Diabatic constrained relativistic mean field approach
L"u, H F; Meng, J
2005-01-01
A diabatic (configuration-fixed) constrained approach to calculate the potential energy surface (PES) of the nucleus is developed in the relativistic mean field model. The potential energy surfaces of $^{208}$Pb obtained from both adiabatic and diabatic constrained approaches are investigated and compared. The diabatic constrained approach enables one to decompose the segmented PES obtained in usual adiabatic approaches into separate parts uniquely characterized by different configurations, to define the single particle orbits at very deformed region by their quantum numbers, and to obtain several well defined deformed excited states which can hardly be expected from the adiabatic PES's.
Relativistic mean field description of cluster radioactivity
Bhagwat, A.; Gambhir, Y. K.
2005-01-01
Comprehensive investigations of the observed cluster radioactivity are carried out. First, the relativistic mean field (RMF) theory is employed for the calculations of the ground-state properties of relevant nuclei. The calculations reproduce the experiment well. The calculated RMF point densities are folded with the density-dependent M3Y nucleon-nucleon interaction to obtain the cluster-daughter interaction potential. This, along with the calculated and experimental Q values, is used in the WKB approximation for estimating the half-lives of the parent nuclei against cluster decay. The calculations qualitatively agree with the experiment. Sensitive dependence of the half-lives on Q values is explicitly demonstrated.
Relativistic mean-field mass models
Peña-Arteaga, D.; Goriely, S.; Chamel, N.
2016-10-01
We present a new effort to develop viable mass models within the relativistic mean-field approach with density-dependent meson couplings, separable pairing and microscopic estimations for the translational and rotational correction energies. Two interactions, DD-MEB1 and DD-MEB2, are fitted to essentially all experimental masses, and also to charge radii and infinite nuclear matter properties as determined by microscopic models using realistic interactions. While DD-MEB1 includes the σ, ω and ρ meson fields, DD-MEB2 also considers the δ meson. Both mass models describe the 2353 experimental masses with a root mean square deviation of about 1.1 MeV and the 882 measured charge radii with a root mean square deviation of 0.029 fm. In addition, we show that the Pb isotopic shifts and moments of inertia are rather well reproduced, and the equation of state in pure neutron matter as well as symmetric nuclear matter are in relatively good agreement with existing realistic calculations. Both models predict a maximum neutron-star mass of more than 2.6 solar masses, and thus are able to accommodate the heaviest neutron stars observed so far. However, the new Lagrangians, like all previously determined RMF models, present the drawback of being characterized by a low effective mass, which leads to strong shell effects due to the strong coupling between the spin-orbit splitting and the effective mass. Complete mass tables have been generated and a comparison with other mass models is presented.
Relativistic mean-field mass models
Pena-Arteaga, D.; Goriely, S.; Chamel, N. [Universite Libre de Bruxelles, Institut d' Astronomie et d' Astrophysique, CP-226, Brussels (Belgium)
2016-10-15
We present a new effort to develop viable mass models within the relativistic mean-field approach with density-dependent meson couplings, separable pairing and microscopic estimations for the translational and rotational correction energies. Two interactions, DD-MEB1 and DD-MEB2, are fitted to essentially all experimental masses, and also to charge radii and infinite nuclear matter properties as determined by microscopic models using realistic interactions. While DD-MEB1 includes the σ, ω and ρ meson fields, DD-MEB2 also considers the δ meson. Both mass models describe the 2353 experimental masses with a root mean square deviation of about 1.1 MeV and the 882 measured charge radii with a root mean square deviation of 0.029 fm. In addition, we show that the Pb isotopic shifts and moments of inertia are rather well reproduced, and the equation of state in pure neutron matter as well as symmetric nuclear matter are in relatively good agreement with existing realistic calculations. Both models predict a maximum neutron-star mass of more than 2.6 solar masses, and thus are able to accommodate the heaviest neutron stars observed so far. However, the new Lagrangians, like all previously determined RMF models, present the drawback of being characterized by a low effective mass, which leads to strong shell effects due to the strong coupling between the spin-orbit splitting and the effective mass. Complete mass tables have been generated and a comparison with other mass models is presented. (orig.)
Relativistic Consistent Angular-Momentum Projected Shell-Model:Relativistic Mean Field
LI Yan-Song; LONG Gui-Lu
2004-01-01
We develop a relativistic nuclear structure model, relativistic consistent angular-momentum projected shellmodel (RECAPS), which combines the relativistic mean-field theory with the angular-momentum projection method.In this new model, nuclear ground-state properties are first calculated consistently using relativistic mean-field (RMF)theory. Then angular momentum projection method is used to project out states with good angular momentum from a few important configurations. By diagonalizing the hamiltonian, the energy levels and wave functions are obtained.This model is a new attempt for the understanding of nuclear structure of normal nuclei and for the prediction of nuclear properties of nuclei far from stability. In this paper, we will describe the treatment of the relativistic mean field. A computer code, RECAPS-RMF, is developed. It solves the relativistic mean field with axial-symmetric deformation in the spherical harmonic oscillator basis. Comparisons between our calculations and existing relativistic mean-field calculations are made to test the model. These include the ground-state properties of spherical nuclei 16O and 208Pb,the deformed nucleus 20Ne. Good agreement is obtained.
Spurious Shell Closures in the Relativistic Mean Field Model
Geng, L S; Toki, H; Long, W H; Shen, G
2006-01-01
Following a systematic theoretical study of the ground-state properties of over 7000 nuclei from the proton drip line to the neutron drip line in the relativistic mean field model [Prog. Theor. Phys. 113 (2005) 785], which is in fair agreement with existing experimental data, we observe a few spurious shell closures, i.e. proton shell closures at Z=58 and Z=92. These spurious shell closures are found to persist in all the effective forces of the relativistic mean field model, e.g. TMA, NL3, PKDD and DD-ME2.
General Relativistic Mean Field Theory for rotating nuclei
Madokoro, Hideki [Kyushu Univ., Fukuoka (Japan). Dept. of Physics; Matsuzaki, Masayuki
1998-03-01
The {sigma}-{omega} model Lagrangian is generalized to an accelerated frame by using the technique of general relativity which is known as tetrad formalism. We apply this model to the description of rotating nuclei within the mean field approximation, which we call General Relativistic Mean Field Theory (GRMFT) for rotating nuclei. The resulting equations of motion coincide with those of Munich group whose formulation was not based on the general relativistic transformation property of the spinor fields. Some numerical results are shown for the yrast states of the Mg isotopes and the superdeformed rotational bands in the A {approx} 60 mass region. (author)
Cranked Relativistic Mean Field Description of Superdeformed Rotational Bands
Afanasjev, A. V.; Lalazissis, G. A.; Ring, P.
1997-01-01
The cranked relativistic mean field theory is applied for a detailed investigation of eight superdeformed rotational bands observed in $^{151}$Tb. It is shown that this theory is able to reproduce reasonably well not only the dynamic moments of inertia $J^{(2)}$ of the observed bands but also the alignment properties of the single-particle orbitals.
Cluster decay in very heavy nuclei in Relativistic Mean Field
Bhattacharya, Madhubrata; Gangopadhyay, G.
2008-01-01
Exotic cluster decay of very heavy nuclei has been studied in the microscopic Super-Asymmetric Fission Model. Relativistic Mean Field model with the force FSU Gold has been employed to obtain the densities of the cluster and the daughter nuclei. The microscopic nuclear interaction DDM3Y1, which has an exponential density dependence, and the Coulomb interaction have been used in the double folding model to obtain the potential between the cluster and the daughter. Half life values have been ca...
Relativistic Mean Field Study on Halo Structures of Mirror Nuclei
LIANG Yu-Jie; LI Yan-Song; LIU Zu-Hua; ZHOU Hong-Yu
2009-01-01
Halo structures of some light mirror nuclei are investigated with the relativistic mean field (RMF) theory.The calculations show that the dispersion of the valence proton is larger than that of the valence neutron in its mirror nucleus,the difference between the root-mean-square (rms) radius of the valence nucleon in each pair of mirror nuclei becomes smailer with the increase of the mass number A,and all the ratios of the rms radius of the valence nucleon to that of the matter in each pair o~ mirror nuclei decrease almost linearly with the increase of the mass number A.
A New Parameter Set for the Relativistic Mean Field Theory
Nerlo-Pomorska, B; Nerlo-Pomorska, Bozena; Sykut, Joanna
2004-01-01
Subtracting the Strutinsky shell corrections from the selfconsistent energies obtained within the Relativistic Mean Field Theory (RMFT) we have got estimates for the macroscopic part of the binding energies of 142 spherical even-even nuclei. By minimizing their root mean square deviations from the values obtained with the Lublin-Srasbourg Drop (LSD) model with respect to the nine RMFT parameters we have found the optimal set (NL4). The new parameters reproduce also the radii of these nuclei with an accuracy comparable with that obtained with the NL1 and NL3 sets.
Relativistic Mean-Field Models and Nuclear Matter Constraints
Dutra, M; Carlson, B V; Delfino, A; Menezes, D P; Avancini, S S; Stone, J R; Providência, C; Typel, S
2013-01-01
This work presents a preliminary study of 147 relativistic mean-field (RMF) hadronic models used in the literature, regarding their behavior in the nuclear matter regime. We analyze here different kinds of such models, namely: (i) linear models, (ii) nonlinear \\sigma^3+\\sigma^4 models, (iii) \\sigma^3+\\sigma^4+\\omega^4 models, (iv) models containing mixing terms in the fields \\sigma and \\omega, (v) density dependent models, and (vi) point-coupling ones. In the finite range models, the attractive (repulsive) interaction is described in the Lagrangian density by the \\sigma (\\omega) field. The isospin dependence of the interaction is modeled by the \\rho meson field. We submit these sets of RMF models to eleven macroscopic (experimental and empirical) constraints, used in a recent study in which 240 Skyrme parametrizations were analyzed. Such constraints cover a wide range of properties related to symmetric nuclear matter (SNM), pure neutron matter (PNM), and both SNM and PNM.
Cluster decay in very heavy nuclei in Relativistic Mean Field
Bhattacharya, Madhubrata
2008-01-01
Exotic cluster decay of very heavy nuclei has been studied in the microscopic Super-Asymmetric Fission Model. Relativistic Mean Field model with the force FSU Gold has been employed to obtain the densities of the cluster and the daughter nuclei. The microscopic nuclear interaction DDM3Y1, which has an exponential density dependence, and the Coulomb interaction have been used in the double folding model to obtain the potential between the cluster and the daughter. Half life values have been calculated in the WKB approximation and the spectroscopic factors have been extracted. The latter values are seen to have a simple dependence of the mass of the cluster as has been observed earlier. Predictions have been made for some possible decays.
Quantum Corrections on Relativistic Mean Field Theory for Nuclear Matter
ZHANG Qi-Ren; GAO Chun-Yuan
2011-01-01
We propose a quantization procedure for the nucleon-scalar meson system, in which an arbitrary mean scalar meson field Φ is introduced.The equivalence of this procedure with the usual one is proven for any given value of Φ.By use of this procedure, the scalar meson field in the Walecka's MFA and in Chin's RHA are quantized around the mean field.Its corrections on these theories are considered by perturbation up to the second order.The arbitrariness of Φ makes us free to fix it at any stage in the calculation.When we fix it in the way of Walecka's MFA, the quantum corrections are big, and the result does not converge.When we fix it in the way of Chin's RHA, the quantum correction is negligibly small, and the convergence is excellent.It shows that RHA covers the leading part of quantum field theory for nuclear systems and is an excellent zeroth order approximation for further quantum corrections, while the Walecka's MFA does not.We suggest to fix the parameter Φ at the end of the whole calculation by minimizing the total energy per-nucleon for the nuclear matter or the total energy for the finite nucleus, to make the quantized relativistic mean field theory (QRMFT) a variational method.
Relativistic mean-field models and nuclear matter constraints
Dutra, M.; Lourenco, O.; Carlson, B. V. [Departamento de Fisica, Instituto Tecnologico de Aeronautica-CTA, 12228-900, Sao Jose dos Campos, SP (Brazil); Delfino, A. [Instituto de Fisica, Universidade Federal Fluminense, 24210-150, Boa Viagem, Niteroi, RJ (Brazil); Menezes, D. P.; Avancini, S. S. [Departamento de Fisica, CFM, Universidade Federal de Santa Catarina, CP. 476, CEP 88.040-900, Florianopolis, SC (Brazil); Stone, J. R. [Oxford Physics, University of Oxford, OX1 3PU Oxford (United Kingdom) and Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996 (United States); Providencia, C. [Centro de Fisica Computacional, Department of Physics, University of Coimbra, P-3004-516 Coimbra (Portugal); Typel, S. [GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, Theorie, Planckstrasse 1,D-64291 Darmstadt (Germany)
2013-05-06
This work presents a preliminary study of 147 relativistic mean-field (RMF) hadronic models used in the literature, regarding their behavior in the nuclear matter regime. We analyze here different kinds of such models, namely: (i) linear models, (ii) nonlinear {sigma}{sup 3}+{sigma}{sup 4} models, (iii) {sigma}{sup 3}+{sigma}{sup 4}+{omega}{sup 4} models, (iv) models containing mixing terms in the fields {sigma} and {omega}, (v) density dependent models, and (vi) point-coupling ones. In the finite range models, the attractive (repulsive) interaction is described in the Lagrangian density by the {sigma} ({omega}) field. The isospin dependence of the interaction is modeled by the {rho} meson field. We submit these sets of RMF models to eleven macroscopic (experimental and empirical) constraints, used in a recent study in which 240 Skyrme parametrizations were analyzed. Such constraints cover a wide range of properties related to symmetric nuclear matter (SNM), pure neutron matter (PNM), and both SNM and PNM.
Green's function relativistic mean field theory for Λ hypernuclei
Ren, S.-H.; Sun, T.-T.; Zhang, W.
2017-05-01
The relativistic mean field theory with the Green's function method is extended to study Λ hypernuclei. Taking the hypernucleus Ca61Λ as an example, the single-particle resonant states for Λ hyperons are investigated by analyzing the density of states, and the corresponding energies and widths are given. Different behaviors are observed for the resonant states, i.e., the distributions of the very narrow 1 f5 /2 and 1 f7 /2 states are very similar to bound states while those of the wide 1 g7 /2 and 1 g9 /2 states are like scattering states. Besides, the impurity effect of Λ hyperons on the single-neutron resonant states is investigated. For most of the resonant states, both the energies and widths decrease with adding more Λ hyperons due to the attractive Λ N interaction. Finally, the energy level structure of Λ hyperons in the Ca hypernucleus isotopes with mass number A =53 -73 are studied; obvious shell structure and small spin-orbit splitting are found for the single-Λ spectrum.
Tidal deformability of neutron and hyperon star with relativistic mean field equations of state
Kumar, Bharat; Patra, S K
2016-01-01
We systematically study the tidal deformability for neutron and hyperon stars using relativistic mean field (RMF) equations of state (EOSs). The tidal effect plays an important role during the early part of the evolution of compact binaries. Although, the deformability associated with the EOSs has a small correction, it gives a clean gravitational wave signature in binary inspiral. These are characterized by various love numbers kl (l=2, 3, 4), that depend on the EOS of a star for a given mass and radius. The tidal effect of star could be efficiently measured through advanced LIGO detector from the final stages of inspiraling binary neutron star (BNS) merger.
Tidal deformability of neutron and hyperon stars within relativistic mean field equations of state
Kumar, Bharat; Biswal, S. K.; Patra, S. K.
2017-01-01
We systematically study the tidal deformability for neutron and hyperon stars using relativistic mean field equations of state (EOSs). The tidal effect plays an important role during the early part of the evolution of compact binaries. Although, the deformability associated with the EOSs has a small correction, it gives a clean gravitational wave signature in binary inspiral. These are characterized by various Love numbers kl(l =2 ,3 ,4 ), that depend on the EOS of a star for a given mass and radius. The tidal effect of star could be efficiently measured through an advanced LIGO detector from the final stages of an inspiraling binary neutron star merger.
COMPRESSIBILITY OF NUCLEI IN RELATIVISTIC MEAN FIELD-THEORY
BOERSMA, HF; MALFLIET, R; SCHOLTEN, O
1991-01-01
Using the relativistic Hartree approximation in the sigma-omega model we study the isoscalar giant monopole resonance. It is shown that the ISGMR of lighter nuclei has non-negligible anharmonic terms. The compressibility of nuclear matter is determined using a leptodermous expansion.
Hot and dense matter beyond relativistic mean field theory
Zhang, Xilin
2016-01-01
Properties of hot and dense matter are calculated in the framework of quantum hadro-dynamics by including contributions from two-loop (TL) diagrams arising from the exchange of iso-scalar and iso-vector mesons between nucleons. Our extension of mean-field theory (MFT) employs the same five density-independent coupling strengths which are calibrated using the empirical properties at the equilibrium density of iso-spin symmetric matter. Results of calculations from the MFT and TL approximations are compared for conditions of density, temperature, and proton fraction encountered in astrophysics applications involving compact objects. The TL results for the equation of state (EOS) of cold pure neutron matter at sub- and near-nuclear densities agree well with those of modern quantum Monte Carlo and effective field-theoretical approaches. Although the high-density EOS in the TL approximation for neutron-star matter is substantially softer than its MFT counterpart, it is able to support a $2M_\\odot$ neutron star req...
Quantum corrections to the Relativistic mean-field theory
Maydanyuk, Sergei P; Bakry, Ahmed
2016-01-01
In this paper, we compare the RMF theory and the model of deformed oscillator shells (DOS) in description of the quantum properties of the bound states of the spherically symmetric light nuclei. We obtain an explicit analytical relation between differential equations for the RMF theory and DOS model, which determine wave functions for nucleons. On such a basis we perform analysis of correspondence of quantum properties of nuclei. We find: (1) Potential $V_{RMF}$ of the RMF theory for nucleons has the wave functions $f$ and $g$ with joint part $h$ coincident exactly with the nucleon wave function of DOS model with potential $V_{\\rm shell}$. But, a difference between $V_{RMF}$ and $V_{\\rm shell}$ is essential for any nucleus. (2) The nucleon wave functions and densities obtained by the DOS and RMF theories are essentially different. The nucleon densities of the RMF theory contradict to knowledge about distribution of the proton and neutron densities inside the nuclei obtained from experimental data. This indica...
Analytic Beyond-Mean-Field BEC Wave Functions
Dunn, Martin; Laing, W. Blake; Watson, Deborah K.; Loeser, John G.
2006-05-01
We present analytic N-body beyond-mean-field wave functions for Bose-Einstein condensates. This extends our previous beyond-mean-field energy calculations to the substantially more difficult problem of determining correlated N-body wave functions for a confined system. The tools used to achieve this have been carefully chosen to maximize the use of symmetry and minimize the dependence on numerical computation. We handle the huge number of interactions when N is large (˜N^2/2 two-body interactions) by bringing together three theoretical methods. These are dimensional perturbation theory, the FG method of Wilson et al, and the group theory of the symmetric group. The wave function is then used to derive the density profile of a condensate in a cylindrical trap.This method makes no assumptions regarding the form or strength of the interactions and is applicable to both small-N and large-N systems.
Relativistic spherical plasma waves
Bulanov, S. S.; Maksimchuk, A.; Schroeder, C. B.; Zhidkov, A. G.; Esarey, E.; Leemans, W. P.
2012-02-01
Tightly focused laser pulses that diverge or converge in underdense plasma can generate wake waves, having local structures that are spherical waves. Here we study theoretically and numerically relativistic spherical wake waves and their properties, including wave breaking.
Multiple chiral doublet candidate nucleus $^{105}$Rh in a relativistic mean-field approach
Li, Jian; Meng, J; 10.1103/PhysRevC.83.037301
2011-01-01
Following the reports of two pairs of chiral doublet bands observed in $^{105}$Rh, the adiabatic and configuration-fixed constrained triaxial relativistic mean-field (RMF) calculations are performed to investigate their triaxial deformations with the corresponding configuration and the possible multiple chiral doublet (M$\\chi$D) phenomenon. The existence of M$\\chi$D phenomenon in $^{105}$Rh is highly expected.
Shape Coexistence for 179Hg in Relativistic Mean-Field Theory
WANG Nan; MENG Jie; ZHAO En-Guang
2005-01-01
The potential energy surface of179 Hg is traced and the multi-shape coexistence phenomenon in that nucleus is studied within the relativistic mean-field theory with quadrupole moment constraint. The calculation results of binding energies and charge radii of mercury isotopes are in good agreement with the experimental data.
One-Proton Halo in 31Cl with Relativistic Mean-Field Theory
蔡翔舟; 沈文庆; 任中洲; 蒋维洲; 方德清; 张虎勇; 钟晨; 魏义彬; 郭威; 马余刚; 朱志远
2002-01-01
We investigate proton-rich isotopes s1,32Cl using the nonlinear relativistic mean-field model. It is shown that this model can reproduce the properties of these nuclei well. A long tail appears in the calculated proton density distribution of 31 Cl. The results of relativistic density-dependent Hartree theory show a similar trend of tail density distribution. It is strongly suggested that there is a proton halo in 31Cl and it is indicated that there may be a proton skin in 32 Cl. The relation between the proton halo in 31Cl and the new proton magic number is discussed.
Beyond the relativistic mean-field approximation (III): collective Hamiltonian in five dimensions
Niksic, T; Vretenar, D; Prochniak, L; Meng, J; Ring, P
2008-01-01
The framework of relativistic energy density functionals is extended to include correlations related to restoration of broken symmetries and fluctuations of collective variables. A model is developed for the solution of the eigenvalue problem of a five-dimensional collective Hamiltonian for quadrupole vibrational and rotational degrees of freedom, with parameters determined by constrained self-consistent relativistic mean-field calculations for triaxial shapes. The model is tested in a series of illustrative calculations of potential energy surfaces and the resulting collective excitation spectra and transition probabilities of the chain of even-even gadolinium isotopes.
Systematic nuclear structure studies using relativistic mean field theory in mass region A ˜ 130
Shukla, A.; Åberg, Sven; Bajpeyi, Awanish
2017-02-01
Nuclear structure studies for even-even nuclei in the mass region \\backsim 130, have been performed, with a special focus around N or Z = 64. On the onset of deformation and lying between two closed shell, these nuclei have attracted attention in a number of studies. A revisit to these experimentally accessible nuclei has been made via the relativistic mean field. The role of pairing and density depletion in the interior has been specially investigated. Qualitative analysis between two versions of relativistic mean field suggests that there is no significant difference between the two approaches. Moreover, the role of the filling {{{s}}}1/2 orbital in density depletion towards the centre has been found to be consistent with our earlier work on the subject Shukla and Åberg (2014 Phys. Rev. C 89 014329).
Proton rich nuclei at and beyond the proton drip line in the Relativistic Mean Field theory
Geng, L S; Meng, J
2003-01-01
The Relativistic Mean Field theory is applied to the analysis of ground-state properties of deformed proton-rich odd-Z nuclei in the region $55\\le Z \\le 73$ >. The model uses the TMA and NL3 effective interactions in the mean-field Lagrangian, and describes pairing correlations by the density-independent delta-function interaction. The model predicts the location of the proton drip line, the ground-state quadrupole deformation, one-proton separation energy at and beyond the proton drip line, the deformed single-particle orbital occupied by the odd valence proton and the corresponding spectroscopic factor. The results are in good agreement with the available experimental data except for some odd-odd nuclei in which the proton-neutron pairing may become important and are close to those of Relativistic Hartree-Bogoliubov model.
Description of $^{178}$Hf$^{m2}$ in the constrained relativistic mean field theory
Wei, Zhang; Shuang-Quan, Zhang
2009-01-01
The properties of the ground state of $^{178}$Hf and the isomeric state $^{178}$Hf$^{m2}$ are studied within the adiabatic and diabatic constrained relativistic mean field (RMF) approaches. The RMF calculations reproduce well the binding energy and the deformation for the ground state of $^{178}$Hf. Using the ground state single-particle eigenvalues obtained in the present calculation, the lowest excitation configuration with $K^\\pi=16^+$ is found to be $\
Restoration of rotational symmetry in deformed relativistic mean-field theory
YAO Jiang-Ming; MENG Jie; Pena Arteaga Daniel; Ring Peter
2009-01-01
We report on a very recently developed three-dimensional angular momentum projected relativistic mean-field theory with point-coupling interaction (3DAMP+RMF-PC). Using this approach the same effective nucleon-nucleon interaction is adopted to describe both the single-particle and collective motions in nuclei.Collective states with good quantum angular momentum are built projecting out the intrinsic deformed meanfield states. Results for 24Mg are shown as an illustrative application.
Finite Size Corrected Relativistic Mean-Field Model and QCD Critical End Point
Uddin, Saeed; Ahmad, Jan Shabir
2012-01-01
The effect of finite size of hadrons on the QCD phase diagram is analyzed using relativistic mean field model for the hadronic phase and the Bag model for the QGP phase. The corrections to the EOS for hadronic phase are incorporated in a thermodynamic consistent manner for Van der Waals like interaction. It is found that the effect of finite size of baryons is to shift CEP to higher chemical potential values.
Relativistic mean field study of the superdeformed rotational bands in the A {approx} 60 mass region
Madokoro, Hideki [Dept. of Physics, Kyushu Univ., Fukuoka (Japan); Matsuzaki, Masayuki
1999-03-01
The superdeformed rotational bands in {sup 62}Zn, which were recently discovered, are examined using Relativistic Mean Field model. The experimental dynamical moments of inertia and deformations are well reproduced, but the calculated bands which seem to correspond to the experimental data do not become yrast. This seems to be connected with the wrong position of the g{sup 9/2} single neutron orbit. (author)
Antimagnetic rotation in 108,110In with tilted axis cranking relativistic mean-field approach
Sun, Wu-Ji; Xu, Hai-Dan; Li, Jian; Liu, Yong-Hao; Ma, Ke-Yan; Yang, Dong; Lu, Jing-Bing; Ma, Ying-Jun
2016-08-01
Based on tilted axis cranking relativistic mean-field theory within point-coupling interaction PC-PK1, the rotational structure and the characteristic features of antimagnetic rotation for ΔI = 2 bands in 108,110In are studied. Tilted axis cranking relativistic mean-field calculations reproduce the experimental energy spectrum well and are in agreement with the experimental I ∼ ω plot, although the calculated spin overestimates the experimental values. In addition, the two-shears-like mechanism in candidate antimagnetic rotation bands is clearly illustrated and the contributions from two-shears-like orbits, neutron (gd) orbits above Z = 50 shell and Z = 50, N = 50 core are investigated microscopically. The predicted B(E2), dynamic moment of inertia ℑ(2), deformation parameters β and γ, and ℑ(2)/B(E2) ratios in tilted axis cranking relativistic mean-field calculations are discussed and the characteristic features of antimagnetic rotation for the bands before and after alignment are shown. Supported by National Natural Science Foundation of China (11205068, 11205069, 11405072, 11475072, 11547308) and China Postdoctoral Science Foundation (2012M520667)
Nuclear Matter in Relativistic Mean Field Theory with Isovector Scalar Meson
Kubis, S
1997-01-01
Relativistic mean field (RMF) theory of nuclear matter with the isovector scalar mean field corresponding to the delta-meson [a_0(980)] is studied. While the delta-meson mean field vanishes in symmetric nuclear matter, it can influence properties of asymmetric nuclear matter in neutron stars. The RMF contribution due to delta-field to the nuclear symmetry energy is negative. To fit the empirical value, E_s=30 MeV, a stronger rho-meson coupling is required than in the absence of the delta-field. The energy per particle of neutron matter is then larger at high densities than the one with no delta-field included. Also, the proton fraction of beta-stable matter increases. Splitting of proton and neutron effective masses due to the delta-field can affect transport properties of neutron star matter.
Neutron Stars in Relativistic Mean Field Theory with Isovector Scalar Meson
Kubis, S; Stachniewicz, S
1998-01-01
We study the equation of state of beta-stable dense matter and models of neutron stars in the relativistic mean field theory with the isovector scalar mean field corresponding to the delta-meson [a_0(980)]. A range of values of the delta-meson coupling compatible with the Bonn potentials is explored. Parameters of the model in the isovector sector are constrained to fit the nuclear symmetry energy, E_s=30 MeV. We find that the quantity most sensitive to the delta-meson coupling is the proton fraction of neutron star matter. It increases significantly in the presence of the delta-field. The energy per baryon also increases but the effect is smaller. The equation of state becomes slightly stiffer and the maximum neutron star mass increases for stronger delta-meson coupling.
Three-dimensional angular momentum projection in relativistic mean-field theory
Yao, J M; Ring, P; Arteaga, D Pena
2009-01-01
Based on a relativistic mean-field theory with an effective point coupling between the nucleons, three-dimensional angular momentum projection is implemented for the first time to project out states with designed angular momentum from deformed intrinsic states generated by triaxial quadrupole constraints. The same effective parameter set PC-F1 of the effective interaction is used for deriving the mean field and the collective Hamiltonian. Pairing correlations are taken into account by the BCS method using both monopole forces and zero range d-forces with strength parameters adjusted to experimental even-odd mass differences. The method is applied successfully to the isotopes 24Mg, 30Mg, and 32Mg.
Relativistic heavy ion collisions with realistic non-equilibrium mean fields
Fuchs, C; Wolter, H H
1996-01-01
We study the influence of non-equilibrium phase space effects on the dynamics of heavy ion reactions within the relativistic BUU approach. We use realistic Dirac-Brueckner-Hartree-Fock (DBHF) mean fields determined for two-Fermi-ellipsoid configurations, i.e. for colliding nuclear matter, in a local phase space configuration approximation (LCA). We compare to DBHF mean fields in the local density approximation (LDA) and to the non-linear Walecka model. The results are further compared to flow data of the reaction Au on Au at 400 MeV per nucleon measured by the FOPI collaboration. We find that the DBHF fields reproduce the experiment if the configuration dependence is taken into account. This has also implications on the determination of the equation of state from heavy ion collisions.
Time-dependent Relativistic Mean-field Theory and Random Phase Approximation
P.Ring; D.Vretenar; A.Wandelt; NguyenVanGiai; MAZhong-yu; CAOLi-gang
2001-01-01
The relativistic random phase approximation (RRPA) is derived from the time-dependent relativistic mean field (TD RMF) theory in the limit of small amplitude oscillations. In the no-sea approximation of the RMF theory, the RRPA configuration space includes not only the usual particle-hole ph-states, but also ah configurations, i.e. pairs formed from occupied states in the Fermi sea and empty negative-energy states in the Dirac sea. The contribution of the negative energy states to the RRPA matrices is examined in a schematic model, and the large effect of Dirac sea states on isoscalar strength distributions is illustrated for the giant monopole resonance in 116Sn. It is shown that
Shell evolution at N=20 in the constrained relativistic mean field approach
无
2008-01-01
The shell evolution at N = 20, a disappearing neutron magic number observed experimentally in very neutron-rich nuclides, is investigated in the constrained relativistic mean field (RMF) theory. The trend of the shell closure observed experimentally towards the neutron drip-line can be reproduced. The predicted two-neutron separation energies, neutron shell gap energies and deformation parameters of ground states are shown as well. These results are compared with the recent Hartree-Fock-Bogliubov (HFB-14) model and the available experimental data. The perspective towards a better understanding of the shell evolution is discussed.
Fission Barrier for 240Pu in the Quadrupole Constrained Relativistic Mean Field Approach
L(U) Hong-Feng; GENG Li-Sheng; MENG Jie
2006-01-01
@@ The fission barrier for 240Pu is investigated beyond the second saddle point in the potential energy surface by the constrained relativistic mean field method with the newly proposed parameter set PK1. The microscopic correction for the centre-of-mass motion is essential to provide the correct potential energy surface. The shell effects that stabilize the nuclei against the fission is also investigated by the Strutinsky method. The shapes for the ground state, fission isomer and saddle-points, etc, are studied in detail.
Delta isobars in relativistic mean-field models with $\\sigma$-scaled hadron masses and couplings
Kolomeitsev, E E; Voskresensky, D N
2016-01-01
We extend the relativistic mean-field models with hadron masses and meson-baryon coupling constants dependent on the scalar $\\sigma$ field, studied previously to incorporate $\\Delta(1232)$ baryons. Available empirical information is analyzed to put constraints on the couplings of $\\Delta$s with meson fields. Conditions for the appearance of $\\Delta$s are studied. We demonstrate that with inclusion of the $\\Delta$s our equations of state continue to fulfill majority of known empirical constraints including the pressure-density constraint from heavy-ion collisions, the constraint on the maximum mass of the neutron stars, the direct Urca and the gravitational-baryon mass ratio constraints.
Pasta phases in neutron star studied with extended relativistic mean field models
Gupta, Neha
2013-01-01
To explain several properties of finite nuclei, infinite matter, and neutron stars in a unified way within the relativistic mean field models, it is important to extend them either with higher order couplings or with density-dependent couplings. These extensions are known to have strong impact in the high-density regime. Here we explore their role on the equation of state at densities lower than the saturation density of finite nuclei which govern the phase transitions associated with pasta structures in the crust of neutron stars.
Ground state properties of La isotopes in reflection asymmetric relativistic mean field theory
无
2009-01-01
The ground state properties of La isotopes are investigated with the reflection asymmetric relativistic mean field(RAS-RMF) model.The calculation results of binding energies and the quadrupole moments are in good agreements with the experiment.The calculation results indicate the change of the quadrupole deformation with the nuclear mass number.The "kink" on the isotope shifts is observed at A = 139 where the neutron number is the magic number N = 82.It is also found that the octupole deformations may exist in the La isotopes with mass number A ～ 145-155.
Ground state properties of La isotopes in reflection asymmetric relativistic mean field theory
WANG Nan; GUO Lu
2009-01-01
The ground state properties of La isotopes are investigated with the reflection asymmetric relativistic mean field (RAS-RMF) model.The calculation results of binding energies and the quadrupole moments are in good agreements with the experiment.The calculation results indicate the change of the quadrupole deformation with the nuclear mass number.The "kink" on the isotope shifts is observed at A=139 where the neutron number is the magic number N=82.It is also found that the octupole deformations may exist in the La isotopes with mass number A～ 145-155.
Proton and neutron skins of light nuclei within the Relativistic Mean Field theory
Geng, L S; Ozawa, A; Meng, J
2004-01-01
The Relativistic Mean Field (RMF) theory is applied to the analysis of ground-state properties of Ne, Na, Cl and Ar isotopes. In particular, we study the recently established proton skin in Ar isotopes and neutron skin in Na isotopes as a function of the difference between the proton and the neutron separation energy. We take the TMA effective interaction in the RMF Lagrangian, and describe pairing correlation by the density-independent delta-function interaction. We calculate single neutron and proton separation energies, quadrupole deformations, nuclear matter radii, and differences in proton radii and neutron radii, and compare these results with the recent experimental data.
Shell-model-like Approach (SLAP) for the Nuclear Properties in Relativistic Mean field Theory
MENG Jie; GUO Jian-you; LIU Lang; ZHANG Shuang-quan
2006-01-01
A Shell-model-like approach suggested to treat the pairing correlations in relativistic mean field theory is introduced,in which the occupancies thus obtained have been iterated back into the densities.The formalism and numerical techniques are given in detail.As examples,the ground state properties and low-lying excited states for Ne isotopes are studied.The results thus obtained are compared with the data available.The binding energies,the odd-even staggering,as well as the tendency for the change of the shapes in Ne isotopes are correctly reproduced.
Relativistic spherical plasma waves
Bulanov, S S; Schroeder, C B; Zhidkov, A G; Esarey, E; Leemans, W P
2011-01-01
Tightly focused laser pulses as they diverge or converge in underdense plasma can generate wake waves, having local structures that are spherical waves. Here we report on theoretical study of relativistic spherical wake waves and their properties, including wave breaking. These waves may be suitable as particle injectors or as flying mirrors that both reflect and focus radiation, enabling unique X-ray sources and nonlinear QED phenomena.
Description of Drip-Line Nuclei within Relativistic Mean-Field Plus BCS Approach
Yadav, H L; Toki, H
2004-01-01
Recently it has been demonstrated, considering Ni and Ca isotopes as prototypes, that the relativistic mean-field plus BCS (RMF+BCS) approach wherein the single particle continuum corresponding to the RMF is replaced by a set of discrete positive energy states for the calculation of pairing energy provides a good approximation to the full relativistic Hartree-Bogoliubov (RHB) description of the ground state properties of the drip-line neutron rich nuclei. The applicability of RMF+BCS is essentially due to the fact that the main contribution to the pairing correlations is provided by the low-lying resonant states. General validity of this approach is demonstrated by the detailed calculations for the ground state properties of the chains of isotopes of O, Ca, Ni, Zr, Sn and Pb nuclei. The TMA and NL-SH force parameter sets have been used for the effective mean-field Lagrangian. Comprehensive results for the two neutron separation energy, rms radii, single particle pairing gaps and pairing energies etc. are pres...
New parameterization of the effective field theory motivated relativistic mean field model
Kumar, Bharat; Singh, S. K.; Agrawal, B. K.; Patra, S. K.
2017-10-01
A new parameter set is generated for finite and infinite nuclear system within the effective field theory motivated relativistic mean field (ERMF) formalism. The isovector part of the ERMF model employed in the present study includes the coupling of nucleons to the δ and ρ mesons and the cross-coupling of ρ mesons to the σ and ω mesons. The results for the finite and infinite nuclear systems obtained using our parameter set are in harmony with the available experimental data. We find the maximum mass of the neutron star to be 2.03M⊙ and yet a relatively smaller radius at the canonical mass, 12.69 km, as required by the available data.
Hyperons in neutron star matter within relativistic mean-field models
Oertel, M; Gulminelli, F; Raduta, A R
2014-01-01
Since the discovery of neutron stars with masses around 2 solar masses the composition of matter in the central part of these massive stars has been intensively discussed. Within this paper we will (re)investigate the question of the appearance of hyperons. To that end we will perform an extensive parameter study within relativistic mean field models. We will show that it is possible to obtain high mass neutron stars (i) with a substantial amount of hyperons, (ii) radii of 12-13 km for the canonical mass of 1.4 solar masses, and (iii) a spinodal instability at the onset of hyperons. The results depend strongly on the interaction in the hyperon-hyperon channels, on which only very little information is available from terrestrial experiments up to now.
B-Spline Finite Elements and their Efficiency in Solving Relativistic Mean Field Equations
Pöschl, W
1997-01-01
A finite element method using B-splines is presented and compared with a conventional finite element method of Lagrangian type. The efficiency of both methods has been investigated at the example of a coupled non-linear system of Dirac eigenvalue equations and inhomogeneous Klein-Gordon equations which describe a nuclear system in the framework of relativistic mean field theory. Although, FEM has been applied with great success in nuclear RMF recently, a well known problem is the appearance of spurious solutions in the spectra of the Dirac equation. The question, whether B-splines lead to a reduction of spurious solutions is analyzed. Numerical expenses, precision and behavior of convergence are compared for both methods in view of their use in large scale computation on FEM grids with more dimensions. A B-spline version of the object oriented C++ code for spherical nuclei has been used for this investigation.
Ground State Properties of Ds Isotopes Within the Relativistic Mean Field Theory
张海飞; 张鸿飞; 李君清
2012-01-01
The ground state properties of Ds (Z=110) isotopes (N=151-195) are studied in the framework of the relativistic mean field (RMF) theory with the effective interaction NL-Z2.The pairing correlation is treated within the conventional BCS approximation.The calculated binding energies are consistent with the results from finite-range droplet model (FRDM) and Macroscopic-microscopic method (MMM).The quadrupole deformation,α-decay energy,α-decay half-live,charge radius,two-neutron separation energy and single-particle spectra are analyzed for Ds isotopes to find new characteristics of superheavy nuclei (SHN).Among the calculated results it is rather distinct that the isotopic shift appears evidently at neutron number N=184.
Description of 178 Hfm2 in the Constrained Relativistic Mean Field Theory
ZHANG Wei; PENG Jing; ZHANG Shuang-Quan
2009-01-01
Properties of the ground state of 178 Hf and the isomeric state 178Hfn2 are studied within the adiabatic and diabatic constrained relativistic mean field (RMF) approaches. The RMF calculations reproduce well the binding energy and the deformation for the ground state of 178Hf. Using the ground state single-particle eigenvalues obtained in the present calculation, the lowest excitation configuration with Kπ = 16+ is found to be v(7/2- [514])-1 (9/2+ [624])1 π(7/2+ [404])-1 (9/2-[514])1. Its excitation energy calculated by the RMF theory with time-odd fields taken into account is equal to 2.801 MeV, i.e., close to the 178 Hfm2 experimental excitation energy 2.446 MeV. The self-consistent procedure accounting for the time-odd component of the meson fields is the most important aspect of the present calculation.
Cluster decay in very heavy nuclei in a relativistic mean field model
Bhattacharya, Madhubrata; Gangopadhyay, G.
2008-02-01
Exotic cluster decay of very heavy nuclei was studied in the microscopic Super-Asymmetric Fission Model. The Relativistic Mean Field model with the force FSU Gold was employed to obtain the densities of the cluster and the daughter nuclei. The microscopic nuclear interaction DDM3Y1, which has an exponential density dependence, and the Coulomb interaction were used in the double folding model to obtain the potential between the cluster and the daughter. Half-life values were calculated in the WKB approximation and the spectroscopic factors were extracted. The latter values are seen to have a simple dependence of the mass of the cluster as has been observed earlier. Predictions were made for some possible decays.
Study of reaction and decay using densities from relativistic mean field theory
Gangopadhyay, G
2012-01-01
Relativistic mean field calculations have been performed to obtain nuclear density pro- file. Microscopic interactions have been folded with the calculated densities of finite nuclei to obtain a semi-microscopic potential. Life time values for the emission of proton, alpha particles and complex clusters have been calculated in the WKB approach assum- ing a tunneling process through the potential barrier. Elastic scattering cross sections have been estimated for proton-nucleus scattering in light neutron rich nuclei. Low en- ergy proton reactions have been studied and their astrophysical implications have been discussed. The success of the semi-microscopic potentials obtained in the folding model with RMF densities in explaining nuclear decays and reactions has been emphasized.
Ground-State Properties of Z = 59 Nuclei in the Relativistic Mean-Field Theory
ZHOU Yong; MA Zhong-Yu; CHEN Bao-Qiu; LI Jun-Qing
2000-01-01
Ground-state properties of Pr isotopes are studied in a framework of the relativistic mean-field (RMF) theory using the recently proposed parameter set TM1. Bardeen-Cooper-Schrieffer (BCS) pproximation and blocking method is adopted to deal with pairing interaction and the odd nucleon, respectively. The pairing forces are taken to be isospin dependent. The domain of the validity of the BCS theory and the positions of neutron and proton drip lines are studied. It is shown that RMF theory has provided a good description of the binding energy,isotope shifts and deformation of nuclei over a large range of Pr isotopes, which are in good agreement with those obtained in the finite-range droplet model.
Investigation of A＋c- and Ab-Hypernuclei in Relativistic Mean-Field Model
TANYu-Hong; CAIChong-Hai; LILei; NINGPing-Zhi
2003-01-01
We investigate the properties of A+c- and Ab-hypernuclei within the framework of the relativistic mean-field model (RMF). It is found that no A+c bound states can exist if the A+c potential well depth |UA+c| in nuclear matter is less than 10 MeV. If |UA+c|is less than 20 MeV, A+c cannot bind to the heavier nuclei with atomic number larger than 100. We suggest it is preferable to search the A+c-hypernuclei from medium-heavy nuclear systems in experiment. Very small spin-orbit splitting for the A+c in hypernuclei is a/so observed, and for the Ab it is nearly zero.
Magnetic moments of 33Mg in the time-odd relativistic mean field approach
无
2009-01-01
The configuration-fixed deformation constrained relativistic mean field approach with time-odd component has been applied to investigate the ground state properties of 33Mg with effective interaction PK1.The ground state of 33Mg has been found to be prolate deformed,β2=0.23,with the odd neutron in 1/2[330] orbital and the energy -251.85 MeV which is close to the data -252.06 MeV.The magnetic moment -0.9134 μN is obtained with the effective electromagnetic current which well reproduces the data -0.7456 μN self-consistently without introducing any parameter.The energy splittings of time reversal conjugate states,the neutron current,the energy contribution from the nuclear magnetic potential,and the effect of core polarization are discussed in detail.
K--nucleus relativistic mean field potentials consistent with kaonic atoms
Friedman, E.; Gal, A.; Mareš, J.; Cieplý, A.
1999-08-01
K- atomic data are used to test several models of the K- nucleus interaction. The t(ρ)ρ optical potential, due to coupled channel models incorporating the Λ(1405) dynamics, fails to reproduce these data. A standard relativistic mean field (RMF) potential, disregarding the Λ(1405) dynamics at low densities, also fails. The only successful model is a hybrid of a theoretically motivated RMF approach in the nuclear interior and a completely phenomenological density dependent potential, which respects the low density theorem in the nuclear surface region. This best-fit K- optical potential is found to be strongly attractive, with a depth of 180+/-20 MeV at the nuclear interior, in agreement with previous phenomenological analyses.
Corinaldesi, Ernesto
1963-01-01
Geared toward advanced undergraduate and graduate students of physics, this text provides readers with a background in relativistic wave mechanics and prepares them for the study of field theory. The treatment originated as a series of lectures from a course on advanced quantum mechanics that has been further amplified by student contributions.An introductory section related to particles and wave functions precedes the three-part treatment. An examination of particles of spin zero follows, addressing wave equation, Lagrangian formalism, physical quantities as mean values, translation and rotat
Madokoro, Hideki; Matsuzaki, Masayuki
1997-01-01
Relativistic Mean Field Theory is applied to the description of rotating nuclei. Since the previous formulation of Munich group was based on a special relativistic transformation property of the spinor fields, we reformulate in a fully covariant manner using tetrad formalism. The numerical calculations are performed for 3 zinc isotopes, including the newly discovered superdeformed band in $^{62}$Zn which is the first experimental observation in this mass region.
Madokoro, H.; Matsuzaki, M.
Relativistic Mean Field Theory is applied to the description of rotating nuclei. Since the previous formulation of Munich group was based on a special relativistic transformation property of the spinor fields, we reformulate in a fully covariant manner using tetrad formalism. The numerical calculations are performed for 3 zinc isotopes, including the newly discovered superdeformed band in $^{62}$Zn which is the first experimental observation in this mass region.
A Study of Multi-Λ Hypernuclei Within Spherical Relativistic Mean-Field Approach
Rather, Asloob A.; Ikram, M.; Usmani, A. A.; Kumar, B.; Patra, S. K.
2017-09-01
This research article is a follow up of an earlier work by M. Ikram et al., reported in Int. J. Mod. Phys. E 25, 1650103 (2016) where we searched for Λ magic numbers in experimentally confirmed doubly magic nucleonic cores in light to heavy mass region (i.e., 16 O-208 P b) by injecting Λ's into them. In the present manuscript, working within the state of the art relativistic mean field theory with the inclusion of ΛN and ΛΛ interaction in addition to nucleon-meson NL 3∗ effective force, we extend the search of lambda magic numbers in multi- Λ hypernuclei using the predicted doubly magic nucleonic cores 292120, 304120, 360132, 370132, 336138, 396138 of the elusive superheavy mass regime. In analogy to well established signatures of magicity in conventional nuclear theory, the prediction of hypernuclear magicities is made on the basis of one-, two- Λ separation energy (S Λ,S 2Λ) and two lambda shell gaps (δ 2Λ) in multi- Λ hypernuclei. The calculations suggest that the Λ numbers 92, 106, 126, 138, 184, 198, 240, and 258 might be the Λ shell closures after introducing the Λ's in the elusive superheavy nucleonic cores. The appearance of new lambda shell closures apart from the nucleonic ones predicted by various relativistic and non-relativistic theoretical investigations can be attributed to the relatively weak strength of the spin-orbit coupling in hypernuclei compared to normal nuclei. Further, the predictions made in multi- Λ hypernuclei under study resembles closely the magic numbers in conventional nuclear theory suggested by various relativistic and non-relativistic theoretical models. Moreover, in support of the Λ shell closure, the investigation of Λ pairing energy and effective Λ pairing gap has been made. We noticed a very close agreement of the predicted Λ shell closures with the survey made on the pretext of S Λ, S 2Λ, and δ 2Λ except for the appearance of magic numbers corresponding to Λ = 156 which manifest in Λ effective
Nucleon Finite Volume Effect and Nuclear Matter Properties in a Relativistic Mean-Field Theory
R. Costa; A.J. Santiago; H. Rodrigues; J. Sa Borges
2006-01-01
Effects of excluded volume of nucleons on nuclear matter are studied, and the nuclear properties that follow from different relativistic mean-field model parametrizations are compared. We show that, for all tested parametrizations,the resulting volume energy a1 and the symmetry energy J are around the acceptable values of 16 MeV and 30 MeV,and the density symmetry L is around 100 Me V. On the other hand, models that consider only linear terms lead to incompressibility K0 much higher than expected. For most parameter sets there exists a critical point (ρc,δc), where the minimum and the maximum of the equation of state are coincident and the incompressibility equals zero. This critical point depends on the excluded volume parameter r. If this parameter is larger than 0.5 fm, there is no critical point and the pure neutron matter is predicted to be bound. The maximum value for neutron star mass is 1.85M⊙, which is in agreement with the mass of the heaviest observed neutron star 4U0900-40 and corresponds to r = 0.72 fm. We also show that the light neutron star mass (1.2M⊙) is obtained for r (≌) 0.9 fm.
A Second Relativistic Mean Field and Virial Equation of State for Astrophysical Simulations
Shen, G; O'Connor, E
2011-01-01
We generate a second equation of state (EOS) of nuclear matter for a wide range of temperatures, densities, and proton fractions for use in supernovae, neutron star mergers, and black hole formation simulations. We employ full relativistic mean field (RMF) calculations for matter at intermediate density and high density, and the Virial expansion of a non-ideal gas for matter at low density. For this EOS we use the RMF effective interaction FSUGold, whereas our earlier EOS was based on the RMF effective interaction NL3. The FSUGold interaction has a lower pressure at high densities compared to the NL3 interaction. We calculate the resulting EOS at over 100,000 grid points in the temperature range $T$ = 0 to 80 MeV, the density range $n_B$ = 10$^{-8}$ to 1.6 fm$^{-3}$, and the proton fraction range $Y_p$ = 0 to 0.56. We then interpolate these data points using a suitable scheme to generate a thermodynamically consistent equation of state table on a finer grid. We discuss differences between this EOS, our NL3 ba...
Properties and structure of N=Z nuclei within relativistic mean field theory
GAO Yuan; DONG Jian-Min; ZHANG Hong-Fei; ZUO Wei; LI Jun-Qing
2009-01-01
The axially deformed relativistic mean field theory with the force NLSH has been performed in the blocked BCS approximation to investigate the properties and structure of N=Z nuclei from Z=20 to Z=48.Some ground state quantities such as binding energies, quadrupole deformations, one/two-nucleon separation energies, root-mean-square (rms) radii of charge and neutron, and shell gaps have been calculated.The results suggest that large deformations can be found in medium-heavy nuclei with N=Z=38-42.The charge and neutron rms radii increase rapidly beyond the magic number N=Z=28 until Z=42 with increasing nucleon number, which is similar to isotope shift, yet beyond Z=42, they decrease dramatically as the structure changes greatly from Z=42 to Z=43.The evolution of shell gaps with proton number Z can be clearly observed.Besides the appearance of possible new shell closures, some conventional shell closures have been found to disappear in some region.In addition, we found that the Coulomb interaction is not strong enough to breakdown the shell structure of protons in the current region.
