The shape gradient of the least-squares objective functional in optimal shape design problems of radiative heat transfer

Optimal shape design problems of steady-state radiative heat transfer are considered. The optimal shape design problem (in the three-dimensional space) is formulated as an inverse one, i.e., in the form of an operator equation of the first kind with respect to a surface to be optimized. The operator equation is reduced to a minimization problem via a least-squares objective functional. The minimization problem has to be solved numerically. Gradient minimization methods need the gradient of a functional to be minimized. In this paper the shape gradient of the least-squares objective functional is derived with the help of the shape sensitivity analysis and adjoint problem method. In practice a surface to be optimized may be (or, most likely, is to be) given in a parametric form by a finite number of parameters. In this case the objective functional is, in fact, a function in a finite-dimensional space and the shape gradient becomes an ordinary gradient. The gradient of the objective functional, in the case that the surface to be optimized is given in a finite-parametric form, is derived from the shape gradient. A particular case, that a surface to be optimized is a “two-dimensional” polyhedral one, is considered. The technique, developed in the paper, is applied to a synthetic problem of designing a “two-dimensional” radiant enclosure.     

Numerical study of the heat transfer and electro-thermo-convective flow patterns in dielectric liquid layer subjected to unipolar injection

In this article we study the electro-thermal convection in a dielectric liquid layer placed between two electrodes and subjected to the simultaneous action of an electric field and a thermal gradient. The full set of equations describing the electro-thermo-convective phenomena is directly solved using a finite volume method. We first heat the liquid from below at time t = 0, wait for the thermal steady state and then inject the electric charges by applying the electric potential. The development of the electro-convective motion is analysed in detail in two cases: 1) strong injection from the lower electrode, 2) strong injection from the upper one. We also study the heat transfer enhancement due to electro-convection. The evolution in time of the Nusselt number Nu for different combinations of the two usual non-dimensional parameters associated to the electro-thermo-convection phenomena (Rayleigh number Ra and the electrical parameter T) is also given and analysed.     

Computing numerically the functional derivative of an effective action

The functional derivative of the effective action with respect to an external field is part of the equation of motion of this field if one-loop effects induced by quantum fluctuations or thermal fluctuations are included in minimizing the action of this field. Examples occur in all field theories displaying classical solutions or 3 - as the Nambu-Jona-Lasinio model 3 - selfconsistent field configurations. We describe here a numerical method for computing such functional derivatives; we use a fermion field with Yukawa interaction to an external field as an example which is sufficiently simple and sufficiently general. We compare the computed action to analytical estimates.     

Semiclassical functional integrals for self-dual gauge fields

The semiclassical approximation to the functional integral for four-dimensional Euclidean gauge theories is discussed in detail for general stationary points of the action. It is shown how to take the limit from a compact space to flat space, and the zero modes corresponding to global gauge transformations are carefully discussed. The results are specialised to general self-dual multi-instanton gauge fields given by the general construction of Atiyah et al. It is shown how the normalization matrix of the zero modes can be determined and the complete expression for the functional measure is given for the two instanton case. This is shown to factorise for well-separated instantons. Some technical matters are discussed in an appendix and a resume of results for multi-instanton functional determinants is included.     

Correction for the Effect of Induced B0 Shifts in Localized Spectroscopy and Imaging by Direct Frequency Modulation

A new method is presented for the amelioration of eddy-current-induced B₀ shifts based on direct FM modulation of the spectrometer transmitter and receiver reference frequencies. The waveform for correction is based on a dynamic spherical-harmonic expansion of the temporal field, requiring no functional fitting and accounting fully for all gradient transitions in a given sequence. The importance of fully sequence-specific correction of these B₀ shifts during slice selection in imaging and localized experiments is demonstrated experimentally and modeled in part using rotation-matrix calculations. The results demonstrate the utility of the correction technique and indicate that it is advantageous to correct even the small shifts associated with shielded gradients in order to produce optimal slice refocusing.     

The effects of the choice of the k-interval number on radiative calculations

The selection of the number of k-interval is a foundation to correlated k-distribution method and the problem of how to do it still remains unsettled. It is pointed out by numerical computation in this work that choosing the number of k-interval is a major factor affecting accuracy and speed in radiative calculation. To increase the number of k-interval is an efficient method to improve the accuracy. However, it is found by this study that there exists a saturation of the accuracy to an increase of the number. The optimal rules on the number of k-interval choosing are proposed in the paper. Then, five versions on atmospheric absorption by gases appropriate for GCMs are given according to them.     

Cellular theory of ordered AB alloys

The heat and volume of formation of ordered simple metal AB alloys are calculated using the density functional formalism. A new method is proposed in which the alloy is partitioned into cells defined by surfaces on which the gradient of the electron density vanishes. The total alloy energy is formulated in terms of cellular and Madelung contributions and is minimized subject to the constraint of equal A and B cell boundary densities. Quantitative results for LiMg are presented.     

