermat quadric hypersurface, leading to complete asymptotic expansions holding on expanding subintervals of [-1,1].
Asymptotic behaviour of a non-commutative rational series with a nonnegative linear representation
Directory of Open Access Journals (Sweden)
Philippe Dumas
2007-01-01
Full Text Available We analyse the asymptotic behaviour in the mean of a non-commutative rational series, which originates from differential cryptanalysis, using tools from probability theory, and from analytic number theory. We derive a Fourier representation of a first-order summation function obtained by interpreting this rational series as a non-classical rational sequence via the octal numeration system. The method is applicable to a wide class of sequences rational with respect to a numeration system essentially under the condition that they admit a linear representation with nonnegative coefficients.
Asymptotic equivalence of neutron diffusion and transport in time-independent reactor systems
International Nuclear Information System (INIS)
Borysiewicz, M.; Mika, J.; Spiga, G.
1982-01-01
Presented in this paper is the asymptotic analysis of the time-independent neutron transport equation in the second-order variational formulation. The small parameter introduced into the equation is an estimate of the ratio of absorption and leakage to scattering in the system considered. When the ratio tends to zero, the weak solution to the transport problem tends to the weak solution of the diffusion problem, including properly defined boundary conditions. A formula for the diffusion coefficient different from that based on averaging the transport mean-free-path is derived
International Nuclear Information System (INIS)
Helton, J.C.; Brown, J.B.; Iman, R.L.
1981-02-01
The Environmental Transport Model is a compartmental model developed to represent the surface movement of radionuclides. The purpose of the present study is to investigate the asymptotic behavior of the model and to acquire insight with respect to such behavior and the variables which influence it. For four variations of a hypothetical river receiving a radionuclide discharge, the following properties are considered: predicted asymptotic values for environmental radionuclide concentrations and time required for environmental radionuclide concentrations to reach 90% of their predicted asymptotic values. Independent variables of two types are used to define each variation of the river: variables which define physical properties of the river system (e.g., soil depth, river discharge and sediment resuspension) and variables which summarize radionuclide properties (i.e., distribution coefficients). Sensitivity analysis techniques based on stepwise regression are used to determine the dominant variables influencing the behavior of the model. This work constitutes part of a project at Sandia National Laboratories funded by the Nuclear Regulatory Commission to develop a methodology to assess the risk associated with geologic disposal of radioactive waste
Asymptotic behavior and Hamiltonian analysis of anti-de Sitter gravity coupled to scalar fields
International Nuclear Information System (INIS)
Henneaux, Marc; Martinez, Cristian; Troncoso, Ricardo; Zanelli, Jorge
2007-01-01
We examine anti-de Sitter gravity minimally coupled to a self-interacting scalar field in D>=4 dimensions when the mass of the scalar field is in the range m * 2 = 2 * 2 +l -2 . Here, l is the AdS radius, and m * 2 is the Breitenlohner-Freedman mass. We show that even though the scalar field generically has a slow fall-off at infinity which back reacts on the metric so as to modify its standard asymptotic behavior, one can still formulate asymptotic conditions (i) that are anti-de Sitter invariant; and (ii) that allows the construction of well-defined and finite Hamiltonian generators for all elements of the anti-de Sitter algebra. This requires imposing a functional relationship on the coefficients a, b that control the two independent terms in the asymptotic expansion of the scalar field. The anti-de Sitter charges are found to involve a scalar field contribution. Subtleties associated with the self-interactions of the scalar field as well as its gravitational back reaction, not discussed in previous treatments, are explicitly analyzed. In particular, it is shown that the fields develop extra logarithmic branches for specific values of the scalar field mass (in addition to the known logarithmic branch at the B-F bound)
On asymptotic continuity of functions of quantum states
International Nuclear Information System (INIS)
Synak-Radtke, Barbara; Horodecki, Michal
2006-01-01
A useful kind of continuity of quantum states functions in asymptotic regime is so-called asymptotic continuity. In this letter, we provide general tools for checking if a function possesses this property. First we prove equivalence of asymptotic continuity with so-called robustness under admixture. This allows us to show that relative entropy distance from a convex set including a maximally mixed state is asymptotically continuous. Subsequently, we consider arrowing-a way of building a new function out of a given one. The procedure originates from constructions of intrinsic information and entanglement of formation. We show that arrowing preserves asymptotic continuity for a class of functions (so-called subextensive ones). The result is illustrated by means of several examples. (letter to the editor)
Asymptotics of eigenvalues and eigenvectors of Toeplitz matrices
Böttcher, A.; Bogoya, J. M.; Grudsky, S. M.; Maximenko, E. A.
2017-11-01
Analysis of the asymptotic behaviour of the spectral characteristics of Toeplitz matrices as the dimension of the matrix tends to infinity has a history of over 100 years. For instance, quite a number of versions of Szegő's theorem on the asymptotic behaviour of eigenvalues and of the so-called strong Szegő theorem on the asymptotic behaviour of the determinants of Toeplitz matrices are known. Starting in the 1950s, the asymptotics of the maximum and minimum eigenvalues were actively investigated. However, investigation of the individual asymptotics of all the eigenvalues and eigenvectors of Toeplitz matrices started only quite recently: the first papers on this subject were published in 2009-2010. A survey of this new field is presented here. Bibliography: 55 titles.
Directory of Open Access Journals (Sweden)
R. Kenna
2014-09-01
Full Text Available We analyze the resistance between two nodes in a cobweb network of resistors. Based on an exact expression, we derive the asymptotic expansions for the resistance between the center node and a node on the boundary of the M x N cobweb network with resistors r and s in the two spatial directions. All coefficients in this expansion are expressed through analytical functions.
Asymptotic behavior of local dipolar fields in thin films
Energy Technology Data Exchange (ETDEWEB)
Bowden, G.J., E-mail: gjb@phys.soton.ac.uk [School of Physics and Astronomy, University of Southampton, SO17 1BJ (United Kingdom); Stenning, G.B.G., E-mail: Gerrit.vanderlaan@diamond.ac.uk [Magnetic Spectroscopy Group, Diamond Light Source, Didcot OX11 0DE (United Kingdom); Laan, G. van der, E-mail: gavin.stenning@stfc.ac.uk [ISIS Neutron and Muon Source, Rutherford Appleton Laboratory, Didcot OX11 0QX (United Kingdom)
2016-10-15
A simple method, based on layer by layer direct summation, is used to determine the local dipolar fields in uniformly magnetized thin films. The results show that the dipolar constants converge ~1/m where the number of spins in a square film is given by (2m+1){sup 2}. Dipolar field results for sc, bcc, fcc, and hexagonal lattices are presented and discussed. The results can be used to calculate local dipolar fields in films with either ferromagnetic, antiferromagnetic, spiral, exponential decay behavior, provided the magnetic order only changes normal to the film. Differences between the atomistic (local fields) and macroscopic fields (Maxwellian) are also examined. For the latter, the macro B-field inside the film is uniform and falls to zero sharply outside, in accord with Maxwell boundary conditions. In contrast, the local field for the atomistic point dipole model is highly non-linear inside and falls to zero at about three lattice spacing outside the film. Finally, it is argued that the continuum field B (used by the micromagnetic community) and the local field B{sub loc}(r) (used by the FMR community) will lead to differing values for the overall demagnetization energy. - Highlights: • Point-dipolar fields in uniformly magnetized thin films are characterized by just three numbers. • Maxwell's boundary condition is partially violated in the point-dipole approximation. • Asymptotic values of point dipolar fields in circular monolayers scale as π/r.
Transport Coefficients of Fluids
Eu, Byung Chan
2006-01-01
Until recently the formal statistical mechanical approach offered no practicable method for computing the transport coefficients of liquids, and so most practitioners had to resort to empirical fitting formulas. This has now changed, as demonstrated in this innovative monograph. The author presents and applies new methods based on statistical mechanics for calculating the transport coefficients of simple and complex liquids over wide ranges of density and temperature. These molecular theories enable the transport coefficients to be calculated in terms of equilibrium thermodynamic properties, and the results are shown to account satisfactorily for experimental observations, including even the non-Newtonian behavior of fluids far from equilibrium.
Gontscharuk, Veronika; Landwehr, Sandra; Finner, Helmut
2015-01-01
The higher criticism (HC) statistic, which can be seen as a normalized version of the famous Kolmogorov-Smirnov statistic, has a long history, dating back to the mid seventies. Originally, HC statistics were used in connection with goodness of fit (GOF) tests but they recently gained some attention in the context of testing the global null hypothesis in high dimensional data. The continuing interest for HC seems to be inspired by a series of nice asymptotic properties related to this statistic. For example, unlike Kolmogorov-Smirnov tests, GOF tests based on the HC statistic are known to be asymptotically sensitive in the moderate tails, hence it is favorably applied for detecting the presence of signals in sparse mixture models. However, some questions around the asymptotic behavior of the HC statistic are still open. We focus on two of them, namely, why a specific intermediate range is crucial for GOF tests based on the HC statistic and why the convergence of the HC distribution to the limiting one is extremely slow. Moreover, the inconsistency in the asymptotic and finite behavior of the HC statistic prompts us to provide a new HC test that has better finite properties than the original HC test while showing the same asymptotics. This test is motivated by the asymptotic behavior of the so-called local levels related to the original HC test. By means of numerical calculations and simulations we show that the new HC test is typically more powerful than the original HC test in normal mixture models. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Variation in aerodynamic coefficients with altitude
Directory of Open Access Journals (Sweden)
Faiza Shahid
Full Text Available Precise aerodynamics performance prediction plays key role for a flying vehicle to get its mission completed within desired accuracy. Aerodynamic coefficients for same Mach number can be different at different altitude due to difference in Reynolds number. Prediction of these aerodynamics coefficients can be made through experiments, analytical solution or Computational Fluid Dynamics (CFD. Advancements in computational power have generated the concept of using CFD as a virtual Wind Tunnel (WT, hence aerodynamic performance prediction in present study is based upon CFD (numerical test rig. Simulations at different altitudes for a range of Mach numbers with zero angle of attack are performed to predict axial force coefficient behavior with altitude (Reynolds number. Similar simulations for a fixed Mach number â3â and a range of angle of attacks are also carried out to envisage the variation in normal force and pitching moment coefficients with altitude (Reynolds number. Results clearly depict that the axial force coefficient is a function of altitude (Reynolds number and increase as altitude increases, especially for subsonic region. Variation in axial force coefficient with altitude (Reynolds number slightly increases for larger values of angle of attacks. Normal force and pitching moment coefficients do not depend on altitude (Reynolds number at smaller values of angle of attacks but show slight decrease as altitude increases. Present study suggests that variation of normal force and pitching moment coefficients with altitude can be neglected but the variation of axial force coefficient with altitude should be considered for vehicle fly in dense atmosphere. It is recommended to continue this study to more complex configurations for various Mach numbers with side slip and real gas effects. Keywords: Mach number, Reynolds number, Blunt body, Altitude effect, Angle of attacks
Variation in aerodynamic coefficients with altitude
Shahid, Faiza; Hussain, Mukkarum; Baig, Mirza Mehmood; Haq, Ihtram ul
Precise aerodynamics performance prediction plays key role for a flying vehicle to get its mission completed within desired accuracy. Aerodynamic coefficients for same Mach number can be different at different altitude due to difference in Reynolds number. Prediction of these aerodynamics coefficients can be made through experiments, analytical solution or Computational Fluid Dynamics (CFD). Advancements in computational power have generated the concept of using CFD as a virtual Wind Tunnel (WT), hence aerodynamic performance prediction in present study is based upon CFD (numerical test rig). Simulations at different altitudes for a range of Mach numbers with zero angle of attack are performed to predict axial force coefficient behavior with altitude (Reynolds number). Similar simulations for a fixed Mach number '3' and a range of angle of attacks are also carried out to envisage the variation in normal force and pitching moment coefficients with altitude (Reynolds number). Results clearly depict that the axial force coefficient is a function of altitude (Reynolds number) and increase as altitude increases, especially for subsonic region. Variation in axial force coefficient with altitude (Reynolds number) slightly increases for larger values of angle of attacks. Normal force and pitching moment coefficients do not depend on altitude (Reynolds number) at smaller values of angle of attacks but show slight decrease as altitude increases. Present study suggests that variation of normal force and pitching moment coefficients with altitude can be neglected but the variation of axial force coefficient with altitude should be considered for vehicle fly in dense atmosphere. It is recommended to continue this study to more complex configurations for various Mach numbers with side slip and real gas effects.
Partial differential equations II elements of the modern theory equations with constant coefficients
Shubin, M
1994-01-01
This book, the first printing of which was published as Volume 31 of the Encyclopaedia of Mathematical Sciences, contains a survey of the modern theory of general linear partial differential equations and a detailed review of equations with constant coefficients. Readers will be interested in an introduction to microlocal analysis and its applications including singular integral operators, pseudodifferential operators, Fourier integral operators and wavefronts, a survey of the most important results about the mixed problem for hyperbolic equations, a review of asymptotic methods including short wave asymptotics, the Maslov canonical operator and spectral asymptotics, a detailed description of the applications of distribution theory to partial differential equations with constant coefficients including numerous interesting special topics.
Asymptotics of quantum weighted Hurwitz numbers
Harnad, J.; Ortmann, Janosch
2018-06-01
This work concerns both the semiclassical and zero temperature asymptotics of quantum weighted double Hurwitz numbers. The partition function for quantum weighted double Hurwitz numbers can be interpreted in terms of the energy distribution of a quantum Bose gas with vanishing fugacity. We compute the leading semiclassical term of the partition function for three versions of the quantum weighted Hurwitz numbers, as well as lower order semiclassical corrections. The classical limit is shown to reproduce the simple single and double Hurwitz numbers studied by Okounkov and Pandharipande (2000 Math. Res. Lett. 7 447–53, 2000 Lett. Math. Phys. 53 59–74). The KP-Toda τ-function that serves as generating function for the quantum Hurwitz numbers is shown to have the τ-function of Okounkov and Pandharipande (2000 Math. Res. Lett. 7 447–53, 2000 Lett. Math. Phys. 53 59–74) as its leading term in the classical limit, and, with suitable scaling, the same holds for the partition function, the weights and expectations of Hurwitz numbers. We also compute the zero temperature limit of the partition function and quantum weighted Hurwitz numbers. The KP or Toda τ-function serving as generating function for the quantum Hurwitz numbers are shown to give the one for Belyi curves in the zero temperature limit and, with suitable scaling, the same holds true for the partition function, the weights and the expectations of Hurwitz numbers.