Nuclear matter fourth-order symmetry energy in relativistic mean field models
Cai, Bao-Jun
2011-01-01
Within the nonlinear relativistic mean field model, we derive the analytical expression of the nuclear matter fourth-order symmetry energy $E_{4}(\\rho)$. Our results show that the value of $E_{4}(\\rho)$ at normal nuclear matter density $\\rho_{0}$ is generally less than 1 MeV, confirming the empirical parabolic approximation to the equation of state for asymmetric nuclear matter at $\\rho_{0}$. On the other hand, we find that the $E_{4}(\\rho)$ may become nonnegligible at high densities. Furthermore, the analytical form of the $E_{4}(\\rho)$ provides the possibility to study the higher-order effects on the isobaric incompressibility of asymmetric nuclear matter, i.e., $K_{\\mathrm{sat}}(\\delta)=K_{0}+K_{\\mathrm{{sat},2}}\\delta ^{2}+K_{\\mathrm{{sat},4}}\\delta ^{4}+\\mathcal{O}(\\delta ^{6})$ where $\\delta =(\\rho_{n}-\\rho_{p})/\\rho $ is the isospin asymmetry, and we find that the value of $K_{\\mathrm{{sat},4}}$ is generally comparable with that of the $K_{\\mathrm{{sat},2}}$. In addition, we study the effects of the $E...
Lu, Bing-Nan; Zhao, En-Guang; Zhou, Shan-Gui
2013-01-01
In this contribution we present some results of potential energy surfaces of actinide and transfermium nuclei from multi-dimensional constrained relativistic mean field (MDC-RMF) models. Recently we developed multi-dimensional constrained covariant density functional theories (MDC-CDFT) in which all shape degrees of freedom $\\beta_{\\lambda\\mu}$ with even $\\mu$ are allowed and the functional can be one of the following four forms: the meson exchange or point-coupling nucleon interactions combined with the non-linear or density-dependent couplings. In MDC-RMF models, the pairing correlations are treated with the BCS method. With MDC-RMF models, the potential energy surfaces of even-even actinide nuclei were investigated and the effect of triaxiality on the fission barriers in these nuclei was discussed. The non-axial reflection-asymmetric $\\beta_{32}$ shape in some transfermium nuclei with $N=150$, namely $^{246}$Cm, $^{248}$Cf, $^{250}$Fm, and $^{252}$No were also studied.
Maslov, K A; Voskresensky, D N
2016-01-01
Knowledge of the equation of state of the baryon matter plays a decisive role in the description of neutron stars. With an increase of the baryon density the filling of Fermi seas of hyperons and $\\Delta$ isobars becomes possible. Their inclusion into standard relativistic mean-field models results in a strong softening of the equation of state and a lowering of the maximum neutron star mass below the measured values. We extend a relativistic mean-field model with scaled hadron masses and coupling constants developed in our previous works and take into account now not only hyperons but also the $\\Delta$ isobars. We analyze available empirical information to put constraints on coupling constants of $\\Delta$s to mesonic mean fields. We show that the resulting equation of state satisfies majority of presently known experimental constraints.
Multidimensionally constrained relativistic mean-field study of triple-humped barriers in actinides
Zhao, Jie; Lu, Bing-Nan; Vretenar, Dario; Zhao, En-Guang; Zhou, Shan-Gui
2015-01-01
Background: Potential energy surfaces (PES's) of actinide nuclei are characterized by a two-humped barrier structure. At large deformations beyond the second barrier, the occurrence of a third barrier was predicted by macroscopic-microscopic model calculations in the 1970s, but contradictory results were later reported by a number of studies that used different methods. Purpose: Triple-humped barriers in actinide nuclei are investigated in the framework of covariant density functional theory (CDFT). Methods: Calculations are performed using the multidimensionally constrained relativistic mean field (MDC-RMF) model, with the nonlinear point-coupling functional PC-PK1 and the density-dependent meson exchange functional DD-ME2 in the particle-hole channel. Pairing correlations are treated in the BCS approximation with a separable pairing force of finite range. Results: Two-dimensional PES's of 226,228,230,232Th and 232,235,236,238U are mapped and the third minima on these surfaces are located. Then one-dimensional potential energy curves along the fission path are analyzed in detail and the energies of the second barrier, the third minimum, and the third barrier are determined. The functional DD-ME2 predicts the occurrence of a third barrier in all Th nuclei and 238U . The third minima in 230 ,232Th are very shallow, whereas those in 226 ,228Th and 238U are quite prominent. With the functional PC-PK1 a third barrier is found only in 226 ,228 ,230Th . Single-nucleon levels around the Fermi surface are analyzed in 226Th, and it is found that the formation of the third minimum is mainly due to the Z =90 proton energy gap at β20≈1.5 and β30≈0.7 . Conclusions: The possible occurrence of a third barrier on the PES's of actinide nuclei depends on the effective interaction used in multidimensional CDFT calculations. More pronounced minima are predicted by the DD-ME2 functional, as compared to the functional PC-PK1. The depth of the third well in Th isotopes decreases
Study of the Alpha-Decay Chain for7753 194Rn with Relativistic Mean-Field Theory
SHENG Zong-Qiang; GUO Jian-You
2008-01-01
The structures of the nuclei on the alpha-decay chain of 194Rn are investigated in the deformed relativistic mean-field theory with the effective interaction TMA. We put an emphasis on the ground state properties of 194Rn. The calculated alpha-decay energies and lifetimes are both very close to the experimental data for 186pb and 190po. For 194 Rn, the deviations are a little large on both the alpha-decay energy and the lifetime. We also calculate the alpha-decay energies for the isotopes 192～208Rn. The tendency for the change of the alpha-decay energies with neutron number is correctly reproduced in the relativistic mean-field theory (RMF). In general, the RMF theory can give a good description of the alpha decay chain of 194Rn.
A systematic study of even-even nuclei in the nuclear chart by the relativistic mean field theory
Sumiyoshi, K.; Hirata, D.; Tanihata, I.; Sugahara, Y.; Toki, H. [Institute of Physical and Chemical Research, Wako, Saitama (Japan)
1997-03-01
We study systematically the properties of nuclei in the whole mass range up to the drip lines by the relativistic mean field (RMF) theory with deformations as a microscopic framework to provide the data of nuclear structure in the nuclear chart. The RMF theory is a phenomenological many-body framework, in which the self-consistent equations for nucleons and mesons are solved with arbitrary deformation, and has a potential ability to provide all the essential information of nuclear structure such as masses, radii and deformations together with single particle states and wave functions from the effective lagrangian containing nuclear interaction. As a first step toward the whole project, we study the ground state properties of even-even nuclei ranging from Z=8 to Z=120 up to the proton and neutron drip lines in the RMF theory. We adopt the parameter set TMA, which has been determined by the experimental masses and charge radii in a wide mass range, for the effective lagrangian of the RMF theory. We take into account the axially symmetric deformation using the constrained method on the quadrupole moment. We provide the properties of all even-even nuclei with all the possible ground state deformations extracted from the deformation energy curves by the constrained calculations. By studying the calculated ground state properties systematically, we aim to explore the general trend of masses, radii and deformations in the whole region of the nuclear chart. We discuss the agreement with experimental data and the predictions such as magicness and triaxial deformations beyond the experimental frontier. (author)
Geng, L S; Meng, J
2005-01-01
We perform a systematic study of the ground-state properties of all the nuclei from the proton drip line to the neutron drip line throughout the periodic table employing the relativistic mean field model. The TMA parameter set is used for the mean-field Lagrangian density, and a state-dependent BCS method is adopted to describe the pairing correlation. The ground-state properties of a total of 6969 nuclei with $Z,N\\ge 8$ and $Z\\le 100$ from the proton drip line to the neutron drip line, including the binding energies, the separation energies, the deformations, and the rms charge radii, are calculated and compared with existing experimental data and those of the FRDM and HFB-2 mass formulae. This study provides the first complete picture of the current status of the descriptions of nuclear ground-state properties in the relativistic mean field model. The deviations from existing experimental data indicate either that new degrees of freedom are needed, such as triaxial deformations, or that serious effort is ne...
Treating Coulomb exchange contributions in relativistic mean field calculations: why and how
Van Giai, Nguyen; Gu, Huai-Qiang; Long, Wenhui; Meng, Jie
2014-01-01
The energy density functional (EDF) method is very widely used in nuclear physics, and among the various existing functionals those based on the relativistic Hartree (RH) approximation are very popular because the exchange contributions (Fock terms) are numerically rather onerous to calculate. Although it is possible to somehow 'mock up' the effects of meson-induced exchange terms by adjusting the meson-nucleon couplings, the lack of Coulomb exchange contributions hampers the accuracy of predictions. In this note, we show that the Coulomb exchange effects can be easily included with a good accuracy in a perturbative approach. Therefore, it would be desirable for future relativistic EDF models to incorporate Coulomb exchange effects, at least to some order of perturbation.
Mean-field effects on flows in relativistic heavy-ion collisions
Isse, M.; Ohnishi, A. [Hokkaido Univ., Graduate School of Science, Sapporo, Hokkaido (Japan); Otuka, N. [Hokkaido Univ., Graduate School of Engineering, Sapporo, Hokkaido (Japan); Sahu, P.K. [Istituto Nazionale di Fisica Nucleare, Sezione di Catania (Italy); Nara, Y. [Brookhaven National Laboratory, RIKEN BNL Research Center, Upton, NY (United States)
2002-09-01
At RHIC experiments, started in 2000, the data obtained recently seem to exhibit QGP formation, but the conclusion is not drawn yet. Here, we pay out attention to the collective flows at hadronic freeze-out as an evidence of QGP formation. To discuss it, the mean-field effect on the flows is not negligible. It is dominant at SIS or AGS energy, and our conjecture is that it is negligible at SPS or RHIC energy. We formed a model to investigate our assumption, and some simulated results are shown. (author)
Building relativistic mean field models for finite nuclei and neutron stars
Chen, Wei-Chia; Piekarewicz, J.
2014-10-01
Background: Theoretical approaches based on density functional theory provide the only tractable method to incorporate the wide range of densities and isospin asymmetries required to describe finite nuclei, infinite nuclear matter, and neutron stars. Purpose: A relativistic energy density functional (EDF) is developed to address the complexity of such diverse nuclear systems. Moreover, a statistical perspective is adopted to describe the information content of various physical observables. Methods: We implement the model optimization by minimizing a suitably constructed χ2 objective function using various properties of finite nuclei and neutron stars. The minimization is then supplemented by a covariance analysis that includes both uncertainty estimates and correlation coefficients. Results: A new model, "FSUGold2," is created that can well reproduce the ground-state properties of finite nuclei, their monopole response, and that accounts for the maximum neutron-star mass observed up to date. In particular, the model predicts both a stiff symmetry energy and a soft equation of state for symmetric nuclear matter, suggesting a fairly large neutron-skin thickness in Pb208 and a moderate value of the nuclear incompressibility. Conclusions: We conclude that without any meaningful constraint on the isovector sector, relativistic EDFs will continue to predict significantly large neutron skins. However, the calibration scheme adopted here is flexible enough to create models with different assumptions on various observables. Such a scheme—properly supplemented by a covariance analysis—provides a powerful tool to identify the critical measurements required to place meaningful constraints on theoretical models.
Building relativistic mean field models for finite nuclei and neutron stars
Chen, Wei-Chia
2014-01-01
Background: Theoretical approaches based on density functional theory provide the only tractable method to incorporate the wide range of densities and isospin asymmetries required to describe finite nuclei, infinite nuclear matter, and neutron stars. Purpose: A relativistic energy density functional (EDF) is developed to address the complexity of such diverse nuclear systems. Moreover, a statistical perspective is adopted to describe the information content of various physical observables. Methods: We implement the model optimization by minimizing a suitably constructed chi-square objective function using various properties of finite nuclei and neutron stars. The minimization is then supplemented by a covariance analysis that includes both uncertainty estimates and correlation coefficients. Results: A new model, FSUGold2, is created that can well reproduce the ground-state properties of finite nuclei, their monopole response, and that accounts for the maximum neutron star mass observed up to date. In particul...
CHEN Jin-Gen; ZHOU Xing-Fei; WANG Kun; MA Guo-Liang; TIAN Wen-Dong; ZUO Jia-Xu; MA Chun-Wang; CHEN Jin-Hui; YAN Ting-Zhi; SHEN Wen-Qing; CAI Xiang-Zhou; WANG Ting-Tai; MA Yu-Gang; REN Zhong-Zhou; FANG De-Qing; ZHONG Chen; WEI Yi-Bin; GUO Wei
2004-01-01
@@ A candidate for proton halo nucleus 23Al is investigated based on the constrained calculations in the framework of the deformed relativistic mean field (RMF) model with the NL075 parameter set. It is shown by the constrained calculations that the ground state of 23Al has a large deformation that corresponds to the prolate shape. With that large deformation, the non-constrained RMF calculation predicts that there appears an inversion between the 2s1/2 [211] and 1d5/2 [202] shells. The valence proton of 23Al is weakly bound and occupies 2s1/2 [211] and 1d5/2 [202] with the weights of 56% and 29%, respectively. The calculated RMS radius for matter is in agreement with the experimental one. It is also predicted that the difference between the proton RMS radius and the neutron one is very large. This suggests that there exists a proton halo in 23Al.
Sulaksono, A; Agrawal, B K
2014-01-01
The model dependence and the symmetry energy dependence of the core-crust transition properties for the neutron stars are studied using three different families of systematically varied extended relativistic mean field model. Several forces within each of the families are so considered that they yield wide variations in the values of the nuclear symmetry energy $a_{\\rm sym}$ and its slope parameter $L$ at the saturation density. The core-crust transition density is calculated using a method based on random-phase-approximation. The core-crust transition density is strongly correlated, in a model independent manner, with the symmetry energy slope parameter evaluated at the saturation density. The pressure at the transition point dose not show any meaningful correlations with the symmetry energy parameters at the saturation density. At best, pressure at the transition point is correlated with the symmetry energy parameters and their linear combination evaluated at the some sub-saturation density. Yet, such corre...
Zhao, Jie; Niksic, Tamara; Vretenar, Dario; Zhou, Shan-Gui
2016-01-01
Studies of fission dynamics, based on nuclear energy density functionals, have shown that the coupling between shape and pairing degrees of freedom has a pronounced effect on the nonperturbative collective inertia and, therefore, on dynamic (least-action) spontaneous fission paths and half-lives. Collective potentials and nonperturbative cranking collective inertia tensors are calculated using the multidimensionally-constrained relativistic mean-field (MDC-RMF) model. Pairing correlations are treated in the BCS approximation using a separable pairing force of finite range. Pairing fluctuations are included as a collective variable using a constraint on particle-number dispersion. Fission paths are determined with the dynamic programming method by minimizing the action in multidimensional collective spaces. The dynamics of spontaneous fission of $^{264}$Fm and $^{250}$Fm are explored. Fission paths, action integrals and corresponding half-lives computed in the three-dimensional collective space of shape and pa...
Bai, Hong-Bo; Zhang, Zhen-Hua; Li, Xiao-Wei
2016-11-01
Ground state properties for Mg isotopes, including binding energies, one- and two-neutron separation energies, pairing energies, nuclear matter radii and quadrupole deformation parameters, are obtained from the self-consistent relativistic mean field (RMF) model with the pairing correlations treated by a shell-mode-like approach (SLAP), in which the particle-number is conserved and the blocking effects are treated exactly. The experimental data, including the binding energies and the one- and two-neutron separation energies, which are sensitive to the treatment of pairing correlations and block effects, are well reproduced by the RMF+SLAP calculations. Supported by NSFC (11465001,11275098, 11275248, 11505058,11165001) and Natural Science Foundation of Inner Mongolia of China (2016BS0102)
Afanasjev, A. V.; König, J.; Ring, P.
1996-02-01
The cranked relativistic mean field approach is applied for a systematic investigation of superdeformed rotational bands observed in the A ˜ 140-150 mass region. The present investigation covers yrast and in some cases also excited superdeformed bands of all nuclei of this mass region in which such bands have been observed so far. Using the parameter set NL1, which has been adjusted ten years ago to a few spherical nuclei, reasonable agreement with experimental data is obtained throughout the mass region under investigation. It is shown that the calculated properties of superdeformed rotational bands such as the dependence of the dynamic moment of inertia J(2) with respect to the rotational frequency and the absolute value of the charge quadrupole moment Q0 depends sensitively on the number of occupied high- N intruder orbitals. This is agreement both with previous investigations within the cranked Nilsson-Strutinsky and the cranked Woods-Saxon-Strutinsky approaches and with available experimental data.
Typel, S.; Wolter, H.H. [Sektion Physik, Univ. Muenchen, Garching (Germany)
1998-06-01
Nuclear matter and ground state properties for (proton and neutron) semi-closed shell nuclei are described in relativistic mean field theory with coupling constants which depend on the vector density. The parametrization of the density dependence for {sigma}-, {omega}- and {rho}-mesons is obtained by fitting to properties of nuclear matter and some finite nuclei. The equation of state for symmetric and asymmetric nuclear matter is discussed. Finite nuclei are described in Hartree approximation, including a charge and an improved center-of-mass correction. Pairing is considered in the BCS approximation. Special attention is directed to the predictions for properties at the neutron and proton driplines, e.g. for separation energies, spin-orbit splittings and density distributions. (orig.)
Houlrik, Jens Madsen
2009-01-01
The Lorentz transformation applies directly to the kinematics of moving particles viewed as geometric points. Wave propagation, on the other hand, involves moving planes which are extended objects defined by simultaneity. By treating a plane wave as a geometric object moving at the phase velocity, novel results are obtained that illustrate the…
Afanasjev, A.V. [Technische Univ. Muenchen, Garching (Germany). Physik-Department]|[Latvian Acad. of Sci., Salaspils (Latvia). Dept. of Math. Phys.]|[Lund Inst. of Tech. (Sweden). Dept. of Mathematical Physics; Koenig, J. [Technische Univ. Muenchen, Garching (Germany). Physik-Department; Ring, P. [Technische Univ. Muenchen, Garching (Germany). Physik-Department
1996-10-14
The cranked relativistic mean field approach is applied for a systematic investigation of superdeformed rotational bands observed in the A {proportional_to}140-150 mass region. The present investigation covers yrast and in some cases also excited superdeformed bands of all nuclei of this mass region in which such bands have been observed so far. Using the parameter set NL1, which has been adjusted ten years ago to a few spherical nuclei, reasonable agreement with experimental data is obtained throughout the mass region under investigation. It is shown that the calculated properties of superdeformed rotational bands such as the dependence of the dynamic moment of inertia J{sup (2)} with respect to the rotational frequency and the absolute value of the charge quadrupole moment Q{sub 0} depends sensitively on the number of occupied high-N intruder orbitals. This is in agreement both with previous investigations within the cranked Nilsson-Strutinsky and the cranked Woods-Saxon-Strutinsky approaches and with available experimental data. (orig.).
ZhangHongfei; ZuoWei; SoojaeRenIm; ZhouXiaohong; LiJunqing
2003-01-01
In recent years the discovery of Super Heavy Element (SHE) with atomic number Z=108～116 has opened up a new era of research in nuclear physics, however, the extreme difficulties to synthesize SHE greatly restrict the experimental studies on it, so that the theoretical studies are very important. The Relativistic Mean Field theory (RMF) is proved to be a simple and successful theory due to its great success in describing the bulk properties at the β-stable valley, as well as nuclei far from the β-stable line, and gives good predictions for nuclei far beyond the end of the known periodic table. In the framework of RMF we have calculated the properties on SHN such as the binding energy, the deformation, single and double neutron separation energy, and the a-decay half-life and so on for nuclei Z=108～114 and N=156～190. The axial deformations considered by using the expansion of harmonic oscillator basis. The Lagrangian wc have used is as the following form:
Ponderomotive Acceleration by Relativistic Waves
Lau, Calvin; Yeh, Po-Chun; Luk, Onnie; McClenaghan, Joseph; Ebisuzaki, Toshikazu; Tajima, Toshiki
2014-01-01
In the extreme high intensity regime of electromagnetic (EM) waves in plasma, the acceleration process is found to be dominated by the ponderomotive acceleration (PA). While the wakefields driven by the ponderomotive force of the relativistic intensity EM waves are important, they may be overtaken by the PA itself in the extreme high intensity regime when the dimensionless vector potential $a_0$ of the EM waves far exceeds unity. The energy gain by this regime (in 1D) is shown to be (approximately) proportional to $a_0^2$. Before reaching this extreme regime, the coexistence of the PA and the wakefield acceleration (WA) is observed where the wave structures driven by the wakefields show the phenomenon of multiple and folded wave-breakings. Investigated are various signatures of the acceleration processes such as the dependence on the mass ratio for the energy gain as well as the energy spectral features. The relevance to high energy cosmic ray acceleration and to the relativistic laser acceleration is conside...
M MOUSAVI; M R SHOJAEI
2017-02-01
In this work, we have obtained energy levels and charge radius for the $\\beta$-stability line nucleus, in relativistic shell model. In this model, we considered a close shell for each nucleus containing double magicnumber and a single nucleon energy level. Here we have taken $^{41}$Ca with a single neutron in the $^{40}$Ca core as an illustrative example. Then we have selected the Eckart plus Hulthen potentials for interaction between the coreand the single nucleon. By using parametric Nikiforov–Uvarov (PNU) method, we have calculated the energy values and wave function. Finally, we have calculated the charge radius for 17O, $^{41}$Ca, $^{49}$Ca and $^{57}$Ni. Our results are in agreement with experimental values and hence this model can be applied for similar nuclei.
Mean field theory of charge-density wave state in magnetic field
Grigoriev, Pavel; Lyubshin, Dmitrij
2005-03-01
We develop a mean field theory of charge-density wave (CDW) state in magnetic field and study properties of this state below the transition temperature. We show that the CDW state with shifted wave vector in high magnetic field (CDWx phase) has a double harmonic modulation on the most part of the phase diagram. At perfect nesting the single harmonic CDW state with shifted wave vector exists only in a very narrow region near the triple point. We show that the transition from CDW0 to CDWx state below the critical temperature is accompanied by a jump of the CDW order parameter and of the CDW wave vector rather than by their continuous increase. This implies a first order transition between these CDW states and explains a strong hysteresis accompanying this transition. The similarities between CDW in high magnetic field and nonuniform LOFF superconducting phase are pointed out. Our investigation provides a theoretical description for recent experiments on organic metal α-(BEDT-TTF)2KHg(SCN)4 and other compounds. In particular, we explain the higher value of the kink transition field and provide the calculation of the phase diagram in the case of perfect nesting.
Transverse relativistic effects in paraxial wave interference
Bliokh, Konstantin Y; Nori, Franco
2013-01-01
We consider relativistic deformations of interfering paraxial waves moving in the transverse direction. Owing to superluminal transverse phase velocities, noticeable deformations of the interference patterns arise when the waves move with respect to each other with non-relativistic velocities. Similar distortions also appear on a mutual tilt of the interfering waves, which causes a phase delay analogous to the relativistic time delay. We illustrate these observations by the interference between a vortex wave beam and a plane wave, which exhibits a pronounced deformation of the radial fringes into a fork-like pattern (relativistic Hall effect). Furthermore, we describe an additional relativistic motion of the interference fringes (a counter-rotation in the vortex case), which become noticeable at the same non-relativistic velocities.
Out-of-equilibrium mean-field dynamics of a model for wave-particle interaction
de Buyl, Pierre; Bachelard, Romain; De Ninno, Giovanni
2009-01-01
The out-of-equilibrium mean-field dynamics of a model for wave-particle interaction is investigated. Such a model can be regarded as a general formulation for all those applications where the complex interplay between particles and fields is known to be central, e.g., electrostatic instabilities in plasma physics, particle acceleration and free-electron lasers. The latter case is here assumed as a paradigmatic example. A transition separating different macroscopic regimes is numerically identified and interpreted by making use of the so-called violent relaxation theory. In this context, the transition is explained as a dynamical switch between two metastable regimes, and related to the change of nature of a stationary point of an entropic functional.
Simple waves in relativistic fluids.
Lyutikov, Maxim
2010-11-01
We consider the Riemann problem for relativistic flows of polytropic fluids and find relations for the flow characteristics. Evolution of physical quantities takes especially simple form for the case of cold magnetized plasmas. We find exact explicit analytical solutions for one-dimensional expansion of magnetized plasma into vacuum, valid for arbitrary magnetization. We also consider expansion into cold unmagnetized external medium both for stationary initial conditions and for initially moving plasma, as well as reflection of rarefaction wave from a wall. We also find self-similar structure of three-dimensional magnetized outflows into vacuum, valid close to the plasma-vacuum interface.
Bhuyan, M.; Gupta, S. K. Patra Raj K.
2010-01-01
We have calculated the binding energy, root-mean-square radius and quadrupole deformation parameter for the recently synthesized superheavy element Z=117, using the axially deformed relativistic mean field (RMF) model. The calculation is extended to various isotopes of Z=117 element, strarting from A=286 till A=310. We predict almost spherical structures in the ground state for almost all the isotopes. A shape transition appears at about A=292 from prolate to a oblate shape structures of Z=11...
Rodrigues, Serafim [Department of Mathematical Sciences, Loughborough University, Leicestershire, LE11 3TU (United Kingdom); Terry, John R. [Department of Mathematical Sciences, Loughborough University, Leicestershire, LE11 3TU (United Kingdom)]. E-mail: j.r.terry@lboro.ac.uk; Breakspear, Michael [Black Dog Institute, Randwick, NSW 2031 (Australia); School of Psychiatry, UNSW, NSW 2030 (Australia)
2006-07-10
In this Letter, the genesis of spike-wave activity-a hallmark of many generalized epileptic seizures-is investigated in a reduced mean-field model of human neural activity. Drawing upon brain modelling and dynamical systems theory, we demonstrate that the thalamic circuitry of the system is crucial for the generation of these abnormal rhythms, observing that the combination of inhibition from reticular nuclei and excitation from the cortical signal, interplay to generate the spike-wave oscillation. The mechanism revealed provides an explanation of why approaches based on linear stability and Heaviside approximations to the activation function have failed to explain the phenomena of spike-wave behaviour in mean-field models. A mathematical understanding of this transition is a crucial step towards relating spiking network models and mean-field approaches to human brain modelling.
Relativistic suppression of wave packet spreading.
Su, Q; Smetanko, B; Grobe, R
1998-03-30
We investigate numerically the solution of Dirac equation and analytically the Klein-Gordon equation and discuss the relativistic motion of an electron wave packet in the presence of an intense static electric field. In contrast to the predictions of the (non-relativistic) Schroedinger theory, the spreading rate in the field's polarization direction as well as in the transverse directions is reduced.
Valor, A; Bonche, P
2000-01-01
We present in this paper the general framework of a method which permits to restore the rotational and particle number symmetries of wave functions obtained in Skyrme HF+BCS calculations. This restoration is nothing but a projection of mean-field intrinsic wave functions onto good particle number and good angular momentum. The method allows also to mix projected wave functions. Such a configuration mixing is discussed for sets of HF+BCS intrinsic states generated in constrained calculations with suitable collective variables. This procedure gives collective states which are eigenstates of the particle number and the angular momentum operators and between which transition probabilities are calculated. An application to 24Mg is presented, with mean-field wave functions generated by axial quadrupole constraints. Theoretical spectra and transition probabilities are compared to the experiment.
Bhuyan, M
2010-01-01
We have calculated the binding energy, root-mean-square radius and quadrupole deformation parameter for the recently synthesized superheavy element Z=117, using the axially deformed relativistic mean field (RMF) model. The calculation is extended to various isotopes of Z=117 element, strarting from A=286 till A=310. We predict almost spherical structures in the ground state for almost all the isotopes. A shape transition appears at about A=292 from prolate to a oblate shape structures of Z=117 nucleus in our mean field approach. The most stable isotope (largest binding energy per nucleon) is found to be the $^{288}$117 nucleus. Also, the Q-value of $\\alpha$-decay $Q_\\alpha$ and the half-lives $T_{\\alpha}$ are calculated for the $\\alpha$-decay chains of $^{293}$117 and $^{294}$117, supporting the magic numbers at N=172 and/ or 184.
Weakly relativistic dispersion of Bernstein waves
Robinson, P. A.
1988-01-01
Weakly relativistic effects on the dispersion of Bernstein waves are investigated for waves propagating nearly perpendicular to a uniform magnetic field in a Maxwellian plasma. Attention is focused on those large-wave-vector branches that are either weakly damped or join continuously onto weakly damped branches since these are the modes of most interest in applications. The transition between dispersion at perpendicular and oblique propagation is examined and major weakly relativistic effects can dominate even in low-temperature plasmas. A number of simple analytic criteria are obtained which delimit the ranges of harmonic number and propagation angle within which various types of weakly damped Bernstein modes can exist.
Weakly relativistic dispersion of Bernstein waves
Robinson, P. A.
1988-01-01
Weakly relativistic effects on the dispersion of Bernstein waves are investigated for waves propagating nearly perpendicular to a uniform magnetic field in a Maxwellian plasma. Attention is focused on those large-wave-vector branches that are either weakly damped or join continuously onto weakly damped branches since these are the modes of most interest in applications. The transition between dispersion at perpendicular and oblique propagation is examined and major weakly relativistic effects can dominate even in low-temperature plasmas. A number of simple analytic criteria are obtained which delimit the ranges of harmonic number and propagation angle within which various types of weakly damped Bernstein modes can exist.
Pais, Helena
2016-01-01
The Vlasov formalism is extended to relativistic mean-field hadron models with non-linear terms up to fourth order and applied to the calculation of the crust-core transition density. The effect of the nonlinear $\\omega\\rho$ and $\\sigma\\rho$ coupling terms on the crust-core transition density and pressure, and on the macroscopic properties of some families of hadronic stars is investigated. For that purpose, six families of relativistic mean field models are considered. Within each family, the members differ in the symmetry energy behavior. For all the models, the dynamical spinodals are calculated, and the crust-core transition density and pressure, and the neutron star mass-radius relations are obtained. The effect on the star radius of the inclusion of a pasta calculation in the inner crust is discussed. The set of six models that best satisfy terrestrial and observational constraints predicts a radius of 13.6$\\pm$0.3 km and a crust thickness of $1.36\\pm 0.06$km for a 1.4 $M_\\odot$ star.
Workshop on gravitational waves and relativistic astrophysics
Patrick Das Gupta
2004-10-01
Discussions related to gravitational wave experiments viz. LIGO and LISA as well as to observations of supermassive black holes dominated the workshop sessions on gravitational waves and relativistic astrophysics in the ICGC-2004. A summary of seven papers that were presented in these workshop sessions has been provided in this article.
Solitary Waves in Relativistic Electromagnetic Plasma
XIE Bai-Song; HUA Cun-Cai
2005-01-01
Solitary waves in relativistic electromagnetic plasmas are obtained numerically. The longitudinal momentum of electrons has been taken into account in the problem. It is found that in the moving frame with electromagnetic field propagating the solitary waves can exist in both cases, where the vector potential frequency is larger or smaller than the plasma characteristic frequency.
Yang, Min-Fong; Sun, Shih-Jye; Hong, Tzay-Ming
1993-12-01
We show that a special kind of slave-boson mean-field approximation, which allows for the symmetry-broken states appropriate for a bipartite lattice, can give essentially the same results as those by the variational-wave-function approach proposed by Gula´csi, Strack, and Vollhardt [Phys. Rev. B 47, 8594 (1993)]. The advantages of our approach are briefly discussed.
Corrugation of relativistic magnetized shock waves
Lemoine, M; Gremillet, L
2016-01-01
As a shock front interacts with turbulence, it develops corrugation which induces outgoing wave modes in the downstream plasma. For a fast shock wave, the incoming wave modes can either be fast magnetosonic waves originating from downstream, outrunning the shock, or eigenmodes of the upstream plasma drifting through the shock. Using linear perturbation theory in relativistic MHD, this paper provides a general analysis of the corrugation of relativistic magnetized fast shock waves resulting from their interaction with small amplitude disturbances. Transfer functions characterizing the linear response for each of the outgoing modes are calculated as a function of the magnetization of the upstream medium and as a function of the nature of the incoming wave. Interestingly, if the latter is an eigenmode of the upstream plasma, we find that there exists a resonance at which the (linear) response of the shock becomes large or even diverges. This result may have profound consequences on the phenomenology of astrophys...
Nonlinear waves in strongly interacting relativistic fluids
Fogaça, D A; Filho, L G Ferreira
2013-01-01
During the past decades the study of strongly interacting fluids experienced a tremendous progress. In the relativistic heavy ion accelerators, specially the RHIC and LHC colliders, it became possible to study not only fluids made of hadronic matter but also fluids of quarks and gluons. Part of the physics program of these machines is the observation of waves in this strongly interacting medium. From the theoretical point of view, these waves are often treated with li-nearized hydrodynamics. In this text we review the attempts to go beyond linearization. We show how to use the Reductive Perturbation Method to expand the equations of (ideal and viscous) relativistic hydrodynamics to obtain nonlinear wave equations. These nonlinear wave equations govern the evolution of energy density perturbations (in hot quark gluon plasma) or baryon density perturbations (in cold quark gluon plasma and nuclear matter). Different nonlinear wave equations, such as the breaking wave, Korteweg-de Vries and Burgers equations, are...
Relativistic wave equations: an operational approach
Dattoli, G.; Sabia, E.; Górska, K.; Horzela, A.; Penson, K. A.
2015-03-01
The use of operator methods of an algebraic nature is shown to be a very powerful tool to deal with different forms of relativistic wave equations. The methods provide either exact or approximate solutions for various forms of differential equations, such as relativistic Schrödinger, Klein-Gordon, and Dirac. We discuss the free-particle hypotheses and those relevant to particles subject to non-trivial potentials. In the latter case we will show how the proposed method leads to easily implementable numerical algorithms.
Wang, Zaijun; Ren, Zhongzhou; Dong, Tiekuang; Xu, Chang
2014-08-01
The ground-state spins and parities of the odd-A phosphorus isotopes 25-47P are studied with the relativistic mean-field (RMF) model and relativistic elastic magnetic electron-scattering theory (REMES). Results of the RMF model with the NL-SH, TM2, and NL3 parameters show that the 2s1/2 and 1d3/2 proton level inversion may occur for the neutron-rich isotopes 37-47P, and, consequently, the possible spin-parity values of 37-47P may be 3/2+, which, except for P47, differs from those given by the NUBASE2012 nuclear data table by Audi et al. Calculations of the elastic magnetic electron scattering of 37-47P with the single valence proton in the 2s1/2 and 1d3/2 state show that the form factors have significant differences. The results imply that elastic magnetic electron scattering can be a possible way to study the 2s1/2 and 1d3/2 level inversion and the spin-parity values of 37-47P. The results can also provide new tests as to what extent the RMF model, along with its various parameter sets, is valid for describing the nuclear structures. In addition, the contributions of the upper and lower components of the Dirac four-spinors to the form factors and the isotopic shifts of the magnetic form factors are discussed.
Relativistic NN scattering without partial wave decomposition
Ramalho, G; Peña, M T
2004-01-01
We consider the covariant Spectator equation with an appropriate OBE kernel, and apply it to the NN system. We develop a method, based on the Pad\\'e method,to solve the Spectator equation without partial wave decomposition, which is essential for high energies. Relativistic effects such as retardation and negative energy state components are considered. The on- and off-mass-shell amplitudes are calculated. The differential cross section obtained agrees fairly well with data at low energies.
Investigation on shock waves stability in relativistic gas dynamics
Alexander Blokhin
1993-05-01
Full Text Available This paper is devoted to investigation of the linearized mixed problem of shock waves stability in relativistic gas dynamics. The problem of symmetrization of relativistic gas dynamics equations is also discussed.
Biswal, S K
2014-01-01
We study the isoscalar giant monopole resonance for drip-lines and super heavy nuclei in the frame work of a relativistic mean field theory with scaling approach. The well known extended Thomas-Fermi approximation in the non-linear $\\sigma$-$\\omega$ model is used to estimate the giant monopole excitation energy for some selected light spherical nuclei starting from the region of proton to neutron drip-lines. The application is extended to super heavy region for Z=114 and 120, which are predicted by several models as the next proton magic number beyond Z=82. We compared the excitation energy obtained by four successful force parameters NL1, NL3, NL3$^*$ and FSUGold. The monopole energy decreases toward the proton and neutron drip-lines in an isotopic chain for lighter mass nuclei contrary to a monotonous decrease for super heavy isotopes. The maximum and minimum monopole excitation energies are obtained for nuclei with minimum and maximum isospin, respectively in an isotopic chain.
Lu, Bing-Nan; Zhao, En-Guang; Zhou, Shan-Gui
2013-01-01
We have developed multi-dimensional constrained covariant density functional theories (MDC-CDFT) for finite nuclei in which the shape degrees of freedom \\beta_{\\lambda\\mu} with even \\mu, e.g., \\beta_{20}, \\beta_{22}, \\beta_{30}, \\beta_{32}, \\beta_{40}, etc., can be described simultaneously. The functional can be one of the following four forms: the meson exchange or point-coupling nucleon interactions combined with the non-linear or density-dependent couplings. For the pp channel, either the BCS approach or the Bogoliubov transformation is implemented. The MDC-CDFTs with the BCS approach for the pairing (in the following labelled as MDC-RMF models with RMF standing for "relativistic mean field") have been applied to investigate multi-dimensional potential energy surfaces and the non-axial octupole $Y_{32}$-correlations in N=150 isotones. In this contribution we present briefly the formalism of MDC-RMF models and some results from these models. The potential energy surfaces with and without triaxial deformatio...
Sharma, M M; Münzenberg, G
2004-01-01
We have investigated properties of $\\alpha$-decay chains of recently produced superheavy elements Z=115 and Z=113 using the new Lagrangian model NL-SV1 with inclusion of the vector self-coupling of $\\omega$ meson in the framework of the relativistic mean-field theory. It is shown that the experimentally observed alpha-decay energies and half-lives are reproduced well by this Lagrangian model. Further calculations for the heavier elements with Z=117-125 show that these nuclei are superdeformed with a prolate shape in the ground state. A superdeformed shell-closure at Z=118 lends an additional binding and an extra stability to nuclei in this region. Consequently, it is predicted that the corresponding $Q_\\alpha$ values provide $\\alpha$-decay half-lives for heavier superheavy nuclei within the experimentally feasible conditions. The results are compared with those of macroscopic-microscopic approaches. A perspective of the difference in shell effects amongst various approaches is presented and its consequences o...
Linear wave propagation in relativistic magnetohydrodynamics
Keppens, R
2008-01-01
The properties of linear Alfv\\'en, slow, and fast magnetoacoustic waves for uniform plasmas in relativistic magnetohydrodynamics (MHD) are discussed, augmenting the well-known expressions for their phase speeds with knowledge on the group speed. A 3+1 formalism is purposely adopted to make direct comparison with the Newtonian MHD limits easier and to stress the graphical representation of their anisotropic linear wave properties using the phase and group speed diagrams. By drawing these for both the fluid rest frame and for a laboratory Lorentzian frame which sees the plasma move with a three-velocity having an arbitrary orientation with respect to the magnetic field, a graphical view of the relativistic aberration effects is obtained for all three MHD wave families. Moreover, it is confirmed that the classical Huygens construction relates the phase and group speed diagram in the usual way, even for the lab frame viewpoint. Since the group speed diagrams correspond to exact solutions for initial conditions co...
Equations of motion for a relativistic wave packet
L Kocis
2012-05-01
The time derivative of the position of a relativistic wave packet is evaluated. It is found that it is equal to the mean value of the momentum of the wave packet divided by the mass of the particle. The equation derived represents a relativistic version of the second Ehrenfest theorem.
Ion waves driven by shear flow in a relativistic degenerate astrophysical plasma
KHAN SHABBIR A; BAKHTIAR-UD-DIN; ILYAS MUHAMMAD; WAZIR ZAFAR
2016-05-01
We investigate the existence and propagation of low-frequency (in comparison to ion cyclotron frequency) electrostatic ion waves in highly dense inhomogeneous astrophysical magnetoplasma comprising relativistic degenerate electrons and non-degenerate ions. The dispersion equation is obtained by Fourier analysis under mean-field quantum hydrodynamics approximationfor various limits of the ratio of rest mass energy to Fermi energy of electrons, relevant to ultrarelativistic, weakly-relativistic and non-relativistic regimes. It is found that the system admits an oscillatory instability under certain condition in the presence of velocity shear parallel to ambient magnetic field. The dispersive role of plasma density and magnetic field is also discussed parametrically in the scenario of dense and degenerate astrophysical plasmas.
Valor, A; Bonche, P
2000-01-01
We present in this paper the general framework of a method which permits to restore the rotational and particle number symmetries of wave functions obtained in Skyrme HF + BCS calculations. This restoration is nothing but a projection of mean-field intrinsic wave functions onto good particle number and good angular momentum. The method allows us also to mix projected wave functions. Such a configuration mixing is discussed for sets of HF + BCS intrinsic states generated in constrained calculations with suitable collective variables. This procedure gives collective states which are eigenstates of the particle number and the angular momentum operators and between which transition probabilities are calculated. An application to sup 2 sup 4 Mg is presented, with mean-field wave functions generated by axial quadrupole constraints. Theoretical spectra and transition probabilities are compared to the experiment.
Relativistic soliton-like collisionless ionization wave
Arefiev, Alexey; McCormick, Matthew; Quevedo, Hernan; Bengtson, Roger; Ditmire, Todd
2014-10-01
It has been observed in recent experiments with laser-irradiated gas jets that a plasma filament produced by the laser and containing energetic electrons can launch a relativistic ionization wave into ambient gas. Here we present a self-consistent theory that explains how a collisionless ionization wave can propagate in a self-sustaining regime. A population of hot electrons necessarily generates a sheath electric field at the plasma boundary. This field penetrates the ambient gas, ionizing the gas atoms and thus causing the plasma boundary to expand. We show that the motion of the newly generated electrons can form a potential well adjacent to the plasma boundary. The outwards motion of the well causes a bunch of energetic electrons to become trapped, while allowing the newly generated electrons to escape into the plasma without retaining much energy. The resulting soliton-like ionizing field structure propagates outwards with a bunch of hot electrons that maintain a strong sheath field despite significant plasma expansion. We also present 1D and 2D particle-in-cell simulations that illustrate the described mechanism. The simulations were performed using HPC resources provided by the Texas Advanced Computing Center. This work was supported by NNSA Contract No. DE-FC52-08NA28512 and U.S. DOE Contract No. DE-FG02-04ER54742.
Rehman, M. A.; Qureshi, M. N. S. [Department of Physics, GC University, Kachery Road, Lahore 54000 (Pakistan); Shah, H. A. [Department of Physics, Forman Christian College, Ferozepur Road, Lahore 54600 (Pakistan); Masood, W. [COMSATS, Institute of Information Technology, Park Road, Chak Shehzad, Islamabad 44000 (Pakistan); National Centre for Physics (NCP) Shahdra Valley Road, Islamabad (Pakistan)
2015-10-15
Nonlinear circularly polarized Alfvén waves are studied in magnetized nonrelativistic, relativistic, and ultrarelativistic degenerate Fermi plasmas. Using the quantum hydrodynamic model, Zakharov equations are derived and the Sagdeev potential approach is used to investigate the properties of the electromagnetic solitary structures. It is seen that the amplitude increases with the increase of electron density in the relativistic and ultrarelativistic cases but decreases in the nonrelativistic case. Both right and left handed waves are considered, and it is seen that supersonic, subsonic, and super- and sub-Alfvénic solitary structures are obtained for different polarizations and under different relativistic regimes.
Quantum ion-acoustic solitary waves in weak relativistic plasma
Biswajit Sahu
2011-06-01
Small amplitude quantum ion-acoustic solitary waves are studied in an unmagnetized twospecies relativistic quantum plasma system, comprised of electrons and ions. The one-dimensional quantum hydrodynamic model (QHD) is used to obtain a deformed Korteweg–de Vries (dKdV) equation by reductive perturbation method. A linear dispersion relation is also obtained taking into account the relativistic effect. The properties of quantum ion-acoustic solitary waves, obtained from the deformed KdV equation, are studied taking into account the quantum mechanical effects in the weak relativistic limit. It is found that relativistic effects signiﬁcantly modify the properties of quantum ion-acoustic waves. Also the effect of the quantum parameter on the nature of solitary wave solutions is studied in some detail.
Relativistic wave equation for hypothetic composite quarks
Krolikowski, W. [Institute of Theoretical Physics, Warsaw University, Warsaw (Poland)
1997-05-01
A two-body wave equation is derived, corresponding to the hypothesis (discussed already in the past) that u and d current quarks are relativistic bound states of a spin-1/2 preon existing in two weak flavors and three colors, and a spin-0 preon with no weak flavor nor color, held together by a new strong but Abelian, vectorlike gauge force. Some non-conventional (though somewhat nostalgic) consequences of this strong Abelian binding within composite quarks are pointed out. Among them are: new tiny magnetic-type moments of quarks (and nucleons) and new isomeric nucleon states possibly excitable at some high energies. The letter may arise through a rearrangement mechanism for quark preons inside nucleons. In the interaction q (anti)q{yields}q (anti)q of preon-composite quarks, beside the color forces, there act additional exchange forces corresponding to diagrams analogical to the so called dual diagrams for the interaction {pi}{pi}{yields}{pi}{pi} of quark-composite pions. (author)
Hussain, S.; Mahmood, S.; Rehman, Aman-ur- [Theoretical Physics Division (TPD), PINSTECH, P.O. Nilore, Islamabad 44000, Pakistan and Pakistan Institute of Engineering and Applied Sciences (PIEAS), P.O. Nilore, Islamabad 44000 (Pakistan)
2014-11-15
Linear and nonlinear propagation of magnetosonic waves in the perpendicular direction to the ambient magnetic field is studied in dense plasmas for non-relativistic and ultra-relativistic degenerate electrons pressure. The sources of nonlinearities are the divergence of the ions and electrons fluxes, Lorentz forces on ions and electrons fluids and the plasma current density in the system. The Korteweg-de Vries equation for magnetosonic waves propagating in the perpendicular direction of the magnetic field is derived by employing reductive perturbation method for non-relativistic as well as ultra-relativistic degenerate electrons pressure cases in dense plasmas. The plots of the magnetosonic wave solitons are also shown using numerical values of the plasma parameters such a plasma density and magnetic field intensity of the white dwarfs from literature. The dependence of plasma density and magnetic field intensity on the magnetosonic wave propagation is also pointed out in dense plasmas for both non-relativistic and ultra-relativistic degenerate electrons pressure cases.
New Relativistic Effects in the Dynamics of Nonlinear Hydrodynamical Waves
Rezzolla, L
2002-01-01
In Newtonian and relativistic hydrodynamics the Riemann problem consists of calculating the evolution of a fluid which is initially characterized by two states having different values of uniform rest-mass density, pressure and velocity. When the fluid is allowed to relax, one of three possible wave-patterns is produced, corresponding to the propagation in opposite directions of two nonlinear hydrodynamical waves. New effects emerge in a special relativistic Riemann problem when velocities tangential to the initial discontinuity surface are present. We show that a smooth transition from one wave-pattern to another can be produced by varying the initial tangential velocities while otherwise maintaining the initial states unmodified. These special relativistic effects are produced by the coupling through the relativistic Lorentz factors and do not have a Newtonian counterpart.
Merino-Aceituno, Sara
2016-12-01
The isotropic 4-wave kinetic equation is considered in its weak formulation using model (simplified) homogeneous kernels. Existence and uniqueness of solutions is proven in a particular setting where the kernels have a rate of growth at most linear. We also consider finite stochastic particle systems undergoing instantaneous coagulation-fragmentation phenomena and give conditions in which this system approximates the solution of the equation (mean-field limit).
Mean-field models and exotic nuclei
Bender, M.; Buervenich, T.; Maruhn, J.A.; Greiner, W. [Inst. fuer Theoretische Physik, Univ. Frankfurt (Germany); Rutz, K. [Inst. fuer Theoretische Physik, Univ. Frankfurt (Germany)]|[Gesellschaft fuer Schwerionenforschung mbH, Darmstadt (Germany); Reinhard, P.G. [Inst. fuer Theoretische Physik, Univ. Erlangen (Germany)
1998-06-01
We discuss two widely used nuclear mean-field models, the relativistic mean-field model and the (nonrelativistic) Skyrme-Hartree-Fock model, and their capability to describe exotic nuclei. Test cases are superheavy nuclei and neutron-rich Sn isotopes. New information in this regime helps to fix hitherto loosely determined aspects of the models. (orig.)
Waves in relativistic electron beam in low-density plasma
Sheinman, I.; Sheinman (Chernenco, J.
2016-11-01
Waves in electron beam in low-density plasma are analyzed. The analysis is based on complete electrodynamics consideration. Dependencies of dispersion laws from system parameters are investigated. It is shown that when relativistic electron beam is passed through low-density plasma surface waves of two types may exist. The first type is a high frequency wave on a boundary between the beam and neutralization area and the second type wave is on the boundary between neutralization area and stationary plasma.
Investigating EMIC Waves as a Precipitation Mechanism for Relativistic Electrons
Li, Z.; Millan, R. M.; Woodger, L. A.
2012-12-01
Evidence has indicated that EMIC waves may be one of the major causes of relativistic electron precipitation (REP). We solved the pitch-angle diffusion equation for the scattering of relativistic electrons by EMIC waves, and generated flux-energy spectra of the precipitating electrons. After being converted into Bremsstrahlung X-ray counts, these spectra can be directly compared with previous (e.g. MAXIS, MINIS, BARREL test campaigns) and future (e.g. BARREL) balloon spectra measurements to determine if EMIC waves are the causes of the REP events. Parameter studies have also been conducted to investigate the influence of various geomagnetic parameters and environmental conditions on the REP spectra.
RELATIVISTIC ELECTRON LOSSES RELATED TO PROTON PRECIPITATION AND EMIC WAVES
Soraas, F.; Sandanger, M. I.; Aarsnes, K.; Oksavik, K.; Evans, D. S.
2009-12-01
Observations of loss of relativistic electrons to the atmosphere is presented and related to SW parameters. It is shown that the L-region of relativistic electron loss matched the anisotropic proton zone. In this zone the pitch angle distribution of the protons are unstable and can generate/amplify EMIC waves which in turn scatter the electrons into the atmosphere. In spatial limited regions, located close to the plasma pause, there can be enhanced losses of protons (sometime completely filling the loss cone). These regions of proton losses (spikes) are shown to give rise to EMIC waves leading to enhance scattering of the relativistic electrons. In the main phase of the storm the proton spikes are located in the midnight/evening sector, but in the storm recovery phase they are located at all MLTs. The anisotropic proton zone and proton spikes are observed in all storms, but not all storms contain an elevated flux of relativistic electrons.
Propagation of linear waves in relativistic anisotropic magnetohydrodynamics.
Gebretsadkan, W B; Kalra, G L
2002-11-01
Gedalin [Phys. Rev. E 47, 4354 (1993)] derived a dispersion relation for linear waves in relativistic anisotropic Magnetohydrodynamics (MHD). This dispersion relation is used to point out the regions where the relativistic anisotropic MHD leads to new results that cannot be obtained using usual collisional relativistic MHD. This is highlighted by plotting a Fresnal ray surface. Conditions for the onset of firehose and mirror instabilities are also indicated. Such a study can be applied to astrophysical features such as pulsar winds, propagation of cosmic rays, etc.
Artemyev, A. V., E-mail: ante0226@gmail.com [Space Research Institute, RAS, Moscow (Russian Federation); Mourenas, D.; Krasnoselskikh, V. V. [LPC2E/CNRS - University of Orleans, Orleans (France); Agapitov, O. V. [Space Sciences Laboratory, University of California, Berkeley, California 94720 (United States)
2015-06-15
In this paper, we study relativistic electron scattering by fast magnetosonic waves. We compare results of test particle simulations and the quasi-linear theory for different spectra of waves to investigate how a fine structure of the wave emission can influence electron resonant scattering. We show that for a realistically wide distribution of wave normal angles θ (i.e., when the dispersion δθ≥0.5{sup °}), relativistic electron scattering is similar for a wide wave spectrum and for a spectrum consisting in well-separated ion cyclotron harmonics. Comparisons of test particle simulations with quasi-linear theory show that for δθ>0.5{sup °}, the quasi-linear approximation describes resonant scattering correctly for a large enough plasma frequency. For a very narrow θ distribution (when δθ∼0.05{sup °}), however, the effect of a fine structure in the wave spectrum becomes important. In this case, quasi-linear theory clearly fails in describing accurately electron scattering by fast magnetosonic waves. We also study the effect of high wave amplitudes on relativistic electron scattering. For typical conditions in the earth's radiation belts, the quasi-linear approximation cannot accurately describe electron scattering for waves with averaged amplitudes >300 pT. We discuss various applications of the obtained results for modeling electron dynamics in the radiation belts and in the Earth's magnetotail.
