Robust and accurate filtered spherical harmonics expansions for radiative transfer

We present a novel application of filters to the spherical harmonics (P_N) expansion for radiative transfer problems in the high-energy-density regime. The filter we use is based on non-oscillatory spherical splines and a filter strength chosen to (i) preserve the equilibrium diffusion limit and (ii) vanish as the expansion order tends to infinity. Our implementation is based on modified equations that are derived by applying the filter after every time step in a simple first-order time integration scheme. The method is readily applied to existing codes that solve the P_N equations. Numerical results demonstrate that the solution to the filtered P_N equations are (i) more robust and less oscillatory than standard P_N solutions and (ii) more accurate than discrete ordinates solutions of comparable order. In particular, the filtered P₇ solution demonstrates comparable accuracy to an implicit Monte Carlo solution for a benchmark hohlraum problem in 2D Cartesian geometry.     

Stochastic (white noise) analysis of resonant absorption in laser generated plasma

We suggest to use stochastic differential equations for laser-plasma problems. Using this technique we solve analytically the motion of the electrons at the critical layer and calculate the density profile scaling length (L). For an Nd laser flux of 10¹⁷ W/cm² we estimate L ≈ 0.15 μm, while for a CO₂ laser flux of 10¹⁵ W/cm² we get L ≈ 1.5 μm.     

The Lorenz model for single-mode homogeneously broadened laser: analytical determination of the unpredictable zone

We have applied harmonic expansion to derive an analytical solution for the Lorenz-Haken equations. This method is used to describe the regular and periodic self-pulsing regime of the single mode homogeneously broadened laser. These periodic solutions emerge when the ratio of the population decay rate ? is smaller than 0:11. We have also demonstrated the tendency of the Lorenz-Haken dissipative system to behave periodic for a characteristic pumping rate “2C _P ”[7], close to the second laser threshold “2C _2th ”(threshold of instability). When the pumping parameter “2C” increases, the laser undergoes a period doubling sequence. This cascade of period doubling leads towards chaos. We study this type of solutions and indicate the zone of the control parameters for which the system undergoes irregular pulsing solutions. We had previously applied this analytical procedure to derive the amplitude of the first, third and fifth order harmonics for the laser-field expansion [7, 17]. In this work, we extend this method in the aim of obtaining the higher harmonics. We show that this iterative method is indeed limited to the fifth order, and that above, the obtained analytical solution diverges from the numerical direct resolution of the equations.     

啁啾激光与半周期脉冲形成的组合场驱动原子产生单个阿秒脉冲

提出了由波长为800 nm、脉冲宽度为5 fs的啁啾激光与半周期脉冲形成组合场,并利用这种组合场驱动一维模型氦原子获得单个阿秒脉冲. 通过数值求解一维氦原子的含时薛定谔方程,发现氦原子在组合场驱动下高次谐波谱的截止位置可以扩展到I_p+21.6U_p. 对第二平台区域不同范围内高次谐波的叠加都能得到单个阿秒脉冲,最短可达37 as,特别是对平台区域的前端进行叠加不仅能够得到较短的单个阿秒脉冲,而且与截止位置附近高次谐波构造的阿秒脉冲相比,强度提高了3个数量级. 关键词： 啁啾激光场 半周期脉冲 高次谐波 阿秒脉冲     

Angular spectrum representation of the electromagnetic multipole fields, and their reflection at a perfect conductor

Angular spectrum representations are derived for electric and magnetic multipole fields of arbitrary order. The result involves generalized spherical harmonics and generalized vector spherical harmonics, and the representations are in the form of integrals over the k_∥-plane. The representations are especially useful for the study of reflection and transmission of multipole radiation by a plane interface. As an example, we have considered the reflection at a perfect conductor. The reflected field of a multipole field could be expressed in the form of an angular spectrum with a very simple relation to the angular spectrum of the source field. The radiation pattern of a multipole near the perfect conductor is obtained with the method of stationary phase. We also introduce a method for determining the mirror image of the source of an arbitrary multipole.     

Quantum phase transition in the anisotropic one-dimensional XY model with long-range interactions

In this paper we study the one-dimensional XY model with single ion anisotropy and long-range interaction that decay as a power law. The model has a quantum phase transition, at zero temperature, at a critical value D_c of the anisotropy parameter D. For values of D below D_c we use a self-consistent harmonic approximation. We have found that the critical temperature increases with D for small values of this parameter. For values of D above D_c we use the bond operator technique and calculate the gap as a function of D, at zero temperature.     