An h-adaptive finite element solver for the calculations of the electronic structures

In this paper, a framework of using h-adaptive finite element method for the Kohn–Sham equation on the tetrahedron mesh is presented. The Kohn–Sham equation is discretized by the finite element method, and the h-adaptive technique is adopted to optimize the accuracy and the efficiency of the algorithm. The locally optimal block preconditioned conjugate gradient method is employed for solving the generalized eigenvalue problem, and an algebraic multigrid preconditioner is used to accelerate the solver. A variety of numerical experiments demonstrate the effectiveness of our algorithm for both the all-electron and the pseudo-potential calculations.     

Non-perturbative calculation of the mass-gap in the Gross-Neveu model

We calculate a fully renormalizable effective action for local composite operators in the U(N) Gross-Neveu model, recently introduced by one of us, to two loop order. We obtain results for the massgap in one and two loops which are optimized using the Grunberg method of effective charges. At one loop the accuracy is of the order of 2% or less (except for N = 2). At two loops the accuracy is significantly improved for N ≥ 5.     

Critical bubbles and fluctuations at the electroweak phase transition

We discuss the critical bubbles of the electroweak phase transition using an effective high-temperature 3-dimensional action for the Higgs field ϕ. The separate integration of gauge and Goldstone boson degrees of freedom is conveniently described in the 't Hooft-Feynman covariant background gauge. The effective dimensionless gauge coupling g3 (T) z in the broken phase is well behaved throughout the phase transition. However, the behavior of the one-loop Z(ϕ) factors of the Higgs and gauge kinetic terms signalizes the breakdown of the derivative expansion and of the perturbative expansion for a range of small ϕ values increasing with the Higgs mass m_H Taking a functional S_z [ϕ] with constant Z(ϕ) = z instead of the full non-local effective action in some neighborhood of the saddle point we are calculating the critical bubbles for several temperatures. The fluctuation determinant is calculated to high accuracy using a variant of the heat kernel method. It gives a strong suppression of the transition rate compared to previous estimates.     

Majorana Solutions to the Two-Electron Problem

The two-electron atom is the simplest nontrivial quantum system not amenable to exact solutions. Today, its relevance in the development of quantum mechanics and its pedagogical value within the realm of atomic physics are widely recognized. In this work, an historical review of the known different methods and results devised to study such a problem is presented, with an emphasis to the calculations of the ground state energy of helium. Then we discuss several, related, unpublished results obtained around the same years by Ettore Majorana, which remained unknown till recent times. Among them a general variant of the variational method appears to be particularly interesting, even for current research in atomic and nuclear physics: it takes directly into account, already in the trial wavefunction, the action of the full Hamiltonian operator of a given quantum system. Further relevant contributions, specialized to the two-electron problem, include the introduction of the remarkable concept of an effective nuclear charge different for the two electrons (thus generalizing previous known results) and an application of the perturbative method, where the atomic number Z was treated effectively as a continuous variable. Finally a survey of results, relevant mainly for pedagogical reasons, is given; in particular we focus on simple broad range estimates of the helium ionization potential, obtained by suitable choices for the wavefunction, as well as on a simple alternative to Hylleraas’ method, which led Majorana to first order calculations comparable in accuracy with well-known order 11 results derived, in turn, by Hylleraas.     

A posteriori error estimation and adaptive mesh refinement for a multiscale operator decomposition approach to fluid–solid heat transfer

We analyze a multiscale operator decomposition finite element method for a conjugate heat transfer problem consisting of a fluid and a solid coupled through a common boundary. We derive accurate a posteriori error estimates that account for all sources of error, and in particular the transfer of error between fluid and solid domains. We use these estimates to guide adaptive mesh refinement. In addition, we provide compelling numerical evidence that the order of convergence of the operator decomposition method is limited by the accuracy of the transferred gradient information, and adapt a so-called boundary flux recovery method developed for elliptic problems in order to regain the optimal order of accuracy in an efficient manner. In an appendix, we provide an argument that explains the numerical results provided sufficient smoothness is assumed.     

Hybridized kinetic energy functional for orbital-free density functional method

We propose a hybridized kinetic energy functional, aTTF+bTvW, where TTF is the Thomas-Fermi functional and TvW the von Weizsäcker functional while a and b are adjustable parameters. The new functional is implemented in orbital-free plane-wave density functional method, in which a conjugate-gradient line-search scheme of electronic minimization is incorporated. Calculations with the fitted a and b show that this kinetic energy functional can describe the structures of small Si, Al and Si-Al alloy clusters with reasonable accuracy.     

基于对偶数理论的资料同化新方法

针对变分资料同化中目标泛函梯度计算精度不高且复杂等问题, 提出了一种基于对偶数理论的资料同化新方法, 主要优点是: 能避免复杂的伴随模式开发及其逆向积分, 只需在对偶数空间通过正向积分就能同时计算出目标泛函和梯度向量的值. 首先利用对偶数理论把梯度分析过程转换为对偶数空间中目标泛函计算过程, 简单、高效和高精度地获得梯度向量值; 其次结合典型的最优化方法, 给出了非线性物理系统资料同化问题的新求解算法; 最后对Lorenz 63混沌系统、包含开关的不可微物理模型和抛物型偏微分方程分别进行了资料同化数值实验, 结果表明: 新方法能有效和准确地估计出预报模式的初始条件或物理参数值.     