ASYMPTOTIC STRUCTURE OF POYNTING-DOMINATED JETS
International Nuclear Information System (INIS)
Lyubarsky, Yuri
2009-01-01
In relativistic, Poynting-dominated outflows, acceleration and collimation are intimately connected. An important point is that the Lorentz force is nearly compensated by the electric force; therefore the acceleration zone spans a large range of scales. We derived the asymptotic equations describing relativistic, axisymmetric magnetohydrodynamic flows far beyond the light cylinder. These equations do not contain either intrinsic small scales (like the light cylinder radius) or terms that nearly cancel each other (like the electric and magnetic forces); therefore they could be easily solved numerically. They also suit well for qualitative analysis of the flow and, in many cases, they could even be solved analytically or semianalytically. We show that there are generally two collimation regimes. In the first regime, the residual of the hoop stress and the electric force is counterbalanced by the pressure of the poloidal magnetic field so that, at any distance from the source, the structure of the flow is the same as the structure of an appropriate cylindrical equilibrium configuration. In the second regime, the pressure of the poloidal magnetic field is negligibly small so that the flow could be conceived as composed from coaxial magnetic loops. In the two collimation regimes, the flow is accelerated in different ways. We study in detail the structure of jets confined by the external pressure with a power-law profile. In particular, we obtained simple scalings for the extent of the acceleration zone, for the terminal Lorentz factor, and for the collimation angle.
Asymptotic laws for random knot diagrams
Chapman, Harrison
2017-06-01
We study random knotting by considering knot and link diagrams as decorated, (rooted) topological maps on spheres and pulling them uniformly from among sets of a given number of vertices n, as first established in recent work with Cantarella and Mastin. The knot diagram model is an exciting new model which captures both the random geometry of space curve models of knotting as well as the ease of computing invariants from diagrams. We prove that unknot diagrams are asymptotically exponentially rare, an analogue of Sumners and Whittington’s landmark result for self-avoiding polygons. Our proof uses the same key idea: we first show that knot diagrams obey a pattern theorem, which describes their fractal structure. We examine how quickly this behavior occurs in practice. As a consequence, almost all diagrams are asymmetric, simplifying sampling from this model. We conclude with experimental data on knotting in this model. This model of random knotting is similar to those studied by Diao et al, and Dunfield et al.
Asymptotic estimation of reactor fueling optimal strategy
International Nuclear Information System (INIS)
Simonov, V.D.
1985-01-01
The problem of improving the technical-economic factors of operating. and designed nuclear power plant blocks by developino. internal fuel cycle strategy (reactor fueling regime optimization), taking into account energy system structural peculiarities altogether, is considered. It is shown, that in search of asymptotic solutions of reactor fueling planning tasks the model of fuel energy potential (FEP) is the most ssuitable and effective. FEP represents energy which may be produced from the fuel in a reactor with real dimensions and power, but with hypothetical fresh fuel supply, regime, providing smilar burnup of all the fuel, passing through the reactor, and continuous overloading of infinitely small fuel portion under fule power, and infinitely rapid mixing of fuel in the reactor core volume. Reactor fuel run with such a standard fuel cycle may serve as FEP quantitative measure. Assessment results of optimal WWER-440 reactor fresh fuel supply periodicity are given as an example. The conclusion is drawn that with fuel enrichment x=3.3% the run which is 300 days, is economically justified, taking into account that the cost of one energy unit production is > 3 cop/KW/h
Wall roughness induces asymptotic ultimate turbulence
Zhu, Xiaojue; Verschoof, Ruben A.; Bakhuis, Dennis; Huisman, Sander G.; Verzicco, Roberto; Sun, Chao; Lohse, Detlef
2018-04-01
Turbulence governs the transport of heat, mass and momentum on multiple scales. In real-world applications, wall-bounded turbulence typically involves surfaces that are rough; however, characterizing and understanding the effects of wall roughness on turbulence remains a challenge. Here, by combining extensive experiments and numerical simulations, we examine the paradigmatic Taylor-Couette system, which describes the closed flow between two independently rotating coaxial cylinders. We show how wall roughness greatly enhances the overall transport properties and the corresponding scaling exponents associated with wall-bounded turbulence. We reveal that if only one of the walls is rough, the bulk velocity is slaved to the rough side, due to the much stronger coupling to that wall by the detaching flow structures. If both walls are rough, the viscosity dependence is eliminated, giving rise to asymptotic ultimate turbulence—the upper limit of transport—the existence of which was predicted more than 50 years ago. In this limit, the scaling laws can be extrapolated to arbitrarily large Reynolds numbers.
Qualitative and Asymptotic Theory of Detonations
Faria, Luiz
2014-11-09
Shock waves in reactive media possess very rich dynamics: from formation of cells in multiple dimensions to oscillating shock fronts in one-dimension. Because of the extreme complexity of the equations of combustion theory, most of the current understanding of unstable detonation waves relies on extensive numerical simulations of the reactive compressible Euler/Navier-Stokes equations. Attempts at a simplified theory have been made in the past, most of which are very successful in describing steady detonation waves. In this work we focus on obtaining simplified theories capable of capturing not only the steady, but also the unsteady behavior of detonation waves. The first part of this thesis is focused on qualitative theories of detonation, where ad hoc models are proposed and analyzed. We show that equations as simple as a forced Burgers equation can capture most of the complex phenomena observed in detonations. In the second part of this thesis we focus on rational theories, and derive a weakly nonlinear model of multi-dimensional detonations. We also show, by analysis and numerical simulations, that the asymptotic equations provide good quantitative predictions.
Asymptotics of Heavy-Meson Form Factors
Grozin, A.G.; Grozin, Andrey G.; Neubert, Matthias
1997-01-01
Using methods developed for hard exclusive QCD processes, we calculate the asymptotic behaviour of heavy-meson form factors at large recoil. It is determined by the leading- and subleading-twist meson wave functions. For $1\\ll |v\\cdot v'|\\ll m_Q/\\Lambda$, the form factors are dominated by the Isgur--Wise function, which is determined by the interference between the wave functions of leading and subleading twist. At $|v\\cdot v'|\\gg m_Q/\\Lambda$, they are dominated by two functions arising at order $1/m_Q$ in the heavy-quark expansion, which are determined by the leading-twist wave function alone. The sum of these contributions describes the form factors in the whole region $|v\\cdot v'|\\gg 1$. As a consequence, there is an exact zero in the form factor for the scattering of longitudinally polarized $B^*$ mesons at some value $v\\cdot v'\\sim m_b/\\Lambda$, and an approximate zero in the form factor of $B$ mesons in the timelike region ($v\\cdot v'\\sim -m_b/\\Lambda$). We obtain the evolution equations and sum rules ...
Asymptotic scalings of developing curved pipe flow
Ault, Jesse; Chen, Kevin; Stone, Howard
2015-11-01
Asymptotic velocity and pressure scalings are identified for the developing curved pipe flow problem in the limit of small pipe curvature and high Reynolds numbers. The continuity and Navier-Stokes equations in toroidal coordinates are linearized about Dean's analytical curved pipe flow solution (Dean 1927). Applying appropriate scaling arguments to the perturbation pressure and velocity components and taking the limits of small curvature and large Reynolds number yields a set of governing equations and boundary conditions for the perturbations, independent of any Reynolds number and pipe curvature dependence. Direct numerical simulations are used to confirm these scaling arguments. Fully developed straight pipe flow is simulated entering a curved pipe section for a range of Reynolds numbers and pipe-to-curvature radius ratios. The maximum values of the axial and secondary velocity perturbation components along with the maximum value of the pressure perturbation are plotted along the curved pipe section. The results collapse when the scaling arguments are applied. The numerically solved decay of the velocity perturbation is also used to determine the entrance/development lengths for the curved pipe flows, which are shown to scale linearly with the Reynolds number.
Application of Normal Family to the Spread Inequality and the Paley ...
African Journals Online (AJOL)
In this paper we derive a Paley type inequality for subharmonic functions of order λ,0 < λ≤½ and describe the asymptotic behaviour of the extremal functions near Pòlya peaks. We also give an alternative proof for the spread inequality using a non-asymptotic method via - a normal family of δ -subharmonic functions.
Asymptotic Solution of the Theory of Shells Boundary Value Problem
Directory of Open Access Journals (Sweden)
I. V. Andrianov
2007-01-01
Full Text Available This paper provides a state-of-the-art review of asymptotic methods in the theory of plates and shells. Asymptotic methods of solving problems related to theory of plates and shells have been developed by many authors. The main features of our paper are: (i it is devoted to the fundamental principles of asymptotic approaches, and (ii it deals with both traditional approaches, and less widely used, new approaches. The authors have paid special attention to examples and discussion of results rather than to burying the ideas in formalism, notation, and technical details.
Global asymptotic stability of density dependent integral population projection models.
Rebarber, Richard; Tenhumberg, Brigitte; Townley, Stuart
2012-02-01
Many stage-structured density dependent populations with a continuum of stages can be naturally modeled using nonlinear integral projection models. In this paper, we study a trichotomy of global stability result for a class of density dependent systems which include a Platte thistle model. Specifically, we identify those systems parameters for which zero is globally asymptotically stable, parameters for which there is a positive asymptotically stable equilibrium, and parameters for which there is no asymptotically stable equilibrium. Copyright © 2011 Elsevier Inc. All rights reserved.
Asymptotically double lacunry equivalent sequences defined by Orlicz functions
Directory of Open Access Journals (Sweden)
Ayhan Esi
2014-04-01
Full Text Available This paper presents the following definition which is natural combition of the definition for asymptotically equivalent and Orlicz function. The two nonnegative double sequences x=(x_{k,l} and y=(y_{k,l} are said to be M-asymptotically double equivalent to multiple L provided that for every ε>0, P-lim_{k,l}M(((|((x_{k,l}/(y_{k,l}-L|/ρ=0, for some ρ>0, (denoted by x∽y and simply M-asymptotically double equivalent if L=1. Also we give some new concepts related to this definition and some inclusion theorems.
Asymptotic failure rate of a continuously monitored system
International Nuclear Information System (INIS)
Grall, A.; Dieulle, L.; Berenguer, C.; Roussignol, M.
2006-01-01
This paper deals with a perfectly continuously monitored system which gradually and stochastically deteriorates. The system is renewed by a delayed maintenance operation, which is triggered when the measured deterioration level exceeds an alarm threshold. A mathematical model is developed to study the asymptotic behavior of the reliability function. A procedure is proposed which allows us to identify the asymptotic failure rate of the maintained system. Numerical experiments illustrate the efficiency of the proposed procedure and emphasize the relevance of the asymptotic failure rate as an interesting indicator for the evaluation of the control-limit preventive replacement policy
Asymptotic failure rate of a continuously monitored system
Energy Technology Data Exchange (ETDEWEB)
Grall, A. [Institut des Sciences et Technologies de l' Information de Troyes (CNRS-FRE 2732), Equipe de Modelisation et de Surete des Systemes, Universite de Technologie de Troyes, 12 rue Marie Curie, BP 2060, 10010 Troyes Cedex (France)]. E-mail: antoine.grall@utt.fr; Dieulle, L. [Institut des Sciences et Technologies de l' Information de Troyes (CNRS-FRE 2732), Equipe de Modelisation et de Surete des Systemes, Universite de Technologie de Troyes, 12 rue Marie Curie, BP 2060, 10010 Troyes Cedex (France)]. E-mail: laurence.dieulle@utt.fr; Berenguer, C. [Institut des Sciences et Technologies de l' Information de Troyes (CNRS-FRE 2732), Equipe de Modelisation et de Surete des Systemes, Universite de Technologie de Troyes, 12 rue Marie Curie, BP 2060, 10010 Troyes Cedex (France)]. E-mail: christophe.berenguer@utt.fr; Roussignol, M. [Laboratoire d' Analyse et de Mathematiques Appliquees, Universite de Marne la Vallee, 5 bd Descartes, Champs sur Marne, 77454 Marne la Vallee, Cedex 2 (France)]. E-mail: michel.roussignol@univ-mlv.fr
2006-02-01
This paper deals with a perfectly continuously monitored system which gradually and stochastically deteriorates. The system is renewed by a delayed maintenance operation, which is triggered when the measured deterioration level exceeds an alarm threshold. A mathematical model is developed to study the asymptotic behavior of the reliability function. A procedure is proposed which allows us to identify the asymptotic failure rate of the maintained system. Numerical experiments illustrate the efficiency of the proposed procedure and emphasize the relevance of the asymptotic failure rate as an interesting indicator for the evaluation of the control-limit preventive replacement policy.
Asymptotics for the Kummer function of Bose plasmas
International Nuclear Information System (INIS)
Kowalenko, V.; Frankel, N.E.
