A reduced basis method for electromagnetic scattering by multiple particles in three dimensions

We consider the development of efficient and fast computational methods for parametrized electromagnetic scattering problems involving many scattering three dimensional bodies. The parametrization may describe the location, orientation, size, shape and number of scattering bodies as well as properties of the source field such as frequency, polarization and incident direction. The emphasis is on problems that need to be solved rapidly to accurately simulate the interaction of scattered fields under parametric variation, e.g., for design, detection, or uncertainty quantification. For such problems, the use of a brute force approach is often ruled out due to the computational cost associated with solving the problem for each parameter value.In this work, we propose an iterative reduced basis method based on a boundary element discretization of few reference scatterers to resolve the computationally challenging large scale problem. The approach includes (i) a computationally intensive offline procedure to create a selection of a set of snapshot parameters and the construction of an associated reduced basis for each reference scatterer and (ii) an inexpensive online algorithm to generate the surface current and scattered field of the parametrized configuration, for any choice of parameters within the parameter domains used in the offline procedure. Comparison of our numerical results with directly measured results for some benchmark configurations demonstrate the power of our method to rapidly simulate the interacting electromagnetic fields under parametric variation of the overall multiple particle configuration.     

Quantization of superparametrized monopoles

Classical finite-energy solutions of the SU(2) Yang-Mills-Higgs system in four-dimensional space-time are embedded in the supersymmetric extension of the theory. Finite supertranslations are constructed and are used to obtain a family of solutions to the supersymmetric field equations, parametrized by fermionic Majorana spinor parameters. The quantum theory around arbitrary classical solutions, parametrized by arbitrary bosonic (global and local) as well as fermionic (global) parameters, is constructed and discussed.     

Midisuperspace Models of Canonical Quantum Gravity

A midisuperspace model is a field theoryobtained by symmetry reduction of a parent gravitationaltheory. Such models have proven useful for exploring theclassical and quantum dynamics of the gravitational field. I present three recent classes ofresults pertinent to canonical quantization of vacuumgeneral relativity in the context of midisuperspacemodels. (1) I give necessary and sufficient conditions such that a given symmetry reduction can beperformed at the level of the Lagrangian or Hamiltonian.(2) I discuss the Hamiltonian formulation of modelsbased upon cylindrical and toroidal symmetry. In particular, I explain how these models can beidentified with parametrized field theories of wavemaps; thus a natural strategy for canonical quantizationis available. (3) The quantization of a parametrized field theory, such as the midisuperspace modelsconsidered in (2), requires construction of a quantumfield theory on a fixed (flat) spacetime that allows fortime evolution along arbitrary foliations of spacetime. I discuss some recent results on thepossibility of finding such a quantum fieldtheory.     

海底反射损失的一种反演方法

本文以浅海平滑平均声场理论为基础,提出一种由传播衰减反演海底反射损失的方法.我们用一组参数来分段线性表示海底反射损失,要求计算的与测量得到的传播衰减之间的均方误差最小.文中采用Gauss-Newton迭代法将问题分解为一系列线性最小二乘问题,利用Levenberg-Marquardt方法改善了解的稳定性.最后列举了计算机模拟与反演实例,表明本方法可获得满意的结果。     

Applicability of Parametrized Form of Fully Dressed Quark Propagator

According to extensive study of the Dyson-Schwinger equations for a fully dressed quark propagator in the "rainbow" approximation with an effective gluon propagator, a parametrized fully dressed confining quark propagator is suggested in this paper. The parametrized quark propagator describes a confined quark propagation in hadron, and is analytic everywhere in complex p2-plane and has no Lehmann representation. The vector and scalar self-energy functions [1 - Af(p2)] and [Bf(p2) - mf], dynamically running effective mass of quark Mf(p2) and the structure of non-local quark vacuum condensates as well as local quark vacuum condensates are predicted by use of the parametrized quark propagator. The results are compatible with other theoretical calculations.     

Geometry and integrability of topological-antitopological fusion

Integrability of equations of topological-antitopological fusion (being proposed by Cecotti and Vafa) describing the ground state metric on a given 2D topological field theory (TFT) model, is proved. For massive TFT models these equations are reduced to a universal form (being independent on the given TFT model) by gauge transformations. For massive perturbations of topological conformal field theory models the separatrix solutions of the equations bounded at infinity are found by the isomonodromy deformations method. Also it is shown that the ground state metric together with some part of the underlined TFT structure can be parametrized by pluriharmonic maps of the coupling space to the symmetric space of real positive definite quadratic forms.     