Relativistic electromagnetic waves in an electron-ion plasma
Chian, Abraham C.-L.; Kennel, Charles F.
1987-01-01
High power laser beams can drive plasma particles to relativistic energies. An accurate description of strong waves requires the inclusion of ion dynamics in the analysis. The equations governing the propagation of relativistic electromagnetic waves in a cold electron-ion plasma can be reduced to two equations expressing conservation of energy-momentum of the system. The two conservation constants are functions of the plasma stream velocity, the wave velocity, the wave amplitude, and the electron-ion mass ratio. The dynamic parameter, expressing electron-ion momentum conversation in the laboratory frame, can be regarded as an adjustable quantity, a suitable choice of which will yield self-consistent solutions when other plasma parameters were specified. Circularly polarized electromagnetic waves and electrostatic plasma waves are used as illustrations.
Stable Propagating Waves and Wake Fields in Relativistic Electromagnetic Plasma
DUAN Yi-Shi; XIE Bai-Song; TIAN Miao; YIN Xin-Tao; ZHANG Xin-Hui
2008-01-01
Stable propagating waves and wake fields in relativistic electromagnetic plasma are investigated. The incident electromagnetic field has a finite initial constant amplitude meanwhile the longitudinal momentum of electrons is taken into account in the problem. It is found that in the moving frame with transverse wave group velocity the stable propagating transverse electromagnetic waves and longitudinal plasma wake fields can exist in the appropriate regime of plasma.
Investigation of Relativistic Electron Resonance with EMIC Waves
Woodger, L. A.; Millan, R. M.; Denton, R. E.
2008-12-01
Wave-particle interaction of relativistic electrons with EMIC waves has been proposed as an important loss mechanism for radiation belt electrons (e.g. Thorne and Andreoli, 1980). Lorentzen et al (2000) and Millan et al (2002) suggested this mechanism to be responsible for dusk side relativistic electron precipitation (REP) detected by balloon borne instrumentation. This study will use the linear electromagnetic dispersion code WHAMP to investigate the effects of density, magnetic field, anisotropy, and heavy ions on the minimum resonance energy for relativistic electrons with EMIC waves. Results will be compared with observations of REP during the MAXIS balloon campaign on Jan. 19, 2000 and the MINIS balloon campaign on Jan. 21, 2005.
Yamaguchi, Yoshiyuki Y
2011-07-01
Traveling clusters are ubiquitously observed in the Hamiltonian mean-field model for a wide class of initial states, which are not predicted to become spatially inhomogeneous states by nonequilibrium statistical mechanics and by nonlinear Landau damping. To predict such a cluster state from a given initial state, we combine nonequilibrium statistical mechanics and a construction method of Bernstein-Greene-Kruskal (BGK) waves with the aid of phenomenological assumptions. The phenomenological theory is partially successful, and the theoretically constructed cluster states are in good agreement with N-body simulations. Robustness of the theory is also discussed for unsuccessful initial states.
Bulanov, Stepan; Maksimchuk, Anatoly; Zhidkov, Alexei
2009-11-01
We report on the analytic and computer simulation study of a relativistic spherical wake wave. Such a wave in the breaking regime, traveling towards the center is able to reflect and focus the incoming radiation and up-shifting its frequency. The reflected and focused electromagnetic pulse can have such high intensity, that it is able to create e^+e^- pairs via Schwinger process.
Gomes, Diogo A.
2014-01-06
In this talk we will report on new results concerning the existence of smooth solutions for time dependent mean-field games. This new result is established through a combination of various tools including several a-priori estimates for time-dependent mean-field games combined with new techniques for the regularity of Hamilton-Jacobi equations.
Derivation of relativistic wave equation from the Poisson process
Tomoshige Kudo; Ichiro Ohba
2002-08-01
A Poisson process is one of the fundamental descriptions for relativistic particles: both fermions and bosons. A generalized linear photon wave equation in dispersive and homogeneous medium with dissipation is derived using the formulation of the Poisson process. This formulation provides a possible interpretation of the passage time of a photon moving in the medium, which never exceeds the speed of light in vacuum.
Rarefaction wave in relativistic steady magnetohydrodynamic flows
Sapountzis, Konstantinos, E-mail: ksapountzis@phys.uoa.gr; Vlahakis, Nektarios, E-mail: vlahakis@phys.uoa.gr [Faculty of Physics, University of Athens, 15784 Zografos, Athens (Greece)
2014-07-15
We construct and analyze a model of the relativistic steady-state magnetohydrodynamic rarefaction that is induced when a planar symmetric flow (with one ignorable Cartesian coordinate) propagates under a steep drop of the external pressure profile. Using the method of self-similarity, we derive a system of ordinary differential equations that describe the flow dynamics. In the specific limit of an initially homogeneous flow, we also provide analytical results and accurate scaling laws. We consider that limit as a generalization of the previous Newtonian and hydrodynamic solutions already present in the literature. The model includes magnetic field and bulk flow speed having all components, whose role is explored with a parametric study.
Petersen, Kaare Brandt
2006-01-01
This thesis describes investigations and improvements of a technique for Independent Component Analysis (ICA), called "Mean Field ICA". The main focus of the thesis is the optimization part of the algorithm, the so-called "EM algorithm". Using different approaches it is demonstrated that the EM...... Gradient Recipe is applicable to a wide selection of models. Furthermore, the Mean Field ICA model is extended to incorporate ltering over time in a so-called "convolutive ICA" model. Finally, by using mixture of Gaussians as source priors, the generative and ltering approach to ICA is compared...
Development of a 2 MW relativistic backward wave oscillator
Yaduvendra Choyal; Lalit Gupta; Prasad Deshpande; Krishna Prasad Maheshwari; Kailash Chander Mittal; Suresh Chand Bapna
2008-12-01
In this paper, a high power relativistic backward wave oscillator (BWO) experiment is reported. A 230 keV, 2 kA, 150 ns relativistic electron beam is generated using a Marx generator. The beam is then injected into a hollow rippled wall metallic cylindrical tube that forms a slow wave structure. The beam is guided using an axial pulsed magnetic field having a peak value 1 T and duration 1 ms. The field is generated by the discharge of a capacitor bank into a solenoidal coil. A synchronization circuit ensures the generation of the electron beam at the instant when the axial magnetic field attains its peak value. The beam interacts with the SWS modes and generates microwaves due to Cherenkov interaction. Estimated power of 2 MW in TM 01 mode is observed.
Guerra, E.M. de [Inst. de Estructura de la Materia, Consejo Superior de Investigaciones Cientificas (Spain)
2001-07-01
In these talks, we review non relativistic selfconsistent mean field theories, their scope and limitations. We first discuss static and time dependent mean field approaches for particles and quasiparticles, together with applications. We then discuss extensions that go beyond the non-relativistic independent particle limit. On the one hand, we consider extensions concerned with restoration of symmetries and with the treatment of collective modes, particularly by means of quantized ATDHF. On the other hand, we consider extensions concerned with the relativistic dynamics of bound nucleons. We present data on nucleon momentum distributions that show the need for relativistic mean field approach and probe the limits of the mean field concept. Illustrative applications of various methods are presented stressing the role that selfconsistency plays in providing a unifying reliable framework to study all sorts of properties and phenomena. From global properties such as size, mass, lifetime,.., to detailed structure in excitation spectra (high spin, RPA modes,..), as well as charge, magnetization and velocity distributions. (orig.)
X band bifrequency coaxial relativistic backward wave oscillator
Dong Wang
2011-12-01
Full Text Available An idea of azimuthally dividing the slow wave structure (SWS of a relativistic backward wave oscillator (RBWO into two parts is introduced to realize a bifrequency oscillation. To enhance the stability of this device, two sectorial waveguides are inserted into the SWS specially. The synchronization condition that is necessary to get a sustainable microwave output is derived. In Particle in cell simulation, bifrequency microwave at frequencies of 9.7 GHz and 9.87 GHz is generated with average power of 0.66 GW, conversion efficiency is 15.8% when beam voltage is 520 kV and current 8 kA.
Chaotic Motion of Relativistic Electrons Driven by Whistler Waves
Khazanov, G. V.; Telnikhin, A. A.; Kronberg, Tatiana K.
2007-01-01
Canonical equations governing an electron motion in electromagnetic field of the whistler mode waves propagating along the direction of an ambient magnetic field are derived. The physical processes on which the equations of motion are based .are identified. It is shown that relativistic electrons interacting with these fields demonstrate chaotic motion, which is accompanied by the particle stochastic heating and significant pitch angle diffusion. Evolution of distribution functions is described by the Fokker-Planck-Kolmogorov equations. It is shown that the whistler mode waves could provide a viable mechanism for stochastic energization of electrons with energies up to 50 MeV in the Jovian magnetosphere.
Generalized relativistic wave equations with intrinsic maximum momentum
Ching, Chee Leong; Ng, Wei Khim
2014-05-01
We examine the nonperturbative effect of maximum momentum on the relativistic wave equations. In momentum representation, we obtain the exact eigen-energies and wave functions of one-dimensional Klein-Gordon and Dirac equation with linear confining potentials, and the Dirac oscillator. Bound state solutions are only possible when the strength of scalar potential is stronger than vector potential. The energy spectrum of the systems studied is bounded from above, whereby classical characteristics are observed in the uncertainties of position and momentum operators. Also, there is a truncation in the maximum number of bound states that is allowed. Some of these quantum-gravitational features may have future applications.
Whistler wave generation by non-gyrotropic, relativistic, electron beams
Skender, Marina
2014-01-01
Particle-in-cell code, EPOCH, is used for studying features of the wave component evident to propagate backwards from the front of the non-gyrotropic, relativistic beam of electrons injected in the Maxwellian, magnetised background plasma with decreasing density profile. According to recent findings presented in Tsiklauri (2011), Schmitz & Tsiklauri (2013) and Pechhacker & Tsiklauri (2012), in a 1.5-dimensional magnetised plasma system, the non-gyrotropic beam generates freely escaping electromagnetic radiation with properties similar to the Type-III solar radio bursts. In this study the backwards propagating wave component evident in the perpendicular components of the elecromagnetic field in such a system is presented for the first time. Background magnetic field strength in the system is varied in order to prove that the backwards propagating wave's frequency, prescribed by the whistler wave dispersion relation, is proportional to the specified magnetic field. Moreover, the identified whistlers are...
Self-similar ultra-relativistic jetted blast wave
Keshet, Uri
2015-01-01
Following a suggestion that a directed relativistic explosion may have a universal intermediate asymptotic, we derive a self-similar solution for an ultra-relativistic jetted blast wave. The solution involves three distinct regions: an approximately paraboloid head where the Lorentz factor $\\gamma$ exceeds $\\sim1/2$ of its maximal, nose value; a geometrically self-similar, expanding envelope slightly narrower than a paraboloid; and an axial core in which the radial flow $U$ converges inward towards the axis. Most ($\\sim 80\\%$) of the energy lies well beyond the head. Here, a radial cross section shows a maximal $\\gamma$ (separating the core and the envelope), a sign reversal in $U$, and a minimal $\\gamma$, at respectively $\\sim 1/6$, $\\sim1/4$, and $\\sim3/4$ of the shock radius. The solution is apparently unique, and approximately agrees with previous simulations, of different initial conditions, that resolved the head. This suggests that unlike a spherical relativistic blast wave, our solution is an attracto...
Anton, L; Marti, J M; Ibanez, J M; Aloy, M A; Mimica, P
2009-01-01
We obtain renormalized sets of right and left eigenvectors of the flux vector Jacobians of the relativistic MHD equations, which are regular and span a complete basis in any physical state including degenerate ones. The renormalization procedure relies on the characterization of the degeneracy types in terms of the normal and tangential components of the magnetic field to the wavefront in the fluid rest frame. Proper expressions of the renormalized eigenvectors in conserved variables are obtained through the corresponding matrix transformations. Our work completes previous analysis that present different sets of right eigenvectors for non-degenerate and degenerate states, and can be seen as a relativistic generalization of earlier work performed in classical MHD. Based on the full wave decomposition (FWD) provided by the the renormalized set of eigenvectors in conserved variables, we have also developed a linearized (Roe-type) Riemann solver. Extensive testing against one- and two-dimensional standard numeric...
EFFECT OF INTERACTING RAREFACTION WAVES ON RELATIVISTICALLY HOT JETS
Matsumoto, Jin; Shibata, Kazunari [Kwasan and Hida Observatories, Kyoto University, Kyoto (Japan); Masada, Youhei, E-mail: jin@kusastro.kyoto-u.ac.jp [Graduate School of System Informatics, Department of Computational Science, Kobe University, Kobe (Japan)
2012-06-01
The effect of rarefaction acceleration on the propagation dynamics and structure of relativistically hot jets is studied through relativistic hydrodynamic simulations. We emphasize the nonlinear interaction of rarefaction waves excited at the interface between a cylindrical jet and the surrounding medium. From simplified one-dimensional (1D) models with radial jet structure, we find that a decrease in the relativistic pressure due to the interacting rarefaction waves in the central zone of the jet transiently yields a more powerful boost of the bulk jet than that expected from single rarefaction acceleration. This leads to a cyclic in situ energy conversion between thermal and bulk kinetic energies, which induces radial oscillating motion of the jet. The oscillation timescale is characterized by the initial pressure ratio of the jet to the ambient medium and follows a simple scaling relation, {tau}{sub oscillation}{proportional_to}(P{sub jet,0}/P{sub amb,0}){sup 1/2}. Extended two-dimensional simulations confirm that this radial oscillating motion in the 1D system manifests as modulation of the structure of the jet in a more realistic situation where a relativistically hot jet propagates through an ambient medium. We find that when the ambient medium has a power-law pressure distribution, the size of the reconfinement region along the propagation direction of the jet in the modulation structure {lambda} evolves according to a self-similar relation {lambda}{proportional_to}t{sup {alpha}/2}, where {alpha} is the power-law index of the pressure distribution.
Relativistic effects on the modulational instability of electron plasma waves in quantum plasma
Basudev Ghosh; Swarniv Chandra; Sailendra Nath Paul
2012-05-01
Relativistic effects on the linear and nonlinear properties of electron plasma waves are investigated using the one-dimensional quantum hydrodynamic (QHD) model for a twocomponent electron–ion dense quantum plasma. Using standard perturbation technique, a nonlinear Schrödinger equation (NLSE) containing both relativistic and quantum effects has been derived. This equation has been used to discuss the modulational instability of the wave. Through numerical calculations it is shown that relativistic effects signiﬁcantly change the linear dispersion character of the wave. Unlike quantum effects, relativistic effects are shown to reduce the instability growth rate of electron plasma waves.
Confirmation of EMIC wave-driven relativistic electron precipitation
Hendry, Aaron T.; Rodger, Craig J.; Clilverd, Mark A.; Engebretson, Mark J.; Mann, Ian R.; Lessard, Marc R.; Raita, Tero; Milling, David K.
2016-06-01
Electromagnetic ion cyclotron (EMIC) waves are believed to be an important source of pitch angle scattering driven relativistic electron loss from the radiation belts. To date, investigations of this precipitation have been largely theoretical in nature, limited to calculations of precipitation characteristics based on wave observations and small-scale studies. Large-scale investigation of EMIC wave-driven electron precipitation has been hindered by a lack of combined wave and precipitation measurements. Analysis of electron flux data from the POES (Polar Orbiting Environmental Satellites) spacecraft has been suggested as a means of investigating EMIC wave-driven electron precipitation characteristics, using a precipitation signature particular to EMIC waves. Until now the lack of supporting wave measurements for these POES-detected precipitation events has resulted in uncertainty regarding the driver of the precipitation. In this paper we complete a statistical study comparing POES precipitation measurements with wave data from several ground-based search coil magnetometers; we further present a case study examining the global nature of this precipitation. We show that a significant proportion of the precipitation events correspond with EMIC wave detections on the ground; for precipitation events that occur directly over the magnetometers, this detection rate can be as high as 90%. Our results demonstrate that the precipitation region is often stationary in magnetic local time, narrow in L, and close to the expected plasmapause position. Predominantly, the precipitation is associated with helium band rising tone Pc1 waves on the ground. The success of this study proves the viability of POES precipitation data for investigating EMIC wave-driven electron precipitation.
Baryon Wave Functions in Covariant Relativistic Quark Models
Dillig, M
2002-01-01
We derive covariant baryon wave functions for arbitrary Lorentz boosts. Modeling baryons as quark-diquark systems, we reduce their manifestly covariant Bethe-Salpeter equation to a covariant 3-dimensional form by projecting on the relative quark-diquark energy. Guided by a phenomenological multigluon exchange representation of a covariant confining kernel, we derive for practical applications explicit solutions for harmonic confinement and for the MIT Bag Model. We briefly comment on the interplay of boosts and center-of-mass corrections in relativistic quark models.
Synchrotron signature of a relativistic blast wave with decaying microturbulence
Lemoine, M
2012-01-01
Microphysics of weakly magnetized relativistic collisionless shock waves, corroborated by recent high performance numerical simulations, indicate the presence of a microturbulent layer of large magnetic field strength behind the shock front, which must decay beyond some hundreds of skin depths. The present paper discusses the dynamics of such microturbulence, borrowing from these same numerical simulations, and calculates the synchrotron signature of a powerlaw of shock accelerated particles. The decaying microturbulent layer is found to leave distinct signatures in the spectro-temporal evolution of the spectrum $F_\
Generalized Relativistic Wave Equations with Intrinsic Maximum Momentum
Ching, Chee Leong
2013-01-01
We examine the nonperturbative effect of maximum momentum on the relativistic wave equations. In momentum representation, we obtain the exact eigen-energies and wavefunctions of one-dimensional Klein-Gordon and Dirac equation with linear confining potentials, and the Dirac oscillator. Bound state solutions are only possible when the strength of scalar potential are stronger than vector potential. The energy spectrum of the systems studied are bounded from above, whereby classical characteristics are observed in the uncertainties of position and momentum operators. Also, there is a truncation in the maximum number of bound states that is allowed. Some of these quantum-gravitational features may have future applications.
Thermodynamics of relativistic quantum fields: extracting energy from gravitational waves
Bruschi, David Edward
2016-01-01
We investigate the quantum thermodynamical properties of localised relativistic quantum fields that can be used as quantum thermal machines. We study the efficiency and power of energy transfer between the classical degrees of freedom, such as the energy input due to motion or to an impinging gravitational wave, and the excitations of the confined quantum field. We find that the efficiency of energy transfer depends dramatically on the input initial state of the system. Furthermore, we investigate the ability to extract the energy and to store it in a battery. This process is inefficient in optical cavities but is significantly enhanced when employing trapped Bose Einstein Condensates. Finally, we apply our techniques to a setup where an impinging gravitational wave excites the phononic modes of a Bose Einstein Condensate. We find that, in this case, the amount of energy transfer to the phonons increases with time and quickly approaches unity. These results suggest that, in the future, it might be possible to...
Massless and Massive Gauge-Invariant Fields in the Theory of Relativistic Wave Equations
Pletyukhov, V A
2010-01-01
In this work consideration is given to massless and massive gauge-invariant spin 0 and spin 1 fields (particles) within the scope of a theory of the generalized relativistic wave equations with an extended set of the Lorentz group representations. The results obtained may be useful as regards the application of a relativistic wave-equation theory in modern field models.
Ding, Min; Li, Yachun
2017-04-01
We study the 1-D piston problem for the relativistic Euler equations under the assumption that the total variations of both the initial data and the velocity of the piston are sufficiently small. By a modified wave front tracking method, we establish the global existence of entropy solutions including a strong rarefaction wave without restriction on the strength. Meanwhile, we consider the convergence of the entropy solutions to the corresponding entropy solutions of the classical non-relativistic Euler equations as the light speed c→ +∞.
On electromagnetic instabilities at ultra-relativistic shock waves
Lemoine, Martin
2009-01-01
(Abridged) This paper addresses the issue of magnetic field generation in a relativistic shock precursor through micro-instabilities. The level of magnetization of the upstream plasma turns out to be a crucial parameter, notably because the length scale of the shock precursor is limited by the Larmor rotation of the accelerated particles in the background magnetic field and the speed of the shock wave. We discuss in detail and calculate the growth rates of the following beam plasma instabilities seeded by the accelerated and reflected particle populations: for an unmagnetized shock, the Weibel and filamentation instabilities, as well as the Cerenkov resonant longitudinal and oblique modes; for a magnetized shock, in a generic oblique configuration, the Weibel instability and the resonant Cerenkov instabilities with Alfven, Whisler and extraordinary modes. All these instabilities are generated upstream, then they are transmitted downstream. The modes excited by Cerenkov resonant instabilities take on particula...
Unified relativistic physics from a standing wave particle model
Vera, R A
1995-01-01
An extremely simple and unified base for physics comes out by starting all over from a single postulate on the common nature of matter and stationary forms of radiation quanta. Basic relativistic, gravitational (G) and quantum mechanical properties of a standing wave particle model have been derived. This has been done from just dual properties of radiation's and strictly homogeneous relationships for nonlocal cases in G fields. This way reduces the number of independent variables and puts into relief (and avoid) important inhomogeneity errors of some G theories. It unifies and accounts for basic principles and postulates physics. The results for gravity depend on linear radiation properties but not on arbitrary field relations. They agree with the conventional tests. However they have some fundamental differences with current G theories. The particle model, at a difference of the conventional theories, also fixes well-defined cosmological and astrophysical models that are different from the rather convention...
Vacuum-Structure and a Relativistic Pilot Wave
Salehi, H; Golshani, M; Salehi, Hadi; Motavali, Hossein; Golshani, Mehdi
2000-01-01
We study a model for analyzing the effect of a principal violation of the Lorentz-invariance on the structure of vacuum. The model is based on the divergence theory developed by Salehi (1997). It is shown that the divergence theory can be used to model an ensemble of particles. The ensemble is characterized by the condition that its members are basically at rest in the rest frame of a preferred inertial observer in vacuum. In this way we find a direct dynamical interplay between a particle and its associated ensemble. We show that this effect can be understood in terms of the interaction of a particle with a relativistic pilot wave through an associated quantum potential.
Relativistic orbits and Gravitational Waves from gravitomagnetic corrections
Capozziello, Salvatore; Forte, Luca; Garufi, Fabio; Milano, Leopoldo
2010-01-01
Corrections to the relativistic theory of orbits are discussed considering higher order approximations induced by gravitomagnetic effects. Beside the standard periastron effect of General Relativity (GR), a new nutation effect was found due to the ${\\displaystyle c^{-3}}$ orbital correction. According to the presence of that new nutation effect we studied the gravitational waveforms emitted through the capture in a gravitational field of a massive black hole (MBH) of a compact object (neutron star (NS) or BH) via the quadrupole approximation. We made a numerical study to obtain the emitted gravitational wave (GW) amplitudes. We conclude that the effects we studied could be of interest for the future space laser interferometric GW antenna LISA.
Whistler wave generation by non-gyrotropic, relativistic, electron beams
Skender, Marina; Tsiklauri, David
2014-05-01
]. In this study [5], for the first time, the backwards propagating wave component evident in the perpendicular components of the electromagnetic field in such a system is presented. Features of the wave component propagating backwards from the front of the non-gyrotropic, relativistic, beam of electrons injected in the Maxwellian, magnetised background plasma with decreasing density profile are studied by using the Particle-In-Cell code EPOCH. Magnetic field in the 1.5-dimensional system is varied in order to prove that the backwards propagating wave is harmonic of the electron cyclotron frequency. The analysis has lead to the identification of the backwards travelling waves as whistlers. Moreover, the whistlers are shown to be generated by the normal and anomalous Doppler resonance. Large fraction of the energy of the perpendicular electromagnetic field components is found to be carried away by the whistler waves. [1] D. Tsiklauri, Phys. Plasmas 18, 052903 (2011). [2] D. Tsiklauri, H. Schmitz, Geophys. Res. Abs. 15, EGU2013-5403 (2013). [3] H. Schmitz, D. Tsiklauri, Phys. Plasmas 20, 062903 (2013). [4] R. Pechhacker, D. Tsiklauri, Phys. Plasmas 19, 112903 (2012). [5] M. Skender, D. Tsiklauri, submitted to Phys. Plasmas (2013): http://astro.qmul.ac.uk/ tsiklauri/
A repetitive 0.14 THz relativistic surface wave oscillator
Wang Guangqiang; Tong Changjiang; Li Xiaoze; Wang Xuefeng; Li Shuang; Lu Xicheng [Northwest Institute of Nuclear Technology, P.O. Box 69-1, Xi' an 710024 (China); Wang Jianguo [Northwest Institute of Nuclear Technology, P.O. Box 69-1, Xi' an 710024 (China); School of Electronic and Information Engineering, Xi' an Jiaotong University, Xi' an 710049 (China)
2013-04-15
Preliminary experimental results of a repetitive 0.14 THz overmoded relativistic surface wave oscillator (RSWO) are presented in this paper. The repetitive RSWO is developed by using a rectangularly corrugated slow-wave structure with overmoded ratio of 3 and a foilless diode emitting annular electron beam with thickness of 0.5 mm. The high quality electron beams at the repetition rate of 10 are obtained over a wide range of diode voltage (180 kV < U < 240 kV) and current (700 A < I < 1.2 kA). The generation experiments of RSWO are conducted at an axial pulsed magnetic field whose maximum strength and duration can reach about 2.7 T and 1 s, respectively. The experimental results show that the RSWO successfully produces reasonable uniform terahertz pulses at repetition rate of 10, and the pulse duration, frequency, and power of a single pulse are about 1.5 ns, 0.154 THz, and 2.6 MW, respectively, whereas the dominated radiation mode of the RSWO is TM{sub 02}.
Whistler-Mode Waves Growth by a Generalized Relativistic Kappa-Type Distribution
ZHOU Qing-Hua; JIANG Bin; SHI Xiang-Hua; LI Jun-Qiu
2009-01-01
The instability of field-aligned Whistler-mode waves in space plasmas is studied by using a recently developed generalized relativistic kappa-type (KT) distribution. Numerical calculations are performed for a direct compar-ison between the new KT distribution and the current kappa distribution. We show that the wave growth for the KT distribution tends to occur in the lower wave frequency (e.g., ω 0.1Ωe) due to a larger fractional num-ber of the resonant electrons ηrel (which controls the wave growth), while primarily locating in the higher wave frequency for the kappa distribution. Moreover, the relativistic anisotropy Arel by the KT distribution is found to be smaller than that by the kappa distribution, leading to a smaller peak of wave growth. The results present a further understanding of plasma wave instability particularly in those plasmas where relativistic electrons are present.
Wave-induced loss of ultra-relativistic electrons in the Van Allen radiation belts
Shprits, Yuri Y.; Drozdov, Alexander Y.; Spasojevic, Maria; Kellerman, Adam C.; Usanova, Maria E.; Engebretson, Mark J.; Agapitov, Oleksiy V.; Zhelavskaya, Irina S.; Raita, Tero J.; Spence, Harlan E.; Baker, Daniel N.; Zhu, Hui; Aseev, Nikita A.
2016-01-01
The dipole configuration of the Earth's magnetic field allows for the trapping of highly energetic particles, which form the radiation belts. Although significant advances have been made in understanding the acceleration mechanisms in the radiation belts, the loss processes remain poorly understood. Unique observations on 17 January 2013 provide detailed information throughout the belts on the energy spectrum and pitch angle (angle between the velocity of a particle and the magnetic field) distribution of electrons up to ultra-relativistic energies. Here we show that although relativistic electrons are enhanced, ultra-relativistic electrons become depleted and distributions of particles show very clear telltale signatures of electromagnetic ion cyclotron wave-induced loss. Comparisons between observations and modelling of the evolution of the electron flux and pitch angle show that electromagnetic ion cyclotron waves provide the dominant loss mechanism at ultra-relativistic energies and produce a profound dropout of the ultra-relativistic radiation belt fluxes. PMID:27678050
Wave-induced loss of ultra-relativistic electrons in the Van Allen radiation belts.
Shprits, Yuri Y; Drozdov, Alexander Y; Spasojevic, Maria; Kellerman, Adam C; Usanova, Maria E; Engebretson, Mark J; Agapitov, Oleksiy V; Zhelavskaya, Irina S; Raita, Tero J; Spence, Harlan E; Baker, Daniel N; Zhu, Hui; Aseev, Nikita A
2016-09-28
The dipole configuration of the Earth's magnetic field allows for the trapping of highly energetic particles, which form the radiation belts. Although significant advances have been made in understanding the acceleration mechanisms in the radiation belts, the loss processes remain poorly understood. Unique observations on 17 January 2013 provide detailed information throughout the belts on the energy spectrum and pitch angle (angle between the velocity of a particle and the magnetic field) distribution of electrons up to ultra-relativistic energies. Here we show that although relativistic electrons are enhanced, ultra-relativistic electrons become depleted and distributions of particles show very clear telltale signatures of electromagnetic ion cyclotron wave-induced loss. Comparisons between observations and modelling of the evolution of the electron flux and pitch angle show that electromagnetic ion cyclotron waves provide the dominant loss mechanism at ultra-relativistic energies and produce a profound dropout of the ultra-relativistic radiation belt fluxes.
Wave-induced loss of ultra-relativistic electrons in the Van Allen radiation belts
Shprits, Yuri Y.; Drozdov, Alexander Y.; Spasojevic, Maria; Kellerman, Adam C.; Usanova, Maria E.; Engebretson, Mark J.; Agapitov, Oleksiy V.; Zhelavskaya, Irina S.; Raita, Tero J.; Spence, Harlan E.; Baker, Daniel N.; Zhu, Hui; Aseev, Nikita A.
2016-09-01
The dipole configuration of the Earth's magnetic field allows for the trapping of highly energetic particles, which form the radiation belts. Although significant advances have been made in understanding the acceleration mechanisms in the radiation belts, the loss processes remain poorly understood. Unique observations on 17 January 2013 provide detailed information throughout the belts on the energy spectrum and pitch angle (angle between the velocity of a particle and the magnetic field) distribution of electrons up to ultra-relativistic energies. Here we show that although relativistic electrons are enhanced, ultra-relativistic electrons become depleted and distributions of particles show very clear telltale signatures of electromagnetic ion cyclotron wave-induced loss. Comparisons between observations and modelling of the evolution of the electron flux and pitch angle show that electromagnetic ion cyclotron waves provide the dominant loss mechanism at ultra-relativistic energies and produce a profound dropout of the ultra-relativistic radiation belt fluxes.
Modeling of modified electron-acoustic solitary waves in a relativistic degenerate plasma
Hossen, M. R.; Mamun, A. A. [Jahangirnagar University, Savar, Dhaka (Bangladesh)
2014-12-15
The modeling of a theoretical and numerical study on the nonlinear propagation of modified electron-acoustic (mEA) solitary waves has been carried out in an unmagnetized, collisionless, relativistic, degenerate quantum plasma (containing non-relativistic degenerate inertial cold electrons, both non-relativistic and ultra-relativistic degenerate hot electron and inertial positron fluids, and positively-charged static ions). A reductive perturbation technique is used to derive the planar and the nonplanar Korteweg-de Vries (K-dV) equations, which admit a localized wave solution for the solitary profile. The solitary wave's characteristics are found to have been influenced significantly for the non-relativistic and the ultra-relativistic limits. The mEA solitary waves are also found to have been significantly modified due to the effects of the degenerate pressure and the number densities of this dense plasma's constituents. The properties of the planar K-dV solitary wave are quite different from those of the nonplanar K-dV solitary wave. The relevance of our results to astrophysical objects (like white dwarfs and neutron stars), which are of scientific interest, is briefly mentioned.
Waves in General Relativistic Two-fluid Plasma around a Schwarzschild Black Hole
Rahman, M Atiqur
2010-01-01
Waves propagating in the relativistic electron-positron or ions plasma are investigated in a frame of two-fluid equations using the 3+1 formalism of general relativity developed by Thorne, Price and Macdonald (TPM). The plasma is assumed to be freefalling in the radial direction toward the event horizon due to the strong gravitational field of a Schwarzschild black hole. The local dispersion relations for transverse and longitudinal waves have been derived, in analogy with the special relativistic formulation as explained in an earlier paper, to take account of relativistic effects due to the event horizon using WKB approximation
Effect of EMIC Wave Normal Angle Distribution on Relativistic Electron Scattering
Gamayunov, K. V.; Khazanov, G. V.
2006-01-01
The flux level of outer-zone relativistic electrons (above 1 MeV) is extremely variable during geomagnetic storms, and controlled by a competition between acceleration and loss. Precipitation of these electrons due to resonant pitch-angle scattering by electromagnetic ion cyclotron (EMIC) waves is considered one of the major loss mechanisms. This mechanism was suggested in early theoretical studies more than three decades ago. However, direct experimental evidence of the wave role in relativistic electrons precipitation is difficult to obtain because of lack of concurrent measurements of precipitating electrons at low altitudes and the waves in a magnetically conjugate equatorial region. Recently, the data from balloon-borne X-ray instruments provided indirect but strong evidence on an efficiency of the EMIC wave induced loss for the outer-zone relativistic electrons. These observations stimulated theoretical studies that, particularly, demonstrated that EMIC wave induced pitch-angle diffusion of MeV electrons can operate in the strong diffusion limit and this mechanism can compete with relativistic electron depletion caused by the Dst effect during the initial and main phases of storm. Although an effectiveness of relativistic electron scattering by EMIC waves depends strongly on the wave spectral properties, the most favorable assumptions regarding wave characteristics has been made in all previous theoretical studies. Particularly, only quasi field-aligned EMIC waves have been considered as a driver for relativistic electron loss. At the same time, there is growing experimental and theoretical evidence that these waves can be highly oblique; EMIC wave energy can occupy not only the region of generation, i.e. the region of small wave normal angles, but also the entire wave normal angle region, and even only the region near 90 degrees. The latter can dramatically change he effectiveness of relativistic electron scattering by EMIC waves. In the present study, we
Shahmansouri, M.; Misra, A. P.
2016-12-01
The modulational instability (MI) and the evolution of weakly nonlinear two-dimensional (2D) Langmuir wave (LW) packets are studied in an unmagnetized collisionless plasma with weakly relativistic electron flow. By using a 2D self-consistent relativistic fluid model and employing the standard multiple-scale technique, a coupled set of Davey-Stewartson (DS)-like equations is derived, which governs the slow modulation and the evolution of LW packets in relativistic plasmas. It is found that the relativistic effects favor the instability of LW envelopes in the k - θ plane, where k is the wave number and θ ( 0 ≤ θ ≤ π ) the angle of modulation. It is also found that as the electron thermal velocity or θ increases, the growth rate of MI increases with cutoffs at higher wave numbers of modulation. Furthermore, in the nonlinear evolution of the DS-like equations, it is seen that with an effect of the relativistic flow, a Gaussian wave beam collapses in a finite time, and the collapse can be arrested when the effect of the thermal pressure or the relativistic flow is slightly relaxed. The present results may be useful to the MI and the formation of localized LW envelopes in cosmic plasmas with a relativistic flow of electrons.
Towards Relativistic Atomic Physics and Post-Minkowskian Gravitational Waves
Lusanna, Luca
2009-01-01
A review is given of the formulation of relativistic atomic theory, in which there is an explicit realization of the Poincare' generators, both in the inertial and in the non-inertial rest-frame instant form of dynamics in Minkowski space-time. This implies the need to solve the problem of the relativistic center of mass of an isolated system and to describe the transitions from different conventions for clock synchronization, namely for the identifications of instantaneous 3-spaces, as gauge transformations. These problems, stemming from the Lorentz signature of space-time, are a source of non-locality, which induces a spatial non-separability in relativistic quantum mechanics, with implications for relativistic entanglement. Then the classical system of charged particles plus the electro-magnetic field is studied in the framework of ADM canonical tetrad gravity in asymptotically Minkowskian space-times admitting the ADM Poincare' group at spatial infinity, which allows to get the general relativistic extens...
Hafez, M. G.; Talukder, M. R.; Hossain Ali, M.
2017-04-01
The Burgers equation is obtained to study the characteristics of nonlinear propagation of ionacoustic shock, singular kink, and periodic waves in weakly relativistic plasmas containing relativistic thermal ions, nonextensive distributed electrons, Boltzmann distributed positrons, and kinematic viscosity of ions using the well-known reductive perturbation technique. This equation is solved by employing the ( G'/ G)-expansion method taking unperturbed positron-to-electron concentration ratio, electron-to-positron temperature ratio, strength of electrons nonextensivity, ion kinematic viscosity, and weakly relativistic streaming factor. The influences of plasma parameters on nonlinear propagation of ion-acoustic shock, periodic, and singular kink waves are displayed graphically and the relevant physical explanations are described. It is found that these parameters extensively modify the shock structures excitation. The obtained results may be useful in understanding the features of small but finite amplitude localized relativistic ion-acoustic shock waves in an unmagnetized plasma system for some astrophysical compact objects and space plasmas.
Ultra-low-frequency wave-driven diffusion of radiation belt relativistic electrons.
Su, Zhenpeng; Zhu, Hui; Xiao, Fuliang; Zong, Q-G; Zhou, X-Z; Zheng, Huinan; Wang, Yuming; Wang, Shui; Hao, Y-X; Gao, Zhonglei; He, Zhaoguo; Baker, D N; Spence, H E; Reeves, G D; Blake, J B; Wygant, J R
2015-12-22
Van Allen radiation belts are typically two zones of energetic particles encircling the Earth separated by the slot region. How the outer radiation belt electrons are accelerated to relativistic energies remains an unanswered question. Recent studies have presented compelling evidence for the local acceleration by very-low-frequency (VLF) chorus waves. However, there has been a competing theory to the local acceleration, radial diffusion by ultra-low-frequency (ULF) waves, whose importance has not yet been determined definitively. Here we report a unique radiation belt event with intense ULF waves but no detectable VLF chorus waves. Our results demonstrate that the ULF waves moved the inner edge of the outer radiation belt earthward 0.3 Earth radii and enhanced the relativistic electron fluxes by up to one order of magnitude near the slot region within about 10 h, providing strong evidence for the radial diffusion of radiation belt relativistic electrons.
Kersten, K.; Cattell, C. A.; Breneman, A.; Goetz, K.; Kellogg, P. J.; Wygant, J. R.; Wilson, L. B., III; Blake, J. B.; Looper, M. D.; Roth, I.
2011-01-01
We present multi-satellite observations of large amplitude radiation belt whistler-mode waves and relativistic electron precipitation. On separate occasions during the Wind petal orbits and STEREO phasing orbits, Wind and STEREO recorded intense whistler-mode waves in the outer nightside equatorial radiation belt with peak-to-peak amplitudes exceeding 300 mV/m. During these intervals of intense wave activity, SAMPEX recorded relativistic electron microbursts in near magnetic conjunction with Wind and STEREO. This evidence of microburst precipitation occurring at the same time and at nearly the same magnetic local time and L-shell with a bursty temporal structure similar to that of the observed large amplitude wave packets suggests a causal connection between the two phenomena. Simulation studies corroborate this idea, showing that nonlinear wave.particle interactions may result in rapid energization and scattering on timescales comparable to those of the impulsive relativistic electron precipitation.
Compression-amplified EMIC waves and their effects on relativistic electrons
Li, L. Y., E-mail: lyli-ssri@buaa.edu.cn; Yu, J.; Cao, J. B. [School of Space and Environment, Beihang University, Beijing (China); Yuan, Z. G. [School of Electronic Information, Wuhan University, Wuhan (China)
2016-06-15
During enhancement of solar wind dynamic pressure, we observe the periodic emissions of electromagnetic ion cyclotron (EMIC) waves near the nightside geosynchronous orbit (6.6R{sub E}). In the hydrogen and helium bands, the different polarized EMIC waves have different influences on relativistic electrons (>0.8 MeV). The flux of relativistic electrons is relatively stable if there are only the linearly polarized EMIC waves, but their flux decreases if the left-hand polarized (L-mode) EMIC waves are sufficiently amplified (power spectral density (PSD) ≥ 1 nT{sup 2}/Hz). The larger-amplitude L-mode waves can cause more electron losses. In contrast, the R-mode EMIC waves are very weak (PSD < 1 nT{sup 2}/Hz) during the electron flux dropouts; thus, their influence may be ignored here. During the electron flux dropouts, the relativistic electron precipitation is observed by POES satellite near the foot point (∼850 km) of the wave emission region. The quasi-linear simulation of wave-particle interactions indicates that the L-mode EMIC waves can cause the rapid precipitation loss of relativistic electrons, especially when the initial resonant electrons have a butterfly-like pitch angle distribution.
SU Zhen-Peng; ZHENG Hui-Nan
2009-01-01
The bounce-averaged Fokker-Planck equation is solved to study the relativistic electron phase space density(PSD)evolution in the outer radiation belt due to resonant interactions with plasmaspheric plume electromagnetic ion cyclotron(EMIC)waves.It is found that the PSDs of relativistic electrons can be depleted by 1-3 orders of magnitude in 5h,supporting the previous finding that resonant interactions with EMIC waves may account for the frequently observed relativistic electron flux dropouts in the outer radiation belt during the main phase of a storm.The significant precipitation Joss of ～Me V electrons is primarily induced by the EMIC waves in H~+ and He~+ bands.The rapid remove of highly relativistic electrons(＞5 MeV)is mainly driven by the EMIC waves in O~+ band at lower pitch-angles,as well as the EMIC waves in H~+ and He~+ bands at larger pitch-angles.Moreover,a stronger depletion of relativistic electrons is found to occur over a wider pitch angle range when EMIC waves are centering relatively higher in the band.
Hafez, M. G.; Talukder, M. R.; Sakthivel, R.
2016-05-01
The theoretical and numerical studies have been investigated on nonlinear propagation of weakly relativistic ion acoustic solitary waves in an unmagnetized plasma system consisting of nonextensive electrons, positrons and relativistic thermal ions. To study the characteristics of nonlinear propagation of the three-component plasma system, the reductive perturbation technique has been applied to derive the Korteweg-de Vries equation, which divulges the soliton-like solitary wave solution. The ansatz method is employed to carry out the integration of this equation. The effects of nonextensive electrons, positrons and relativistic thermal ions on phase velocity, amplitude and width of soliton and electrostatic nonlinear propagation of weakly relativistic ion acoustic solitary waves have been discussed taking different plasma parameters into consideration. The obtained results can be useful in understanding the features of small amplitude localized relativistic ion acoustic solitary waves in an unmagnetized three-component plasma system for hard thermal photon production with relativistic heavy ions collision in quark-gluon plasma as well as for astrophysical plasmas.
Investigation of EMIC Waves During Balloon Detected Relativistic Electron Precipitation Events
Woodger, L. A.; Millan, R. M.
2009-12-01
Multiple relativistic electron precipitation (REP) events were detected by balloon-borne instrumentation during the MAXIS 2000 and MINIS 2005 campaigns. It has been suggested that resonance with EMIC waves caused these precipitation events (Lorentzen et al, 2000 and Millan et al, 2002) due to their location in the dusk sector. We present observations of dusk-side relativistic electron precipitation events, and use supporting satellite and theoretical data to investigate the relationship between EMIC waves and the detected REP. Satellite data can provide direct measurements of not only the waves themselves but also important resonance condition parameters. The data will be presented collectively with each event to showcase similarities and differences between events and the challenges that arise in trying to understand the relationship between dusk-side relativistic electron precipitation and EMIC waves.
Hafez, M. G.; Talukder, M. R.
2015-09-01
This work investigates the theoretical and numerical studies on nonlinear propagation of ion acoustic solitary waves (IASWs) in an unmagnetized plasma consisting of nonextensive electrons, Boltzmann positrons and relativistic thermal ions. The Korteweg-de Vries (KdV) equation is derived by using the well known reductive perturbation method. This equation admits the soliton like solitary wave solution. The effects of phase velocity, amplitude of soliton, width of soliton and electrostatic nonlinear propagation of weakly relativistic ion-acoustic solitary waves have been discussed with graphical representation found in the variation of the plasma parameters. The obtained results can be helpful in understanding the features of small but finite amplitude localized relativistic ion-acoustic waves for an unmagnetized three component plasma system in astrophysical compact objects.
Relativistic regimes for dispersive shock-waves in non-paraxial nonlinear optics
Gentilini, Silvia; Conti, Claudio
2014-01-01
We investigate the effect of non-paraxiality in the dynamics of dispersive shock waves in the defocusing nonlinear Schroedinger equation. We show that the problem can be described in terms of a relativistic particle moving in a potential. Lowest order corrections enhance the wave-breaking and impose a limit to the highest achievable spectrum in an amount experimentally testable.
Dynamics and stability of relativistic gamma-ray-bursts blast waves
Meliani, Z.; Keppens, R.
2010-01-01
Aims. In gamma-ray-bursts (GRBs), ultra-relativistic blast waves are ejected into the circumburst medium. We analyse in unprecedented detail the deceleration of a self-similar Blandford-McKee blast wave from a Lorentz factor 25 to the nonrelativistic Sedov phase. Our goal is to determine the stabili
Relativistic n-body wave equations in scalar quantum field theory
Emami-Razavi, Mohsen [Centre for Research in Earth and Space Science, York University, Toronto, Ontario, M3J 1P3 (Canada)]. E-mail: mohsen@yorku.ca
2006-09-21
The variational method in a reformulated Hamiltonian formalism of Quantum Field Theory (QFT) is used to derive relativistic n-body wave equations for scalar particles (bosons) interacting via a massive or massless mediating scalar field (the scalar Yukawa model). Simple Fock-space variational trial states are used to derive relativistic n-body wave equations. The equations are shown to have the Schroedinger non-relativistic limits, with Coulombic interparticle potentials in the case of a massless mediating field and Yukawa interparticle potentials in the case of a massive mediating field. Some examples of approximate ground state solutions of the n-body relativistic equations are obtained for various strengths of coupling, for both massive and massless mediating fields.
Simulation of laser-driven plasma beat-wave propagation in collisional weakly relativistic plasmas
Kaur, Maninder; Nandan Gupta, Devki
2016-11-01
The process of interaction of lasers beating in a plasma has been explored by virtue of particle-in-cell (PIC) simulations in the presence of electron-ion collisions. A plasma beat wave is resonantly excited by ponderomotive force by two relatively long laser pulses of different frequencies. The amplitude of the plasma wave become maximum, when the difference in the frequencies is equal to the plasma frequency. We propose to demonstrate the energy transfer between the laser beat wave and the plasma wave in the presence of electron-ion collision in nearly relativistic regime with 2D-PIC simulations. The relativistic effect and electron-ion collision both affect the energy transfer between the interacting waves. The finding of simulation results shows that there is a considerable decay in the plasma wave and the field energy over time in the presence of electron-ion collisions.
Noureen, S.; Abbas, G.; Farooq, H.
2017-09-01
Using Vlasov-Maxwell's equations, the spectra of the perpendicular propagating Bernstein wave and Extraordinary wave in ultra-relativistic fully degenerate electron plasma are studied. The equilibrium particle distribution function is assumed to be isotropic Fermian. The analysis of high frequency spectra of the waves is carried out in the weak propagation limit Ω≫k .v and in the weak magnetic field limit |ω-k .v | ≫Ω and graphically observed.
Kozyreva, O. V.; Pilipenko, V. A.; Engebretson, M. J.; Yumoto, K.
2004-05-01
A new ULF wave index, characterizing the turbulent level of the geomagnetic field, has been calculated and applied for the analysis of relativistic electron enhancements during Space Weather Month (10-30 September 1999). The wave index has been produced from the INTERMAGNET, MACCS and CPMN dense arrays of ULF magnetometers in the Northern hemisphere. During the analyzed period two magnetic storms occurred (on September 12 and 22), and several significant increases of relativistic electron flux at geostationary orbit (up to 2-3 orders of magnitude) were detected by geostationary monitors. However, these electron enhancements were not related to the magnetic storm intervals. Instead, and rather unexpectedly, they correlated well with intervals of elevated ULF wave index, caused by the occurrence of intense Pc5 pulsations in the magnetosphere. This comparison is an additional indication of the possible importance of magnetospheric turbulence in energizing relativistic electrons.
Shahmansouri, M
2016-01-01
The modulational instability (MI) and the evolution of weakly nonlinear two-dimensional (2D) Langmuir wave (LW) packets are studied in an unmagnetized collisionless plasma with weakly relativistic electron flow. By using a 2D self-consistent relativistic fluid model and employing the standard multiple-scale technique, a coupled set of Davey-Stewartson (DS)-like equations is derived which governs the slow modulation and the evolution of LW packets in relativistic plasmas. It is found that the relativistic effects favor the instability of LW envelopes in the k{\\theta} plane, where k is the wave number and {\\theta} the angle of modulation. It is also found that as the electron thermal velocity or {\\theta} increases, the growth rate of MI increases with cutoffs at higher wave numbers of modulation. Furthermore, in the nonlinear evolution of the DS-like equations, it is seen that with an effect of the relativistic flow, a Gaussian wave beam collapses in a finite time, and the collapse can be arrested when the effe...
Development of the relativistic backward wave oscillator with a permanent magnet
MA Qiao-Sheng; LIU Zhong; LI Zheng-Hong; JIN Xiao
2012-01-01
Firstly,an X-band relativistic backward wave oscillator with a low guiding magnetic field is simulated,whose output microwave power is 520 MW.Then,an experiment is carried out on an accelerator to investigate a relativistic backward wave oscillator with a permanent magnetic field whose strength is 0.46 T.When the energy of the electron is 630 keV and the current of the electron beam is 6.7 kA,a 15 ns width pulsed microwave with 510 MW output power at 8.0 GHz microwave frequency is achieved.
Nonasymptotic mean-field games
Tembine, Hamidou
2014-12-01
Mean-field games have been studied under the assumption of very large number of players. For such large systems, the basic idea consists to approximate large games by a stylized game model with a continuum of players. The approach has been shown to be useful in some applications. However, the stylized game model with continuum of decision-makers is rarely observed in practice and the approximation proposed in the asymptotic regime is meaningless for networked systems with few entities. In this paper we propose a mean-field framework that is suitable not only for large systems but also for a small world with few number of entities. The applicability of the proposed framework is illustrated through a dynamic auction with asymmetric valuation distributions.
Nonasymptotic mean-field games
Tembine, Hamidou
2014-12-01
Mean-field games have been studied under the assumption of very large number of players. For such large systems, the basic idea consists of approximating large games by a stylized game model with a continuum of players. The approach has been shown to be useful in some applications. However, the stylized game model with continuum of decision-makers is rarely observed in practice and the approximation proposed in the asymptotic regime is meaningless for networks with few entities. In this paper, we propose a mean-field framework that is suitable not only for large systems but also for a small world with few number of entities. The applicability of the proposed framework is illustrated through various examples including dynamic auction with asymmetric valuation distributions, and spiteful bidders.
Vollhardt, D.; Byczuk, K.; Kollar, M.
2011-01-01
The dynamical mean-field theory (DMFT) is a widely applicable approximation scheme for the investigation of correlated quantum many-particle systems on a lattice, e.g., electrons in solids and cold atoms in optical lattices. In particular, the combination of the DMFT with conventional methods for the calculation of electronic band structures has led to a powerful numerical approach which allows one to explore the properties of correlated materials. In this introductory article we discuss the ...
Bauso, Dario
2014-01-06
The myth of marriage has been and is still a fascinating historical societal phenomenon. Paradoxically, the empirical divorce rates are at an all-time high. This work describes a unique paradigm for preserving relationships and marital stability from mean-field game theory. We show that optimizing the long-term well-being via effort and society feeling state distribution will help in stabilizing relationships.