1993-01-01
The asymptotic expansions for the Kummer function obtained in the study of the linear response of magnetised Bose plasmas at T = 0 K are presented for large and small values of its parameter, thereby displaying the function's asymptotic non-uniformity. The large parameter expansion plays a determining role in the behaviour of these Bose systems in the limit that the external magnetic field B →0. This particular expansion is generalised herein and its validity tested by determining the asymptotic expansion for the Hurwitz zeta function. 18 refs., 1 tab., 2 figs
A Fast, Simple, and Stable Chebyshev--Legendre Transform Using an Asymptotic Formula
Hale, Nicholas
2014-02-06
A fast, simple, and numerically stable transform for converting between Legendre and Chebyshev coefficients of a degree N polynomial in O(N(log N)2/ log log N) operations is derived. The fundamental idea of the algorithm is to rewrite a well-known asymptotic formula for Legendre polynomials of large degree as a weighted linear combination of Chebyshev polynomials, which can then be evaluated by using the discrete cosine transform. Numerical results are provided to demonstrate the efficiency and numerical stability. Since the algorithm evaluates a Legendre expansion at an N +1 Chebyshev grid as an intermediate step, it also provides a fast transform between Legendre coefficients and values on a Chebyshev grid. © 2014 Society for Industrial and Applied Mathematics.
Pade approximants for entire functions with regularly decreasing Taylor coefficients
International Nuclear Information System (INIS)
Rusak, V N; Starovoitov, A P
2002-01-01
For a class of entire functions the asymptotic behaviour of the Hadamard determinants D n,m as 0≤m≤m(n)→∞ and n→∞ is described. This enables one to study the behaviour of parabolic sequences from Pade and Chebyshev tables for many individual entire functions. The central result of the paper is as follows: for some sequences {(n,m(n))} in certain classes of entire functions (with regular Taylor coefficients) the Pade approximants {π n,m(n) }, which provide the locally best possible rational approximations, converge to the given function uniformly on the compact set D={z:|z|≤1} with asymptotically best rate
New results for virial coefficients of hard spheres in D dimensions
Indian Academy of Sciences (India)
We present new results for the virial coefficients Bk for k ≤ 10 for hard spheres in dimensions D ... for the hard sphere gas of particles of diameter σ in D dimensions defined by the two-body potential. U(r) = ..... [22] A J Guttmann, Asymptotic analysis of power-series expansions, in Phase transitions and critical phenomena ...
Recent results on the 3-loop heavy flavor Wilson coefficients in deep-inelastic scattering
Energy Technology Data Exchange (ETDEWEB)
Bluemlein, J.; Freitas A. de; Raab, C.; Wissbrock, F. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Ablinger, J.; Hasselhuhn, A.; Round, M.; Schneider, C. [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation; Manteuffel, A. von [Mainz Univ. (Germany). PRISMA Cluster of Excellence; Mainz Univ. (Germany). Inst. fuer Physik
2013-07-15
We report on recent progress in the calculation of the 3-loop massive Wilson coefficients in deep-inelastic scattering at general values of N for neutral and charged current reactions in the asymptotic region Q{sup 2}>>m{sup 2}.
Time-varying coefficient estimation in SURE models. Application to portfolio management
DEFF Research Database (Denmark)
Casas, Isabel; Ferreira, Eva; Orbe, Susan
This paper provides a detailed analysis of the asymptotic properties of a kernel estimator for a Seemingly Unrelated Regression Equations model with time-varying coefficients (tv-SURE) under very general conditions. Theoretical results together with a simulation study differentiates the cases...
International Nuclear Information System (INIS)
Telyakovskii, S A
2002-01-01
The functions under consideration are those satisfying the condition Δa i =Δb i =0 for all i≠n j , where {n j } is a lacunary sequence. An asymptotic estimate of the rate of decrease of the modulus of continuity in the L-metric of such functions in terms of their Fourier coefficients is obtained
Obtaining the general forms of the effective coefficients of laminate magneto-electro - elastic
International Nuclear Information System (INIS)
Cabañas, J. H.; Otero, A.; Castillero, B.; Rodríguez, R.
2008-01-01
In this work using the asymptotic homogenization method obtained general expressions for the calculation of the effective characteristics of magnetoelectro-elastic laminates with layers of any symmetry. You will reach an array of auxiliary functions for determining the effective coefficients for a serial connection and displays a result similar to the case of parallel connection.
Asymptotic theory of circular polarization memory.
Dark, Julia P; Kim, Arnold D
2017-09-01
We establish a quantitative theory of circular polarization memory, which is the unexpected persistence of the incident circular polarization state in a strongly scattering medium. Using an asymptotic analysis of the three-dimensional vector radiative transfer equation (VRTE) in the limit of strong scattering, we find that circular polarization memory must occur in a boundary layer near the portion of the boundary on which polarized light is incident. The boundary layer solution satisfies a one-dimensional conservative scattering VRTE. Through a spectral analysis of this boundary layer problem, we introduce the dominant mode, which is the slowest-decaying mode in the boundary layer. To observe circular polarization memory for a particular set of optical parameters, we find that this dominant mode must pass three tests: (1) this dominant mode is given by the largest, discrete eigenvalue of a reduced problem that corresponds to Fourier mode k=0 in the azimuthal angle, and depends only on Stokes parameters U and V; (2) the polarization state of this dominant mode is largely circular polarized so that |V|≫|U|; and (3) the circular polarization of this dominant mode is maintained for all directions so that V is sign-definite. By applying these three tests to numerical calculations for monodisperse distributions of Mie scatterers, we determine the values of the size and relative refractive index when circular polarization memory occurs. In addition, we identify a reduced, scalar-like problem that provides an accurate approximation for the dominant mode when circular polarization memory occurs.
Stationarity-conservation laws for fractional differential equations with variable coefficients
Energy Technology Data Exchange (ETDEWEB)
Klimek, Malgorzata [Institute of Mathematics and Computer Science, Technical University of Czestochowa, Czestochowa (Poland)
2002-08-09
In this paper, we study linear fractional differential equations with variable coefficients. It is shown that, by assuming some conditions for the coefficients, the stationarity-conservation laws can be derived. The area where these are valid is restricted by the asymptotic properties of solutions of the respective equation. Applications of the proposed procedure include the fractional Fokker-Planck equation in (1+1)- and (d+1)-dimensional space and the fractional Klein-Kramers equation. (author)
Stationarity-conservation laws for fractional differential equations with variable coefficients
International Nuclear Information System (INIS)
Klimek, Malgorzata
2002-01-01
In this paper, we study linear fractional differential equations with variable coefficients. It is shown that, by assuming some conditions for the coefficients, the stationarity-conservation laws can be derived. The area where these are valid is restricted by the asymptotic properties of solutions of the respective equation. Applications of the proposed procedure include the fractional Fokker-Planck equation in (1+1)- and (d+1)-dimensional space and the fractional Klein-Kramers equation. (author)
Asymptotic Co- and Post-seismic displacements in a homogeneous Maxwell sphere
Tang, He; Sun, Wenke
2018-05-01
The deformations of the Earth caused by internal and external forces are usually expressed through Green's functions or the superposition of normal modes, i.e. via numerical methods, which are applicable for computing both co- and post-seismic deformations. It is difficult to express these deformations in an analytical form, even for a uniform viscoelastic sphere. In this study, we present a set of asymptotic solutions for computing co- and post-seismic displacements; these solutions can be further applied to solving co- and post-seismic geoid, gravity, and strain changes. Expressions are derived for a uniform Maxwell Earth by combining the reciprocity theorem, which links earthquake, tidal, shear and loading deformations, with the asymptotic solutions of these three external forces (tidal, shear and loading) and analytical inverse Laplace transformation formulae. Since the asymptotic solutions are given in a purely analytical form without series summations or extra convergence skills, they can be practically applied in an efficient way, especially when computing post-seismic deformations and glacial isotactic adjustments of the Earth over long timescales.
AdS-like spectrum of the asymptotically Goedel space-times
International Nuclear Information System (INIS)
Konoplya, R. A.; Zhidenko, A.
2011-01-01
A black hole immersed in a rotating universe, described by the Gimon-Hashimoto solution, is tested on stability against scalar field perturbations. Unlike the previous studies on perturbations of this solution, which dealt only with the limit of slow universe rotation j, we managed to separate variables in the perturbation equation for the general case of arbitrary rotation. This leads to qualitatively different dynamics of perturbations, because the exact effective potential does not allow for Schwarzschild-like asymptotic of the wave function in the form of purely outgoing waves. The Dirichlet boundary conditions are allowed instead, which result in a totally different spectrum of asymptotically Goedel black holes: the spectrum of quasinormal frequencies is similar to the one of asymptotically anti-de Sitter black holes. At large and intermediate overtones N, the spectrum is equidistant in N. In the limit of small black holes, quasinormal modes (QNMs) approach the normal modes of the empty Goedel space-time. There is no evidence of instability in the found frequencies, which supports the idea that the existence of closed timelike curves (CTCs) and the onset of instability correlate (if at all) not in a straightforward way.
The Semiparametric Normal Variance-Mean Mixture Model
DEFF Research Database (Denmark)
Korsholm, Lars
1997-01-01
We discuss the normal vairance-mean mixture model from a semi-parametric point of view, i.e. we let the mixing distribution belong to a non parametric family. The main results are consistency of the non parametric maximum likelihood estimat or in this case, and construction of an asymptotically...... normal and efficient estimator....
Carpenter, Donald A.
2008-01-01
Confusion exists among database textbooks as to the goal of normalization as well as to which normal form a designer should aspire. This article discusses such discrepancies with the intention of simplifying normalization for both teacher and student. This author's industry and classroom experiences indicate such simplification yields quicker…
Ogilvie, Karen; Olde Daalhuis, Adri B.
2015-11-01
By application of the theory for second-order linear differential equations with two turning points developed in [Olver F.W.J., Philos. Trans. Roy. Soc. London Ser. A 278 (1975), 137-174], uniform asymptotic approximations are obtained in the first part of this paper for the Lamé and Mathieu functions with a large real parameter. These approximations are expressed in terms of parabolic cylinder functions, and are uniformly valid in their respective real open intervals. In all cases explicit bounds are supplied for the error terms associated with the approximations. Approximations are also obtained for the large order behaviour for the respective eigenvalues. We restrict ourselves to a two term uniform approximation. Theoretically more terms in these approximations could be computed, but the coefficients would be very complicated. In the second part of this paper we use a simplified method to obtain uniform asymptotic expansions for these functions. The coefficients are just polynomials and satisfy simple recurrence relations. The price to pay is that these asymptotic expansions hold only in a shrinking interval as their respective parameters become large; this interval however encapsulates all the interesting oscillatory behaviour of the functions. This simplified method also gives many terms in asymptotic expansions for these eigenvalues, derived simultaneously with the coefficients in the function expansions. We provide rigorous realistic error bounds for the function expansions when truncated and order estimates for the error when the eigenvalue expansions are truncated. With this paper we confirm that many of the formal results in the literature are correct.
Directory of Open Access Journals (Sweden)
Jichul Ryu
2016-04-01
Full Text Available In this study, 52 asymptotic Curve Number (CN regression equations were developed for combinations of representative land covers and hydrologic soil groups. In addition, to overcome the limitations of the original Long-term Hydrologic Impact Assessment (L-THIA model when it is applied to larger watersheds, a watershed-scale L-THIA Asymptotic CN (ACN regression equation model (watershed-scale L-THIA ACN model was developed by integrating the asymptotic CN regressions and various modules for direct runoff/baseflow/channel routing. The watershed-scale L-THIA ACN model was applied to four watersheds in South Korea to evaluate the accuracy of its streamflow prediction. The coefficient of determination (R2 and Nash–Sutcliffe Efficiency (NSE values for observed versus simulated streamflows over intervals of eight days were greater than 0.6 for all four of the watersheds. The watershed-scale L-THIA ACN model, including the asymptotic CN regression equation method, can simulate long-term streamflow sufficiently well with the ten parameters that have been added for the characterization of streamflow.
On approach to double asymptotic scaling at low x
International Nuclear Information System (INIS)
Choudhury, D.K.
1994-10-01
We obtain the finite x correlations to the gluon structure function which exhibits double asymptotic scaling at low x. The technique used is the GLAP equation for gluon approximated at low x by a Taylor expansion. (author). 27 refs
Asymptotically anti-de Sitter spacetimes in topologically massive gravity
International Nuclear Information System (INIS)
Henneaux, Marc; Martinez, Cristian; Troncoso, Ricardo
2009-01-01
We consider asymptotically anti-de Sitter spacetimes in three-dimensional topologically massive gravity with a negative cosmological constant, for all values of the mass parameter μ (μ≠0). We provide consistent boundary conditions that accommodate the recent solutions considered in the literature, which may have a slower falloff than the one relevant for general relativity. These conditions are such that the asymptotic symmetry is in all cases the conformal group, in the sense that they are invariant under asymptotic conformal transformations and that the corresponding Virasoro generators are finite. It is found that, at the chiral point |μl|=1 (where l is the anti-de Sitter radius), allowing for logarithmic terms (absent for general relativity) in the asymptotic behavior of the metric makes both sets of Virasoro generators nonzero even though one of the central charges vanishes.
Confinement and asymptotic freedom seen with a golden eye
International Nuclear Information System (INIS)
Elokaby, A.
2009-01-01
The present short note is an attempt to reconcile the current conventional understanding of quarks confinement and asymptotic freedom with the results found by El Naschie using the exact renormalization equation of his quantum golden field theory.
Preheating in an asymptotically safe quantum field theory
DEFF Research Database (Denmark)
Svendsen, Ole; Moghaddam, Hossein Bazrafshan; Brandenberger, Robert
2016-01-01
. High Energy Phys. 01 (2016) 081]. These theories allow for an inflationary phase in the very early universe. Inflation ends with a period of reheating. Since the models contain many scalar fields which are intrinsically coupled to the inflaton there is the possibility of parametric resonance...... fluctuations induced by the parametrically amplified entropy modes do not exceed the upper observational bounds puts a lower bound on the number of fields which the model followed in [D. F. Litim and F. Sannino, Asymptotic safety guaranteed, J. High Energy Phys. 12 (2014) 178; D. F. Litim, M. Mojaza, and F......We consider reheating in a class of asymptotically safe quantum field theories recently studied in [D. F. Litim and F. Sannino, Asymptotic safety guaranteed, J. High Energy Phys. 12 (2014) 178; D. F. Litim, M. Mojaza, and F. Sannino, Vacuum stability of asymptotically safe gauge-Yukawa theories, J...