Effects of internal viscous damping on the stability of a rotating shaft driven through a universal joint

A rotating flexible shaft, with both external and internal viscous damping, driven through a universal joint is considered. The mathematical model consists of a set of coupled, linear partial differential equations with time-dependent coefficients. Use of Galerkin's technique leads to a set of coupled linear differential equations with time-dependent coefficients. Using these differential equations some effects of internal viscous damping on parametric and flutter instability zones are investigated by the monodromy matrix technique. The flutter zones are also obtained on discarding the time-dependent coefficients in the differential equations which leads to an eigenvalue analysis. A one-term Galerkin approximation aided this analysis. Two different shafts (“automotive” and “lab”) were considered. Increasing internal damping is always stabilizing as regards to parametric instabilities. For flutter type instabilities it was found that increasing internal damping is always stabilizing for rotational speeds v below the first critical speed, v₁. For v>v₁, there is a value of the internal viscous damping coefficient, C_iv, which depends on the rotational speed and torque, above which destabilization occurs.The value of C_iv (“critical value”) at which the unstable zone first enters the practical range of operation was determined. The dependence of C_iv critical on the external damping was investigated. It was found for the automotive case that a four-fold increase in external damping led to an increase of about 20% of the critical value. For the lab model an increase of two orders of magnitude of the external damping led to an increase of critical value of only 10%.For the automotive shaft it was found that this critical value also removed the parametric instabilities out of the practical range. For the lab model it is not always possible to completely stabilize the system by increasing the internal damping. For this model using C_iv critical, parametric instabilities are still found in the practical range of operation.     

Elliptic PDE formulation and boundary conditions of the spherical harmonics method of arbitrary order for general three-dimensional geometries

The inherent complexity of the radiative transfer equation makes the exact treatment of radiative heat transfer impossible even for idealized situations and simple boundary conditions. Therefore, a wide variety of efficient solution methods have been developed for the RTE. Among these solution methods the spherical harmonics method, the moment method, and the discrete ordinates method provide means to obtain higher-order approximate solutions to the equation of radiative transfer. Although the assembly of the governing equations for the spherical harmonics method requires tedious algebra, their final form promises great accuracy for any given order, since it is a spectral method (rather than finite difference/finite volume in the case of discrete ordinates). In this study, a new methodology outlined in a previous paper on the spherical harmonics method (P_N) is further developed. The new methodology employs successive elimination of spherical harmonic tensors, thus reducing the number of first-order partial differential equations needed to be solved simultaneously by previous P_N approximations (=(N+1)²). The result is a relatively small set (=N(N+1)/2) of second-order, elliptic partial differential equations, which can be solved with standard PDE solution packages. General boundary conditions and supplementary conditions using rotation of spherical harmonics in terms of local coordinates are formulated for the general P_N approximation for arbitrary three-dimensional geometries. Accuracy of the P_N approximation can be further improved by applying the “modified differential approximation” approach first developed for the P₁-approximation. Numerical computations are carried out with the P₃ approximation for several new two-dimensional problems with emitting, absorbing, and scattering media. Results are compared to Monte Carlo solutions and discrete ordinates simulations and a discussion of ray effects and false scattering is provided.     

A new group theoretical technique for the analysis of Bianchi identities and its application to the auxiliary field problem of D = 5 supergravity

For any (super)group and hence for any geometrical (super)theory Bianchi identities imply that certain 3-forms vanish. In order to perform a systematic analysis of their implications in the presence of constraints one needs a complete basis of independent 3-forms spanning the 3-form linear space. In this paper we discuss a general procedure for the derivation of such a basis in the case of supersymmetric theories involving commuting spinor 1-forms. Our technique is based on the decomposition of the product of group representations into irreducible components and replaces all Fierz rearrangements. We give as examples the cases of N = 1, d = 4, N = 2, d = 4 and N = 2, d = 5 supergravity. Then applying our algebraic techniques to the last of these three models, the only other known example, besides N = 1, d = 4 supergravity, of a pure geometrical theory, we derive its off-shell structure containing 48 bosons and 48 fermions. The torsion-like constraints which we implement in the Bianchis in order to obtain our set of auxiliary fields are a subset of the complete set of variational equations of the theory so that we derive our off-shell multiplet without any reference to an embedding conformal symmetry. The point with which we still need to use ingenuity is the selection of those equations which are to be kept and those which are to be thrown out.     