Ultrafast ignition with relativistic shock waves induced by high power lasers
Shalom; Eliezer; Noaz; Nissim; Shirly; Vinikman; Pinhasi; Erez; Raicher; José; Maria; Martinez; Val
2014-01-01
In this paper we consider laser intensities greater than 1016 W cm-2where the ablation pressure is negligible in comparison with the radiation pressure.The radiation pressure is caused by the ponderomotive force acting mainly on the electrons that are separated from the ions to create a double layer(DL).This DL is accelerated into the target,like a piston that pushes the matter in such a way that a shock wave is created.Here we discuss two novel ideas.Firstly,the transition domain between the relativistic and non-relativistic laser-induced shock waves.Our solution is based on relativistic hydrodynamics also for the above transition domain.The relativistic shock wave parameters,such as compression,pressure,shock wave and particle flow velocities,sound velocity and rarefaction wave velocity in the compressed target,and temperature are calculated.Secondly,we would like to use this transition domain for shockwave-induced ultrafast ignition of a pre-compressed target.The laser parameters for these purposes are calculated and the main advantages of this scheme are described.If this scheme is successful a new source of energy in large quantities may become feasible.
Interacting relativistic quantum dynamics for multi-time wave functions
Lienert Matthias
2016-01-01
Full Text Available In this paper, we report on recent progress about a rigorous and manifestly covariant interacting model for two Dirac particles in 1+1 dimensions [9, 10]. It is formulated using the multi-time formalism of Dirac, Tomonaga and Schwinger. The mechanism of interaction is a relativistic generalization of contact interactions, and it is achieved going beyond the usual functional-analytic Hamiltonian method.
Interacting relativistic quantum dynamics for multi-time wave functions
Lienert, Matthias
2016-11-01
In this paper, we report on recent progress about a rigorous and manifestly covariant interacting model for two Dirac particles in 1+1 dimensions [9, 10]. It is formulated using the multi-time formalism of Dirac, Tomonaga and Schwinger. The mechanism of interaction is a relativistic generalization of contact interactions, and it is achieved going beyond the usual functional-analytic Hamiltonian method.
Nonlinear propagation of weakly relativistic ion-acoustic waves in electron–positron–ion plasma
M G HAFEZ; M R TALUKDER; M HOSSAIN ALI
2016-11-01
This work presents theoretical and numerical discussion on the dynamics of ion-acoustic solitary wave for weakly relativistic regime in unmagnetized plasma comprising non-extensive electrons, Boltzmann positrons and relativistic ions. In order to analyse the nonlinear propagation phenomena, the Korteweg–de Vries(KdV) equation is derived using the well-known reductive perturbation method. The integration of the derived equation is carried out using the ansatz method and the generalized Riccati equation mapping method. The influenceof plasma parameters on the amplitude and width of the soliton and the electrostatic nonlinear propagation of weakly relativistic ion-acoustic solitary waves are described. The obtained results of the nonlinear low-frequencywaves in such plasmas may be helpful to understand various phenomena in astrophysical compact object and space physics.
Nonlinear ion-acoustic cnoidal waves in a dense relativistic degenerate magnetoplasma
El-Shamy, E. F.
2015-03-01
The complex pattern and propagation characteristics of nonlinear periodic ion-acoustic waves, namely, ion-acoustic cnoidal waves, in a dense relativistic degenerate magnetoplasma consisting of relativistic degenerate electrons and nondegenerate cold ions are investigated. By means of the reductive perturbation method and appropriate boundary conditions for nonlinear periodic waves, a nonlinear modified Korteweg-de Vries (KdV) equation is derived and its cnoidal wave is analyzed. The various solutions of nonlinear ion-acoustic cnoidal and solitary waves are presented numerically with the Sagdeev potential approach. The analytical solution and numerical simulation of nonlinear ion-acoustic cnoidal waves of the nonlinear modified KdV equation are studied. Clearly, it is found that the features (amplitude and width) of nonlinear ion-acoustic cnoidal waves are proportional to plasma number density, ion cyclotron frequency, and direction cosines. The numerical results are applied to high density astrophysical situations, such as in superdense white dwarfs. This research will be helpful in understanding the properties of compact astrophysical objects containing cold ions with relativistic degenerate electrons.
2015-05-05
AND SUBTITLE LASER-DRIVEN ULTRA-RELATIVISTIC PLASMAS - NUCLEAR FUSION IN COULOMB SHOCK WAVES, ROUGE WAVES, AND BACKGROUND MATTER. 5a. CONTRACT...blackbody radiation on free electrons .........................9 2.vi. Proposal of ultimate test of laser nuclear fusion efficiency in clusters...domain of energies and temperatures, with applications in particular to controlled nuclear fusion . 2. Final technical report on the grant #F49620-11-1
Uzbekov, Bogdan; Shprits, Yuri Y.; Orlova, Ksenia
2016-10-01
Electromagnetic Ion Cyclotron (EMIC) waves are transverse plasma waves that are generated in the Earth magnetosphere by ring current protons with temperature anisotropy in three different bands: below the H+, He+ and O+ ion gyrofrequencies. EMIC events are enhanced during the main phase of a geomagnetic storm when intensifications in the electric field result in enhanced injections of ions and are usually confined to high-density regions just inside the plasmapause or within drainage plumes. EMIC waves are capable of scattering radiation belt electrons and thus provide an important link between the intensification of the electric field, ion populations, and radiation belt electrons. Bounce-averaged diffusion coefficients computed with the assumption of parallel wave propagation are compared to the results of the code that uses the full cold plasma dispersion relation taking into account oblique propagation of waves and higher-order resonances. We study the sensitivity of the scattering rates to a number of included higher-order resonances, wave spectral distribution parameters, wave normal angle distribution parameters, ambient plasma density, and ion composition. Inaccuracies associated with the neglect of higher-order resonances and oblique propagation of waves are compared to potential errors introduced by uncertainties in the model input parameters.
Frequency conversion of probe wave produced by 2D interaction with relativistic ionization front
Yan Li-Xin; Zhang Yong-Sheng; Liu Jing-Ru; Lü Min
2005-01-01
Frequency conversion of probe electromagnetic wave induced by relativistic ionization front is theoretically analysed based on ray-tracing equations in different regimes. Downshifting as well as upshifting in frequency produced by the front is predicted. The reflected and transmitted angles can be also dramatically changed in certain cases.
Zhang, Sun, E-mail: szhang@pmo.ac.cn [Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210008 (China); Key Laboratory of Dark Matter and Space Astronomy, Chinese Academy of Sciences, Nanjing 210008 (China); Joint Center for Particle, Nuclear Physics and Cosmology (J-CPNPC), PMO-NJU, Nanjing 210008 (China)
2014-02-05
In this Letter, we have studied the shock wave and discontinuity propagation for relativistic superfluid with spontaneous U(1) symmetry breaking in the framework of hydrodynamics. General features of shock waves are provided, the propagation of discontinuity and the sound modes of shock waves are also presented. The first sound and the second sound are identified as the propagation of discontinuity, and the results are in agreement with earlier theoretical studies. Moreover, a differential equation, called the growth equation, is obtained to describe the decay and growth of the discontinuity propagating along its normal trajectory. The solution is in an integral form and special cases of diverging waves are also discussed.
Clayton, C. E.; Marsh, K. A.; Dyson, A.; Everett, M.; Lal, A.; Leemans, W. P.; Williams, R.; Joshi, C.
1993-01-01
High-gradient acceleration of externally injected 2.1-MeV electrons by a laser beat wave driven relativistic plasma wave has been demonstrated for the first time. Electrons with energies up to the detection limit of 9.1 MeV were detected when such a plasma wave was resonantly excited using a two-frequency laser. This implies a gradient of 0.7 GeV/m, corresponding to a plasma-wave amplitude of more than 8%. The electron signal was below detection threshold without injection or when the laser was operated on a single frequency.
Relativistic wave equations for interacting massive particles with arbitrary half-intreger spins
Niederle, J
2001-01-01
New formulation of relativistic wave equations (RWE) for massive particles with arbitrary half-integer spins $s$ interacting with external electromagnetic fields are proposed. They are based on wave functions which are irreducible tensors of rank $2n$ ($n=s-\\frac12$) antisymmetric w.r.t. $n$ pairs of indices, whose components are bispinors. The form of RWE is straightforward and free of inconsistencies associated with the other approaches to equations describing interacting higher spin particles.
Particle acceleration in ultra-relativistic parallel shock waves
Meli, A
2003-01-01
Monte-Carlo computations for highly relativistic parallel shock particle acceleration are presented for upstream flow gamma factors, $\\Gamma=(1-V_{1}^{2}/c^{2})^{-0.5}$ with values between 5 and $10^{3}$. The results show that the spectral shape at the shock depends on whether or not the particle scattering is small angle with $\\delta \\theta 2r_{g} \\Gamma^{2}$ where $\\lambda$ is the scattering mean free path along the field line and $r_{g}$ the gyroradius, these quantities being measured in the plasma flow frame. The large angle scattering case exhibits distinctive structure superimposed on the basic power-law spectrum, largely absent in the pitch angle case. Also, both cases yield an acceleration rate faster than estimated by the conventional, non-relativistic expression, $t_{acc}=[c/(V_{1}-V_{2})] [\\lambda_{1}/V_{1}+\\lambda_{2}/V_{2}]$ where '1' and '2' refer to upstream and downstream and $\\lambda$ is the mean free path. A $\\Gamma^{2}$ energy enhancement factor in the first shock crossing cycle and a sign...
Strong electromagnetic waves in a magnetized relativistic electron-positron plasma
Yu, M.Y.; Shukla, P.K.; Rao, N.N. (Bochum Univ. (Germany, F.R.). Inst. fuer Theoretische Physik)
1984-12-01
It is shown that in a strongly magnetized relativistic electron-positron plasma, strongly localized large amplitude circularly polarized electromagnetic wave pulses exist. The localization is due to relativistic mass variation as well as ponderomotive force effects. Three types of pulses are found analytically: the sharply spiked pulse in a strongly magnetized cold plasma, the smooth pulse in a weak magnetized warm plasma, and the moderately spiked pulse for a weakly magnetized cold plasma. The physical mechanisms giving rise to these pulses are distinct for each case. Possible implications of our investigation to pulsar radiation are discussed.
Propagation of ion-acoustic solitary waves in a relativistic electron-positron-ion plasma
Saberian, E; Akbari-Moghanjoughi, M
2011-01-01
Propagation of large amplitude ion-acoustic solitary waves (IASWs) in a fully relativistic plasma consisting of cold ions and ultrarelativistic hot electrons and positrons is investigated using the Sagdeev's pseudopotential method in a relativistic hydrodynamics model. Effects of streaming speed of plasma fluid, thermal energy, positron density and positron temperature on large amplitude IASWs are studied by analysis of the pseudopotential structure. It is found that in regions that the streaming speed of plasma fluid is larger than that of solitary wave, by increasing the streaming speed of plasma fluid the depth and width of potential well increases and resulting in narrower solitons with larger amplitude. This behavior is opposite for the case where the streaming speed of plasma fluid is smaller than that of solitary wave. On the other hand, increase of the thermal energy results in wider solitons with smaller amplitude, because the depth and width of potential well decreases in that case. Additionally, th...
Maroof, R. [Department of Physics, Abdul Wali Khan University, Mardan 23200 (Pakistan); Department of Physics, University of Peshawar, Peshawar 25000 (Pakistan); National Center for Physics (NCP) at QAU Campus, Shahdra Valley Road, Islamabad 44000 (Pakistan); Ali, S. [National Center for Physics (NCP) at QAU Campus, Shahdra Valley Road, Islamabad 44000 (Pakistan); Mushtaq, A. [Department of Physics, Abdul Wali Khan University, Mardan 23200 (Pakistan); National Center for Physics (NCP) at QAU Campus, Shahdra Valley Road, Islamabad 44000 (Pakistan); Qamar, A. [Department of Physics, University of Peshawar, Peshawar 25000 (Pakistan)
2015-11-15
Linear properties of high and low frequency waves are studied in an electron-positron-ion (e-p-i) dense plasma with spin and relativity effects. In a low frequency regime, the magnetohydrodynamic (MHD) waves, namely, the magnetoacoustic and Alfven waves are presented in a magnetized plasma, in which the inertial ions are taken as spinless and non-degenerate, whereas the electrons and positrons are treated quantum mechanically due to their smaller mass. Quantum corrections associated with the spin magnetization and density correlations for electrons and positrons are re-considered and a generalized dispersion relation for the low frequency MHD waves is derived to account for relativistic degeneracy effects. On the basis of angles of propagation, the dispersion relations of different modes are discussed analytically in a degenerate relativistic plasma. Numerical results reveal that electron and positron relativistic degeneracy effects significantly modify the dispersive properties of MHD waves. Our present analysis should be useful for understanding the collective interactions in dense astrophysical compact objects, like, the white dwarfs and in atmosphere of neutron stars.
A nonextensive statistics approach for Langmuir waves in relativistic plasmas
V. Muñoz
2006-01-01
Full Text Available The nonextensive statistics formalism proposed by Tsallis has found many applications in systems with memory effects, long range spatial correlations, and in general whenever the phase space has fractal or multi-fractal structure. These features may appear naturally in turbulent or non-neutral plasmas. In fact, the equilibrium distribution functions which maximize the nonextensive entropy strongly resemble the non-Maxwellian particle distribution functions observed in space and laboratory and turbulent pure electron plasmas. In this article we apply the Tsallis entropy formalism to the problem of longitudinal oscillations in a proton-electron plasma. In particular, we study the equilibrium distribution function and the dispersion relation of longitudinal oscillations in a relativistic plasma, finding interesting differences with the nonrelativistic treatment.
The efficiency of fast wave current drive for a weakly relativistic plasma
Chiu, S. C.; Lin-Liu, Y. R.; Karney, C. F. F.
1994-10-01
Current drive by fast waves (FWCD) is an important candidate for steady-state operation of tokamaks. Major experiments using this scheme are being carried out on DIII-D. There has been considerable study of the theoretical efficiency of FWCD. In Refs. 4 and 5, the nonrelativistic efficiency of FWCD at arbitrary frequencies was studied. For DIII-D parameters, the results can be considerably different from the Landau and Alfvén limits. At the high temperatures of reactors and DIII-D upgrade, relativistic effects become important. In this paper, the relativistic FWCD efficiency for arbitrary frequencies is studied. Assuming that the plasma is weakly relativistic, i.e., Te/mc2 is small, an analytic expression for FWCD is obtained for high resonant energies (uph/uTe≫1). Comparisons with the results from a numerical code ADJ and the nonrelativistic results shall be made and analytical fits in the whole range of velocities shall be presented.
Gravitational Waves from Perturbed Black Holes and Relativistic Stars
Rezzolla, Luciano
2003-01-01
These lectures aim at providing an introduction to the properties of gravitational waves and in particular to those gravitational waves that are expected as a consequence of perturbations of black holes and neutron stars. Imprinted in the gravitational radiation emitted by these objects is, in fact, a wealth of physical information. In the case of black holes, a detailed knowledge of the gravitational radiation emitted as a response to perturbations will reveal us important details about thei...
Franz Gross, Alfred Stadler
2010-09-01
We present the effective range expansions for the 1S0 and 3S1 scattering phase shifts, and the relativistic deuteron wave functions that accompany our recent high precision fits (with \\chi^2/N{data} \\simeq 1) to the 2007 world np data below 350 MeV. The wave functions are expanded in a series of analytical functions (with the correct asymptotic behavior at both large and small arguments) that can be Fourier-transformed from momentum to coordinate space and are convenient to use in any application. A fortran subroutine to compute these wave functions can be obtained from the authors.
Karkheck, John; Stell, George
1981-08-01
A kinetic mean-field theory for the evolution of the one-particle distribution function is derived from maximizing the entropy. For a potential with a hard-sphere core plus tail, the resulting theory treats the hard-core part as in the revised Enskog theory. The tail, weighted by the hard-sphere pair distribution function, appears linearly in a mean-field term. The kinetic equation is accompanied by an entropy functional for which an H theorem was proven earlier. The revised Enskog theory is obtained by setting the potential tail to zero, the Vlasov equation is obtained by setting the hard-sphere diameter to zero, and an equation of the Enskog-Vlasov type is obtained by effecting the Kac limit on the potential tail. At equilibrium, the theory yields a radial distribution function that is given by the hard-sphere reference system and thus furnishes through the internal energy a thermodynamic description which is exact to first order in inverse temperature. A second natural route to thermodynamics (from the momentum flux which yields an approximate equation of state) gives somewhat different results; both routes coincide and become exact in the Kac limit. Our theory furnishes a conceptual basis for the association in the heuristically based modified Enskog theory (MET) of the contact value of the radial distribution function with the ''thermal pressure'' since this association follows from our theory (using either route to thermodynamics) and moreover becomes exact in the Kac limit. Our transport theory is readily extended to the general case of a soft repulsive core, e.g., as exhibited by the Lennard-Jones potential, via by-now-standard statistical-mechanical methods involving an effective hard-core potential, thus providing a self-contained statistical-mechanical basis for application to such potentials that is lacking in the standard versions of the MET. We obtain very good agreement with experiment for the thermal conductivity and shear viscosity of several
Solitary waves in dusty plasmas with weak relativistic effects in electrons and ions
Kalita, B. C., E-mail: bckalita123@gmail.com [Gauhati University, Department of Mathematics (India); Choudhury, M., E-mail: choudhurymamani@gmail.com [Handique Girls’ College, Department of Mathematics (India)
2016-10-15
Two distinct classes of dust ion acoustic (DIA) solitary waves based on relativistic ions and electrons, dust charge Z{sub d} and ion-to-dust mass ratio Q’ = m{sub i}/m{sub d} are established in this model of multicomponent plasmas. At the increase of mass ratio Q’ due to increase of relativistic ion mass and accumulation of more negative dust charges into the plasma causing decrease of dust mass, relativistic DIA solitons of negative potentials are abundantly observed. Of course, relativistic compressive DIA solitons are also found to exist simultaneously. Further, the decrease of temperature inherent in the speed of light c causes the nonlinear term to be more active that increases the amplitude of the rarefactive solitons and dampens the growth of compressive solitons for relatively low and high mass ratio Q’, respectively. The impact of higher initial streaming of the massive ions is observed to identify the point of maximum dust density N{sub d} to yield rarefactive relativistic solitons of maximum amplitude.
Relativistic warm plasma theory of nonlinear laser-driven electron plasma waves.
Schroeder, C B; Esarey, E
2010-05-01
A relativistic, warm fluid model of a nonequilibrium, collisionless plasma is developed and applied to examine nonlinear Langmuir waves excited by relativistically intense, short-pulse lasers. Closure of the covariant fluid theory is obtained via an asymptotic expansion assuming a nonrelativistic plasma temperature. The momentum spread is calculated in the presence of an intense laser field and shown to be intrinsically anisotropic. Coupling between the transverse and longitudinal momentum variances is enabled by the laser field. A generalized dispersion relation is derived for Langmuir waves in a thermal plasma in the presence of an intense laser field. Including thermal fluctuations in three-velocity-space dimensions, the properties of the nonlinear electron plasma wave, such as the plasma temperature evolution and nonlinear wavelength, are examined and the maximum amplitude of the nonlinear oscillation is derived. The presence of a relativistically intense laser pulse is shown to strongly influence the maximum plasma wave amplitude for nonrelativistic phase velocities owing to the coupling between the longitudinal and transverse momentum variances.
Disperson relation of finite amplitude Alfven wave in a relativistic electron- positron plasma
Hada, T; Muñoz, V; Hada, Tohru; Matsukiyo, Shuichi; Munoz, Victor
2004-01-01
The linear dispersion relation of a finite amplitude, parallel, circularly polarized Alfv\\'en wave in a relativistic electron-positron plasma is derived. In the nonrelativistic regime, the dispersion relation has two branches, one electromagnetic wave, with a low frequency cutoff at $\\sqrt{1+2\\omega_p^2/\\Omega_p^2}$ (where $\\omega_p=(4\\pi n e^2/m)^{1/2}$ is the electron/positron plasma frequency), and an Alfv\\'en wave, with high frequency cutoff at the positron gyrofrequency $\\Omega_p$. There is only one forward propagating mode for a given frequency. However, due to relativistic effects, there is no low frequency cutoff for the electromagnetic branch, and there appears a critical wave number above which the Alfv\\'en wave ceases to exist. This critical wave number is given by $ck_c/\\Omega_p=a/\\eta$, where $a=\\omega_p^2/\\Omega_p^2$ and $\\eta$ is the ratio between the Alfv\\'en wave magnetic field amplitude and the background magnetic field. In this case, for each frequency in the Alfv\\'en branch, two additional...
Interaction of Oblique Incident Electromagnetic Wave with Relativistic Ionization Front
无
2005-01-01
Interactions of oblique incident probe wave with oncoming ionization fronts have been investigated using moving boundary conditions. Field conversion coefficients of reflection,transmission and magnetic modes produced in the interactions are derived. Phase matching conditions at the front and frequency up-shifting formulas for the three modes are also presented.
Non-linear collisionless damping of Weibel turbulence in relativistic blast waves
Lemoine, Martin
2014-01-01
The Weibel/filamentation instability is known to play a key role in the physics of weakly magnetized collisionless shock waves. From the point of view of high energy astrophysics, this instability also plays a crucial role because its development in the shock precursor populates the downstream with a small-scale magneto-static turbulence which shapes the acceleration and radiative processes of suprathermal particles. The present work discusses the physics of the dissipation of this Weibel-generated turbulence downstream of relativistic collisionless shock waves. It calculates explicitly the first-order non-linear terms associated to the diffusive nature of the particle trajectories. These corrections are found to systematically increase the damping rate, assuming that the scattering length remains larger than the coherence length of the magnetic fluctuations. The relevance of such corrections is discussed in a broader astrophysical perspective, in particular regarding the physics of the external relativistic ...
Trapped electron acceleration by a laser-driven relativistic plasma wave
Everett, M.; Lal, A.; Gordon, D.; Clayton, C. E.; Marsh, K. A.; Joshi, C.
1994-04-01
THE aim of new approaches for high-energy particle acceleration1 is to push the acceleration rate beyond the limit (~100 MeV m-1) imposed by radio-frequency breakdown in conventional accelerators. Relativistic plasma waves, having phase velocities very close to the speed of light, have been proposed2-6 as a means of accelerating charged particles, and this has recently been demonstrated7,8. Here we show that the charged particles can be trapped by relativistic plasma waves-a necessary condition for obtaining the maximum amount of energy theoretically possible for such schemes. In our experiments, plasma waves are excited in a hydrogen plasma by beats induced by two collinear laser beams, the difference in whose frequencies matches the plasma frequency. Electrons with an energy of 2 MeV are injected into the excited plasma, and the energy spectrum of the exiting electrons is analysed. We detect electrons with velocities exceeding that of the plasma wave, demonstrating that some electrons are 'trapped' by the wave potential and therefore move synchronously with the plasma wave. We observe a maximum energy gain of 28 MeV, corresponding to an acceleration rate of about 2.8 GeV m-1.
Sarkadi, L.
2017-03-01
The program MTRDCOUL [1] calculates the matrix elements of the Coulomb interaction between a charged particle and an atomic electron, ∫ ψf∗ (r) ∣ R - r∣-1ψi(r) d r. Bound-free transitions are considered, and relativistic hydrogenic wave functions are used. In this revised version a bug discovered in the F3Y CPC Program Library subprogram [2] is fixed.
Coherent keV backscattering from plasma-wave boosted relativistic electron mirrors
Li, F Y; Chen, M; Wu, H C; Liu, Y; Meyer-ter-Vehn, J; Mori, W B; Zhang, J
2014-01-01
A new parameter regime of laser wakefield acceleration driven by sub-petawatt femotsecond lasers is proposed, which enables the generation of relativistic electron mirrors further accelerated by the plasma wave. Integrated particle-in-cell simulation including the mirror formation and Thomson scattering demonstrates that efficient coherent backscattering up to keV photon energy can be obtained with moderate driver laser intensities and high density gas targets.
Kh. H. EL-SHORBAGY
2008-01-01
The effect of a high frequency (HF) electric field on the propagation of electrostatic wave in a 2D non-uniform relativistic plasma waveguide is investigated. A variable separation method is applied to the two-fluid plasma model. An analytical study of the reflection of electro-static wave propagation along a magnetized non-uniform relativistic plasma slab subjected to an intense HF electric field is presented and compared with the case of a non relativistic plasma. It is found that, when the frequency of the incident wave is close to the relativistic electron plasma frequency, the plasma is less reflective due to the presence of both an HF field and the effect of rel-ativistic electrons. On the other hand, for a low-frequency incident wave the reflection coefficient is directly proportional to the amplitude of the HF field. Also, it is shown that the relativistic electron plasma leads to a decrease in the value of reflection coefficient in comparison with the case of the non relativistic plasma.
Relativistic two-boson system in presence of electromagnetic plane waves
Droz-Vincent, Philippe
2015-01-01
The relativistic two-body problem is considered for spinless particles subject to an external macroscopic electromagnetic field. When this field is made of the monochromatic superposition of two conter-propagating plane waves (and provided the mutual interaction between particles is known), it is possible to write down explicitly a pair of coupled wave equations (corresponding to a pair of mass-shell constraints) which takes into account also the field contribution. These equations are manifestly covariant; constants of the motion are exhibited, so one ends up with a reduced problem concerning five degrees of freedom.
Terahertz radiation emission from plasma beat-wave interactions with a relativistic electron beam
Gupta, D. N.; Kulagin, V. V.; Suk, H.
2017-10-01
We present a mechanism to generate terahertz radiation from laser-driven plasma beat-wave interacting with an electron beam. The theory of the energy transfer between the plasma beat-wave and terahertz radiation is elaborated through nonlinear coupling in the presence of a negative-energy relativistic electron beam. An expression of terahertz radiation field is obtained to find out the efficiency of the process. Our results show that the efficiency of terahertz radiation emission is strongly sensitive to the electron beam energy. Emitted field strength of the terahertz radiation is calculated as a function of electron beam velocity.
Relativistic Covariance and Quark-Diquark Wave Functions
Dillig, M
2006-01-01
We derive covariant wave functions for hadrons composed of two constituents for arbitrary Lorentz boosts. Focussing explicitly on baryons as quark-diquark systems, we reduce their manifestly covariant Bethe-Salpeter equation to covariant 3-dimensional forms by projecting on the relative quark-diquark energy. Guided by a phenomenological multi gluon exchange representation of covariant confining kernels, we derive explicit solutions for harmonic confinement and for the MIT Bag Model. We briefly sketch implications of breaking the spherical symmetry of the ground state and the transition from the instant form to the light cone via the infinite momentum frame.
Relativistic two-, three- and four-body wave equations in scalar QFT
Emami-Razavi, Mohsen; Darewych, Jurij W [Centre for Research in Earth and Space Science and Department of Physics and Astronomy, York University, Toronto, Ontario M3J 1P3 (Canada)
2005-09-01
We use the variational method within the Hamiltonian formalism of QFT to derive relativistic two-, three- and four-body wave equations for scalar particles interacting via a massive or massless mediating scalar field (the scalar Yukawa model). The Lagrangian of the theory is reformulated by using Green's functions to express the mediating field in terms of the particle fields. The QFT is then constructed from the resulting reformulated Hamiltonian. Simple Fock-space variational trial states are used to derive relativistic two-, three- and four-body equations. The equations are shown to have the Schroedinger non-relativistic limit, with Coulombic interparticle potentials in the case of a massless mediating field and Yukawa interparticle potentials in the case of a massive mediating field. Ground-state solutions of the relativistic equations are obtained approximately for various strengths of coupling, for both massive and massless mediating fields, and a comparison of the two-, three- and four-particle binding energies is presented.
Theoretical analysis of a relativistic travelling wave tube filled with plasma
Xie Hong-Quan; Liu Pu-Kun
2007-01-01
A cold and uniform plasma-filled travelling wave tube with sinusoidally corrugated slow wave structure is driven by a finite thick annular intense relal:ivistic electron beam with the entire system immersed in a strong longitudinal magnetic field.By means of the linear field theory,the dispersion relation for the relativistic travelling wave tube (RTWT) is derived.By numerical computation,the dispersion characteristics of the RTWT are analysed in difierent cases of various geometric parameters of the slow wave structure and plasma densities.Also the gain versus frequency for three difierent plasma densities and the peak gain of the tube versus plasma density are analysed.Some useful results are obtained on the basis of the discussion.
Mean field interaction in biochemical reaction networks
Tembine, Hamidou
2011-09-01
In this paper we establish a relationship between chemical dynamics and mean field game dynamics. We show that chemical reaction networks can be studied using noisy mean field limits. We provide deterministic, noisy and switching mean field limits and illustrate them with numerical examples. © 2011 IEEE.
Analytic Representation of Relativistic Wave Equations I The Dirac Case
Tepper, L; Zachary, W W
2003-01-01
In this paper we construct an analytical separation (diagonalization) of the full (minimal coupling) Dirac equation into particle and antiparticle components. The diagonalization is analytic in that it is achieved without transforming the wave functions, as is done by the Foldy-Wouthuysen method, and reveals the nonlocal time behavior of the particle-antiparticle relationship. It is well known that the Foldy-Wouthuysen transformation leads to a diagonalization that is nonlocal in space. We interpret the zitterbewegung, and the result that a velocity measurement (of a Dirac particle) at any instant in time is +(-)c, as reflections of the fact that the Dirac equation makes a spatially extended particle appear as a point in the present by forcing it to oscillate between the past and future at speed c. This suggests that although the Dirac Hamiltonian and the square-root Hamiltonian, are mathematically, they are not physically, equivalent. Furthermore, we see that alt! ho! ugh the form of the Dirac equation serve...
Ion-acoustic rogue waves and breathers in relativistically degenerate electron-positron plasmas
Abdikian, A.; Ismaeel, S.
2017-08-01
In this paper, we employ a weakly relativistic fluid model to study the nonlinear amplitude modulation of electrostatic waves in an unmagnetized electron-positron-ion plasma. It is assumed that the degeneracy pressure law for electrons and positrons follows the Chandrasekhar limit of state whereas ions are warm and classical. The hydrodynamic approach along with the perturbation method have been applied to obtain the corresponding nonlinear Schrödinger equation (NLSE) in which nonlinearity is in balance with the dispersive terms. Using the NLSE, we could evaluate the modulational instability to show that various types of localized ion acoustic excitations exist in the form of either bright-type envelope solitons or dark-type envelope solitons. The regions of the stable and unstable envelope wave have been confined punctually for various regimes. Furthermore, it is proposed that the exact solutions of the NLSE for breather waves are the rogue waves (RWs), Akhmediev breather (AB), and Kuznetsov-Ma breather (KM) soliton. In order to show that the characteristics of breather structures is influenced by the plasma parameters (namely, relativistic parameter, positron concentration, and ionic temperature), the relevant numerical analysis of the NLSE is examined. In particular, it is observed that by increasing the values of the mentioned plasma parameters, the amplitude of the RWs will be decreased. Our results help researchers to explain the formation and dynamics of nonlinear electrostatic excitations in super dense astrophysical regimes.
Touil, B.; Bendib, A.; Bendib-Kalache, K.
2017-02-01
The longitudinal dielectric function is derived analytically from the relativistic Vlasov equation for arbitrary values of the relevant parameters z = m c 2 / T , where m is the rest electron mass, c is the speed of light, and T is the electron temperature in energy units. A new analytical approach based on the Legendre polynomial expansion and continued fractions was used. Analytical expression of the electron distribution function was derived. The real part of the dispersion relation and the damping rate of electron plasma waves are calculated both analytically and numerically in the whole range of the parameter z . The results obtained improve significantly the previous results reported in the literature. For practical purposes, explicit expressions of the real part of the dispersion relation and the damping rate in the range z > 30 and strongly relativistic regime are also proposed.
Relativistic electron beam driven longitudinal wake-wave breaking in a cold plasma
Bera, Ratan Kumar; Sengupta, Sudip; Das, Amita
2016-01-01
Space-time evolution of relativistic electron beam driven wake-field in a cold, homogeneous plasma, is studied using 1D-fluid simulation techniques. It is observed that the wake wave gradu- ally evolves and eventually breaks, exhibiting sharp spikes in the density profile and sawtooth like features in the electric field profile [1]. It is shown here that the excited wakefield is a longitudi- nal Akhiezer-Polovin mode [2] and its steepening (breaking) can be understood in terms of phase mixing of this mode, which arises because of relativistic mass variation effects. Further the phase mixing time (breaking time) is studied as a function of beam density and beam velocity and is found to follow the well known scaling presented in ref.[3].
LISA sensitivities to gravitational waves from relativistic metric theories of gravity
Tinto, Massimo; Alves, Márcio Eduardo Da Silva
2010-12-01
The direct observation of gravitational waves will provide a unique tool for probing the dynamical properties of highly compact astrophysical objects, mapping ultrarelativistic regions of space-time, and testing Einstein’s general theory of relativity. LISA (Laser Interferometer Space Antenna), a joint National Aeronautics and Space Administration and European Space Agency mission to be launched in the next decade, will perform these scientific tasks by detecting and studying low-frequency cosmic gravitational waves through their influence on the phases of six modulated laser beams exchanged between three remote spacecraft. By directly measuring the polarization components of the waves LISA will detect, we will be able to test Einstein’s theory of relativity with good sensitivity. Since a gravitational wave signal predicted by the most general relativistic metric theory of gravity accounts for six polarization modes (the usual two Einstein’s tensor polarizations as well as two vector and two scalar wave components), we have derived the LISA time-delay interferometric responses and estimated their sensitivities to vector- and scalar-type waves. We find that (i) at frequencies larger than roughly the inverse of the one-way light time (≈6×10-2Hz), LISA is more than ten times sensitive to scalar-longitudinal and vector signals than to tensor and scalar-transverse waves, and (ii) in the low part of its frequency band is equally sensitive to tensor and vector waves and somewhat less sensitive to scalar signals.
Chen, Zaigao; Wang, Jianguo; Wang, Yue; Qiao, Hailiang; Zhang, Dianhui; Guo, Weijie
2013-11-01
Optimal design method of high-power microwave source using particle simulation and parallel genetic algorithms is presented in this paper. The output power, simulated by the fully electromagnetic particle simulation code UNIPIC, of the high-power microwave device is given as the fitness function, and the float-encoding genetic algorithms are used to optimize the high-power microwave devices. Using this method, we encode the heights of non-uniform slow wave structure in the relativistic backward wave oscillators (RBWO), and optimize the parameters on massively parallel processors. Simulation results demonstrate that we can obtain the optimal parameters of non-uniform slow wave structure in the RBWO, and the output microwave power enhances 52.6% after the device is optimized.
Observation of Self-Sustaining Relativistic Ionization Wave Launched by a Sheath Field
McCormick, M.; Arefiev, A. V.; Quevedo, H. J.; Bengtson, R. D.; Ditmire, T.
2014-01-01
We present experimental evidence supported by simulations of a relativistic ionization wave launched into a surrounding gas by the sheath field of a plasma filament with high energy electrons. Such a filament is created by irradiating a clustering gas jet with a short pulse laser (115 fs) at a peak intensity of 5×1017 W/cm2. We observe an ionization wave propagating radially through the gas for about 2 ps at 0.2-0.5 c after the laser has passed, doubling the initial radius of the filament. The gas is ionized by the sheath field, while the longevity of the wave is explained by a moving field structure that traps the high energy electrons near the boundary, maintaining a strong sheath field despite the significant expansion of the plasma.
Observation of Self-Sustaining Relativistic Ionization Wave Launched by Sheath Field
McCormick, M W; Quevedo, H J; Bengtson, R D; Ditmire, T
2013-01-01
We present experimental evidence supported by simulations of a relativistic ionization wave launched into surrounding gas by the sheath field of a plasma filament with high energy electrons. Such filament is created by irradiating a clustering gas jet with a short pulse laser ($\\sim$115 fs) at a peak intensity of $5 \\times 10^{17}$ W/cm$^2$. We observe an ionization wave propagating radially through the gas for about 2 ps at 0.2-0.5 $c$ after the laser has passed, doubling the initial radius of the filament. The gas is ionized by the sheath field, while the longevity of the wave is explained by a moving field structure that traps the high energy electrons near the boundary, maintaining a strong sheath field despite the significant expansion of the plasma.
Caballero, J.A. [Univ. de Sevilla (Spain). Dept. de Fisica Atomica, Molecular y Nucl.]|[Instituto de Estructura de la Materia, Consejo Superior de Investigaciones Cientificas, Serrano 123, Madrid 28006 (Spain); Donnelly, T.W. [Centre for Theoretical Physics, Laboratory for Nuclear Science and Dept. of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139-4307 (United States); Moya de Guerra, E. [Instituto de Estructura de la Materia, Consejo Superior de Investigaciones Cientificas, Serrano 123, Madrid 28006 (Spain); Udias, J.M. [Departamento de Fisica Atomica, Molecular y Nuclear, Universidad Complutense de Madrid, Avda. Complutense s/n, Madrid 28040 (Spain)
1998-03-23
The issue of factorization within the context of coincidence quasi-elastic electron scattering is revisited. Using a relativistic formalism for the entire reaction mechanism and restricting ourselves to the case of plane waves for the outgoing proton, we discuss the role of the negative-energy components of the bound nucleon wave function. (orig.). 30 refs.
A five-wave Harten-Lax-van Leer Riemann solver for relativistic magnetohydrodynamics
Mignone, A.; Ugliano, M.; Bodo, G.
2009-03-01
We present a five-wave Riemann solver for the equations of ideal relativistic magneto-hydrodynamics. Our solver can be regarded as a relativistic extension of the five-wave HLLD Riemann solver initially developed by Miyoshi & Kusano for the equations of ideal magnetohydrodynamics. The solution to the Riemann problem is approximated by a five-wave pattern, comprising two outermost fast shocks, two rotational discontinuities and a contact surface in the middle. The proposed scheme is considerably more elaborate than in the classical case since the normal velocity is no longer constant across the rotational modes. Still, proper closure to the Rankine-Hugoniot jump conditions can be attained by solving a non-linear scalar equation in the total pressure variable which, for the chosen configuration, has to be constant over the whole Riemann fan. The accuracy of the new Riemann solver is validated against one-dimensional tests and multidimensional applications. It is shown that our new solver considerably improves over the popular Harten-Lax-van Leer solver or the recently proposed HLLC schemes.
Risk-sensitive mean-field games
Tembine, Hamidou
2014-04-01
In this paper, we study a class of risk-sensitive mean-field stochastic differential games. We show that under appropriate regularity conditions, the mean-field value of the stochastic differential game with exponentiated integral cost functional coincides with the value function satisfying a Hamilton -Jacobi- Bellman (HJB) equation with an additional quadratic term. We provide an explicit solution of the mean-field best response when the instantaneous cost functions are log-quadratic and the state dynamics are affine in the control. An equivalent mean-field risk-neutral problem is formulated and the corresponding mean-field equilibria are characterized in terms of backward-forward macroscopic McKean-Vlasov equations, Fokker-Planck-Kolmogorov equations, and HJB equations. We provide numerical examples on the mean field behavior to illustrate both linear and McKean-Vlasov dynamics. © 1963-2012 IEEE.
Continuous time finite state mean field games
Gomes, Diogo A.
2013-04-23
In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary differential equations with initial-terminal data. For this mean field problem we prove a trend to equilibrium theorem, that is convergence, in an appropriate limit, to stationary solutions. Then we study an N+1-player problem, which the mean field model attempts to approximate. Our main result is the convergence as N→∞ of the mean field model and an estimate of the rate of convergence. We end the paper with some further examples for potential mean field games. © 2013 Springer Science+Business Media New York.
Relativistic quantum mechanical spin-1 wave equation in 2+1 dimensional spacetime
Dernek, Mustafa; Sucu, Yusuf; Unal, Nuri
2016-01-01
In the study, we introduce a relativistic quantum mechanical wave equation of the spin-1 particle as an excited state of the zitterbewegung and show that it is consistent with the 2+1 dimensional Proca theory. At the same time, we see that this equation has two eigenstates, particle and antiparticle states or negative and positive energy eigenstates, respectively, in the rest frame and the spin-1 matrices satisfy $SO(2,1)$ spin algebra. As practical applications, we derive the exact solutions of the equation in the presence of a constant magnetic field and a curved spacetime. From these solutions, we construct the current components of the spin-1 particle.
Hadron Mass Spectra and Decay Rates in a Potential Model with Relativistic Wave Equations.
Namgung, Wuk
Hadron properties of mass spectra and decay rates are calculated in a quark potential model. Wave equations based on the Klein-Gordon and Todorov equations both of which incorporate the feature of relativistic two-body kinematics are used. The wave equations are modified to contain potentials which transform either like a Lorentz scalar or like a time-component of a four-vector. Potentials based on the Fogleman-Lichtenberg-Wills potential which has the properties suggested by QCD of both confinement and asymptotic freedom are used. The potentials, motivated by QCD but otherwise phenomenological, are further generalized to forms which can apply to any color representation. To break the degeneracy between vector and pseudoscalar mesons or between spin-3/2 and spin-1/2 baryons, the essential feature of spin dependence is included in the potentials. The masses of vector and pseudoscalar mesons are calculated with only a small number of adjustable parameters, and good qualitative agreement with experiment is obtained for both heavy and light mesons. Baryons are treated in this framework by making use of a quark-diquark two-body model of baryons. First, diquark properties are calculated without any additional parameters. The g-factors of diquarks and spin-flavor configuration of baryons, which are necessary for the calculation of baryons, are given. Then baryon masses are calculated also without additional parameters. The results of the masses of ground-state baryons are in good qualitative agreement with experiment. Also effective constituent quark masses are obtained using current quark masses as input. The calculated effective constituent quark masses are in the right range of the values that most theoretical estimates have given. The general qualitative features of hadron spectra are similar with the two relativistic wave equations, although there are differences in detail. The Van Royen-Weisskopf formula for electromagnetic decay widths of vector mesons into lepton
Extended Deterministic Mean-Field Games
Gomes, Diogo A.
2016-04-21
In this paper, we consider mean-field games where the interaction of each player with the mean field takes into account not only the states of the players but also their collective behavior. To do so, we develop a random variable framework that is particularly convenient for these problems. We prove an existence result for extended mean-field games and establish uniqueness conditions. In the last section, we consider the Master Equation and discuss properties of its solutions.
Zhang, Hong Lin; Sampson, D.H. (Pennsylvania State Univ., University Park, PA (USA). Dept. of Astronomy)
1990-10-22
The rapid relativistic distorted wave method of Zhang et al for excitation, which uses the atomic structure data of Sampson et al, has been extended to ionization. In this approach the same Dirac-Fock-Slater potential evaluated using a single mean configuration is used in calculating the orbitals of all electrons bound and free. Values for the cross sections Q for ionization of various ions have been calculated and generally good agreement is obtained with other recent relativistic calculations. When results are expressed in terms of the reduced ionization cross section Q{sub R}, which is proportional to I{sup 2}Q, they are close to the non-relativistic Coulomb-Born-Exchange values of Moores et al for hydrogenic ions except for high Z and/or high energies. This suggests that fits of the Q{sub R} to simple functions of the impact electron energy in threshold units with coefficients that are quite slowly varying functions of an effective Z can probably be made. This would be convenient for plasma modeling applications. 24 refs., 2 tabs.
Gamayunov, K. V.; Khazanov, G. V.
2007-01-01
We consider the effect of oblique EMIC waves on relativistic electron scattering in the outer radiation belt using simultaneous observations of plasma and wave parameters from CRRES. The main findings can be s ummarized as follows: 1. In 1comparison with field-aligned waves, int ermediate and highly oblique distributions decrease the range of pitc h-angles subject to diffusion, and reduce the local scattering rate b y an order of magnitude at pitch-angles where the principle absolute value of n = 1 resonances operate. Oblique waves allow the absolute va lue of n > 1 resonances to operate, extending the range of local pitc h-angle diffusion down to the loss cone, and increasing the diffusion at lower pitch angles by orders of magnitude; 2. The local diffusion coefficients derived from CRRES data are qualitatively similar to the local results obtained for prescribed plasma/wave parameters. Conseq uently, it is likely that the bounce-averaged diffusion coefficients, if estimated from concurrent data, will exhibit the dependencies similar to those we found for model calculations; 3. In comparison with f ield-aligned waves, intermediate and highly oblique waves decrease th e bounce-averaged scattering rate near the edge of the equatorial lo ss cone by orders of magnitude if the electron energy does not excee d a threshold (approximately equal to 2 - 5 MeV) depending on specified plasma and/or wave parameters; 4. For greater electron energies_ ob lique waves operating the absolute value of n > 1 resonances are more effective and provide the same bounce_averaged diffusion rate near the loss cone as fiel_aligned waves do.
Mean field theory for fermion-based U(2) anyons
McGraw, P
1996-01-01
The energy density is computed for a U(2) Chern-Simons theory coupled to a non-relativistic fermion field (a theory of ``non-Abelian anyons'') under the assumptions of uniform charge and matter density. When the matter field is a spinless fermion, we find that this energy is independent of the two Chern-Simons coupling constants and is minimized when the non-Abelian charge density is zero. This suggests that there is no spontaneous breaking of the SU(2) subgroup of the symmetry, at least in this mean-field approximation. For spin-1/2 fermions, we find self-consistent mean-field states with a small non-Abelian charge density, which vanishes as the theory of free fermions is approached.
Effect of EMIC Wave Normal Angle Distribution on Relativistic Electron Scattering in Outer RB
Khazanov, G. V.; Gamayunov, K. V.
2007-01-01
We present the equatorial and bounce average pitch angle diffusion coefficients for scattering of relativistic electrons by the H+ mode of EMIC waves. Both the model (prescribed) and self consistent distributions over the wave normal angle are considered. The main results of our calculation can be summarized as follows: First, in comparison with field aligned waves, the intermediate and highly oblique waves reduce the pitch angle range subject to diffusion, and strongly suppress the scattering rate for low energy electrons (E less than 2 MeV). Second, for electron energies greater than 5 MeV, the |n| = 1 resonances operate only in a narrow region at large pitch-angles, and despite their greatest contribution in case of field aligned waves, cannot cause electron diffusion into the loss cone. For those energies, oblique waves at |n| greater than 1 resonances are more effective, extending the range of pitch angle diffusion down to the loss cone boundary, and increasing diffusion at small pitch angles by orders of magnitude.
Mean field approaches for $\\Xi^-$ hypernuclei and current experimental data
Sun, T T; Sagawa, H; Schulze, H -J; Meng, J
2016-01-01
Motivated by the recently observed hypernucleus (Kiso event) $^{15}_{\\Xi}$C ($^{14}$N$+\\Xi^-$), we identify the state of this system theoretically within the framework of the relativistic-mean-field and Skyrme-Hartree-Fock models. The $\\Xi N$ interactions are constructed to reproduce the two possibly observed $\\Xi^-$ removal energies, $4.38\\pm 0.25$ MeV or $1.11\\pm 0.25$ MeV. The present result is preferable to be $^{14}{\\rm N}({\\rm g.s.})+\\Xi^-(1p)$, corresponding to the latter value.
Abram, M; Zegrodnik, M; Spałek, J
2017-09-13
In the first part of the paper, we study the stability of antiferromagnetic (AF), charge density wave (CDW), and superconducting (SC) states within the t-J-U-V model of strongly correlated electrons by using the statistically consistent Gutzwiller approximation (SGA). We concentrate on the role of the intersite Coulomb interaction term V in stabilizing the CDW phase. In particular, we show that the charge ordering appears only above a critical value of V in a limited hole-doping range δ. The effect of the V term on SC and AF phases is that a strong interaction suppresses SC, whereas the AF order is not significantly influenced by its presence. In the second part, separate calculations for the case of a pure SC phase have been carried out within an extended approach (the diagrammatic expansion for the Gutzwiller wave function, DE-GWF) in order to analyze the influence of the intersite Coulomb repulsion on the SC phase with the higher-order corrections included beyond the SGA method. The upper concentration for the SC disappearance decreases with increasing V, bringing the results closer to experiment. In appendices A and B we discuss the ambiguity connected with the choice of the Gutzwiller renormalization factors within the renormalized mean filed theory when either AF or CDW orders are considered. At the end, we overview briefly the possible extensions of the current models to put descriptions of the SC, AF, and CDW states on equal footing.
Abram, M.; Zegrodnik, M.; Spałek, J.
2017-09-01
In the first part of the paper, we study the stability of antiferromagnetic (AF), charge density wave (CDW), and superconducting (SC) states within the t-J-U-V model of strongly correlated electrons by using the statistically consistent Gutzwiller approximation (SGA). We concentrate on the role of the intersite Coulomb interaction term V in stabilizing the CDW phase. In particular, we show that the charge ordering appears only above a critical value of V in a limited hole-doping range δ. The effect of the V term on SC and AF phases is that a strong interaction suppresses SC, whereas the AF order is not significantly influenced by its presence. In the second part, separate calculations for the case of a pure SC phase have been carried out within an extended approach (the diagrammatic expansion for the Gutzwiller wave function, DE-GWF) in order to analyze the influence of the intersite Coulomb repulsion on the SC phase with the higher-order corrections included beyond the SGA method. The upper concentration for the SC disappearance decreases with increasing V, bringing the results closer to experiment. In appendices A and B we discuss the ambiguity connected with the choice of the Gutzwiller renormalization factors within the renormalized mean filed theory when either AF or CDW orders are considered. At the end, we overview briefly the possible extensions of the current models to put descriptions of the SC, AF, and CDW states on equal footing.
Hafez, M. G.; Roy, N. C.; Talukder, M. R.; Hossain Ali, M.
2016-09-01
This work investigates the oblique nonlinear propagation of ion acoustic (IA) shock waves for both weakly and highly relativistic plasmas composed of nonthermal electrons and positrons with relativistic thermal ions. The KdVB-like equation, involving dispersive, weakly transverse dispersive, nonlinearity and dissipative coefficients, is derived employing the well known reductive perturbation method. The integration of this equation is carried out by the {tanh} method taking the stable shock formation condition into account. The effects of nonthermal electrons and positrons, nonthermal electrons with isothermal positrons, isothermal electrons with nonthermal positrons, and isothermal electrons and positrons on oblique propagation of IA shock waves in weakly relativistic regime are described. Furthermore, the effects of plasma parameters on oblique propagation of IA shock waves in highly relativistic regime are discussed and compared with weakly relativistic case. It is seen that the plasma parameters within certain limits significantly modify the structures of the IA shock waves in both cases. The results may be useful for better understanding of the interactions of charged particles with extra-galactic jets as well as astrophysical compact objects.
Investigation of a K-band large coaxial relativistic backward wave oscillator
Zeng, Fanzheng, E-mail: zengfanzheng92@163.com; Du, Guangxing; Wang, Honggang; Shi, Difu [College of Optoelectronic Science and Engineering, National University of Defense Technology, Changsha 410073 (China)
2016-01-15
A K-band large coaxial relativistic backward wave oscillator has been investigated by the 2.5-D particle-in-cell code. This device can generate high-power microwave at a constant frequency with a constant efficiency by increasing the radius of the electron beam and the average radius of the slow-wave structure. The simulation results show that the power conversion efficiency can reach 38.8% at the frequency of 25.48 GHz with the output power of 1.65 GW, while the electron beam has the energy of 196 kV and carries the current of 21.6 kA guided by the magnetic field of 2.5 T.
A compact relativistic backward-wave oscillator with metallized plastic components
Ge, Xingjun; Zhang, Jun; Zhong, Huihuang; Qian, Baoliang
2014-09-01
This letter presents the mechanism and realization of a compact relativistic backward-wave oscillator with metallized plastic components. The physical idea, specific structure, and the main testing results are presented. The three periods slow-wave structures with both inner and outer ripples and the coaxial extractor are designed to reduce the volume and increase the efficiency of the device. The metallized plastic components replacing the stainless steel components in the high power microwave (HPM) sources are put forward to reduce the device weight. In the initial experiment, a microwave with frequency of 1.54 GHz, power of 1.97 GW, efficiency of 33.5%, and pulse duration above 47 ns is generated, which proves that this technical route is feasible. Undoubtedly, the technical route can provide a guide to design other types of HPM sources and be benefit to the practical application of the compact HPM systems.