Pseudo-random number generator based on asymptotic deterministic randomness
Wang, Kai; Pei, Wenjiang; Xia, Haishan; Cheung, Yiu-ming
2008-06-01
A novel approach to generate the pseudorandom-bit sequence from the asymptotic deterministic randomness system is proposed in this Letter. We study the characteristic of multi-value correspondence of the asymptotic deterministic randomness constructed by the piecewise linear map and the noninvertible nonlinearity transform, and then give the discretized systems in the finite digitized state space. The statistic characteristics of the asymptotic deterministic randomness are investigated numerically, such as stationary probability density function and random-like behavior. Furthermore, we analyze the dynamics of the symbolic sequence. Both theoretical and experimental results show that the symbolic sequence of the asymptotic deterministic randomness possesses very good cryptographic properties, which improve the security of chaos based PRBGs and increase the resistance against entropy attacks and symbolic dynamics attacks.
Pseudo-random number generator based on asymptotic deterministic randomness
International Nuclear Information System (INIS)
Wang Kai; Pei Wenjiang; Xia Haishan; Cheung Yiuming
2008-01-01
A novel approach to generate the pseudorandom-bit sequence from the asymptotic deterministic randomness system is proposed in this Letter. We study the characteristic of multi-value correspondence of the asymptotic deterministic randomness constructed by the piecewise linear map and the noninvertible nonlinearity transform, and then give the discretized systems in the finite digitized state space. The statistic characteristics of the asymptotic deterministic randomness are investigated numerically, such as stationary probability density function and random-like behavior. Furthermore, we analyze the dynamics of the symbolic sequence. Both theoretical and experimental results show that the symbolic sequence of the asymptotic deterministic randomness possesses very good cryptographic properties, which improve the security of chaos based PRBGs and increase the resistance against entropy attacks and symbolic dynamics attacks
Asymptotically Almost Periodic Solutions of Evolution Equations in Banach Spaces
Ruess, W. M.; Phong, V. Q.
Tile linear abstract evolution equation (∗) u'( t) = Au( t) + ƒ( t), t ∈ R, is considered, where A: D( A) ⊂ E → E is the generator of a strongly continuous semigroup of operators in the Banach space E. Starting from analogs of Kadets' and Loomis' Theorems for vector valued almost periodic Functions, we show that if σ( A) ∩ iR is countable and ƒ: R → E is [asymptotically] almost periodic, then every bounded and uniformly continuous solution u to (∗) is [asymptotically] almost periodic, provided e-λ tu( t) has uniformly convergent means for all λ ∈ σ( A) ∩ iR. Related results on Eberlein-weakly asymptotically almost periodic, periodic, asymptotically periodic and C 0-solutions of (∗), as well as on the discrete case of solutions of difference equations are included.
Asymptotic behavior of quark masses induced by instantons
International Nuclear Information System (INIS)
Carneiro, C.E.I.; Frenkel, J.
1984-02-01
A simple argument which shows that the dynamical mass induced by interactions of massless quarks with pseudo-particle configurations, behaves like p -6 for asymptotically large quark momenta is presented. (Author) [pt
Asymptotically Safe Standard Model Extensions arXiv
Pelaggi, Giulio Maria; Salvio, Alberto; Sannino, Francesco; Smirnov, Juri; Strumia, Alessandro
We consider theories with a large number NF of charged fermions and compute the renormalisation group equations for the gauge, Yukawa and quartic couplings resummed at leading order in NF. We construct extensions of the Standard Model where SU(2) and/or SU(3) are asymptotically safe. When the same procedure is applied to the Abelian U(1) factor, we find that the Higgs quartic can not be made asymptotically safe and stay perturbative at the same time.
Asymptotic Expansions for Higher-Order Scalar Difference Equations
Directory of Open Access Journals (Sweden)
Ravi P. Agarwal
2007-04-01
Full Text Available We give an asymptotic expansion of the solutions of higher-order PoincarÃƒÂ© difference equation in terms of the characteristic solutions of the limiting equation. As a consequence, we obtain an asymptotic description of the solutions approaching a hyperbolic equilibrium of a higher-order nonlinear difference equation with sufficiently smooth nonlinearity. The proof is based on the inversion formula for the z -transform and the residue theorem.
Asymptotic Expansions for Higher-Order Scalar Difference Equations
Directory of Open Access Journals (Sweden)
Pituk Mihály
2007-01-01
Full Text Available We give an asymptotic expansion of the solutions of higher-order Poincaré difference equation in terms of the characteristic solutions of the limiting equation. As a consequence, we obtain an asymptotic description of the solutions approaching a hyperbolic equilibrium of a higher-order nonlinear difference equation with sufficiently smooth nonlinearity. The proof is based on the inversion formula for the z -transform and the residue theorem.
Asymptotical behaviour of pion electromagnetic form factor in QCD
International Nuclear Information System (INIS)
Efremov, A.V.; Radyushkin, A.V.
1978-01-01
In the framework of the renormalizable quantum field theory a new approach is developed to the investigation of asymptotical behaviour of two-particle bound state electromagnetic form factor. It is shown that the behaviour of the pion EM form factor in quantum chromodynamics at sufficiently large momentum transfers is controlled by the short-distance dynamics only. The formula is obtained which expresses the asymptotical behaviour of the pion form factor in terms of the fundamental constants of the theory
Non-Asymptotic Confidence Sets for Circular Means
Directory of Open Access Journals (Sweden)
Thomas Hotz
2016-10-01
Full Text Available The mean of data on the unit circle is defined as the minimizer of the average squared Euclidean distance to the data. Based on Hoeffding’s mass concentration inequalities, non-asymptotic confidence sets for circular means are constructed which are universal in the sense that they require no distributional assumptions. These are then compared with asymptotic confidence sets in simulations and for a real data set.
Global asymptotic stability of delayed Cohen-Grossberg neural networks
International Nuclear Information System (INIS)
Wu Wei; Cui Baotong; Huang Min
2007-01-01
In this letter, the global asymptotic stability of a class of Cohen-Grossberg neural networks with time-varying delays is discussed. A new set of sufficient conditions for the neural networks are proposed to guarantee the global asymptotic convergence. Our criteria represent an extension of the existing results in literatures. An example is also presented to compare our results with the previous results
Asymptotic freedom and the symplectic and G2 groups
International Nuclear Information System (INIS)
Chaichian, M; Kolmakov, Yu. N.; Nelipa, N. F.
1978-01-01
It is shown that the symplectic Sp(4), Sp(6) and the exceptional G 2 gauge field theories with complete Spontaneous symmetry breaking through the Higgs mechanism are not asymptotically free. This, together with earlier results for other groups, hints at the existence of a general theorem according to which it would no longer be possible for asymptotic freedom to coexist with the absence of infrared divergences. (author)
Discrete Weighted Pseudo Asymptotic Periodicity of Second Order Difference Equations
Directory of Open Access Journals (Sweden)
Zhinan Xia
2014-01-01
Full Text Available We define the concept of discrete weighted pseudo-S-asymptotically periodic function and prove some basic results including composition theorem. We investigate the existence, and uniqueness of discrete weighted pseudo-S-asymptotically periodic solution to nonautonomous semilinear difference equations. Furthermore, an application to scalar second order difference equations is given. The working tools are based on the exponential dichotomy theory and fixed point theorem.
Asymptotic stability of a genetic network under impulsive control
International Nuclear Information System (INIS)
Li Fangfei; Sun Jitao
2010-01-01
The study of the stability of genetic network is an important motif for the understanding of the living organism at both molecular and cellular levels. In this Letter, we provide a theoretical method for analyzing the asymptotic stability of a genetic network under impulsive control. And the sufficient conditions of its asymptotic stability under impulsive control are obtained. Finally, an example is given to illustrate the effectiveness of the obtained method.
Ratio asymptotics of Hermite-Pade polynomials for Nikishin systems
International Nuclear Information System (INIS)
Aptekarev, A I; Lopez, Guillermo L; Rocha, I A
2005-01-01
The existence of ratio asymptotics is proved for a sequence of multiple orthogonal polynomials with orthogonality relations distributed among a system of m finite Borel measures with support on a bounded interval of the real line which form a so-called Nikishin system. For m=1 this result reduces to Rakhmanov's celebrated theorem on the ratio asymptotics for orthogonal polynomials on the real line.
arXiv Asymptotically Safe Standard Model Extensions?
Pelaggi, Giulio Maria; Salvio, Alberto; Sannino, Francesco; Smirnov, Juri; Strumia, Alessandro
2018-05-15
We consider theories with a large number NF of charged fermions and compute the renormalization group equations for the gauge, Yukawa and quartic couplings resummed at leading order in 1/NF. We construct extensions of the standard model where SU(2) and/or SU(3) are asymptotically safe. When the same procedure is applied to the Abelian U(1) factor, we find that the Higgs quartic can not be made asymptotically safe and stay perturbative at the same time.
The asymptotic variance of departures in critically loaded queues
Al Hanbali, Ahmad; Mandjes, M.R.H.; Nazarathy, Y.; Whitt, W.
2011-01-01
We consider the asymptotic variance of the departure counting process D(t) of the GI/G/1 queue; D(t) denotes the number of departures up to time t. We focus on the case where the system load ϱ equals 1, and prove that the asymptotic variance rate satisfies limt→∞varD(t) / t = λ(1 - 2 / π)(ca2 +
International Nuclear Information System (INIS)
Ablinger, J.; Hasselhuhn, A.; Schneider, C.; Behring, A.; Bluemlein, J.; Freitas, A. de; Raab, C.; Round, M.; Manteuffel, A. von
2014-07-01
We report on our latest results in the calculation of the three-loop heavy flavor contributions to the Wilson coefficients in deep-inelastic scattering in the asymptotic region Q 2 >>m 2 . We discuss the different methods used to compute the required operator matrix elements and the corresponding Feynman integrals. These methods very recently allowed us to obtain a series of new operator matrix elements and Wilson coefficients like the flavor non-singlet and pure singlet Wilson coefficients.
Boson exchange mechanisms, bounds and asymptotic limits
International Nuclear Information System (INIS)
Carbotte, J.P.; Marsiglio, F.
1989-01-01
BCS theory predicts universal laws for the normalized thermodynamic and other properties of superconductors. The only parameter in the theory, which models the pairing interaction, can be fit to the measured size of the critical temperature and everything else follows. For example, the ratio of twice the gap edge Δ o to the critical temperature is 3.54 while the specific heat jump at T c (ΔC(T c )) normalized to the normal state value of the electronic specific heat γ o T c (with γ o the Sommerfeld constant) is 1.43. Other universal numbers also apply. In real materials, deviations from BCS laws are observed 2 - 6 which carry information on details of the microscopic parameters involved that cannot be modeled well by a constant pairing potential approximation
AVACOM-ETAP, Availability and Element Transient and Asymptotic Repair Process
International Nuclear Information System (INIS)
Reina, G.
1987-01-01
1 - Description of program or function: In reliability theory, the term 'availability' generally indicates the probability of the proper functioning of a system or of a component at a general time t when various possible replacement or repair policies are considered. AVACOM-ETARP calculates the transient and asymptotic availability of a component subject to a repair process with generic failure and repair laws. Five of the most commonly used distributions have been included as options: exponential, normal; lognormal; gamma; Weibull. 2 - Method of solution: The used mathematical model considers the failure-restoration process as a 2-state non-homogeneous Markov process containing the homogeneous Markov one as a particular case
On the asymptotic ergodic capacity of FSO links with generalized pointing error model
Al-Quwaiee, Hessa
2015-09-11
Free-space optical (FSO) communication systems are negatively affected by two physical phenomenon, namely, scintillation due to atmospheric turbulence and pointing errors. To quantize the effect of these two factors on FSO system performance, we need an effective mathematical model for them. Scintillations are typically modeled by the log-normal and Gamma-Gamma distributions for weak and strong turbulence conditions, respectively. In this paper, we propose and study a generalized pointing error model based on the Beckmann distribution. We then derive the asymptotic ergodic capacity of FSO systems under the joint impact of turbulence and generalized pointing error impairments. © 2015 IEEE.
DEFF Research Database (Denmark)
Ørregård Nielsen, Morten
This paper proves consistency and asymptotic normality for the conditional-sum-of-squares estimator, which is equivalent to the conditional maximum likelihood estimator, in multivariate fractional time series models. The model is parametric and quite general, and, in particular, encompasses...... the multivariate non-cointegrated fractional ARIMA model. The novelty of the consistency result, in particular, is that it applies to a multivariate model and to an arbitrarily large set of admissible parameter values, for which the objective function does not converge uniformly in probablity, thus making...
STARDUST FROM ASYMPTOTIC GIANT BRANCH STARS
International Nuclear Information System (INIS)
Gail, H.-P.; Zhukovska, S. V.; Hoppe, P.; Trieloff, M.
2009-01-01
The formation of dust in the outflows of low- and intermediate-mass stars on the first giant branch and asymptotic giant branch (AGB) is studied and the relative contributions of stars of different initial masses and metallicities to the interstellar medium (ISM) at the instant of solar system formation are derived. These predictions are compared with the characteristics of the parent stars of presolar dust grains found in primitive meteorites and interplanetary dust particles (IDPs) inferred from their isotopic compositions. For this purpose, model calculations for dust condensation in stellar outflows are combined with synthetic models of stellar evolution on the first giant branch and AGB and an evolution model of the Milky Way for the solar neighborhood. The dust components considered are olivine, pyroxene, carbon, SiC, and iron. The corresponding dust production rates are derived for the solar vicinity. From these rates and taking into account dust destruction by supernova shocks in the ISM, the contributions to the inventory of presolar dust grains in the solar system are derived for stars of different initial masses and metallicities. It is shown that stars on the first giant branch and the early AGB are not expected to form dust, in accord with astronomical observations. Dust formation is concentrated in the last phase of evolution, the thermally pulsing AGB. Due to the limited lifetime of dust grains in the ISM only parent stars from a narrow range of metallicities are expected to contribute to the population of presolar dust grains. Silicate and silicon carbide dust grains are predicted to come from parent stars with metallicities not less than about Z ∼ 0.008 (0.6 x solar). This metallicity limit is higher than that inferred from presolar SiC grain isotope data. The population of presolar carbon dust grains is predicted to originate from a wider range of metallicities, down to Z ∼ 0.004. Masses of AGB stars that produce C-rich dust are in the range
Loop quantum gravity in asymptotically flat spaces
International Nuclear Information System (INIS)
Arnsdorf, M.