Simulating radiative transfer with filtered spherical harmonics

This Letter presents a novel application of filters to the spherical harmonics (PN) expansion for radiative transfer problems in the high-energy-density regime. The filter, which is based on non-oscillatory spherical splines, preserves both the equilibrium diffusion limit and formal convergence properties of the unfiltered expansion. While the method requires further mathematical justification and computational studies, preliminary results demonstrate that solutions to the filtered PN equations are (1) more robust and less oscillatory than standard PN solutions and (2) more accurate than discrete ordinates solutions of comparable order. The filtered P₇ solution demonstrates comparable accuracy to an implicit Monte Carlo solution for a benchmark hohlraum problem. Given the benefits of this method we believe it will enable more routine use of high-fidelity radiation-hydrodynamics calculations in the simulation of physical systems.     

Negative Virial Coefficients and the Dominance of Loose Packed Diagrams for D-Dimensional Hard Spheres

We study the virial coefficients B _k of hard spheres in D dimensions by means of Monte-Carlo integration. We find that B ₅ is positive in all dimensions but that B ₆ is negative for all D≥6. For 7≤k≤17 we compute sets of Ree–Hoover diagrams and find that either for large D or large k the dominant diagrams are “loose packed.” We use these results to study the radius of convergence and the validity of the many approximations used for the equations of state for hard spheres.     

Interference of resonances in the angular distribution of hadrons in νN scattering

We present an efficient way of calculating the angular distribution of pions in the νN→μπN′ reaction in terms of spherical harmonics. Generalizing the helicity formalism to pion production from a coherent superposition of states we are able to take into account several contributing resonances. The formulas derived are model independent. For explicit numerical calculation we use results for the hadronic matrix elements obtained in the framework of the harmonic oscillator model. Our results are compared to the recent measurement of the BEBC collaboration. The refined predictions reveal a better agreement with experiment than previous calculations.     

“Artificial vacuum” for T-violation experiment

We point out the possible use of matrix isolation spectroscopy in experimental tests of fundamental physics. As a concrete example we show how this technique might be applied to measuring the T-violation electron electric dipole moment d_e. We estimate that a dipole moment could be detected down to d_e ∼ 6 × 10⁻²⁸e cm, in comparison to the current limit of d_e < 10⁻²⁴e cm.     

Elliptic dichroism, ellipticity and the offset angle of high harmonics generated by arbitrary homonuclear diatomic molecules

The nth harmonic emission rate has contributions of the components of the T-matrix element in the direction of the laser-field polarization and in the direction perpendicular to it. Using both components of the T-matrix element we present a theoretical approach for calculation of the ellipticity and the offset angle of high harmonics. The molecular bound state is represented by HOMO or by HOMO-1. We show that high harmonics, generated by molecules oriented by an angle ??_L with respect to the major semiaxis of the laserfield polarization ellipse, are elliptically polarized even if the applied field is linearly polarized. Using examples of N₂ and O₂ molecules we show the existence of extrema and sudden changes of the harmonic ellipticity and the offset angle for particular molecular alignment. The interference between different contributions to the T-matrix element depends on the molecular symmetry. Presenting partial or total parameters of elliptic dichroism in the (??_L, n) plane clear interference minima are observed. Therefore, the measurement of the elliptic dichroism may reveal information about the molecular structure and symmetry.     

Wormhole solutions in the Einstein-Yang-Mills-Higgs system: Solution of first-order equations forG=SU(2)

For anSU(2) Einstein-Yang-Mills-Higgs model we study the extreme wormhole solutions. We use an iterative method based on expansion in the radial distanceN from the boundary of the hole. Here we present the nontrivial solutions of the first-order equations. They give useful information about existing extremal wormholes. Especially we note that although the zero-order solution which we use is abelian, this is not the case for all solutions of first-order equations. The method employed in solving these equations is to expand all first-order fields in the appropriate generalized harmonics. We find a non-abelian solution if the value of the Higgs scalar at the horizon is equal to the Planck mass and if the magnetic chargeb and the electric chargee of the hole satisfyb=1/e.Work supported by Schweizerischer Nationalfonds.     