A viscous blast-wave model for relativistic heavy-ion collisions
Jaiswal, Amaresh
2015-01-01
Using a viscosity-based survival scale for geometrical perturbations formed in the early stages of relativistic heavy-ion collisions, we model the radial flow velocity during freeze-out. Subsequently, we employ the Cooper-Frye freeze-out prescription, with first-order viscous corrections to the distribution function, to obtain the transverse momentum distribution of particle yields and flow harmonics. For initial eccentricities, we use the results of Monte Carlo Glauber model. We fix the blast-wave model parameters by fitting the transverse momentum spectra of identified particles at the Large Hadron Collider (LHC) and demonstrate that this leads to a fairly good agreement with transverse momentum distribution of elliptic and triangular flow for various centralities. Within this viscous blast-wave model, we estimate the shear viscosity to entropy density ratio $\\eta/s\\simeq 0.24$ at the LHC.
On Fermi acceleration and MHD-instabilities at ultra-relativistic magnetized shock waves
Pelletier, Guy; Marcowith, Alexandre
2008-01-01
Fermi acceleration can take place at ultra-relativistic shock waves if the upstream or downstream magnetic field has been remodeled so that most of the magnetic power lies on short spatial scales. The relevant conditions under which Fermi acceleration become efficient in the presence of both a coherent and a short scale turbulent magnetic field are addressed. Within the MHD approximation, this paper then studies the amplification of a pre-existing magnetic field through the streaming of cosmic rays upstream of a relativistic shock wave. The magnetic field is assumed to be perpendicular in the shock front frame, as generally expected in the limit of large shock Lorentz factor. In the MHD regime, compressive instabilities seeded by the net cosmic-ray charge in the shock precursor (as seen in the shock front frame) develop on the shortest spatial scales but saturate at a moderate level $\\delta B/B \\sim 1$, which is not sufficient for Fermi acceleration. As we argue, it is possible that other instabilities outsid...
Investigating the Relationship of EMIC Waves and Relativistic Electron Precipitation Events
Woodger, L. A.; Millan, R. M.; Goldstein, J.; McCarthy, M. P.; Smith, D. M.; Sample, J. G.
2007-05-01
EMIC waves are generated and driven by anisotropic ring current protons. These unstable protons are injected into the inner magnetosphere by increased earthward convection during periods of elevated geomagnetic activity. A study by Meredith et al. (2003) showed EMIC wave events resonant with radiation belt electrons of energies less then 2MeV were located near the plasmapause in high density regions typical of the plasmaspheric plume. This study seeks to investigate the theory of relativistic electron precipitation (REP) due to wave particle interaction with EMIC waves. REP events were detected by balloon borne instrumentation during the MAXIS and MINIS balloon campaigns conducted in Jan. of 2000 and 2005 respectively. The location of these events with respect to the plasmapause will be explored using a plasmapause test particle simulation code and IMAGE EUV data. Also, data provided by the LANL satellite MPA instrument will be used to investigate the temperature anisotropy of ring current protons that may drive EMIC waves in the region of detected REP.
Chen, Zaigao; Wang, Jianguo; Wang, Yue
2015-01-01
This letter optimizes synchronously 18 parameters of a relativistic backward wave oscillator with non-uniform slow wave structure (SWS) and a resonant reflector by using the parallel genetic algorithms and particle-in-cell simulation. The optimization results show that the generation efficiency of microwave from the electron beam has increased 32% compared to that of the original device. After optimization, the electromagnetic mode propagating in the resonant changes from the original TM020 mode of reflector to higher-order TM021 mode, which has a high reflection coefficient in a broader frequency range than that of the former. The modulation of current inside the optimized device is much deeper than that in the original one. The product of the electric field and current is defined. Observing this product, it is found that the interaction of the electron beam with the electromagnetic wave in the optimized device is much stronger than that in the original device, and at the rear part of SWS of the optimized device, the electron beam dominantly gives out the energy to the electromagnetic wave, leading to the higher generation efficiency of microwave than that of the original device.
Kozyreva, O.; Pilipenko, V.; Engebretson, M. J.; Yumoto, K.; Watermann, J.; Romanova, N.
2007-04-01
A new ULF wave index, characterizing the turbulent level of the geomagnetic field, has been calculated and applied to the analysis of relativistic electron enhancements during space weather events in March-May 1994 and September 1999. This global wave index has been produced from the INTERMAGNET, MACCS, CPMN, and Greenland dense magnetometer arrays in the northern hemisphere. A similar ULF wave index has been calculated using magnetometer data from geostationary (GOES) and interplanetary (Wind, ACE) satellites. During the periods analyzed several magnetic storms occurred, and several significant increases of relativistic electron flux up to 2-3 orders of magnitude were detected by geostationary monitors. However, these electron enhancements were not directly related to the intensity of magnetic storms. Instead, they correlated well with intervals of elevated ULF wave index, caused by the occurrence of intense Pc5 pulsations in the magnetosphere. This comparison confirmed earlier results showing the importance of magnetospheric ULF turbulence in energizing relativistic electrons. In addition to relativistic electron energization, a wide range of space physics and geophysics studies will benefit from the introduction of the ULF wave index. The ULF index database is freely available via anonymous FTP for all interested researchers for further validation and statistical studies.
Saini, N. S.; Singh, Kuldeep
2016-10-01
A head-on collision between two dust ion acoustic solitary waves (DIASWs) travelling in the opposite direction in a weakly relativistic plasma composed of four distinct particle populations, namely, weakly relativistic ion fluid, superthermal electrons as well as positrons, and immobile dust, is investigated. By employing extended Poincaré-Lighthill-Kuo method, two Korteweg-de Vries (KdV) equations are derived. The analytical phase shift after a head-on collision of two dust ion acoustic (DIA) solitary waves is also obtained. The combined effects of relativistic factor (β), electron to positron temperature ratio (α), ion to electron temperature ratio (σ), positron to electron density ratio (P), dust density ratio (d), and superthermality of electrons as well as positrons (via κ) on the phase shifts are numerically studied. All these physical parameters have also changed the potential amplitude and the width of colliding solitary waves. It is found that the presence of superthermal electrons as well as positrons and dust grains has emphatic influence on the phase shifts and potential pulse profiles of compressive DIA solitons. Our results are general and may be helpful in understanding a head-on collision between two DIASWs in astrophysical and laboratory plasmas, especially the interaction of pulsar relativistic winds with supernova ejecta that produces the superthermal particles and relativistic ions.
Effect of end reflections on conversion efficiency of coaxial relativistic backward wave oscillator
Teng, Yan; Chen, Changhua; Sun, Jun; Shi, Yanchao; Ye, Hu; Wu, Ping; Li, Shuang; Xiong, Xiaolong
2015-11-01
This paper theoretically investigates the effect of end reflections on the operation of the coaxial relativistic backward wave oscillator (CRBWO). It is found that the considerable enhancement of the end reflection at one end increases the conversion efficiency, but excessively large end reflections at both ends weaken the asynchronous wave-beam interaction and thus reduce the conversion efficiency. Perfect reflection at the post end significantly improves the interaction between the electron beam and the asynchronous harmonic so that the conversion efficiency is notably increased. Based on the theoretical research, the diffraction-CRBWO with the generated microwave diffracted and output through the front end of the coaxial slow wave structure cavity is proposed. The post end is conductively closed to provide the perfect reflection. This promotes the amplitude and uniformity of the longitudinal electric field on the beam transmission line and improves the asynchronous wave-beam interaction. In numerical simulations under the diode voltage and current of 450 kV and 5.84 kA, microwave generation with the power of 1.45 GW and the conversion efficiency of 55% are obtained at the frequency of 7.45 GHz.
Effect of end reflections on conversion efficiency of coaxial relativistic backward wave oscillator
Teng, Yan; Chen, Changhua; Sun, Jun; Shi, Yanchao; Ye, Hu; Wu, Ping; Li, Shuang; Xiong, Xiaolong [Science and Technology on High Power Microwave Laboratory, Northwest Institute of Nuclear Technology, Xi' an 710024 (China)
2015-11-07
This paper theoretically investigates the effect of end reflections on the operation of the coaxial relativistic backward wave oscillator (CRBWO). It is found that the considerable enhancement of the end reflection at one end increases the conversion efficiency, but excessively large end reflections at both ends weaken the asynchronous wave-beam interaction and thus reduce the conversion efficiency. Perfect reflection at the post end significantly improves the interaction between the electron beam and the asynchronous harmonic so that the conversion efficiency is notably increased. Based on the theoretical research, the diffraction-CRBWO with the generated microwave diffracted and output through the front end of the coaxial slow wave structure cavity is proposed. The post end is conductively closed to provide the perfect reflection. This promotes the amplitude and uniformity of the longitudinal electric field on the beam transmission line and improves the asynchronous wave-beam interaction. In numerical simulations under the diode voltage and current of 450 kV and 5.84 kA, microwave generation with the power of 1.45 GW and the conversion efficiency of 55% are obtained at the frequency of 7.45 GHz.
Bauso, Dario
2014-05-07
This article examines mean-field games for marriage. The results support the argument that optimizing the long-term well-being through effort and social feeling state distribution (mean-field) will help to stabilize marriage. However, if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple using mean-field sentimental games. We show that, in mean-field equilibrium, the optimal effort is always higher than the one-shot optimal effort. We illustrate numerically the influence of the couple\\'s network on their feeling states and their well-being. © 2014 Bauso et al.
M, G. Hafez; N, C. Roy; M, R. Talukder; M Hossain, Ali
2017-01-01
A comparative study is carried out for the nonlinear propagation of ion acoustic shock waves both for the weakly and highly relativistic plasmas consisting of relativistic ions and q-distributed electrons and positions. The Burgers equation is derived to reveal the physical phenomena using the well known reductive perturbation technique. The integration of the Burgers equation is performed by the (G\\prime /G)-expansion method. The effects of positron concentration, ion–electron temperature ratio, electron–positron temperature ratio, ion viscosity coefficient, relativistic streaming factor and the strength of the electron and positron nonextensivity on the nonlinear propagation of ion acoustic shock and periodic waves are presented graphically and the relevant physical explanations are provided.
Degenerate second order mean field games systems
Tonon, Daniela; Cardaliaguet, Pierre; Graber, Philip,; Poretta, Alessio
2014-01-01
Parallel session; International audience; We consider degenerate second order mean field games systems with a local coupling. The starting point is the idea that mean field games systems can be understood as an optimality condition for optimal control of PDEs. Developing this strategy for the degenerate second order case, we discuss the existence and uniqueness of a weak solution as well as its stability (vanishing viscosity limit). Speaker: Daniela TONON
Back-reaction beyond the mean field approximation
Kluger, Y.
1993-12-01
A method for solving an initial value problem of a closed system consisting of an electromagnetic mean field and its quantum fluctuations coupled to fermions is presented. By tailoring the large N{sub f} expansion method to the Schwinger-Keldysh closed time path (CTP) formulation of the quantum effective action, causality of the resulting equations of motion is ensured, and a systematic energy conserving and gauge invariant expansion about the electromagnetic mean field in powers of 1/N{sub f} is developed. The resulting equations may be used to study the quantum nonequilibrium effects of pair creation in strong electric fields and the scattering and transport processes of a relativistic e{sup +}e{sup {minus}} plasma. Using the Bjorken ansatz of boost invariance initial conditions in which the initial electric mean field depends on the proper time only, we show numerical results for the case in which the N{sub f} expansion is truncated in the lowest order, and compare them with those of a phenomenological transport equation.
Zhang, Hong Lin; Sampson, Douglas H.
1990-11-01
The rapid relativistic distorted-wave method of Zhang, Sampson, and Mohanty [Phys. Rev. A 40, 616 (1989)] for excitation, which uses the atomic-structure data of Sampson et al. [Phys. Rev. A 40, 604 (1989)], has been extended to ionization. In this approach the same Dirac-Fock-Slater potential evaluated using a single mean configuration is used in calculating the orbitals of all electrons bound and free. Values for the cross sections Q for ionization of various ions have been calculated, and generally good agreement is obtained with other recent relativistic calculations. When results are expressed in terms of the reduced ionization cross section QR, which is proportional to I2Q, they are close to the nonrelativistic Coulomb-Born-exchange values of Moores, Golden, and Sampson [J. Phys. B 13, 385 (1980)] for hydrogenic ions except for high Z and/or high energies. This suggests that fits of the QR to simple functions of the impact electron energy in threshold units with coefficients that are quite slowly varying functions of an effective Z can probably be made. This would be convenient for plasma-modeling applications.
General Relativistic Radiant Shock Waves in the Post-Quasistatic Approximation
H, Jorge A Rueda [Centro de Fisica Fundamental, Universidad de Los Andes, Merida 5101, Venezuela Escuela de Fisica, Universidad Industrial de Santander, A.A. 678, Bucaramanga (Colombia); Nunez, L A [Centro de Fisica Fundamental, Universidad de Los Andes, Merida 5101, Venezuela Centro Nacional de Calculo Cientifico, Universidad de Los Andes, CeCalCULA, Corporacion Parque Tecnologico de Merida, Merida 5101, Venezuela (Venezuela)
2007-05-15
An evolution of radiant shock wave front is considered in the framework of a recently presented method to study self-gravitating relativistic spheres, whose rationale becomes intelligible and finds full justification within the context of a suitable definition of the post-quasistatic approximation. The spherical matter configuration is divided into two regions by the shock and each side of the interface having a different equation of state and anisotropic phase. In order to simulate dissipation effects due to the transfer of photons and/or neutrinos within the matter configuration, we introduce the flux factor, the variable Eddington factor and a closure relation between them. As we expected the strong of the shock increases the speed of the fluid to relativistic ones and for some critical values is larger than light speed. In addition, we find that energy conditions are very sensible to the anisotropy, specially the strong energy condition. As a special feature of the model, we find that the contribution of the matter and radiation to the radial pressure are the same order of magnitude as in the mant as in the core, moreover, in the core radiation pressure is larger than matter pressure.
M. G. Hafez
2016-01-01
Full Text Available Two-dimensional three-component plasma system consisting of nonextensive electrons, positrons, and relativistic thermal ions is considered. The well-known Kadomtsev-Petviashvili-Burgers and Kadomtsev-Petviashvili equations are derived to study the basic characteristics of small but finite amplitude ion acoustic waves of the plasmas by using the reductive perturbation method. The influences of positron concentration, electron-positron and ion-electron temperature ratios, strength of electron and positrons nonextensivity, and relativistic streaming factor on the propagation of ion acoustic waves in the plasmas are investigated. It is revealed that the electrostatic compressive and rarefactive ion acoustic waves are obtained for superthermal electrons and positrons, but only compressive ion acoustic waves are found and the potential profiles become steeper in case of subthermal positrons and electrons.
Nonrelativistic mean-field description of the deformation of Λ hypernuclei
无
2009-01-01
The deformations of light Λ hypernuclei are studied in an extended nonrelativistic deformed Skyrme-Hartree-Fock approach with realistic modern nucleonic Skyrme forces,pairing correlations,and a microscopical lambda-nucleon interaction derived from Brueckner-Hartree-Fock calculations.Compared to the large effect of an additional Λ particle on nuclear deformation in the light soft nuclei within relativistic mean field method,this effect is much smaller in the nonrelativistic mean-field approximation.
Shokri, B. [Physics Department and Laser-Plasma Research Institute of Shahid Beheshti University, Tehran (Iran, Islamic Republic of) and Institute for Studies in Theoretical Physics and Mathematics, P.O. Box 19395-1795, Tehran (Iran, Islamic Republic of)]. E-mail: b-shokri@cc.sbu.ac.ir; Khorashadizadeh, S.M. [Physics Department of Shahid Beheshti University, Tehran (Iran, Islamic Republic of); Physics Department of Birjand University, Birjand (Iran, Islamic Republic of)
2005-09-19
The possibility of the dissipative instability of a relativistic electron beam streaming near a conducting medium is investigated. The development of this dissipative beam instability through the surface wave excitation slightly disturbs the beam leading to the slightly heating of the conducting medium.
Lysenko, Alexander V.; Volk, Iurii I.; Serozhko, A.
2017-01-01
We elaborate a quadratic nonlinear theory of plural interactions of growing space charge wave (SCW) harmonics during the development of the two-stream instability in helical relativistic electron beams. It is found that in helical two-stream electron beams the growth rate of the two-stream instab...
Gisin, Boris V
2012-01-01
Dirac's equation in the field of a circularly polarized electromagnetic wave and constant magnetic field has exact localized non-stationary solutions. The solutions corresponds relativistic fermions only. Among them singular solutions with energy eigenvalues close to each other are found. The solutions are most practicable and can be separated by means of the phase matching between the momentum of the electromagnetic wave and spinor. Characteristic parameters of the singular states are defined.
Relativistic nonlinearity and wave-guide propagation of rippled laser beam in plasma
R K Khanna; K Baheti
2001-06-01
In the present paper we have investigated the self-focusing behaviour of radially symmetrical rippled Gaussian laser beam propagating in a plasma. Considering the nonlinearity to arise from relativistic phenomena and following the approach of Akhmanov et al, which is based on the WKB and paraxial-ray approximation, the self-focusing behaviour has been investigated in some detail. The effect of the position and width of the ripple on the self-focusing of laser beam has been studied for arbitrary large magnitude of nonlinearity. Results indicate that the medium behaves as an oscillatory wave-guide. The self-focusing is found to depend on the position parameter of ripple as well as on the beam width. Values of critical power has been calculated for different values of the position parameter of ripple. Effects of axially and radially inhomogeneous plasma on self-focusing behaviour have been investigated and presented here.
The detuning of relativistic Langmuir waves in the beat-wave accelerator
McKinstrie, C. J.; Forslund, D. W.
1987-03-01
In the beat-wave accelerator, a large-amplitude Langmuir wave is produced by the beating of two laser beams whose frequencies differ by approximately the plasma frequency. The growth of this Langmuir wave saturates because of a nonlinear shift in its natural frequency. At present, there are three different formulas for the nonlinear frequency shift in the literature. By taking all relevant nonlinearities into account, the original result of Akhiezer and Polovin [Dokl. Akad. Nauk SSSR 102, 919 (1955)] is shown to be correct. The maximum amplitude of the Langmuir wave depends on the incident laser intensity and the frequency mismatch, which is the difference between the beat frequency of the incident waves and the plasma frequency. Two different studies have produced contradictory conclusions on the ``optimum'' frequency mismatch. The reasons for this contradiction are discussed and the result of Tang, Sprangle, and Sudan [Phys. Fluids 28, 1974 (1985)] is shown to be essentially correct. However, the requirements for effective beam loading make practical use of the optimum configuration impossible.
Zheleznyakov, V. V.; Bespalov, P. A.
2016-04-01
In part I of this work [1], we study the dispersion characteristics of low-frequency waves in a relativistic electron-positron plasma. In part II, we examine the electromagnetic wave instability in this plasma caused by an admixture of nonrelativistic protons with energy comparable with the energy of relativistic low-mass particles. The instability occurs in the frequency band between the fundamental harmonic of proton gyrofrequency and the fundamental harmonic of relativistic electron gyrofrequency. The results can be used for the interpretation of known observations of the pulsar emissions obtained with a high time and frequency resolution. The considered instability can probably be the initial stage of the microwave radio emission nanoshots typical of the pulsar in the Crab Nebula.
Pion mean fields and heavy baryons
Yang, Ghil-Seok; Polyakov, Maxim V; Praszałowicz, Michał
2016-01-01
We show that the masses of the lowest-lying heavy baryons can be very well described in a pion mean-field approach. We consider a heavy baryon as a system consisting of the $N_c-1$ light quarks that induce the pion mean field, and a heavy quark as a static color source under the influence of this mean field. In this approach we derive a number of \\textit{model-independent} relations and calculate the heavy baryon masses using those of the lowest-lying light baryons as input. The results are in remarkable agreement with the experimental data. In addition, the mass of the $\\Omega_b^*$ baryon is predicted.
Mean Field Games with a Dominating Player
Bensoussan, A., E-mail: axb046100@utdallas.edu [The University of Texas at Dallas, International Center for Decision and Risk Analysis, Jindal School of Management (United States); Chau, M. H. M., E-mail: michaelchaumanho@gmail.com; Yam, S. C. P., E-mail: scpyam@sta.cuhk.edu.hk [The Chinese University of Hong Kong, Department of Statistics (Hong Kong, People’s Republic of China) (China)
2016-08-15
In this article, we consider mean field games between a dominating player and a group of representative agents, each of which acts similarly and also interacts with each other through a mean field term being substantially influenced by the dominating player. We first provide the general theory and discuss the necessary condition for the optimal controls and equilibrium condition by adopting adjoint equation approach. We then present a special case in the context of linear-quadratic framework, in which a necessary and sufficient condition can be asserted by stochastic maximum principle; we finally establish the sufficient condition that guarantees the unique existence of the equilibrium control. The proof of the convergence result of finite player game to mean field counterpart is provided in Appendix.
Mean field games for cognitive radio networks
Tembine, Hamidou
2012-06-01
In this paper we study mobility effect and power saving in cognitive radio networks using mean field games. We consider two types of users: primary and secondary users. When active, each secondary transmitter-receiver uses carrier sensing and is subject to long-term energy constraint. We formulate the interaction between primary user and large number of secondary users as an hierarchical mean field game. In contrast to the classical large-scale approaches based on stochastic geometry, percolation theory and large random matrices, the proposed mean field framework allows one to describe the evolution of the density distribution and the associated performance metrics using coupled partial differential equations. We provide explicit formulas and algorithmic power management for both primary and secondary users. A complete characterization of the optimal distribution of energy and probability of success is given.
Ghizzo, A. [Institut Jean Lamour UMR 7163, Université de Lorraine, BP 239 F-54506 Vandoeuvre les Nancy (France)
2013-08-15
The stationary state with magnetically trapped particles is investigated at the saturation of the relativistic Weibel instability, within the “multiring” model in a Hamiltonian framework. The multistream model and its multiring extension have been developed in Paper I, under the assumption that the generalized canonical momentum is conserved in the perpendicular direction. One dimensional relativistic Bernstein-Greene-Kruskal waves with deeply trapped particles are addressed using similar mathematical formalism developed by Lontano et al.[Phys. Plasmas 9, 2562 (2002); Phys. Plasmas 10, 639 (2003)] using several streams and in the presence of both electrostatic and magnetic trapping mechanisms.
Pokhotelov, D.; Rae, I. J.; Murphy, K. R.; Mann, I. R.
2016-12-01
Electromagnetic ultralow-frequency (ULF) waves are known to play a substantial role in radial transport, acceleration, and loss of relativistic particles trapped in the Earth's outer radiation belt. Using in situ observations by multiple spacecraft operating in the vicinity of outer radiation belts, we analyze the temporal and spatial behavior of ULF waves throughout the geomagnetic storm of 8-9 October 2012 and compare with the dynamics of relativistic electron fluxes on board the twin Van Allen Probes spacecraft. The analysis shows that the relativistic electron fluxes reduce from their prestorm levels during the first phase of the storm and rapidly increase during the second phase of the storm. We demonstrate that the behavior of ULF wave power changes throughout the storm, from ULF oscillations being a mixture of compressional and shear magnetic components during the first phase of the storm to ULF oscillations being dominated by transverse (shear) components during the second phase. We analyze the parameters of ULF-driven radial diffusion throughout the storm and compare the observed diffusion coefficients with their statistical averages. We demonstrate that the observed diffusion coefficients are strong enough to impact the redistribution of relativistic electron fluxes from and to the outer boundary of radiation belts and the diffusion might influence the effects of any local electron acceleration by transporting fluxes inward or outward according to phase space density gradients.
Obstacle mean-field game problem
Gomes, Diogo A.
2015-01-01
In this paper, we introduce and study a first-order mean-field game obstacle problem. We examine the case of local dependence on the measure under assumptions that include both the logarithmic case and power-like nonlinearities. Since the obstacle operator is not differentiable, the equations for first-order mean field game problems have to be discussed carefully. Hence, we begin by considering a penalized problem. We prove this problem admits a unique solution satisfying uniform bounds. These bounds serve to pass to the limit in the penalized problem and to characterize the limiting equations. Finally, we prove uniqueness of solutions. © European Mathematical Society 2015.
Mean-field magnetohydrodynamics and dynamo theory
Krause, F
2013-01-01
Mean-Field Magnetohydrodynamics and Dynamo Theory provides a systematic introduction to mean-field magnetohydrodynamics and the dynamo theory, along with the results achieved. Topics covered include turbulence and large-scale structures; general properties of the turbulent electromotive force; homogeneity, isotropy, and mirror symmetry of turbulent fields; and turbulent electromotive force in the case of non-vanishing mean flow. The turbulent electromotive force in the case of rotational mean motion is also considered. This book is comprised of 17 chapters and opens with an overview of the gen
Xiao Renzhen; Zhang Xiaowei; Zhang Ligang; Li Xiaoze; Zhang Lijun [National Key Laboratory of Science and Technology on High Power Microwave, Northwest Institute of Nuclear Technology, Xi' an 710024 (China)
2012-07-15
In this paper, we analyze the factors that affect the microwave pulse duration in a klystron-like relativistic backward wave oscillator (RBWO), including the diode voltage, the guiding magnetic field, the electron beam collector, the extraction cavity, and the gap between the electron beam and the slow wave structure (SWS). The results show that the microwave pulse duration increases with the diode voltage until breakdown occurs on the surface of the extraction cavity. The pulse duration at low guiding magnetic field is generally 5-10 ns smaller than that at high magnetic field due to the asymmetric electron emission and the larger energy spread of the electron beam. The electron beam collector can affect the microwave pulse duration significantly because of the anode plasma generated by bombardment of the electron beam on the collector surface. The introduction of the extraction cavity only slightly changes the pulse duration. The decrease of the gap between the electron beam and the SWS can increase the microwave pulse duration greatly.
Design of a high efficiency relativistic backward wave oscillator with low guiding magnetic field
Li, Xiaoze; Song, Wei; Tan, Weibing; Zhang, Ligang; Su, Jiancang; Zhu, Xiaoxin; Hu, Xianggang; Shen, Zhiyuan; Liang, Xu; Ning, Qi [Science and Technology on High Power Microwave Laboratory, Northwest Institute of Nuclear Technology, Xi' an 710024 (China)
2016-07-15
A high efficiency relativistic backward wave oscillator working at a low guiding magnetic field is designed and simulated. A trapezoidal resonant reflector is used to reduce the modulation field in the resonant reflector to avoid overmodulation of the electron beam which will lead to a large momentum spread and then low conversion efficiency. The envelope of the inner radius of the slow wave structure (SWS) increases stepwise to keep conformal to the trajectory of the electron beam which will alleviate the bombardment of the electron on the surface of the SWS. The length of period of the SWS is reduced gradually to make a better match between phase velocity and electron beam, which decelerates continually and improves the RF current distribution. Meanwhile the modulation field is reduced by the introduction of nonuniform SWS also. The particle in cell simulation results reveal that a microwave with a power of 1.8 GW and a frequency of 14.7 GHz is generated with an efficiency of 47% when the diode voltage is 620 kV, the beam current 6.1 kA, and the guiding magnetic field 0.95 T.
On plane-wave relativistic electrodynamics in plasmas and in vacuum
Fiore, Gaetano
2016-01-01
We revisit the exact microscopic equations (in differential, and equivalent integral form) ruling a relativistic cold plasma after the plane-wave Ansatz, without customary approximations. We show that in the Eulerian description the motion of a very diluted plasma initially at rest and excited by an arbitrary transverse plane electromagnetic travelling-wave has a very simple and explicit dependence on the transverse electromagnetic potential; for a non-zero density plasma the above motion is a good approximation of the real one as long as the back-reaction of the charges on the electromagnetic field can be neglected, i.e. for a time lapse decreasing with the plasma density, and can be used as initial step in an iterative resolution scheme. As one of many possible applications, we use these results to describe how the ponderomotive force of a very intense and short plane laser pulse hitting normally the surface of a plasma boosts the surface electrons into the ion background. Because of this penetration the el...
Propagation peculiarities of mean field massive gravity
S. Deser
2015-10-01
Full Text Available Massive gravity (mGR describes a dynamical “metric” on a fiducial, background one. We investigate fluctuations of the dynamics about mGR solutions, that is about its “mean field theory”. Analyzing mean field massive gravity (m‾GR propagation characteristics is not only equivalent to studying those of the full non-linear theory, but also in direct correspondence with earlier analyses of charged higher spin systems, the oldest example being the charged, massive spin 3/2 Rarita–Schwinger (RS theory. The fiducial and mGR mean field background metrics in the m‾GR model correspond to the RS Minkowski metric and external EM field. The common implications in both systems are that hyperbolicity holds only in a weak background-mean-field limit, immediately ruling both theories out as fundamental theories; a situation in stark contrast with general relativity (GR which is at least a consistent classical theory. Moreover, even though both m‾GR and RS theories can still in principle be considered as predictive effective models in the weak regime, their lower helicities then exhibit superluminal behavior: lower helicity gravitons are superluminal as compared to photons propagating on either the fiducial or background metric. Thus our approach has uncovered a novel, dispersive, “crystal-like” phenomenon of differing helicities having differing propagation speeds. This applies both to m‾GR and mGR, and is a peculiar feature that is also problematic for consistent coupling to matter.
Weakly coupled mean-field game systems
Gomes, Diogo A.
2016-07-14
Here, we prove the existence of solutions to first-order mean-field games (MFGs) arising in optimal switching. First, we use the penalization method to construct approximate solutions. Then, we prove uniform estimates for the penalized problem. Finally, by a limiting procedure, we obtain solutions to the MFG problem. © 2016 Elsevier Ltd
A mean field approach to watershed hydrology
Bartlett, Mark; Porporato, Amilcare
2016-04-01
Mean field theory (also known as self-consistent field theory) is commonly used in statistical physics when modeling the space-time behavior of complex systems. The mean field theory approximates a complex multi-component system by considering a lumped (or average) effect for all individual components acting on a single component. Thus, the many body problem is reduced to a one body problem. For watershed hydrology, a mean field theory reduces the numerous point component effects to more tractable watershed averages, resulting in a consistent method for linking the average watershed fluxes to the local fluxes at each point. We apply this approach to the spatial distribution of soil moisture, and as a result, the numerous local interactions related to lateral fluxes of soil water are parameterized in terms of the average soil moisture. The mean field approach provides a basis for unifying and extending common event-based models (e.g. Soil Conservation Service curve number (SCS-CN) method) with more modern semi-distributed models (e.g. Variable Infiltration Capacity (VIC) model, the Probability Distributed (PDM) model, and TOPMODEL). We obtain simple equations for the fractions of the different source areas of runoff, the spatial variability of runoff, and the average runoff value (i.e., the so-called runoff curve). The resulting space time distribution of soil moisture offers a concise description of the variability of watershed fluxes.
A regularized stationary mean-field game
Yang, Xianjin
2016-04-19
In the thesis, we discuss the existence and numerical approximations of solutions of a regularized mean-field game with a low-order regularization. In the first part, we prove a priori estimates and use the continuation method to obtain the existence of a solution with a positive density. Finally, we introduce the monotone flow method and solve the system numerically.
Kuzichev, Ilya; Shklyar, David
2016-04-01
One of the most challenging problems of the radiation belt studies is the problem of particles energization. Being related to the process of particle precipitation and posing a threat to scientific instruments on satellites, the problem of highly energetic particles in the radiation belts turns out to be very important. A lot of progress has been made in this field, but still some aspects of the energization process remain open. The main mechanism of particle energization in the radiation belts is the resonant interaction with different waves, mainly, in whistler frequency range. The problem of special interest is the resonant wave-particle interaction of the electrons of relativistic energies. Relativistic resonance condition provides some important features such as the so-called relativistic turning acceleration discovered by Omura et al. [1, 2]. This process appears to be a very efficient mechanism of acceleration in the case of interaction with the whistler-mode waves propagating along geomagnetic field lines. But some whistler-mode waves propagate obliquely to the magnetic field lines, and the efficiency of relativistic turning acceleration in this case is to be studied. In this report, we present the Hamiltonian theory of the resonant interaction of relativistic electrons with oblique monochromatic whistler-mode waves. We have shown that the presence of turning point requires a special treatment when one aims to derive the resonant Hamiltonian, and we have obtained two different resonant Hamiltonians: one to be applied far enough from the turning point, while another is valid in the vicinity of the turning point. We have performed numerical simulation of relativistic electron interaction with whistler-mode waves generated in the ionosphere by a monochromatic source. It could be, for example, a low-frequency transmitter. The wave-field distribution along unperturbed particle trajectory is calculated by means of geometrical optics. We show that the obliquity of
Thermal Effects in Dense Matter Beyond Mean Field Theory
Constantinou, Constantinos; Prakash, Madappa
2016-01-01
The formalism of next-to-leading order Fermi Liquid Theory is employed to calculate the thermal properties of symmetric nuclear and pure neutron matter in a relativistic many-body theory beyond the mean field level which includes two-loop effects. For all thermal variables, the semi-analytical next-to-leading order corrections reproduce results of the exact numerical calculations for entropies per baryon up to 2. This corresponds to excellent agreement down to sub-nuclear densities for temperatures up to $20$ MeV. In addition to providing physical insights, a rapid evaluation of the equation of state in the homogeneous phase of hot and dense matter is achieved through the use of the zero-temperature Landau effective mass function and its derivatives.
Kourakis, I.; McKerr, M.; Elkamash, I. S.; Haas, F.
2017-10-01
The dispersion properties of electrostatic waves propagating in ultrahigh density plasma are investigated, from first principles, in a one-dimensional geometry. A self-consistent multispecies plasma fluid model is taken as starting point, incorporating electron degeneracy and relativistic effects. The inertia of all plasma components is retained, for rigor. Exact expressions are obtained for the oscillation frequency, and the phase and group velocity of electrostatic waves is computed. Two branches are obtained, viz. an acoustic low-frequency dispersion branch and an upper (optic-like) branch: these may be interpreted as ion-acoustic and electron plasma (Langmuir) waves, respectively, as in classical plasmas, yet bearing an explicit correction in account of relativistic and electron degeneracy effects. The electron plasma frequency is shown to reduce significantly at high values of the density, due to the relativistic effect. The result is compared with approximate models, wherein either electrons are considered inertialess (low-frequency ionic scale) or ions are considered to be stationary (Langmuir-wave limit).
Mean-field learning for satisfactory solutions
Tembine, Hamidou
2013-12-01
One of the fundamental challenges in distributed interactive systems is to design efficient, accurate, and fair solutions. In such systems, a satisfactory solution is an innovative approach that aims to provide all players with a satisfactory payoff anytime and anywhere. In this paper we study fully distributed learning schemes for satisfactory solutions in games with continuous action space. Considering games where the payoff function depends only on own-action and an aggregate term, we show that the complexity of learning systems can be significantly reduced, leading to the so-called mean-field learning. We provide sufficient conditions for convergence to a satisfactory solution and we give explicit convergence time bounds. Then, several acceleration techniques are used in order to improve the convergence rate. We illustrate numerically the proposed mean-field learning schemes for quality-of-service management in communication networks. © 2013 IEEE.
Mean field methods for cortical network dynamics
Hertz, J.; Lerchner, Alexander; Ahmadi, M.
2004-01-01
We review the use of mean field theory for describing the dynamics of dense, randomly connected cortical circuits. For a simple network of excitatory and inhibitory leaky integrate- and-fire neurons, we can show how the firing irregularity, as measured by the Fano factor, increases with the stren...... cortex. Finally, an extension of the model to describe an orientation hypercolumn provides understanding of how cortical interactions sharpen orientation tuning, in a way that is consistent with observed firing statistics...
Bosonic Dynamical Mean-Field Theory
Snoek, Michiel; Hofstetter, Walter
2013-02-01
We derive the bosonic dynamical mean-field equations for bosonic atoms in optical lattices with arbitrary lattice geometry. The equations are presented as a systematic expansion in 1/z, z being the number of lattice neighbours. Hence the theory is applicable in sufficiently high-dimensional lattices. We apply the method to a two-component mixture, for which a rich phase diagram with spin order is revealed.
Mean field games systems of first order
Cardaliaguet, Pierre; Graber, Philip Jameson
2014-01-01
International audience; We consider a system of mean field games with local coupling in the deterministic limit. Under general structure conditions on the Hamiltonian and coupling, we prove existence and uniqueness of the weak solution, characterizing this solution as the minimizer of some optimal control of Hamilton-Jacobi and continuity equations. We also prove that this solution converges in the long time average to the solution of the associated ergodic problem.
S. A. El-Wakil
2012-01-01
Full Text Available The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV equation for small- but finite-amplitude electrostatic ion-acoustic waves in weakly relativistic plasma consisting of warm ions and isothermal electrons. An algebraic method with computerized symbolic computation is applied in obtaining a series of exact solutions of the KdV equation. Numerical studies have been made using plasma parameters which reveal different solutions, that is, bell-shaped solitary pulses, rational pulses, and solutions with singularity at finite points, which called “blowup” solutions in addition to the propagation of an explosive pulses. The weakly relativistic effect is found to significantly change the basic properties (namely, the amplitude and the width of the ion-acoustic waves. The result of the present investigation may be applicable to some plasma environments, such as ionosphere region.
'Phase diagram' of a mean field game
Swiecicki, Igor; Ullmo, Denis
2015-01-01
Mean field games were introduced by J-M.Lasry and P-L. Lions in the mathematical community, and independently by M. Huang and co-workers in the engineering community, to deal with optimization problems when the number of agents becomes very large. In this article we study in detail a particular example called the 'seminar problem' introduced by O.Gu\\'eant, J-M Lasry, and P-L. Lions in 2010. This model contains the main ingredients of any mean field game but has the particular feature that all agent are coupled only through a simple random event (the seminar starting time) that they all contribute to form. In the mean field limit, this event becomes deterministic and its value can be fixed through a self consistent procedure. This allows for a rather thorough understanding of the solutions of the problem, through both exact results and a detailed analysis of various limiting regimes. For a sensible class of initial configurations, distinct behaviors can be associated to different domains in the parameter space...
Lu, Ding; Xie, Bai-Song
2013-01-01
Effects of ion mobility and positron fraction on solitary waves of envelop of laser field and potential of electrostatic field in weak relativistic electron-positron-ion plasma are investigated. The parameter region for the existence of solitary waves is obtained analytically, and the reasonable choice of parameters is clarified. Both cases of mobile and immobile ions are considered. It is found that the amplitudes of solitary waves in the former case are larger compared to the latter case. For small plasma density, the localized solitary wave solutions in terms of approximate perturbation analytical method are consistent well with that by exact numerical calculations. However as the plasma density increases the analytical method loses its validity more and more. The influence of the positron fraction on the amplitudes of solitary waves shows a monotonous increasing relation. Implication of our results to the particle acceleration is also discussed briefly.
Lu, Ding; Li, Zi-Liang; Xie, Bai-Song
2013-09-01
The effects of ion mobility and positron fraction on the solitary waves of the laser field envelope and the potential of the electrostatic field in weak relativistic electron-positron-ion plasma are investigated. The parameter region for the existence of solitary waves is obtained analytically, and a reasonable choice of parameters is clarified. Both cases of mobile and immobile ions are considered. It is found that the amplitudes of solitary waves in the former case are larger compared to the latter case. For small plasma density, the localized solitary wave solutions in terms of the approximate perturbation analytical method are very consistent with those by exact numerical calculations. However, as the plasma density increases the analytical method loses its validity more and more. The influence of the positron fraction on the amplitudes of solitary waves shows a monotonous increasing relation. The implications of our results to particle acceleration are also discussed briefly.
Quarkonium and hydrogen spectra with spin-dependent relativistic wave equation
V H Zaveri
2010-10-01
The non-linear non-perturbative relativistic atomic theory introduces spin in the dynamics of particle motion. The resulting energy levels of hydrogen atom are exactly the same as that of Dirac theory. The theory accounts for the energy due to spin-orbit interaction and for the additional potential energy due to spin and spin-orbit coupling. Spin angular momentum operator is integrated into the equation of motion. This requires modification to classical Laplacian operator. Consequently, the Dirac matrices and the k operator of Dirac’s theory are dispensed with. The theory points out that the curvature of the orbit draws on certain amount of kinetic and potential energies affecting the momentum of electron and the spin-orbit interaction energy constitutes a part of this energy. The theory is developed for spin-1/2 bound state single electron in Coulomb potential and then extended further to quarkonium physics by introducing the linear confining potential. The unique feature of this quarkonium model is that the radial distance can be exactly determined and does not have a statistical interpretation. The established radial distance is then used to determine the wave function. The observed energy levels are used as the input parameters and the radial distance and the string tension are predicted. This ensures 100% conformance to all observed energy levels for the heavy quarkonium.
Lifetime experimental study of graphite cathode for relativistic backward wave oscillator
Wu, Ping; Sun, Jun; Chen, Changhua
2016-07-01
Graphite cathodes are widely used due to their good emission properties, especially their long lifetime. Some previous papers have researched their lifetime under certain conditions and uncovered some important phenomena. This paper is dedicated to research the lifetime of the graphite cathode under higher power. In the lifetime test, the voltage and current amplitudes are about 970 kV and 9.7 kA, respectively. The repetition rate is 20 Hz. An X-band relativistic backward wave oscillator is used to generate high power microwave by utilizing the electron beam energy. The experimental results demonstrate that the emission property of the graphite cathode remains quite stable during 105 pulses, despite some slight deteriorations regarding the beam and microwave parameters. The macroscopic morphology change of the cathode blade due to material evaporation is observed by a laser microscope. The mass loss of the graphite cathode is about 60 μg/C. Meanwhile, the observation by a scanning electron microscope uncovers that the original numerous flaky micro-structures are totally replaced by a relatively smooth surface at the mid region of the cathode blade and a large number of new micro-protrusions at the blade edges during the lifetime test.
Effective suppression of pulse shortening in a relativistic backward wave oscillator
Cao, Yibing; Song, Zhimin; Wu, Ping; Fan, Zhiqiang; Zhang, Yuchuan; Teng, Yan; Sun, Jun
2017-03-01
This paper discusses pulse shortening present in a C-band relativistic backward wave oscillator (RBWO). Effects of the collector plasma are believed to be the main cause. This viewpoint is first verified in numerical simulation. The simulation results show that light charged particles such as hydrogen ions in the collector plasma would axially enter into the beam-microwave interaction region and suppress high-power microwave (HPM) generation. Simultaneously, heavy charged particles such as oxygen or ferric ions in the collector plasma would radially expand out and change the end reflection of the RBWO. All these effects can result in pulse shortening. Simulations also demonstrate that a coaxial collector can effectively suppress plasma effects by retarding their axial and radial expansions. Furthermore, a HPM experiment has confirmed the validity of the coaxial collector. Using this structure, the output power of the RBWO has been increased from 2.5 GW to 3 GW. No pulse shortening has been observed in the HPM experiment.
Time-odd mean fields in covariant density functional theory: Rotating systems
Afanasjev, A V; 10.1103/PhysRev.82.034329
2010-01-01
Time-odd mean fields (nuclear magnetism) and their impact on physical observables in rotating nuclei are studied in the framework of covariant density functional theory (CDFT). It is shown that they have profound effect on the dynamic and kinematic moments of inertia. Particle number, configuration and rotational frequency dependences of their impact on the moments of inertia have been analysed in a systematic way. Nuclear magnetism can also considerably modify the band crossing features such as crossing frequencies and the properties of the kinematic and dynamic moments of inertia in the band crossing region. The impact of time-odd mean fields on the moments of inertia in the regions away from band crossing only weakly depends on the relativistic mean field parametrization, reflecting good localization of the properties of time-odd mean fields in CDFT. The moments of inertia of normal-deformed nuclei considerably deviate from the rigid body value. On the contrary, superdeformed and hyperdeformed nuclei have ...
Mean field methods for cortical network dynamics
Hertz, J.; Lerchner, Alexander; Ahmadi, M.
2004-01-01
We review the use of mean field theory for describing the dynamics of dense, randomly connected cortical circuits. For a simple network of excitatory and inhibitory leaky integrate- and-fire neurons, we can show how the firing irregularity, as measured by the Fano factor, increases...... with the strength of the synapses in the network and with the value to which the membrane potential is reset after a spike. Generalizing the model to include conductance-based synapses gives insight into the connection between the firing statistics and the high- conductance state observed experimentally in visual...
Mean-field behavior of cluster dynamics
Persky, N.; Ben-Av, R.; Kanter, I.; Domany, E.
1996-09-01
The dynamic behavior of cluster algorithms is analyzed in the classical mean-field limit. Rigorous analytical results below Tc establish that the dynamic exponent has the value zSW=1 for the Swendsen-Wang algorithm and zW=0 for the Wolff algorithm. An efficient Monte Carlo implementation is introduced, adapted for using these algorithms for fully connected graphs. Extensive simulations both above and below Tc demonstrate scaling and evaluate the finite-size scaling function by means of a rather impressive collapse of the data.
HBT Pion Interferometry with Phenomenological Mean Field Interaction
Hattori, K.
2010-11-01
To extract information on hadron production dynamics in the ultrarelativistic heavy ion collision, the space-time structure of the hadron source has been measured using Hanbury Brown and Twiss interferometry. We study the distortion of the source images due to the effect of a final state interaction. We describe the interaction, taking place during penetrating through a cloud formed by evaporating particles, in terms of a one-body mean field potential localized in the vicinity of the source region. By adopting the semiclassical method, the modification of the propagation of an emitted particle is examined. In analogy to the optical model applied to nuclear reactions, our phenomenological model has an imaginary part of the potential, which describes the absorption in the cloud. In this work, we focus on the pion interferometry and mean field interaction obtained using a phenomenological pipi forward scattering amplitude in the elastic channels. The p-wave scattering wit h rho meson resonance leads to an attractive mean field interaction, and the presence of the absorptive part is mainly attributed to the formation of this resonance. We also incorporate a simple time dependence of the potential reflecting the dynamics of the evaporating source. Using the obtained potential, we examine how and to what extent the so-called HBT Gaussian radius is varied by the modification of the propagation.
Li, Xiaoze; Ye, Hu; Zhang, Yuchuan; Song, Wei; Su, Jiancang; Zhang, Ligang; Tan, Weibing; Hu, Xianggang; Zhu, Xiaoxin; Shen, Zhiyuan; Zhang, Min [Science and Technology on High Power Microwave Laboratory, Northwest Institute of Nuclear Technology, Xi' an 710024 (China)
2016-05-15
A high power capacity relativistic backward wave oscillator with an electron collection cavity (ECC) placed at the downstream of the slow wave structure (SWS) is presented. The breakdown threshold is increased, and the density of seed electron is suppressed by preventing the secondary electron, plasma, and powder generated from the bombardment of spent electron beam on the surface of the collector drifting to the extractor and beam-wave interaction region. The maximum longitudinal electric field in the device is reduced through extension of the span between electron beam and slow wave structure and weakening the Cerenkov radiation. The conversion efficiency reaches up to 52% owing to enhanced transit time radiation taking place at the entrance of the ECC. The maximum longitudinal electric field is 1.1 MV/cm on the surface of SWSs when the output power is 7.3 GW and the power capacity improves significantly.
Pedestrian Flow in the Mean Field Limit
Haji Ali, Abdul Lateef
2012-11-01
We study the mean-field limit of a particle-based system modeling the behavior of many indistinguishable pedestrians as their number increases. The base model is a modified version of Helbing\\'s social force model. In the mean-field limit, the time-dependent density of two-dimensional pedestrians satisfies a four-dimensional integro-differential Fokker-Planck equation. To approximate the solution of the Fokker-Planck equation we use a time-splitting approach and solve the diffusion part using a Crank-Nicholson method. The advection part is solved using a Lax-Wendroff-Leveque method or an upwind Backward Euler method depending on the advection speed. Moreover, we use multilevel Monte Carlo to estimate observables from the particle-based system. We discuss these numerical methods, and present numerical results showing the convergence of observables that were calculated using the particle-based model as the number of pedestrians increases to those calculated using the probability density function satisfying the Fokker-Planck equation.
Nuclear matter EOS with light clusters within the mean-field approximation
Ferreira, Márcio
2013-01-01
The crust of a neutron star is essentially determined by the low-density region ($\\rho<\\rho_0\\approx0.15-0.16\\unit{fm}^{-3}$) of the equation of state. At the bottom of the inner crust, where the density is $\\rho\\lesssim0.1\\rho_0$, the formation of light clusters in nuclear matter will be energetically favorable at finite temperature. At very low densities and moderate temperatures, the few body correlations are expected to become important and light nuclei like deuterons, tritons, helions and $\\alpha$-particles will form. Due to Pauli blocking, these clusters will dissolve at higher densities $\\rho\\gtrsim 0.1\\rho_0$. The presence of these clusters influences the cooling process and quantities, such as the neutrino emissivity and gravitational waves emission. The dissolution density of these light clusters, treated as point-like particles, will be studied within the Relativistic Mean Field approximation. In particular, the dependence of the dissolution density on the clusters-meson couplings is studied.
Mean field magnetization of gapped anisotropic multiplet
Paixão, L. S.; Reis, M. S.
2014-06-01
Some materials have a large gap between the ground and first excited states. At temperatures smaller than the gap value, the thermodynamic properties of such materials are mainly ruled by the ground state. It is also common to find materials with magnetocrystalline anisotropy, which arises due to interatomic interactions. The present paper uses a classical approach to deal large angular momenta in such materials. Based on analytical expressions for the thermodynamics of paramagnetic gapped anisotropic multiplets, we use mean field theory to study the influence of the anisotropy upon the properties of interacting systems. We also use Landau theory to determine the influence of the anisotropy in first and second order phase transitions. It is found that the anisotropy increases the critical temperature, and enlarges the hysteresis of first order transitions. We present analytical expressions for the quantities analyzed.
Invisible dynamo in mean-field models
Reshetnyak, M. Yu.
2016-07-01
The inverse problem in a spherical shell to find the two-dimensional spatial distributions of the α-effect and differential rotation in a mean-field dynamo model has been solved. The derived distributions lead to the generation of a magnetic field concentrated inside the convection zone. The magnetic field is shown to have no time to rise from the region of maximum generation located in the lower layers to the surface in the polarity reversal time due to magnetic diffusion. The ratio of the maximum magnetic energy in the convection zone to its value at the outer boundary reaches two orders of magnitude or more. This result is important in interpreting the observed stellar and planetary magnetic fields. The proposed method of solving the inverse nonlinear dynamo problem is easily adapted for a wide class of mathematical-physics problems.
Mean-field models for disordered crystals
Cancès, Eric; Lewin, Mathieu
2012-01-01
In this article, we set up a functional setting for mean-field electronic structure models of Hartree-Fock or Kohn-Sham types for disordered crystals. The electrons are quantum particles and the nuclei are classical point-like articles whose positions and charges are random. We prove the existence of a minimizer of the energy per unit volume and the uniqueness of the ground state density of such disordered crystals, for the reduced Hartree-Fock model (rHF). We consider both (short-range) Yukawa and (long-range) Coulomb interactions. In the former case, we prove in addition that the rHF ground state density matrix satisfies a self-consistent equation, and that our model for disordered crystals is the thermodynamic limit of the supercell model.
Mean-field Ensemble Kalman Filter
Law, Kody
2015-01-07
A proof of convergence of the standard EnKF generalized to non-Gaussian state space models is provided. A density-based deterministic approximation of the mean-field limiting EnKF (MFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for d < 2 . The fidelity of approximation of the true distribution is also established using an extension of total variation metric to random measures. This is limited by a Gaussian bias term arising from non-linearity/non-Gaussianity of the model, which arises in both deterministic and standard EnKF. Numerical results support and extend the theory.