2000-01-01
This thesis describes applications and extensions of the loop variable approach to non-perturbative quantum gravity. The common theme of the work presented, is the need to generalise loop quantum gravity to be applicable in cases where space is asymptotically flat, and no longer compact as is usually assumed. This is important for the study of isolated gravitational systems. It also presents a natural context in which to search for the semi-classical limit, one of the main outstanding problems in loop quantum gravity. In the first part of the thesis we study how isolated gravitational systems can be attributed particle-like properties. In particular, we show how spinorial states can arise in pure loop quantum gravity if spatial topology is non-trivial, thus confirming an old conjecture of Friedman and Sorkin. Heuristically, this corresponds to the idea that we can rotate isolated regions of spatial topology relative to the environment at infinity, and that only a 4π-rotation will take us back to the original configuration. To do this we extend the standard loop quantum gravity formalism by introducing a compactification of our non-compact spatial manifold, and study the knotting of embedded graphs. The second part of the thesis takes a more systematic approach to the study of loop quantum gravity on non-compact spaces. We look for new representations of the loop algebra, which give rise to quantum theories that are inequivalent to the standard one. These theories naturally describe excitations of a fiducial background state, which is specified via the choice of its vacuum expectation values. In particular, we can choose background states that describe the geometries of non-compact manifolds. We also discuss how suitable background states can be constructed that can approximate classical phase space data, in our case holonomies along embedded paths and geometrical quantities related to areas and volumes. These states extend the notion of the weave and provide a
Coefficient Omega Bootstrap Confidence Intervals: Nonnormal Distributions
Padilla, Miguel A.; Divers, Jasmin
2013-01-01
The performance of the normal theory bootstrap (NTB), the percentile bootstrap (PB), and the bias-corrected and accelerated (BCa) bootstrap confidence intervals (CIs) for coefficient omega was assessed through a Monte Carlo simulation under conditions not previously investigated. Of particular interests were nonnormal Likert-type and binary items.…
Cucker-Smale model with normalized communication weights and time delay
Choi, Young-Pil; Haskovec, Jan
2017-01-01
We study a Cucker-Smale-type system with time delay in which agents interact with each other through normalized communication weights. We construct a Lyapunov functional for the system and provide sufficient conditions for asymptotic flocking, i
Size Matters: Individual Variation in Ectotherm Growth and Asymptotic Size.
Directory of Open Access Journals (Sweden)
Richard B King
Full Text Available Body size, and, by extension, growth has impacts on physiology, survival, attainment of sexual maturity, fecundity, generation time, and population dynamics, especially in ectotherm animals that often exhibit extensive growth following attainment of sexual maturity. Frequently, growth is analyzed at the population level, providing useful population mean growth parameters but ignoring individual variation that is also of ecological and evolutionary significance. Our long-term study of Lake Erie Watersnakes, Nerodia sipedon insularum, provides data sufficient for a detailed analysis of population and individual growth. We describe population mean growth separately for males and females based on size of known age individuals (847 captures of 769 males, 748 captures of 684 females and annual growth increments of individuals of unknown age (1,152 males, 730 females. We characterize individual variation in asymptotic size based on repeated measurements of 69 males and 71 females that were each captured in five to nine different years. The most striking result of our analyses is that asymptotic size varies dramatically among individuals, ranging from 631-820 mm snout-vent length in males and from 835-1125 mm in females. Because female fecundity increases with increasing body size, we explore the impact of individual variation in asymptotic size on lifetime reproductive success using a range of realistic estimates of annual survival. When all females commence reproduction at the same age, lifetime reproductive success is greatest for females with greater asymptotic size regardless of annual survival. But when reproduction is delayed in females with greater asymptotic size, lifetime reproductive success is greatest for females with lower asymptotic size when annual survival is low. Possible causes of individual variation in asymptotic size, including individual- and cohort-specific variation in size at birth and early growth, warrant further
Size Matters: Individual Variation in Ectotherm Growth and Asymptotic Size
King, Richard B.
2016-01-01
Body size, and, by extension, growth has impacts on physiology, survival, attainment of sexual maturity, fecundity, generation time, and population dynamics, especially in ectotherm animals that often exhibit extensive growth following attainment of sexual maturity. Frequently, growth is analyzed at the population level, providing useful population mean growth parameters but ignoring individual variation that is also of ecological and evolutionary significance. Our long-term study of Lake Erie Watersnakes, Nerodia sipedon insularum, provides data sufficient for a detailed analysis of population and individual growth. We describe population mean growth separately for males and females based on size of known age individuals (847 captures of 769 males, 748 captures of 684 females) and annual growth increments of individuals of unknown age (1,152 males, 730 females). We characterize individual variation in asymptotic size based on repeated measurements of 69 males and 71 females that were each captured in five to nine different years. The most striking result of our analyses is that asymptotic size varies dramatically among individuals, ranging from 631–820 mm snout-vent length in males and from 835–1125 mm in females. Because female fecundity increases with increasing body size, we explore the impact of individual variation in asymptotic size on lifetime reproductive success using a range of realistic estimates of annual survival. When all females commence reproduction at the same age, lifetime reproductive success is greatest for females with greater asymptotic size regardless of annual survival. But when reproduction is delayed in females with greater asymptotic size, lifetime reproductive success is greatest for females with lower asymptotic size when annual survival is low. Possible causes of individual variation in asymptotic size, including individual- and cohort-specific variation in size at birth and early growth, warrant further investigation. PMID
Ren, Fengli; Cao, Jinde
2007-03-01
In this paper, several sufficient conditions are obtained ensuring existence, global attractivity and global asymptotic stability of the periodic solution for the higher-order bidirectional associative memory neural networks with periodic coefficients and delays by using the continuation theorem of Mawhin's coincidence degree theory, the Lyapunov functional and the non-singular M-matrix. Two examples are exploited to illustrate the effectiveness of the proposed criteria. These results are more effective than the ones in the literature for some neural networks, and can be applied to the design of globally attractive or globally asymptotically stable networks and thus have important significance in both theory and applications.
Max-Min SINR in Large-Scale Single-Cell MU-MIMO: Asymptotic Analysis and Low Complexity Transceivers
Sifaou, Houssem
2016-12-28
This work focuses on the downlink and uplink of large-scale single-cell MU-MIMO systems in which the base station (BS) endowed with M antennas communicates with K single-antenna user equipments (UEs). Particularly, we aim at reducing the complexity of the linear precoder and receiver that maximize the minimum signal-to-interference-plus-noise ratio subject to a given power constraint. To this end, we consider the asymptotic regime in which M and K grow large with a given ratio. Tools from random matrix theory (RMT) are then used to compute, in closed form, accurate approximations for the parameters of the optimal precoder and receiver, when imperfect channel state information (modeled by the generic Gauss-Markov formulation form) is available at the BS. The asymptotic analysis allows us to derive the asymptotically optimal linear precoder and receiver that are characterized by a lower complexity (due to the dependence on the large scale components of the channel) and, possibly, by a better resilience to imperfect channel state information. However, the implementation of both is still challenging as it requires fast inversions of large matrices in every coherence period. To overcome this issue, we apply the truncated polynomial expansion (TPE) technique to the precoding and receiving vector of each UE and make use of RMT to determine the optimal weighting coefficients on a per- UE basis that asymptotically solve the max-min SINR problem. Numerical results are used to validate the asymptotic analysis in the finite system regime and to show that the proposed TPE transceivers efficiently mimic the optimal ones, while requiring much lower computational complexity.
Attenuation coefficients of soils
International Nuclear Information System (INIS)
Martini, E.; Naziry, M.J.
1989-01-01
As a prerequisite to the interpretation of gamma-spectrometric in situ measurements of activity concentrations of soil radionuclides the attenuation of 60 to 1332 keV gamma radiation by soil samples varying in water content and density has been investigated. A useful empirical equation could be set up to describe the dependence of the mass attenuation coefficient upon photon energy for soil with a mean water content of 10%, with the results comparing well with data in the literature. The mean density of soil in the GDR was estimated at 1.6 g/cm 3 . This value was used to derive the linear attenuation coefficients, their range of variation being 10%. 7 figs., 5 tabs. (author)
Broer, H.; Hoveijn, I.; Lunter, G.; Vegter, G.
2003-01-01
The Birkhoff normal form procedure is a widely used tool for approximating a Hamiltonian systems by a simpler one. This chapter starts out with an introduction to Hamiltonian mechanics, followed by an explanation of the Birkhoff normal form procedure. Finally we discuss several algorithms for
Energy Technology Data Exchange (ETDEWEB)
Jin, Shi, E-mail: sjin@wisc.edu [Department of Mathematics, University of Wisconsin–Madison, Madison, WI 53706 (United States); Institute of Natural Sciences, School of Mathematical Science, MOELSEC and SHL-MAC, Shanghai Jiao Tong University, Shanghai 200240 (China); Shu, Ruiwen, E-mail: rshu2@math.wisc.edu [Department of Mathematics, University of Wisconsin–Madison, Madison, WI 53706 (United States)
2017-04-15
In this paper we consider a kinetic-fluid model for disperse two-phase flows with uncertainty. We propose a stochastic asymptotic-preserving (s-AP) scheme in the generalized polynomial chaos stochastic Galerkin (gPC-sG) framework, which allows the efficient computation of the problem in both kinetic and hydrodynamic regimes. The s-AP property is proved by deriving the equilibrium of the gPC version of the Fokker–Planck operator. The coefficient matrices that arise in a Helmholtz equation and a Poisson equation, essential ingredients of the algorithms, are proved to be positive definite under reasonable and mild assumptions. The computation of the gPC version of a translation operator that arises in the inversion of the Fokker–Planck operator is accelerated by a spectrally accurate splitting method. Numerical examples illustrate the s-AP property and the efficiency of the gPC-sG method in various asymptotic regimes.
Schlemm, Eckhard
2015-09-01
The Bak-Sneppen model is an abstract representation of a biological system that evolves according to the Darwinian principles of random mutation and selection. The species in the system are characterized by a numerical fitness value between zero and one. We show that in the case of five species the steady-state fitness distribution can be obtained as a solution to a linear differential equation of order five with hypergeometric coefficients. Similar representations for the asymptotic fitness distribution in larger systems may help pave the way towards a resolution of the question of whether or not, in the limit of infinitely many species, the fitness is asymptotically uniformly distributed on the interval [fc, 1] with fc ≳ 2/3. Copyright © 2015 Elsevier Inc. All rights reserved.
Directory of Open Access Journals (Sweden)
V. P. Gribkova
2014-01-01
Full Text Available The paper offers a new method for approximate solution of one type of singular integral equations for elasticity theory which have been studied by other authors. The approximate solution is found in the form of asymptotic polynomial function of a low degree (first approximation based on the Chebyshev second order polynomial. Other authors have obtained a solution (only in separate points using a method of mechanical quadrature and though they used also the Chebyshev polynomial of the second order they applied another system of junctures which were used for the creation of the required formulas.The suggested method allows not only to find an approximate solution for the whole interval in the form of polynomial, but it also makes it possible to obtain a remainder term in the form of infinite expansion where coefficients are linear functional of the given integral equation and basis functions are the Chebyshev polynomial of the second order. Such presentation of the remainder term of the first approximation permits to find a summand of the infinite series, which will serve as a start for fulfilling the given solution accuracy. This number is a degree of the asymptotic polynomial (second approximation, which will give the approximation to the exact solution with the given accuracy. The examined polynomial functions tend asymptotically to the polynomial of the best uniform approximation in the space C, created for the given operator.The paper demonstrates a convergence of the approximate solution to the exact one and provides an error estimation. The proposed algorithm for obtaining of the approximate solution and error estimation is easily realized with the help of computing technique and does not require considerable preliminary preparation during programming.
Large gauge symmetries and asymptotic states in QED
Energy Technology Data Exchange (ETDEWEB)
Gabai, Barak; Sever, Amit [School of Physics and Astronomy, Tel Aviv University,Ramat Aviv 69978 (Israel)
2016-12-19
Large Gauge Transformations (LGT) are gauge transformations that do not vanish at infinity. Instead, they asymptotically approach arbitrary functions on the conformal sphere at infinity. Recently, it was argued that the LGT should be treated as an infinite set of global symmetries which are spontaneously broken by the vacuum. It was established that in QED, the Ward identities of their induced symmetries are equivalent to the Soft Photon Theorem. In this paper we study the implications of LGT on the S-matrix between physical asymptotic states in massive QED. In appose to the naively free scattering states, physical asymptotic states incorporate the long range electric field between asymptotic charged particles and were already constructed in 1970 by Kulish and Faddeev. We find that the LGT charge is independent of the particles’ momenta and may be associated to the vacuum. The soft theorem’s manifestation as a Ward identity turns out to be an outcome of not working with the physical asymptotic states.