Investigation of the correlation between internal gradients and dephasing effect in inhomogeneous field

Internal magnetic gradient plays a significant role in Nuclear Magnetic Resonance (NMR) measurements of fluid saturated porous media. The quantitative characterization and application of this physical phenomenon could effectively improve the accuracy of NMR measurements and interpretations. In this paper, by using the equivalent magnetic dipole method, the three-dimensional distribution of internal induced magnetic field and its gradients in the randomly packed water saturated glass beads are quantitatively characterized. By simulating the diffusive motion of water molecules in porous media with random walk method, the computational dephasing effects equation related to internal gradients is deduced. Thereafter, the echo amplitudes are obtained and the corresponding T ₂-G spectrum is also inverted. For the sake of verifying the simulation results, an experiment is carried out using the Halbach core analyzing system (B ₀=0.18 T, G=2.3 T/m) to detect the induced internal field and gradients. The simulation results indicate the equivalent internal gradient is a distribution of 0.12–0.3 T/m, which matched well with the experimental results.     

A fast-saliency method for real-time infrared small target detection

Infrared small target detection plays an important role in applications including military reconnaissance, early warning and terminal guidance. In this paper, we present a fast method, called fast-saliency, with very low computational complexity, for real-time small target detection in single image frame under various complex backgrounds. Different from traditional algorithms, the proposed method is inspired by a recent research on visual saliency detection indicating that small salient signals could be well detected by a gradient enhancement operation combined with Gaussian smoothing, which is able to delineate regions of small targets in infrared images. Concisely, there are only four simple steps contained in fast-saliency. In order, they are gradient operation, square computation, Gaussian smoothing and automatic thresholding, representing the four procedures as highpass filtering, target enhancement, noise suppression and target segmentation, respectively. Especially, for the most crucial step, gradient operation, we innovatively propose a 5 × 5 facet kernel operator that holds the key for separating the small targets from backgrounds. To verify the effectiveness of our proposed method, a set of real infrared images covering typical backgrounds with sea, sky and ground clutters are tested in experiments. The results demonstrate that it outperforms the state-of-the-art methods not only in detection accuracy, but also in computation efficiency.     

First-principles calculations of the structural, electronic and optical properties of cubic BxGa1−xAs alloys

Density functional calculations are performed to study the structural, electronic and optical properties of technologically important B_xGa_1−xAs ternary alloys. The calculations are based on the total-energy calculations within the full-potential augmented plane-wave (FP-LAPW) method. For exchange-correlation potential, local density approximation (LDA) and the generalized gradient approximation (GGA) have been used. The structural properties, including lattice constants, bulk modulus and their pressure derivatives, are in very good agreement with the available experimental and theoretical data. The electronic band structure, density of states for the binary compounds and their ternary alloys are given. The dielectric function and the refractive index are also calculated using different models. The obtained results compare very well with previous calculations and experimental measurements.     

Multiloop calculations of effective action for local composite operators

Effective action for local composite operators is described for both the standard loop expansion formulation and an improved two-particle irreducible formulation. Rules for calculating multiloop contributions to the effective action are given in both formulations and are exemplified in the Gross-Neveu model in the large-N limit. Calculation of the exact effective action in the Gross-Neveu model is considerably simplified in the improved formulation. Results obtained from the conventional auxiliary field method, like dynamical symmetry breaking, non-classical solitions, etc., can all be obtained in the present formulation by dealing with the composite operators directly without introducing auxiliary fields. The present method can be applied to models in which the auxiliary field method is difficult to implement.     

On the low-energy effective action of N = 2 supersymmetric Yang-Mills theory

We investigate the perturbative part of Seiberg's low-energy effective action of N = 2 supersymmetric Yang-Mills theory in Wess-Zumino gauge in the conventional effective field theory technique. Using the method of constant field approximation and restricting the effective action with at most two derivatives and not more than four-fermion couplings, we show some features of the low-energy effective action given by Seiberg based on U(1)_R anomaly and non-perturbative β-function arguments.     

The spin effect in zinc-blende CdEuS and CdEuSe: GGA and GGA+U studies

We have investigated the structural, electronic and magnetic properties of substitutional europium rare earth impurity in cubic CdS and CdSe by employing the ab-initio method. Calculations were performed by using the full potential linearized augmented plane wave plus local orbitals (FP-L/APW+lo) method within the framework of spin-polarized density functional theory (DFT). The electronic exchange-correlation energy is described by generalized gradient approximation GGA and GGA+U (U is the Hubbard correction). The GGA+U method is applied to the rare-earth 4f states. We have calculated the lattice parameters, bulk modulii, the first pressure derivatives of the bulk modulii and the cohesive energies. The calculated densities of states presented in this study identify the metallic behavior of CdEuS and CdEuSe when we use the GGA scheme, whereas when we use the GGA+U, we see that these compounds are half-metallic.