Time dependent mean-field games
Gomes, Diogo A.
2014-01-06
We consider time dependent mean-field games (MFG) with a local power-like dependence on the measure and Hamiltonians satisfying both sub and superquadratic growth conditions. We establish existence of smooth solutions under a certain set of conditions depending both on the growth of the Hamiltonian as well as on the dimension. In the subquadratic case this is done by combining a Gagliardo-Nirenberg type of argument with a new class of polynomial estimates for solutions of the Fokker-Planck equation in terms of LrLp- norms of DpH. These techniques do not apply to the superquadratic case. In this setting we recur to a delicate argument that combines the non-linear adjoint method with polynomial estimates for solutions of the Fokker-Planck equation in terms of L1L1-norms of DpH. Concerning the subquadratic case, we substantially improve and extend the results previously obtained. Furthermore, to the best of our knowledge, the superquadratic case has not been addressed in the literature yet. In fact, it is likely that our estimates may also add to the current understanding of Hamilton-Jacobi equations with superquadratic Hamiltonians.
Deterministic Mean-Field Ensemble Kalman Filtering
Law, Kody J. H.
2016-05-03
The proof of convergence of the standard ensemble Kalman filter (EnKF) from Le Gland, Monbet, and Tran [Large sample asymptotics for the ensemble Kalman filter, in The Oxford Handbook of Nonlinear Filtering, Oxford University Press, Oxford, UK, 2011, pp. 598--631] is extended to non-Gaussian state-space models. A density-based deterministic approximation of the mean-field limit EnKF (DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence k between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for dimension d<2k. The fidelity of approximation of the true distribution is also established using an extension of the total variation metric to random measures. This is limited by a Gaussian bias term arising from nonlinearity/non-Gaussianity of the model, which arises in both deterministic and standard EnKF. Numerical results support and extend the theory.
Nonequilibrium dynamical mean-field theory
Eckstein, Martin
2009-12-21
The aim of this thesis is the investigation of strongly interacting quantum many-particle systems in nonequilibrium by means of the dynamical mean-field theory (DMFT). An efficient numerical implementation of the nonequilibrium DMFT equations within the Keldysh formalism is provided, as well a discussion of several approaches to solve effective single-site problem to which lattice models such as the Hubbard-model are mapped within DMFT. DMFT is then used to study the relaxation of the thermodynamic state after a sudden increase of the interaction parameter in two different models: the Hubbard model and the Falicov-Kimball model. In the latter case an exact solution can be given, which shows that the state does not even thermalize after infinite waiting times. For a slow change of the interaction, a transition to adiabatic behavior is found. The Hubbard model, on the other hand, shows a very sensitive dependence of the relaxation on the interaction, which may be called a dynamical phase transition. Rapid thermalization only occurs at the interaction parameter which corresponds to this transition. (orig.)
Time-odd mean fields in the rotating frame microscopic nature of nuclear magnetism
Afanasiev, A V
2000-01-01
The microscopic role of nuclear magnetism in rotating frame is investigated for the first time in the framework of the cranked relativistic mean field theory. It is shown that nuclear magnetism modifies the expectation values of single-particle spin, orbital and total angular momenta along the rotational axis effectively creating additional angular momentum. This effect leads to the increase of kinematic and dynamic moments of inertia at given rotational frequency and has an impact on effective alignments.
Shell Effect of Superheavy Nuclei in Self-consistent Mean-Field Models
RENZhong-Zhou; TAIFei; XUChang; CHENDing-Han; ZHANGHu-Yong; CAIXiang-Zhou; SHENWen-Qing
2004-01-01
We analyze in detail the numerical results of superheavy nuclei in deformed relativistic mean-field model and deformed Skyrme-Hartree-Fock model. The common points and differences of both models are systematically compared and discussed. Their consequences on the stability of superheavy nuclei are explored and explained. The theoreticalresults are compared with new data of superheavy nuclei from GSI and from Dubna and reasonable agreement is reached.Nuclear shell effect in superheavy region is analyzed and discussed. The spherical shell effect disappears in some cases due to the appearance of deformation or superdeformation in the ground states of nuclei, where valence nucleons occupysignificantly the intruder levels of nuclei. It is shown for the first time that the significant occupation of vaJence nucleons on the intruder states plays an important role for the ground state properties of superheavy nuclei. Nuclei are stable in the deformed or superdeformed configurations. We further point out that one cannot obtain the octupole deformation of even-even nuclei in the present relativistic mean-field model with the σ，ω and ρ mesons because there is no parityviolating interaction and the conservation of parity of even-even nuclei is a basic assumption of the present relativistic mean-field model.
Hafez, M. G.; Talukder, M. R.; Hossain Ali, M.
2016-01-01
The Korteweg-de Vries Burgers (KdVB) -like equation is derived to study the characteristics of nonlinear propagation of ion acoustic solitions in a highly relativistic plasma containing relativistic ions and nonextensive distribution of electrons and positrons using the well known reductive perturbation technique. The KdVB-like equation is solved employing the Bernoulli's equation method taking unperturbed positron to electron concentration ratio, electron to positron temperature ratio, strength of nonextensivity, ion kinematic viscosity, and highly relativistic streaming factor. It is found that these parameters significantly modify the structures of the solitonic excitation. The ion acoustic shock profiles are observed due to the influence of ion kinematic viscosity. In the absence of dissipative term to the KdVB equation, compressive and rarefactive solitons are observed in case of superthermality, but only compressive solitons are found for the case of subthermality.
Non-local correlations within dynamical mean field theory
Li, Gang
2009-03-15
The contributions from the non-local fluctuations to the dynamical mean field theory (DMFT) were studied using the recently proposed dual fermion approach. Straight forward cluster extensions of DMFT need the solution of a small cluster, where all the short-range correlations are fully taken into account. All the correlations beyond the cluster scope are treated in the mean-field level. In the dual fermion method, only a single impurity problem needs to be solved. Both the short and long-range correlations could be considered on equal footing in this method. The weak-coupling nature of the dual fermion ensures the validity of the finite order diagram expansion. The one and two particle Green's functions calculated from the dual fermion approach agree well with the Quantum Monte Carlo solutions, and the computation time is considerably less than with the latter method. The access of the long-range order allows us to investigate the collective behavior of the electron system, e.g. spin wave excitations. (orig.)
Pandey, R. S.; Kaur, Rajbir
2016-10-01
In present paper, field aligned whistler mode waves are analyzed, in the presence of DC field in background plasma having relativistic distribution function in the magnetosphere of Uranus. The work has been examined for relativistic Maxwellian and loss-cone distribution function. In both the cases, we have studied the effect of various plasma parameters on the growth rate of waves by using the method of characteristics and discussed using data provided by Voyager 2. Growth rate has increased by increasing the magnitude of electric field, temperature anisotropy, energy density and number density of particles for Maxwellian and loss-cone background. However, when relativistic factor (λ =√{ 1 -v2 /c2 }) increases, growth rate decreases. The significant increase in real frequency of whistler waves can be observed. The results can be used for comparative study of planetary magnetospheres. The derivation can also be adapted to study various other instabilities in magnetosphere of Uranus.
Yuan, Yuzhang; Zhang, Jun; Zhong, Huihuang; Zhang, Dian
2016-07-01
Overmoded RBWO (Relativistic Backward Wave Oscillators) is utilized more and more often for its high power capacity. However, both sides of SWS (Slow Wave Structure) of overmoded RBWO consist multi TM0n modes; in order to achieve the design of reflector, it is essential to make clear of the mode composition of TM0n. NUDT (National University of Defence Technology) had done research of the output mode composition in overmoded O-type Cerenkov HPM (High Power Microwave) Oscillators in detail, but in the area where the electron beam exists, the influence of electron beam must be taken into account. Hot-cavity dispersion equation is figured out in this article first, and then analyzes the hot-cavity mode composition of an X-band overmoded RBWO tentatively. The results show that in collimating hole, the hot-cavity mode analysis is more accurate.
Misra, A P
2010-01-01
We consider the nonlinear propagation of electrostatic wave packets in an ultra-relativistic (UR) degenerate dense electron-ion plasma, whose dynamics is governed by the nonlocal two-dimensional nonlinear Schroedinger-like equations. The coupled set of equations are then used to study the modulational instability (MI) of a uniform wave train to an infinitesimal perturbation of multi-dimensional form. The condition for the MI is obtained, and it is shown that the nondimensional parameter, $\\beta\\propto\\lambda_C n_0^{1/3}$ (where $\\lambda_C$ is the reduced Compton wavelength and $n_0$ is the particle number density), associated with the UR pressure of degenerate electrons, shifts the stable (unstable) regions at $n_{0}\\sim10^{30}$ cm$^{-3}$ to unstable (stable) ones at higher densities, i.e. $n_{0}\\gtrsim7\\times10^{33}$. It is also found that higher the values of $n_{0}$, the lower is the growth rate of MI with cut-offs at lower wave numbers of modulation. Furthermore, the dynamical evolution of the wave packet...
Whirling Waves and the Aharonov-Bohm Effect for Relativistic Spinning Particles
Girotti, H O
1996-01-01
The formulation of Berry for the Aharonov-Bohm effect is generalized to the relativistic regime. Then, the problem of finding the self-adjoint extensions of the (2+1)-dimensional Dirac Hamiltonian, in an Aharonov-Bohm background potential, is solved in a novel way. The same treatment also solves the problem of finding the self-adjoint extensions of the Dirac Hamiltonian in a background Aharonov-Casher.
Keith, Todd A; Frisch, Michael J
2011-11-17
Scalar-relativistic, all-electron density functional theory (DFT) calculations were done for free, neutral atoms of all elements of the periodic table using the universal Gaussian basis set. Each core, closed-subshell contribution to a total atomic electron density distribution was separately fitted to a spherical electron density function: a linear combination of s-type Gaussian functions. The resulting core subshell electron densities are useful for systematically and compactly approximating total core electron densities of atoms in molecules, for any atomic core defined in terms of closed subshells. When used to augment the electron density from a wave function based on a calculation using effective core potentials (ECPs) in the Hamiltonian, the atomic core electron densities are sufficient to restore the otherwise-absent electron density maxima at the nuclear positions and eliminate spurious critical points in the neighborhood of the atom, thus enabling quantum theory of atoms in molecules (QTAIM) analyses to be done in the neighborhoods of atoms for which ECPs were used. Comparison of results from QTAIM analyses with all-electron, relativistic and nonrelativistic molecular wave functions validates the use of the atomic core electron densities for augmenting electron densities from ECP-based wave functions. For an atom in a molecule for which a small-core or medium-core ECPs is used, simply representing the core using a simplistic, tightly localized electron density function is actually sufficient to obtain a correct electron density topology and perform QTAIM analyses to obtain at least semiquantitatively meaningful results, but this is often not true when a large-core ECP is used. Comparison of QTAIM results from augmenting ECP-based molecular wave functions with the realistic atomic core electron densities presented here versus augmenting with the limiting case of tight core densities may be useful for diagnosing the reliability of large-core ECP models in
Coronado, Y.; López-Corona, O.; Mendoza, S.
2016-10-01
Knots or blobs observed in astrophysical jets are commonly interpreted as shock waves moving along them. Long-time observations of the HST-1 knot inside the jet of the galaxy M87 have produced detailed multiwavelength light curves. In this paper, we model these light curves using the semi-analytical approach developed by Mendoza et al. This model was developed to account for the light curves produced by working surfaces (blobs) moving along relativistic jets. These working surfaces are generated by periodic oscillations of the injected flow velocity and mass ejection rates at the base of the jet. Using genetic algorithms to fit the parameters of the model, we are able to explain the outbursts observed in the light curves of the HST-1 knot with an accuracy greater than a 2σ statistical confidence level.
Ceccotti, T; Sgattoni, A; Bigongiari, A; Raynaud, M; Riconda, C; Heron, A; Baffigi, F; Labate, L; Gizzi, L A; Vassura, L; Fuchs, J; Passoni, M; Kveton, M; Novotny, F; Possolt, M; Prokupek, J; Proska, J; Psikal, J; Stolcova, L; Velyhan, A; Bougeard, M; D'Oliveira, P; Tcherbakoff, O; Reau, F; Martin, P; Macchi, A
2013-01-01
The interaction of laser pulses with thin grating targets, having a periodic groove at the irradiated surface, has been experimentally investigated. Ultrahigh contrast ($\\sim 10^{12}$) pulses allowed to demonstrate an enhanced laser-target coupling for the first time in the relativistic regime of ultra-high intensity $>10^{19} \\mbox{W/cm}^{2}$. A maximum increase by a factor of 2.5 of the cut-off energy of protons produced by Target Normal Sheath Acceleration has been observed with respect to plane targets, around the incidence angle expected for resonant excitation of surface waves. A significant enhancement is also observed for small angles of incidence, out of resonance.
Fedele, Renato; De Nicola, Sergio; Shukla, P K; Jovanovic, Dusan
2011-01-01
Thermal Wave Model is used to study the strong self-consistent Plasma Wake Field interaction (transverse effects) between a strongly magnetized plasma and a relativistic electron/positron beam travelling along the external magnetic field, in the long beam limit, in terms of a nonlocal NLS equation and the virial equation. In the linear regime, vortices predicted in terms of Laguerre-Gauss beams characterized by non-zero orbital angular momentum (vortex charge). In the nonlinear regime, criteria for collapse and stable oscillations is established and the thin plasma lens mechanism is investigated, for beam size much greater than the plasma wavelength. The beam squeezing and the self-pinching equilibrium is predicted, for beam size much smaller than the plasma wavelength, taking the aberrationless solution of the nonlocal Nonlinear Schroeding equation.
Wu, Ping; Sun, Jun; Song, Zhimin; Teng, Yan
2017-01-01
Explosive emission cathodes (EECs) are widely used in high power microwave generators. This paper researches the influence of the emission threshold and the current increase rate of annular EECs on the microwave starting time of a relativistic backward wave oscillator (RBWO) when the current amplitude is not affected. The results show that a moderate delay in explosive emission, as long as it's not too long and the current increase rate keeps fast enough, won't bring about a corresponding delay in the starting time of microwave, but inversely, may suppress the mode competition and thus expedite the starting process slightly. The current increase rate, however, has more prominent influence on the starting time of the RBWO. A slower current increase rate will delay the time when the beam current reaches the starting current and lead to a longer starting time.
Unitary representations of the Poincaré group and relativistic wave equations
Ohnuki, Yoshio
1976-01-01
This book is devoted to an extensive and systematic study on unitary representations of the Poincaré group. The Poincaré group plays an important role in understanding the relativistic picture of particles in quantum mechanics. Complete knowledge of every free particle states and their behaviour can be obtained once all the unitary irreducible representations of the Poincaré group are found. It is a surprising fact that a simple framework such as the Poincaré group, when unified with quantum theory, fixes our possible picture of particles severely and without exception. In this connection, the
Relativistic wave equations with fractional derivatives and pseudo-differential operators
Závada, P
2000-01-01
The class of the free relativistic covariant equations generated by the fractional powers of the D'Alambertian operator $(\\Box ^{1/n})$ is studied. Meanwhile the equations corresponding to n=1 and 2 (Klein-Gordon and Dirac equations) are local in their nature, the multicomponent equations for arbitrary n>2 are non-local. It is shown, how the representation of generalized algebra of Pauli and Dirac matrices looks like and how these matrices are related to the algebra of SU(n) group. The corresponding representations of the Poincar\\'e group and further symmetry transformations on the obtained equations are discussed. The construction of the related Green functions is suggested.
Alberdi, A.; Gomez, J.L.; Marcaide, J.M.
1993-01-01
The structure of the compact radio sources at milliarcsecond angular resolution can be explained in terms of shock waves propagating along bent jets. These jets consist of narrow-angle cones of plasma flowing at bulk relativistic velocities, within tangled magnetic fields, emitting synchrotron radiation. We have developed a numerical code which solves the synchrotron radiation transfer equations to compute the total and polarized emission of bent shocked relativistic jets, and we have applied it to reproduce the compact structure, kenimatic evolution and time flux density evolution of the superluminal radio source 4C 39.25 and to obtain its jet physical parameters. (Author) 23 ref.
The Relativistic Transformation for an Electromagnetic Plane Wave with General Time Dependence
Smith, Glenn S.
2012-01-01
In special relativity, the transformation between inertial frames for an electromagnetic plane wave is usually derived for the time-harmonic case (the field is a sinusoid of infinite duration), even though all practical waves are of finite duration and may not even contain a dominant sinusoid. This paper presents an alternative derivation in which…
Nonequilibrium Dynamical Mean-Field Theory for Bosonic Lattice Models
2015-01-01
We develop the nonequilibrium extension of bosonic dynamical mean-field theory and a Nambu real-time strong-coupling perturbative impurity solver. In contrast to Gutzwiller mean-field theory and strong-coupling perturbative approaches, nonequilibrium bosonic dynamical mean-field theory captures not only dynamical transitions but also damping and thermalization effects at finite temperature. We apply the formalism to quenches in the Bose-Hubbard model, starting from both the normal and the Bos...
Modified Mean Field approximation for the Ising Model
Di Bartolo, Cayetano
2009-01-01
We study a modified mean-field approximation for the Ising Model in arbitrary dimension. Instead of taking a "central" spin, or a small "drop" of fluctuating spins coupled to the effective field of their nearest neighbors as in the Mean-Field or the Bethe-Peierls-Weiss methods, we take an infinite chain of fluctuating spins coupled to the mean field of the rest of the lattice. This results in a significative improvement of the Mean-Field approximation with a small extra effort.
One-Dimensional Forward–Forward Mean-Field Games
Gomes, Diogo A.
2016-11-01
While the general theory for the terminal-initial value problem for mean-field games (MFGs) has achieved a substantial progress, the corresponding forward–forward problem is still poorly understood—even in the one-dimensional setting. Here, we consider one-dimensional forward–forward MFGs, study the existence of solutions and their long-time convergence. First, we discuss the relation between these models and systems of conservation laws. In particular, we identify new conserved quantities and study some qualitative properties of these systems. Next, we introduce a class of wave-like equations that are equivalent to forward–forward MFGs, and we derive a novel formulation as a system of conservation laws. For first-order logarithmic forward–forward MFG, we establish the existence of a global solution. Then, we consider a class of explicit solutions and show the existence of shocks. Finally, we examine parabolic forward–forward MFGs and establish the long-time convergence of the solutions.
One-Dimensional Forward–Forward Mean-Field Games
Gomes, Diogo A., E-mail: diogo.gomes@kaust.edu.sa; Nurbekyan, Levon; Sedjro, Marc [King Abdullah University of Science and Technology (KAUST), CEMSE Division (Saudi Arabia)
2016-12-15
While the general theory for the terminal-initial value problem for mean-field games (MFGs) has achieved a substantial progress, the corresponding forward–forward problem is still poorly understood—even in the one-dimensional setting. Here, we consider one-dimensional forward–forward MFGs, study the existence of solutions and their long-time convergence. First, we discuss the relation between these models and systems of conservation laws. In particular, we identify new conserved quantities and study some qualitative properties of these systems. Next, we introduce a class of wave-like equations that are equivalent to forward–forward MFGs, and we derive a novel formulation as a system of conservation laws. For first-order logarithmic forward–forward MFG, we establish the existence of a global solution. Then, we consider a class of explicit solutions and show the existence of shocks. Finally, we examine parabolic forward–forward MFGs and establish the long-time convergence of the solutions.
Analytically Solvable Mean-Field Potential for Stable and Exotic Nuclei
Stoitsov, M. V.; S. S. Dimitrova(INRNE, Sofia); Pittel, S.; Van Isacker, P.(GANIL, CEA/DSM–CNRS/IN2P3, Bd Henri Becquerel, BP 55027, F-14076 Caen Cedex 5, France); Frank, A
1997-01-01
Slater determinants built from the single-particle wave functions of the analytically solvable Ginocchio potential are used to approximate the self-consistent Hartree-Fock solutions for the ground states of nuclei. The results indicate that the Ginocchio potential provides a good parametrization of the nuclear mean field for a wide range of nuclei, including those at the limit of particle stability.
刘铁路; 王云良; 路彦珍
2015-01-01
The nonlinear propagation of quantum ion acoustic wave (QIAW) is investigated in a four-component plasma com-posed of warm classical positive ions and negative ions, as well as inertialess relativistically degenerate electrons and positrons. A nonlinear Schr ¨odinger equation is derived by using the reductive perturbation method, which governs the dynamics of QIAW packets. The modulation instability analysis of QIAWs is considered based on the typical parameters of the white dwarf. The results exhibit that both in weakly relativistic limit and in ultrarelativistic limit, the modulational instability regions are sensitively dependent on the ratios of temperature and number density of negative ions to those of positive ions respectively, and on relativistically degenerate effect as well.
The Fock-Kemmer approach to precursor shock waves in relativistic field theory
Abdullah, Rawand H
2016-01-01
We use distribution theory (generalized functions) to extend and justify the Fock-Kemmer approach to the propagation of precursor shock wave discontinuities in classical and quantum field theory. We apply lightcone causality arguments to propose that shock wave singularities in non-linear classical field theories and in Maxwell's equations for responsive media require a form of classical renormalization analogous to Wilson operator product expansions in quantum field theories.
Spinless relativistic particle in energy-dependent potential and normalization of the wave function
Benchikha, Amar; Chetouani, Lyazid
2014-06-01
The problem of normalization related to a Klein-Gordon particle subjected to vector plus scalar energy-dependent potentials is clarified in the context of the path integral approach. In addition the correction relating to the normalizing constant of wave functions is exactly determined. As examples, the energy dependent linear and Coulomb potentials are considered. The wave functions obtained via spectral decomposition, were found exactly normalized.
Refined Study of ECR Wave Propagation and Absorption in the Weakly Relativistic Plasma
SHIBingren; LONGYongxin
2001-01-01
The ECR wave heating is now a routine method for plasma heating and profile control in fusion devices and also in plasma applications. Theoretical study of ECR wave propagation and absorption began very early in 1950's. Basic theoretical work had accomplished in 1970～1980. For toroidal devices like the tokamak, the fundamental O-mode and X-mode with nearly perpendicular propagation were used very often. For pure O-mode and X-mode with kx=O,
Relativistic magnetohydrodynamics
Hernandez, Juan; Kovtun, Pavel
2017-05-01
We present the equations of relativistic hydrodynamics coupled to dynamical electromagnetic fields, including the effects of polarization, electric fields, and the derivative expansion. We enumerate the transport coefficients at leading order in derivatives, including electrical conductivities, viscosities, and thermodynamic coefficients. We find the constraints on transport coefficients due to the positivity of entropy production, and derive the corresponding Kubo formulas. For the neutral state in a magnetic field, small fluctuations include Alfvén waves, magnetosonic waves, and the dissipative modes. For the state with a non-zero dynamical charge density in a magnetic field, plasma oscillations gap out all propagating modes, except for Alfvén-like waves with a quadratic dispersion relation. We relate the transport coefficients in the "conventional" magnetohydrodynamics (formulated using Maxwell's equations in matter) to those in the "dual" version of magnetohydrodynamics (formulated using the conserved magnetic flux).
Verbalization of Mean Field Utterances in German Instructions
Tayupova O. I.
2013-01-01
Full Text Available The article investigates ways of actualization of mean field utterances used in modern German instructions considering the type of the text. The author determines and analyzes similarities and differences in linguistic means used in mean field utterances in the context of such text subtypes as instructions to household appliances, cosmetic products directions and prescribing information for pharmaceutical drugs use.
Alam, M. S.; Hafez, M. G.; Talukder, M. R.; Hossain Ali, M.
2017-07-01
A comparative study of the interactions between nonlinear ion acoustic solitary waves (IASWs) propagating toward each other, and the electrostatic nonlinear propagation of IASWs, both for the weakly and relativistic regimes consisting of relativistic warm ions, nonthermal electrons, and positrons, is carried out. Two-sided Korteweg-de Vries (KdV) equations are derived using the extended Poincaré-Lighthill-Kuo (PLK) method to reveal the physical issues concerned. The effects of positron concentration, ion-electron temperature ratio, electron-positron temperature ratio, relativistic streaming factor, the population of electron, and positron nonthermality on the electrostatic resonances and their phase shifts are investigated for both regimes. It is found that the plasma parameters significantly modify the phase shifts, electrostatic resonances, hump-shaped electrostatic potential profiles, and the electric fields on the nonlinear propagation characteristics of IASWs. The results obtained may be useful for clarifications of interaction between IASWs in astrophysical and laboratory plasmas, especially in pulsar magnetosphere, laser produced, inertial confinement plasmas, and pulsar relativistic winds with supernova ejecta that produce nonthermal electrons, positrons, and relativistic ions.
Electron acceleration to relativistic energies at a strong quasi-parallel shock wave
Masters, A; Fujimoto, M; Schwartz, S J; Sergis, N; Thomsen, M F; Retinò, A; Hasegawa, H; Lewis, G R; Coates, A J; Canu, P; Dougherty, M K
2013-01-01
Electrons can be accelerated to ultrarelativistic energies at strong (high-Mach number) collisionless shock waves that form when stellar debris rapidly expands after a supernova. Collisionless shock waves also form in the flow of particles from the Sun (the solar wind), and extensive spacecraft observations have established that electron acceleration at these shocks is effectively absent whenever the upstream magnetic field is roughly parallel to the shock surface normal (quasi-parallel conditions). However, it is unclear whether this magnetic dependence of electron acceleration also applies to the far stronger shocks around young supernova remnants, where local magnetic conditions are poorly understood. Here we present Cassini spacecraft observations of an unusually strong solar system shock wave (Saturn's bow shock) where significant local electron acceleration has been confirmed under quasi-parallel magnetic conditions for the first time, contradicting the established magnetic dependence of electron accele...
Khazanov, G. V.; Gallagher, D. L.; Gamayunov, K.
2007-01-01
It is well known that the effects of EMIC waves on RC ion and RB electron dynamics strongly depend on such particle/wave characteristics as the phase-space distribution function, frequency, wave-normal angle, wave energy, and the form of wave spectral energy density. Therefore, realistic characteristics of EMIC waves should be properly determined by modeling the RC-EMIC waves evolution self-consistently. Such a selfconsistent model progressively has been developing by Khaznnov et al. [2002-2006]. It solves a system of two coupled kinetic equations: one equation describes the RC ion dynamics and another equation describes the energy density evolution of EMIC waves. Using this model, we present the effectiveness of relativistic electron scattering and compare our results with previous work in this area of research.
Jones, Bernard J. T.; Markovic, Dragoljub
1997-06-01
Preface; Prologue: Conference overview Bernard Carr; Part I. The Universe At Large and Very Large Redshifts: 2. The size and age of the Universe Gustav A. Tammann; 3. Active galaxies at large redshifts Malcolm S. Longair; 4. Observational cosmology with the cosmic microwave background George F. Smoot; 5. Future prospects in measuring the CMB power spectrum Philip M. Lubin; 6. Inflationary cosmology Michael S. Turner; 7. The signature of the Universe Bernard J. T. Jones; 8. Theory of large-scale structure Sergei F. Shandarin; 9. The origin of matter in the universe Lev A. Kofman; 10. New guises for cold-dark matter suspects Edward W. Kolb; Part II. Physics and Astrophysics Of Relativistic Compact Objects: 11. On the unification of gravitational and inertial forces Donald Lynden-Bell; 12. Internal structure of astrophysical black holes Werner Israel; 13. Black hole entropy: external facade and internal reality Valery Frolov; 14. Accretion disks around black holes Marek A. Abramowicz; 15. Black hole X-ray transients J. Craig Wheeler; 16. X-rays and gamma rays from active galactic nuclei Roland Svensson; 17. Gamma-ray bursts: a challenge to relativistic astrophysics Martin Rees; 18. Probing black holes and other exotic objects with gravitational waves Kip Thorne; Epilogue: the past and future of relativistic astrophysics Igor D. Novikov; I. D. Novikov's scientific papers and books.
On Relativistic Quantum Information Properties of Entangled Wave Vectors of Massive Fermions
Cafaro, C; Mancini, S
2011-01-01
We study special relativistic effects on the entanglement between either spins or momenta of composite quantum systems of two spin-1/2 massive particles, either indistinguishable or distinguishable, in inertial reference frames in relative motion. For the case of indistinguishable particles, we consider a balanced scenario where the momenta of the pair are well-defined but not maximally entangled in the rest frame while the spins of the pair are described by a one-parameter ($\\eta$) family of entangled bipartite states. For the case of distinguishable particles, we consider an unbalanced scenario where the momenta of the pair are well-defined and maximally entangled in the rest frame while the spins of the pair are described by a one-parameter ($\\xi$) family of non-maximally entangled bipartite states. In both cases, we show that neither the spin-spin ($ss$) nor the momentum-momentum ($mm$) entanglements quantified by means of Wootters' concurrence are Lorentz invariant quantities: the total amount of entangl...
On Social Optima of Non-Cooperative Mean Field Games
Li, Sen; Zhang, Wei; Zhao, Lin; Lian, Jianming; Kalsi, Karanjit
2016-12-12
This paper studies the social optima in noncooperative mean-field games for a large population of agents with heterogeneous stochastic dynamic systems. Each agent seeks to maximize an individual utility functional, and utility functionals of different agents are coupled through a mean field term that depends on the mean of the population states/controls. The paper has the following contributions. First, we derive a set of control strategies for the agents that possess *-Nash equilibrium property, and converge to the mean-field Nash equilibrium as the population size goes to infinity. Second, we study the social optimal in the mean field game. We derive the conditions, termed the socially optimal conditions, under which the *-Nash equilibrium of the mean field game maximizes the social welfare. Third, a primal-dual algorithm is proposed to compute the *-Nash equilibrium of the mean field game. Since the *-Nash equilibrium of the mean field game is socially optimal, we can compute the equilibrium by solving the social welfare maximization problem, which can be addressed by a decentralized primal-dual algorithm. Numerical simulations are presented to demonstrate the effectiveness of the proposed approach.
Quantum correlations in nuclear mean field theory through source terms
Lee, S J
1996-01-01
Starting from full quantum field theory, various mean field approaches are derived systematically. With a full consideration of external source dependence, the stationary phase approximation of an action gives a nuclear mean field theory which includes quantum correlation effects (such as particle-hole or ladder diagram) in a simpler way than the Brueckner-Hartree-Fock approach. Implementing further approximation, the result can be reduced to Hartree-Fock or Hartree approximation. The role of the source dependence in a mean field theory is examined.
Mean Field Games for Stochastic Growth with Relative Utility
Huang, Minyi, E-mail: mhuang@math.carleton.ca [Carleton University, School of Mathematics and Statistics (Canada); Nguyen, Son Luu, E-mail: sonluu.nguyen@upr.edu [University of Puerto Rico, Department of Mathematics (United States)
2016-12-15
This paper considers continuous time stochastic growth-consumption optimization in a mean field game setting. The individual capital stock evolution is determined by a Cobb–Douglas production function, consumption and stochastic depreciation. The individual utility functional combines an own utility and a relative utility with respect to the population. The use of the relative utility reflects human psychology, leading to a natural pattern of mean field interaction. The fixed point equation of the mean field game is derived with the aid of some ordinary differential equations. Due to the relative utility interaction, our performance analysis depends on some ratio based approximation error estimate.
On Relativistic Quantum Information Properties of Entangled Wave Vectors of Massive Fermions
Cafaro, Carlo; Capozziello, Salvatore; Mancini, Stefano
2012-08-01
We study special relativistic effects on the entanglement between either spins or momenta of composite quantum systems of two spin-1/2 massive particles, either indistinguishable or distinguishable, in inertial reference frames in relative motion. For the case of indistinguishable particles, we consider a balanced scenario where the momenta of the pair are well-defined but not maximally entangled in the rest frame while the spins of the pair are described by a one-parameter ( η) family of entangled bipartite states. For the case of distinguishable particles, we consider an unbalanced scenario where the momenta of the pair are well-defined and maximally entangled in the rest frame while the spins of the pair are described by a one-parameter ( ξ) family of non-maximally entangled bipartite states. In both cases, we show that neither the spin-spin ( ss) nor the momentum-momentum ( mm) entanglements quantified by means of Wootters' concurrence are Lorentz invariant quantities: the total amount of entanglement regarded as the sum of these entanglements is not the same in different inertial moving frames. In particular, for any value of the entangling parameters, both ss and mm-entanglements are attenuated by Lorentz transformations and their parametric rates of change with respect to the entanglements observed in a rest frame have the same monotonic behavior. However, for indistinguishable (distinguishable) particles, the change in entanglement for the momenta is (is not) the same as the change in entanglement for spins. As a consequence, in both cases, no entanglement compensation between spin and momentum degrees of freedom occurs.
Yang, Dewen; Deng, Yuqun; Teng, Yan; Shi, Yanchao; Wu, Ping; Chen, Changhua
2017-05-01
Phase locking is the key point of coherent power combination, which is very important for the development of high power microwave sources. In this paper, theoretical analysis and particle-in-cell simulations investigate the influence of the diode voltage rise time on phase locking by the priming effect in a weakly resonant relativistic backward wave oscillator (RBWO). When the diode voltage rise time becomes long and the final output frequency remains unchanged, the initial operation frequency may fluctuate around a value which is not equal to the final output frequency. Moreover, this state may last for several nanoseconds and then jumps to the final output frequency, which is very important for phase locking. Besides, it is suggested that, due to the weak resonance of the RF cavity without the electron beam, the microwave signal with frequency which is much lower than the final output frequency is usually excited at the beginning of the starting process. Finally, it is found that, when the injected frequency approaches the frequency of the initial microwave signal, the phase locking by the priming effect in the RBWO with long voltage rise time is noticeably improved, and the starting process becomes more rapid as well. The simulation results agree well with theoretical analysis.
Mean-field instabilities and cluster formation in nuclear reactions
Colonna, M; Baran, V
2016-01-01
We review recent results on intermediate mass cluster production in heavy ion collisions at Fermi energy and in spallation reactions. Our studies are based on modern transport theories, employing effective interactions for the nuclear mean-field and incorporating two-body correlations and fluctuations. Namely we will consider the Stochastic Mean Field (SMF) approach and the recently developed Boltzmann-Langevin One Body (BLOB) model. We focus on cluster production emerging from the possible occurrence of low-density mean-field instabilities in heavy ion reactions. Within such a framework, the respective role of one and two-body effects, in the two models considered, will be carefully analysed. We will discuss, in particular, fragment production in central and semi-peripheral heavy ion collisions, which is the object of many recent experimental investigations. Moreover, in the context of spallation reactions, we will show how thermal expansion may trigger the development of mean-field instabilities, leading to...
Mean Field Games Models-A Brief Survey
Gomes, Diogo A.
2013-11-20
The mean-field framework was developed to study systems with an infinite number of rational agents in competition, which arise naturally in many applications. The systematic study of these problems was started, in the mathematical community by Lasry and Lions, and independently around the same time in the engineering community by P. Caines, Minyi Huang, and Roland Malhamé. Since these seminal contributions, the research in mean-field games has grown exponentially, and in this paper we present a brief survey of mean-field models as well as recent results and techniques. In the first part of this paper, we study reduced mean-field games, that is, mean-field games, which are written as a system of a Hamilton-Jacobi equation and a transport or Fokker-Planck equation. We start by the derivation of the models and by describing some of the existence results available in the literature. Then we discuss the uniqueness of a solution and propose a definition of relaxed solution for mean-field games that allows to establish uniqueness under minimal regularity hypothesis. A special class of mean-field games that we discuss in some detail is equivalent to the Euler-Lagrange equation of suitable functionals. We present in detail various additional examples, including extensions to population dynamics models. This section ends with a brief overview of the random variables point of view as well as some applications to extended mean-field games models. These extended models arise in problems where the costs incurred by the agents depend not only on the distribution of the other agents, but also on their actions. The second part of the paper concerns mean-field games in master form. These mean-field games can be modeled as a partial differential equation in an infinite dimensional space. We discuss both deterministic models as well as problems where the agents are correlated. We end the paper with a mean-field model for price impact. © 2013 Springer Science+Business Media New York.
Mode conversion of large-amplitude electromagnetic waves in relativistic critical density plasmas
Pesch, T.C.; Kull, H.J. [Aachen Univ., Institute of Theoretical Physics A, RWTH (Germany)
2009-01-15
The propagation of linearly polarized large-amplitude electromagnetic waves in critical density plasmas is studied in the framework of the Akiezer-Polovin model. A new mechanism of mode conversion is presented. The well-known periodic solutions are generalized to quasiperiodic solutions taking into account additional electrostatic oscillations. Nearly periodic circle-like solutions are found to be stabilized by intrinsic mode coupling whereas for nearly periodic eight-like solutions an effective mode conversion mechanism is discovered. Finally, the modulation timescales are considered. (authors)
Nechaev, I. A.; Krasovskii, E. E.
2016-11-01
We present a method to microscopically derive a small-size k .p Hamiltonian in a Hilbert space spanned by physically chosen ab initio spinor wave functions. Without imposing any complementary symmetry constraints, our formalism equally treats three- and two-dimensional systems and simultaneously yields the Hamiltonian parameters and the true Z2 topological invariant. We consider bulk crystals and thin films of Bi2Se3 , Bi2Te3 , and Sb2Te3 . It turns out that the effective continuous k .p models with open boundary conditions often incorrectly predict the topological character of thin films.
Mondragon-Suarez, J. H.; Sandoval-Villalbazo, A.; Garcia-Perciante, A. L.
2013-09-01
The problem of structure formation in relativistic dissipative fluids was analyzed in a previous work within Eckart's framework, in which the heat flux is coupled to the hydrodynamic acceleration, additional to the usual temperature gradient term. It was shown that in such case, the pathological behavior of fluctuations leads to the disappearance of the gravitational instability responsible for structure formation (Mondragon-Suarez and Sandoval-Villalbazo in Gen Relativ Gravit 44:139-145, 2012). In the present work the problem is revisited using a constitutive equation derived from relativistic kinetic theory. This new relation, in which the heat flux is not coupled to the hydrodynamic acceleration, leads to a consistent first order in the gradients formalism. In this case the gravitational instability remains, and only relativistic corrections to the Jeans wave number are obtained. In the calculation here shown the non-relativistic limit is recovered, opposite to what happens in Eckart's case (Hiscock and Lindblom in Phys Rev D 31:725-733, 1985).
Nuclear matter properties in the relativistic mean field model with $\\sigma-\\omega$ coupling
Chung, K C; Santiago, A J; Zhang, J W
2001-01-01
The possibility of extending the linear sigma-omega model by introducing a sigma-omega coupling phenomenologically is explored. It is shown that, in contrast to the usual Walecka model, not only the effective nucleon mass M* but also the effective sigma meson mass m*_sigma and the effective omega meson mass m*_omega are nucleon density dependent. When the model parameters are fitted to the nuclear saturation point (the nuclear radius constant r_0=1.14fm and volume energy a_1=16.0MeV) as well as to the effective nucleon mass M*=0.85M, the model yields m*_sigma=1.09m_sigma and m*_omega=0.90m_omega at the saturation point, and the nuclear incompressibility K_0=501MeV. The lowest value of K_0 given by this model by adjusting the model parameters is around 227MeV.
Deformed neutron stars due to strong magnetic field in terms of relativistic mean field theories
Yanase, Kota; Yoshinaga, Naotaka
2014-09-01
Some observations suggest that magnetic field intensity of neutron stars that have particularly strong magnetic field, magnetars, reaches values up to 1014-15G. It is expected that there exists more strong magnetic field of several orders of magnitude in the interior of such stars. Neutron star matter is so affected by magnetic fields caused by intrinsic magnetic moments and electric charges of baryons that masses of neutron stars calculated by using Tolman-Oppenheimer-Volkoff equation is therefore modified. We calculate equation of state (EOS) in density-dependent magnetic field by using sigma-omega-rho model that can reproduce properties of stable nuclear matter in laboratory Furthermore we calculate modified masses of deformed neutron stars.
Scattering of strong electromagnetic wave by relativistic electrons: Thomson and Compton regimes
Potylitsyn, A. P.; Kolchuzhkin, A. M.
2017-04-01
The processes of the nonlinear Compton and the nonlinear Thomson scattering in a field of intense plane electromagnetic wave in terms of photon yield have been considered. The quantum consideration of the Compton scattering process allows us to calculate the probability of a few successive collisions k of an electron with laser photons accompanied by the absorption of n photons (nonlinear regime) when the number of collisions and the number of absorbed photons are of random quantities. The photon spectrum of the nonlinear Thomson scattering process was obtained from the classical formula for intensity using the Planck's law. The conditions for which the difference between the classical and the quantum regimes is manifested was obtained. Such a condition is determined by a discrete quantum radiation mechanism, namely, by the mean number of photons k bar emitted by an electron passing through the laser pulse.
Uncertainty quantification for mean field games in social interactions
Dia, Ben Mansour
2016-01-09
We present an overview of mean field games formulation. A comparative analysis of the optimality for a stochastic McKean-Vlasov process with time-dependent probability is presented. Then we examine mean-field games for social interactions and we show that optimizing the long-term well-being through effort and social feeling state distribution (mean-field) will help to stabilize couple (marriage). However , if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple using mean field sentimental games. We show that, in mean-field equilibrium, the optimal effort is always higher than the one-shot optimal effort. Finally we introduce the Wiener chaos expansion for the construction of solution of stochastic differential equations of Mckean-Vlasov type. The method is based on the Cameron-Martin version of the Wiener Chaos expansion and allow to quantify the uncertainty in the optimality system.
Mean-Field Calculations for the Three-Dimensional Holstein Model
罗强; 刘川
2002-01-01
The electron-phonon Holstein model is studied in three spatial dimensions. It is argued that this model can be used to account for major features of the high-To BaPb1-xBixO3 and BaxK1-xBiO3 systems. Mean-field calculations are performed via a path integral representation of the model. Charge-density-wave order parameters and transition temperatures are obtained.
Relativistic quantum revivals.
Strange, P
2010-03-26
Quantum revivals are now a well-known phenomena within nonrelativistic quantum theory. In this Letter we display the effects of relativity on revivals and quantum carpets. It is generally believed that revivals do not occur within a relativistic regime. Here we show that while this is generally true, it is possible, in principle, to set up wave packets with specific mathematical properties that do exhibit exact revivals within a fully relativistic theory.
Regularity theory for mean-field game systems
Gomes, Diogo A; Voskanyan, Vardan
2016-01-01
Beginning with a concise introduction to the theory of mean-field games (MFGs), this book presents the key elements of the regularity theory for MFGs. It then introduces a series of techniques for well-posedness in the context of mean-field problems, including stationary and time-dependent MFGs, subquadratic and superquadratic MFG formulations, and distinct classes of mean-field couplings. It also explores stationary and time-dependent MFGs through a series of a-priori estimates for solutions of the Hamilton-Jacobi and Fokker-Planck equation. It shows sophisticated a-priori systems derived using a range of analytical techniques, and builds on previous results to explain classical solutions. The final chapter discusses the potential applications, models and natural extensions of MFGs. As MFGs connect common problems in pure mathematics, engineering, economics and data management, this book is a valuable resource for researchers and graduate students in these fields.
Accretion Disks and Dynamos: Toward a Unified Mean Field Theory
Blackman, Eric G
2012-01-01
Conversion of gravitational energy into radiation near stars and compact objects in accretion disks the origin of large scale magnetic fields in astrophysical rotators have long been distinct topics of active research in astrophysics. In semi-analytic work on both problems it has been useful to presume large scale symmetries, which necessarily results in mean field theories; magnetohydrodynamic turbulence makes the underlying systems locally asymmetric and highly nonlinear. Synergy between theory and simulations should aim for the development of practical, semi-analytic mean field models that capture the essential physics and can be used for observational modeling. Mean field dynamo (MFD) theory and alpha-viscosity accretion disc theory have exemplified such distinct pursuits. Both are presently incomplete, but 21st century MFD theory has nonlinear predictive power compared to 20th century MFD. in contrast, alpha-viscosity accretion theory is still in a 20th century state. In fact, insights from MFD theory ar...
Nonequilibrium Dynamical Mean-Field Theory for Bosonic Lattice Models
Strand, Hugo U. R.; Eckstein, Martin; Werner, Philipp
2015-01-01
We develop the nonequilibrium extension of bosonic dynamical mean-field theory and a Nambu real-time strong-coupling perturbative impurity solver. In contrast to Gutzwiller mean-field theory and strong-coupling perturbative approaches, nonequilibrium bosonic dynamical mean-field theory captures not only dynamical transitions but also damping and thermalization effects at finite temperature. We apply the formalism to quenches in the Bose-Hubbard model, starting from both the normal and the Bose-condensed phases. Depending on the parameter regime, one observes qualitatively different dynamical properties, such as rapid thermalization, trapping in metastable superfluid or normal states, as well as long-lived or strongly damped amplitude oscillations. We summarize our results in nonequilibrium "phase diagrams" that map out the different dynamical regimes.
Mean field limit for bosons and propagation of Wigner measures
Ammari, Z
2008-01-01
We consider the N-body Schr\\"{o}dinger dynamics of bosons in the mean field limit with a bounded pair-interaction potential. According to the previous work \\cite{AmNi}, the mean field limit is translated into a semiclassical problem with a small parameter $\\epsilon\\to 0$, after introducing an $\\epsilon$-dependent bosonic quantization. The limit is expressed as a push-forward by a nonlinear flow (e.g. Hartree) of the associated Wigner measures. These object and their basic properties were introduced in \\cite{AmNi} in the infinite dimensional setting. The additional result presented here states that the transport by the nonlinear flow holds for rather general class of quantum states in their mean field limit.
Regularity Theory for Mean-Field Game Systems
Gomes, Diogo A.
2016-09-14
Beginning with a concise introduction to the theory of mean-field games (MFGs), this book presents the key elements of the regularity theory for MFGs. It then introduces a series of techniques for well-posedness in the context of mean-field problems, including stationary and time-dependent MFGs, subquadratic and superquadratic MFG formulations, and distinct classes of mean-field couplings. It also explores stationary and time-dependent MFGs through a series of a-priori estimates for solutions of the Hamilton-Jacobi and Fokker-Planck equation. It shows sophisticated a-priori systems derived using a range of analytical techniques, and builds on previous results to explain classical solutions. The final chapter discusses the potential applications, models and natural extensions of MFGs. As MFGs connect common problems in pure mathematics, engineering, economics and data management, this book is a valuable resource for researchers and graduate students in these fields.
Mueller, Bernhard; Marek, Andreas
2012-01-01
We present a detailed theoretical analysis of the gravitational-wave (GW) signal of the post-bounce evolution of core-collapse supernovae (SNe), employing for the first time relativistic, two-dimensional (2D) explosion models with multi-group, three-flavor neutrino transport based on the ray-by-ray-plus approximation. The waveforms reflect the accelerated mass motions associated with the characteristic evolutionary stages that were also identified in previous works: A quasi-periodic modulation by prompt postshock convection is followed by a phase of relative quiescence before growing amplitudes signal violent hydrodynamical activity due to convection and the standing accretion shock instability during the accretion period of the stalled shock. Finally, a high-frequency, low-amplitude variation from proto-neutron star (PNS) convection below the neutrinosphere appears superimposed on the low-frequency trend associated with the aspherical expansion of the SN shock after the onset of the explosion. Relativistic e...
A mean field theory of coded CDMA systems
Yano, Toru [Graduate School of Science and Technology, Keio University, Hiyoshi, Kohoku-ku, Yokohama-shi, Kanagawa 223-8522 (Japan); Tanaka, Toshiyuki [Graduate School of Informatics, Kyoto University, Yoshida Hon-machi, Sakyo-ku, Kyoto-shi, Kyoto 606-8501 (Japan); Saad, David [Neural Computing Research Group, Aston University, Birmingham B4 7ET (United Kingdom)], E-mail: yano@thx.appi.keio.ac.jp
2008-08-15
We present a mean field theory of code-division multiple-access (CDMA) systems with error-control coding. On the basis of the relation between the free energy and mutual information, we obtain an analytical expression of the maximum spectral efficiency of the coded CDMA system, from which a mean-field description of the coded CDMA system is provided in terms of a bank of scalar Gaussian channels whose variances in general vary at different code symbol positions. Regular low-density parity-check (LDPC)-coded CDMA systems are also discussed as an example of the coded CDMA systems.
Large amplitude motion with a stochastic mean-field approach
Yilmaz Bulent
2012-12-01
Full Text Available In the stochastic mean-field approach, an ensemble of initial conditions is considered to incorporate correlations beyond the mean-field. Then each starting point is propagated separately using the Time-Dependent Hartree-Fock equation of motion. This approach provides a rather simple tool to better describe fluctuations compared to the standard TDHF. Several illustrations are presented showing that this theory can be rather effective to treat the dynamics close to a quantum phase transition. Applications to fusion and transfer reactions demonstrate the great improvement in the description of mass dispersion.
An Adaptive Filtering Algorithm using Mean Field Annealing Techniques
Persson, Per; Nordebo, Sven; Claesson, Ingvar
2002-01-01
We present a new approach to discrete adaptive filtering based on the mean field annealing algorithm. The main idea is to find the discrete filter vector that minimizes the matrix form of the Wiener-Hopf equations in a least-squares sense by a generalized mean field annealing algorithm. It is indicated by simulations that this approach, with complexity O(M^2) where M is the filter length, finds a solution comparable to the one obtained by the recursive least squares (RLS) algorithm but withou...
Socio-economic applications of finite state mean field games
Gomes, Diogo A.
2014-10-06
In this paper, we present different applications of finite state mean field games to socio-economic sciences. Examples include paradigm shifts in the scientific community or consumer choice behaviour in the free market. The corresponding finite state mean field game models are hyperbolic systems of partial differential equations, for which we present and validate different numerical methods. We illustrate the behaviour of solutions with various numerical experiments,which show interesting phenomena such as shock formation. Hence, we conclude with an investigation of the shock structure in the case of two-state problems.
Suppression of oscillations in mean-field diffusion
Neeraj Kumar Kamal; Pooja Rani Sharma; Manish Dev Shrimali
2015-02-01
We study the role of mean-field diffusive coupling on suppression of oscillations for systems of limit cycle oscillators. We show that this coupling scheme not only induces amplitude death (AD) but also oscillation death (OD) in coupled identical systems. The suppression of oscillations in the parameter space crucially depends on the value of mean-field diffusion parameter. It is also found that the transition from oscillatory solutions to OD in conjugate coupling case is different from the case when the coupling is through similar variable. We rationalize our study using linear stability analysis.
Mean-field versus microconvection effects in nanofluid thermal conduction.
Eapen, Jacob; Williams, Wesley C; Buongiorno, Jacopo; Hu, Lin-Wen; Yip, Sidney; Rusconi, Roberto; Piazza, Roberto
2007-08-31
Transient hot-wire data on thermal conductivity of suspensions of silica and perfluorinated particles show agreement with the mean-field theory of Maxwell but not with the recently postulated microconvection mechanism. The influence of interfacial thermal resistance, convective effects at microscales, and the possibility of thermal conductivity enhancements beyond the Maxwell limit are discussed.
Dynamical mean-field theory from a quantum chemical perspective.
Zgid, Dominika; Chan, Garnet Kin-Lic
2011-03-07
We investigate the dynamical mean-field theory (DMFT) from a quantum chemical perspective. Dynamical mean-field theory offers a formalism to extend quantum chemical methods for finite systems to infinite periodic problems within a local correlation approximation. In addition, quantum chemical techniques can be used to construct new ab initio Hamiltonians and impurity solvers for DMFT. Here, we explore some ways in which these things may be achieved. First, we present an informal overview of dynamical mean-field theory to connect to quantum chemical language. Next, we describe an implementation of dynamical mean-field theory where we start from an ab initio Hartree-Fock Hamiltonian that avoids double counting issues present in many applications of DMFT. We then explore the use of the configuration interaction hierarchy in DMFT as an approximate solver for the impurity problem. We also investigate some numerical issues of convergence within DMFT. Our studies are carried out in the context of the cubic hydrogen model, a simple but challenging test for correlation methods. Finally, we finish with some conclusions for future directions.