Black hole thermodynamics from a variational principle: asymptotically conical backgrounds
Energy Technology Data Exchange (ETDEWEB)
An, Ok Song [SISSA and INFN, Sezione di Trieste,Via Bonomea 265, 34136 Trieste (Italy); Department of Physics, Kim Il Sung University,Ryongnam Dong, TaeSong District, Pyongyang, D.P.R. (Korea, Republic of); ICTP,Strada Costiera 11, 34014 Trieste (Italy); Cvetič, Mirjam [Department of Physics and Astronomy, University of Pennsylvania,209 S 33rd St, Philadelphia, PA 19104 (United States); Center for Applied Mathematics and Theoretical Physics, University of Maribor,Mladinska 3, SI2000 Maribor (Slovenia); Papadimitriou, Ioannis [SISSA and INFN, Sezione di Trieste,Via Bonomea 265, 34136 Trieste (Italy)
2016-03-14
The variational problem of gravity theories is directly related to black hole thermodynamics. For asymptotically locally AdS backgrounds it is known that holographic renormalization results in a variational principle in terms of equivalence classes of boundary data under the local asymptotic symmetries of the theory, which automatically leads to finite conserved charges satisfying the first law of thermodynamics. We show that this connection holds well beyond asymptotically AdS black holes. In particular, we formulate the variational problem for N=2 STU supergravity in four dimensions with boundary conditions corresponding to those obeyed by the so called ‘subtracted geometries’. We show that such boundary conditions can be imposed covariantly in terms of a set of asymptotic second class constraints, and we derive the appropriate boundary terms that render the variational problem well posed in two different duality frames of the STU model. This allows us to define finite conserved charges associated with any asymptotic Killing vector and to demonstrate that these charges satisfy the Smarr formula and the first law of thermodynamics. Moreover, by uplifting the theory to five dimensions and then reducing on a 2-sphere, we provide a precise map between the thermodynamic observables of the subtracted geometries and those of the BTZ black hole. Surface terms play a crucial role in this identification.
Non-Markovian dynamics of quantum systems: formalism, transport coefficients
International Nuclear Information System (INIS)
Kanokov, Z.; Palchikov, Yu.V.; Antonenko, N.V.; Adamian, G.G.; Kanokov, Z.; Adamian, G.G.; Scheid, W.
2004-01-01
Full text: The generalized Linbland equations with non-stationary transport coefficients are derived from the Langevin equations for the case of nonlinear non-Markovian noise [1]. The equations of motion for the collective coordinates are consistent with the generalized quantum fluctuation dissipation relations. The microscopic justification of the Linbland axiomatic approach is performed. Explicit expressions for the time-dependent transport coefficients are presented for the case of FC- and RWA-oscillators and a general linear coupling in coordinate and in momentum between the collective subsystem and heat bath. The explicit equations for the correlation functions show that the Onsanger's regression hypothesis does not hold exactly for the non-Markovian equations of motion. However, under some conditions the regression of fluctuations goes to zero in the same manner as the average values. In the low and high temperature regimes we found that the dissipation leads to long-time tails in correlation functions in the RWA-oscillator. In the case of the FC-oscillator a non-exponential power-like decay of the correlation function in coordinate is only obtained only at the low temperature limit. The calculated results depend rather weakly on the memory time in many applications. The found transient times for diffusion coefficients D pp (t), D qp (t) and D qq (t) are quite short. The value of classical diffusion coefficients in momentum underestimates the asymptotic value of quantum one D pp (t), but the asymptotic values of classical σ qq c and quantum σ qq second moments are close due to the negativity of quantum mixed diffusion coefficient D qp (t)
The Truth About Ballistic Coefficients
Courtney, Michael; Courtney, Amy
2007-01-01
The ballistic coefficient of a bullet describes how it slows in flight due to air resistance. This article presents experimental determinations of ballistic coefficients showing that the majority of bullets tested have their previously published ballistic coefficients exaggerated from 5-25% by the bullet manufacturers. These exaggerated ballistic coefficients lead to inaccurate predictions of long range bullet drop, retained energy and wind drift.
The Asymptotic Joint Distribution of Self-Normalized Censored Sums and Sums of Squares
Hahn, Marjorie G.; Kuelbs, Jim; Weiner, Daniel C.
1990-01-01
Empirical versions of appropriate centering and scale constants for random variables which can fail to have second or even first moments are obtainable in various ways via suitable modifications of the summands in the partial sum. This paper discusses a particular modification, called censoring (which is a kind of winsorization), where the (random) number of summands altered tends to infinity but the proportion altered tends to zero as the number of summands increases. Some analytic advantage...
Applications of Asymptotic Sampling on High Dimensional Structural Dynamic Problems
DEFF Research Database (Denmark)
Sichani, Mahdi Teimouri; Nielsen, Søren R.K.; Bucher, Christian
2011-01-01
The paper represents application of the asymptotic sampling on various structural models subjected to random excitations. A detailed study on the effect of different distributions of the so-called support points is performed. This study shows that the distribution of the support points has consid...... dimensional reliability problems in structural dynamics.......The paper represents application of the asymptotic sampling on various structural models subjected to random excitations. A detailed study on the effect of different distributions of the so-called support points is performed. This study shows that the distribution of the support points has...... is minimized. Next, the method is applied on different cases of linear and nonlinear systems with a large number of random variables representing the dynamic excitation. The results show that asymptotic sampling is capable of providing good approximations of low failure probability events for very high...
Contact mechanics of articular cartilage layers asymptotic models
Argatov, Ivan
2015-01-01
This book presents a comprehensive and unifying approach to articular contact mechanics with an emphasis on frictionless contact interaction of thin cartilage layers. The first part of the book (Chapters 1–4) reviews the results of asymptotic analysis of the deformational behavior of thin elastic and viscoelastic layers. A comprehensive review of the literature is combined with the authors’ original contributions. The compressible and incompressible cases are treated separately with a focus on exact solutions for asymptotic models of frictionless contact for thin transversely isotropic layers bonded to rigid substrates shaped like elliptic paraboloids. The second part (Chapters 5, 6, and 7) deals with the non-axisymmetric contact of thin transversely isotropic biphasic layers and presents the asymptotic modelling methodology for tibio-femoral contact. The third part of the book consists of Chapter 8, which covers contact problems for thin bonded inhomogeneous transversely isotropic elastic layers, and Cha...
Scalar hairy black holes and solitons in asymptotically flat spacetimes
International Nuclear Information System (INIS)
Nucamendi, Ulises; Salgado, Marcelo
2003-01-01
A numerical analysis shows that the Einstein field equations allow static and spherically symmetric black hole solutions with scalar-field hair in asymptotically flat spacetimes. When regularity at the origin is imposed (i.e., in the absence of a horizon) globally regular scalar solitons are found. The asymptotically flat solutions are obtained provided that the scalar potential V(φ) of the theory is not positive semidefinite and such that its local minimum is also a zero of the potential, the scalar field settling asymptotically at that minimum. The configurations, although unstable under spherically symmetric linear perturbations, are regular and thus can serve as counterexamples to the no-scalar-hair conjecture
Asymptotic chaos expansions in finance theory and practice
Nicolay, David
2014-01-01
Stochastic instantaneous volatility models such as Heston, SABR or SV-LMM have mostly been developed to control the shape and joint dynamics of the implied volatility surface. In principle, they are well suited for pricing and hedging vanilla and exotic options, for relative value strategies or for risk management. In practice however, most SV models lack a closed form valuation for European options. This book presents the recently developed Asymptotic Chaos Expansions methodology (ACE) which addresses that issue. Indeed its generic algorithm provides, for any regular SV model, the pure asymptotes at any order for both the static and dynamic maps of the implied volatility surface. Furthermore, ACE is programmable and can complement other approximation methods. Hence it allows a systematic approach to designing, parameterising, calibrating and exploiting SV models, typically for Vega hedging or American Monte-Carlo. Asymptotic Chaos Expansions in Finance illustrates the ACE approach for single underlyings (suc...
Asymptotic Analysis in MIMO MRT/MRC Systems
Directory of Open Access Journals (Sweden)
Zhou Quan
2006-01-01
Full Text Available Through the analysis of the probability density function of the squared largest singular value of a complex Gaussian matrix at the origin and tail, we obtain two asymptotic results related to the multi-input multi-output (MIMO maximum-ratio-transmission/maximum-ratio-combining (MRT/MRC systems. One is the asymptotic error performance (in terms of SNR in a single-user system, and the other is the asymptotic system capacity (in terms of the number of users in the multiuser scenario when multiuser diversity is exploited. Similar results are also obtained for two other MIMO diversity schemes, space-time block coding and selection combining. Our results reveal a simple connection with system parameters, providing good insights for the design of MIMO diversity systems.
Watermelon configurations with wall interaction: exact and asymptotic results
Energy Technology Data Exchange (ETDEWEB)
Krattenthaler, C [Institut Camille Jordan, Universite Claude Bernard Lyon-I, 21, avenue Claude Bernard, F-69622 Villeurbanne Cedex (France)
2006-06-15
We perform an exact and asymptotic analysis of the model of n vicious walkers interacting with a wall via contact potentials, a model introduced by Brak, Essam and Owczarek. More specifically, we study the partition function of watermelon configurations which start on the wall, but may end at arbitrary height, and their mean number of contacts with the wall. We improve and extend the earlier (partially nonrigorous) results by Brak, Essam and Owczarek, providing new exact results, and more precise and more general asymptotic results, in particular full asymptotic expansions for the partition function and the mean number of contacts. Furthermore, we relate this circle of problems to earlier results in the combinatorial and statistical literature.
Watermelon configurations with wall interaction: exact and asymptotic results
International Nuclear Information System (INIS)
Krattenthaler, C
2006-01-01
We perform an exact and asymptotic analysis of the model of n vicious walkers interacting with a wall via contact potentials, a model introduced by Brak, Essam and Owczarek. More specifically, we study the partition function of watermelon configurations which start on the wall, but may end at arbitrary height, and their mean number of contacts with the wall. We improve and extend the earlier (partially nonrigorous) results by Brak, Essam and Owczarek, providing new exact results, and more precise and more general asymptotic results, in particular full asymptotic expansions for the partition function and the mean number of contacts. Furthermore, we relate this circle of problems to earlier results in the combinatorial and statistical literature
Watermelon configurations with wall interaction: exact and asymptotic results
Krattenthaler, C.
2006-06-01
We perform an exact and asymptotic analysis of the model of n vicious walkers interacting with a wall via contact potentials, a model introduced by Brak, Essam and Owczarek. More specifically, we study the partition function of watermelon configurations which start on the wall, but may end at arbitrary height, and their mean number of contacts with the wall. We improve and extend the earlier (partially nonrigorous) results by Brak, Essam and Owczarek, providing new exact results, and more precise and more general asymptotic results, in particular full asymptotic expansions for the partition function and the mean number of contacts. Furthermore, we relate this circle of problems to earlier results in the combinatorial and statistical literature.
On the asymptotic stability of nonlinear mechanical switched systems
Platonov, A. V.
2018-05-01
Some classes of switched mechanical systems with dissipative and potential forces are considered. The case, where either dissipative or potential forces are essentially nonlinear, is studied. It is assumed that the zero equilibrium position of the system is asymptotically stable at least for one operating mode. We will look for sufficient conditions which guarantee the preservation of asymptotic stability of the equilibrium position under the switching of modes. The Lyapunov direct method is used. A Lyapunov function for considered system is constructed, which satisfies the differential inequality of special form for every operating mode. This inequality is nonlinear for the chosen mode with asymptotically stable equilibrium position, and it is linear for the rest modes. The correlations between the intervals of activity of the pointed mode and the intervals of activity of the rest modes are obtained which guarantee the required properties.
Polymers and Random graphs: Asymptotic equivalence to branching processes
International Nuclear Information System (INIS)
Spouge, J.L.
1985-01-01
In 1974, Falk and Thomas did a computer simulation of Flory's Equireactive RA/sub f/ Polymer model, rings forbidden and rings allowed. Asymptotically, the Rings Forbidden model tended to Stockmayer's RA/sub f/ distribution (in which the sol distribution ''sticks'' after gelation), while the Rings Allowed model tended to the Flory version of the RA/sub f/ distribution. In 1965, Whittle introduced the Tree and Pseudomultigraph models. We show that these random graphs generalize the Falk and Thomas models by incorporating first-shell substitution effects. Moreover, asymptotically the Tree model displays postgelation ''sticking.'' Hence this phenomenon results from the absence of rings and occurs independently of equireactivity. We also show that the Pseudomultigraph model is asymptotically identical to the Branching Process model introduced by Gordon in 1962. This provides a possible basis for the Branching Process model in standard statistical mechanics
ADM Mass for Asymptotically de Sitter Space-Time
International Nuclear Information System (INIS)
Huang Shiming; Yue Ruihong; Jia Dongyan
2010-01-01
In this paper, an ADM mass formula for asymptotically de Sitter(dS) space-time is derived from the energy-momentum tensor. We take the vacuum dS space as the background and investigate the ADM mass of the (d + 3)-dimensional sphere-symmetric space with a positive cosmological constant, and find that the ADM mass of asymptotically dS space is based on the ADM mass of Schwarzschild field and the cosmological background brings some small mass contribution as well. (general)
Selected asymptotic methods with applications to electromagnetics and antennas
Fikioris, George; Bakas, Odysseas N
2013-01-01
This book describes and illustrates the application of several asymptotic methods that have proved useful in the authors' research in electromagnetics and antennas. We first define asymptotic approximations and expansions and explain these concepts in detail. We then develop certain prerequisites from complex analysis such as power series, multivalued functions (including the concepts of branch points and branch cuts), and the all-important gamma function. Of particular importance is the idea of analytic continuation (of functions of a single complex variable); our discussions here include som
Asymptotic solutions of diffusion models for risk reserves
Directory of Open Access Journals (Sweden)
S. Shao
2003-01-01
Full Text Available We study a family of diffusion models for risk reserves which account for the investment income earned and for the inflation experienced on claim amounts. After we defined the process of the conditional probability of ruin over finite time and imposed the appropriate boundary conditions, classical results from the theory of diffusion processes turn the stochastic differential equation to a special class of initial and boundary value problems defined by a linear diffusion equation. Armed with asymptotic analysis and perturbation theory, we obtain the asymptotic solutions of the diffusion models (possibly degenerate governing the conditional probability of ruin over a finite time in terms of interest rate.