Symmetry analysis in neutron diffraction studies of magnetic structures: 3. An example: the magnetic structure of spinels

Using the symmetry analysis technique developed in the two earlier papers of this series a study is made of the magnetic structures in spinels (space group O⁷_h). The magnetic structures with the wave vector K = 0 and those with K ≠ 0 are considered in detail. As an example, an analysis is given of the magnetic ordering in MgV₂O₄ which is characterized by the three-arm star {bdK₁₀} (in Kovalev's notation) and of that in HgCr₂S₄ where a helical structure corresponding to the star {bdK₆} has been found. For each of the three stars we have determined the composition of the magnetic representation and calculated the basis functions of the irreducible representations. For the magnetic structures determined experimentally we have specified the irreducible representations by which these structures should be described. The examples furnished illustrate the typical situations liable to occur when performing symmetry analysis of magnetic structures of crystals.     

Transparent potentials at fixed energy in dimension two. Fixed-energy dispersion relations for the fast decaying potentials

For the two-dimensional Schrödinger equation $$[ - \Delta + v(x)]\psi = E\psi , x \in \mathbb{R}^2 , E = E_{fixed} > 0 (*)$$ at a fixed positive energy with a fast decaying at infinity potentialv(x) dispersion relations on the scattering data are given. Under “small norm” assumption using these dispersion relations we give (without a complete proof of sufficiency) a characterization of scattering data for the potentials from the Schwartz classS=C _∞ ^(∞) (?²). For the potentials with zero scattering amplitude at a fixed energyE _fixed (transparent potentials) we give a complete proof of this characterization. As a consequence we construct a family (parametrized by a function of one variable) of two-dimensional spherically-symmetric real potentials from the Schwartz classS transparent at a given energy. For the two-dimensional case (without assumption that the potential is small) we show that there are no nonzero real exponentially decreasing, at infinity, potentials transparent at a fixed energy. For any dimension greater or equal to 1 we prove that there are no nonzero real potentials with zero forward scattering amplitude at an energy interval. We show that KdV-type equations in dimension 2+1 related with the scattering problem (*) (the Novikov-Veselov equations) do not preserve, in general, these dispersion relations starting from the second one. As a corollary these equations do not preserve, in general, the decay rate faster than |x|^?3 for initial data from the Schwartz class.     

Resonances Generated by the Vector Meson-Baryon Dynamics

We have recently studied vector meson-octet baryon (VB) interactions with the aim to find dynamical generation of resonances in such systems. For this, we consider the s-, t-, u-channel diagrams along with a contact interaction originating from the hidden local symmetry Lagrangian. We find the contribution from all these sources, except the s-channel, to be important. The amplitudes obtained by solving the coupled channel Bethe–Salpeter equations for the systems with total strangeness zero show generation of one isospin 3/2, spin 1/2 resonance and three isospin 1/2 resonances: two with spin 3/2 and one with spin 1/2. We identify these resonances with Δ (1900) S ₃₁, N*(2080) D ₁₃, N* (1700) D ₁₃, and N*(2090) S ₁₁, respectively. Further, we briefly discuss the results of our investigation of the VB systems when coupled to the pseudoscalar meson-baryon (PB) channels. We find that the low-lying resonances couple strongly to the VB channels, a result which can be useful in studying the reactions involving pseudoscalar and vector meson exchanges. In case of the higher mass resonances (in the 1,800–2,200 MeV region), we find that some of the states claimed as dynamically generated states in the VB system can disappear due to their coupling to the PB channels. We also find that new states can appear from PB–VB coupled channel dynamics; for example, we find that a Σ resonance near 1,400 MeV gets developed due to such an effect.     

A lower bound to the π0π0 S-wave scattering length

A new lower bound to the π⁰π⁰ S-wave scattering length is found in terms of the D-wave scattering length. The main ingredients of the method are the Roy exact partial-wave equations and an extensive use of unitarity in the physical region. For a value of a₂ = 7.3 × 10^?4, we get the bound a₀ ? ?0.33.     

Zakharov equations with zeroth harmonic and a new type of modulation instability

It has been shown that the system of Zakharov equations for the amplitudes of the first and zeroth harmonics of the waves on the surface of an ideal liquid describes not only the known type of the modulation instability of the envelope of the main harmonic with respect to harmonic perturbations with small wave vectors κ (Benjamin-Feier modulation instability), but also the modulation instability of a combination of the main and zeroth harmonics at κ values on the order of the wave vector k ₀ of the main harmonic. In contrast to the Benjamin-Feier modulation instability typical for large depths, the described modulation instability does not disappear at k ₀ h < 1.363.