Robust mean field games for coupled Markov jump linear systems
Moon, Jun; Başar, Tamer
2016-07-01
We consider robust stochastic large population games for coupled Markov jump linear systems (MJLSs). The N agents' individual MJLSs are governed by different infinitesimal generators, and are affected not only by the control input but also by an individual disturbance (or adversarial) input. The mean field term, representing the average behaviour of N agents, is included in the individual worst-case cost function to capture coupling effects among agents. To circumvent the computational complexity and analyse the worst-case effect of the disturbance, we use robust mean field game theory to design low-complexity robust decentralised controllers and to characterise the associated worst-case disturbance. We show that with the individual robust decentralised controller and the corresponding worst-case disturbance, which constitute a saddle-point solution to a generic stochastic differential game for MJLSs, the actual mean field behaviour can be approximated by a deterministic function which is a fixed-point solution to the constructed mean field system. We further show that the closed-loop system is uniformly stable independent of N, and an approximate optimality can be obtained in the sense of ε-Nash equilibrium, where ε can be taken to be arbitrarily close to zero as N becomes sufficiently large. A numerical example is included to illustrate the results.
Mean Field Approach to the Giant Wormhole Problem
Gamba, A.; Kolokolov, I.; Martellini, M.
We introduce a gaussian probability density for the space-time distribution of worm-holes, thus taking effectively into account wormhole interaction. Using a mean-field approximation for the free energy, we show that giant wormholes are probabilistically suppressed in a homogenous isotropic “large” universe.
Critical fluctuations for quantum mean-field models
Fannes, M.; Kossakowski, A.; Verbeure, A. (Univ. Louvain (Belgium))
1991-11-01
A Ginzburg-Landau-type approximation is proposed for the local Gibbs states for quantum mean-field models that leads to the exact thermodynamics. Using this approach, the spin fluctuations are computed for some spin-1/2 models. At the critical temperature, the distribution function showing abnormal fluctuations is found explicitly.
Two numerical methods for mean-field games
Gomes, Diogo A.
2016-01-09
Here, we consider numerical methods for stationary mean-field games (MFG) and investigate two classes of algorithms. The first one is a gradient flow method based on the variational characterization of certain MFG. The second one uses monotonicity properties of MFG. We illustrate our methods with various examples, including one-dimensional periodic MFG, congestion problems, and higher-dimensional models.
Mean-field dynamo action in renovating shearing flows.
Kolekar, Sanved; Subramanian, Kandaswamy; Sridhar, S
2012-08-01
We study mean-field dynamo action in renovating flows with finite and nonzero correlation time (τ) in the presence of shear. Previous results obtained when shear was absent are generalized to the case with shear. The question of whether the mean magnetic field can grow in the presence of shear and nonhelical turbulence, as seen in numerical simulations, is examined. We show in a general manner that, if the motions are strictly nonhelical, then such mean-field dynamo action is not possible. This result is not limited to low (fluid or magnetic) Reynolds numbers nor does it use any closure approximation; it only assumes that the flow renovates itself after each time interval τ. Specifying to a particular form of the renovating flow with helicity, we recover the standard dispersion relation of the α(2)Ω dynamo, in the small τ or large wavelength limit. Thus mean fields grow even in the presence of rapidly growing fluctuations, surprisingly, in a manner predicted by the standard quasilinear closure, even though such a closure is not strictly justified. Our work also suggests the possibility of obtaining mean-field dynamo growth in the presence of helicity fluctuations, although having a coherent helicity will be more efficient.
Condition monitoring with Mean field independent components analysis
Pontoppidan, Niels Henrik; Sigurdsson, Sigurdur; Larsen, Jan
2005-01-01
We discuss condition monitoring based on mean field independent components analysis of acoustic emission energy signals. Within this framework it is possible to formulate a generative model that explains the sources, their mixing and also the noise statistics of the observed signals. By using...
Mean-Field Versus Microconvection Effects in Nanofluid Thermal Conduction
Eapen, Jacob; Williams, Wesley C.; Buongiorno, Jacopo; Hu, Lin-Wen; Yip, Sidney; Rusconi, Roberto; Piazza, Roberto
2007-08-01
Transient hot-wire data on thermal conductivity of suspensions of silica and perfluorinated particles show agreement with the mean-field theory of Maxwell but not with the recently postulated microconvection mechanism. The influence of interfacial thermal resistance, convective effects at microscales, and the possibility of thermal conductivity enhancements beyond the Maxwell limit are discussed.
Model-checking mean-field models: algorithms & applications
Kolesnichenko, Anna Victorovna
2014-01-01
Large systems of interacting objects are highly prevalent in today's world. In this thesis we primarily address such large systems in computer science. We model such large systems using mean-field approximation, which allows to compute the limiting behaviour of an infinite population of identical o
Merging Belief Propagation and the Mean Field Approximation
Riegler, Erwin; Kirkelund, Gunvor Elisabeth; Manchón, Carles Navarro
2010-01-01
We present a joint message passing approach that combines belief propagation and the mean field approximation. Our analysis is based on the region-based free energy approximation method proposed by Yedidia et al., which allows to use the same objective function (Kullback-Leibler divergence...
Going Beyond a Mean-field Model for the Learning Cortex: Second-Order Statistics
Steyn-Ross, Moira L.; Steyn-Ross, D. A.; Sleigh, J. W.
2008-01-01
Mean-field models of the cortex have been used successfully to interpret the origin of features on the electroencephalogram under situations such as sleep, anesthesia, and seizures. In a mean-field scheme, dynamic changes in synaptic weights can be considered through fluctuation-based Hebbian learning rules. However, because such implementations deal with population-averaged properties, they are not well suited to memory and learning applications where individual synaptic weights can be important. We demonstrate that, through an extended system of equations, the mean-field models can be developed further to look at higher-order statistics, in particular, the distribution of synaptic weights within a cortical column. This allows us to make some general conclusions on memory through a mean-field scheme. Specifically, we expect large changes in the standard deviation of the distribution of synaptic weights when fluctuation in the mean soma potentials are large, such as during the transitions between the “up” and “down” states of slow-wave sleep. Moreover, a cortex that has low structure in its neuronal connections is most likely to decrease its standard deviation in the weights of excitatory to excitatory synapses, relative to the square of the mean, whereas a cortex with strongly patterned connections is most likely to increase this measure. This suggests that fluctuations are used to condense the coding of strong (presumably useful) memories into fewer, but dynamic, neuron connections, while at the same time removing weaker (less useful) memories. PMID:19669541
Buehring, W.
1983-03-01
Non-relativistic scattering phase shifts, bound state energies, and wave function normalization factors for a screened Coulomb potential of the Hulthen type are presented in the form of relatively simple analytic expressions. These formulae have been obtained by a suitable renormalization procedure applied to the quantities derived from an approximate Schroedinger equation which contains the exact Hulthen potential together with an approximate angular momentum term. When the screening exponent vanishes, our formulae reduce to the exact Coulomb expresions. The interrelation between our formulae and Pratt's analytic perturbation theory for screened Coulomb potentials' is discussed.
Hadron resonance gas and mean-field nuclear matter for baryon number fluctuations
Fukushima, Kenji
2014-01-01
We give an estimate for the skewness and the kurtosis of the baryon number distribution in two representative models; i.e., models for a hadron resonance gas and relativistic mean-field nuclear matter. We emphasize formal similarity between these two descriptions. The hadron resonance gas leads to a deviation from the Skellam distribution if quantum statistical correlation is taken into account at high baryon density, but this effect is not strong enough to explain fluctuation data seen in the beam-energy scan at RHIC/STAR. In the calculation of mean-field nuclear matter the density correlation with the vector \\omega-field rather than the effective mass with the scalar \\sigma-field renders the kurtosis suppressed at higher baryon density so as to account for the observed behavior of the kurtosis. We finally discuss the difference between the baryon number and the proton number fluctuations from correlation effects in isospin space. Our numerical results suggest that such effects are only minor even in the cas...
Bashinov, Aleksei V.; Gonoskov, Arkady A.; Kim, A. V.; Marklund, Mattias; Mourou, G.; Sergeev, Aleksandr M.
2013-04-01
A comparative analysis is performed of the electron emission characteristics as the electrons move in laser fields with ultra-relativistic intensity and different configurations corresponding to a plane or tightly focused wave. For a plane travelling wave, analytical expressions are derived for the emission characteristics, and it is shown that the angular distribution of the radiation intensity changes qualitatively even when the wave intensity is much less than that in the case of the radiation-dominated regime. An important conclusion is drawn that the electrons in a travelling wave tend to synchronised motion under the radiation reaction force. The characteristic features of the motion of electrons are found in a converging dipole wave, associated with the curvature of the phase front and nonuniformity of the field distribution. The values of the maximum achievable longitudinal momenta of electrons accelerated to the centre, as well as their distribution function are determined. The existence of quasi-periodic trajectories near the focal region of the dipole wave is shown, and the characteristics of the emission of both accelerated and oscillating electrons are analysed.
Entanglement spectrum in cluster dynamical mean-field theory
Udagawa, Masafumi; Motome, Yukitoshi
2015-01-01
We study the entanglement spectrum of the Hubbard model at half filling on a kagome lattice. The entanglement spectrum is defined by the set of eigenvalues of a reduced thermal density matrix, which is naturally obtained in the framework of the dynamical mean-field theory. Adopting the cluster dynamical mean-field theory combined with continuous-time auxiliary-field Monte Carlo method, we calculate the entanglement spectrum for a three-site triangular cluster in the kagome Hubbard model. We find that the results at the three-particle sector well capture the qualitative nature of the system. In particular, the eigenvalue of the reduced density matrix, corresponding to the chiral degrees of freedom, exhibits a characteristic temperature scale Tchiral, below which a metallic state with large quasiparticle mass is stabilized. The entanglement spectra at different particle number sectors also exhibit characteristic changes around Tchiral, implying the development of inter-triangular ferromagnetic correlations in the correlated metallic regime.
Mean-field theory of echo state networks
Massar, Marc; Massar, Serge
2013-04-01
Dynamical systems driven by strong external signals are ubiquitous in nature and engineering. Here we study “echo state networks,” networks of a large number of randomly connected nodes, which represent a simple model of a neural network, and have important applications in machine learning. We develop a mean-field theory of echo state networks. The dynamics of the network is captured by the evolution law, similar to a logistic map, for a single collective variable. When the network is driven by many independent external signals, this collective variable reaches a steady state. But when the network is driven by a single external signal, the collective variable is non stationary but can be characterized by its time averaged distribution. The predictions of the mean-field theory, including the value of the largest Lyapunov exponent, are compared with the numerical integration of the equations of motion.
Characterizing the mean-field dynamo in turbulent accretion disks
Gressel, Oliver
2015-01-01
The formation and evolution of a wide class of astrophysical objects is governed by turbulent, magnetized accretion disks. Understanding their secular dynamics is of primary importance. Apart from enabling mass accretion via the transport of angular momentum, the turbulence affects the long-term evolution of the embedded magnetic flux, which in turn regulates the efficiency of the transport. In this paper, we take a comprehensive next step towards an effective mean-field model for turbulent astrophysical disks by systematically studying the key properties of magnetorotational turbulence in vertically-stratified, isothermal shearing boxes. This allows us to infer emergent properties of the ensuing chaotic flow as a function of the shear parameter as well as the amount of net-vertical flux. Using the test-field method, we furthermore characterize the mean-field dynamo coefficients that describe the long-term evolution of large-scale fields. We simultaneously infer the vertical shape and the spectral scale depen...
Nuclear collective vibrations in extended mean-field theory
Lacroix, D. [Lab. de Physique Corpusculaire/ ENSICAEN, 14 - Caen (France); Ayik, S. [Tennessee Technological Univ., Cookeville, TN (United States); Chomaz, Ph. [Grand Accelerateur National d' Ions Lourds (GANIL), 14 - Caen (France)
2003-07-01
The extended mean-field theory, which includes both the incoherent dissipation mechanism due to nucleon-nucleon collisions and the coherent dissipation mechanism due to coupling to low-lying surface vibrations, is briefly reviewed. Expressions of the strength functions for the collective excitations are presented in the small amplitude limit of this approach. This fully microscopic theory is applied by employing effective Skyrme forces to various giant resonance excitations at zero and finite temperature. The theory is able to describe the gross properties of giant resonance excitations, the fragmentation of the strength distributions as well as their fine structure. At finite temperature, the success and limitations of this extended mean-field description are discussed. (authors)
Schrödinger Approach to Mean Field Games
Swiecicki, Igor; Gobron, Thierry; Ullmo, Denis
2016-03-01
Mean field games (MFG) provide a theoretical frame to model socioeconomic systems. In this Letter, we study a particular class of MFG that shows strong analogies with the nonlinear Schrödinger and Gross-Pitaevskii equations introduced in physics to describe a variety of physical phenomena. Using this bridge, many results and techniques developed along the years in the latter context can be transferred to the former, which provides both a new domain of application for the nonlinear Schrödinger equation and a new and fruitful approach in the study of mean field games. Utilizing this approach, we analyze in detail a population dynamics model in which the "players" are under a strong incentive to coordinate themselves.
Mean-field theory of a recurrent epidemiological model.
Nagy, Viktor
2009-06-01
Our purpose is to provide a mean-field theory for the discrete time-step susceptible-infected-recovered-susceptible (SIRS) model on uncorrelated networks with arbitrary degree distributions. The effect of network structure, time delays, and infection rate on the stability of oscillating and fixed point solutions is examined through analysis of discrete time mean-field equations. Consideration of two scenarios for disease contagion demonstrates that the manner in which contagion is transmitted from an infected individual to a contacted susceptible individual is of primary importance. In particular, the manner of contagion transmission determines how the degree distribution affects model behavior. We find excellent agreement between our theoretical results and numerical simulations on networks with large average connectivity.
Relativistic quantum mechanics; Mecanique quantique relativiste
Ollitrault, J.Y. [CEA Saclay, 91 - Gif-sur-Yvette (France). Service de Physique Theorique]|[Universite Pierre et Marie Curie, 75 - Paris (France)
1998-12-01
These notes form an introduction to relativistic quantum mechanics. The mathematical formalism has been reduced to the minimum in order to enable the reader to calculate elementary physical processes. The second quantification and the field theory are the logical followings of this course. The reader is expected to know analytical mechanics (Lagrangian and Hamiltonian), non-relativistic quantum mechanics and some basis of restricted relativity. The purpose of the first 3 chapters is to define the quantum mechanics framework for already known notions about rotation transformations, wave propagation and restricted theory of relativity. The next 3 chapters are devoted to the application of relativistic quantum mechanics to a particle with 0,1/5 and 1 spin value. The last chapter deals with the processes involving several particles, these processes require field theory framework to be thoroughly described. (A.C.) 2 refs.
Bliokh, Konstantin Y
2011-01-01
We consider the relativistic deformation of quantum waves and mechanical bodies carrying intrinsic angular momentum (AM). When observed in a moving reference frame, the centroid of the object undergoes an AM-dependent transverse shift. This is the relativistic analogue of the spin Hall effect, which occurs in free space without any external fields. Remarkably, the shifts of the geometric and energy centroids differ by a factor of 2, and both centroids are crucial for the correct Lorentz transformations of the AM tensor. We examine manifestations of the relativistic Hall effect in quantum vortices, mechanical flywheel, and discuss various fundamental aspects of the phenomenon. The perfect agreement of quantum and relativistic approaches allows applications at strikingly different scales: from elementary spinning particles, through classical light, to rotating black-holes.
Dynamical mean field theory of optical third harmonic generation
Jafari, S. A.; Tohyama, T.; Maekawa, S.
2006-01-01
We formulate the third harmonic generation (THG) within the dynamical mean field theory (DMFT) approximation of the Hubbard model. In the limit of large dimensions, where DMFT becomes exact, the vertex corrections to current vertices are identically zero, and hence the calculation of the THG spectrum reduces to a time-ordered convolution, followd by appropriate analytic continuuation. We present the typical THG spectrum of the Hubbard model obtained by this method. Within our DMFT calculation...
Communication patterns in mean field models for wireless sensor networks
2015-01-01
Wireless sensor networks are usually composed of a large number of nodes, and with the increasing processing power and power consumption efficiency they are expected to run more complex protocols in the future. These pose problems in the field of verification and performance evaluation of wireless networks. In this paper, we tailor the mean-field theory as a modeling technique to analyze their behavior. We apply this method to the slotted ALOHA protocol, and establish results on the long term...
A new approach to spinel ferrites through mean field approximation
Yazdani, A. [Tarbyat Modares University, Tehran P.C 14115-175 (Iran, Islamic Republic of)]. E-mail: yazdania@modares.ac.ir; Jalilian Nosrati, M.R. [Islamic Azad University Central Tehran Branch, Tehran P.C 14168-94351 (Iran, Islamic Republic of); Ghasemi, R. [Islamic Azad University Central Tehran Branch, Tehran P.C 14168-94351 (Iran, Islamic Republic of)
2006-09-15
The magnetic behavior and specification of spinel ferrites regarding exchange interactions is being studied. The strength of interactions has been examined through the cation substitution with application of mean field approximation of exchange interaction J{sub ij} . Two correlation and approximation parameters have been defined: correlation length R {sub c} in super-exchange and the magnetic effect of ion on the electron fluctuation J {sub 0}.
Dynamical mean-field theory for flat-band ferromagnetism
Nguyen, Hong-Son; Tran, Minh-Tien
2016-09-01
The magnetically ordered phase in the Hubbard model on the infinite-dimensional hyper-perovskite lattice is investigated within dynamical mean-field theory. It turns out for the infinite-dimensional hyper-perovskite lattice the self-consistent equations of dynamical mean-field theory are exactly solved, and this makes the Hubbard model exactly solvable. We find electron spins are aligned in the ferromagnetic or ferrimagnetic configuration at zero temperature and half filling of the edge-centered sites of the hyper-perovskite lattice. A ferromagnetic-ferrimagnetic phase transition driven by the energy level splitting is found and it occurs through a phase separation. The origin of ferromagnetism and ferrimagnetism arises from the band flatness and the virtual hybridization between macroscopically degenerate flat bands and dispersive ones. Based on the exact solution in the infinite-dimensional limit, a modified exact diagonalization as the impurity solver for dynamical mean-field theory on finite-dimensional perovskite lattices is also proposed and examined.
Resummed mean-field inference for strongly coupled data
Jacquin, Hugo; Rançon, A.
2016-10-01
We present a resummed mean-field approximation for inferring the parameters of an Ising or a Potts model from empirical, noisy, one- and two-point correlation functions. Based on a resummation of a class of diagrams of the small correlation expansion of the log-likelihood, the method outperforms standard mean-field inference methods, even when they are regularized. The inference is stable with respect to sampling noise, contrarily to previous works based either on the small correlation expansion, on the Bethe free energy, or on the mean-field and Gaussian models. Because it is mostly analytic, its complexity is still very low, requiring an iterative algorithm to solve for N auxiliary variables, that resorts only to matrix inversions and multiplications. We test our algorithm on the Sherrington-Kirkpatrick model submitted to a random external field and large random couplings, and demonstrate that even without regularization, the inference is stable across the whole phase diagram. In addition, the calculation leads to a consistent estimation of the entropy of the data and allows us to sample form the inferred distribution to obtain artificial data that are consistent with the empirical distribution.
Point form relativistic quantum mechanics and relativistic SU(6)
Klink, W. H.
1993-01-01
The point form is used as a framework for formulating a relativistic quantum mechanics, with the mass operator carrying the interactions of underlying constituents. A symplectic Lie algebra of mass operators is introduced from which a relativistic harmonic oscillator mass operator is formed. Mass splittings within the degenerate harmonic oscillator levels arise from relativistically invariant spin-spin, spin-orbit, and tensor mass operators. Internal flavor (and color) symmetries are introduced which make it possible to formulate a relativistic SU(6) model of baryons (and mesons). Careful attention is paid to the permutation symmetry properties of the hadronic wave functions, which are written as polynomials in Bargmann spaces.
Tsurutani, B. T.; Hajra, R.; Tanimori, T.; Takada, A.; Bhanu, R.; Mannucci, A. J.; Lakhina, G. S.; Kozyra, J. U.; Shiokawa, K.; Lee, L. C.; Echer, E.; Reddy, R. V.; Gonzalez, W. D.
2016-10-01
A new scenario is presented for the cause of magnetospheric relativistic electron decreases (REDs) and potential effects in the atmosphere and on climate. High-density solar wind heliospheric plasmasheet (HPS) events impinge onto the magnetosphere, compressing it along with remnant noon-sector outer-zone magnetospheric 10-100 keV protons. The betatron accelerated protons generate coherent electromagnetic ion cyclotron (EMIC) waves through a temperature anisotropy (T⊥/T|| > 1) instability. The waves in turn interact with relativistic electrons and cause the rapid loss of these particles to a small region of the atmosphere. A peak total energy deposition of 3 × 1020 ergs is derived for the precipitating electrons. Maximum energy deposition and creation of electron-ion pairs at 30-50 km and at Wilcox et al. (1973) noted a correlation between solar wind heliospheric current sheet (HCS) crossings and high atmospheric vorticity centers at 300 mb altitude. Tinsley et al. has constructed a global circuit model which depends on particle precipitation into the atmosphere. Other possible scenarios potentially affecting weather/climate change are also discussed.
Mean-field and non-mean-field behaviors in scale-free networks with random Boolean dynamics
Castro e Silva, A [Departamento de Fisica, Universidade Federal de Ouro Preto, Campus Universitario, 35.400-000 Ouro Preto, Minas Gerais (Brazil); Kamphorst Leal da Silva, J, E-mail: alcidescs@gmail.co, E-mail: jaff@fisica.ufmg.b [Departamento de Fisica, Universidade Federal de Minas Gerais, Caixa Postal 702, 30.161-970, Belo Horizonte, Minas Gerais (Brazil)
2010-06-04
We study two types of simplified Boolean dynamics in scale-free networks, both with a synchronous update. Assigning only the Boolean functions AND and XOR to the nodes with probabilities 1 - p and p, respectively, we are able to analyze the density of 1's and the Hamming distance on the network by numerical simulations and by a mean-field approximation (annealed approximation). We show that the behavior is quite different if the node always enters in the dynamics as its own input (self-regulation) or not. The same conclusion holds for the Kauffman NK model. Moreover, the simulation results and the mean-field ones (i) agree well when there is no self-regulation and (ii) disagree for small p when self-regulation is present in the model.
Mean-Field and Non-Mean-Field Behaviors in Scale-free Networks with Random Boolean Dynamics
Silva, A Castro e
2009-01-01
We study two types of simplified Boolean dynamics over scale-free networks, both with synchronous update. Assigning only Boolean functions AND and XOR to the nodes with probability $1-p$ and $p$, respectively, we are able to analyze the density of 1's and the Hamming distance on the network by numerical simulations and by a mean-field approximation (annealed approximation). We show that the behavior is quite different if the node always enters in the dynamic as its own input (self-regulation) or not. The same conclusion holds for the Kauffman KN model. Moreover, the simulation results and the mean-field ones (i) agree well when there is no self-regulation, and (ii) disagree for small $p$ when self-regulation is present in the model.
Relativistic RPA in axial symmetry
Arteaga, D Pena; 10.1103/PhysRevC.77.034317
2009-01-01
Covariant density functional theory, in the framework of self-consistent Relativistic Mean Field (RMF) and Relativistic Random Phase approximation (RPA), is for the first time applied to axially deformed nuclei. The fully self-consistent RMF+RRPA equations are posed for the case of axial symmetry and non-linear energy functionals, and solved with the help of a new parallel code. Formal properties of RPA theory are studied and special care is taken in order to validate the proper decoupling of spurious modes and their influence on the physical response. Sample applications to the magnetic and electric dipole transitions in $^{20}$Ne are presented and analyzed.
Relativistic magnetohydrodynamics in one dimension.
Lyutikov, Maxim; Hadden, Samuel
2012-02-01
We derive a number of solutions for one-dimensional dynamics of relativistic magnetized plasma that can be used as benchmark estimates in relativistic hydrodynamic and magnetohydrodynamic numerical codes. First, we analyze the properties of simple waves of fast modes propagating orthogonally to the magnetic field in relativistically hot plasma. The magnetic and kinetic pressures obey different equations of state, so that the system behaves as a mixture of gases with different polytropic indices. We find the self-similar solutions for the expansion of hot strongly magnetized plasma into vacuum. Second, we derive linear hodograph and Darboux equations for the relativistic Khalatnikov potential, which describe arbitrary one-dimensional isentropic relativistic motion of cold magnetized plasma and find their general and particular solutions. The obtained hodograph and Darboux equations are very powerful: A system of highly nonlinear, relativistic, time-dependent equations describing arbitrary (not necessarily self-similar) dynamics of highly magnetized plasma reduces to a single linear differential equation.
Skymapping with OSSE via the Mean Field Annealing Pixon Technique
Dixon, D D; Zych, A D; Cheng, L X; Johnson, W N; Kurfess, J D; Pina, R K; Pütter, R C; Purcell, W R; Wheaton, W A; Wheaton, Wm. A.
1997-01-01
We present progress toward using scanned OSSE observations for mapping and sky survey work. To this end, we have developed a technique for detecting pointlike sources of unknown number and location, given that they appear in a background which is relatively featureless or which can be modeled. The technique, based on the newly developed concept and mean field annealing, is described, with sample reconstructions of data from the OSSE Virgo Survey. The results demonstrate the capability of reconstructing source information without any a priori information about the number and/or location of pointlike sources in the field-of-view.
Fictive impurity approach to dynamical mean field theory
Fuhrmann, A.
2006-10-15
A new extension of the dynamical mean-field theory was investigated in the regime of large Coulomb repulsion. A number of physical quantities such as single-particle density of states, spin-spin correlation, internal energy and Neel temperature, were computed for a two-dimensional Hubbard model at half-filling. The numerical data were compared to our analytical results as well as to the results computed using the dynamical cluster approximation. In the second part of this work we consider a two-plane Hubbard model. The transport properties of the bilayer were investigated and the phase diagram was obtained. (orig.)
Small-world network spectra in mean-field theory.
Grabow, Carsten; Grosskinsky, Stefan; Timme, Marc
2012-05-25
Collective dynamics on small-world networks emerge in a broad range of systems with their spectra characterizing fundamental asymptotic features. Here we derive analytic mean-field predictions for the spectra of small-world models that systematically interpolate between regular and random topologies by varying their randomness. These theoretical predictions agree well with the actual spectra (obtained by numerical diagonalization) for undirected and directed networks and from fully regular to strongly random topologies. These results may provide analytical insights to empirically found features of dynamics on small-world networks from various research fields, including biology, physics, engineering, and social science.
Mean Field Evolution of Fermions with Coulomb Interaction
Porta, Marcello; Rademacher, Simone; Saffirio, Chiara; Schlein, Benjamin
2017-03-01
We study the many body Schrödinger evolution of weakly coupled fermions interacting through a Coulomb potential. We are interested in a joint mean field and semiclassical scaling, that emerges naturally for initially confined particles. For initial data describing approximate Slater determinants, we prove convergence of the many-body evolution towards Hartree-Fock dynamics. Our result holds under a condition on the solution of the Hartree-Fock equation, that we can only show in a very special situation (translation invariant data, whose Hartree-Fock evolution is trivial), but that we expect to hold more generally.
Time-Dependent Mean-Field Games with Logarithmic Nonlinearities
Gomes, Diogo A.
2015-10-06
In this paper, we prove the existence of classical solutions for time-dependent mean-field games with a logarithmic nonlinearity and subquadratic Hamiltonians. Because the logarithm is unbounded from below, this nonlinearity poses substantial mathematical challenges that have not been addressed in the literature. Our result is proven by recurring to a delicate argument which combines Lipschitz regularity for the Hamilton-Jacobi equation with estimates for the nonlinearity in suitable Lebesgue spaces. Lipschitz estimates follow from an application of the nonlinear adjoint method. These are then combined with a priori bounds for solutions of the Fokker-Planck equation and a concavity argument for the nonlinearity.
Dynamical mean-field theory for quantum chemistry.
Lin, Nan; Marianetti, C A; Millis, Andrew J; Reichman, David R
2011-03-04
The dynamical mean-field concept of approximating an unsolvable many-body problem in terms of the solution of an auxiliary quantum impurity problem, introduced to study bulk materials with a continuous energy spectrum, is here extended to molecules, i.e., finite systems with a discrete energy spectrum. The application to small clusters of hydrogen atoms yields ground state energies which are competitive with leading quantum chemical approaches at intermediate and large interatomic distances as well as good approximations to the excitation spectrum.
A mean-field game economic growth model
Gomes, Diogo A.
2016-08-05
Here, we examine a mean-field game (MFG) that models the economic growth of a population of non-cooperative, rational agents. In this MFG, agents are described by two state variables - the capital and consumer goods they own. Each agent seeks to maximize his/her utility by taking into account statistical data about the whole population. The individual actions drive the evolution of the players, and a market-clearing condition determines the relative price of capital and consumer goods. We study the existence and uniqueness of optimal strategies of the agents and develop numerical methods to compute these strategies and the equilibrium price.
Mean-field theory and self-consistent dynamo modeling
Yoshizawa, Akira; Yokoi, Nobumitsu [Tokyo Univ. (Japan). Inst. of Industrial Science; Itoh, Sanae-I [Kyushu Univ., Fukuoka (Japan). Research Inst. for Applied Mechanics; Itoh, Kimitaka [National Inst. for Fusion Science, Toki, Gifu (Japan)
2001-12-01
Mean-field theory of dynamo is discussed with emphasis on the statistical formulation of turbulence effects on the magnetohydrodynamic equations and the construction of a self-consistent dynamo model. The dynamo mechanism is sought in the combination of the turbulent residual-helicity and cross-helicity effects. On the basis of this mechanism, discussions are made on the generation of planetary magnetic fields such as geomagnetic field and sunspots and on the occurrence of flow by magnetic fields in planetary and fusion phenomena. (author)
Asymptotics of Mean-Field O( N) Models
Kirkpatrick, Kay; Nawaz, Tayyab
2016-12-01
We study mean-field classical N-vector models, for integers N≥2. We use the theory of large deviations and Stein's method to study the total spin and its typical behavior, specifically obtaining non-normal limit theorems at the critical temperatures and central limit theorems away from criticality. Important special cases of these models are the XY (N=2) model of superconductors, the Heisenberg (N=3) model [previously studied in Kirkpatrick and Meckes (J Stat Phys 152:54-92, 2013) but with a correction to the critical distribution here], and the Toy (N=4) model of the Higgs sector in particle physics.
Asymptotics of the mean-field Heisenberg model
Kirkpatrick, Kay
2012-01-01
We consider the mean-field classical Heisenberg model and obtain detailed information about the magnetization by studying the model on a complete graph and sending the number of vertices to infinity. In particular, we obtain Cram\\`er- and Sanov-type large deviations principles for the magnetization and the empirical spin distribution and demonstrate a second-order phase transition in the Gibbs measures. We also study the asymptotics of the magnetization throughout the phase transition using Stein's method, proving central limit theorems in the sub- and supercritical phases and a nonnormal limit theorem at the critical temperature.
A mechanical approach to mean field spin models
Genovese, Giuseppe
2008-01-01
Inspired by the bridge pioneered by Guerra among statistical mechanics on lattice and analytical mechanics on 1+1 continuous Euclidean space-time, we built a self-consistent method to solve for the thermodynamics of mean-field models defined on lattice, whose order parameters self average. We show the whole procedure by analyzing in full details the simplest test case, namely the Curie-Weiss model. Further we report some applications also to models whose order parameters do not self-average, by using the Sherrington-Kirkpatrick spin glass as a guide.
Seki, K.; Amano, T.; Saito, S.; Miyoshi, Y.; Matsumoto, Y.; Umeda, T.; Keika, K.; Miyashita, Y.
2014-12-01
Mechanism to cause drastic variation of the Earth's outer radiation belt is one of outstanding problems of the magnetospheric researches. While the radial diffusion of the electrons driven by ULF waves in Pc5 frequency range has been considered as one of the candidate mechanisms, it is pointed out that the radial transport of relativistic electrons by ULF waves is not necessarily reach the radial diffusion limit and collective motion of the outer belt electrons can exhibit large deviations from the radial diffusion [Ukhorskiy et al., JATSP, 2008]. Thus it is important to understand the form of radial transport of electrons under realistic ULF distribution in the inner magnetosphere. We have developed a physics-based model for the global dynamics of the ring current (GEMSIS-RC model). The GEMSIS-RC model is a self-consistent numerical simulation code solving the five-dimensional collisionless drift-kinetic equation for the ring-current ions in the inner-magnetosphere coupled with Maxwell equations [Amano et al., JGR, 2011]. We applied the GEMSIS-RC model for simulation of global distribution of ULF Pc5 waves. Comparison between runs with/without ring current ions show that the existence of hot ring current ions can deform the original sinusoidal waveforms. The deformation causes the energy cascade to higher frequency range (Pc4 and Pc3 ranges). The cascade is more pronounced in the high beta case. It is also shown that the existence of plasmapause strengthens ULFs outside the plasmapause and widens the MLT region where the E_r (toroidal) component is excited from initially-given E_phi (poloidal) component. In order to investigate the characteristics of radial transport of relativistic electrons, we then use the global magnetic and electric fields variation obtained by the GEMNIS-RC model as input field models for the test particle simulations of radiation belt electrons (GEMSIS-RB) [Saito et al., JGR, 2010]. The combination of GEMSIS-RC and RB models reproduced
Relativistic viscoelastic fluid mechanics.
Fukuma, Masafumi; Sakatani, Yuho
2011-08-01
A detailed study is carried out for the relativistic theory of viscoelasticity which was recently constructed on the basis of Onsager's linear nonequilibrium thermodynamics. After rederiving the theory using a local argument with the entropy current, we show that this theory universally reduces to the standard relativistic Navier-Stokes fluid mechanics in the long time limit. Since effects of elasticity are taken into account, the dynamics at short time scales is modified from that given by the Navier-Stokes equations, so that acausal problems intrinsic to relativistic Navier-Stokes fluids are significantly remedied. We in particular show that the wave equations for the propagation of disturbance around a hydrostatic equilibrium in Minkowski space-time become symmetric hyperbolic for some range of parameters, so that the model is free of acausality problems. This observation suggests that the relativistic viscoelastic model with such parameters can be regarded as a causal completion of relativistic Navier-Stokes fluid mechanics. By adjusting parameters to various values, this theory can treat a wide variety of materials including elastic materials, Maxwell materials, Kelvin-Voigt materials, and (a nonlinearly generalized version of) simplified Israel-Stewart fluids, and thus we expect the theory to be the most universal description of single-component relativistic continuum materials. We also show that the presence of strains and the corresponding change in temperature are naturally unified through the Tolman law in a generally covariant description of continuum mechanics.
Mean field theory for U(n) dynamical groups
Rosensteel, G, E-mail: george.rosensteel@tulane.edu [Department of Physics, Tulane University, New Orleans, LA 70118 (United States)
2011-04-22
Algebraic mean field theory (AMFT) is a many-body physics modeling tool which firstly, is a generalization of Hartree-Fock mean field theory, and secondly, an application of the orbit method from Lie representation theory. The AMFT ansatz is that the physical system enjoys a dynamical group, which may be either a strong or a weak dynamical Lie group G. When G is a strong dynamical group, the quantum states are, by definition, vectors in one irreducible unitary representation (irrep) space, and AMFT is equivalent to the Kirillov orbit method for deducing properties of a representation from a direct geometrical analysis of the associated integral co-adjoint orbit. AMFT can be the only tractable method for analyzing some complex many-body systems when the dimension of the irrep space of the strong dynamical group is very large or infinite. When G is a weak dynamical group, the quantum states are not vectors in one irrep space, but AMFT applies if the densities of the states lie on one non-integral co-adjoint orbit. The computational simplicity of AMFT is the same for both strong and weak dynamical groups. This paper formulates AMFT explicitly for unitary Lie algebras, and applies the general method to the Lipkin-Meshkov-Glick su(2) model and the Elliott su(3) model. When the energy in the su(3) theory is a rotational scalar function, Marsden-Weinstein reduction simplifies AMFT dynamics to a two-dimensional phase space.
Control and Nash Games with Mean Field Effect
Alain BENSOUSSAN; Jens FREHSE
2013-01-01
Mean field theory has raised a lot of interest in the recent years (see in particular the results of Lasry-Lions in 2006 and 2007,of Gueant-Lasry-Lions in 2011,of HuangCaines-Malham in 2007 and many others).There are a lot of applications.In general,the applications concern approximating an infinite number of players with common behavior by a representative agent.This agent has to solve a control problem perturbed by a field equation,representing in some way the behavior of the average infinite number of agents.This approach does not lead easily to the problems of Nash equilibrium for a finite number of players,perturbed by field equations,unless one considers averaging within different groups,which has not been done in the literature,and seems quite challenging.In this paper,the authors approach similar problems with a different motivation which makes sense for control and also for differential games.Thus the systems of nonlinear partial differential equations with mean field terms,which have not been addressed in the literature so far,are considered here.
Simulated Tempering and Swapping on Mean-Field Models
Bhatnagar, Nayantara; Randall, Dana
2016-08-01
Simulated and parallel tempering are families of Markov Chain Monte Carlo algorithms where a temperature parameter is varied during the simulation to overcome bottlenecks to convergence due to multimodality. In this work we introduce and analyze the convergence for a set of new tempering distributions which we call entropy dampening. For asymmetric exponential distributions and the mean field Ising model with an external field simulated tempering is known to converge slowly. We show that tempering with entropy dampening distributions mixes in polynomial time for these models. Examining slow mixing times of tempering more closely, we show that for the mean-field 3-state ferromagnetic Potts model, tempering converges slowly regardless of the temperature schedule chosen. On the other hand, tempering with entropy dampening distributions converges in polynomial time to stationarity. Finally we show that the slow mixing can be very expensive practically. In particular, the mixing time of simulated tempering is an exponential factor longer than the mixing time at the fixed temperature.
Benchmarking mean-field approximations to level densities
Alhassid, Y; Gilbreth, C N; Nakada, H
2015-01-01
We assess the accuracy of finite-temperature mean-field theory using as a standard the Hamiltonian and model space of the shell model Monte Carlo calculations. Two examples are considered: the nucleus $^{162}$Dy, representing a heavy deformed nucleus, and $^{148}$Sm, representing a nearby heavy spherical nucleus with strong pairing correlations. The errors inherent in the finite-temperature Hartree-Fock and Hartree-Fock-Bogoliubov approximations are analyzed by comparing the entropies of the grand canonical and canonical ensembles, as well as the level density at the neutron resonance threshold, with shell model Monte Carlo (SMMC) calculations, which are accurate up to well-controlled statistical errors. The main weak points in the mean-field treatments are seen to be: (i) the extraction of number-projected densities from the grand canonical ensembles, and (ii) the symmetry breaking by deformation or by the pairing condensate. In the absence of a pairing condensate, we confirm that the usual saddle-point appr...
Nonlinear regimes in mean-field full-sphere dynamo
Pipin, V V
2016-01-01
The mean-field dynamo model is employed to study the non-linear dynamo regimes in a fully convective star of mass 0.3$M_{\\odot}$ rotating with period of 10 days. The differential rotation law was estimated using the mean-field hydrodynamic and heat transport equations. For the intermediate parameter of the turbulent magnetic Reynolds number, $Pm_{T}=3$ we found the oscillating dynamo regimes with period about 40Yr. The higher $Pm_{T}$ results to longer dynamo periods. The meridional circulation has one cell per hemisphere. It is counter-clockwise in the Northen hemisphere. The amplitude of the flow at the surface around 1 m/s. Tne models with regards for meridional circulation show the anti-symmetric relative to equator magnetic field. If the large-scale flows is fixed we find that the dynamo transits from axisymmetric to non-axisymmetric regimes for the overcritical parameter of the $\\alpha$effect. The change of dynamo regime occurs because of the non-axisymmetric non-linear $\\alpha$-effect. The situation pe...
Kinetic and mean field description of Gibrat's law
Toscani, Giuseppe
2016-01-01
We introduce and analyze a linear kinetic model that describes the evolution of the probability density of the number of firms in a society, in which the microscopic rate of change obeys to the so-called law of proportional effect proposed by Gibrat. Despite its apparent simplicity, the possible mean field limits of the kinetic model are varied. In some cases, the asymptotic limit can be described by a first-order partial differential equation. In other cases, the mean field equation is a linear diffusion with a non constant diffusion coefficient that models also the geometric Brownian motion and can be studied analytically. In this case, it is shown that the large-time behavior of the solution is represented, for a large class of initial data, by a lognormal distribution with constant mean value and variance increasing exponentially in time at a precise rate. The relationship between the kinetic and the diffusion models allow to introduce an easy-to- implement expression for computing the Fourier transform o...
Topological properties of the mean-field ϕ4 model
Andronico, A.; Angelani, L.; Ruocco, G.; Zamponi, F.
2004-10-01
We study the thermodynamics and the properties of the stationary points (saddles and minima) of the potential energy for a ϕ4 mean-field model. We compare the critical energy vc [i.e., the potential energy v(T) evaluated at the phase transition temperature Tc ] with the energy vθ at which the saddle energy distribution show a discontinuity in its derivative. We find that, in this model, vc≫vθ , at variance to what has been found in different mean-field and short ranged systems, where the thermodynamic phase transitions take place at vc=vθ [Casetti, Pettini and Cohen, Phys. Rep. 337, 237 (2000)]. By direct calculation of the energy vs(T) of the “inherent saddles,” i.e., the saddles visited by the equilibrated system at temperature T , we find that vs(Tc)˜vθ . Thus, we argue that the thermodynamic phase transition is related to a change in the properties of the inherent saddles rather than to a change of the topology of the potential energy surface at T=Tc . Finally, we discuss the approximation involved in our analysis and the generality of our method.
The effectiveness of mean-field theory for avalanche distributions
Lee, Edward; Raju, Archishman; Sethna, James
We explore the mean-field theory of the pseudogap found in avalanche systems with long-range anisotropic interactions using analytical and numerical tools. The pseudogap in the density of low-stability states emerges from the competition between stabilizing interactions between spins in an avalanche and the destabilizing random movement towards the threshold caused by anisotropic couplings. Pazmandi et al. have shown that for the Sherrington-Kirkpatrick model, the pseudogap scales linearly and produces a distribution of avalanche sizes with exponent t=1 in contrast with that predicted from RFIM t=3/2. Lin et al. have argued that the scaling exponent ? of the pseudogap depends on the tail of the distribution of couplings and on non-universal values like the strain rate and the magnitude of the coupling strength. Yet others have argued that the relationship between the pseudogap scaling and the distribution of avalanche sizes is dependent on dynamical details. Despite the theoretical arguments, the class of RFIM mean-field models is surprisingly good at predicting the distribution of avalanche sizes in a variety of different magnetic systems. We investigate these differences with a combination of theory and simulation.
Kinetic and mean field description of Gibrat's law
Toscani, Giuseppe
2016-11-01
I introduce and analyze a linear kinetic model that describes the evolution of the probability density of the number of firms in a society, in which the microscopic rate of change obeys to the so-called law of proportional effect proposed by Gibrat (1930, 1931). Despite its apparent simplicity, the possible mean field limits of the kinetic model are varied. In some cases, the asymptotic limit can be described by a first-order partial differential equation. In other cases, the mean field equation is a linear diffusion with a non constant diffusion coefficient that can be studied analytically, by virtue of a transformation of variables recently utilized in Iagar and Sánchez (2013) to study the heat equation in a nonhomogeneous medium with critical density. In this case, it is shown that the large-time behavior of the solution is represented, for a large class of initial data, by a lognormal distribution with constant mean value and variance increasing exponentially in time at a precise rate.
Mean field theory of high Tc cuprate superconductivity
K. Maki
2006-09-01
Full Text Available Two decades ago the epoch making discovery of high Tc cuprate superconductivity by Bednorz and Müller shocked the world’s superconductivity community. However, already in 1979 and 1980, the first heavy fermion superconductor CeCu2Si2 and organic superconductor (TMTSF2PF6 have been discovered respectively. Also we know now that all these superconductors are unconventional and nodal. Further the quasiparticles in the normal state in these systems are Fermi liquids and the superconducting states are described in terms of generalized BCS wave function. Also the pseudogap phase in underdoped high Tc cuprates is described in terms of d-wave density wave. This implies necessarily that the superconductivity in underdoped cuprates is gossamer (i.e. d-wave superconductivity coexists with d-wave density wave. We shall present some quantitative tests of these new concepts, notions and ideas.
Demianski, Marek
2013-01-01
Relativistic Astrophysics brings together important astronomical discoveries and the significant achievements, as well as the difficulties in the field of relativistic astrophysics. This book is divided into 10 chapters that tackle some aspects of the field, including the gravitational field, stellar equilibrium, black holes, and cosmology. The opening chapters introduce the theories to delineate gravitational field and the elements of relativistic thermodynamics and hydrodynamics. The succeeding chapters deal with the gravitational fields in matter; stellar equilibrium and general relativity
RELATIVISTIC CALCULATIONS OF THE SUPERHEAVY NUCLEUS 114-298
BOERSMA, HF
1993-01-01
We investigate ground-state properties of the superheavy nucleus with N = 184 and Z = 114, (298)114, using conventional relativistic mean-field theory and density-dependent mean-field theory, which reproduces Dirac-Brueckner calculations in nuclear matter. Our calculations provide support for N = 18
Oliveira, Diego F.M., E-mail: diegofregolente@gmail.com [Institute for Multiscale Simulations, Friedrich-Alexander Universität, D-91052, Erlangen (Germany); Leonel, Edson D., E-mail: edleonel@rc.unesp.br [Departamento de Estatística, Matemática Aplicada e Computação, UNESP, Univ. Estadual Paulista, Av. 24A, 1515, Bela Vista, 13506-900, Rio Claro, SP (Brazil); Departamento de Física, UNESP, Univ. Estadual Paulista, Av. 24A, 1515, 13506-900, Rio Claro, SP (Brazil)
2012-11-01
We study some dynamical properties for the problem of a charged particle in an electric field considering both the low velocity and relativistic cases. The dynamics for both approaches is described in terms of a two-dimensional and nonlinear mapping. The structure of the phase spaces is mixed and we introduce a hole in the chaotic sea to let the particles to escape. By changing the size of the hole we show that the survival probability decays exponentially for both cases. Additionally, we show for the relativistic dynamics, that the introduction of dissipation changes the mixed phase space and attractors appear. We study the parameter space by using the Lyapunov exponent and the average energy over the orbit and show that the system has a very rich structure with infinite family of self-similar shrimp shaped embedded in a chaotic region.
Beneke, M.; Hellmann, C.; Ruiz-Femenia, P.
2012-01-01
We compute analytically the tree-level annihilation rates of a collection of non-relativistic neutralino and chargino two-particle states in the general MSSM, including the previously unknown off-diagonal rates. The results are prerequisites to the calculation of the Sommerfeld enhancement in the MSSM, which will be presented in subsequent work. They can also be used to obtain concise analytic expressions for MSSM dark matter pair annihilation in the present Universe for a large number of exc...
Graber, P. Jameson, E-mail: jameson-graber@baylor.edu [Baylor University, Department of Mathematics (United States)
2016-12-15
We study a general linear quadratic mean field type control problem and connect it to mean field games of a similar type. The solution is given both in terms of a forward/backward system of stochastic differential equations and by a pair of Riccati equations. In certain cases, the solution to the mean field type control is also the equilibrium strategy for a class of mean field games. We use this fact to study an economic model of production of exhaustible resources.
Neural Population Dynamics Modeled by Mean-Field Graphs
Kozma, Robert; Puljic, Marko
2011-09-01
In this work we apply random graph theory approach to describe neural population dynamics. There are important advantages of using random graph theory approach in addition to ordinary and partial differential equations. The mathematical theory of large-scale random graphs provides an efficient tool to describe transitions between high- and low-dimensional spaces. Recent advances in studying neural correlates of higher cognition indicate the significance of sudden changes in space-time neurodynamics, which can be efficiently described as phase transitions in the neuropil medium. Phase transitions are rigorously defined mathematically on random graph sequences and they can be naturally generalized to a class of percolation processes called neuropercolation. In this work we employ mean-field graphs with given vertex degree distribution and edge strength distribution. We demonstrate the emergence of collective oscillations in the style of brains.
Spectral Synthesis via Mean Field approach Independent Component Analysis
Hu, Ning; Kong, Xu
2015-01-01
In this paper, we apply a new statistical analysis technique, Mean Field approach to Bayesian Independent Component Analysis (MF-ICA), on galaxy spectral analysis. This algorithm can compress the stellar spectral library into a few Independent Components (ICs), and galaxy spectrum can be reconstructed by these ICs. Comparing to other algorithms which decompose a galaxy spectrum into a combination of several simple stellar populations, MF-ICA approach offers a large improvement in the efficiency. To check the reliability of this spectral analysis method, three different methods are used: (1) parameter-recover for simulated galaxies, (2) comparison with parameters estimated by other methods, and (3) consistency test of parameters from the Sloan Digital Sky Survey galaxies. We find that our MF-ICA method not only can fit the observed galaxy spectra efficiently, but also can recover the physical parameters of galaxies accurately. We also apply our spectral analysis method to the DEEP2 spectroscopic data, and find...
Non-mean-field screening by multivalent counterions
Loth, M S; Shklovskii, B I, E-mail: loth@physics.umn.ed [Department of Physics, University of Minnesota, Minneapolis, MN 55455 (United States)
2009-10-21
Screening of a strongly charged macroion by its multivalent counterions cannot be described in the framework of a mean-field Poisson-Boltzmann (PB) theory because multivalent counterions form a strongly correlated liquid (SCL) on the surface of the macroion. It was predicted that a distant counterion polarizes the SCL as if it were a metallic surface and creates an electrostatic image. The attractive potential energy of the image is the reason why the charge density of counterions decreases faster with distance from the charged surface than in PB theory. Using the Monte Carlo method to find the equilibrium distribution of counterions around the macroion, we confirm the existence of the image potential energy. It is also shown that, due to the negative screening length of the SCL, -2xi, the effective metallic surface is actually above the SCL by |xi|.
Explicit Solutions for One-Dimensional Mean-Field Games
Prazeres, Mariana
2017-04-05
In this thesis, we consider stationary one-dimensional mean-field games (MFGs) with or without congestion. Our aim is to understand the qualitative features of these games through the analysis of explicit solutions. We are particularly interested in MFGs with a nonmonotonic behavior, which corresponds to situations where agents tend to aggregate. First, we derive the MFG equations from control theory. Then, we compute explicit solutions using the current formulation and examine their behavior. Finally, we represent the solutions and analyze the results. This thesis main contributions are the following: First, we develop the current method to solve MFG explicitly. Second, we analyze in detail non-monotonic MFGs and discover new phenomena: non-uniqueness, discontinuous solutions, empty regions and unhappiness traps. Finally, we address several regularization procedures and examine the stability of MFGs.
Mean field games with nonlinear mobilities in pedestrian dynamics
Burger, Martin
2014-04-01
In this paper we present an optimal control approach modeling fast exit scenarios in pedestrian crowds. In particular we consider the case of a large human crowd trying to exit a room as fast as possible. The motion of every pedestrian is determined by minimizing a cost functional, which depends on his/her position, velocity, exit time and the overall density of people. This microscopic setup leads in the mean-field limit to a parabolic optimal control problem. We discuss the modeling of the macroscopic optimal control approach and show how the optimal conditions relate to the Hughes model for pedestrian flow. Furthermore we provide results on the existence and uniqueness of minimizers and illustrate the behavior of the model with various numerical results.