Convergence Theorem for Finite Family of Total Asymptotically Nonexpansive Mappings
Directory of Open Access Journals (Sweden)
E.U. Ofoedu
2015-11-01
Full Text Available In this paper we introduce an explicit iteration process and prove strong convergence of the scheme in a real Hilbert space $H$ to the common fixed point of finite family of total asymptotically nonexpansive mappings which is nearest to the point $u \\in H$. Our results improve previously known ones obtained for the class of asymptotically nonexpansive mappings. As application, iterative method for: approximation of solution of variational Inequality problem, finite family of continuous pseudocontractive mappings, approximation of solutions of classical equilibrium problems and approximation of solutions of convex minimization problems are proposed. Our theorems unify and complement many recently announced results.
New rigorous asymptotic theorems for inverse scattering amplitudes
International Nuclear Information System (INIS)
Lomsadze, Sh.Yu.; Lomsadze, Yu.M.
1984-01-01
The rigorous asymptotic theorems both of integral and local types obtained earlier and establishing logarithmic and in some cases even power correlations aetdeen the real and imaginary parts of scattering amplitudes Fsub(+-) are extended to the inverse amplitudes 1/Fsub(+-). One also succeeds in establishing power correlations of a new type between the real and imaginary parts, both for the amplitudes themselves and for the inverse ones. All the obtained assertions are convenient to be tested in high energy experiments when the amplitudes show asymptotic behaviour
Centrally extended symmetry algebra of asymptotically Goedel spacetimes
International Nuclear Information System (INIS)
Compere, Geoffrey; Detournay, Stephane
2007-01-01
We define an asymptotic symmetry algebra for three-dimensional Goedel spacetimes supported by a gauge field which turns out to be the semi-direct sum of the diffeomorphisms on the circle with two loop algebras. A class of fields admitting this asymptotic symmetry algebra and leading to well-defined conserved charges is found. The covariant Poisson bracket of the conserved charges is then shown to be centrally extended to the semi-direct sum of a Virasoro algebra and two affine algebras. The subsequent analysis of three-dimensional Goedel black holes indicates that the Virasoro central charge is negative
Asymptotic inverse periods of reflected reactors above prompt critical
International Nuclear Information System (INIS)
Spriggs, G.D.; Busch, R.D.
1995-01-01
It is commonly assumed that the kinetic behavior of reflected and unreflected reactors is identical. In particular, it is often accepted that a given reactivity change in either type of system will result in an identical asymptotic inverse period. This is generally true for reactivities below prompt critical. For reactivities above prompt critical, however, the asymptotic inverse period can vary in a highly nonlinear fashion with system reactivity depending on the reflector return fraction, the neutron lifetime in the core, and the neutron lifetime in the reflector
Self similar asymptotics of the drift ion acoustic waves
International Nuclear Information System (INIS)
Taranov, V.B.
2004-01-01
A 3D model for the coupled drift and ion acoustic waves is considered. It is shown that self-similar solutions can exist due to the symmetry extension in asymptotic regimes. The form of these solutions is determined in the presence of the magnetic shear as well as in the shear less case. Some of the most symmetric exact solutions are obtained explicitly. In particular, solutions describing asymptotics of zonal flow interaction with monochromatic waves are presented and corresponding frequency shifts are determined
Gravitational charges of transverse asymptotically AdS spacetimes
International Nuclear Information System (INIS)
Cebeci, Hakan; Sarioglu, Oezguer; Tekin, Bayram
2006-01-01
Using Killing-Yano symmetries, we construct conserved charges of spacetimes that asymptotically approach to the flat or anti-de Sitter spaces only in certain directions. In D dimensions, this allows one to define gravitational charges (such as mass and angular momenta densities) of p-dimensional branes/solitons or any other extended objects that curve the transverse space into an asymptotically flat or AdS one. Our construction answers the question of what kind of charges the antisymmetric Killing-Yano tensors lead to
Global Asymptotic Stability of Switched Neural Networks with Delays
Directory of Open Access Journals (Sweden)
Zhenyu Lu
2015-01-01
Full Text Available This paper investigates the global asymptotic stability of a class of switched neural networks with delays. Several new criteria ensuring global asymptotic stability in terms of linear matrix inequalities (LMIs are obtained via Lyapunov-Krasovskii functional. And here, we adopt the quadratic convex approach, which is different from the linear and reciprocal convex combinations that are extensively used in recent literature. In addition, the proposed results here are very easy to be verified and complemented. Finally, a numerical example is provided to illustrate the effectiveness of the results.
Non-pionic effects in deuteron asymptotic observables
International Nuclear Information System (INIS)
Ballot, J.L.; Robilotta, M.R.
1991-01-01
It is well known that pion dynamics dominates deuteron asymptotic observables, especially η, the D/S ratio and Q, the quadrupole moment. A procedure has been discussed earlier that allows the unambiguous determination of the pion contribution to these observables as function of the pion-nucleon coupling constant. This problem is discussed in the framework of a specific model for the nucleon-nucleon interaction, namely the potential developed by the Tourreil, Rouben and Sprung. The contribution of non-pionic dynamics to deuteron asymptotic observables is investigated. It is shown that effects due to ρ and ω exchanges are negligible. (K.A.) 8 refs., 1 fig., 1 tab
Vacuum energy in asymptotically flat 2 + 1 gravity
Energy Technology Data Exchange (ETDEWEB)
Miskovic, Olivera, E-mail: olivera.miskovic@pucv.cl [Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso (Chile); Olea, Rodrigo, E-mail: rodrigo.olea@unab.cl [Departamento de Ciencias Físicas, Universidad Andres Bello, Sazié 2212, Piso 7, Santiago (Chile); Roy, Debraj, E-mail: roy.debraj@pucv.cl [Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso (Chile)
2017-04-10
We compute the vacuum energy of three-dimensional asymptotically flat space based on a Chern–Simons formulation for the Poincaré group. The equivalent action is nothing but the Einstein–Hilbert term in the bulk plus half of the Gibbons–Hawking term at the boundary. The derivation is based on the evaluation of the Noether charges in the vacuum. We obtain that the vacuum energy of this space has the same value as the one of the asymptotically flat limit of three-dimensional anti-de Sitter space.
Vacuum energy in asymptotically flat 2 + 1 gravity
International Nuclear Information System (INIS)
Miskovic, Olivera; Olea, Rodrigo; Roy, Debraj
2017-01-01
We compute the vacuum energy of three-dimensional asymptotically flat space based on a Chern–Simons formulation for the Poincaré group. The equivalent action is nothing but the Einstein–Hilbert term in the bulk plus half of the Gibbons–Hawking term at the boundary. The derivation is based on the evaluation of the Noether charges in the vacuum. We obtain that the vacuum energy of this space has the same value as the one of the asymptotically flat limit of three-dimensional anti-de Sitter space.
Asymptotic analysis of spatial discretizations in implicit Monte Carlo
International Nuclear Information System (INIS)
Densmore, Jeffery D.
2009-01-01
We perform an asymptotic analysis of spatial discretizations in Implicit Monte Carlo (IMC). We consider two asymptotic scalings: one that represents a time step that resolves the mean-free time, and one that corresponds to a fixed, optically large time step. We show that only the latter scaling results in a valid spatial discretization of the proper diffusion equation, and thus we conclude that IMC only yields accurate solutions when using optically large spatial cells if time steps are also optically large. We demonstrate the validity of our analysis with a set of numerical examples.
Low-frequency asymptotic analysis of seismic reflection from afluid-saturated medium
Energy Technology Data Exchange (ETDEWEB)
Silin, D.B.; Korneev, V.A.; Goloshubin, G.M.; Patzek, T.W.
2004-04-14
Reflection of a seismic wave from a plane interface betweentwo elastic media does not depend on the frequency. If one of the mediais poroelastic and fluid-saturated, then the reflection becomesfrequency-dependent. This paper presents a low-frequency asymptoticformula for the reflection of seismic plane p-wave from a fluid-saturatedporous medium. The obtained asymptotic scaling of the frequency-dependentcomponent of the reflection coefficient shows that it is asymptoticallyproportional to the square root of the product of the reservoir fluidmobility and the frequency of the signal. The dependence of this scalingon the dynamic Darcy's law relaxation time is investigated as well.Derivation of the main equations of the theory of poroelasticity from thedynamic filtration theory reveals that this relaxation time isproportional to Biot's tortuosity parameter.
Zhou, Yunyi; Tao, Chenyang; Lu, Wenlian; Feng, Jianfeng
2018-04-20
Functional connectivity is among the most important tools to study brain. The correlation coefficient, between time series of different brain areas, is the most popular method to quantify functional connectivity. Correlation coefficient in practical use assumes the data to be temporally independent. However, the time series data of brain can manifest significant temporal auto-correlation. A widely applicable method is proposed for correcting temporal auto-correlation. We considered two types of time series models: (1) auto-regressive-moving-average model, (2) nonlinear dynamical system model with noisy fluctuations, and derived their respective asymptotic distributions of correlation coefficient. These two types of models are most commonly used in neuroscience studies. We show the respective asymptotic distributions share a unified expression. We have verified the validity of our method, and shown our method exhibited sufficient statistical power for detecting true correlation on numerical experiments. Employing our method on real dataset yields more robust functional network and higher classification accuracy than conventional methods. Our method robustly controls the type I error while maintaining sufficient statistical power for detecting true correlation in numerical experiments, where existing methods measuring association (linear and nonlinear) fail. In this work, we proposed a widely applicable approach for correcting the effect of temporal auto-correlation on functional connectivity. Empirical results favor the use of our method in functional network analysis. Copyright © 2018. Published by Elsevier B.V.
International Nuclear Information System (INIS)
Misguich, J.H.
1978-09-01
The physical meaning of perturbed trajectories in turbulent fields is analysed. Special care is devoted to the asymptotic description of average trajectories for long time intervals, as occuring in many recent plasma turbulence theories. Equivalence is proved between asymptotic average trajectories described as well (i) by the propagators V(t,t-tau) for retrodiction and Wsub(J)(t,t+tau) for prediction, and (ii) by the long time secular behavior of the solution of the equations of motion. This confirms the equivalence between perturbed orbit theories and renormalized theories, including non-Markovian contributions
Asymptotics for a special solution to the second member of the Painleve I hierarchy
International Nuclear Information System (INIS)
Claeys, T
2010-01-01
We study the asymptotic behavior of a special smooth solution y(x, t) to the second member of the Painleve I hierarchy. This solution arises in random matrix theory and in the study of the Hamiltonian perturbations of hyperbolic equations. The asymptotic behavior of y(x, t) if x → ±∞ (for fixed t) is known and relatively simple, but it turns out to be more subtle when x and t tend to infinity simultaneously. We distinguish a region of algebraic asymptotic behavior and a region of elliptic asymptotic behavior, and we obtain rigorous asymptotics in both regions. We also discuss two critical transitional asymptotic regimes.
NP-Hardness of optimizing the sum of Rational Linear Functions over an Asymptotic-Linear-Program
Chermakani, Deepak Ponvel
2012-01-01
We convert, within polynomial-time and sequential processing, an NP-Complete Problem into a real-variable problem of minimizing a sum of Rational Linear Functions constrained by an Asymptotic-Linear-Program. The coefficients and constants in the real-variable problem are 0, 1, -1, K, or -K, where K is the time parameter that tends to positive infinity. The number of variables, constraints, and rational linear functions in the objective, of the real-variable problem is bounded by a polynomial ...
Parabolic cyclinder functions : examples of error bounds for asymptotic expansions
R. Vidunas; N.M. Temme (Nico)
2002-01-01
textabstractSeveral asymptotic expansions of parabolic cylinder functions are discussedand error bounds for remainders in the expansions are presented. Inparticular Poincaré-type expansions for large values of the argument$z$ and uniform expansions for large values of the parameter areconsidered.
Asymptotic behaviour near extinction of continuous-state branching processes
Berzunza, Gabriel; Pardo, Juan Carlos
2016-01-01
In this note, we study the asymptotic behaviour near extinction of (sub-) critical continuous state branching processes. In particular, we establish an analogue of Khintchin's law of the iterated logarithm near extinction time for a continuous state branching process whose branching mechanism satisfies a given condition and its reflected process at its infimum.
Small Bandwidth Asymptotics for Density-Weighted Average Derivatives
DEFF Research Database (Denmark)
Cattaneo, Matias D.; Crump, Richard K.; Jansson, Michael
This paper proposes (apparently) novel standard error formulas for the density-weighted average derivative estimator of Powell, Stock, and Stoker (1989). Asymptotic validity of the standard errors developed in this paper does not require the use of higher-order kernels and the standard errors...
TAIL ASYMPTOTICS OF LIGHT-TAILED WEIBULL-LIKE SUMS
DEFF Research Database (Denmark)
Asmussen, Soren; Hashorva, Enkelejd; Laub, Patrick J.
2017-01-01
We consider sums of n i.i.d. random variables with tails close to exp{-x(beta)} for some beta > 1. Asymptotics developed by Rootzen (1987) and Balkema, Kluppelberg, and Resnick (1993) are discussed from the point of view of tails rather than of densities, using a somewhat different angle...
Asymptotic expansions of Mathieu functions in wave mechanics
International Nuclear Information System (INIS)
Hunter, G.; Kuriyan, M.
1976-01-01
Solutions of the radial Schroedinger equation containing a polarization potential r -4 are expanded in a form appropriate for large values of r. These expansions of the Mathieu functions are used in association with the numerical solution of the Schroedinger equation to impose the asymptotic boundary condition in the case of bound states, and to extract phase shifts in the case of scattering states
On asymptotic isotropy for a hydrodynamic model of liquid crystals
Czech Academy of Sciences Publication Activity Database
Dai, M.; Feireisl, Eduard; Rocca, E.; Schimperna, G.; Schonbek, M.E.