Manifestly Covariant Quantum Theory with Invariant Evolution Parameter in Relativistic Dynamics

Manifestly covariant quantum theory with invariant evolution parameter is a parametrized relativistic dynamical theory. The study of parameterized relativistic dynamics (PRD) helps us understand the consequences of changing key assumptions of quantum field theory (QFT). QFT has been very successful at explaining physical observations and is the basis of the conventional paradigm, which includes the Standard Model of electroweak and strong interactions. Despite its record of success, some phenomena are anomalies that may require a modification of the Standard Model. The anomalies include neutrino oscillations, non-locality, and gravity.     

New post-Newtonian parameter to test Chern-Simons gravity

We study Chern-Simons (CS) gravity in the parametrized post-Newtonian (PPN) framework through a weak-field solution of the modified field equations. We find that CS gravity possesses the same PPN parameters as general relativity, except for the inclusion of a new term, proportional to the CS coupling and the curl of the PPN vector potential. This new term leads to a modification of frame dragging and gyroscopic precession and we provide an estimate of its size. This correction might be used in experiments, such as Gravity Probe B, to bound CS gravity and test string theory.     

Index Theory, Gerbes, and Hamiltonian Quantization

We give an Atiyah-Patodi-Singer index theory construction of the bundle of fermionic Fock spaces parametrized by vector potentials in odd space dimensions and prove that this leads in a simple manner to the known Schwinger terms (Faddeev-Mickelsson cocycle) for the gauge group action. We relate the APS construction to the bundle gerbe approach discussed recently by Carey and Murray, including an explicit computation of the Dixmier-Douady class. An advantage of our method is that it can be applied whenever one has a form of the APS theorem at hand, as in the case of fermions in an external gravitational field. Received:     

Deep Neural Network Model for Approximating Eigenmodes Localized by a Confining Potential

We study eigenmode localization for a class of elliptic reaction-diffusion operators. As the prototype model problem we use a family of Schrödinger Hamiltonians parametrized by random potentials and study the associated effective confining potential. This problem is posed in the finite domain and we compute localized bounded states at the lower end of the spectrum. We present several deep network architectures that predict the localization of bounded states from a sample of a potential. For tackling higher dimensional problems, we consider a class of physics-informed deep dense networks. In particular, we focus on the interpretability of the proposed approaches. Deep network is used as a general reduced order model that describes the nonlinear connection between the potential and the ground state. The performance of the surrogate reduced model is controlled by an error estimator and the model is updated if necessary. Finally, we present a host of experiments to measure the accuracy and performance of the proposed algorithm.     

Entanglement dephasing of spatially separated multiparticle GHZ states coupled to a squeezed environment

In tokamak plasmas, it is recognized that ITG (ion temperature gradient instability) and trapped electron modes (TEM) are held responsible for turbulence giving rise to anomalous transport. The present work focuses on the building of a model including trapped kinetic ions and trapped kinetic electrons. For this purpose, the dimensionality is reduced by averaging the motion over the cyclotron motion and the “banana” orbits, according to the fact that the instabilities are characterized by frequencies of the order of the low trapped particle precession frequency. Moreover, a set of action-angle variables is used. The final model is 4D (two-dimensional phase space parametrized by the two first adiabatic invariants namely the particle energy and the trapping parameter). In this paper, the trapped ion and electron modes (TIM and TEM) are studied by using a linear analysis of the model. This work is currently performed in order to include trapped electrons in an existing semi lagrangian code for which TIM modes are already taken into account. This study can be considered as a first step in order to include kinetic trapped electrons in the 5D gyrokinetic code GYSELA [J. Abiteboul et al., ESAIM Proc. 32, 103 (2011)].     

Black holes with scalar charge

Previously it had been thought that a stationary black hole with an exterior devoid of matter can be parametrized only by mass, angular momentum, and electric charge. We show here that scalar charge is also an admissible parameter. Our starting point is a new solution of Einstein's equations with stress-energy of electromagnetic and conformal scalar fields which we presented earlier. It has a black-hole geometry, and is parametrized by electric and scalar charges. Its conformal scalar field is unbounded at the event horizon, and we originally regarded this feature as incompatible with a black hole interpretation. However, following a suggestion of B. DeWitt, we show here that the infinity in the scalar field need not be physically pathological: it is not associated with an infinite potential barrier for test scalar charges; it does not cause the termination of any trajectories of these test particles at finite proper time; and it is not connected with unbounded tidal accelerations between neighboring trajectories. In view of these facts, we now regard the new solution as a genuine black hole solution.     

Wireless ultraviolet light MIMO assisted UAV direction perception and collision avoidance method

In order to solve the problem of UAV’s direction perception and collision prevention in the limited radio communication environment, we use wireless ultraviolet (UV) communication as an auxiliary communication method in UAVs. We improve the traditional artificial potential field (APF) method, design a UV- MIMO model installed on the UAV, and propose the improved artificial potential field (IAPF) method. On this basis, the determination of the threat source direction in IAPF algorithm is further simplified, and the improved artificial potential field based on ultraviolet MIMO (IAPF-UVMIMO) algorithm is proposed. Experimental results show that IAPF effectively solves the problems of unreachable targets, path oscillations and local minimums that exist in the traditional artificial potential field method. In addition, IAPF-UVMIMO also improves the tolerance of the threat source direction. Compared with IAPF, the number of collisions with actual collision threats is reduced by 22.6%.     