Mean-field vs. Stochastic Models for Transcriptional Regulation
Blossey, Ralf; Giuraniuc, Claudiu
2009-03-01
We introduce a minimal model description for the dynamics of transcriptional regulatory networks. It is studied within a mean-field approximation, i.e., by deterministic ode's representing the reaction kinetics, and by stochastic simulations employing the Gillespie algorithm. We elucidate the different results both approaches can deliver, depending on the network under study, and in particular depending on the level of detail retained in the respective description. Two examples are addressed in detail: the repressilator, a transcriptional clock based on a three-gene network realized experimentally in E. coli, and a bistable two-gene circuit under external driving, a transcriptional network motif recently proposed to play a role in cellular development.
Mean-field versus stochastic models for transcriptional regulation
Blossey, R.; Giuraniuc, C. V.
2008-09-01
We introduce a minimal model description for the dynamics of transcriptional regulatory networks. It is studied within a mean-field approximation, i.e., by deterministic ODE’s representing the reaction kinetics, and by stochastic simulations employing the Gillespie algorithm. We elucidate the different results that both approaches can deliver, depending on the network under study, and in particular depending on the level of detail retained in the respective description. Two examples are addressed in detail: The repressilator, a transcriptional clock based on a three-gene network realized experimentally in E. coli, and a bistable two-gene circuit under external driving, a transcriptional network motif recently proposed to play a role in cellular development.
Nuclear Level Density: Shell Model vs Mean Field
Sen'kov, Roman
2015-01-01
The knowledge of the nuclear level density is necessary for understanding various reactions including those in the stellar environment. Usually the combinatorics of Fermi-gas plus pairing is used for finding the level density. Recently a practical algorithm avoiding diagonalization of huge matrices was developed for calculating the density of many-body nuclear energy levels with certain quantum numbers for a full shell-model Hamiltonian. The underlying physics is that of quantum chaos and intrinsic thermalization in a closed system of interacting particles. We briefly explain this algorithm and, when possible, demonstrate the agreement of the results with those derived from exact diagonalization. The resulting level density is much smoother than that coming from the conventional mean-field combinatorics. We study the role of various components of residual interactions in the process of thermalization, stressing the influence of incoherent collision-like processes. The shell-model results for the traditionally...
Metabifurcation analysis of a mean field model of the cortex
Frascoli, Federico; Bojak, Ingo; Liley, David T J
2010-01-01
Mean field models (MFMs) of cortical tissue incorporate salient features of neural masses to model activity at the population level. One of the common aspects of MFM descriptions is the presence of a high dimensional parameter space capturing neurobiological attributes relevant to brain dynamics. We study the physiological parameter space of a MFM of electrocortical activity and discover robust correlations between physiological attributes of the model cortex and its dynamical features. These correlations are revealed by the study of bifurcation plots, which show that the model responses to changes in inhibition belong to two families. After investigating and characterizing these, we discuss their essential differences in terms of four important aspects: power responses with respect to the modeled action of anesthetics, reaction to exogenous stimuli, distribution of model parameters and oscillatory repertoires when inhibition is enhanced. Furthermore, while the complexity of sustained periodic orbits differs ...
Double binding energy differences: Mean-field or pairing effect?
Qi, Chong
2012-10-01
In this Letter we present a systematic analysis on the average interaction between the last protons and neutrons in atomic nuclei, which can be extracted from the double differences of nuclear binding energies. The empirical average proton-neutron interaction Vpn thus derived from experimental data can be described in a very simple form as the interplay of the nuclear mean field and the pairing interaction. It is found that the smooth behavior as well as the local fluctuations of the Vpn in even-even nuclei with N ≠ Z are dominated by the contribution from the proton-neutron monopole interactions. A strong additional contribution from the isoscalar monopole interaction and isovector proton-neutron pairing interaction is seen in the Vpn for even-even N = Z nuclei and for the adjacent odd-A nuclei with one neutron or proton being subtracted.
Mean-field games with logistic population dynamics
Gomes, Diogo A.
2013-12-01
In its standard form, a mean-field game can be defined by coupled system of equations, a Hamilton-Jacobi equation for the value function of agents and a Fokker-Planck equation for the density of agents. Traditionally, the latter equation is adjoint to the linearization of the former. Since the Fokker-Planck equation models a population dynamic, we introduce natural features such as seeding and birth, and nonlinear death rates. In this paper we analyze a stationary meanfield game in one dimension, illustrating various techniques to obtain regularity of solutions in this class of systems. In particular we consider a logistic-type model for birth and death of the agents which is natural in problems where crowding affects the death rate of the agents. The introduction of these new terms requires a number of new ideas to obtain wellposedness. In a forthcoming publication we will address higher dimensional models. ©2013 IEEE.
Glauber Dynamics for the mean-field Potts Model
Cuff, Paul; Louidor, Oren; Lubetzky, Eyal; Peres, Yuval; Sly, Allan
2012-01-01
We study Glauber dynamics for the mean-field (Curie-Weiss) Potts model with $q\\geq 3$ states and show that it undergoes a critical slowdown at an inverse-temperature $\\beta_s(q)$ strictly lower than the critical $\\beta_c(q)$ for uniqueness of the thermodynamic limit. The dynamical critical $\\beta_s(q)$ is the spinodal point marking the onset of metastability. We prove that when $\\beta\\beta_s(q)$ the mixing time is exponentially large in $n$. Furthermore, as $\\beta \\uparrow \\beta_s$ with $n$, the mixing time interpolates smoothly from subcritical to critical behavior, with the latter reached at a scaling window of $O(n^{-2/3})$ around $\\beta_s$. These results form the first complete analysis of the critical slowdown of a dynamics with a first order phase transition.
Glauber Dynamics for the Mean-Field Potts Model
Cuff, P.; Ding, J.; Louidor, O.; Lubetzky, E.; Peres, Y.; Sly, A.
2012-11-01
We study Glauber dynamics for the mean-field (Curie-Weiss) Potts model with q≥3 states and show that it undergoes a critical slowdown at an inverse-temperature β s ( q) strictly lower than the critical β c ( q) for uniqueness of the thermodynamic limit. The dynamical critical β s ( q) is the spinodal point marking the onset of metastability. We prove that when β β s ( q) the mixing time is exponentially large in n. Furthermore, as β↑ β s with n, the mixing time interpolates smoothly from subcritical to critical behavior, with the latter reached at a scaling window of O( n -2/3) around β s . These results form the first complete analysis of mixing around the critical dynamical temperature—including the critical power law—for a model with a first order phase transition.
Quasi-isotropic cascade in MHD turbulence with mean field
Grappin, Roland; Gürcan, Özgür
2012-01-01
We propose a phenomenological theory of incompressible magnetohydrodynamic turbulence in the presence of a strong large-scale magnetic field, which establishes a link between the known anisotropic models of strong and weak MHD turbulence We argue that the Iroshnikov-Kraichnan isotropic cascade develops naturally within the plane perpendicular to the mean field, while oblique-parallel cascades with weaker amplitudes can develop, triggered by the perpendicular cascade, with a reduced flux resulting from a quasi-resonance condition. The resulting energy spectrum $E(k_\\parallel,k_\\bot)$ has the same slope in all directions. The ratio between the extents of the inertial range in the parallel and perpendicular directions is equal to $b_{rms}/B_0$. These properties match those found in recent 3D MHD simulations with isotropic forcing reported in [R. Grappin and W.-C. M\\"uller, Phys. Rev. E \\textbf{82}, 26406 (2010)].
Two stochastic mean-field polycrystal plasticity methods
Tonks, Michael [Los Alamos National Laboratory
2008-01-01
In this work, we develop two mean-field polycrystal plasticity models in which the L{sup c} are approximated stochastically. Through comprehensive CPFEM analyses of an idealized tantalum polycrystal, we verify that the L{sup c} tend to follow a normal distribution and surmise that this is due to the crystal interactions. We draw on these results to develop the STM and the stochastic no-constraints model (SNCM), which differ in the manner in which the crystal strain rates D{sup c} are prescribed. Calibration and validation of the models are performed using data from tantalum compression experiments. Both models predict the compression textures more accurately than the FCM, and the SNCM predicts them more accurately than the STM. The STM is extremely computationally efficient, only slightly more expensive than the FCM, while the SNCM is three times more computationally expensive than the STM.
Mean field theory for U(n) dynamical groups
Rosensteel, G.
2011-04-01
Algebraic mean field theory (AMFT) is a many-body physics modeling tool which firstly, is a generalization of Hartree-Fock mean field theory, and secondly, an application of the orbit method from Lie representation theory. The AMFT ansatz is that the physical system enjoys a dynamical group, which may be either a strong or a weak dynamical Lie group G. When G is a strong dynamical group, the quantum states are, by definition, vectors in one irreducible unitary representation (irrep) space, and AMFT is equivalent to the Kirillov orbit method for deducing properties of a representation from a direct geometrical analysis of the associated integral co-adjoint orbit. AMFT can be the only tractable method for analyzing some complex many-body systems when the dimension of the irrep space of the strong dynamical group is very large or infinite. When G is a weak dynamical group, the quantum states are not vectors in one irrep space, but AMFT applies if the densities of the states lie on one non-integral co-adjoint orbit. The computational simplicity of AMFT is the same for both strong and weak dynamical groups. This paper formulates AMFT explicitly for unitary Lie algebras, and applies the general method to the Lipkin-Meshkov-Glick {\\mathfrak s}{\\mathfrak u} (2) model and the Elliott {\\mathfrak s}{\\mathfrak u} (3) model. When the energy in the {\\mathfrak s}{\\mathfrak u} (3) theory is a rotational scalar function, Marsden-Weinstein reduction simplifies AMFT dynamics to a two-dimensional phase space.
Conserving Gapless Mean-Field Theory for Weakly Interacting Bose Gases
Kita, Takafumi
2006-04-01
This paper presents a conserving gapless mean-field theory for weakly interacting Bose gases. We first construct a mean-field Luttinger-Ward thermodynamic functional in terms of the condensate wave function \\Psi and the Nambu Green’s function \\hat{G} for the quasiparticle field. Imposing its stationarity respect to \\Psi and \\hat{G} yields a set of equations to determine the equilibrium for general non-uniform systems. They have a plausible property of satisfying the Hugenholtz-Pines theorem to provide a gapless excitation spectrum. Also, the corresponding dynamical equations of motion obey various conservation laws. Thus, the present mean-field theory shares two important properties with the exact theory: “conserving” and “gapless.” The theory is then applied to a homogeneous weakly interacting Bose gas with s-wave scattering length a and particle mass m to clarify its basic thermodynamic properties under two complementary conditions of constant density n and constant pressure p. The superfluid transition is predicted to be first-order because of the non-analytic nature of the order-parameter expansion near Tc inherent in Bose systems, i.e., the Landau-Ginzburg expansion is not possible here. The transition temperature Tc shows quite a different interaction dependence between the n-fixed and p-fixed cases. In the former case Tc increases from the ideal gas value T0 as Tc/T0= 1+ 2.33 an1/3, whereas it decreases in the latter as Tc/T0= 1- 3.84a(m p/2π\\hbar2)1/5. Temperature dependences of basic thermodynamic quantities are clarified explicitly.
Kaki, K
2001-01-01
We calculate proton elastic scattering with sup 5 sup 8 Ni and sup 1 sup 2 sup 0 Sn at various intermediate energies with relativistic impulse approximation (RIA). We use the ground-state wave functions of the relativistic mean-field (RMF) calculation with the use of the TMA parameter set. We found good agreement with experimental data for the elastic scattering observables. In addition to the standard scalar and vector densities, we include also the tensor density. We study the Pauli effect and the vacuum polarization effect on the elastic scattering observables using the prescription of Horowitz and Serot at lower energy.
Bulanov, Sergei V.; Esirkepov, Timur Z.; Hayashi, Yukio; Kando, Masaki; Kiriyama, Hiromitsu; Koga, James K.; Kondo, Kiminori; Kotaki, Hideyuki; Pirozhkov, Alexander S.; Bulanov, Stepan S.; Zhidkov, Alexei G.; Chen, Pisin; Neely, David; Kato, Yoshiaki; Narozhny, Nikolay B.; Korn, Georg
2011-06-01
The critical electric field of quantum electrodynamics, called also the Schwinger field, is so strong that it produces electron-positron pairs from vacuum, converting the energy of light into matter. Since the dawn of quantum electrodynamics, there has been a dream on how to reach it on Earth. With the rise of laser technology this field has become feasible through the construction of extremely high power lasers or/and with the sophisticated use of nonlinear processes in relativistic plasmas. This is one of the most attractive motivations for extremely high power laser development, i.e. producing matter from vacuum by pure light in fundamental process of quantum electrodynamics in the nonperturbative regime. Recently it has been realized that a laser with intensity well below the Schwinger limit can create an avalanche of electron-positron pairs similar to a discharge before attaining the Schwinger field. It has also been realized that the Schwinger limit can be reached using an appropriate configuration of laser beams. In experiments on the collision of laser light and high intensity electromagnetic pulses generated by relativistic flying mirrors, with electron bunches produced by a conventional accelerator and with laser wake field accelerated electrons the studying of extreme field limits in the nonlinear interaction of electromagnetic waves is proposed. The regimes of dominant radiation reaction, which completely changes the electromagnetic wave-matter interaction, will be revealed. This will result in a new powerful source of high brightness gamma-rays. A possibility of the demonstration of the electronpositron pair creation in vacuum via multi-photon processes can be realized. This will allow modeling under terrestrial laboratory conditions neutron star magnetospheres, cosmological gamma ray bursts and the Leptonic Era of the Universe.
Bubin, Sergiy; Stanke, Monika; Adamowicz, Ludwik
2017-06-01
In our previous work S. Bubin et al., Chem. Phys. Lett. 647, 122 (2016), 10.1016/j.cplett.2016.01.056, it was established that complex explicitly correlated one-center all-particle Gaussian functions (CECGs) provide effective basis functions for very accurate nonrelativistic molecular non-Born-Oppenheimer calculations. In this work, we advance the molecular CECGs approach further by deriving and implementing algorithms for calculating the leading relativistic corrections within this approach. The algorithms are tested in the calculations of the corrections for all 23 bound pure vibrational states of the HD+ ion.
Novak, Jerome; Dimmelmeier, Harrald; Font-Roda, Jose A.
2004-12-01
We present a new three-dimensional general relativistic hydrodynamics code which can be applied to study stellar core collapses and the resulting gravitational radiation. This code uses two different numerical techniques to solve partial differential equations arising in the model: high-resolution shock capturing (HRSC) schemes for the evolution of hydrodynamic quantities and spectral methods for the solution of Einstein equations. The equations are written and solved using spherical polar coordinates, best suited to stellar topology. Einstein equations are formulated within the 3+1 formalism and conformal flat condition (CFC) for the 3-metric and gravitational radiation is extracted using Newtonian quadrupole formulation.
Artemyev, A. V., E-mail: ante0226@gmail.com; Vasiliev, A. A.; Neishtadt, A. I. [Space Research Institute, RAS, Moscow, Russia, 117997 (Russian Federation); Mourenas, D.; Krasnoselskikh, V. [LPC2E/CNRS—University of Orleans, 3A, Avenue de la Recherche Scientifique, F-45071 Orleans Cedex (France); Agapitov, O. V. [Space Sciences Laboratory, University of California, Berkeley, California 94720 (United States)
2015-11-15
We investigate electron trapping by high-amplitude whistler-mode waves propagating at small as well as large angles relative to geomagnetic field lines. The inhomogeneity of the background magnetic field can result in an effective acceleration of trapped particles. Here, we derive useful analytical expressions for the probability of electron trapping by both parallel and oblique waves, paving the way for a full analytical description of trapping effects on the particle distribution. Numerical integrations of particle trajectories allow to demonstrate the accuracy of the derived analytical estimates. For realistic wave amplitudes, the levels of probabilities of trapping are generally comparable for oblique and parallel waves, but they turn out to be most efficient over complementary energy ranges. Trapping acceleration of <100 keV electrons is mainly provided by oblique waves, while parallel waves are responsible for the trapping acceleration of >100 keV electrons.
The quark mean field model with pion and gluon corrections
Xing, Xueyong; Shen, Hong
2016-01-01
The properties of nuclear matter and finite nuclei are studied within the quark mean field (QMF) model by taking the effects of pion and gluon into account at the quark level. The nucleon is described as the combination of three constituent quarks confined by a harmonic oscillator potential. To satisfy the spirit of QCD theory, the contributions of pion and gluon on the nucleon structure are treated in second-order perturbation theory. For the nuclear many-body system, nucleons interact with each other by exchanging mesons between quarks. With different constituent quark mass, $m_q$, we determine three parameter sets about the coupling constants between mesons and quarks, named as QMF-NK1, QMF-NK2, and QMF-NK3 by fitting the ground-state properties of several closed-shell nuclei. It is found that all of the three parameter sets can give satisfactory description on properties of nuclear matter and finite nuclei, meanwhile they can also predict the larger neutron star mass around $2.3M_\\odot$ without the hypero...
Quark mean field model with pion and gluon corrections
Xing, Xueyong; Hu, Jinniu; Shen, Hong
2016-10-01
The properties of nuclear matter and finite nuclei are studied within the quark mean field (QMF) model by taking the effects of pions and gluons into account at the quark level. The nucleon is described as the combination of three constituent quarks confined by a harmonic oscillator potential. To satisfy the spirit of QCD theory, the contributions of pions and gluons on the nucleon structure are treated in second-order perturbation theory. In a nuclear many-body system, nucleons interact with each other by exchanging mesons between quarks. With different constituent quark mass, mq, we determine three parameter sets for the coupling constants between mesons and quarks, named QMF-NK1, QMF-NK2, and QMF-NK3, by fitting the ground-state properties of several closed-shell nuclei. It is found that all of the three parameter sets can give a satisfactory description of properties of nuclear matter and finite nuclei, moreover they also predict a larger neutron star mass around 2.3 M⊙ without hyperon degrees of freedom.
Nuclear mean field from chiral pion-nucleon dynamics
Kaiser, N; Weise, W
2002-01-01
Using the two-loop approximation of chiral perturbation theory, we calculate the momentum- and density-dependent single-particle potential of nucleons in isospin-symmetric nuclear matter. The contributions from one- and two-pion exchange diagrams give rise to a potential depth for a nucleon at rest of U(0,k sub f sub 0)=-53.2 MeV at saturation density. The momentum dependence of the real part of the single-particle potential U(p,k sub f sub 0) is nonmonotonic and can be translated into a mean effective nucleon mass of M*bar approx =0.8M. The imaginary part of the single-particle potential W(p,k sub f) is generated to that order entirely by iterated one-pion exchange. The resulting half width of a nucleon hole-state at the bottom of the Fermi sea comes out as W(0,k sub f sub 0)=29.7 MeV. The basic theorems of Hugenholtz-Van-Hove and Luttinger are satisfied in our perturbative two-loop calculation of the nuclear mean field.
Modeling distributed axonal delays in mean-field brain dynamics
Roberts, J. A.; Robinson, P. A.
2008-11-01
The range of conduction delays between connected neuronal populations is often modeled as a single discrete delay, assumed to be an effective value averaging over all fiber velocities. This paper shows the effects of distributed delays on signal propagation. A distribution acts as a linear filter, imposing an upper frequency cutoff that is inversely proportional to the delay width. Distributed thalamocortical and corticothalamic delays are incorporated into a physiologically based mean-field model of the cortex and thalamus to illustrate their effects on the electroencephalogram (EEG). The power spectrum is acutely sensitive to the width of the thalamocortical delay distribution, and more so than the corticothalamic distribution, because all input signals must travel along the thalamocortical pathway. This imposes a cutoff frequency above which the spectrum is overly damped. The positions of spectral peaks in the resting EEG depend primarily on the distribution mean, with only weak dependences on distribution width. Increasing distribution width increases the stability of fixed point solutions. A single discrete delay successfully approximates a distribution for frequencies below a cutoff that is inversely proportional to the delay width, provided that other model parameters are moderately adjusted. A pair of discrete delays together having the same mean, variance, and skewness as the distribution approximates the distribution over the same frequency range without needing parameter adjustment. Delay distributions with large fractional widths are well approximated by low-order differential equations.
A Mean-Field Theory for Coarsening Faceted Surfaces
Norris, Scott A
2009-01-01
A mean-field theory is developed for the scale-invariant length distributions observed during the coarsening of one-dimensional faceted surfaces. This theory closely follows the Lifshitz-Slyozov-Wagner theory of Ostwald ripening in two-phase systems [1-3], but the mechanism of coarsening in faceted surfaces requires the addition of convolution terms recalling the work of Smoluchowski [4] and Schumann [5] on coalescence. The model is solved by the exponential distribution, but agreement with experiment is limited by the assumption that neighboring facet lengths are uncorrelated. However, the method concisely describes the essential processes operating in the scaling state, illuminates a clear path for future refinement, and offers a framework for the investigation of faceted surfaces evolving under arbitrary dynamics. [1] I. Lifshitz, V. Slezov, Soviet Physics JETP 38 (1959) 331-339. [2] I. Lifshitz, V. Slyozov, J. Phys. Chem. Solids 19 (1961) 35-50. [3] C. Wagner, Elektrochemie 65 (1961) 581-591. [4] M. von S...
Spectral Synthesis via Mean Field approach to Independent Component Analysis
Hu, Ning; Su, Shan-Shan; Kong, Xu
2016-03-01
We apply a new statistical analysis technique, the Mean Field approach to Independent Component Analysis (MF-ICA) in a Bayseian framework, to galaxy spectral analysis. This algorithm can compress a stellar spectral library into a few Independent Components (ICs), and the galaxy spectrum can be reconstructed by these ICs. Compared to other algorithms which decompose a galaxy spectrum into a combination of several simple stellar populations, the MF-ICA approach offers a large improvement in efficiency. To check the reliability of this spectral analysis method, three different methods are used: (1) parameter recovery for simulated galaxies, (2) comparison with parameters estimated by other methods, and (3) consistency test of parameters derived with galaxies from the Sloan Digital Sky Survey. We find that our MF-ICA method can not only fit the observed galaxy spectra efficiently, but can also accurately recover the physical parameters of galaxies. We also apply our spectral analysis method to the DEEP2 spectroscopic data, and find it can provide excellent fitting results for low signal-to-noise spectra.
Metastability for the Exclusion Process with Mean-Field Interaction
Asselah, Amine; Giacomin, Giambattista
1998-12-01
We consider an exclusion particle system with long-range, mean-field-type interactions at temperature 1/β. The hydrodynamic limit of such a system is given by an integrodifferential equation with one conservation law on the circle C: it is the gradient flux of the Kac free energy functional F β. For β≤1, any constant function with value m ∈ [-1, +1] is the global minimizer of F β in the space \\{ u:int_C {u(x)} dx = m\\} . For β>1, F β restricted to \\{ u:int_C {u(x)} dx = m\\} may have several local minima: in particular, the constant solution may not be the absolute minimizer of F β. We therefore study the long-time behavior of the particle system when the initial condition is close to a homogeneous stable state, giving results on the time of exit from (suitable) subsets of its domain of attraction. We follow the Freidlin-Wentzell approach: first, we study in detail F β together with the time asymptotics of the solution of the hydrodynamic equation; then we study the probability of rare events for the particle system, i.e., large deviations from the hydrodynamic limit.
Mean-field study of $^{12}$C+$^{12}$C fusion
Chien, Le Hoang; Khoa, Dao T
2016-01-01
The nuclear mean-field potential arising from the $^{12}$C+$^{12}$C interaction at the low energies relevant for the astrophysical carbon burning process has been constructed within the double-folding model, using the realistic nuclear ground-state density of the $^{12}$C nucleus and the effective M3Y nucleon-nucleon (NN) interaction constructed from the G-matrix of the Paris (free) NN potential. To explore the nuclear medium effect, both the original density independent M3Y-Paris interaction and its density dependent CDM3Y6 version have been used in the folding model calculation of the $^{12}$C+$^{12}$C potential. The folded potentials at the different energies were used in the optical model description of the elastic $^{12}$C+$^{12}$C scattering at the energies around and below the Coulomb barrier, as well as in the barrier penetration model to estimate the fusion cross section and astrophysical $S$ factor of the $^{12}$C+$^{12}$C reactions at the low energies. The obtained results are in good agreement wit...
Individual based and mean-field modeling of direct aggregation
Burger, Martin
2013-10-01
We introduce two models of biological aggregation, based on randomly moving particles with individual stochasticity depending on the perceived average population density in their neighborhood. In the firstorder model the location of each individual is subject to a density-dependent random walk, while in the second-order model the density-dependent random walk acts on the velocity variable, together with a density-dependent damping term. The main novelty of our models is that we do not assume any explicit aggregative force acting on the individuals; instead, aggregation is obtained exclusively by reducing the individual stochasticity in response to higher perceived density. We formally derive the corresponding mean-field limits, leading to nonlocal degenerate diffusions. Then, we carry out the mathematical analysis of the first-order model, in particular, we prove the existence of weak solutions and show that it allows for measure-valued steady states. We also perform linear stability analysis and identify conditions for pattern formation. Moreover, we discuss the role of the nonlocality for well-posedness of the first-order model. Finally, we present results of numerical simulations for both the first- and second-order model on the individual-based and continuum levels of description. 2012 Elsevier B.V. All rights reserved.
Real-space renormalized dynamical mean field theory
Kubota, Dai; Sakai, Shiro; Imada, Masatoshi
2016-05-01
We propose real-space renormalized dynamical mean field theory (rr-DMFT) to deal with large clusters in the framework of a cluster extension of the DMFT. In the rr-DMFT, large clusters are decomposed into multiple smaller clusters through a real-space renormalization. In this work, the renormalization effect is taken into account only at the lowest order with respect to the intercluster coupling, which nonetheless reproduces exactly both the noninteracting and atomic limits. Our method allows us large cluster-size calculations which are intractable with the conventional cluster extensions of the DMFT with impurity solvers, such as the continuous-time quantum Monte Carlo and exact diagonalization methods. We benchmark the rr-DMFT for the two-dimensional Hubbard model on a square lattice at and away from half filling, where the spatial correlations play important roles. Our results on the spin structure factor indicate that the growth of the antiferromagnetic spin correlation is taken into account beyond the decomposed cluster size. We also show that the self-energy obtained from the large-cluster solver is reproduced by our method better than the solution obtained directly for the smaller cluster. When applied to the Mott metal-insulator transition, the rr-DMFT is able to reproduce the reduced critical value for the Coulomb interaction comparable to the large cluster result.
Fast lattice Boltzmann solver for relativistic hydrodynamics.
Mendoza, M; Boghosian, B M; Herrmann, H J; Succi, S
2010-07-01
A lattice Boltzmann formulation for relativistic fluids is presented and numerically validated through quantitative comparison with recent hydrodynamic simulations of relativistic fluids. In order to illustrate its capability to handle complex geometries, the scheme is also applied to the case of a three-dimensional relativistic shock wave, generated by a supernova explosion, impacting on a massive interstellar cloud. This formulation opens up the possibility of exporting the proven advantages of lattice Boltzmann methods, namely, computational efficiency and easy handling of complex geometries, to the context of (mildly) relativistic fluid dynamics at large, from quark-gluon plasmas up to supernovae with relativistic outflows.
Relativistic MHD with Adaptive Mesh Refinement
Anderson, M; Liebling, S L; Neilsen, D; Anderson, Matthew; Hirschmann, Eric; Liebling, Steven L.; Neilsen, David
2006-01-01
We solve the relativistic magnetohydrodynamics (MHD) equations using a finite difference Convex ENO method (CENO) in 3+1 dimensions within a distributed parallel adaptive mesh refinement (AMR) infrastructure. In flat space we examine a Balsara blast wave problem along with a spherical blast wave and a relativistic rotor test both with unigrid and AMR simulations. The AMR simulations substantially improve performance while reproducing the resolution equivalent unigrid simulation results. We also investigate the impact of hyperbolic divergence cleaning for the spherical blast wave and relativistic rotor. We include unigrid and mesh refinement parallel performance measurements for the spherical blast wave.
Combining Few-Body Cluster Structures with Many-Body Mean-Field Methods
Hove, D.; Garrido, E.; Jensen, A. S.; Sarriguren, P.; Fynbo, H. O. U.; Fedorov, D. V.; Zinner, N. T.
2017-03-01
Nuclear cluster physics implicitly assumes a distinction between groups of degrees-of-freedom, that is the (frozen) intrinsic and (explicitly treated) relative cluster motion. We formulate a realistic and practical method to describe the coupled motion of these two sets of degrees-of-freedom. We derive a coupled set of differential equations for the system using the phenomenologically adjusted effective in-medium Skyrme type of nucleon-nucleon interaction. We select a two-nucleon plus core system where the mean-field approximation corresponding to the Skyrme interaction is used for the core. A hyperspherical adiabatic expansion of the Faddeev equations is used for the relative cluster motion. We shall specifically compare both the structure and the decay mechanism found from the traditional three-body calculations with the result using the new boundary condition provided by the full microscopic structure at small distance. The extended Hilbert space guaranties an improved wave function compared to both mean-field and three-body solutions. We shall investigate the structures and decay mechanism of ^{22}C (^{20}C+n+n). In conclusion, we have developed a method combining nuclear few- and many-body techniques without losing the descriptive power of each approximation at medium-to-large distances and small distances respectively. The coupled set of equations are solved self-consistently, and both structure and dynamic evolution are studied.
Isospin-symmetry-breaking effects in A∼70 nuclei within beyond-mean-field approach
Petrovici, A.; Andrei, O. [National Institute for Physics and Nuclear Engineering, R-077125 Bucharest (Romania)
2015-02-24
Particular isospin-symmetry-breaking probes including Coulomb energy differences (CED), mirror energy differences (MED), and triplet energy differences (TED) manifest anomalies in the A∼70 isovector triplets of nuclei. The structure of proton-rich nuclei in the A∼70 mass region suggests shape coexistence and competition between pairing correlations in different channels. Recent results concerning the interplay between isospin-mixing and shape-coexistence effects on exotic phenomena in A∼70 nuclei obtained within the beyond-mean-field complex Excited Vampir variational model with symmetry projection before variation using a realistic effective interaction in a relatively large model space are presented. Excited Vampir predictions concerning the Gamow-Teller β decay to the odd-odd N=Z {sup 66}As and {sup 70}Br nuclei correlated with the pair structure analysis in the T=1 and T=0 channel of the involved wave functions are discussed.
Ground state correlations and mean field in 16O
Heisenberg, Jochen H.; Mihaila, Bogdan
1999-03-01
We use the coupled cluster expansion [exp(S) method] to generate the complete ground state correlations due to the NN interaction. Part of this procedure is the calculation of the two-body G matrix inside the nucleus in which it is being used. This formalism is being applied to 16O in a configuration space of 50ħω. The resulting ground state wave function is used to calculate the binding energy and one- and two-body densities for the ground state of 16O.
Ground state correlations and mean-field in $^{16}$O
Heisenberg, J H; Heisenberg, Jochen H.; Mihaila, Bogdan.
1999-01-01
We use the coupled cluster expansion ($\\exp(S)$ method) to generate the complete ground state correlations due to the $NN$ interaction. Part of this procedure is the calculation of the two-body ${\\mathbf G}$ matrix inside the nucleus in which it is being used. This formalism is being applied to $^{16}$O in a configuration space of 35 $\\hbar\\omega$. The resulting ground state wave function is used to calculate the binding energy and one- and two-body densities for the ground state of~$^{16}$O.
Luciano, Rezzolla
2013-01-01
Relativistic hydrodynamics is a very successful theoretical framework to describe the dynamics of matter from scales as small as those of colliding elementary particles, up to the largest scales in the universe. This book provides an up-to-date, lively, and approachable introduction to the mathematical formalism, numerical techniques, and applications of relativistic hydrodynamics. The topic is typically covered either by very formal or by very phenomenological books, but is instead presented here in a form that will be appreciated both by students and researchers in the field. The topics covered in the book are the results of work carried out over the last 40 years, which can be found in rather technical research articles with dissimilar notations and styles. The book is not just a collection of scattered information, but a well-organized description of relativistic hydrodynamics, from the basic principles of statistical kinetic theory, down to the technical aspects of numerical methods devised for the solut...
Mean-field concept and direct numerical simulations of rotating magnetoconvection and the geodynamo
Schrinner, M; Schmitt, D; Rheinhardt, M; Christensen, U R
2006-01-01
A comparison is made between mean-field models and direct numerical simulations of rotating magnetoconvection and the geodynamo. The mean-field coefficients are calculated with the fluid velocity taken from the direct numerical simulations. The magnetic fields resulting from mean-field models are then compared with the mean magnetic field from the direct numerical simulations.
Fang, F; Clayton, C E; Marsh, K A; Pak, A E; Ralph, J E; Joshi, C [Department of Electrical Engineering, University of California, Los Angeles, CA 90095 (United States); Lopes, N C [Grupo de Lasers e Plasmas, Instituto Superior Tecnico, Lisbon (Portugal)], E-mail: cclayton@ucla.edu
2009-02-15
In a forced laser-wakefield accelerator experiment (Malka et al 2002 Science 298 1596) where the length of the pump laser pulse is a few plasma periods long, the leading edge of the laser pulse undergoes frequency downshifting and head erosion as the laser energy is transferred to the wake. Therefore, after some propagation distance, the group velocity of the leading edge of the pump pulse-and thus of the driven electron plasma wave-will slow down. This can have implications for the dephasing length of the accelerated electrons and therefore needs to be understood experimentally. We have carried out an experimental investigation where we have measured the velocity v{sub f} of the 'wave-front' of the plasma wave driven by a nominally 50 fs (full width half maximum), intense (a{sub 0} {approx_equal} 1), 0.815 {mu}m laser pulse. To determine the speed of the wave front, time- and space-resolved refractometry, interferometry and Thomson scattering were used. Although a laser pulse propagating through a relatively low-density plasma (n{sub e} = 1.3 x 10{sup 19} cm{sup -3}) showed no measurable changes in v{sub f} over 1.3 mm (and no accelerated electrons), a high-density plasma (n{sub e} = 5 x 10{sup 19} cm{sup -3}) generated accelerated electrons and showed a continuous change in v{sub f} as the laser pulse propagated through the plasma. Possible causes and consequences of the observed v{sub f} evolution are discussed.
Magnetic Dissipation in Relativistic Jets
Yosuke Mizuno
2016-10-01
Full Text Available The most promising mechanisms for producing and accelerating relativistic jets, and maintaining collimated structure of relativistic jets involve magnetohydrodynamical (MHD processes. We have investigated the magnetic dissipation mechanism in relativistic jets via relativistic MHD simulations. We found that the relativistic jets involving a helical magnetic field are unstable for the current-driven kink instability, which leads to helically distorted structure in relativistic jets. We identified the regions of high current density in filamentary current sheets, indicative of magnetic reconnection, which are associated to the kink unstable regions and correlated to the converted regions of magnetic to kinetic energies of the jets. We also found that an over-pressured relativistic jet leads to the generation of a series of stationary recollimation shocks and rarefaction structures by the nonlinear interaction of shocks and rarefaction waves. The differences in the recollimation shock structure due to the difference of the magnetic field topologies and strengths may be observable through mm-VLBI observations and space-VLBI mission.
Mean field spin glasses treated with PDE techniques
Barra, Adriano; Del Ferraro, Gino; Tantari, Daniele
2013-07-01
Following an original idea of Guerra, in these notes we analyze the Sherrington-Kirkpatrick model from different perspectives, all sharing the underlying approach which consists in linking the resolution of the statistical mechanics of the model (e.g. solving for the free energy) to well-known partial differential equation (PDE) problems (in suitable spaces). The plan is then to solve the related PDE using techniques involved in their native field and lastly bringing back the solution in the proper statistical mechanics framework. Within this strand, after a streamlined test-case on the Curie-Weiss model to highlight the methods more than the physics behind, we solve the SK both at the replica symmetric and at the 1-RSB level, obtaining the correct expression for the free energy via an analogy to a Fourier equation and for the self-consistencies with an analogy to a Burger equation, whose shock wave develops exactly at critical noise level (triggering the phase transition). Our approach, beyond acting as a new alternative method (with respect to the standard routes) for tackling the complexity of spin glasses, links symmetries in PDE theory with constraints in statistical mechanics and, as a novel result from the theoretical physics perspective, we obtain a new class of polynomial identities (namely of Aizenman-Contucci type, but merged within the Guerra's broken replica measures), whose interest lies in understanding, via the recent Panchenko breakthroughs, how to force the overlap organization to the ultrametric tree predicted by Parisi.
Chen, Zaigao; Wang, Jianguo; Wang, Yue
2016-09-01
The cathode plasma expansion has been widely investigated and is recognized as impedance collapse in a relativistic backward wave oscillator (RBWO). However, the process of formation and expansion of cathode plasma is very complicated, and the thickness of plasma is only several millimeters, so the simulation of cathode plasma requires high temporal and spatial resolutions. Only the scaled-down diode model and the thin gas layer model are considered in the previous hybrid simulation, and there are few numerical studies on the effect of cathode plasma expansion on the RBWO. In this paper, the moving-boundary conformal particle-in-cell method is proposed; the cathode plasma front is treated in this novel method as the actual cathode surface, and the explosive electron emission boundary moves as the expansion of cathode plasma. Moreover, in order to accurately simulate the electromagnetic field near the cathode surface, the conformal finite-difference time-domain method based on the enlarged cell technique is adopted. The numerical simulation indicates that the diode voltage decreases and the beam current increases as cathode plasma expands; when the cathode plasma velocity is 10 cm/μs, the pulse duration of the generated microwave decreases from 30 ns to 10 ns, the working frequency decreases from 9.83 GHz to 9.64 GHz, and the output power decreases 30% in the course of cathode plasma expansion.
Lattice Boltzmann equation for relativistic quantum mechanics.
Succi, Sauro
2002-03-15
Relativistic versions of the quantum lattice Boltzmann equation are discussed. It is shown that the inclusion of nonlinear interactions requires the standard collision operator to be replaced by a pair of dynamic fields coupling to the relativistic wave function in a way which can be described by a multicomponent complex lattice Boltzmann equation.
A relativistic symmetry in nuclei
Ginocchio, J N [MS B283, Theoretical Division, Los Alamos National Laboratory Los Alamos, New Mexico 87545 (Mexico)
2007-11-15
We review some of the empirical and theoretical evidence supporting pseudospin symmetry in nuclei as a relativistic symmetry. We review the case that the eigenfunctions of realistic relativistic nuclear mean fields approximately conserve pseudospin symmetry in nuclei. We discuss the implications of pseudospin symmetry for magnetic dipole transitions and Gamow-Teller transitions between states in pseudospin doublets. We explore a more fundamental rationale for pseudospin symmetry in terms of quantum chromodynamics (QCD), the basic theory of the strong interactions. We show that pseudospin symmetry in nuclei implies spin symmetry for an anti-nucleon in a nuclear environment. We also discuss the future and what role pseudospin symmetry may be expected to play in an effective field theory of nucleons.
Haba, Z
2009-02-01
We discuss relativistic diffusion in proper time in the approach of Schay (Ph.D. thesis, Princeton University, Princeton, NJ, 1961) and Dudley [Ark. Mat. 6, 241 (1965)]. We derive (Langevin) stochastic differential equations in various coordinates. We show that in some coordinates the stochastic differential equations become linear. We obtain momentum probability distribution in an explicit form. We discuss a relativistic particle diffusing in an external electromagnetic field. We solve the Langevin equations in the case of parallel electric and magnetic fields. We derive a kinetic equation for the evolution of the probability distribution. We discuss drag terms leading to an equilibrium distribution. The relativistic analog of the Ornstein-Uhlenbeck process is not unique. We show that if the drag comes from a diffusion approximation to the master equation then its form is strongly restricted. The drag leading to the Tsallis equilibrium distribution satisfies this restriction whereas the one of the Jüttner distribution does not. We show that any function of the relativistic energy can be the equilibrium distribution for a particle in a static electric field. A preliminary study of the time evolution with friction is presented. It is shown that the problem is equivalent to quantum mechanics of a particle moving on a hyperboloid with a potential determined by the drag. A relation to diffusions appearing in heavy ion collisions is briefly discussed.
Sahoo, Raghunath
2016-01-01
This lecture note covers Relativistic Kinematics, which is very useful for the beginners in the field of high-energy physics. A very practical approach has been taken, which answers "why and how" of the kinematics useful for students working in the related areas.
Khazanov, G. V.; Tel'nikhin, A. A.; Kronberg, T. K.
2007-01-01
In the Hamiltonian approach an electron motion in a coherent packet of the whistler mode waves propagating along the direction of an ambient magnetic field is studied. The physical processes by which these particles are accelerated to high energy are established. Equations governing a particle motion were transformed in to a closed pair of nonlinear difference equations. The solutions of these equations have shown there exists the energetic threshold below that the electron motion is regular, and when the initial energy is above the threshold an electron moves stochastically. Particle energy spectra and pitch angle electron scattering are described by the Fokker-Planck-Kolmogorov equations. Calculating the stochastic diffusion of electrons due to a spectrum of whistler modes is presented. The parametric dependence of the diffusion coefficients on the plasma particle density, magnitude of wave field, and the strength of magnetic field is studies. It is shown that significant pitch angle diffusion occurs for the Earth radiation belt electrons with energies from a few keV up to a few MeV.
Lu, K Q; Li, Z P; Yao, J M; Meng, J
2015-01-01
We report the first global study of dynamic correlation energies (DCEs) associated with rotational motion and quadrupole shape vibrational motion in a covariant energy density functional (CEDF) for 575 even-even nuclei with proton numbers ranging from $Z=8$ to $Z=108$ by solving a five-dimensional collective Hamiltonian, the collective parameters of which are determined from triaxial relativistic mean-field plus BCS calculation using the PC-PK1 force. After taking into account these beyond mean-field DCEs, the root-mean-square (rms) deviation with respect to nuclear masses is reduced significantly down to 1.14 MeV, which is smaller than those of other successful CEDFs: NL3* (2.96 MeV), DD-ME2 (2.39 MeV), DD-ME$\\delta$ (2.29 MeV) and DD-PC1 (2.01 MeV). Moreover, the rms deviation for two-nucleon separation energies is reduced by $\\sim34\\%$ in comparison with cranking prescription.
Relativistic Cyclotron Instability in Anisotropic Plasmas
López, Rodrigo A.; Moya, Pablo S.; Navarro, Roberto E.; Araneda, Jaime A.; Muñoz, Víctor; Viñas, Adolfo F.; Alejandro Valdivia, J.
2016-11-01
A sufficiently large temperature anisotropy can sometimes drive various types of electromagnetic plasma micro-instabilities, which can play an important role in the dynamics of relativistic pair plasmas in space, astrophysics, and laboratory environments. Here, we provide a detailed description of the cyclotron instability of parallel propagating electromagnetic waves in relativistic pair plasmas on the basis of a relativistic anisotropic distribution function. Using plasma kinetic theory and particle-in-cell simulations, we study the influence of the relativistic temperature and the temperature anisotropy on the collective and noncollective modes of these plasmas. Growth rates and dispersion curves from the linear theory show a good agreement with simulations results.
Vladimirov, Andrey E; Ellison, Donald C
2009-01-01
We model strong forward shocks in young supernova remnants with efficient particle acceleration where a nonresonant instability driven by the cosmic ray current amplifies magnetic turbulence in the shock precursor. Particle injection, magnetic field amplification (MFA) and the nonlinear feedback of particles and fields on the bulk flow are derived consistently. The shock structure depends critically on the efficiency of turbulence cascading. If cascading is suppressed, MFA is strong, the shock precursor is stratified, and the turbulence spectrum contains several discrete peaks. These peaks, as well as the amount of MFA, should influence synchrotron X-rays, allowing observational tests of cascading and other assumptions intrinsic to the nonlinear model of nonresonant wave growth.
Smoller, Joel
2012-01-01
We prove that the Einstein equations in Standard Schwarzschild Coordinates close to form a system of three ordinary differential equations for a family of spherically symmetric, self-similar expansion waves, and the critical ($k=0$) Friedmann universe associated with the pure radiation phase of the Standard Model of Cosmology (FRW), is embedded as a single point in this family. Removing a scaling law and imposing regularity at the center, we prove that the family reduces to an implicitly defined one parameter family of distinct spacetimes determined by the value of a new {\\it acceleration parameter} $a$, such that $a=1$ corresponds to FRW. We prove that all self-similar spacetimes in the family are distinct from the non-critical $k\
Pireaux, S
2008-01-01
The Relativistic Motion Integrator (RMI) consists in integrating numerically the EXACT relativistic equations of motion, with respect to the appropriate gravitational metric, instead of Newtonian equations plus relativistic corrections. The aim of the present paper is to validate the method, and to illustrate how RMI can be used for space missions to produce relativistic ephemerides of satellites. Indeed, nowadays, relativistic effects have to be taken into account, and comparing a RMI ephemeris with a classical keplerian one helps to quantify such effects. LISA is a relevant example to use RMI. This mission is an interferometer formed by three spacecraft which aims at the detection of gravitational waves. Precise ephemerides of LISA spacecraft are needed not only for the sake of the orbitography but also to compute the photon flight time in laser links between spacecraft, required in LISA data pre-processing in order to reach the gravitational wave detection level. Relativistic effects in LISA orbitography n...
Kouno, H.; Kakuta, N.; Noda, N.; Koide, K.; Mitsumori, T.; Hasegawa, A.; Nakano, M. (Department of Physics, Saga University, Saga 840 (Japan))
1995-04-01
We have studied the equations of state of nuclear matter using the nonlinear [sigma]-[omega] model. At the normal density, there is a strong correlation among the effective nucleon mass [ital M][sub 0][sup *], the incompressibility, [ital K] and the third derivative [ital K][prime] of binding energy. The results are compared with the empirical analysis of the giant isoscalar monopole resonances data. It is difficult to fit the data when [ital K][approx lt]200 MeV, using the model. It is also found that [ital K]=300[plus minus]50 MeV is favorable to account for the volume-symmetry properties of nuclear matter.
Alpha-decay chains of $^{288}_{173}115$ and $^{287}_{172}115$ in the Relativistic Mean Field theory
Geng, L S; Meng, J
2003-01-01
The results of experiments designed to synthesize element 115 in the $^{243}$Am+$^{48}$Ca reaction are reported at Dubna in Russia \\cite{ogan.03}. With a beam dose of $4.3\\times 10^{18}$ 248-MeV $^{48}$Ca projectiles, three similar decay chains consisting of five consecutive $\\alpha$-decays are observed. At a higher bombarding energy of 253 MeV, with an equal $^{48}$Ca beam dose, a different decay chain of four consecutive $\\alpha$-decays are detected. The decay properties of these synthesized nuclei are consistent with consecutive $\\alpha$-decay originating from the parent isotopes of the new element 115, $^{288}115$ and $^{287}115$, respectively. In the present work, the recently developed deformed RMF+BCS method with a density-independent delta-function interaction in the pairing channel is applied to the analysis of these newly synthesized superheavy nuclei $^{288}115$, $^{287}115$, and their $\\alpha$-decay daughter nuclei. The calculated $\\alpha$-decay energies and half-lives agree well with the experime...
Classical simulation of relativistic Zitterbewegung in photonic lattices.
Dreisow, Felix; Heinrich, Matthias; Keil, Robert; Tünnermann, Andreas; Nolte, Stefan; Longhi, Stefano; Szameit, Alexander
2010-10-01
We present the first experimental realization of an optical analog for relativistic quantum mechanics by simulating the Zitterbewegung (trembling motion) of a free Dirac electron in an optical superlattice. Our photonic setting enables a direct visualization of Zitterbewegung as a spatial oscillatory motion of an optical beam. Direct measurements of the wave packet expectation values in superlattices with tuned miniband gaps clearly show the transition from weak-relativistic to relativistic and far-relativistic regimes.
State-of-the-art of beyond mean field theories with nuclear density functionals
Egido, J. Luis
2016-07-01
We present an overview of different beyond mean field theories (BMFTs) based on the generator coordinate method (GCM) and the recovery of symmetries used in many body nuclear physics with effective forces. In a first step a short reminder of the Hartree-Fock-Bogoliubov (HFB) theory is given. A general discussion of the shortcomings of any mean field approximation (MFA), stemming either from the lack of the elementary symmetries (like particle number and angular momentum) or the absence of fluctuations around the mean values, is presented. The recovery of the symmetries spontaneously broken in the HFB approach, in particular the angular momentum, is necessary, among others, to describe excited states and transitions. Particle number projection is also needed to guarantee the right number of protons and neutrons. Furthermore a projection before the variation prevents the pairing collapse in the weak pairing regime. A whole chapter is devoted to illustrate with examples the convenience of recovering symmetries and the differences between the projection before and after the variation. The lack of fluctuations around the average values of the MFA is a big shortcoming inherent to this approach. To build in correlations in BMFT one selects the relevant degrees of freedom of the atomic nucleus. In the low energy part of the spectrum these are the quadrupole, octupole and the pairing vibrations as well as the single particle degrees of freedom. In the GCM the operators representing these degrees of freedom are used as coordinates to generate, by the constrained (projected) HFB theory, a collective subspace. The highly correlated GCM wave function is finally written as a linear combination of a projected basis of this space. The variation of the coefficients of the linear combination leads to the Hill-Wheeler equation. The flexibility of the GCM Ansatz allows to describe a whole palette of physical situations by conveniently choosing the generator coordinates. We discuss the
Hakim, Rémi
1994-01-01
Il existe à l'heure actuelle un certain nombre de théories relativistes de la gravitation compatibles avec l'expérience et l'observation. Toutefois, la relativité générale d'Einstein fut historiquement la première à fournir des résultats théoriques corrects en accord précis avec les faits.
The Accuracy of Mean-Field Approximation for Susceptible-Infected-Susceptible Epidemic Spreading
Qu, Bo
2016-01-01
The epidemic spreading has been studied for years by applying the mean-field approach in both homogeneous case, where each node may get infected by an infected neighbor with the same rate, and heterogeneous case, where the infection rates between different pairs of nodes are different. Researchers have discussed whether the mean-field approaches could accurately describe the epidemic spreading for the homogeneous cases but not for the heterogeneous cases. In this paper, we explore under what conditions the mean-field approach could perform well when the infection rates are heterogeneous. In particular, we employ the Susceptible-Infected-Susceptible (SIS) model and compare the average fraction of infected nodes in the metastable state obtained by the continuous-time simulation and the mean-field approximation. We concentrate on an individual-based mean-field approximation called the N-intertwined Mean Field Approximation (NIMFA), which is an advanced approach considered the underlying network topology. Moreove...
Zhang Hong Lin
2002-01-01
Relativistic distorted-wave collision strengths have been calculated for the 45 DELTA n=0 transitions with n=2 in the 79 O-like ions with nuclear charge number Z in the range 14<=Z<=92. The calculations were made for the six final, or scattered, electron energies E'=0.03, 0.08, 0.20, 0.42, 0.80, and 1.40, where E' is in units of Z sup 2 sub e sub f sub f Ry with Z sub e sub f sub f =Z-5.83. In addition, the transition energies and electric dipole oscillator strengths are given. To our knowledge the present work is the first comprehensive publication of the results of fully relativistic calculations of the collision strengths for excitation of highly charged O-like ions.
Optimized $\\delta$ expansion for relativistic nuclear models
Krein, G I; Peres-Menezes, D; Nielsen, M; Pinto, M B
1998-01-01
The optimized $\\delta$-expansion is a nonperturbative approach for field theoretic models which combines the techniques of perturbation theory and the variational principle. This technique is discussed in the $\\lambda \\phi^4$ model and then implemented in the Walecka model for the equation of state of nuclear matter. The results obtained with the $\\delta$ expansion are compared with those obtained with the traditional mean field, relativistic Hartree and Hartree-Fock approximations.
The First Principle Formula of the Relativistic Heat Conductivity of Coulomb Electronic Plasmas
TIAN Chu-Shun; ZHANG Chi; LU Quan-Kang
2001-01-01
Making use of the relativistic BBGKY technique,the relativistic generalization of Landau collision integral is obtained.Furthermore,we calculate the relativistic hydrodynamic modes up to the second order in the hydrodynamic wave number.Combining Résibois' method,we present the first principle formula of the relativistic heat conductivity of Coulomb electronic plasmas for low-order corrections.