2016-01-01
Roč. 97, 3-4 (2016), s. 189-210 ISSN 0921-7134 Grant - others:European Research Council(XE) MATHEF(320078) Institutional support: RVO:67985840 Keywords : liquid crystal * Q-tensor description * long-time behavior Subject RIV: BA - General Mathematics Impact factor: 0.933, year: 2016 http://content.iospress.com/articles/asymptotic-analysis/asy1348
Asymptotic behavior of tidal damping in alluvial estuaries
Cai, H.; Savenije, H.H.G.
2013-01-01
Tidal wave propagation can be described analytically by a set of four implicit equations, i.e., the phase lag equation, the scaling equation, the damping equation, and the celerity equation. It is demonstrated that this system of equations has an asymptotic solution for an infinite channel,
The Asymptotic Solution for the Steady Variable-Viscosity Free ...
African Journals Online (AJOL)
Under an arbitrary time-dependent heating of an infinite vertical plate (or wall), the steady viscosity-dependent free convection flow of a viscous incompressible fluid is investigated. Using the asymptotic method of solution on the governing equations of motion and energy, the resulting Ordinary differential equations were ...
From A to Z : Asymptotic expansions by van Zwet
Albers, Willem/Wim; de Gunst, Mathisca; Klaasen, Chris; van der Vaart, Aad
2001-01-01
Refinements of first order asymptotic results axe reviewed, with a number of Ph.D. projects supervised by van Zwet serving as stepping stones. Berry-Esseen bounds and Edgeworth expansions are discussed for R-, L- and [/-statistics. After these special classes, the question about a general second
Conformal techniques for OPE in asymptotically free quantum field theory
International Nuclear Information System (INIS)
Craigie, N.S.; Dobrev, V.K.
1982-06-01
We discuss the relationship between the short-distance behaviour of vertex functions and conformal invariance in asymptotically free theories. We show how conformal group techniques can be used to derive spectral representations of wave functions and vertex functions in QCD. (author)
Asymptotics of sums of lognormal random variables with Gaussian copula
DEFF Research Database (Denmark)
Asmussen, Søren; Rojas-Nandayapa, Leonardo
2008-01-01
Let (Y1, ..., Yn) have a joint n-dimensional Gaussian distribution with a general mean vector and a general covariance matrix, and let Xi = eYi, Sn = X1 + ⋯ + Xn. The asymptotics of P (Sn > x) as n → ∞ are shown to be the same as for the independent case with the same lognormal marginals. In part...
The running QCD coupling in the pre-asymptotic region
Energy Technology Data Exchange (ETDEWEB)
Burgio, G.; Di Renzo, F.; Parrinello, C.; Pittori, C
1999-03-01
We study deviations from the perturbative asymptotic behaviour in the running QCD coupling by analysing non-perturbative measurements of {alpha}{sub s}(p) at low momenta (p {approx} 2 GeV) as obtained from the lattice three-gluon vertex. Our exploratory study provides some evidence for power corrections to the perturbative running proportional to 1/p{sup 2}.
Asymptotic analysis of methane-hydrogen-air mixtures
Hermanns, R.T.E.; Bastiaans, R.J.M.; Goey, de L.P.H.
2005-01-01
In this paper an asymptotic analysis of de Goey et al.concerning premixed stoichiometric methane-hydrogen-air flames is analyzed in depth. The analysis is performed with up to 50 mole percent of hydrogen in the fuel, at gas inlet temperatures ranging from 300 K to 650 K and pressures from 1 to 15
Asymptotic behaviour of a rescattering series for nonlinear reggeons
International Nuclear Information System (INIS)
Akkelin, S.V.; Martynov, E.S.
1990-01-01
A series of elastic re-scattering (both quasi-eikonal and U-matrix ones) for reggeons with nonlinear trajectories are estimated asymptotically. The calculations are performed for models of supercritical and dipole pomerons. A weak dependence of the series of re-scattering on reggeon trajectory nonlinearity is revealed. 13 refs.; 3 figs
Asymptotics and Numerics for Laminar Flow over Finite Flat Plate
Dijkstra, D.; Kuerten, J.G.M.; Kaper, Hans G.; Garbey, Mare; Pieper, Gail W.
1992-01-01
A compilation of theoretical results from the literature on the finite flat-plate flow at zero incidence is presented. This includes the Blasius solution, the Triple Deck at the trailing edge, asymptotics in the wake, and properties near the edges of the plate. In addition, new formulas for skin
Outwards pointing hysteresis operators and asymptotic behaviour of evolution equations
Czech Academy of Sciences Publication Activity Database
Klein, O.; Krejčí, Pavel
2003-01-01
Roč. 4, č. 5 (2003), s. 755-785 ISSN 1468-1218 Keywords : hysteresis operators * Prandtl-Ishlinskii operator * asymptotic behaviour Subject RIV: BA - General Mathematics Impact factor: 0.257, year: 2003 http://www.wias-berlin.de/preprint/748/wias_preprints_748.pdf
Asymptotic Structure of the Seismic Radiation from an Explosive Column
Directory of Open Access Journals (Sweden)
Marco Rosales-Vera
2018-01-01
Full Text Available We study the structure of the seismic radiation in the far field produced by an explosive column. Using an asymptotic solution for the far field of vibration (Heelan’s solution, we find analytical expressions to the peak particle velocity (PPV diagrams. These results are extended to the case of a charge with finite velocity of detonation.
Level shift and charm mass: a test of asymptotic planarity
International Nuclear Information System (INIS)
Palmer, W.F.; Pinsky, S.S.; Shi, C.C.
1976-01-01
Level shifts and mixings away from exact exchange degeneracy are examined with respect to the ''asymptotic planarity'' predictions of Chew and Rosenzweig. It is found that the data in the J/sup P/ = 0 - , 1 - , and 2 + multiplets support neither the general shape nor the special relation proposed by Chew and Rosenzweig for the tensor and vector ''cylinder'' corrections
Asymptotic Expansions of Generalized Nevanlinna Functions and their Spectral Properties
Derkach, Vladimir; Hassi, Seppo; de Snoo, Hendrik
2007-01-01
Asymptotic expansions of generalized Nevanlinna functions Q are investigated by means of a factorization model involving a part of the generalized zeros and poles of nonpositive type of the function Q. The main results in this paper arise from the explicit construction of maximal Jordan chains in
High energy asymptotics of the scattering amplitude for the ...
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
Keywords. Scattering matrix; asymptotic expansion; high energy; diagonal singula- ..... (see subsection 2 of § 3) with functions of the generator of dilations. A = 1. 2 d ..... ness in quantum scattering theory, Ann. Inst. Henri Poincaré, Phys. Théor.
Models of Regge behaviour in an asymptotically free theory
International Nuclear Information System (INIS)
Polkinghorne, J.C.
1976-01-01
Two simple Feynman integral models are presented which reproduce the features expected to be of physical importance in the Regge behaviour of asymptotically free theories. Analysis confirms the result, expected on general grounds, that phi 3 in six dimensions has an essential singularity at l=-1. The extension to gauge theories is discussed. (Auth.)
Some asymptotic theory for variance function smoothing | Kibua ...
African Journals Online (AJOL)
Simple selection of the smoothing parameter is suggested. Both homoscedastic and heteroscedastic regression models are considered. Keywords: Asymptotic, Smoothing, Kernel, Bandwidth, Bias, Variance, Mean squared error, Homoscedastic, Heteroscedastic. > East African Journal of Statistics Vol. 1 (1) 2005: pp. 9-22 ...
Pointwise asymptotic convergence of solutions for a phase separation model
Czech Academy of Sciences Publication Activity Database
Krejčí, Pavel; Zheng, S.
2006-01-01
Roč. 16, č. 1 (2006), s. 1-18 ISSN 1078-0947 Institutional research plan: CEZ:AV0Z10190503 Keywords : phase-field system * asymptotic phase separation * energy Subject RIV: BA - General Mathematics Impact factor: 1.087, year: 2006 http://aimsciences.org/journals/pdfs.jsp?paperID=1875&mode=full
Asymptotic behavior of second-order impulsive differential equations
Directory of Open Access Journals (Sweden)
Haifeng Liu
2011-02-01
Full Text Available In this article, we study the asymptotic behavior of all solutions of 2-th order nonlinear delay differential equation with impulses. Our main tools are impulsive differential inequalities and the Riccati transformation. We illustrate the results by an example.
A convergence theorem for asymptotic expansions of Feynman amplitudes
International Nuclear Information System (INIS)
Mabouisson, A.P.C.
1999-06-01
The Mellin representations of Feynman integrals is revisited. From this representation, and asymptotic expansion for generic Feynman amplitudes, for any set of invariants going to zero or to ∞, may be obtained. In the case of all masses going to zero in Euclidean metric, we show that the truncated expansion has a rest compatible with convergence of the series. (author)
Tail asymptotics for dependent subexponential diﬀerences
DEFF Research Database (Denmark)
Albrecher, H; Asmussen, Søren; Kortschak, D.
We study the asymptotic behavior of P(X − Y > u) as u → ∞, where X is subexponential and X, Y are positive random variables that may be dependent. We give criteria under which the subtraction of Y does not change the tail behavior of X. It is also studied under which conditions the comonotonic co...
Asymptotic absolute continuity for perturbed time-dependent ...
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
We study the notion of asymptotic velocity for a class of perturbed time- ... for Mathematical Physics and Stochastics, funded by a grant from the Danish National Research Foun- .... Using (2.4) we can readily continue α(t) to the whole half-axis.
Technicolor and the asymptotic behavior of dynamically generated masses
International Nuclear Information System (INIS)
Natale, A.A.
1984-01-01
Arguments are given in favor of a hard asymptotic behavior of dynamically generated masses, its consequences for technicolor models are analyzed and a model is proposed, where effects of flavor changing neutral currents are highly supressed and pseudo Goldstone bosons get masses of O(30-90) GeV. (Author) [pt
Ergodic Retractions for Families of Asymptotically Nonexpansive Mappings
Directory of Open Access Journals (Sweden)
Saeidi Shahram
2010-01-01
Full Text Available We prove some theorems for the existence of ergodic retractions onto the set of common fixed points of a family of asymptotically nonexpansive mappings. Our results extend corresponding results of Benavides and Ramírez (2001, and Li and Sims (2002.
Formal matched asymptotics for degenerate Ricci flow neckpinches
International Nuclear Information System (INIS)
Angenent, Sigurd B; Isenberg, James; Knopf, Dan
2011-01-01
Gu and Zhu (2008 Commun. Anal. Geom. 16 467–94) have shown that type-II Ricci flow singularities develop from nongeneric rotationally symmetric Riemannian metrics on S n+1 (n≥2). In this paper, we describe and provide plausibility arguments for a detailed asymptotic profile and rate of curvature blow-up that we predict such solutions exhibit
Deep inelastic scattering in an asymptotically free gauge theory
International Nuclear Information System (INIS)
Fujiwara, Tsutomu
1977-01-01
This paper reviews the success of the asymptotically free gauge theory which describes the deep inelastic lepton-hadron scattering. The asymptotically free gauge theory was discussed as well as the reason why the parton has the nature like free particles by the aid of the field theory. The asymptotically free gauge theory (AFGT) gives the prediction that the Bjorken scaling gives rise to logarithmic violation. The theory was applied to the exchange processes of single photon and two photons. First, this paper describes the approaches to the Bjorken scaling. The approaches are the discussion of the scaling law dependent on the model and the discussion of the scaling law independent of the model. The field theoretical treatment in described. This is called the method of the renormalization group introduced by Wilson. The asymptotically free gauge theory was formed on the basis of the Callan-Symanzik equation (CSE) and of the Weinberg's power counting theorem. The exact Bjorken scaling does not hold in the quantum field theory, at least there must be logarithmic violation. The pattern of the scaling violation cannot be clarified by the present data. Discussions concerning two gamma process are presented. The measurement of the photon-photon scattering process will give the judgement whether the prediction of the AFGT is correct or not. (Kato, T.)
Gap asymptotics in a weakly bent leaky quantum wire
Czech Academy of Sciences Publication Activity Database
Exner, Pavel; Kondej, S.
2015-01-01
Roč. 48, č. 49 (2015), s. 495301 ISSN 1751-8113 R&D Projects: GA ČR(CZ) GA14-06818S Institutional support: RVO:61389005 Keywords : singular Schroedinger operators * delta interaction * leaky quantum wires * weak perturbation * asymptotic expansion Subject RIV: BE - Theoretical Physics Impact factor: 1.933, year: 2015
Chemical Analysis of Asymptotic Giant Branch Stars in M62
Lapenna, E.; Mucciarelli, A.; Ferraro, F. R.; Origlia, L.; Lanzoni, B.; Massari, D.; Dalessandro, E.
2015-01-01
We have collected UVES-FLAMES high-resolution spectra for a sample of 6 asymptotic giant branch (AGB) and 13 red giant branch (RGB) stars in the Galactic globular cluster (GC) M62 (NGC 6266). Here we present the detailed abundance analysis of iron, titanium, and light elements (O, Na, Mg, and Al).
On asymptotic isotropy for a hydrodynamic model of liquid crystals
Czech Academy of Sciences Publication Activity Database
Dai, M.; Feireisl, Eduard; Rocca, E.; Schimperna, G.; Schonbek, M.E.
2016-01-01
Roč. 97, 3-4 (2016), s. 189-210 ISSN 0921-7134 Grant - others:European Research Council(XE) MATHEF(320078) Institutional support: RVO:67985840 Keywords : liquid crystal * Q-tensor description * long-time behavior Subject RIV: BA - General Mathematics Impact factor: 0.933, year: 2016 http://content.iospress.com/articles/asymptotic- analysis /asy1348