Spacetime as Manifold of Internal Symmetry Orbits in External Symmetries

Interactions and particles in the standard model are characterized by the action of internal and external symmetry groups. The four symmetry regimes involved are related to each other in the context of induced group representations. In addition to Wigner's induced representations of external Poincaré group operations, parametrized by energy-momenta, and the induced internal hyperisospin representations, parametrized by the standard model Higgs field, the external operations, including the Lorentz group, can also be considered to be induced by the internal operations of the hypercharge–isospin group. In such an interpretation nonlinear spacetime is parametrized by the orbits of the internal action group in the external action group.     

Adaptive sparse polynomial chaos expansion based on least angle regression

Polynomial chaos (PC) expansions are used in stochastic finite element analysis to represent the random model response by a set of coefficients in a suitable (so-called polynomial chaos) basis. The number of terms to be computed grows dramatically with the size of the input random vector, which makes the computational cost of classical solution schemes (may it be intrusive (i.e. of Galerkin type) or non intrusive) unaffordable when the deterministic finite element model is expensive to evaluate.To address such problems, the paper describes a non intrusive method that builds a sparse PC expansion. First, an original strategy for truncating the PC expansions, based on hyperbolic index sets, is proposed. Then an adaptive algorithm based on least angle regression (LAR) is devised for automatically detecting the significant coefficients of the PC expansion. Beside the sparsity of the basis, the experimental design used at each step of the algorithm is systematically complemented in order to avoid the overfitting phenomenon. The accuracy of the PC metamodel is checked using an estimate inspired by statistical learning theory, namely the corrected leave-one-out error. As a consequence, a rather small number of PC terms are eventually retained (sparse representation), which may be obtained at a reduced computational cost compared to the classical “full” PC approximation. The convergence of the algorithm is shown on an analytical function. Then the method is illustrated on three stochastic finite element problems. The first model features 10 input random variables, whereas the two others involve an input random field, which is discretized into 38 and 30 ? 500 random variables, respectively.     

Representations of spacetime diffeomorphisms. I. Canonical parametrized field theories

The super-Hamiltonian and supermomentum in canonical geometrodynamics or in a parametried field theory on a given Riemannian background have Poisson brackets which obey the Dirac relations. By smearing the supermomentum with vector fields V^→∈ L Diff Σ on the space manifold Σ, the Lie algebra L Diff Σ of the spatial diffeomorphism group Diff Σ can be mapped antihomomorphically into the Poisson bracket algebra on the phase space of the system. The explicit dependence of the Poisson brackets between two super-Hamiltonians on canonical coordinates (spatial metrics in geometrodynamics and embedding variables in parametrized theories) is usually regarded as an indication that the Dirac relations cannot be connected with a representation of the complete Lie algebra L Diff M of spacetime diffeomorphisms.We show how this difficulty may be overcome and construct a homomorphic mapping of spacetime vector fields V ∈ L Diff M into the Poisson bracket algebra on the phase space of the system. In the present paper, I, we explain how the technique works in the case of a parametrized field theory and in the following paper, II, we generalize it to canonical geometrodynamics. In a parametrized theory, the phase space of the system is the ordinary phase space of the field augmented by the embedding variables X: Σ →Mand their conjugate momenta. The dynamical variable H(V) which represents V ∈ L Diff M generates a deformation of the embedding along the flow lines of V accompanied by the correct dynamical evolution of the field data and preserves the constraints in the extended phase space of the system. We also establish the relation between the representations of Diff Σ and DiffM.     

Relations between some analytic representations of one-loop scalar integrals

We compare several parametrized analytic expressions for an arbitrary, off-shell one-loopn-point function in scalar field theory inD-dimensional space-time, and show their equivalence both directly and through path-integral methods.     

Computing Lagrangian coherent structures from their variational theory

Using the recently developed variational theory of hyperbolic Lagrangian coherent structures (LCSs), we introduce a computational approach that renders attracting and repelling LCSs as smooth, parametrized curves in two-dimensional flows. The curves are obtained as trajectories of an autonomous ordinary differential equation for the tensor lines of the Cauchy-Green strain tensor. This approach eliminates false positives and negatives in LCS detection by separating true exponential stretching from shear in a frame-independent fashion. Having an explicitly parametrized form for hyperbolic LCSs also allows for their further in-depth analysis and accurate advection as material lines. We illustrate these results on a kinematic model flow and on a direct numerical simulation of two-dimensional turbulence.